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%!TEX encoding = UTF-8 Unicode
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pdfauthor = {APMEP},
pdfsubject = {Baccalauréat S},
pdftitle = {Polynésie juin 2013},
allbordercolors = white,
pdfstartview=FitH}
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\begin{document}
\setlength\parindent{0mm}
\rhead{\textbf{A. P{}. M. E. P{}.}}
\lhead{\small Baccalauréat S }
\lfoot{\small{Polynésie}}
\rfoot{\small{7 juin 2013}}
\renewcommand \footrulewidth{.2pt}
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\begin{center} {\Large{\textbf{\decofourleft~Baccalauréat S Polynésie~\decofourright\\[4pt]7 juin 2013}}}
\end{center}
\vspace{0,5cm}
\textbf{\textsc{Exercice 1} \hfill 6 points}
\textbf{Commun à tous les candidats}
\medskip
\medskip
On considère la fonction $f$ définie sur $\mathbb{R}$ par
\[f(x) = (x + 2)\text{e}^{-x}.\]\index{fonction exponentielle}
On note $\mathscr C$ la courbe représentative de la fonction $f$ dans un repère orthogonal.
\medskip
\begin{enumerate}
\item Étude de la fonction $f$.
\begin{enumerate}
\item Déterminer les coordonnées des points d'intersection de la courbe $\mathscr C$ avec les axes du repère.
\item Étudier les limites de la fonction $f$ en $-\infty$ et en $+\infty$. En déduire les éventuelles asymptotes de la courbe $\mathscr C$.
\item Étudier les variations de $f$ sur $\mathbb{R}$.
\end{enumerate}
\item Calcul d'une valeur approchée de l'aire sous une courbe.
On note $\mathscr D$ le domaine compris entre l'axe des abscisses, la courbe $\mathscr C$ et les droites d'équation $x=0$ et $x=1$. On approche l'aire du domaine $\mathscr D$ en calculant une somme d'aires de rectangles.
\begin{enumerate}
\item Dans cette question, on découpe l'intervalle $[0~;~1]$ en quatre intervalles de même longueur :
\begin{itemize}
\item[$\bullet$] Sur l'intervalle $\left[0~;~\dfrac{1}{4} \right]$, on construit un rectangle de hauteur $f(0)$
\item[$\bullet$] Sur l'intervalle $\left[\dfrac{1}{4}~;~\dfrac{1}{2} \right]$, on construit un rectangle de hauteur $f\left( \dfrac{1}{4} \right)$
\item[$\bullet$] Sur l'intervalle $\left[\dfrac{1}{2}~;~\dfrac{3}{4} \right]$, on construit un rectangle de hauteur $f\left(\dfrac{1}{2} \right)$
\item[$\bullet$] Sur l'intervalle $\left[ \dfrac{3}{4}~;~1 \right]$, on construit un rectangle de hauteur $f\left( \dfrac{3}{4} \right)$
\end{itemize}
Cette construction est illustrée ci-dessous.
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% \includegraphics{BacS-Polynesie-2013-aire}
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L'algorithme\index{algorithme} ci-dessous permet d'obtenir une valeur approchée de l'aire du domaine $\mathscr D$ en ajoutant les aires des quatre rectangles précédents :
\begin{center}
\begin{tabular}{|rl|}
\hline
Variables : & $k$ est un nombre entier \\
& $S$ est un nombre réel \\
Initialisation : & Affecter à $S$ la valeur 0 \\
Traitement : & Pour $k$ variant de 0 à 3 \\
& $\phantom{a}\left\vert \text{ Affecter à } S \text{ la valeur } S+\dfrac{1}{4} f\left( \dfrac{k}{4} \right)\right.$ \\
& Fin Pour \\
Sortie : & Afficher $S$ \\
\hline
\end{tabular}
\end{center}
Donner une valeur approchée à $10^{-3}$ près du résultat affiché par cet algorithme.
\item Dans cette question, $N$ est un nombre entier strictement supérieur à 1. On découpe l'intervalle $[0~;~1]$ en $N$ intervalles de même longueur. Sur chacun de ces intervalles, on construit un rectangle en procédant de la même manière qu'à la question 2.a.
Modifier l'algorithme précédent afin qu'il affiche en sortie la somme des aires des $N$ rectangles ainsi construits.
\end{enumerate}
\item Calcul de la valeur exacte de l'aire sous une courbe.
Soit $g$ la fonction définie sur $\R$ par
\[g(x)=(- x - 3) \text{e}^{-x}.\]\index{fonction exponentielle}
On admet que $g$ est une primitive de la fonction $f$ sur $\mathbb{R}$.\index{primitive}
\begin{enumerate}
\item Calculer l'aire $\mathscr A$ du domaine $\mathscr D$, exprimée en unités d'aire.
\item Donner une valeur approchée à $10^{-3}$ près de l'erreur commise en remplaçant $\mathscr A$ par la valeur approchée trouvée au moyen de l'algorithme de la question 2. a, c'est-à-dire l'écart entre ces deux valeurs.\hyperlink{Index}{*}
\end{enumerate}
\end{enumerate}
\vspace{0,5cm}
\textbf{Exercice 2 : \hfill 4 points}
\textbf{Commun à tous les candidats}
\medskip
\emph{Cet exercice est un questionnaire à choix multiples. Aucune justification n'est demandée. Pour chacune des questions, une seule des quatre propositions est exacte. Chaque réponse correcte rapporte $1$ point. Une réponse erronée ou une absence de réponse n'ôte pas de point. Le candidat indiquera sur la copie le numéro de la question et la réponse choisie.}
\medskip
\begin{enumerate}
\item Soit $z_1 = \sqrt{6} \text{e}^{\text{i} \frac{\pi}{4}}$ et $z_2 = \sqrt{2} \text{e}^{-\text{i} \frac{\pi}{3}}$. La forme exponentielle de $\text{i} \dfrac{z_1}{z_2}$ est :
\begin{tabularx}{1.0\linewidth}{XXXX}
\textbf{a.~~} $\sqrt{3}\text{e}^{\text{i} \frac{19\pi}{12}}$ &
\textbf{b.~~} $\sqrt{12} \text{e}^{-\text{i} \frac{\pi}{12}}$ &
\textbf{c.~~} $\sqrt{3}\text{e}^{\text{i} \frac{7\pi}{12}}$ &
\textbf{d.~~} $\sqrt{3}\text{e}^{\text{i} \frac{13\pi}{12}}$
\end{tabularx}
\item L'équation $- z = \overline z$, d'inconnue complexe $z$, admet :
\begin{enumerate}
\item une solution
\item deux solutions
\item une infinité de solutions dont les points images dans le plan complexe sont situés sur une droite.
\item une infinité de solutions dont les points images dans le plan complexe sont situés sur un cercle.
\end{enumerate}
\item Dans un repère de l'espace, on considère les trois points $A(1~;~2~;~3)$, $B(-1~;~5~;~4)$ et $C(-1~;~0~;~4)$. La droite parallèle à la droite $(AB)$ passant par le point $C$ a pour représentation paramétrique :
\begin{tabularx}{1.0\linewidth}{XX}
\textbf{a.~~} $\begin{cases}
x = -2t-1 \\ y=\phantom{-}3t \\ z = \phantom{-}t+4
\end{cases}, t\in \mathbb{R}$ &
\textbf{b.~~} $\begin{cases}
x =\phantom{7t} - 1 \\ y = 7t \\ z = 7t+4
\end{cases}, t \in \mathbb{R}$ \\
\textbf{c.~~} $\begin{cases}
x = - 1 - 2t \\ y = \phantom{-}5+3t \\ z = \phantom{-}4+t
\end{cases}, t \in \mathbb{R}$ &
\textbf{d.~~} $\begin{cases}
x = \phantom{-}2t \\ y = - 3t \\ z = -\phantom{2} t
\end{cases}, t \in \mathbb{R}$
\end{tabularx}
\item Dans un repère orthonormé de l'espace, on considère le plan $\mathscr P$ passant par le point $D(-1~;~2~;~3)$ et de vecteur normal $\vect{n}(3~;~-5~;~1)$, et la droite $\Delta$ de représentation paramétrique $\begin{cases}
x = t - 7 \\ y = t + 3 \\ z = 2t + 5
\end{cases}, t \in \mathbb{R}$.\index{equation paramétrique@équation paramétrique}
\begin{enumerate}
\item La droite $\Delta$ est perpendiculaire au plan $\mathscr P$.
\item La droite $\Delta$ est parallèle au plan $\mathscr P$ et n'a pas de point commun avec le plan $\mathscr P$.
\item La droite $\Delta$ et le plan $\mathscr P$ sont sécants.
\item La droite $\Delta$ est incluse dans le plan $\mathscr P$.\hyperlink{Index}{*}
\end{enumerate}
\end{enumerate}
\newpage
\textbf{Exercice 3 : \hfill 5 points}
\textbf{Commun à tous les candidats}
\medskip
\emph{Les $3$ parties peuvent être traitées de façon indépendante.}
\medskip
Thomas possède un lecteur MP3 sur lequel il a stocké plusieurs milliers de morceaux musicaux.
L'ensemble des morceaux musicaux qu'il possède se divise en trois genres distincts selon la répartition suivante :
\begin{center}
30~\% de musique classique, 45~\% de variété, le reste étant du jazz.
\end{center}
Thomas a utilisé deux qualités d'encodage pour stocker ses morceaux musicaux : un encodage de haute qualité et un encodage standard. On sait que :
\begin{itemize}
\item[$\bullet$] les $\dfrac{5}{6}$ des morceaux de musique classique sont encodés en haute qualité.
\item[$\bullet$] les $\dfrac{5}{9}$ des morceaux de variété sont encodés en qualité standard.
\end{itemize}
\medskip
On considérera les évènements suivants :
\begin{description}
\item[$C$ :] \og Le morceau écouté est un morceau de musique classique \fg{} ;
\item[$V$ :] \og Le morceau écouté est un morceau de variété \fg{} ;
\item[$J$ :] \og Le morceau écouté est un morceau de jazz \fg{} ;
\item[$H$ :] \og Le morceau écouté est encodé en haute qualité \fg{} ;
\item[$S$ :] \og Le morceau écouté est encodé en qualité standard \fg.
\end{description}
\medskip
\textbf{Partie 1}
\medskip
Thomas décide d'écouter un morceau au hasard parmi tous les morceaux stockés sur son MP3 en utilisant la fonction \og lecture aléatoire \fg{}.
\emph{On pourra s'aider d'un arbre de probabilités\index{arbre de probabilités}.}
\begin{enumerate}
\item Quelle est la probabilité qu'il s'agisse d'un morceau de musique classique encodé en haute qualité ?
\item On sait que $P(H)=\dfrac{13}{20}$.
\begin{enumerate}
\item Les évènements $C$ et $H$ sont-ils indépendants ?
\item Calculer $P(J \cap H)$ et $P_J(H)$.
\end{enumerate}
\end{enumerate}
\medskip
\textbf{Partie 2}
\medskip
Pendant un long trajet en train, Thomas écoute, en utilisant la fonction \og lecture aléatoire \fg{} de son MP3, 60 morceaux de musique.
\begin{enumerate}
\item Déterminer l'intervalle de fluctuation asymptotique au seuil 95~\% de la proportion de morceaux de musique classique dans un échantillon de taille 60.
\item Thomas a comptabilisé qu'il avait écouté 12 morceaux de musique classique pendant son voyage. Peut-on penser que la fonction \og lecture aléatoire \fg{} du lecteur MP3 de Thomas est défectueuse ?
\end{enumerate}
\medskip
\textbf{Partie 3}
\medskip
On considère la variable aléatoire $X$ qui, à chaque chanson stocké sur le lecteur MP3, associe sa durée exprimée en secondes et on établit que $X$ suit la loi normale\index{loi normale} d'espérance $200$ et d'écart-type $20$.
\medskip
\emph{On pourra utiliser le tableau fourni en annexe dans lequel les valeurs sont arrondies au millième le plus proche.}
\medskip
On écoute un morceau musical au hasard.
\begin{enumerate}
\item Donner une valeur approchée à $10^{-3}$ près de $P(180 \leqslant X \leqslant 220)$.
\item Donner une valeur approchée à $10^{-3}$ près de la probabilité\index{probabilité} que le morceau écouté dure plus de 4 minutes.\hyperlink{Index}{*}
\end{enumerate}
\newpage
\textbf{Exercice 4 : \hfill 5 points}
\textbf{Candidats n'ayant pas suivi l'enseignement de spécialité mathématiques}
\medskip
On considère la suite\index{suite} $(u_n)$ définie par $u_0=\dfrac{1}{2}$ et telle que pour tout entier naturel~$n$,
\[u_{n+1} = \dfrac{3u_n}{1+2u_n}\]
\begin{enumerate}
\item
\begin{enumerate}
\item Calculer $u_1$ et $u_2$.
\item Démontrer, par récurrence, que pour tout entier naturel $n$, $0 < u_n$.
\end{enumerate}
\item On admet que pour tout entier naturel $n$, $u_n<1$.
\begin{enumerate}
\item Démontrer que la suite $\left(u_n\right)$ est croissante.
\item Démontrer que la suite $\left(u_n\right)$ converge.
\end{enumerate}
\item Soit $\left(v_n\right)$ la suite définie, pour tout entier naturel $n$, par $v_n = \dfrac{u_n}{1 - u_n}$.
\begin{enumerate}
\item Montrer que la suite $(v_n)$ est une suite géométrique de raison 3.
\item Exprimer pour tout entier naturel $n$, $v_n$ en fonction de $n$.
\item En déduire que, pour tout entier naturel $n$, $u_n = \dfrac{3^n}{3^n+1}$.
\item Déterminer la limite de la suite $(u_n)$.
\end{enumerate}
\end{enumerate}
\newpage
\textbf{Exercice 4 : \hfill 5 points}
\textbf{Candidats ayant suivi l'enseignement de spécialité mathématiques}
\medskip
Un opérateur téléphonique A souhaite prévoir l'évolution de nombre de ses abonnés dans une grande ville par rapport à son principal concurrent B à partir de 2013.
En 2013, les opérateurs A et B ont chacun $300$ milliers d'abonnés.
\medskip
Pour tout entier naturel $n$, on note $a_n$ le nombre d'abonnés, en milliers, de l'opérateur A la $n$-ième année après 2013, et $b_n$ le nombre d'abonnés, en milliers, de l'opérateur B la $n$-ième année après 2013.
Ainsi, $a_0 = 300$ et $b_0 = 300$.
\medskip
Des observations réalisées les années précédentes conduisent à modéliser la situation par la relation suivante :
pour tout entier naturel $n$,
$\begin{cases}
a_{n+1} = 0,7a_n + 0,2b_n + 60 \\
b_{n+1} = 0,1a_n + 0,6b_n + 70
\end{cases}$.
\medskip
On considère les matrices\index{matrice} $M =
\begin{pmatrix}
0,7 & 0,2 \\ 0,1 & 0,6
\end{pmatrix}$ et $P =
\begin{pmatrix}
60 \\ 70
\end{pmatrix}$.
Pour tout entier naturel $n$, on note $U_n =
\begin{pmatrix}
a_n \\ b_n
\end{pmatrix}$.
\begin{enumerate}
\item
\begin{enumerate}
\item Déterminer $U_1$.
\item Vérifier que, pour tout entier naturel $n$, $U_{n+1} = M \times U_n +P$.
\end{enumerate}
\item On note $I$ la matrice $
\begin{pmatrix}
1 & 0 \\ 0 & 1
\end{pmatrix}$.
\begin{enumerate}
\item Calculer $(I - M)\times
\begin{pmatrix}
4 & 2 \\ 1 & 3
\end{pmatrix}$.
\item En déduire que la matrice $I - M$ est inversible et préciser son inverse.
\item Déterminer la matrice $U$ telle que $U = M \times U + P$.
\end{enumerate}
\item Pour tout entier naturel, on pose $V_n = U_n - U$.
\begin{enumerate}
\item Justifier que, pour tout entier naturel $n$, $V_{n+1} = M \times V_n$.
\item En déduire que, pour tout entier naturel $n$, $V_n = M^n \times V_0$.
\end{enumerate}
\item On admet que, pour tout entier naturel $n$,
\renewcommand\arraystretch{1.8}
\[V_n = \begin{pmatrix}
\dfrac{-100}{3}\times 0,8^n - \dfrac{140}{3} \times 0,5^n \\
\dfrac{-50}{3} \times 0,8^n + \dfrac{140}{3} \times 0,5^n
\end{pmatrix}\]
\renewcommand\arraystretch{1}
\begin{enumerate}
\item Pour tout entier naturel $n$, exprimer $U_n$ en fonction de $n$ et en déduire la limite de la suite\index{suite} $(a_n)$.
\item Estimer le nombre d'abonnés de l'opérateur A à long terme.\hyperlink{Index}{*}
\end{enumerate}
\end{enumerate}
\newpage
\begin{center}
\bfseries \Large ANNEXE de l'exercice 3
\end{center}
$X$ est une variable aléatoire normale d'espérance 200 et d'écart-type 20.
\begin{center}
\begin{tabularx}{.4\linewidth}{|*{2}{>{\centering \arraybackslash}X|}}\hline
$b$ & $P(X \leqslant b)$ \\\hline
140 & 0,001 \\\hline
150 & 0,006 \\\hline
160 & 0,023 \\\hline
170 & 0,067 \\\hline
180 & 0,159 \\\hline
190 & 0,309 \\\hline
200 & 0,500 \\\hline
210 & 0,691 \\\hline
220 & 0,841 \\\hline
230 & 0,933 \\\hline
240 & 0,977 \\\hline
250 & 0,994 \\\hline
260 & 0,999 \\\hline
\end{tabularx}
\end{center}
\end{document}
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\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2008a.00437}
\itemau{Hampe, Robert}
\itemti{Iteration and growth. (Iteration und Wachstum.)}
\itemso{Mathematikunterricht 53, No. 6, 34-44 (2007).}
\itemab
Aus der Einleitung: Bei der Planung einer Unterrichtseinheit zum Thema \lq\lq Wachstumsmodelle\rq\rq ist es zun\"achst verlockend, Differentialgleichungen (DGLen) bzw. Differenzengleichungen (DZGLen) au\ss en vor zu lassen. Sollen jedoch Sch\"uler de facto eine M\"oglichkeit erhalten, selbstst\"andig Wachstumsprozesse zu modellieren (Kompetenzen!), so ist es unumg\"anglich, den Fokus auch auf die Wirkmechanismen und damit auf die DGLen bzw. DZGLen zu richten. Es ist mit einer sinnvollen Hypothese f\"ur die DGL/DZGL zu beginnen und anschlie\ss end muss der Bestandsverlauf mit dem gegebenen verglichen werden. In den weiteren Schritten muss nun die DGL/DZGL sinnvoll bzw. Zielf\"uhrend ge\"andert werden -- dies ist nur m\"oglich, wenn die Sch\"uler qualitativ die DGL/DZGL in den Bestandsverlauf und umgekehrt umwandeln k\"onnen. Oder anders formuliert: Eine DGL/DZGL qualitativ interpretieren, d. h. den Bestandsverlauf vorhersagen zu k\"onnen, ist das Werkzeug bzw. die Kompetenz zum Modellieren von Wachstumsvorg\"angen. Dabei sind Phasendiagramme und Richtungsfelder etablierte Darstellungen, die die DGLen mit dem jeweiligen Wachstumsverlauf in Beziehung setzen und damit eine solche Kompetenz bei Sch\"ulern im Umfeld der DGLen f\"ordern. Der Artikel geht der Frage nach, welche Darstellungen eben dies bei einer diskreten Modellierung -- mit DZGLen -- zu leisten vermag. Zuvor wird jedoch noch die konkrete Situation bei diskreten Wachstumsvorg\"angen detailliert dargestellt.
\itemrv{~}
\itemab
From the introduction: For the planning of a teaching unit on \lq\lq growth models\rq\rq, it is inevitable to focus on differential equations or difference equations. One has to start with a hypothesis for the differential/difference equation. Afterwards, the course of the numbers has to be compared with the given one. Students have to learn the tool or competence to qualitatively interpret a differential/difference equation, i.e. to predict the course of numbers. Phase plots and slope field graphs are established representations relating differential equations to the respective course of growth, thus supporting the development of these competences. The article discusses which representations are suitable to achieve this with discrete modelling of growth processes, i.e. with difference equations.
\itemrv{~}
\itemcc{M10 I70}
\itemut{iterative methods; graphical representations; exponential growth; linear growth; limited growth; mathematical model building; mathematical models; mathematical applications; graphics calculators; increment diagram; lesson planning; educational analysis; iteratives Verfahren; Zuwachsdiagramm; graphische Darstellung; mathematisches Modellieren; Anwendungen der Mathematik; Zirkeliteration; Unterrichtsplanung; didaktische Analyse}
\itemli{}
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\begin{document}
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\begin{center}
\textbf{\Large 応用物理学会学術講演会予稿}
\textbf{\large Extended Abstract of the Japan Society of Applied Physics}
\textbf{$^\bigcirc$応物 太郎$^1$、応物 花子$^2$(1.応用大工、2.応物中研)}
\textbf{$^\bigcirc$Taro Oubutsu$^1$, Hanako Oubutsu$^2$
(1.Oubutsu Univ., 2.Oubutsu Central Research Lab.)}
\textbf{E-mail: [email protected]}
\end{center}
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\begin{document}
%\cftnote
\title{Analysis of a three-component model phase diagram
by Catastrophe Theory}
%
% repeat the \author\address pair as needed
%
\author{J. Gaite%
\thanks{Current address: Departamento de F\'{ \i}sica,
Facultad de Ciencias,
Universidad de Oviedo,
c/ Calvo Sotelo s.n.,
33007 OVIEDO.},
J. Margalef-Roig and S. Miret-Art\'es%
\thanks{Also: Max-Planck-Institut f\"{u}r Str\"{o}mungsforschung,
Bunsenstra{\ss}e 10, D-37073 G\"{o}ttingen, Germany.}
\\
Instituto de Matem\'{a}ticas y F\'{ \i}sica Fundamental \\
Serrano 123, 28006 Madrid, Spain.}
%\resetftnote
\date{30 June 1997}
%\pacs{007}
%
%\date{\23 May, 1994} %
\maketitle
\begin{abstract}
We analyze the thermodynamical potential of a lattice gas model with three
components and five parameters using the methods of Catastrophe Theory. We
find the highest singularity, which has codimension five, and establish its
transversality. Hence the corresponding seven-degree Landau potential,
the canonical form {\em Wigwam} or $A_6$, constitutes the adequate starting
point to study the overall phase diagram of this model.
\end{abstract}
%
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{\small FFUOV-97-5}\\{\small cond-mat/yymmnnn}
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\global\parskip 4pt
\section{Introduction}
\label{Sec1}
The study of phase diagrams of complex systems is an important part of
Thermodynamics and applied physics. Phase diagrams can be constructed either
from experimental data or from theoretical models (for example, molecular
models). Among these, the wide class of lattice gas models is particularly
suitable for a mathematical analysis. Here we will focus our attention on the
lattice gas model for a system with three components which simulates, in
particular, a binary fluid mixture. A wide literature has already been devoted
to it from different points of view \cite[and references therein]{SST,griff2,
Mei,griff1}. We are mainly interested in attempting to present an overall
analysis of its phase diagram, with particular attention to its highest
multicritical point, that is, the one with the highest codimension in the
five-dimensional parameter space that we consider.
In the mean field theory, the Gibbs potential is a function of the
concentration of two of the three components and depends on three
thermodynamical parameters, which can be taken as the temperature and the
chemical potentials of the two components, and on three molecular parameters.
The phase diagram deduced from this function is an accurate description of the
system, except close to the (multi)critical points, where fluctuations become
important and alter significantly the mean field theory predictions. For this
reason, the Gibbs potential has been the basis for determining the
overall phase diagram \cite{griff2,Mei}. The method used in \cite{griff2}
establishes the qualitative features of the phase diagram, namely,
the instability and (multi)critical (hyper)surfaces which divide its various
regions, as well as some coexistence (hyper)surfaces. Those methods are
considerably powerful but not sufficiently rigorous by mathematical standards.
However, a well established mathematical theory for the analysis of
singularities of potentials and hence the associated phase diagrams does exist,
namely, Catastrophe or Singularity Theory (CT).
Catastrophe theory has indeed been applied to the description of phase
transitions \cite{Schu, okada} and, in particular, of phase diagrams of complex
thermodynamical systems including fluid mixtures \cite{okada}. The philosophy
behind these applications is however somewhat perverted: one starts with a
system on which some knowledge of the phase diagram is available, perhaps
its salient features, and surmises a polynomial (Landau) potential from among
the variety supplied by the CT classification (called canonical forms), which
is supposed to embody the properties of the thermodynamical potential of the
system near the phase transition of interest. Usually, this potential is well
analyzed in the mathematical literature and its other properties can be
safely assigned to the physical system. In summary, this procedure is
phenomenological in nature and amounts to fitting of phase diagrams.
Although it utilizes CT,
it is only to take advantage of well studied potentials. However, this
way is, of course, less powerful and precise than the approach
determining the polynomial potentials from a complete singularity analysis of
the actual thermodynamical potential. It is this second approach the one we
shall adopt here. A big advantage of our approach is that it is presented
as a well defined algorithm leading to a systematic
way to analyze any general problem susceptible to be studied within the context
of CT.
Futhermore, this second alternative agrees with the methods of Ref.\
\cite{griff1, griff2}, which in fact approach those of CT from the point of
view of classical thermodynamics. (See \cite{griff1} in regard to the
convergence of both techniques).
We intend to take the best of both worlds for the problem in hand: to draw
intuition from thermodynamical methods and mathematical soundness from the
theorems of CT. In particular, we emphasize the study of transversality of the
actual thermodynamical potentials which guarantees that those simple forms
(polynomial potentials or canonical forms) represent indeed
up to a diffeomorphism the original thermodynamical potential. We shall give a
brief account of the CT algorithm utilized throughout the paper together with
an Appendix for more mathematical details.
Our results essentially agree with and support those in \cite{griff2}. However,
we hinge less on the visualization of the phase diagram and more in the
classification of its singularities, relying for the construction of the phase
diagram on the straightforward method of gluing patches,
each described by a standard canonical form for which the phase diagram can be
found in the literature. Besides, we clearly establish the possibility of Landau
potentials in two variables, that is, of corank-2 canonical forms,
for the system with three components. This possibility was dismissed in
\cite{griff2}. Nevertheless, this case is sufficiently complex on its own
to postpone it for future work.
This work is organized as follows: In section 2 we introduce the fundamental
concepts of CT, the more thechnical points of which are left for an appendix.
In section 3 we describe the thermodynamical potential to be analyzed,
give its physical interpretation and discuss general stability questions which
help connect usual concepts in Thermodynamics with those in Catastrophe Theory.
In section 4 we apply the CT program to the potential previously introduced,
reducing it first to a one-variable potential. In section 5 we show a solution
with the highest codimension and its transversality, thereby concluding that
it is the {\em Wigwam} catastrophe. We also study in this section a peculiar
singularity of lower codimension, associated to the physics of critical azeotropy.
The last section is devoted to a discussion
of the previous results and of the structure of the phase diagram entailed by
them.
\section{Generalities about Catastrophe Theory}
In this section we are going to review very briefly the main concepts of CT.
The reader desirous of more technical details is referred to Refs.\
\cite{poston,gilmore}. As is well known,
CT deals with the singularities of smooth real-valued functions.
The nature of these singularities is revealed by perturbing those functions.
If as a result of a perturbation the qualitative properties of the function
remain unaffected we will say that this function is stable or structurally
stable. In other words, a function is said locally stable at a given point if
there is a smooth change of coordinates so that the new function has the same
structure as the old function. If a function is stable at all points then we
will say that this function is globally stable.
In a more precise way, a given function is a perturbation of another one at a
given point if the distance between both functions is arbitrary small. The
concept of distance leads us to Topology. We can define the Taylor-series
topology in the space $\IR^d$ where $d$ gives the number of the Taylor series
coefficients. Thus the $k$-jet of a given function at a given point is the
Taylor series truncated beyond terms of degree $k$. Several definitions of
distances can be given and all of these are expressed in terms of the $k$-jets
of each function.
Now the next important question is what information is lost when we
truncate the Taylor series of a function around a given point, namely,
the problem of determinacy. It consists of determining whether a function
can be truncated and if so, for what value of the degree of the Taylor
expansion it can be truncated without any loss of substantial information.
Furthermore, to determine the most general
family of functions of the smallest dimension $d$ which contains the original
function is called the problem of unfolding. The unfolding dimension is the
number of parameters describing a general perturbation and the minimum number
to describe it is called the codimension. When all the unfolding terms go to
zero, the remainder of the universal unfolding is called the {\em germ} of the
canonical form.
The next step is to introduce the concept of transversality as a means to
study structure stability and genericity. This concept was originally
introduced by R. Thom \cite{thom} and, in general, is not widely used to
classify physical phenomena in terms of elementary catastrophes. A property is
called generic if the subset for which the property is valid is open and dense
in the original set. In other words, when a property is invariant under a
perturbation, this property is called generic or structurally stable.
The theorem of transversality shows that it is a
generic property of functions to have only isolated {\it critical points}%
\footnote{We warn the reader not to confuse thermodynamical and mathematical
terminology. In thermodynamical terms a critical point is just an equilibrium point
and the
word critical is reserved for a higher singularity.} and such functions are stable
under perturbations. Two manifolds of $\IR^n$ intersect transversally if either
their intersection is empty or they intersect transversally at all their points
of intersection, that is, the direct sum of their tangent spaces at the point
has dimension $n$ or they span the tangent space $\IR^n$ at that point.
CT has usually not been applied in a rigorous way using all these concepts and
theorems needed for its correct implementation. We claim in this work that if
this is done so, the procedure proposed by the theory is not by any means
cumbersome and time consuming. The Catastrophe Program proposed here
provides a very useful and systematic way to examine with not very much effort
general behaviors of physical systems.
Let $F(x,\lambda)$ be a real function with state variables $x_1,\dots,x_n$ ($x
\in \IR^n$) and control parameters $\lambda_1,\dots,\lambda_r$ ($\lambda
\in \IR^r$);
that is, $F : \IR^{n+r} \rightarrow \IR $. We are to proceed as follows:\\
\begin{enumerate}
\item We pick ($x_0,\lambda_0$) such that $x_0$ is a {\em degenerate critical
point} of $F(x,\lambda)$ and we consider the unfolding
$f(x,\lambda)=F(x+x_0,\lambda+\lambda_0)-F(x_0,\lambda_0)$ and $h(x)=f(x,0)$. \\
\item One calculates the determinacy and codimension of $h$ from the $k$-jet of
$h$ (see Appendix).
Of course, if $h$ is $k$-determine then $h \sim j^k(h)$, that is, the
function $h$ is equal to $j^k(h)$ up to a change of coordinates and hence
they are equivalent and have qualitatively the same properties;
therefore, cod$(h)=$ cod$(j^k(h))$.\\
\item One studies the $k$-transversality of $F$ and if this function is
$k$-tranversal we can affirm that $F$ and the canonical form of the unfolding
of $h$ are isomorphic and we can replace the original $F$ function for this
canonical unfolding. If not, we can claim that the $F$ function is not
susceptible to be studied by CT.\\
\end{enumerate}
\section{Description of the Gibbs potential}
According to Ref.\ \cite{griff2} a phenomenological model for a ternary mixture
is obtained by assuming the Gibbs potential in the form
\begin{equation}
\label{GIBBS}
{\bar G} = N [a' yz + b' xz + c' xy + R\,T\,(x \ln x + y \ln y + z \ln z)],
\end{equation}
where $N=N_x + N_y + N_z$ gives the number of total moles and $N_x$,
$N_y$ and $N_z$ the moles of each component. The variables $x,y,z$
are the mole fractions defined by $x=N_x/N$, $y=N_y/N$ and $z=N_z/N$;
and hence we have the constraint
\begin{equation}
\label{CONS}
x + y + z = 1
\end{equation}
where $0 < x , y , z < 1$. Finally, $a', b'$
and $c'$ are phenomenological energy parameters. The energy
part is the most general quadratic term, given that $x + y + z = 1$.
This model can be derived from the mean field theory of a lattice model
Hamiltonian with variables taking three different states, representing the
molecules of the three components \cite{KM}. Then $a',b'$ and $c'$ represent
molecular interaction parameters.
Let us consider the Gibbs potential Eq.\ (\ref{GIBBS}) in a reduced form,
dividing by $NRT$, and thus
\begin{equation}
\label{RGIBBS}
G(x,y,z,a,b,c) = a\,yz + b\,xz +c\,xy + x \ln x + y \ln y + z \ln z
\end{equation}
where now the new parameters $a,b,c$ are defined with respect to
the old ones $a',b',c'$ dividing them by $RT$.
The concentrations are supposed to be determined by some boundary
conditions, such as the values of the chemical potentials of
two components, say $\mu_x$ and $\mu_y$.
The mean field theory prescription is then to minimize the {\it non-equilibrium
Gibbs potential} $G - \mu_x\,x - \mu_y\,y$ with respect to $x$ and $y$
to obtain the equilibrium conditions
$$
\frac{\partial G}{\partial x} = \mu_x,\\
\frac{\partial G}{\partial y} = \mu_y.
$$
They allow to solve for $x$ and $y$ as functions of $\mu_x,\mu_y$ and the
parameters $a,b$ and $c$, provided that the Jacobian
$\det\frac{\partial(\mu_x,\mu_y)}{\partial(x,y)} = \det{\partial_{ij}^2 G}$
is not zero.
Thermodynamical stability further requires that the matrix
${\partial_{ij}^2G}$ be positive definite. This property is called
{\it convexity}
and must hold for any thermodynamical potential, except on the instability
hyper-surfaces, which are the simplest singularities we may encounter in a
phase diagram. An instability can occur only near a phase transition, when two
equilibrium states, one unstable---hence unphysical---and the other
meta-stable coalesce and disappear. In other words, a meta-stable state
becomes unstable and, consequently, we speak of instability. This
is the kind of sudden change in the configuration of a system to which CT
owes its name. In mathematical terms we say that the {\em critical point}
(equilibrium state) is degenerate. As a consequence, one cannot solve for $x$
and $y$ as functions of $\mu_x,\mu_y$ or the solution is multi-valued,
corresponding to the existence of
various equilibrium states. The simplest instability occurs when only one
eigenvalue of the stability matrix vanishes; that is, the instability only
affects one variable. One is to focus on this variable, which is called
{\it relevant}, to consider further singularities. Therefore, it is convenient
to transform the potential into a function of just the relevant variable by
solving the equilibrium conditions for the other variables and
substituting for them. The standard thermodynamical procedure that performs
this operation is the Legendre transform. In fact, this procedure can be used
for potentials in other fields, whenever there is an underlying geometrical
structure in the total space of variables, including state and control
variables, called a {\em contact structure}. We address the reader interested
in the general formulation to the literature \cite{ArnoldCS}. How the Legendre
transform is implemented in our case will be seen in the next section.
Further singularities are studied afterwards with the one-variable potential.
Next comes what can be called critical instability, followed by the
tricritical point and so onwards.
Several systems of interest are described by this Gibbs potential Eq.\
(\ref{GIBBS}):
A ternary mixture at constant volumen, for example, a mixture of metals;
a spin lattice where the molecules have spin one;
a binary fluid mixture, where one of the three states represents a vacancy
instead of a new molecule and the corresponding concentration is associated to
a variable total volumen. In the last case, the possible phases are
vapor, miscible liquid mixture and inmiscible liquid mixture.
The convenient extensive variables are the specific volume $v$ and the relative
concentration $\bar{x} = \frac{x}{x+y}$ of the two fluids and the intensive
variables are the pressure and the chemical potential of one of the fluids.
Moreover, the thermodynamical potential Eq.\ (\ref{GIBBS}) depends on $T,v$ and
$\bar{x}$ and is therefore the Helmholtz potential $F(T,v,\bar{x}).$
This system is perhaps the most interesting
for applications, given the great amount of experimental data on
binary fluid mixtures \cite{Row, McH-K}. However, the potential (\ref{GIBBS})
is not the most popular for fitting data; a related form which has
similar dependence on the relative concentration of the two fluids but
is of Van der Waals type for the volume is usually considered instead. We
believe that this form, which is much more difficult to analyze, gives
essentially the same qualitative behavior.
\section{Applying the CT program}
{}From Eqs.\ (\ref{RGIBBS}) and (\ref{CONS}), we have a function depending only on
two variables, $x$ and $y$, namely,
\begin{equation}
\label{HXY}
H(x,y,a,b,c) = a\, y (1-x-y) + b\, x (1-x-y) + c\,x y + x \ln x + y \ln y +
(1-x-y) \ln (1-x-y) .
\end{equation}
Now consider the function $H_y (x,y,a,b,c) - \mu_2$ (where the subindices
indicate derivatives with respect to the variable explicitely written
and $\mu_2 \equiv \mu_y$) and let
the point $(x_0,y_0,a_0,b_0,c_0,\mu_2^0)$ be such that $H_y(P_0)-
\mu_2^0 = 0$ and $H_{yy} (P_0) > 0$, where $P_0 =(x_0,y_0,a_0,b_0,c_0)$.
The first condition is the equilibrium condition for $y$ and
the second one is required by stability in the $y$ direction.
Then, by the Implicit Function Theorem,
there exists a unique function $\psi (x,a,b,c,\mu_2)$ defined in a neighborhood
of $(x_0,a_0,b_0,c_0,\mu_2^0)$ with values in a neighborhood of $y_0$
such that $H_{yy} (x,y,a,b,c) > 0$, in these neighborhoods, and $H_y
(x,\psi(x,a,b,c,\mu_2),a,b,c) - \mu_2 = 0$ in the domain of $\psi$ and $\psi
(x_0,a_0,b_0,c_0,\mu_2^0) = y_0$.
By solving for $y$ as a function of $\mu_2$ and substituting into $H-\mu_2\,y
$ we have performed a Legendre transformation, effectively eliminating the
variable $y$. Next we substract $\mu_1 x$ (where $\mu_1 \equiv \mu_x$)
to obtain the function
\begin{equation}
\label{LX}
L(x,a,b,c,\mu_1,\mu_2) = H (x,\psi(x,a,b,c,\mu_2),a,b,c) - \mu_2\, \psi
(x,a,b,c,\mu_2) - \mu_1 x,
\end{equation}
representing a one variable non-equilibrium Gibbs potential.
In order to have a function defined in a neighborhood of
${\bar 0} = (0,0,0,0,0,0)$ we consider the new function
\begin{equation}
\label{LL}
L_1(x,a,b,c,\mu_1,\mu_2) =
L(x+x_0,a+a_0,b+b_0,c+c_0,\mu_1+\mu_1^0,\mu_2+\mu_2^0) -
L(x_0,a_0,b_0,c_0,\mu_1^0,\mu_2^0) .
\end{equation}
Then we have the following equations:
\begin{equation}
L_1({\bar 0}) = 0 \label{L10}
\end{equation}
and
\begin{eqnarray}
\lefteqn{L_{1,x} (x,a,b,c,\mu_1,\mu_2) = } \nonumber \\
& & H_x\left[x+x_0,\psi(x+x_0,a+a_0,b+b_0,c+c_0,
\mu_2+\mu_2^0),a+a_0,b+b_0,c+c_0\right] \nonumber \\
& & \mbox{}+ H_y \,\psi_x - (\mu_2+\mu_2^0)\, \psi_x - (\mu_1+\mu_1^0)
\end{eqnarray}
so that
\begin{equation}
L_{1,x} ({\bar 0}) = H_x(P_0) -\mu_1^0 . \label{L1x0}
\end{equation}
Suppose now that $H_x(P_0) - \mu_1^0= 0$ (the remaining equilibrium condition).
Then $0$ would be called a {\it critical
point} of $L_1(x,0,0,0,0,0)$ (in mathematical terminology).
This function will be denoted by $g_1(x)$,
which is the {\em germ} to be studied. Of course, $g_1(0) = 0$ and $g_1' (0) = 0$
from (\ref{L10}) and (\ref{L1x0}).
The two first derivatives of $g_1$ are
\begin{equation}
g_1' (x) = H_x(x+x_0,\psi(x+x_0,a_0,b_0,c_0,\mu_2^0),a_0,b_0,c_0) - \mu_1^0
\end{equation}
and
\begin{equation}
g_1'' (x) = H_{xx}(x+x_0,\psi(x+x_0,a_0,b_0,c_0,\mu_2^0),a_0,b_0,c_0) +
H_{xy} (-) \psi_x (-) .
\end{equation}
In particular
\begin{equation}
g_1'' (0) = H_{xx} (P_0) + H_{xy}(P_0)\, \psi_x (x_0,a_0,b_0,c_0,\mu_2^0)
\end{equation}
with
\begin{equation}
\psi_x (x_0,a_0,b_0,c_0,\mu_2^0) = \frac{- H_{xy} (P_0)}{H_{yy} (P_0)} ,
\end{equation}
as deduced from $H_y-\mu_2 = 0$ by taking the derivative with respect to $x$.
Suppose that the Hessian of $H$ is such that
\begin{equation}
H_{xx} (P_0)\,H_{yy} (P_0) - H_{xy}^2 (P_0) = 0 ,
\end{equation}
then $g_1'' (0) = 0$ and $0$ is a degenerate critical point of
$g_1$. Finally, we also assume that
$g_1''' (0) = g_1^{iv} (0) = g_1^v (0)
= g_1^{vi} (0) = 0$. Then we have imposed five conditions on $g_1$
altogether and we should be able to solve for
$(x_0,y_0,a_0,b_0,c_0)$.
In this case, we say that we have reached the highest codimension. We will see
in the next section that there is indeed such a solution.
\section{Results}
\subsection{Highest singularity}
Now we look for a point which fulfills the 5 conditions for the highest singularity
mentioned above. We succesively have that
\begin{equation}
y_0 = 1 - 2\,x_0,
\end{equation}
\begin{equation}
b_0 = x_0^{-1},
\end{equation}
\begin{equation}
a_0 = c_0 = \frac{1 + 2\, x_0}{8\, x_0\, (1- 2\, x_0)}
\end{equation}
and
\begin{equation}
36\, x_0^2 + 4\, x_0 - 1 = 0 .
\end{equation}
Thus from the last equation we have that $x_0 = \frac{\sqrt{10}-1}{18}\simeq
0.1201265$.
Moreover, $$g_1^{vii} (0) = 6\, x_0^{-2} \left( \psi_{5x} - \frac{1472}{27} \,
x_0^{-4}\right) \neq 0,$$ where $$\psi_{5x} = \frac{256}{162}\, x_0^{-2}
\left[ \frac{157}{10}\, x_0^{-2} - 17 (1-2x_0)^2
+ 5\, \frac{3x_0^2 -4x_0 +1}{x_0^2 (1-2x_0)^2}\right].$$
Now we apply results of Singularity Theory \cite{thom,ww}:
\begin{itemize}
\item The 7-jet of $g_1$ is $j^7 (g_1) = \frac{1}{7!}\, g_1^{vii}(0) \, x^7$
with $g_1^{vii} (0) \neq 0$.
\item the essence of $g_1$ respect the identity is 7 and therefore
$\sigma(g_1) \geq 7$, where $\sigma (g_1)$ is the determinacy of $g_1$
(see Appendix for the definition of this concept).
\item The codimension of $j^7 (g_1)$ is ${\rm cod}(j^7 (g_1)) =
{\rm dim~vect}( \langle x\rangle / \langle x^6 \rangle) = 5 $
(see Appendix) and $\sigma (j^7 (g_1)) \leq 7$. Thus $j^7 (g_1)$ is
7-determinate, $j^7 (g_1) \sim g_1$ and $g_1$ is 7-determinate. Moreover,
${\rm cod} (g_1) = 5$ and $\sigma (g_1) = 7$. A basis of this
quotient vector space is
given by the set $\{ [x],...,[x^5] \}$. Then ${\bar g}_1 (x,\lambda_1,...,
\lambda_5) = g_1(x) + \lambda_1 x + \lambda_2 x^2 + ... + \lambda_5 x^5$ is a
{\it canonical unfolding} $k$-transversal of the {\em germ} $g_1$ for every $k > 0$;
in particular, for $k=7$. Finally $g_1 \sim x^7$.
\item The $L_1$ function is an unfolding 7-transversal of $g_1$ because
one can prove
(see Appendix)
\begin{equation}
\label{TRANS}
\langle x\rangle = \langle x^6\rangle + V_{L_1} + \langle x\rangle ^{7+1},
\end{equation}
where $V_{L_1}$ is the real linear space generated by
$$\{L_{1,a} (x,{\bar 0}) - L_{1,a} (0,{\bar 0}),\dots,L_{1,{\mu_2}} (x,{\bar 0}
) - L_{1,{\mu_2}} (0,{\bar 0}) \},$$ where the subindices $a,\dots,\mu_2$
denote derivatives with respect to the corresponding parameters.
Note that Eq. (\ref{TRANS}) has the following expression
%\newpage
\begin{eqnarray}
%\label{TRANS1}
\langle x \rangle = \langle x^6 \rangle +
\left\{ x \,(-1+2x_0)
+ x^2 \,\frac{2}{3} x_0^{-1}\, (1-3x_0) +
x^3 \left(\frac{2}{3} x_0^{-1} + \frac{4}{9} x_0^{-2} (-1 + 3x_0)\right)+ \right.
\nonumber \\
x^4 \left(- x_0^{-2} \frac{8}{9} + (3x_0-1)\, x_0^{-3} \frac{-352}{1080}\right) +
x^5 \left(\psi_{5x} (3x_0-1) \frac{1}{5!} + \frac{1}{4!} \frac{352}{45} x_0^{-3}
+ \frac{16}{27} x_0^{-3}\right), \nonumber \\
- \frac{1}{3} x^2 + x^3 \frac{2}{9} x_0^{-1} + x^4 \left( - \frac{4}{9}
x_0^{-2} + \frac{1}{24} \frac{352}{45} x_0^{-2}\right) + x^5 \left(\frac{1}{24}
\frac{352}{45} x_0^{-3} - x_0 \frac{1}{5!} \psi_{5x}\right), \nonumber \\
x (1-2x_0) - \frac{2}{3} x^2 + x^3 \frac{-2}{9} x_0^{-1} +
x^4 \frac{1}{24} \frac{128}{45} x_0^{-2} + x^5 \frac{1}{5!} \left(x_0\, \psi_{5x}
- \frac{352}{9} x_0^{-3}\right), \nonumber \\ \left.
- x, \,x^2 \,\frac{2}{3} x_0^{-1} - x^3 \,\frac{4}{9} x_0^{-2} + \frac{1}{4!} x^4\,
x_0^{-3}\, \frac{352}{45} + \frac{1}{5!} x^5\, (- \psi_{5x}) \right\},\nonumber
\end{eqnarray}
\begin{equation} \label{TRANS1}
\end{equation}
\noindent where the Taylor expansions in $V_{L_1}$ have been truncated at
$x^5$ because the terms of degree sixth and higher are already included in
$\langle x^6 \rangle$. The resolution of Eq.\ (\ref{TRANS1}) amounts to prove
that a generic fith-degree polynomial with no independent term can
be generated as a linear combination of the five polynomials between the curly
brackets. Hence it implies the resolution of a linear system whose determinant
is $x_0\,( - 58944\, x_0^2 + 729 \, \psi_{5x}) \neq 0$.
Finally, this equality, Eq.\ (\ref{TRANS1}), holds and consequently
${\bar g}_1$ and $L_1$ are isomorphic as unfoldings and $L_1$ can be
qualitatively studied by the polynomial
$$
x^7 + \lambda_1\, x + \lambda_2\, x^2 + \lambda_3\, x^3 + \lambda_4\, x^4 +
\lambda_5\, x^5,
$$
which in the terminology of CT corresponds to the {\it Wigwam} or $A_6$
catastrophe.
\end{itemize}
As a result of this analysis we can affirm that there are three changes of
coordinates $\varphi_1$, $\varphi_2$ and $\varphi_3$ and a perturbation
$\varepsilon$ of parameters such that
\begin{equation}
\label{LLB}
L_1(x,a,b,c,\mu_1,\mu_2) = u^7 + \lambda_1 u + \lambda u^2 + \cdots +
\lambda u^5 + \varepsilon (a,b,c,\mu_1,\mu_2)
\end{equation}
with
$$
u = \varphi_3\, p_1\, \varphi_1 (x,a,b,c,\mu_1,\mu_2) ,
$$
$$
\varphi_2 (a,b,c,\mu_1,\mu_2) = (\lambda_1,\dots,\lambda_5) .
$$
where $p_1$ means the {\it first projection}, $p_1 : \IR^{1+5}
\rightarrow \IR $, that is, $p_1 (x_1,\dots,x_6) = x_1$.
Moreover, the bifurcation set of Eq.\ (\ref{LL}) and that corresponding to
\begin{equation}
\label{WIG}
u^7 + \lambda_1 u + \lambda u^2 + \cdots + \lambda u^5
\end{equation}
are diffeomorphic and we rather work with Eq.\ (\ref{WIG}) due to its
simplicity. The equilibrium manifold in $(u,\lambda_1,\dots,\lambda_5)$
is obtained from Eq.\ (\ref{WIG}) by equating the first derivative to zero
$$
7 u^6 + \lambda_1 + 2 \lambda_2\, u + 3 \lambda_3\, u^2
+ 4 \lambda_4\, u^3 + 5 \lambda_5\, u^4 = 0
$$
and, furthermore, instability occurs if the second derivative also vanishes,
$$
42 u^5 + 2 \lambda_2 + 6 \lambda_3\, u + 12 \lambda_4\, u^2
+ 20 \lambda_5\, u^3 = 0 .
$$
Now the bifurcation set is obtained by a projection onto the parameter space,
that is, by eliminating the variable $u$ in this system of two equations.
\subsection{Critical azeotropy as a singularity}
In the process of solving the equations that lead to the highest singularity one
goes through singularities of lower codimension. They have no particular interest
by themselves except in one case, which we proceed to describe.
Thus we analyze now the five conditions one by one.
The equilibrium conditions allow one to express $x_0$ and $y_0$ as functions of
the parameters, resulting in $y_0 =\psi(x_0,a_0,b_0,c_0,\mu_2^0)$, already used to
define $g_1(x)$, and an equation for $x_0$ derived from equating (\ref{L1x0})
to zero. However, we prefer to keep $x_0$ and $y_0$ in the equations to follow,
for it is simpler, understanding that they are to be substituted in the end.
The first condition on $g_1(x)$ is $g_1'' (0) = 0$ or
\begin{equation}
\det H_{ij} = H_{xx} (P_0)\,H_{yy} (P_0) - H_{xy}^2 (P_0) = 0 .
\end{equation}
The Hessian matrix is
\begin{equation}
\left(H_{ij}\right) = \left(\begin{array}{lr} \alpha_3 + \alpha_1 & \alpha_3\\
\alpha_3 & \alpha_3 + \alpha_2 \end{array}\right),
\label{Hessm}
\end{equation}
with $\alpha_3 = c-a-b + z^{-1}$, $\alpha_1 = a-c-b + x^{-1}$ y $\alpha_2 = b-a-c +
y^{-1}$. We have reinstated $z=1-x-y$ for the sake of symmetry and we suppress
the subindices zero relative to $P_0$ in the next equations.
>From Eq.\ (\ref{Hessm}),
\begin{equation}
\det H_{ij} = \alpha_3\, \alpha_1 + \alpha_3\, \alpha_2 + \alpha_1\, \alpha_2=0,
\end{equation}
which is a quadratic equation on either $a,b,c$ or $x,y$.
The next condition $g_1'''(0) = 0$ is equivalent to
\begin{equation}
{1\over x^{2}}\,\alpha_2^{3} + {1\over y^{2}}\,\alpha_1^{3} -
{1\over x^{2}}\,(\alpha_1+\alpha_2)^{3} = 0
\end{equation}
or
\begin{equation}
{1\over x^{2}}\,\alpha_3^{3} - {1\over y^{2}}\,(\alpha_3+\alpha_1)^{3} +
{1\over z^{2}}\,\alpha_1^{3} = 0
\end{equation}
or
\begin{equation}
-{1\over x^{2}}\,(\alpha_3+\alpha_2)^{3} + {1\over y^{2}}\,\alpha_3^{3} +
{1\over z^{2}}\,\alpha_2^{3} = 0.
\end{equation}
Each of these is an equation of third degree in $a,b,c$.
Next we consider
$g_1^{iv}(0) = 0$. Again this equation can be separated into three symmetric
options. Each one imposes new conditions on $\alpha_i$ and hence on the elements
of the Hessian matrix. Furthermore, they can only be fulfilled if two
new quantities vanish. In other words, the codimension increases by two units with
only one condition, a non-generic situation.
We choose the solution $\alpha_3=\alpha_1=0$ such that $H_{xx}(P_0) =
H_{xy}(P_0) = 0$. There are two more solutions, obtainable by cyclic permutation
of the labels of the alphas. As a counterpart of the previous extra increase
of the codimension by one unit,
the next condition is identically fulfilled, $g_1^{v}(0) \equiv 0$. Finally,
from $g_1^{vi}(0) = 0$ one obtains the solution quoted in the subsection above.
Let us compare the foregoing analysis with the one in the previous literature
on this model \cite{KM,griff2}. This analysis goes as follows.
The first condition $g_1''(0) = 0$ or, equivalently, that the Hessian of $H$
be null has two types of solutions, namely, a simple solution,
$\alpha_1^{-1}+\alpha_2^{-1}+\alpha_3^{-1}=0$, and a second
solution that requires that two of the $\alpha_i$ vanish simultaneously.
The first type is more
generic but, unfortunately, does not lead to a high codimension singularity,
since the equation $g_1^{iv}(0) = 0$ has no solution for it. The second
solution is the one we have considered in the previous subsection.
It is called a symmetric solution
because the additional condition for the Hessian matrix
elements implies a symmetry in the phase diagram, namely, $a = c$.
Alternatively, we can avoid making any choice on the type of solution until
the last moment, namely, when we demand $g_1^{iv}(0) = 0$. Then this condition
implies by itself $g_1^{v}(0) = 0$. In other words, the singularities given by
these two conditions are
inextricably linked: the first one entails the second one. Moreover,
the first condition led us to take $H_{xx}(P_0) = H_{xy}(P_0) = 0$ in
addition to $\det H_{ij} = 0$. We may recall here that the vanishing of these
two elements of the stability matrix for a binary
fluid mixture has a thermodynamical interpretation: It occurs when there is
critical azeotropy \cite[pages 197--199]{Row}. Azeotropy is not a singularity
on its own but when it superposes on a critical point it enhances its singularity
producing a new one. We see what kind of singularity it is in our case, namely,
the one given by $g_1^{v}(0) = 0$---a tricritical point. At this moment, we are
not able to say if this is just a peculiarity of the particular three-component
model we study or in fact constitutes a general feature.
\section{Discussion}
The solution with the highest codimension, namely, five, which has been found above must be isolated; that is,
it cannot belong to a continuos family of solutions. Nevertheless, there can
be a discrete set of solutions. In fact, we can obtain two other solutions
from this one by using the symmetry of the original potential $G(x,y,z,a,b,c)$
under simultaneous permutations of $(x,y,z)$ and $(a,b,c)$. The way in which
they arise is clear in the last subsection. It is clear as well that there are no
further solutions with codimension five.
Some readers may be concerned by the fact that our solution is a Landau
potential which is not bounded below. This does not mean that there is no
absolute minimum and the Landau potential is meaningless. We must remember
that the Landau potential is a local
object and provides no information on the behavior of the thermodynamical
potential far from the point that we have called $P_0$. This point corresponds
to a degenerate instability rather than to a multicritical point. To be
precise, it arises as a tricritical point, with Landau potential $x^6$,
merges with an unstable equilibrium state and disappears, for which the
appropriate name is tricritical unstable point. Since $g_1^{vii} (0) \neq 0,$
there is no tetracritical point in the phase diagram. In this
we disagree with \cite{griff2}, where they assert to have three tetracritical
points with $g_1^{vii} (0) = 0.$ We attribute this disagreement to a slip on
their part, since the conditions they obtain for their tetracritical points are
precisely the same five conditions we have for our tricritical unstable point
and the codimension of a generic tetracritical point is six. Thus it seems
that they are calling tetracritical points to what actually are tricritical
unstable points.
The topology of the overall phase diagram is formed by gluing 3 patches
corresponding each to the phase diagram of the {\em Wigwam} catastrophe, as
given in the literature \cite{LNM}. The Taylor series expansions on which
the CT is based are supposed to be valid in each patch. The coordinates on each
patch are not related and therefore we can only obtain topological information.
Even the topological matching is not a trivial matter when we deal with
high-dimensional spaces. Since the highest singularities
in our analysis are essentially the same as those in \cite{griff2}, so is the
phase diagram. The phase diagram is of great utility for experimentalists and
we should like to obtain some more concrete information. We must notice that
in a particular model, for example, a binary fluid mixture, the energy
parameters are fixed and one can only tune the chemical potentials---one of
which is to be interpreted as pressure in the binary mixture---and the
temperature. Therefore, one is interested in three-dimensional
sections of the overall phase diagram. In these sections it is not generic
to have a tricritical point, (which has codimension four,) a fact well known
to experimentalists. Generic and non generic sections of the phase diagram of
the {\em Wigwam} catastrophe are expected to cover all the possibilities.
Another solution of $\det H_{ij} = 0$ is, of course, that all the matrix
elements be null so the matrix has rank zero or co-rank 2. This means that one
cannot use the Implicit Function Theorem to reduce to a function of one
variable and one is to proceed with the CT program for a function of two
variables. The next step is to analyze the 3-jet of this function, that is,
the form given by the third derivatives. According to its signature, given by
the sign of its discriminant, there are three possible cases: If it is
negative, the canonical form is $x^3 - 3\,x\,y^2$, called the {\it elliptic
umbilic} catastrophe; if it is positive the canonical
form is $x^3 + 3\,x\,y^2$, called the {\it hyperbolic umbilic} catastrophe;
if it is null, the 3-form is degenerate, and one is to anlyze the
4-jet to determine the type of singularity, which may be the {\it parabolic
umbilic} catastrophe or a type even more complex. The calculations driving at
establishing the highest singularity in our five dimensional parameter space
are complicated and the results for co-rank two shall be reported in the
future \cite{gmm}.
\section{Acknowledgements}
This work has been supported by DGICYT-Spain with Grants PB92-0302,
PB93-0454-C02-01 and PB95-0071. S.M.A. gratefully acknowledges the Alexander
von Humboldt Foundation for a Fellowship.
\newpage
\appendix
\section{Summary of Catastrophe Theory}
In this Appendix we are going to present the main mathematical concepts
widely introduced in Refs.\ \cite{ww,lander} and necessary to follow the main
steps developed in Section 5.
Let us consider real functions of class $\infty$ and defined in a neighbourhood
of $0 \in \IR^n$. We establish that two functions are equivalent if they
coincide in a neighbourhood of $0$. The classes we obtain are called {\em germs} of
functions and the set of {\em germs} is denoted by $E(n)$. The operations $f+g$ and
$f\cdot g$ give to $E(n)$ the estructure of a ring and $M(n) = \{ f \in E(n) /
f(0) = 0 \}$ is a maximal ideal of this ring. Moreover, the operations
$f+g$ and $\lambda \cdot f$ with $\lambda \in \IR$ give to $E(n)$ the structure of
a real vector space of dimension $\infty$. The ideal $M(n)$ is generated by
$x_1,\dots,x_n$, that is, $M(n) = \{ f_1 x_1 + \cdots + f_n x_n \;/\, f_1,\dots,
f_n \in E(n) \}$. In general, if $f_1,\dots,f_n \in E(n)$, we designate by
$\langle f_1,\dots,f_n \rangle $ to the ideal generated by $f_1,\dots,f_n$,
that is,
$$
\langle f_1,\dots,f_n \rangle = \{ f_1 g_1 + \cdots + f_n g_n \,\, /
\, g_1,\dots,g_n \in E(n) \} .
$$
In particular, $M(n) = \langle x_1,\dots,x_n \rangle$.
It is possible to define powers of $M(n)$ as $M(n)^k$. It can be proven that
$M(n)^k$ is equal to the ideal of $E(n)$ generated by the monomials in $x_1,
\dots,x_n$ of degree $k$. In particular, for example, $\langle x,y \rangle ^2 =
\langle x^2,xy,y^2 \rangle$. We have also that
$M(n)^{k+1} = \{f \in E(n) / D^if(0) = 0, i \leq k \}$ where with $D^i$
we mean the derivative of degree $i$.
In a similar way, we can define the {\em germs} of dipheomorphisms of class $\infty$
from $\IR^n$ in $\IR^n$ which transform $0$ in $0$. This set is denoted by
$G(n)$.
We say that two {\em germs} are equivalent if there exists a change of coordinates
$\varphi \in G(n)$ such that $f= g \,\varphi$ and it is denoted by $f \sim g$.
When the $k$-jets ($k \in \IN$ )of two functions are equal we say that these
functions are $k$-equivalent ($f \sim _k g$).
A {\em germ} $f$ is $k$-determinate if for every {\em germ} $g$ such that both
$k$-jets are equal we have that $f \sim g$. The determinacy of a {\em germ} $f$ is
the smallest number $k \in \IN $ such that $f$ is $k$-determinate and it is called
$\sigma (f)$. Therefore, we notice that :
\begin{description}
\item[] If f is $k$-determinate then $f \sim j^k f$ ,
\item[] If f is $k$-determinate and $f \sim _k g$ then $g$ is $k$-determinate ,
\item[] If f is $k$-determinate and $f \sim g$ then $g$ is $k$-determinate.
\end{description}
The ideal of Jacobi of a {\em germ} $f$ is defined by
$$
\Delta (f) = \langle D_{x_1} f,\dots,D_{x_n} f \rangle
$$
where $D_{x_1},\dots,D_{x_n}$ are the partial derivatives with respect to the
$x_1,\dots,x_n$ variables. If $f \sim g$ then $ \Delta (f) \equiv \Delta (g)$.
Now let us assume that $f \in M(n)^2$. Then $\Delta (f) \subset M(n)$ and we can
speak of the quotient vector space $M(n) / \Delta (f)$. The dimension of this
vector space is called codimension of $f$, $\cod (f)$. It can be proven that if
$f \in M(n)$
then $\cod (f)$ is finite if and only if $\sigma (f)$ is finite and in this
case $\sigma (f) - 2 \leq \cod(f) $. Moreover, if $f \sim g$ then $\cod (f) =
\cod (g)$. Thus the codimension generally coincides with the number of conditions
necessary to specify a function germ up to diffeomorphisms, which is the usual
geometrical concept.
If $g \in M(n+r)$ and $f \in M(n)^2$, we say that $g$ is a $r$-unfolding of $f$ if
$g(x,0) = f(x)$ (with $r$ parameters which we define as $y_1,\dots,y_r$).
Now let us assume that $g \in M(n+r)$ is an unfolding of $f \in M(n)^2$ and $k
\in \IN$. We say that $g$ is $k$-transversal if
$$
M(n) = \Delta (f) + M(n)^{k+1} + V_g
$$
where $V_g$ is the real vector subset of $M(n)$ generated by the
vectors $D_{y_1} g(x,0) - D_{y_1} g(0,0),\dots,D_{y_r} g(x,0) - D_{y_r} g(0,0)$.
Finally, the theorem of $k$-transversality for unfoldings can be stated as
follows: Let us consider $ f \in M(n)^2$ $k$-determinate and $g$ and $h$
two unfoldings of $f$ with $r$ parameters which are $k$-tranversal.
Then $g$ and $h$ are isomorphic.
\newpage
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%\samepage
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\end{document}
V.I. Arnold, {\it Mathematical Methods of Classical
Mechanics}
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\begin{document}
\title{A sequence-based foldability score combined with AlphaFold2 predictions
to disentangle the protein order/disorder continuum}
\author[1]{Apolline Bruley}%
\author[1]{Tristan Bitard-Feildel}%
\author[1]{Isabelle Callebaut}%
\author[1]{Elodie Duprat}%
\affil[1]{Institut de Mineralogie de Physique des Materiaux et de Cosmochimie}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
Order and disorder govern protein functions, but there is a great
diversity in disorder, from regions that are -- and stay -- fully
disordered to conditional order. This diversity is still difficult to
decipher even though it is encoded in the amino acid sequences. Here, we
developed an analytic Python package, named \emph{pyHCA}, to estimate
the foldability of a protein segment from the only information of its
amino acid sequence and based on a measure of its density in regular
secondary structures associated with hydrophobic clusters, as defined by
the Hydrophobic Cluster Analysis (HCA) approach. The tool was designed
by optimizing the separation between foldable segments from databases of
disorder (DisProt) and order (SCOPe (soluble domains) and OPM
(transmembrane domains)). It allows to specify the ratio between order,
embodied by regular secondary structures (either participating in the
hydrophobic core of well-folded 3D structures or conditionally formed in
intrinsically disordered regions) and disorder. We illustrated the
relevance of \emph{pyHCA} with several examples and applied it to the
sequences of the proteomes of 21 species ranging from prokaryotes and
archaea to unicellular and multicellular eukaryotes, for which structure
models are provided in the AlphaFold2 databases. Cases of low-confidence
scores related to disorder were distinguished from those of sequences
that we identified as foldable but are still excluded from accurate
modeling by AlphaFold2 due to a lack of sequence homologs or to
compositional biases. Overall, our approach is complementary to
AlphaFold2, providing guides to map structural innovations through
evolutionary processes, at proteome and gene scales.%
\end{abstract}%
\sloppy
\textbf{Hosted file}
\verb`Bruley_et_al_manuscript.docx` available at \url{https://authorea.com/users/498784/articles/579495-a-sequence-based-foldability-score-combined-with-alphafold2-predictions-to-disentangle-the-protein-order-disorder-continuum}\selectlanguage{english}
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\begin{document}
\begin{thebibliography}{1}
\bibitem{Botta2005} Botta, P. (2005). En el texto de B. En J. O{\textquoteright}Neill, \& O. Di Camillo (Eds.), \textit{{\textquotedblleft}La Celestina{\textquotedblright} 1499-1999: Selected Papers from the International Congress in Commemoration of the Quincentennial Anniversary of {\textquotedblleft}La Celestina{\textquotedblright} (New York, November 17-19, 1999)} (pp. 19--40). Nueva York: Hispanic Seminary of Medieval Studies.
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\documentclass{amsart}
\usepackage{amsmath, amssymb, amsthm}
\theoremstyle{definition}
\newtheorem{problem}{Problem}
\theoremstyle{remark}
\newtheorem*{solution}{Solution}
\setcounter{problem}{9}
% Change 9 to n-1 where n is the first exercise of your p-set.
\title{Effective Peer Review}
\date{October 14, 2011}
\begin{document}
\maketitle
\begin{center}
Below are several examples of dialogue between a reviewer (Alice) and author (Bob). Consider what might be effective or ineffective about how they interact.
\end{center}
\bigskip
\begin{center}
\textbf{Example \#1}
\end{center}
\noindent \textsc{Alice}: Well everything looked pretty good. It seems like you did all the math right and I can read it and stuff.
\smallskip
\noindent \textsc{Bob}: Oh, thanks. So, were there any parts that needed some work?
\smallskip
\noindent \textsc{Alice}: I don't know. There were a few parts where maybe you could have used some different words, but I understood all of it. There was guiding text and everything.
\smallskip
\noindent \textsc{Bob}: Cool --- so I shouldn't change anything?
\smallskip
\noindent \textsc{Alice}: Yeah. I think it's fine.
\bigskip
\begin{center}
\textbf{Example \#2}
\end{center}
\noindent \textsc{Alice}: Gosh, where to start? I guess there are some proofs, but just look at this! Your introduction: hardly makes sense. You state Theorem 1 without defining some of its terms. There's no indication of why you're introducing the sets $A$ and $B$ at the start of the proof. And you say you're proving by contrapositive but this is contradiction!
\smallskip
\noindent \textsc{Bob}: Oh, um\ldots yeah, I guess I see what you're saying. So what about\ldots
\smallskip
\noindent \textsc{Alice}: No, that paragraph is horrible.
\smallskip
\noindent \textsc{Bob}: Hm. So, where do you think I should go from here?
\smallskip
\noindent \textsc{Alice}: Well, starting over from scratch would be one idea\ldots
\bigskip
\begin{center}
\textbf{Example \#3}
\end{center}
\noindent \textsc{Alice}: This was pretty nice. There's strong motivation at the start and you state your claim in Theorem 1 very clearly. Now I did want to look at the start of your proof: you leap into a number of technical details without indicating why they're important. I thought you could ease into that with a short guiding paragraph.
\smallskip
\noindent \textsc{Bob}: What do you mean? I mean, it's clear what I'm doing, you have to introduce all those concepts, and I put the pieces together in the fourth paragraph. It's perfectly clear!
\smallskip
\noindent \textsc{Alice}: Right --- I figured it out eventually. I just think you'd place less of a burden on the reader by providing a roadmap of where things are headed.
\smallskip
\noindent \textsc{Bob}: But then won't I say everything twice? I want this to be concise and clean, not boring.
\smallskip
\noindent \textsc{Alice}: OK\ldots well, let's look at Theorem 2. In the proof, you argue for sequential compactness, but you never mention that Heine-Borel reduces the problem to that matter.
\smallskip
\noindent \textsc{Bob}: Oh come on! Everyone knows Heine-Borel!
\bigskip
\begin{center}
\textbf{Example \#4}
\end{center}
\noindent \textsc{Alice}: So I enjoyed this paper --- I think you have a nice perspective on the problem. Things are well-motivated in the first paragraph, the proofs seem complete, and you make some nice use of guiding text.
\smallskip
\noindent \textsc{Bob}: OK, thanks.
\smallskip
\noindent \textsc{Alice}: I did feel that some of the information could have been organized better. For instance, your proof of Theorem 1 is only two paragraphs, but there are at least four distinct steps to your argument.
\smallskip
\noindent \textsc{Bob}: Uh-huh. So maybe it would be better if I split the ideas by paragraph?
\smallskip
\noindent \textsc{Alice}: Exactly. I think that would help a lot. And then I also wanted to draw your attention to the third-to-last paragraph. It's a little hard to tell how you use $\Xi_{15}$ in the rest of the proof.
\smallskip
\noindent \textsc{Bob}: Well, I guess I thought it was important because of the r\^{o}le it plays in a related problem\ldots
\smallskip
\noindent \textsc{Alice}: Right --- I can sort of see that, but I wonder if you should cut that part since it's not really mentioned elsewhere in this paper.
\smallskip
\noindent \textsc{Bob}: Hmm. OK, well, I'll consider that when I make my revisions.
\end{document}
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\hypertarget{comp_8c}{}\subsection{/root/openvpn/src/openvpn/comp.c File Reference}
\label{comp_8c}\index{/root/openvpn/src/openvpn/comp.\+c@{/root/openvpn/src/openvpn/comp.\+c}}
{\ttfamily \#include \char`\"{}syshead.\+h\char`\"{}}\newline
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\leavevmode
\includegraphics[width=350pt]{comp_8c__incl}
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% Python listing setup
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%@P:exocorcp
%@Dif:2
Soient les nombres $a$, $b$, $c$ tels que $a=1\,250$; $b=813,27$ et $c=272,5$.
\par Calcule $b+c$; $ac$ ; $a\times b$; $b\times c$.
%@Correction:
\opadd{813.27}{272.5}\kern2cm\opsub{1250}{272.5}\kern2cm\opmul{1250}{813.27}\kern2cm\opmul{813.27}{272.5}
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\documentstyle[12pt]{article}
\newtheorem{theorem}{Theorem}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{lemma}{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\begin{document}
\bibliographystyle{plain}
\title {Multiple measures of maximal entropy and equilibrium states
for one-dimensional subshifts}
\author{Nicolai Haydn \thanks{Mathematics Department, University of Southern California,
Los Angeles, 90089-1113. Email:$<[email protected]$>$.}}
\date{}
\maketitle
\begin{abstract}
\noindent We give simple examples of a one-dimensional mixing subshift
with positive
topological entropy which have two distinct measures of maximal entropy.
We also give examples of subshifts which have two mutually singular
equilibrium states for H\"{o}lder continuous functions.
\end{abstract}
\section{Introduction}
It is a well known fact that a wide class of uniformly hyperbolic
transformation that satisfy some irreducibility condition have unique
measures of maximal entropy. Irreducible subshifts have unique measures
of maximal entropy if they are for instance
of finite type or sofic (factors of shifts of finite type). More
general hyperbolic systems which satisfy specification have unique
measures of maximal entropy \cite{Bow}. In either case the systems have
a `uniform' mixing property.
Hofbauer had shown in \cite{Hof} that even subshifts of finite
type don't necessarily have unique equilibrium states. However
the potentials in the provided examples lack (of course) regularity
and one
of the equilibrium states is supported on a single fixpoint.
For a large class of H\"{o}lder continuous functions
we get here multiple equilibrium states which are supported on
embedded subshifts.
In this note we shall produce a simple example which
shows that even in the case of an irreducible subshift with positive
entropy one cannot generally expect to have a unique measure of maximal
entropy.
(It was pointed out that Krieger \cite{Kr} gave an example with a
non-unique measure of maximal entropy---although not as simple and
straighforward as this one.)
For two-dimensional subshifts of finite type, Burton and Steiff \cite{B-S}
have recently given examples whose measures of maximal entropy form
simplices that consist of more than single points. Hence:
\begin{example} There exists a subshift $\Sigma$ over a finite
alphabet with a topologically mixing shift transformation
$\sigma: \Sigma\rightarrow\Sigma$ such that $\Sigma$ carries at least
two mutually singular measures of maximal entropy.
\end{example}
\noindent An example is provided in definition 2 of the following section.
Lemmas 1, 2 and 3 serve to prove the properties claimed above.
Extending this example we are then able to produce in section 3
multiple equilibrium states for H\"{o}lder continuous functions
(see section 3 for H\"{o}lder continuity).
\begin{example} There exists a topologically mixing subshift
$\Sigma$ over a finite alphabet and a H\"{o}lder continuous
function $g:\Sigma\rightarrow\mbox{\bf R}$ such that $\Sigma$ carries at least
two mutually singular equilibirium states for $g$.
\end{example}
\section{Example} %%%%%%%%%%%%%%%%%%%% Section 2
We shall construct a subshift over the symbolset ${\cal A} = \{0,1,2,3,4\}$ and
shall refer to the symbols $\{1,2\}$ as the yellow symbols and denote
them by ${\cal Y}$. Similarly we call $\{3,4\}$ the green symbols and write
${\cal G}$ for them. Hence ${\cal A} = {\cal Y} \cup {\cal G} \cup \{0\}$.
Let us denote by $\Sigma_{\cal Y} = {\cal Y}^{\bf Z}$ the (yellow) full two-shift
over the alphabet ${\cal Y}$. Similarly we write $\Sigma_{\cal G}$
for the (green) full two-shift ${\cal G}^{\bf Z}$.
Let $\tau>0$.
The subshift $\Sigma \subset {\cal A}^{\bf Z}$ will consist of the union
of the two monochromatic shift spaces $\Sigma_{\cal Y}$ and
$\Sigma_{\cal G}$, to which we add bicoloured sequences in the
following way. A sequence in $\Sigma$ in which a word $\alpha$ of
one colour (green or yellow) is followed
by a word $\beta$ of the other colour (yellow or green) will have a string
of zeroes $\gamma$ separating the two words $\alpha$ and $\beta$.
The length $|\gamma|$ of that string of zeros is then at least,
$\tau(a + b)$, where $a = |\alpha|, b = |\beta|$ are the lengths of
the coloured words to the `left' and `right' of $\gamma$.
More precisely:
\begin{definition} The shift space $\Sigma \subset {\cal A}^{\bf Z}$
is defined as follows: We have $x \in \Sigma$ if
\noindent (i) either $x \in \Sigma_{\cal Y} \cup \Sigma_{\cal G}$, in which
case we call $x$ a {\em monochromatic} point.
\noindent (ii) or if bi-coloured blocks are of the form:
$$\dots 0y_1y_2\dots y_{a-1}y_a 0^{\lambda}g_1g_2\dots g_{b-s}g_b0\dots$$
or
$$\dots 0g_1g_2\dots g_{a-1}g_a 0^{\lambda}y_1y_2\dots y_{b-s}y_b0\dots$$
where $\lambda \geq \tau(a + b)$ and $y_i \in {\cal Y}, g_i \in {\cal G}$
($0^{\lambda}$ is a string of zeros of length $\lambda$), $\tau>0$.
\end{definition}
\noindent
If $\omega = \omega_m \omega_{m+1} \dots \omega_{m+n-1}$ is an allowed word
of some length $n$ in $\Sigma$, then we denote by $U(\omega)$ the
{\em cylinder set} $\{x \in \Sigma: x_i = \omega_i, m \leq i < m + n \}$.
The shift transformation $\sigma$ on $\Sigma$ is defined in the usual
way by $\sigma(x)_i = s_{i+1}, i \in {\bf Z}$, for $x \in \Sigma$.
Notice that the transition rules are shift invariant. Thus
$\Sigma$ is indeed a subshift which we endow with the usual topology
generated by the cylinder sets $U(\omega)$, where $\omega$
runs over all finite words in $\Sigma$.
Notice that a sequence in $\Sigma$ cannot end in an infinite one-sided
string of one colour unless the sequence already belongs to the
appropriate monochromatic subshift.
If $\tau=0$ then $\Sigma$ is a sofic system in which every string of
zeroes connects to coloured symbols of different colours,
and whose topological entropy is $\log 4$ (see lemma 2).
\begin{lemma} The shift transformation $\sigma$ on $\Sigma$ is
topologically mixing for every $\tau$.
\end{lemma}
\noindent {\bf Proof.}
We have to show that for any two finite words $\omega$
and $\eta$ there exists a number $N$ so that
$U(\omega) \cap \sigma^n(U(\eta))$ is non-empty for all $n \geq N$.
This is evidently true if $\omega$ and $\eta$ are both monochromatic
of the same colour. If the last symbol of $\eta$ and the
first symbol of $\omega$ are of different colour then consider the word
$\pi = \eta 0^{\lambda} \omega$.
Clearly, $\pi$ is an admissable word for every
$\lambda > \tau(|\eta| + |\omega|)$,
and the cylinder set
$U(\pi) \subset U(\omega) \cap \sigma^n(U(\eta))$ is non-empty for all
$n \geq N$, where $N$ can then be chosen to be equal to
$(1+\tau)(|\eta| + |\omega|)$.
If the last symbol of $\eta$ and the first symbol of $\omega$ are of
the same colour, then let us consider the word
$\pi = \eta 0^{\kappa} \varepsilon 0^{\lambda} \omega$,
where $\varepsilon$ is a symbol (or some other short word) of
the other colour. Here we have $\kappa \geq \tau(|\eta| + |\varepsilon|)$
and $\lambda \geq \tau(|\omega| + |\varepsilon|)$. Clearly
$U(\pi)$ is non-empty for those choices of $\lambda$ and $\kappa$.
Thus $U(\omega) \cap \sigma^n(U(\eta)) \not= \emptyset$
if $n \geq N = (\tau+1)(|\eta| + 2|\varepsilon| + |\omega|)$.
\hfill$\Box$
\begin{lemma} The topological entropy $\,h$ of the shift
$\sigma: \Sigma \rightarrow \Sigma$ is
$\max(\log 2,\frac{\log 4}{1+\tau})$.
\end{lemma}
\noindent {\bf Proof.}
Let us first get a lower bound on the topological entropy $h$
of $\Sigma$. For that purpose let us observe that since
$\Sigma$ contains two full two shifts, $\Sigma_{\cal Y}$ and $\Sigma_{\cal G}$,
the topological entropy of $\Sigma$ must be at least $\log 2$.
Let us now estimate the number of the remaining words of length
$n$ from above. We have two cases to consider:
\noindent (i) Monochromatic words that might also contain zeroes.
According to our rules such words begin or end with strings
of zeroes. Thus we obtain purely yellow and green words of lengths
$k = 0,\dots,n$ which on at least one side is framed by strings of zeroes.
Their number turns out to be
$2 \sum_{k=0}^n 2^k=2^{n+1}\sum_{k=0}^n 2^{-k}$.
\noindent (ii)
To estimate the number of words of length $n$ that genuinely contain
symbols of both colours, let us observe that since any such word has at
least one transition from yellow to green or vice versa, it therefore
must also contain at least $n\frac{\tau}{\tau+1}$ zeroes,
that is at most $n'=[\frac{n}{\tau+1}]$ ($[\;]$ denotes integer part)
coloured symbols (i.e.\ symbols in $\{1,2,3,4\}$).
The coloured symbols come in monochromatic blocks of
alternating colour. Denote by $P_{k,\ell}$ the number of possibilities
in which one can arrange $\ell$ symbols in $k$ blocks (separated by
the appropriate number of zeroes), where $k=1,2,\dots,\ell$.
One finds that
$$
P_{k,\ell}=\left(\begin{array}{c}\ell-1\\k-1\end{array}\right),
$$
which is the number of possibilities of picking the first element
of every block but the very first one.
The number of $n$-words
in $\Sigma$ which contain $\ell$ coloured symbols arranged
in $k\leq\ell$ monochromatic blocks of alternating colour
is $2P_{k,\ell}2^{\ell}$.
If $Q_k$ denotes the number of $n$-words in $\Sigma$ with at most
$n'$ coloured symbols in $k$ monochromatic blocks of alternating colour,
then
$$
Q_k=\sum_{\ell=k}^{n'} 2P_{k,\ell}2^{\ell}.
$$
The number of words of lengths $n$ that contain symbols of
both colours is now determined by
%%
\begin{equation}\label{coloured.words}
\sum_{k=2}^{n'}Q_k=2\sum_{\ell=2}^{n'}\sum_{k=2}^{\ell}
\left(\begin{array}{c}\ell-1\\k-1\end{array}\right)2^{\ell}
=2\sum_{\ell=2}^{n'}(2^{\ell-1}-1)2^{\ell}
=r_n2^{2n'},
\end{equation}
%%
where the constants $r_n$ and their reciprocals $1/r_n$ are
subexponential as $n$ goes to infinity.
Thus the total number of words of lengths $n$ (large enough) in the
subshift $\Sigma$ has growth rate
$$
h=\lim_{n\rightarrow\infty} \frac1n\log(2^n+2^{2n'}),
$$
which implies that $\Sigma$ has topological entropy
$h=\max(\log 2, \frac{\log4}{\tau+1})$.
In particular $\Sigma$ has topological entropy $\log 2$
if $\tau\geq 1$.
\hfill$\Box$
\begin{lemma} If $\tau\geq 1$, then there are two mutually
singular measures of maximal entropy on $\Sigma$.
\end{lemma}
\noindent {\bf Proof.}
It is well known \cite{Wal} that the measure of maximal entropy on
the full
two-shift $\{1,2\}^{\bf Z}$ is the Bernoulli measure with the
probability vector $(\frac12,\frac12)$. It's metric entropy
is $\log 2$. Let us define on $\Sigma$ a Bernoulli measure
$\mu_{\cal Y}$ which is given by the probability vector
$(0,\frac12,\frac12,0,0)$ and the measure $\mu_{\cal G}$
with the probabilities $(0,0,0,\frac12,\frac12)$.
Evidently both measures are shift invariant and have metric
entropies $\log 2$ which by lemma 2 is the topological entropy
of $\Sigma$. Hence $\mu_{\cal Y}$ and $\mu_{\cal G}$
(as well as all their linear combinations) are
(distinct) measures of maximal entropy for the subshift $\Sigma$.
\hfill$\Box$
\vspace{3mm}
\noindent In the case when $0<\tau<1$, then there is a unique
measure of maximal entropy which is given by the probability
vector $(0,\frac12,\frac12,\frac12,\frac12)$ whose entropy is
by lemma 2 equal to $\frac{\log 4}{\tau+1}$.
\section{Equilibrium states}%%%%%%%%%%%%%%%%%%%% section 3
\noindent
Let us construct now subshifts with non unique equilibrium states.
We say a function $f$ is H\"{o}lder continuous on a shift space
if there exists a $\vartheta\in(0,1)$ and a constant $C$ so that
for every $n>0$ one has
$$
\sup|f(\vec{x})-f(\vec{y})|\leq C\vartheta^n
$$
where the supremum is over all pairs of sequences
$\vec{x}=\cdots x_{-1}x_0x_1x_2\dots,
\vec{y}=\cdots y_{-1}y_0x_1y_2\dots$ in the shiftspace
for which $x_{-n}\cdots x_n=y_{-n}\cdots y_n$ and either
$x_{-n}\not=y_{-n}$ or $x_n\not=y_n$.
Let $f$ be a real valued H\"{o}lder continuous function on the full
two-shift $\Sigma_*$ (where $*={\cal G},{\cal Y}$)
so that $P_*(f)>\sup f$, where $P_*(f)$ is the pressure
of $f$ (see \cite{Wal}).
Let us define a H\"{o}lder continuous function $g$ on $\Sigma$
by putting $g(x)=f(x)$ if $x$ lies in the full two-shifts
$\Sigma_{\cal G}$ or $\Sigma_{\cal Y}$. We extend $g$ to bi-coloured
words in the following way: If $x_0=0$ then we put $g(x)=\sup f$.
If $x_0\not=0$ and $x\in\Sigma$ is a sequence which contains
symbols of both colours then let $x_{-n}\cdots x_n$ be the
longest monochromatic
string of either green or yellow symbols (that is either $x_{-n}=0$
or $x_n=0$) and pick a monochromatic point $y\in\Sigma_*$
($*={\cal G},{\cal Y}$) in the cylinder
$U(x_{-n}\cdots x_n)$. Now define $g(x)=f(y)$.
In this way $g$ is a H\"{o}lder continuous function on $\Sigma$.
Let us now prove that the pressure of $g$ (on $\Sigma$) is in fact
equal to $P_*(f)$ (on the two-symbol shiftspace) for a suitable
choice of $\tau$.
\begin{lemma}
If
$\tau\geq \frac{\log 4}{P_*(f)-\sup f} -1$, then the pressure
$P(g)$ of $g$ on $\Sigma$ is equal to $P_*(f)$.
\end{lemma}
\noindent {\bf Proof.}
Denote by $W_n$ the collection of $\Sigma$-words
$\alpha=\alpha_1\cdots \alpha_n$ of lengths $n$.
The pressure of $g$ is then given by the exponential
growth rate of the partition function
$$
Z_n=\sum_{\alpha\in W_n} e^{g^n(x(\alpha))},
$$
where $x(\alpha)$ is an arbitrary point in the cylinder set
$U(\alpha)\subset\Sigma$, and
$g^n=g+g\sigma+g\sigma^2+\cdots+g\sigma^{n-1}$ is the $n$-th
ergodic sum of $g$.
If in the above sum we restrict to monochromatic words $\alpha$ of
either colour, then we obtain the green or yellow
partition function $Z^*_n$ ($*={\cal G},{\cal Y}$)
whose growth rates are exactly $P_*(f)$.
Let us note that the growth rate of
$\sum_{k=1}^nZ^*_k$ is also $P_*(f)$. Hence, if we denote by $W'_n$
those words in $W_n$ that contain symbols of exactly one colour and
otherwise at least one zero, then it follows that growth rate of
$Z_n=\sum_{\alpha\in W'_n} e^{g^n(x(\alpha))}$
is also given by $P_*(f)$.
It thus remains to show that the exponential growth rate of
$\sum_{\alpha\in W''_n} e^{g^n(x(\alpha))}$
is $\leq P_*(f)$, where $W''_n$ denotes the genuinely bi-coloured
words in $W_n$ (i.e.\ those words that contain green and yellow symbols).
In lemma 2 equation (\ref{coloured.words}) we estimated
$$
|W''_n|\leq r_n4^{n/(\tau+1)},
$$
where the constants $r_n$ grow at most subexponentially as
$n\rightarrow\infty$. Since $\sup g=\sup f$, we obtain
$$
Z''_n=\sum_{\alpha\in W''_n} e^{g^n(x(\alpha))}
\leq |W''_n|e^{n\sup g}
\leq r_n4^{n/(\tau+1)}e^{n\sup f},
$$
whose growth rate is bounded by $\frac{\log 4}{\tau+1}+\sup f$,
which is $\leq P_*(f)$ exacty if
$\tau+1\geq \frac{\log 4}{P_*(f)-\sup f}$.
\hfill$\Box$
\begin{lemma} If $\tau\geq \frac{\log 4}{P_*(f)-\sup f} -1$,
then there are two mutually
singular equilibrium states for $g$ on $\Sigma$.
\end{lemma}
\noindent {\bf Proof.}
There is an equilibrium state for $f$ on each of the full
two-shifts $\Sigma_{\cal G}$ and $\Sigma_{\cal Y}$ both of which,
by lemma 4,
assume the pressure $P(g)=P_*(f)$ in the variational principle.
These two measures are both invariant and mutually singular.
\hfill$\Box$
\vspace{5mm}
\noindent {\bf Remark:}
This method of constructing examples can be varied and adapted
in many ways. Instead of full two-shifts one can of course
take any subshift of finite type (or other), and one
can have any number of those embedded subshifts yielding a corresponding
number of mutually singular measures of maximal entropy or
equilibria for suitable potentials. In fact it is possible to have
infinitely many embedded subshifts each of which would carry a
measure and all of them would be mutually singular. This can be done
without sacrificing the mixing property;
there still would exist transitive points.
\begin{thebibliography}{99}
\bibitem{Bow} R Bowen: Some Systems with Unique Equilibrium States,
Math.\ Syst.\ Th.\ 8 (1975), 193--202
\bibitem{B-S} R Burton and J E Steif: Nonuniqueness of Measures
of Maximal Entropy for Subshifts of Finite Type, Ergod.\ Th.\
Dynam.\ Sys.\ 14 (1994), 213--235
\bibitem{Hof} Hofbauer: Examples for the nonuniqueness of the
equilibrium state, AMS Transactions, 228 (1977), 223--241
\bibitem{Kr} W Krieger: On the uniqueness of the equilibrium state,
Math.\ Systems Theory 8 (1974), 97--104.
\bibitem{Wal} P Walter: {\em An introduction to ergodic theory},
Springer-Verlag, GTM \#79, 1982
\end{thebibliography}
\end{document}
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\[\mathop{{F_{{4}}}\/}\nolimits\!\left(\alpha;\beta;\gamma,\gamma^{{\prime}};x,y%
\right)=\sum_{{m,n=0}}^{\infty}\frac{\left(\alpha\right)_{{m+n}}\left(\beta%
\right)_{{m+n}}}{\left(\gamma\right)_{{m}}\left(\gamma^{{\prime}}\right)_{{n}}%
m!n!}x^{m}y^{n},\]
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\title{История анархизма в бывшей Югославии}
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Проникновение анархистских идей к народам южного славянства относится ко второй половине XIX века, и в немалой степени было связано с деятельностью тех местных уроженцев, которые либо работали, либо учились в других странах Европы.
Одним из первых последователей Прудона стал сербский социалист Животин Зуйович (1838-1870). Он познакомился с ними в период учебы в Мюнхене и Цюрихе, где изучал право и экономику. Вскоре в Швейцарии возникла целая (хоть и небольшая) колония студентов и революционеров, южнославянского происхождения, которым затем даже удалось наладить тесный контакт с Бакуниным и славянской секцией Юрской
федерации. Среди них были такие известные в дальнейшем деятели как Йован Зуйович, Манойло Хрвачанин (1849-1909), Пера Тодорович и другие. В начале 1872 года в Цюрихе был проведен конгресс сербских социалистов, одним из гостей которого был Бакунин.
Надо отметить, что либертарный социализм 1870-х и 1880-х годов был неразрывно связан с национально-освободительной борьбой против Австро-Венгерской и Оттоманской империй. Многие анархисты приняли активное участие в восстании в Боснии-Герцеговине в 1875 году, причем даже не только те, кто был родом из южных славянских стран, но и из Италии (Эррико Малатестадважды пытался проникнуть в Боснию, чтобы присоединиться к восстанию, но оба раза неудачно), России и других европейских стран. В самом движении в то время начало возникать мощное левое течение, среди лидеров которого были такие деятели как Васа Пеладжич, а также Манойло Хрвачанин и Коста Угринич (1849-1933). Еще в апреле 1871 года Иоганн Мост посетил Любляну, где вступил в контакт с местным "Обществом рабочих". В этом городе одним из активных пропагандистов идей Моста стал Митя Кунч. В начале 1880-х годов власти Австро-Венгерской империи усилили репрессии. Они достигли пика в 1884 году, когда в Загребе, Клагенфурте и Граце прошли несколько судебных процессов, в результате которых многие хорватские и словенские анархисты были приговорены к различным срокам тюремного заключения. В последовавший за этим период анархистские идеи, благодаря усилиям Рудольфа Голоуха, Джованни Марчелли и Ивана Энличера, начали активно распространяться из Триеста и Анконы в Словению, Истрию и Далмацию. В самом начале ХХ века крупные анархистские манифестации прошли в таких городах, как Rovinj (1904) и Сплит(1908). Кстати, интересно то, что в Сплите даже была создана футбольная команда под названием " Анархос", просуществовавшая несколько десятилетий (сегодня называется N.K. Split).
Начиная с 1898 года хорватский учитель Милош Крпан вступил в тесный контакт с швейцарскими анархистами, а вскоре начал вести активную агитационную работу среди социалистов в городе Славонски Брод. Он даже пытался создать международную анархистскую колонию на территории своей усадьбы в Дубовике близ Славонска Брода, но австро-венгерские власти очень быстро пресекли эти начинания.
В Македонию либертарные идеи попали из Швейцарии и Болгарии с помощью македонских студентов, учившихся в этих странах. В 1897-98 годах в Женеве издавались две анархистские газеты на македонском языке: "Glas" и "Otmatchtenie". Несколько позднее македонские анархисты приняли участие в создании Тайного Македонского Революционного Комитета, который повел борьбу за создание Балканской социалистической федерации. В тот период одним из самых ярких пропагандистов идей русского анархистского и народнического движения среди македонцев был Васил Главинов (1869-1929), который познакомил с ними Гоче Делчева (1872-1903) – ведущую фигуру в македонском национально-освободительном движении, основателя македонско-одрийской революционной организации и предводителя Илинденского восстания (1903г.). Это восстание привело к созданию Крушевской республики – первой социалистической республики на Балканах, просуществовавшей ровно три месяца. Делчев был также близким другом болгарских анархистов Михаила Гердикова и Врбана Килифарского, а, кроме того, он боролся бок о бок со многими другими македонскими анархистами, например с Петаром Мандуковым (1879-1966гг.) – автором книги "Азбука анархистского учения" (впервые опубликована в Скопье в 1898 году), Даме Груевым (1879-1906 гг.), Николой Кареевым (1877-1905 гг.), Димо Хадимовым (1875-1924). Вскоре македонские анархисты обзавелись даже собственной террористической группой под названием "Gemidjija", состоявшей главным образом из уроженцев города Фессалонники (Йордан Попьйорданов, Марко Босняков, Димитар Мечев, Константин Кирков, Павел Сатев, Милан Арсов, Владимир Пирсов), которая пыталась привлечь внимание мировой общественности к македонской борьбе посредством целой серии атак в апреле 1903 года. К сожалению, часть участников группы погибла во время терактов, другие же были захвачены иприговорены к длительным срокам тюремного заключения.
В Боснии и Герцеговине наивысшей точкой борьбы за национальное и социальное освобождение стало появление революционного движения " Млада Босна", находившегося под сильным влиянием анархистских идей. В июне 1910 года Богдан Зераджич (1886-1910) попытался устроить покушение на военного губернатора Боснии генерала Варесанина и, увидев, что промахнулся, пустил последнюю пулю себе в сердце. Полиция тайно захоронила тело Зераджича, предварительно отделив голову и заспиртовав ее в качестве образца внешности типичного анархиста. Еще один молодой человек, Лука Джукич, попытался в 1912 году убить губернатора Загреба Cuvaj, но тоже неудачно. Джукич был схвачен и приговорен к пожизненному тюремному заключению, где и пребывал до падения Австро-венгерской империи в 1918 году, в то время как его соучастник, Август Чезареч (1893-1941) получил всего 5- летний срок. Позднее Чезареч стал редактором левой газеты "Пламен" и, согласно некоторым источникам, участвовал в гражданской войне в Испании. Есть очень серьезная версия, что жизнь его оборвалась во время попытки побега из организованного усташами концентрационного лагеря Керестинец, вместе с еще 40 "левыми" интеллектуалами. 28 июня 1914 года члены " Млада Босна" организовали в Сараеве покушение на австрийского эрцгерцога Франца Фердинанда. Молодой рабочий-типограф Неделько Чабринович (1895-1916) бросил в эрцгерцога бомбу, но она не сработала. Затем, увидев неудачу товарища, Гаврило Принцип (1894-1918) выстрелил в Фердинанда из револьвера и убил его. Австрийские власти отдали под суд 25 человек, замешанных в покушении. Из них лишь Данило Илич (1890-1915) был приговорен к смертной казни, остальные получили различные сроки тюремного заключения, вплоть до пожизненного. В частности, Гаврило Принцип, ввиду несовершеннолетия, был приговорен к 20 годам каторжных работ, отбывал свой срок в тюрьме чешского городка Терезин, перенес много страданий и умер там от туберкулеза всего лишь за несколько месяцев до крушения Австро-венгерской монархии. Во время суда Неделько Чабринович объявил, что основной причиной его участия в покушении послужили его анархистские убеждения. Он тоже умер в заключении в возрасте 20 лет. Идеолог "Млады Босны" Владимир Гачинович (1890-1917), будучи студентом в Женеве и Лозанне, познакомился с русскими иммигрантами, а уже через них – с идеями Бакунина, Кропоткина и русских революционеров-народников. В августе 1917 года Владимир был отравлен в результате совместной спецоперации австрийских, сербских и французских спецслужб. В начале ХХ века среди южнославянской молодежи были очень популярны статьи и литературные произведения Димитре Митриновича (1887-1953),в которых присутствовал очень сильный анархистский компонент. В 1914 году Митринович переехал в Лондон. Он был другом Петра Кропоткина, Г. Ландауэра, Г. Рида и многих других известных анархистов. " Млада Босна" находилась в очень тесном контакте с еще одной группой – "Препород" из Любляны, возникшей в 1910-11 гг. вокруг одноименной газеты. Точкой соприкосновения послужило то, что обе группы фактически имели одну и ту же стратегическую цель – создание сильного революционного движения, а в дальнейшем - освобождение и постепенную интеграцию южных славянских народов. Наиболее активными участниками "Препорода" были Франце Фабианжич и Иван Эндлихер. Эндлихер умер в1915 году в тюрьме австрийского города Грац, куда он был заточен после убийства эрцгерцога Франца Фердинанда в Сараево.
На территорию Воеводины идеи революционного синдикализма попали из Венгрии с помощью группы анархистов вокруг Кристо Искурлджева (1881-1914), который был близким другом известного анархо-синдикалиста Эрвина Шабо. Либертарные идеи обрели благодатную почву среди многих сербских социалистов, таких как Драгиса Станоевич (1844-1918), Мита Ченич (1851-1888), Пера Тодорович (1851-1907), Йован Зуйович (1856-1936), Сава Попович (1898-1942). В первом десятилетии ХХ века происходит заметный всплеск анархо-синдикализма: начинается выпуск газет "Пролетер" (1906) и "Радницка борба" (1907)\dots{} Дело доходит даже до того, что в Сербской Социалистической партии образуется радикальное крыло, находившееся под сильным влиянием анархистов и анархо-синдикалистов (правда, некоторое время спустя всех сторонников этого течения исключили из партии). Одной из наиболее заметных фигур в анархо-движении той поры был Крсто Цирвачич (1879-1944), основатель многих газет (среди которых наиболее известны "Хлеб и свобода", 1905, и " Радницка борба", 1907) и анархистских клубов, а также автор книги " Анархистская программа" (1909). Впрочем, вскоре после окончания I Мировой войны Цирвачич покинул движение\dots{}
В период между двумя мировыми войнами развитие анархистского движения застопорилось из-за жестких условий диктатуры короля Александра. Тем не менее, довольно большое число анархистов оказались среди югославских добровольцев, отправившихся в 1936 году в Испанию бороться против фашизма, а кое-кто из югославов проникся анархистскими идеями уже там. После окончания II Мировой войны и прихода к власти маршала Тито анархизм оказался под тяжестью репрессий, так что анархистское движение оказалось фактически парализовано. В 1954 году в Триесте был опубликован перевод избранных работ Малатесты на словенский язык, но эта книга так и не получила широкого распространения из-за общей ситуации в стране. Анархистское движение вновь начало возрождаться лишь в 1970-80-х годах, когда в Югославии были опубликованы переводы работ Прудона, Бакунина, Кропоткина, Даниэля Герена и Мюррея Букчина. Основой этому новому варианту анархистского движения служили академические круги, зачастую тесно связанные с журналом "Praxis" – вскоре, однако, запрещенном властями. Сам Герен посетил остров Корцула для участия в одном из летних семинаров, организованных "Praxis". К этому же времени относится и выпуск в Югославии двух изданий книги Ласло Секеля " Об анархизме". Контакты югославских анархистов с международным анархистским движением были восстановлены в 1984 году, когда несколько анархистов из Хорватии участвовали работе анархистского конгресса в Венеции, а также в апреле 1990 года во время встречи "Восток - Запад" в Триесте. Есть данные, что в 1980-е годы в Загребе существовала группа под названием " Автономия"; к этому же времени относится появление целого ряда небольших групп, возникших в рамках движения анархо-панков. К сожалению, большинство анархистских активистов 1970-80-х годов ныне предпочитают индивидуальный активизм, в подавляющем большинстве случаев ограничивающийся только участием в различных публичных форумах, написанием статей и книг, а также исследовательской работой. Но тем не менее, им на смену пришло новое поколение активистов, которое даже в тяжелых условиях продолжает отстаивать вечные идеалы Анархии.
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Библиотека Анархизма
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Антикопирайт
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Марко Вукович
История анархизма в бывшей Югославии
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Сохранено 17 августа 2018 из https:\Slash{}\Slash{}piter.anarhist.org\Slash{}46jgoslav.htm
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\textbf{ru.theanarchistlibrary.org}
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\newcommand{\mICTWDlgOilsolenoid}{Oil rec solenoid}
\newcommand{\mICTWDlgOiltemp}{Oil rec temp}
\newcommand{\mICTWDlgOnstandbystatus}{On / stand-by status}
\newcommand{\mICTWDlgOtheralarminputs}{Other alarm inputs}
\newcommand{\mICTWDlgOutthreeassignment}{Out 3 assignment}
\newcommand{\mICTWDlgOutputassignment}{Output assignment}
\newcommand{\mICTWDlgOvraldelay}{Override al delay}
\newcommand{\mICTWDlgPhasealdelay}{Phase al delay}
\newcommand{\mICTWDlgPhasemonitor}{Phase monitor}
\newcommand{\mICTWDlgPrbrbecmaster}{Become net master}
\newcommand{\mICTWDlgPrbrdel}{Net silence delay}
\newcommand{\mICTWDlgPrbren}{Press brodcast en}
\newcommand{\mICTWDlgPrbrint}{Press brodcast int}
\newcommand{\mICTWDlgPrbrpolladdtwo}{2nd master address}
\newcommand{\mICTWDlgPrbrpolladdthree}{3rd master address}
\newcommand{\mICTWDlgPrbrpollinttwo}{2nd broadcast int}
\newcommand{\mICTWDlgPrbrpollintthree}{3rd broadcast int}
\newcommand{\mICTWDlgPrbrpollpertwo}{2nd press broadcast}
\newcommand{\mICTWDlgPrbrpollperthree}{3rd press broadcast}
\newcommand{\mICTWDlgPrbrspecorigin}{Specify origin}
\newcommand{\mICTWDlgPreferences}{Preferences}
\newcommand{\mICTWDlgProbecalibration}{Probe calibration}
\newcommand{\mICTWDlgProbenrone}{Probe nr. 1}
\newcommand{\mICTWDlgProbenrtwo}{Probe nr. 2}
\newcommand{\mICTWDlgProbenrthree}{Probe nr. 3}
\newcommand{\mICTWDlgProbenrfour}{Probe nr. 4}
\newcommand{\mICTWDlgProbenrfive}{Probe nr. 5}
\newcommand{\mICTWDlgProbenrsix}{Probe nr. 6}
\newcommand{\mICTWDlgProbenrseven}{Probe nr. 7}
\newcommand{\mICTWDlgProbenreight}{Probe nr. 8}
\newcommand{\mICTWDlgProportionalhumidity}{Proportional humidity}
\newcommand{\mICTWDlgSetpointbar}{Low pressure wanted}
\newcommand{\mICTWDlgSlavedisplay}{Slave display}
\newcommand{\mICTWDlgSlavenumber}{Slave number}
\newcommand{\mICTWDlgSlavepreferences}{Slave preferences}
\newcommand{\mICTWDlgSlaveshow}{Slave show}
\newcommand{\mICTWDlgStandbyon}{Stand-by / on}
\newcommand{\mICTWDlgSuctionpressurebroadcast}{Pressure broadcast}
\newcommand{\mICTWDlgTimer}{Timer}
\newcommand{\mICTWDlgUsagemcone}{Mc1 off/on/auto}
\newcommand{\mICTWDlgUsagemctwo}{Mc2 off/on/auto}
\newcommand{\mICTWDlgUsagemcthree}{Mc3 off/on/auto}
\newcommand{\mICTWExtOverrDel}{After the delay elapsed, the override forces a load. Automatic reset.}
\newcommand{\mICTWExtOverride}{Caution! The external override drives the compressors ignoring high and low pressure; no safety is left except hardware ones. It is recommended to close this contact passing through both contacts of a low pressure and high pressure switch like a kp15. The closed contact is interpreted as "load" while the open contact is neutral. The delays dF4 through dF6 are respected.}
\newcommand{\mICTWHCNomore}{This instrument has no further shortcuts.}
\newcommand{\mICTWHRNone}{none}
\newcommand{\mICTWHSNone}{This instrument has no slave alarm.}
\newcommand{\mICTWHTHfourtwotwoVeightMenu}{Program the menu.}
\newcommand{\mICTWHTHfourtwotwoVeightSby}{Switch between on and stand-by.}
\newcommand{\mICTWHTHfourtwofiveVtwoSet}{Show or change pressure set.}
\newcommand{\mICTWHUHfourtwotwoVeightMenu}{Keep pressed B6 to enter the menu. Navigate up and down with B2 and B5. Select the submenu by B6. Change the parameter by B2 and B5, press B6 to confirm, or B4 to go back without saving. The changes will have effect after the exit from programming pressing B4 repeatedly. Press B1 to exit immediately without saving any parameter.}
\newcommand{\mICTWHUHfourtwofiveVtwoSby}{Keep pressed B3 button, to activate and deactivate stand-by. In stand-by every output is, leds from L1 to L7 blink, timers continue to count.}
\newcommand{\mICTWHUHfourtwofiveVtwoSet}{Press shortly B6 - the display shows the current set point - change it by B2 and B5, and confirm it by B6. As alternative, enter the menu program as explained above, modify the parameter ML0, then confirm it.}
\newcommand{\mICTWIEextoverridealarm}{external override}
\newcommand{\mICTWIEmconealarm}{mc 1 alarm}
\newcommand{\mICTWIEmctwoalarm}{mc 2 alarm}
\newcommand{\mICTWIEmcthreealarm}{mc 3 alarm}
\newcommand{\mICTWIEmcphase}{mc phase}
\newcommand{\mICTWIEnone}{none}
\newcommand{\mICTWIEoilonepressure}{mc 1 oil pressure}
\newcommand{\mICTWIEoiltwopressure}{mc 2 oil pressure}
\newcommand{\mICTWIEoilthreepressure}{mc 3 oil pressure}
\newcommand{\mICTWIEunknown}{unknown}
\newcommand{\mICTWIFextoverridealarm}{The external override contact is driving the controller.}
\newcommand{\mICTWIFmcalarm}{Pressure switch, thermistors, or any other compressor safety device has disconnected.}
\newcommand{\mICTWIFmcphase}{Compressor overload/thermal relay disconnected, or missing mains phase - manual reset.}
\newcommand{\mICTWIFnone}{None}
\newcommand{\mICTWIFoilpressure}{Oil differential pressure remained under minimum value for 120 seconds - manual reset.}
\newcommand{\mICTWIPActualalarm}{Actual alarm}
\newcommand{\mICTWIPAlarm}{Alarm switch}
\newcommand{\mICTWIPCompressorone}{Compressor 1}
\newcommand{\mICTWIPCompressortwo}{Compressor 2}
\newcommand{\mICTWIPCompressorthree}{Compressor 3}
\newcommand{\mICTWIPCompressordelayone}{Mc1 start del}
\newcommand{\mICTWIPCompressordelaytwo}{Mc2 start del}
\newcommand{\mICTWIPCompressordelaythree}{Mc3 start del}
\newcommand{\mICTWIPCompressordelazone}{Mc1 stop del}
\newcommand{\mICTWIPCompressordelaztwo}{Mc2 stop del}
\newcommand{\mICTWIPCompressordelazthree}{Mc3 stop del}
\newcommand{\mICTWIPCondfanspeed}{Cond fan speed}
\newcommand{\mICTWIPCondspeedreg}{Cond speed reg}
\newcommand{\mICTWIPCondwhenmcisoff}{Cond when mc is off}
\newcommand{\mICTWIPCondenserfantwo}{Condenser fan 2}
\newcommand{\mICTWIPCondenserfanthree}{Condenser fan 3}
\newcommand{\mICTWIPCondenserfanfour}{Condenser fan 4}
\newcommand{\mICTWIPDeadbandbar}{Dead band +/-}
\newcommand{\mICTWIPDelextovr}{Ovr delay}
\newcommand{\mICTWIPDiffbar}{Differential}
\newcommand{\mICTWIPDischprunload}{HP unload}
\newcommand{\mICTWIPDischargetemp}{Discharge temp}
\newcommand{\mICTWIPEnextovr}{En ext ovr}
\newcommand{\mICTWIPEnablemcalarmone}{En mc1 al}
\newcommand{\mICTWIPEnablemcalarmtwo}{En mc2 al}
\newcommand{\mICTWIPEnablemcalarmthree}{En mc3 al}
\newcommand{\mICTWIPEnableovral}{En ovr al}
\newcommand{\mICTWIPEnablephaseal}{Enable phase al}
\newcommand{\mICTWIPEnableprobe}{Enable probe}
\newcommand{\mICTWIPEngineroom}{Engine room}
\newcommand{\mICTWIPExternaloverride}{External override}
\newcommand{\mICTWIPFanonestartpressure}{Fan 1 start pressure}
\newcommand{\mICTWIPFanonestoppressure}{Fan 1 stop pressure}
\newcommand{\mICTWIPFantwostartpressure}{Fan 2 start pressure}
\newcommand{\mICTWIPFantwostoppressure}{Fan 2 stop pressure}
\newcommand{\mICTWIPFanthreestartpressure}{Fan 3 start pressure}
\newcommand{\mICTWIPFanthreestoppressure}{Fan 3 stop pressure}
\newcommand{\mICTWIPFanfourstartpressure}{Fan 4 start pressure}
\newcommand{\mICTWIPFanfourstoppressure}{Fan 4 stop pressure}
\newcommand{\mICTWIPFanminimumspeed}{Fan minimum speed}
\newcommand{\mICTWIPHighpressbar}{High press bar}
\newcommand{\mICTWIPHighpressurerestart}{High pressure restart}
\newcommand{\mICTWIPHighpressurestop}{High pressure stop}
\newcommand{\mICTWIPLowpressbar}{Low press bar}
\newcommand{\mICTWIPLowpressurerestart}{Low pressure restart}
\newcommand{\mICTWIPLowpressurestop}{Low pressure stop}
\newcommand{\mICTWIPMasteraddress}{Master address}
\newcommand{\mICTWIPMconesafety}{Mc1 safety}
\newcommand{\mICTWIPMctwosafety}{Mc2 safety}
\newcommand{\mICTWIPMcthreesafety}{Mc3 safety}
\newcommand{\mICTWIPMcalarmdelayone}{Mc1 al del}
\newcommand{\mICTWIPMcalarmdelaytwo}{Mc2 al del}
\newcommand{\mICTWIPMcalarmdelaythree}{Mc3 al del}
\newcommand{\mICTWIPMindischsuctdiff}{Min HP-LP diff}
\newcommand{\mICTWIPMinoilrect}{Min oil temp}
\newcommand{\mICTWIPMinimumoilpressureone}{Oil pr diff 1}
\newcommand{\mICTWIPMinimumoilpressuretwo}{Oil pr diff 2}
\newcommand{\mICTWIPMinimumoilpressurethree}{Oil pr diff 3}
\newcommand{\mICTWIPOilpressmcone}{Oil press mc1}
\newcommand{\mICTWIPOilpressmctwo}{Oil press mc2}
\newcommand{\mICTWIPOilpressmcthree}{Oil press mc3}
\newcommand{\mICTWIPOilpressureone}{Mc1 oil pr}
\newcommand{\mICTWIPOilpressuretwo}{Mc2 oil pr}
\newcommand{\mICTWIPOilpressurethree}{Mc3 oil pr}
\newcommand{\mICTWIPOilrectemp}{Oil receiver temp °C}
\newcommand{\mICTWIPOilsolenoid}{Oil solenoid}
\newcommand{\mICTWIPOiltemp}{Oil temp}
\newcommand{\mICTWIPOutthreeassignment}{Out 3 ass}
\newcommand{\mICTWIPOvraldelay}{Ovr al del}
\newcommand{\mICTWIPPhasealdelay}{Phase al delay}
\newcommand{\mICTWIPPhasemonitor}{Phase monitor}
\newcommand{\mICTWIPPrbrbecmaster}{Pr brd ma}
\newcommand{\mICTWIPPrbrdel}{Pr brd del}
\newcommand{\mICTWIPPrbren}{Pr brd en}
\newcommand{\mICTWIPPrbrint}{Pr brd int}
\newcommand{\mICTWIPPrbrpolladdtwo}{Pr brd 2 add}
\newcommand{\mICTWIPPrbrpolladdthree}{Pr brd 3 add}
\newcommand{\mICTWIPPrbrpollinttwo}{Pr brd 2 int}
\newcommand{\mICTWIPPrbrpollintthree}{Pr brd 3 int}
\newcommand{\mICTWIPPrbrpollpertwo}{Pr brd 2 en}
\newcommand{\mICTWIPPrbrpollperthree}{Pr brd 3 en}
\newcommand{\mICTWIPPrbrspecorigin}{Pr brd or}
\newcommand{\mICTWIPProphumidity}{Proportional humidity}
\newcommand{\mICTWIPSetpointbar}{Set point bar}
\newcommand{\mICTWIPSlavenumber}{Slave number}
\newcommand{\mICTWIPSlaveshow}{Slave show}
\newcommand{\mICTWIPStandbyon}{Stand-by / on}
\newcommand{\mICTWIPTimer}{Timer}
\newcommand{\mICTWIPUsagemcone}{Mc1 usage}
\newcommand{\mICTWIPUsagemctwo}{Mc2 usage}
\newcommand{\mICTWIPUsagemcthree}{Mc3 usage}
\newcommand{\mICTWRemfiveNTC}{In H425V3, starting from revision 03, when MU1 and MU3 are 5.0 and b4A and b6A are oFF, use 5NTC controller for compressors without oil pump; connect HP probe on AN-6 and LP on AN-7.}
\newcommand{\mICTWRemDelayMinus}{The minus sign on display ("-") signals that output is going to start after a delay.}
\newcommand{\mICTWRemFirsttensecondsofrun}{During the first 10 seconds of speed regulation, the n1L is replaced by (n1H+n1L)/2.}
\newcommand{\mICTWRemFixedTime}{Fixed time 120 s and manual reset.}
\newcommand{\mICTWRemOnoffwhendisabled}{When speed regulation is off the fan is operated on-off.}
\newcommand{\mICTWRemPOthreesubcooler}{In H425V3, starting from revision 02, when PO3 is 4, OUT-3 drives the subcooler liquid solenoid; AN-1 input is the subcooler suction temperature; Mut is the wanted overheating, where 8.0 °C means 8.0 °C; maximum overheating is fixed at 99.0 °C; minimum overheating is fixed at 6.0 °C; n4H is the refrigerant type, where 0.1 bar means R404A; n4L is the cycle period, where 0.8 bar means 8 s; H4H is the initial on-time, where 0.5 bar means 5 s; H4L is the adaptation speed, where 0.8 bar means 8. To turn off the subcooler solenoid, set PO3 to 5. The subcooler is enabled just when all of the available motorcompressors are on. From revision 05, when PO3 is 4, the value of A4H*10, said k, determines when subcooler is on: for k<10 is on when OM2<=OM1+k, all mc are on, except at most k; for 10<=k<20 is on when k-10<=OM1, at least k-10 mc are on; for 20<=k is same of k equal to 0, all mc have to be on. Rest as in revision 02. When PO3 is 6, do as when PO3 is 1, but inverted contact (NC). When PO3 is 7, do as when PO3 is 1, plus subcooler on FAN, with oil temperature on AN-1, suction temperature on AN-3, and A4L as wanted overheating, where 8.0 bar means 8.0 °C; all the rest as above. When PO3 is 8, do as when PO3 is 6, plus subcooler on FAN; all the rest as above.}
\newcommand{\mICTWRemPassingfromstandbytoon}{Passing from stand-by to on and at power on, there is a 5 second delay spent in a virtual stand-by.}
\newcommand{\mICTWRemSpeedCaution}{Caution! Speed regulation can cause fan fault or electronic board fault. Low and average minimum speed can increase the risk.}
\newcommand{\mICTWRemUsageOfCompressor}{Caution! Selection by manual override forces compressor to run whatever the high and low pressure; no safety is left except hardware ones. In slave mode the output is used for partialization. In kriwan mode output is off for reset during stand-by.}
\newcommand{\mICTWRemWhenMLHlessMLL}{When MLH<MLL,there is a delay of 10*(MLL-MLH) seconds on lp switch. Eventual pumpdown restart is over MLH+1 bar.}
\newcommand{\mICTWUsMActualalarm}{actual alarm - read only (0 means no alarm)}
\newcommand{\mICTWUsMAlarmandstandby}{Functions about alarm and stand-by}
\newcommand{\mICTWUsMAlarmcentral}{alarm - eventually connected to OUT-3}
\newcommand{\mICTWUsMAnaloginputs}{Analog inputs}
\newcommand{\mICTWUsMAnalogoutputs}{Analog output}
\newcommand{\mICTWUsMCompressorone}{compressor 1}
\newcommand{\mICTWUsMCompressortwo}{compressor 2}
\newcommand{\mICTWUsMCompressorthree}{compressor 3}
\newcommand{\mICTWUsMCompressorcontrol}{Functions about compressor}
\newcommand{\mICTWUsMCompressordelayone}{mc1 start delay}
\newcommand{\mICTWUsMCompressordelaytwo}{mc2 start delay}
\newcommand{\mICTWUsMCompressordelaythree}{mc3 start delay}
\newcommand{\mICTWUsMCompressordelazone}{mc1 stop delay}
\newcommand{\mICTWUsMCompressordelaztwo}{mc2 stop delay}
\newcommand{\mICTWUsMCompressordelazthree}{mc3 stop delay}
\newcommand{\mICTWUsMCondfanspeed}{condenser}
\newcommand{\mICTWUsMCondspeedreg}{enable condenser fans speed regulation}
\newcommand{\mICTWUsMCondwhenmcisoff}{enable condenser fans when compressor is off and discharge pressure is over maximum}
\newcommand{\mICTWUsMCondenserfantwo}{condenser fan 2}
\newcommand{\mICTWUsMCondenserfanthree}{condenser fan 3}
\newcommand{\mICTWUsMCondenserfanfour}{condenser fan 4}
\newcommand{\mICTWUsMDeadbandbar}{suction pressure regulation dead band (ML0 +/- MLb are the upper/lower limits)}
\newcommand{\mICTWUsMDelextovr}{external load override delay}
\newcommand{\mICTWUsMDelayfrompreviousstop}{Delay from previous stop}
\newcommand{\mICTWUsMDelays}{Functions about delays}
\newcommand{\mICTWUsMDiffbar}{suction pressure regulation differential (loading at ML0+MLb+MLd / unl at ML0-MLb-MLd)}
\newcommand{\mICTWUsMDigitalinputs}{Digital input}
\newcommand{\mICTWUsMDigitaloutputs}{Digital output}
\newcommand{\mICTWUsMDischprunload}{discharge (HP) pressure limit forcing the timed compressor unload}
\newcommand{\mICTWUsMDischargetemp}{discharge temperature}
\newcommand{\mICTWUsMEnextovr}{enable external load override on INP-4}
\newcommand{\mICTWUsMEnablemcalarmone}{enable mc1 alarm}
\newcommand{\mICTWUsMEnablemcalarmtwo}{enable mc2 alarm}
\newcommand{\mICTWUsMEnablemcalarmthree}{enable mc3 alarm}
\newcommand{\mICTWUsMEnableovral}{enable external override alarm}
\newcommand{\mICTWUsMEnablephaseal}{enable digital input 5 alarm (compressor phase monitor / thermal overload relay)}
\newcommand{\mICTWUsMEnableprobe}{enable probe}
\newcommand{\mICTWUsMEngineroom}{engine room temperature}
\newcommand{\mICTWUsMExternaloverride}{external override}
\newcommand{\mICTWUsMFanonestartpressure}{fan 1 start pressure ( similar to Danfoss KP5 set point ) - active just when ncr is oFF}
\newcommand{\mICTWUsMFanonestoppressure}{fan 1 stop pressure ( similar to Danfoss KP5 set point - differential )}
\newcommand{\mICTWUsMFantwostartpressure}{fan 2 start pressure}
\newcommand{\mICTWUsMFantwostoppressure}{fan 2 stop pressure}
\newcommand{\mICTWUsMFanthreestartpressure}{fan 3 start pressure}
\newcommand{\mICTWUsMFanthreestoppressure}{fan 3 stop pressure}
\newcommand{\mICTWUsMFanfourstartpressure}{fan 4 start pressure}
\newcommand{\mICTWUsMFanfourstoppressure}{fan 4 stop pressure}
\newcommand{\mICTWUsMFancontrol}{Functions about fans}
\newcommand{\mICTWUsMFanminimumspeed}{fan minimum speed}
\newcommand{\mICTWUsMFunctionsaboutIO}{Functions about input-output and machine state (read only)}
\newcommand{\mICTWUsMFunctionsaboutcondenserfans}{Functions about condenser fans}
\newcommand{\mICTWUsMFunctionsaboutnetworkaddress}{Functions about network address}
\newcommand{\mICTWUsMFunctionsaboutpressureswitches}{Functions about pressure switches}
\newcommand{\mICTWUsMHighpressbar}{high pressure (HP)}
\newcommand{\mICTWUsMHighpressurerestart}{high pressure safety restart ( similar to Danfoss KP15 hp set point - differential )}
\newcommand{\mICTWUsMHighpressurestop}{high pressure safety stop ( similar to Danfoss KP15 hp set point )}
\newcommand{\mICTWUsMLowpressbar}{low pressure (LP)}
\newcommand{\mICTWUsMLowpressurerestart}{low pressure safety restart ( similar to Danfoss KP15 lp set point )}
\newcommand{\mICTWUsMLowpressurestop}{low pressure safety stop ( similar to Danfoss KP15 lp set point - differential )}
\newcommand{\mICTWUsMMasteraddress}{master address for global network communication}
\newcommand{\mICTWUsMMconesafety}{mc1 hardware safety}
\newcommand{\mICTWUsMMctwosafety}{mc2 hardware safety}
\newcommand{\mICTWUsMMcthreesafety}{mc3 hardware safety}
\newcommand{\mICTWUsMMcalarmdelayone}{mc1 alarm delay}
\newcommand{\mICTWUsMMcalarmdelaytwo}{mc2 alarm delay}
\newcommand{\mICTWUsMMcalarmdelaythree}{mc3 alarm delay}
\newcommand{\mICTWUsMMindischsuctdiff}{minimum HP-LP-difference to keep on fans}
\newcommand{\mICTWUsMMinoilrect}{minimum oil receiver temperature before opening the oil solenoid}
\newcommand{\mICTWUsMMinimumoilpressureone}{minimum oil differential pressure of compressor nr. 1}
\newcommand{\mICTWUsMMinimumoilpressuretwo}{minimum oil differential pressure of compressor nr. 2}
\newcommand{\mICTWUsMMinimumoilpressurethree}{minimum oil differential pressure of compressor nr. 3}
\newcommand{\mICTWUsMOilpressmcone}{oil pressure of mc1}
\newcommand{\mICTWUsMOilpressmctwo}{oil pressure of mc2}
\newcommand{\mICTWUsMOilpressmcthree}{oil pressure of mc3}
\newcommand{\mICTWUsMOilpressureone}{mc1 oil pressure}
\newcommand{\mICTWUsMOilpressuretwo}{mc2 oil pressure}
\newcommand{\mICTWUsMOilpressurethree}{mc3 oil pressure}
\newcommand{\mICTWUsMOilrectemp}{oil receiver temperature}
\newcommand{\mICTWUsMOilsolenoid}{oil receiver solenoid - eventually connected to OUT-3}
\newcommand{\mICTWUsMOiltemp}{oil receiver temperature}
\newcommand{\mICTWUsMOnstandbystatus}{On / stand-by status}
\newcommand{\mICTWUsMOtheralarminputs}{Other alarm inputs}
\newcommand{\mICTWUsMOutthreeassignment}{assign out-3 relay to: 0=condenser fan / 1=oil receiver solenoid / 2=alarm / 3=oil heater / 4=subcooler / 5=off / 6=NC oil sol / 7=oil sol plus subcooler on FAN / 8=NC oil sol plus subcooler on FAN / 9=fourth mc / 10=fourth mc plus subcooler on FAN}
\newcommand{\mICTWUsMOutputassignment}{Output assignment}
\newcommand{\mICTWUsMOvraldelay}{override alarm delay}
\newcommand{\mICTWUsMPhasealdelay}{digital input 5 alarm delay}
\newcommand{\mICTWUsMPhasemonitor}{phase software safety}
\newcommand{\mICTWUsMPrbrbecmaster}{become network master after Pbb delay}
\newcommand{\mICTWUsMPrbrdel}{delay between latest received message and broadcasting start}
\newcommand{\mICTWUsMPrbren}{enable suction pressure periodic broadcast over the PC net}
\newcommand{\mICTWUsMPrbrint}{delay between pressure broadcast messages}
\newcommand{\mICTWUsMPrbrpolladdtwo}{master address of second central unit}
\newcommand{\mICTWUsMPrbrpolladdthree}{master address of third central unit}
\newcommand{\mICTWUsMPrbrpollinttwo}{delay between pressure broadcast messages of second central unit}
\newcommand{\mICTWUsMPrbrpollintthree}{delay between pressure broadcast messages of third central unit}
\newcommand{\mICTWUsMPrbrpollpertwo}{poll periodically second central unit for pressure broadcast}
\newcommand{\mICTWUsMPrbrpollperthree}{poll periodically third central unit for pressure broadcast}
\newcommand{\mICTWUsMPrbrspecorigin}{specify originating address in the pressure message}
\newcommand{\mICTWUsMPreferences}{Functions about master preferences}
\newcommand{\mICTWUsMProbecalibration}{Functions about probe calibration}
\newcommand{\mICTWUsMProbenrone}{Probe nr. 1}
\newcommand{\mICTWUsMProbenrtwo}{Probe nr. 2}
\newcommand{\mICTWUsMProbenrthree}{Probe nr. 3}
\newcommand{\mICTWUsMProbenrfour}{Probe nr. 4}
\newcommand{\mICTWUsMProbenrfive}{Probe nr. 5}
\newcommand{\mICTWUsMProbenrsix}{Probe nr. 6}
\newcommand{\mICTWUsMProbenrseven}{Probe nr. 7}
\newcommand{\mICTWUsMProbenreight}{Probe nr. 8}
\newcommand{\mICTWUsMProportionalhumidity}{humidity - 4...20 mA}
\newcommand{\mICTWUsMSetpointbar}{suction low pressure regulation (similar to Danfoss RT1AL set point minus half of neutral zone)}
\newcommand{\mICTWUsMSlavedisplay}{Functions about display}
\newcommand{\mICTWUsMSlavenumber}{number of slaves connected to this master}
\newcommand{\mICTWUsMSlavepreferences}{Functions about slave preferences}
\newcommand{\mICTWUsMSlaveshow}{input to show on display: 1=IA1 / 2=IA2 ...}
\newcommand{\mICTWUsMStandbyon}{actual status: stand-by or on}
\newcommand{\mICTWUsMSuctionpressurebroadcast}{Suction pressure broadcast}
\newcommand{\mICTWUsMTimer}{timer}
\newcommand{\mICTWUsMUsagemcone}{usage of mc nr. 1 output: 0=off / 1=on / 2=auto / 3=slave no / 4=slave nc / 5=kriwan}
\newcommand{\mICTWUsMUsagemctwo}{usage of mc nr. 2 output: 0=off / 1=on / 2=auto / 3=slave no / 4=slave nc / 5=kriwan}
\newcommand{\mICTWUsMUsagemcthree}{usage of mc nr. 3 output: 0=off / 1=on / 2=auto / 3=slave no / 4=slave nc / 5=kriwan}
\newcommand{\mICTWXHAlarm}{Alarm}
\newcommand{\mICTWXHAlarmList}{Alarm list}
\newcommand{\mICTWXHAlarmListSlave}{Slave alarm list}
\newcommand{\mICTWXHBLngdown}{Down navigation in the menu.}
\newcommand{\mICTWXHBLngescsilence}{Exit without saving from any menu - alarm buzzer silence.}
\newcommand{\mICTWXHBLngleft}{Left navigation in the menu.}
\newcommand{\mICTWXHBLngonstandby}{Toggle between on and stand-by.}
\newcommand{\mICTWXHBLngrightmenuset}{Right navigation in the menu - display and modify the set point - enter menu.}
\newcommand{\mICTWXHBLngup}{Up navigation in the menu.}
\newcommand{\mICTWXHBShrdown}{down}
\newcommand{\mICTWXHBShrescsilence}{esc - silence}
\newcommand{\mICTWXHBShrleft}{left}
\newcommand{\mICTWXHBShronstandby}{on / stand-by}
\newcommand{\mICTWXHBShrrightmenuset}{right - menu - set}
\newcommand{\mICTWXHBShrup}{up}
\newcommand{\mICTWXHButtonlist}{Button list}
\newcommand{\mICTWXHButtonstopress}{Buttons to press}
\newcommand{\mICTWXHDefault}{Default}
\newcommand{\mICTWXHDescription}{Description}
\newcommand{\mICTWXHDisplay}{Display}
\newcommand{\mICTWXHFunction}{Function}
\newcommand{\mICTWXHHowto}{How to ...}
\newcommand{\mICTWXHLLngcompressorrunchange}{On during compressor run - blinking slowly during activation and deactivation delay.}
\newcommand{\mICTWXHLLngcondenserrun}{On during condenser run.}
\newcommand{\mICTWXHLShrcompressorone}{compressor 1}
\newcommand{\mICTWXHLShrcompressortwo}{compressor 2}
\newcommand{\mICTWXHLShrcompressorthree}{compressor 3}
\newcommand{\mICTWXHLShrcondenserfanone}{condenser fan 1}
\newcommand{\mICTWXHLShrcondenserfantwo}{condenser fan 2}
\newcommand{\mICTWXHLShrcondenserfanthree}{condenser fan 3}
\newcommand{\mICTWXHLShrcondenserfanfour}{condenser fan 4}
\newcommand{\mICTWXHLed}{Led}
\newcommand{\mICTWXHLedandpushbl}{Led and push button location}
\newcommand{\mICTWXHLedlist}{Led list}
\newcommand{\mICTWXHMaximum}{Maximum}
\newcommand{\mICTWXHMinimum}{Minimum}
\newcommand{\mICTWXHNr}{Nr.}
\newcommand{\mICTWXHParameter}{Parameter}
\newcommand{\mICTWXHParameterlist}{Parameter list}
\newcommand{\mICTWXHParameterremarks}{Parameter remarks}
\newcommand{\mICTWXHPushbutton}{Push button}
\newcommand{\mICTWXHRem}{Rem.}
\newcommand{\mICTWXHRemark}{Remark}
\newcommand{\mICTWXHShortcutdescription}{Shortcut description - keep pressed 5 seconds}
\newcommand{\mICTWXHShortcutlist}{Shortcut list}
\newcommand{\mICTWXHSoftcommand}{Soft command}
\newcommand{\mICTWXHSoftcommandlist}{Soft command list}
\newcommand{\mICTWXHUnit}{Unit}
\newcommand{\mICTWXHUsermanual}{User manual}
% Derived definitions -------------------------------------------------------------------
\author {\mIauth}
\title {\mItitl}
% environment -------------------------------------------------------------------
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\begin{document}
\mIselLang
\frontmatter*
\pagestyle{empty}
% title
\begin{figure}[p]
\ifpdf
\pdfbookmark{Title page}{title}
\fi
\centering
\begin{minipage}[c]{\textwidth}
\centering
\includegraphics[height=\mItihe]\mIlgti
\color{Gray}\HUGE\sffamily\bfseries \mbox{}\\* \mbox{}\\
\mIdocm\\
\mICTWXHUsermanual
\end{minipage}
\end{figure}
\cleardoublepage
% content
\tableofcontents
\newpage
\mainmatter*
\pagestyle{mips}
\chapter{\mICTWXHParameterlist}\label{ch:par}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\setlength{\tabcolsep}{2pt}
\begin{longtabu} to \linewidth [c] {@{\extracolsep {0pt plus 1fil}}{r}{l}X*{3}{r}{l}}
\mICTWXHRem & \mICTWXHParameter & \mICTWXHDescription & \mICTWXHMinimum & \mICTWXHMaximum & \mICTWXHDefault & \mICTWXHUnit \\ \endhead
\, &M\_\_\quad \quad&\mICTWUsMCompressorcontrol&\,&\,&\,&\,\\
\, &\quad MU\_\quad&\mICTWUsMFunctionsaboutpressureswitches&\,&\,&\,&\,\\
\, &\quad \quad ML0&\mICTWUsMSetpointbar&0.0&99.0&2.8&(gauge) bar\\
\, &\quad \quad MLb&\mICTWUsMDeadbandbar&0.0&99.0&0.5&bar\\
\, &\quad \quad MLd&\mICTWUsMDiffbar&0.0&99.0&0.2&bar\\
\, &\quad \quad MH0&\mICTWUsMDischprunload&0.0&99.0&24.0&(gauge) bar\\
\ref{pr:0}&\quad \quad MLH&\mICTWUsMLowpressurerestart&0.0&99.0&1.2&(gauge) bar\\
\, &\quad \quad MLL&\mICTWUsMLowpressurestop&0.0&99.0&0.2&(gauge) bar\\
\, &\quad \quad MHH&\mICTWUsMHighpressurestop&0.0&99.0&28.0&(gauge) bar\\
\, &\quad \quad MHL&\mICTWUsMHighpressurerestart&0.0&99.0&24.0&(gauge) bar\\
\ref{pr:1}&\quad \quad MU1&\mICTWUsMMinimumoilpressureone&0.0&99.0&1.0&bar\\
\, &\quad \quad MU2&\mICTWUsMMinimumoilpressuretwo&0.0&99.0&1.0&bar\\
\ref{pr:2}&\quad \quad MU3&\mICTWUsMMinimumoilpressurethree&0.0&99.0&1.0&bar\\
\, &\quad \quad Mut&\mICTWUsMMinoilrect&-55.0&145.0&25.0&°C\\
\ref{pr:3}&\quad \quad MM1&\mICTWUsMUsagemcone&0&5&2&/\\
\, &\quad \quad MM2&\mICTWUsMUsagemctwo&0&5&2&/\\
\, &\quad \quad MM3&\mICTWUsMUsagemcthree&0&5&2&/\\
\ref{pr:4}&\quad \quad MMH&\mICTWUsMEnextovr&oFF&\_on&oFF&/\\
\ref{pr:5}&\quad \quad MMd&\mICTWUsMDelextovr&0&194 4:20:15&1:00:00&dd hh:mm:ss\\
\, &n\_\_\quad \quad&\mICTWUsMFancontrol&\,&\,&\,&\,\\
\, &\quad nc\_\quad&\mICTWUsMFunctionsaboutcondenserfans&\,&\,&\,&\,\\
\, &\quad \quad ncH&\mICTWUsMCondwhenmcisoff&oFF&\_on&\_on&/\\
\ref{pr:6}&\quad \quad ncr&\mICTWUsMCondspeedreg&oFF&\_on&\_on&/\\
\ref{pr:7}&\quad \quad ncU&\mICTWUsMFanminimumspeed&0&255&40&/\\
\, &\quad \quad ncd&\mICTWUsMMindischsuctdiff&0.0&99.0&2.0&(gauge) bar\\
\, &\quad \quad n1H&\mICTWUsMFanonestartpressure&0.0&99.0&10.0&(gauge) bar\\
\ref{pr:8}&\quad \quad n1L&\mICTWUsMFanonestoppressure&0.0&99.0&6.0&(gauge) bar\\
\, &\quad \quad n2H&\mICTWUsMFantwostartpressure&0.0&99.0&7.0&(gauge) bar\\
\, &\quad \quad n2L&\mICTWUsMFantwostoppressure&0.0&99.0&5.0&(gauge) bar\\
\, &\quad \quad n3H&\mICTWUsMFanthreestartpressure&0.0&99.0&8.0&(gauge) bar\\
\, &\quad \quad n3L&\mICTWUsMFanthreestoppressure&0.0&99.0&6.0&(gauge) bar\\
\, &\quad \quad n4H&\mICTWUsMFanfourstartpressure&0.0&99.0&9.0&(gauge) bar\\
\, &\quad \quad n4L&\mICTWUsMFanfourstoppressure&0.0&99.0&7.0&(gauge) bar\\
\, &b\_\_\quad \quad&\mICTWUsMProbecalibration&\,&\,&\,&\,\\
\, &\quad b1\_\quad&\mICTWUsMProbenrone&\,&\,&\,&\,\\
\, &\quad \quad b1C&\mICTWUsMOiltemp&-99.0&99.0&0.0&K\\
\, &\quad \quad b1A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b2\_\quad&\mICTWUsMProbenrtwo&\,&\,&\,&\,\\
\, &\quad \quad b2C&\mICTWUsMDischargetemp&-99.0&99.0&0.0&K\\
\, &\quad \quad b2A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b3\_\quad&\mICTWUsMProbenrthree&\,&\,&\,&\,\\
\, &\quad \quad b3C&\mICTWUsMEngineroom&-99.0&99.0&0.0&K\\
\, &\quad \quad b3A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b4\_\quad&\mICTWUsMProbenrfour&\,&\,&\,&\,\\
\, &\quad \quad b4C&\mICTWUsMOilpressureone&-99.0&99.0&0.0&bar\\
\, &\quad \quad b4A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b5\_\quad&\mICTWUsMProbenrfive&\,&\,&\,&\,\\
\, &\quad \quad b5C&\mICTWUsMOilpressuretwo&-99.0&99.0&0.0&bar\\
\, &\quad \quad b5A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b6\_\quad&\mICTWUsMProbenrsix&\,&\,&\,&\,\\
\, &\quad \quad b6C&\mICTWUsMOilpressurethree&-99.0&99.0&0.0&bar\\
\, &\quad \quad b6A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b7\_\quad&\mICTWUsMProbenrseven&\,&\,&\,&\,\\
\, &\quad \quad b7C&\mICTWUsMHighpressbar&-99.0&99.0&0.0&bar\\
\, &\quad \quad b7A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &\quad b8\_\quad&\mICTWUsMProbenreight&\,&\,&\,&\,\\
\, &\quad \quad b8C&\mICTWUsMLowpressbar&-99.0&99.0&0.0&bar\\
\, &\quad \quad b8A&\mICTWUsMEnableprobe&oFF&\_on&\_on&/\\
\, &L\_\_\quad \quad&\mICTWUsMAlarmandstandby&\,&\,&\,&\,\\
\, &\quad LI\_\quad&\mICTWUsMOtheralarminputs&\,&\,&\,&\,\\
\, &\quad \quad L1H&\mICTWUsMEnablemcalarmone&oFF&\_on&\_on&/\\
\, &\quad \quad L1d&\mICTWUsMMcalarmdelayone&0&194 4:20:15&30:00&dd hh:mm:ss\\
\, &\quad \quad L2H&\mICTWUsMEnablemcalarmtwo&oFF&\_on&\_on&/\\
\, &\quad \quad L2d&\mICTWUsMMcalarmdelaytwo&0&194 4:20:15&30:00&dd hh:mm:ss\\
\, &\quad \quad L3H&\mICTWUsMEnablemcalarmthree&oFF&\_on&\_on&/\\
\, &\quad \quad L3d&\mICTWUsMMcalarmdelaythree&0&194 4:20:15&30:00&dd hh:mm:ss\\
\, &\quad \quad L4H&\mICTWUsMEnableovral&oFF&\_on&\_on&/\\
\, &\quad \quad L4d&\mICTWUsMOvraldelay&0&194 4:20:15&1:00:00&dd hh:mm:ss\\
\, &\quad \quad L5H&\mICTWUsMEnablephaseal&oFF&\_on&\_on&/\\
\, &\quad \quad L5d&\mICTWUsMPhasealdelay&0&194 4:20:15&1&dd hh:mm:ss\\
\, &\quad Lo\_\quad&\mICTWUsMOnstandbystatus&\,&\,&\,&\,\\
\ref{pr:9}&\quad \quad Loo&\mICTWUsMStandbyon&oFF&\_on&oFF&/\\
\, &d\_\_\quad \quad&\mICTWUsMDelays&\,&\,&\,&\,\\
\, &\quad dF\_\quad&\mICTWUsMDelayfrompreviousstop&\,&\,&\,&\,\\
\, &\quad \quad dF4&\mICTWUsMCompressordelayone&0&194 4:20:15&5:00&dd hh:mm:ss\\
\, &\quad \quad dF5&\mICTWUsMCompressordelaytwo&0&194 4:20:15&10:00&dd hh:mm:ss\\
\, &\quad \quad dF6&\mICTWUsMCompressordelaythree&0&194 4:20:15&15:00&dd hh:mm:ss\\
\, &\quad \quad dS4&\mICTWUsMCompressordelazone&0&194 4:20:15&45&dd hh:mm:ss\\
\, &\quad \quad dS5&\mICTWUsMCompressordelaztwo&0&194 4:20:15&30&dd hh:mm:ss\\
\, &\quad \quad dS6&\mICTWUsMCompressordelazthree&0&194 4:20:15&15&dd hh:mm:ss\\
\, &P\_\_\quad \quad&\mICTWUsMPreferences&\,&\,&\,&\,\\
\, &\quad Pd\_\quad&\mICTWUsMFunctionsaboutnetworkaddress&\,&\,&\,&\,\\
\, &\quad \quad PdM&\mICTWUsMMasteraddress&0&254&1&/\\
\, &\quad \quad PdS&\mICTWUsMSlavenumber&1&2&2&/\\
\, &\quad Pb\_\quad&\mICTWUsMSuctionpressurebroadcast&\,&\,&\,&\,\\
\, &\quad \quad PbH&\mICTWUsMPrbren&oFF&\_on&\_on&/\\
\, &\quad \quad Pbd&\mICTWUsMPrbrint&0&194 4:20:15&30&dd hh:mm:ss\\
\, &\quad \quad Pbb&\mICTWUsMPrbrdel&0&194 4:20:15&2:00&dd hh:mm:ss\\
\, &\quad \quad PbO&\mICTWUsMPrbrspecorigin&oFF&\_on&\_on&/\\
\, &\quad \quad PPM&\mICTWUsMPrbrbecmaster&oFF&\_on&oFF&/\\
\, &\quad \quad P2H&\mICTWUsMPrbrpollpertwo&oFF&\_on&oFF&/\\
\, &\quad \quad P2M&\mICTWUsMPrbrpolladdtwo&0&254&2&/\\
\, &\quad \quad P2d&\mICTWUsMPrbrpollinttwo&0&194 4:20:15&30&dd hh:mm:ss\\
\, &\quad \quad P3H&\mICTWUsMPrbrpollperthree&oFF&\_on&oFF&/\\
\, &\quad \quad P3M&\mICTWUsMPrbrpolladdthree&0&254&3&/\\
\, &\quad \quad P3d&\mICTWUsMPrbrpollintthree&0&194 4:20:15&30&dd hh:mm:ss\\
\, &\quad PO\_\quad&\mICTWUsMOutputassignment&\,&\,&\,&\,\\
\ref{pr:10}&\quad \quad PO3&\mICTWUsMOutthreeassignment&0&255&0&/\\
\, &I\_\_\quad \quad&\mICTWUsMFunctionsaboutIO&\,&\,&\,&\,\\
\, &\quad IA\_\quad&\mICTWUsMAnaloginputs&\,&\,&\,&\,\\
\, &\quad \quad IA1&\mICTWUsMOilrectemp&-55.0&145.0&-55.0&°C\\
\, &\quad \quad IA2&\mICTWUsMDischargetemp&-55.0&145.0&-55.0&°C\\
\, &\quad \quad IA3&\mICTWUsMEngineroom&-55.0&145.0&-55.0&°C\\
\, &\quad \quad IA4&\mICTWUsMOilpressmcone&0.0&30.0&0.0&(gauge) bar\\
\, &\quad \quad IA5&\mICTWUsMOilpressmctwo&0.0&30.0&0.0&(gauge) bar\\
\, &\quad \quad IA6&\mICTWUsMOilpressmcthree&0.0&30.0&0.0&(gauge) bar\\
\, &\quad \quad IA7&\mICTWUsMHighpressbar&0.0&30.0&0.0&(gauge) bar\\
\, &\quad \quad IA8&\mICTWUsMLowpressbar&0.0&30.0&0.0&(gauge) bar\\
\, &\quad Id\_\quad&\mICTWUsMDigitalinputs&\,&\,&\,&\,\\
\, &\quad \quad Id1&\mICTWUsMMconesafety&oFF&\_on&oFF&/\\
\, &\quad \quad Id2&\mICTWUsMMctwosafety&oFF&\_on&oFF&/\\
\, &\quad \quad Id3&\mICTWUsMMcthreesafety&oFF&\_on&oFF&/\\
\, &\quad \quad Id4&\mICTWUsMExternaloverride&oFF&\_on&oFF&/\\
\, &\quad \quad Id5&\mICTWUsMPhasemonitor&oFF&\_on&oFF&/\\
\, &\quad OA\_\quad&\mICTWUsMAnalogoutputs&\,&\,&\,&\,\\
\, &\quad \quad LLA&\mICTWUsMActualalarm&0&255&0&/\\
\, &\quad \quad OA1&\mICTWUsMCondfanspeed&0&255&0&/\\
\, &\quad \quad OA2&\mICTWUsMProportionalhumidity&0&255&0&/\\
\, &\quad Od\_\quad&\mICTWUsMDigitaloutputs&\,&\,&\,&\,\\
\ref{pr:11}&\quad \quad Od1&\mICTWUsMCondenserfantwo&oFF&\_on&oFF&/\\
\, &\quad \quad Od2&\mICTWUsMCondenserfanthree&oFF&\_on&oFF&/\\
\, &\quad \quad Od3&\mICTWUsMCondenserfanfour&oFF&\_on&oFF&/\\
\, &\quad \quad Od4&\mICTWUsMCompressorone&oFF&\_on&oFF&/\\
\, &\quad \quad Od5&\mICTWUsMCompressortwo&oFF&\_on&oFF&/\\
\, &\quad \quad Od6&\mICTWUsMCompressorthree&oFF&\_on&oFF&/\\
\, &\quad \quad Od7&\mICTWUsMOilsolenoid&oFF&\_on&oFF&/\\
\, &\quad \quad Od8&\mICTWUsMAlarmcentral&oFF&\_on&oFF&/\\
\, &E\_\_\quad \quad&\mICTWUsMSlavepreferences&\,&\,&\,&\,\\
\, &\quad EY\_\quad&\mICTWUsMSlavedisplay&\,&\,&\,&\,\\
\, &\quad \quad EYY&\mICTWUsMSlaveshow&0&255&1&/\\
\end{longtabu}
}
\chapter{\mICTWXHParameterremarks} \label{ch:rem}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {rX}
\mICTWXHNr & \mICTWXHRemark \\ \endhead
\parRem{pr:0} & \mICTWRemWhenMLHlessMLL\\
\parRem{pr:1} & \mICTWRemFixedTime\\
\parRem{pr:2} & \mICTWRemfiveNTC\\
\parRem{pr:3} & \mICTWRemUsageOfCompressor\\
\parRem{pr:4} & \mICTWExtOverride\\
\parRem{pr:5} & \mICTWExtOverrDel\\
\parRem{pr:6} & \mICTWRemOnoffwhendisabled\\
\parRem{pr:7} & \mICTWRemSpeedCaution\\
\parRem{pr:8} & \mICTWRemFirsttensecondsofrun\\
\parRem{pr:9} & \mICTWRemPassingfromstandbytoon\\
\parRem{pr:10} & \mICTWRemPOthreesubcooler\\
\parRem{pr:11} & \mICTWRemDelayMinus\\
\end{longtabu}
}
\chapter{\mICTWXHAlarmList} \label{ch:alm}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {clX}
\mICTWXHDisplay & \multicolumn2{l}{\mICTWXHAlarm} \\ \endhead
A01 & \mICTWIEmconealarm & \mICTWIFmcalarm\\
A02 & \mICTWIEmctwoalarm & \mICTWIFmcalarm\\
A03 & \mICTWIEmcthreealarm & \mICTWIFmcalarm\\
A04 & \mICTWIEextoverridealarm & \mICTWIFextoverridealarm\\
A05 & \mICTWIEmcphase & \mICTWIFmcphase\\
A06 & \mICTWIEoilonepressure & \mICTWIFoilpressure\\
A07 & \mICTWIEoiltwopressure & \mICTWIFoilpressure\\
A08 & \mICTWIEoilthreepressure & \mICTWIFoilpressure\\
\end{longtabu}
}
\chapter{\mICTWXHAlarmListSlave} \label{ch:slv}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {clX}
\mICTWXHDisplay & \multicolumn2{l}{\mICTWXHAlarm} \\ \endhead
/ & \mICTWHRNone & \mICTWHSNone\\
\end{longtabu}
}
\chapter{\mICTWXHButtonlist} \label{ch:but}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {llX}
\multicolumn2{l}{\mICTWXHPushbutton} & \mICTWXHFunction \\ \endhead
B1 & \mICTWXHBShrescsilence & \mICTWXHBLngescsilence\\
B2 & \mICTWXHBShrup & \mICTWXHBLngup\\
B3 & \mICTWXHBShronstandby & \mICTWXHBLngonstandby\\
B4 & \mICTWXHBShrleft & \mICTWXHBLngleft\\
B5 & \mICTWXHBShrdown & \mICTWXHBLngdown\\
B6 & \mICTWXHBShrrightmenuset & \mICTWXHBLngrightmenuset\\
\end{longtabu}
}
\chapter{\mICTWXHLedlist} \label{ch:led}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {llX}
\multicolumn2{l}{\mICTWXHLed} & \mICTWXHFunction \\ \endhead
L1 & \mICTWXHLShrcompressorone & \mICTWXHLLngcompressorrunchange\\
L2 & \mICTWXHLShrcompressortwo & \mICTWXHLLngcompressorrunchange\\
L3 & \mICTWXHLShrcompressorthree & \mICTWXHLLngcompressorrunchange\\
L4 & \mICTWXHLShrcondenserfanone & \mICTWXHLLngcondenserrun\\
L5 & \mICTWXHLShrcondenserfantwo & \mICTWXHLLngcondenserrun\\
L6 & \mICTWXHLShrcondenserfanthree & \mICTWXHLLngcondenserrun\\
L7 & \mICTWXHLShrcondenserfanfour & \mICTWXHLLngcondenserrun\\
\end{longtabu}
}
\chapter{\mICTWXHSoftcommandlist} \label{ch:com}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {rlX}
\multicolumn2{l}{\mICTWXHSoftcommand} & \mICTWXHFunction \\ \endhead
\end{longtabu}
}
\chapter{\mICTWXHHowto} \label{ch:how}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {XX[3]}
\mICTWXHHowto & \mICTWXHFunction \\ \endhead
\mICTWHTHfourtwotwoVeightSby & \mICTWHUHfourtwofiveVtwoSby\\
\mICTWHTHfourtwotwoVeightMenu & \mICTWHUHfourtwotwoVeightMenu\\
\mICTWHTHfourtwofiveVtwoSet & \mICTWHUHfourtwofiveVtwoSet\\
\end{longtabu}
}
\chapter{\mICTWXHShortcutlist} \label{ch:cut}
{
\sffamily \tiny
\taburowcolors[2]2{white .. gray!8}
\begin{longtabu} to \linewidth [c] {lX}
\mICTWXHButtonstopress & \mICTWXHShortcutdescription \\ \endhead
/ & \mICTWHCNomore\\
\end{longtabu}
}
\chapter{\mICTWXHLedandpushbl} \label{ch:lpb}
{
\includegraphics[height=\mIblhe]\mIledAndPushButtons
}
\backmatter
\end{document}
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\documentstyle{article}
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\small
\begin{document}
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%VERSION 3
\begin{center}
\begin{tabular}{|p{6.0cm}|p{8.5cm}|} \hline
& \\
\multicolumn{1}{|l|}{\hspace{0.5cm}\LARGE\bf\sf Active}
& \multicolumn{1}{|c|}{\large\em An electronic publication dedicated to}\\ [0.3cm]
\multicolumn{1}{|l|}{\hspace{0.5cm}\LARGE\bf\sf Galaxies} & \multicolumn{1}{|c|}{\large\em the observation and theory of}\\ [0.3cm]
\multicolumn{1}{|l|}{\hspace{0.5cm}\LARGE\bf\sf Newsletter} & \multicolumn{1}{|c|}{\large\em active galaxies}\\ [0.3cm]
\hline
& \\
\multicolumn{1}{|c|}{\large\bf\sf No. 24 --- March 1999 } &
\multicolumn{1}{|c|}{\bf\sf Editor: Matt Redman ([email protected])} \\ [-0.1cm]
& \\ \hline
\end{tabular}
\end{center}
\small
\begin{center}
{\Large\em Abstracts - Thesis Abstracts - Jobs - Meetings}
\end{center}
\begin{center}
{\Large\sf From the Editor}
\end{center}
\vspace*{0.6cm}
The Active Galaxies Newsletter is produced monthly. The deadline for
contributions is the last friday of the month. The Latex macros for
submitting abstracts and dissertation abstracts are appended to each
issue of the newsletter and are also available on the web page.
\newline Matt Redman
\vspace*{1cm}
\begin{center}
{\Large\sf Abstracts of recently accepted papers}
\end{center}
\def\lesssim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$<$}}}}
\def\gtrsim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$>$}}}}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{X-ray study of the NGC\,383 group of galaxies and
the source 1E\,0104+3153}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Stefanie Komossa$^1$ \ and Hans B\"ohringer$^1$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Max-Planck-Institut f\"ur extraterrestrische Physik,
Giessenbachstrasse, 85740 Garching, Germany} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\ros{{\sl ROSAT }}
\def\G{$\Gamma_{\rm x}$ }
%% Within the following brackets you place your text:
We present results from an analysis of the
X-ray properties of the NGC\,383 galaxy group
based on \ros PSPC and HRI data.
X-ray emission can be traced out to $\sim 1 h_{50}^{-1}$ Mpc,
the estimated virial radius of the system.
We determine a total mass of $6\,10^{13} h_{50}^{-1}$
M$_{\odot}$ for the group inside this radius
with a gas mass fraction of 21\%. The intragroup
gas temperature of $1.5$ keV is both consistent
with the galaxy velocity dispersion and the
X-ray luminosity - temperature relation of groups
and clusters suggesting that the group is
fairly relaxed. This is also indicated
by the almost spherically symmetric appearance
of the group's X-ray halo.
The X-ray properties of the radio galaxy NGC\,383 (3C\,31) which is located
near the center of the group are discussed.
Its spectrum is best described by a two-component model,
consisting of emission from a low-temperature Raymond-Smith plasma, and a hard tail.
The emission from NGC\,383 is not resolved by
the \ros HRI.
The possible interaction of the radio jets of 3C\,31 with the IGM is studied.
A spatial, spectral and temporal analysis of the
{\sl Einstein} source 1E0104+3153 located within the field of view is
performed, one goal being the identification of the optical
counterpart (with both, a high-redshift BAL quasar and
a nearby elliptical galaxy, member of a small group, located
within the {\sl Einstein} X-ray error circle).
We find evidence that the IGM of the small group contributes
significantly to the X-ray emission of 1E0104, which
can be described by a Raymond-Smith model of $kT \simeq$ 2 keV
and a soft X-ray luminosity of $L_{\rm x} \simeq 3\,10^{43}$ erg/s.
%% Here you write which journal which accepted your paper, for example:
{Accepted for publication in A\&A}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected] }
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Magnetically Driven Outflows in a Starburst Environment}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{Elisabete M. de Gouveia Dal Pino$^{1,2}$ and
Gustavo A. Medina Tanco$^{1}$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Instituto Astron\^omico e Geof\'{\i}sico,
University of S\~ao Paulo,
Av. Miguel St\'efano, 4200, S\~ao Paulo
04301-904, SP, Brasil}
$^2$ {Astronomy Department,
University of California - Berkeley,
601 Campbell Hall,
Berkeley, CA 94720-3411, USA}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{
We here investigate the
possibility that the observed collimated outflows in luminous
infrared galaxies (LIGs) and some Seyfert galaxies
can be produced in a starburst (SB) environment. In the former source
class, in particular, there seems to be some observational evidence
for the presence of nuclear SBs in some objects (e.g. Scoville,
Lonsdale, \& Lonsdale 1998).
A nuclear disk can be quickly produced by gas infall during star
formation in a $rotating$, stellar cluster. We find that massive
nuclear SBs with core disk masses $M_d \, \sim \,10^8 \, - 10^{9} \,
M_{\odot}$, and supernova rates $\nu_{SN} \simeq 5 \times 10^{-3} \, -
\, 2 $ yr$^{-1}$ (which are consistent with the $\nu_{SN}$ values
inferred from the observed non-thermal radio power in source
candidates) may inject kinetic energies which are high enough to blow
out directed flows from the accreting disk surface, within the SB
lifetimes. In our models, the acceleration and collimation of the
nuclear outflow are provided by magnetic fields anchored into the
rotating SB-disk. The emerging outflow carries a kinetic power that
is only a small fraction (a few percent) of the supernovae energy rate
produced in the SB. Based on conditions determined from observed
outflows and disks, we find that moderate disk magnetic fields
($\gtrsim 8 \times 10^{-4}$ G) are able to accelerate the outflows up
to the observed terminal velocities ($\lesssim$ few 100 km s$^{-1}$ in
the case of the Seyfert galaxies, and $ \sim$ 400 - 950 km s$^{-1}$ in
the case of the LIGs). The outflow is produced within a wind zone in
the disk of radius $\lesssim$ 100 pc in the the LIGs, and $\lesssim$
10 pc in the Seyferts, with wind mass loss to disk accretion rate
ratios $ \dot M_w /\dot M_d \, \gtrsim \, 0.1$ (where $\dot M_d \,
\sim \, 100 \, M_{\odot} $ yr$^{-1}$). The observation of rotating
nuclear disks of gas within $\sim$ few 100 pc scales, like that in the
prototype LIG, Arp 220 (for which $\dot M_d \, \sim 100 \, M_{\odot} $
yr$^{-1}$), and magnetized outflows in Sey galaxies and LIGs (with
terminal $B \, \sim 10^{-5}$ G at the kpc-scales), provide some
observational
support for the magneto-centrifugal disk picture
drawn here.}
{To appear in {\it The Astrophysical Journal 1999, vol. 518} }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],
\newline preprint also available at http://xxx.lanl.gov/abs/astro-ph/9901011}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Parsec-scale radio structures in the nuclei of four Seyfert galaxies}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ M. J. Kukula$^{1,2}$, T. Ghosh$^3$ A. Pedlar$^4$ and R. T. Schilizzi$^5$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, U.S.A.} \\
$^2$ {Institute for Astronomy, University of
Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, U.K.} \\
$^3$ {Arecibo Observatory, P.O. Box 995, Arecibo, Puerto Rico, PR
00613, U.S.A.} \\
$^4$ {NRAL, University of Manchester, Jodrell Bank, Macclesfield SK11
9DL, U.K.} \\
$^5$ {Joint Institute for VLBI in Europe, P.O. Box 2, 7990 AA,
Dwingeloo, the Netherlands}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We present 18-cm radio maps of four Seyfert nuclei, Mrk~1, Mrk~3,
Mrk~231 and Mrk~463E, made with the European VLBI Network
(EVN). Linear radio structures are present in three out of four
sources on scales of $\sim$100~pc to $\sim$1~kpc, and the 20-mas beam
of the EVN enables us to resolve details within the radio structures
on scales of $<10$~pc. Mrk~3 was also imaged using MERLIN and the
data combined with the EVN data to improve the sensitivity to extended
emission. We find an unresolved flat-spectrum core in Mrk~3, which we
identify with the hidden Seyfert~1 nucleus in this object, and we also
see marked differences between the two highly-collimated radio jets
emanating from the core. The western jet terminates in a bright
hotspot and resembles an FRII radio structure, whilst the eastern jet
has more in common with an FRI source. In Mrk~463E, we use the radio
and optical structure of the source to argue that the true nucleus
lies approximately 1~arcsec south of the position of the radio and
optical brightness peaks, which probably represent a hotspot at the
working surface of a radio jet. The EVN data also provide new evidence for
a 100-pc radio jet powering the radio source in the Type~1 nucleus of
Mrk~231. However, the Seyfert~2 galaxy Mrk~1 shows no evidence for
radio jets down to the limits of resolution ($\sim 10$~pc). We discuss
the range of radio source size and morphology which can occur in the
nuclei of Seyfert galaxies and the implications for Seyfert
unification schemes and for radio surveys of large samples of objects.}
%% Here you write which journal which accepted your paper, for example:
{Accepted by the Astrophysical Journal}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
http://www.stsci.edu/science/preprints/prep1326/prep1326.html}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Do Jet-Driven Shocks ionize the Narrow Line Regions of Seyfert
Galaxies?}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ {A. S. Wilson$^1$, J. C. Raymond$^2$ }}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218} \\
$^2$ {Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA 02138} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We consider a model in which the narrow line regions (NLRs) of Seyfert
galaxies are photoionized ``in situ'' by fast (300 -- 1,000 km s$^{-1}$),
radiative shock waves driven into the interstellar medium of the galaxy
by radio jets from the active nucleus.
Such shocks are powerful sources of soft X-rays. We
compute the expected ratio of the count rates in the ROSAT PSPC and
Einstein IPC detectors to the [OIII]$\lambda$5007 flux as a function of
shock velocity, and compare these ratios with observations of type 2 Seyferts.
{\it If} most of the observed soft X-ray emission from these galaxies originates
in the NLR and the absorbing hydrogen column is similar to that inferred from
the reddening of the NLR, a photoionizing shock model with shock velocity
$\simeq$ 400 -- 500 km s$^{-1}$ is compatible with the observed ratios. High
angular resolution observations with AXAF
are needed to isolate the X-ray emission of the
NLR and measure its absorbing column, thus providing a more conclusive test.
We also calculate the expected coronal iron line emission from the shocks.
For most Seyfert 2s, the [Fe X]$\lambda$6374/H$\beta$ ratio is a factor of
2 -- 14 lower than the predictions of 300 -- 500 km s$^{-1}$ shock models,
suggesting that less hot gas is present than required by these models.}
%% Here you write which journal which accepted your paper, for example:
{To be published in Ap. J. Letters, Vol. 513, 1999 March 10 issue}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
http://xxx.lanl.gov/abs/astro-ph/9901329}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{The nature of the luminous X-ray emission of NGC\,6240}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Stefanie Komossa$^1$ \ and Hartmut Schulz$^2$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Max-Planck-Institut f\"ur extraterrestrische Physik,
Giessenbachstrasse, 85740 Garching, Germany} \\
$^2$ {Astronomisches Institut, Ruhr-Universit\"at Bochum} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
We briefly review and extend our discussion of the {\sl ROSAT}
detection of the extraordinarily luminous ($>$$10^{42}$\,erg/s) partly
{\em extended} ($>$30\,kpc diameter) X-ray emission from the
ultraluminous infrared galaxy NGC\,6240. The `standard'-model of
starburst outflow is contrasted with alternatives and a comparison
with the X-ray properties of ellipticals is performed.
%% Here you write which journal which accepted your paper, for example:
{to appear in the proc. of the Ringberg workshop on {\em Ultraluminous
Galaxies: Monsters or Babies}; Ap\&SS, in press}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected] \\ preprint and related
papers available at http://www.xray.mpe.mpg.de/$\sim$ skomossa/}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Long-term optical variability properties of the Palomar-Green quasars}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Uriel Giveon$^1$, Dan Maoz$^1$, Shai Kaspi$^1$, Hagai Netzer$^1$ \ and Paul S. Smith$^2$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {School of Physics and Astronomy and the Wise Observatory,
The Raymond and Beverly Sackler Faculty of Exact Sciences,
Tel-Aviv University, Tel-Aviv 69978, Israel} \\
$^2$ {NOAO, KPNO, P.O. Box 26732, Tucson, AZ 85726-6732, USA} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\gtorder{\mathrel{\raise.3ex\hbox{$>$}\mkern-14mu
\lower0.6ex\hbox{$\sim$}}}
\def\ltorder{\mathrel{\raise.3ex\hbox{$<$}\mkern-14mu
\lower0.6ex\hbox{$\sim$}}}
%% Within the following brackets you place your text:
{We present results from a monitoring program of 42 quasars from the
Palomar-Green sample. The objects were observed for seven years at the
Wise Observatory, as part of a long term effort to monitor AGN of
various types. This is the most extensive program of its kind carried
out to date on a well-defined optically-selected quasar sample. The
typical sampling interval is $\sim 40$ days. One third of the quasars
were observed at $\sim 60$ epochs and the rest at $\sim 30$ epochs in
two bands ($B$ and $R$) with photometric accuracy of $\sim 0.01$ mag.
We present lightcurves for all of the sources and discuss the sample
variability properties. All of the quasars in the sample varied
during the campaign with intrinsic rms amplitudes of
$5\%<\sigma_B<34\%$ and $4\%<\sigma_R<26\%$. The rms amplitude and
colour for the entire sample are $\sigma_B=14\%$, $\sigma_R=12\%$, and
$\sigma_{B-R}=5\%$. On time scales of 100 to 1000 days the power
spectra of the sources have a power-law shape, $P_{\nu}\propto
\nu^{-\gamma}$, with $\gamma\approx 2.0$ and a spread $\ltorder 0.6$.
At least half of the quasars, particularly those that are most
variable, become bluer when they brighten, and the rest do not show
this behaviour. We quantify this phenomenon, which has been observed
previously only in Seyfert galaxies. The quasars which are most
variable tend also to exhibit asymmetry in their variations, in the
sense that the brightening phases last longer than the fading phases.
We have searched for correlations between the measured variability
properties and other parameters of the quasars, such as luminosity,
redshift, radio loudness, and X-ray slope. We find several new
correlations, and reproduce some of the correlations reported by
previous studies. Among them are an anticorrelation of variability
amplitude with luminosity, a trend of the autocorrelation time scale
with luminosity, and an increase in variability amplitude with
H$\beta$ equivalent width. However, all of these trends have a large
scatter despite the low observational uncertainties.}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by MNRAS }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
http://xxx.lanl.gov/abs/astro-ph/9902254}
\newpage
%\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Nuclear activity in nearby galaxies}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{Thaisa Storchi-Bergmann$^1$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Instituto de F\'\i sica, UFRGS, Campus do Vale, CP15051,
Porto Alegre, RS, Brasil}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{I discuss some recent observational results in the research of nearby
active galactic nuclei (AGN). These results cover three main topics:
(i) evidences for the current paradigm for AGN's, which include a
nuclear supermassive blackhole (SMBH) fed via an accretion disk; (ii)
evidence that this paradigm may also apply to LINER's, the lowest
luminous AGN's and to normal galaxies; (iii) evidences of how the
fueling of the SMBH occurs and its relation to recent and intermediate
age (10$^6$ to 10$^8$ yrs old) episodes of star formation.}
%% Here you write which journal which accepted your paper, for example:
{To appear in the Proceedings of the IX Reuni\'on Regional
Latinoamericana da Astronomia (Rev. Mex. Astron. Astrof.),
Tonantzintla, Mexico, Nov. 9-13, 1998,
eds. L. Aguilar and A. Carrami\~nana.}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected], \newline preprint available at
http://xxx.lanl.gov/abs/astro-ph/9903074}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{The Location of the Nucleus of NGC 1068 and the
Three-dimensional Structure of Its Nuclear Region}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Makoto Kishimoto$^1$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Department of Astronomy, Faculty of Science, Kyoto University,
Sakyo-ku, Kyoto 606-8502, Japan}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{The HST archival UV imaging polarimetry data of NGC 1068 is
re-examined. Through an extensive estimation of the observational
errors, we discuss whether the distribution of the position angles
(PAs) of polarization is simply centrosymmetric or not. Taking into
account the effect of a bad focus at the time of the observation, we
conclude that, within the accuracy of HST/FOC polarimetry, the PA
distribution is completely centrosymmetric. This means that the UV
polarization originates only from scattering of the radiation from a
central point-like source.
However, our analysis shows that the most probable location of the
nucleus is only $\sim 0.''08$ ($\sim$ 6 pc) south from the brightest
cloud called ``cloud~B''. The error circle of 99\% confidence level
extends to cloud~B and to ``cloud~A'' which is about $0.''2$ south of
cloud~B. By this FOC observation, Cloud~B is only marginally rejected
as the nucleus.
Assuming that the UV flux is dominated by electron-scattered light, we
have also derived a three-dimensional structure of the nuclear region.
The inferred distribution suggests a linear structure which could be
related to the radio jet.}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by The Astrophysical Journal }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For
example:
{E-mail contact: [email protected],\newline preprint available at
http://xxx.lanl.gov/ps/astro-ph/9902346}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{X-ray Emission from the Prototypical LINER Galaxy NGC 1052}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ K. A. Weaver$^1$, A. S. Wilson$^2$, C. Henkel$^3$ \ and J. A. Braatz$^4$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Code 662, NASA Goddard Space Flight Center, Greenbelt, MD 20771.
Also Johns Hopkins University, Department of Physics and
Astronomy, Homewood campus, 3400 North Charles Street, Baltimore,
MD 21218} \\
$^2$ {Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218. Also Astronomy Department, University of
Maryland, College Park, MD 20742} \\
$^3$ {Max-Planck-Institut f{\"u}r Radioastronomie,
Auf dem H{\"u}gel 69, D-53121 Bonn, Germany} \\
$^4$ {National Radio Astronomy Observatory, P. O. Box 2, Green Bank,
WV 24944}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{ We examine the 0.1 to 10.0 keV X-ray spectrum of the bright nuclear
LINER galaxy NGC 1052, one of two elliptical galaxies known to contain
a luminous H$_2$O maser. The observed $2.0-10.0$ keV spectrum is
unusually flat (photon index $\Gamma\sim0.2$) and best described as
intrinsically power-law shaped nuclear flux that is either (1)
attenuated by a complex absorber with $\sim70\%$ of the nuclear flux
absorbed by a column density of $N_{\rm H} \sim 3\times10^{23}$
cm$^{-2}$ and $\sim30\%$ absorbed by a column density of $N_{\rm H}
\sim3-5\times10^{22}$ cm$^{-2}$, or (2) reprocessed, with the nuclear
source blocked and the X-rays Compton reflected in our direction by
high column density ($\ge10^{24}$ cm$^{-2}$) gas. The moderate
equivalent width of the Fe K$\alpha$ line favors the dual absorption
model as the most likely scenario. The $0.1-2.0$ keV spectrum does
not resemble the few times 10$^6$ to 10$^7$ K thermal emission
typically found in other elliptical galaxies, but instead is best
described as nuclear X-rays leaking through a patchy absorber or
scattered in our direction by low-density, ionized gas plus a
$15\%-20\%$ contribution from a thermal component, which is most
likely due to the galaxy. The absorption-corrected $2-10$ keV
luminosity of the nuclear source is L$_X \sim 8\times10^{41}$ ergs
s$^{-1}$ or L$_X \sim 2\times10^{43}$ ergs s$^{-1}$ for the
dual-absorption and Compton-reflection models, respectively. The
absorbing and H$_2$O masing gases appear to be spatially separate in
this galaxy. }
%% Here you write which journal which accepted your paper, for example:
{ Accepted by the Astrophysical Journal}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected]}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Exploratory ASCA Observations of Broad Absorption Line Quasi-Stellar Objects}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{S. C. Gallagher$^1$, W. N. Brandt$^1$, R. M. Sambruna$^1$,
S. Mathur$^2$ \ and N. Yamasaki$^3$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Department of Astronomy and Astrophysics, Penn State University,
525 Davey Lab, University Park, PA 16802} \\
$^2$ {Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
Cambridge, MA 02138} \\
$^3$ {Department of Physics, Faculty of Science,
Tokyo Metropolitan University, 1-1 Minami-Osawa,
Hachioji, Tokyo 192-03, Japan}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We present the analysis and interpretation of a sample of eight ASCA
observations of Broad Absorption Line Quasi-Stellar Objects (BALQSOs).
This is the first moderate-sized sample of sensitive BALQSO observations
above 2~keV, and the BALQSOs in our sample are among the optically
brightest known ($B=$~14.5--18.5). Despite the ability of
2--10~keV X-rays to penetrate large column densities, we find BALQSOs
to be extremely weak sources above 2~keV, and we are only able to add
two new 2--10~keV detections (0226--104 and IRAS~07598+6508) to
those previously reported.
%
By comparison with non-BALQSOs of similar optical continuum
magnitudes, we derive the column densities needed to suppress
the expected X-ray fluxes of our BALQSOs. In several cases we derive
column densities $>5\times 10^{23}$~cm$^{-2}$ for a neutral absorber
with solar abundances. These are the largest X-ray column densities
yet inferred for BALQSOs, and they exceed ROSAT lower limits by
about an order of magnitude.
Optical brightness does not appear to be a good predictor of
2--10~keV brightness for BALQSOs, but our data do suggest that the
BALQSOs with high optical continuum polarizations {\it may\/} be the
X-ray brighter members of the class. For example, the highly
polarized object PHL~5200 appears to be unusually X-ray bright for a
BALQSO given its optical magnitude.
We discuss the implications of our results for future observations
with AXAF and XMM. If the objects in our sample are representative
of the BALQSO population, precision X-ray spectroscopy of most BALQSOs
will unfortunately prove difficult in the near future.}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by Ap. J. }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
http://www.astro.psu.edu/users/niel/papers/papers.html}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Chimneys in the starburst galaxy M82}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ M.P. Redman$^1$, K.A. Wills$^{1,2}$, T.W. Muxlow$^2$ and A. Pedlar$^2$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Department of Physics \& Astronomy, University of Manchester, Manchester M13 9Pl, U.K.} \\
$^2$ {NRAL, University of Manchester, Jodrell Bank, Macclesfield SK11 9DL, U.K.} \\
%% Within the following brackets you place your text:
{A new radio image of the core of the starburst galaxy M82 is
presented. A pair of probable galactic chimneys are evident. Such
structures have been conjectured to result when a giant shell of
ionized gas breaks out of the dense plane of a galaxy and ejects hot
gas into the halo. In M82, the starburst activity drives a galactic
superwind and theoretical models of this process require a knowledge
of the kinematics of the hot gas in the core of the galaxy. The
results presented here imply that the ejection of material into the
base of the superwind does not occur smoothly over the starburst
region; instead, very localised venting of the hot gas appears to be
taking place.}
% Here you write which journal accepted your paper, for example:
{To be published in `Wolf-Rayet Phenomena in Massive Stars and
Starburst Galaxies', Proc. IAU Symposium No. 193', K. van der Hucht,
G. Koenigsberger \& P. Eenens (eds), San Francisco: ASP (1999)}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected], preprint available at ftp://www.ast.man.ac.uk/outgoing/mpr/mex\_proc.ps.gz}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{
ROSAT HRI monitoring of extreme X-ray variability in the narrow-line quasar PHL~1092}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{W.N. Brandt,$^1$ Th. Boller,$^2$ A.C. Fabian$^3$ \ and M. Ruszkowski$^3$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Department of Astronomy and Astrophysics, Penn State University,
525 Davey Lab, University Park, PA 16802} \\
$^2$ {Max-Planck-Institut f\"ur Extraterrestrische Physik, 85748
Garching, Germany} \\
$^3$ {Institute of Astronomy, Madingley Road, Cambridge CB3 0HA}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We report results from an 18-day ROSAT HRI monitoring campaign on the
ultrasoft Narrow-Line Seyfert~1 (NLS1) class quasar PHL~1092. This
luminous, radio-quiet quasar showed strong X-ray variability in a
short ROSAT PSPC observation, and ROSAT HRI monitoring of the similar
object IRAS~13224--3809 revealed extreme variability on intermediate
timescales. We wanted to determine whether remarkable X-ray
variability persistently occurs in PHL~1092, and we also wanted to
search for outstanding variability events that constrain emission
processes. Given the large luminosity of PHL~1092 ($\sim 5\times
10^{45}$~erg~s$^{-1}$ in the HRI band), we detect extremely rapid and
large-amplitude X-ray variability throughout our monitoring. The
maximum observed variability amplitude is a factor of $\approx 14$,
and in the most rapid variability event the HRI count rate increases
by a factor of $\approx 3.8$ in a rest-frame time interval of
$<3580$~s. The most rapid event has a rate change of luminosity of
$>1.3\times 10^{42}$~erg~s$^{-2}$, making it the most extreme such
event we are aware of from a radio-quiet quasar. Standard `radiative
efficiency limit' arguments imply a radiative efficiency larger than
can be achieved by accretion onto a Kerr black hole rotating at the
maximum plausible rate, although we point out that such arguments
depend upon the geometry of initial radiation release. Relativistic
motions of the X-ray source are probably causing the radiative
efficiency limit to break down; such relativistic motions have also
been inferred in the similar NLS1-class quasar PKS~0558--504.}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by MNRAS }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
http://www.astro.psu.edu/users/niel/papers/papers.html}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{PKS2250-41 and the r\^ole of jet-cloud interactions in powerful
radio galaxies.}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{M. Villar-Mart\'\i n,$^{1,2}$
C. Tadhunter,$^2$ R. Morganti,$^3$ D. Axon $^4$, A. Koekemoer$^5$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Institut d'Astrophysique de Paris, 98 bis Blvd. Arago, F75014
Paris, France}
$^2$ {Department of Physics and Astronomy, University of
Sheffield, Sheffield S3~7RH, UK}
$^3$ {Istituto di Radioastronomia, Via Gobetti 101, 40129 Bologna,
Italy}
$^4$ {Department of Physics and Astronomy, University of Manchester,
Oxford
Road, Manchester, UK}
$^5$ {Space Telescope Science Institute, 3700 San Martin
Drive, Baltimore, MD21218, USA}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{ We present high resolution, long-slit spectra of the jet-cloud
interaction in the powerful southern radio galaxy PKS2250-41. We have
resolved the emission lines into two main kinematic components: a
broad component (FWHM$\geq$900 km s$^{-1}$) and a na\-rrow component
(FWHM$\leq$150 km s$^{-1}$). While the broad component is
characterized by a low ionization level (with particularly weak
HeII$\lambda$4686 emission) and is spatially associated with the radio
lobe, the narrow component is characterized by a higher ioni\-zation
level and extends well beyond the radio lobe. Crucially, we measure a
higher electron temperature for the broad component ($T\sim$30,000 K)
than for the narrow component ($T\sim$15,000 K). The general line
ratios and physical conditions of the two components are consistent
with a model in which the broad component represents gas cooling
behind the shock front driven by the radio jets, while the narrow
component represents the AGN- or shock-photoionized precursor gas.
However, uncertainties remain about the gas acceleration mechanism
behind the shock front: unless the radio components are expanding
unusually fast in this source, it is likely that entrainment of the
warm clouds in the hot post-shock wind or radio plasma is required in
addition to the initial acceleration across the shock front, in order
to explain the large line widths of the broad component.
The similarities between the kinematic properties of
PKS2250-41 and some high redshift radio galaxies suggest that the
ambient and the shocked gas have also been resolved in the more
distant objects. Given the evidence that the emission line processes
are affected by the interactions between the radio and the optical
structures, care must be taken when interpreting the UV spectra of
high redshift radio galaxies.}
%% Here you write which journal which accepted your paper, for example:
{Accepted by MNRAS}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For
example:
{E-mail contact: [email protected]}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Probing the hard X--ray properties of high-redshift Radio-Quiet
Quasars with ASCA}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ C. Vignali$^1$, A. Comastri$^2$, M. Cappi$^3$, G.G.C. Palumbo$^{1,3}$,
M. Matsuoka$^4$ \ and H. Kubo$^4$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Dipartimento di Astronomia, Universit\`a di Bologna,
Via Zamboni 33, I--40126 Bologna, Italy} \\
$^2$ {Osservatorio Astronomico di Bologna, Via Zamboni 33, I--40126 Bologna, Italy} \\
$^3$ {Istituto per le Tecnologie e Studio Radiazioni Extraterrestri,
ITeSRE/CNR, via Gobetti 101, I--40129 Bologna, Italy} \\
$4$ {The Institute of Physical and Chemical Research ({\em RIKEN}),
2-1, Hirosawa, Wako, Saitama, 351-01, Japan}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{This paper reports the X-ray spectral analysis of 5 high-redshift
(z$\ge$2) radio-quiet quasars observed by ASCA. A simple power law
continuum plus cold Galactic absorption model well fits all the
spectra (tipically between $\sim$ 2--30 keV in the sources frame).
Neither the X--ray spectral hardening, attributed to a reflection
component and observed in Seyfert galaxies, nor the excess absorption
previously detected in high-redshift radio-loud quasars, have been
revealed. Only a marginal evidence of a neutral or mildly ionized
FeK$\alpha$ line is found in one of the quasars. The average spectral
slope in the observed 0.7--10 keV energy range, $<\Gamma>$ =
1.67$\pm{0.11}$ (dispersion $\sigma$ $\sim$ 0.07), appears to be
flatter than that of low-z radio-quiet quasars ($\Gamma$ $\simeq$
1.9--2) and slightly steeper, but consistent with $\Gamma$ =
1.61$\pm{0.04}$ ($\sigma$ $\sim$ 0.10) of high-z radio-loud quasars.}
%% Here you write which journal which accepted your paper, for example:
{ Astrophysical Journal, in press }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: l\[email protected],\newline preprint available at
astro-ph/9812176}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{{The Close Environment of Seyfert Galaxies and Its Implication for
Unification Models}}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{D. Dultzin-Hacyan$^1$, Y. Krongold$^1$, I. Fuentes-Guridi$^1$, \ and P.
Marziani$^2$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Instituto de Astronom{\'i}a, UNAM, Apartado
Postal 70--264, M{\'e}xico D. F. 04510, M{\'e}xico}
$^2$ {Osservatorio Astronomico di Padova, Vicolo dell' Osservatorio 5,
I-35122, Padova, Italy} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\ltsima{$\; \buildrel < \over \sim \;$}
\def\simlt{\lower.5ex\hbox{\ltsima}} % < over MMM
\def\gtsima{$\; \buildrel > \over \sim \;$}
\def\simgt{\lower.5ex\hbox{\gtsima}} % > over MMM
\def\ds{$\rm D_S$\/}
\def\dc{$\rm D_C$\/}
%% Within the following brackets you place your text:
{ This paper presents a statistical analysis of the circumgalactic
environment of nearby Seyfert galaxies based on a computer-aided search
of companion galaxies on the Digitized Sky Survey (DSS). We defined a
sample of 72 nearby Seyfert 1 (redshift 0.007 $\leq$ z $\leq 0.034$) and a
sample of 60 Seyfert 2 galaxies ($0.007 \leq$ z$\leq 0.020$), which include
only high galactic latitude objects. In addition, we built two control
samples of non-active galaxies matching the number of sample members,
the redshift, morphological type, and diameter distribution of the
Seyfert 1 and Seyfert 2 samples separately. We stress how our sample
selection introduces important methodological improvements that avoid
several sources of strong bias. An intrinsic difference between the
environment of Seyfert 1 and Seyfert 2 galaxies, suggested by previous
work, is confirmed as statistically significant. For Seyfert 2
galaxies we find a significant excess of large companions (\dc $\simgt 10
$ Kpc) within a search radius $\simlt$ 100 Kpc of projected linear
distance, as well as within a search radius equal to three times the
diameter \ds\ of each Seyfert galaxy. For Seyfert 1 galaxies there is
no clear evidence of any excess of companion galaxies neither within
100 Kpc, nor within 3\ds. For all samples the number of companions
actually counted within a search radius of 3 \ds\ is a factor $\approx$
2 above the expectation values derived from the number density of
galaxies over one square degree fields centered on the sample galaxies,
suggesting a markedly non-Poissonian distribution for galaxies on
scales $\simlt 100$ Kpc. This difference in environment is not
compatible with the simplest formulation of the Unification Model (UM)
for Seyferts: both types 1 and 2 should be intrinsicaly alike, the {\em only}
difference being due to orientation of an obscuring torus. We propose
an alternative formulation.}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by Astroph. J. Letters, March 1999}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
LANL/SISSA repository}
\vspace*{0.6cm}
{\large\bf{UGC~3995: A Close Pair of Spiral Galaxies}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{P. Marziani$^1$, M. D'Onofrio$^2$, D. Dultzin-Hacyan$^3$,
J. W. Sulentic$^4$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Osservatorio Astronomico di Padova, Vicolo dell' Osservatorio 5,
I-35122, Padova, Italy}
$^2$ {Dipartimento di Astronomia, Universit\`a di Padova, Padova, Italia}
$^3$ {{Instituto de Astronom{\'i}a, UNAM, Apartado
Postal 70--264, M{\'e}xico D. F. 04510, M{\'e}xico}
$^4$ {Department of Physics \&\ Astronomy, University of Alabama, Tuscaloosa,
USA} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\ltsima{$\; \buildrel < \over \sim \;$}
\def\simlt{\lower.5ex\hbox{\ltsima}} % < over MMM
\def\gtsima{$\; \buildrel > \over \sim \;$}
\def\simgt{\lower.5ex\hbox{\gtsima}} % > over MMM
\def\ha{{\sc H}$\alpha$}
\def\nii{{\sc [Nii]}$\lambda\lambda$6548,6583\/}
%% Within the following brackets you place your text:
{UGC~3995 is a
close pair of spiral galaxies whose eastern component hosts a Seyfert
2 nucleus. The object was selected because a bright filamentary
structure that apparently connects the nuclei of the two galaxies made
it a good candidate to investigate a possible interaction--AGN
connection. We present a detailed analysis of this system using long
slit spectroscopy and narrow (\ha\ + \nii) as well as broad band (B,
R) imaging and an archive WFPC2 image. The component galaxies reveal
surprisingly small signs of interaction considering their spatial
proximity and almost identical recession velocities, as the bright
filament is probably an optical illusion due to the superposition of
the bar of the Seyfert galaxy and of the spiral arms of the companion.
The broad band morphology, a B--R color map, and a
continuum-subtracted \ha\ + \nii\ image demonstrate that the western
component UGC 3995B is in front of the Seyfert-hosting component
UGC3995A, partly obscuring its western side. The small radial velocity
difference leaves the relative motion of the two galaxies largely
unconstrained. The observed lack of major tidal deformations, along
with some morphological peculiarities, suggests that the galaxies are
proximate in space but may have recently approached each other on the
plane of the sky. The geometry of the system and the radial velocity
curve at P. A. $\approx$ 106$^\circ$\ suggest that the encounter may
be retrograde or, alternatively, prograde before perigalacticon.
The partial overlap of the two galaxies allows us to estimate the optical
thickness of the disk of component B. We derive an extinction $\approx$ 0.18
visual magnitudes in the infra-arms parts of the foreground galaxy disk, and
$\simgt 1-1.5$ visual magnitudes in correspondence of the spiral arms. }
%% Here you write which journal which accepted your paper, for example:
{ Accepted by Astron. J., June 1999}
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
LANL/SISSA repository}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{The Effects of Intrinsic UV Absorption on the Ionizing Continuum and
Narrow Emission Line Ratios in Seyfert Galaxies}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ S.B. Kraemer$^1$, T.J. Turner$^{2,3}$, D.M. Crenshaw$^1$, \& I.M.
George$^2$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Catholic University of America,
NASA/Goddard Space Flight Center, Code 681,
Greenbelt, MD 20771}
$^2$ {Universities Space Research Association,
NASA/Goddard Space Flight Center, Code 660,
Greenbelt, MD 20771}
$^3$ {University of Maryland, Baltimore County} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\arcsecpoint{$''\!.$}
%% Within the following brackets you place your text:
{We explore the effects of UV absorbing material on the shape of the
EUV continuum radiation emitted by the active galactic nucleus, and
on the
relative strengths of emission lines, formed in the narrow line regions of
Seyfert galaxies, excited by this continuum. Within a sample of Seyfert 1.5
galaxies, objects with
flatter soft X-ray slopes tend to have lower values of
He~II $\lambda$4686/H$\beta$, which implies a correlation between the
observed spectral energy distribution of the ionizing continuum and the
narrow emission line strengths. Objects with the flattest soft
X-ray continua tend to possess high column density UV absorption and it is
plausible that the differences in narrow emission line ratios
among these galaxies are an indication of the effects of
absorbing material internal to the narrow line region, rather than intrinsic
differences in continuum shape. We have generated a set of photoionization
models to examine the effect of a range of UV absorbers on the
ionizing continuum and, hence, the resulting conditions in a
typical narrow line cloud. Our results indicate that a
low ionization UV
absorber with large covering factor will indeed produce the combination of
narrow line
ratios and soft X-ray spectral characteristics observed in several
Seyfert 1.5
galaxies. Our results also suggest that low ionization UV absorption
may be more
common than currently believed.
}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by The Astrophysical Journal }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],
\newline preprint available at
http://www.acad.cua.edu/iacs/crenshaw/crenshaw.html}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Intrinsic Absorption Lines in Seyfert 1 Galaxies.
I. Ultraviolet Spectra from the Hubble Space Telescope}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{D. Michael Crenshaw$^1$, Steven B. Kraemer$^1$, Albert Boggess$^2$,
Stephen P. Maran$^3$, Richard F. Mushotzky$^4$, \& Chi-Chao Wu$^5$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Catholic University of America,
NASA's Goddard Space Flight Center, Code 681,
Greenbelt, MD 20771}
$^2$ {2420 Balsam Drive, Boulder, CO 80304}
$^3$ {Space Sciences Directorate, Code 600,
NASA's Goddard Space Flight Center, Greenbelt, MD 20771}
$^4$ {Laboratory for High Energy Astrophysics,
Code 662, NASA's Goddard Space Flight Center, Greenbelt, MD 20771}
$^5$ {Computer Sciences Corporation,
Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\arcsecpoint{$''\!.$}
%% Within the following brackets you place your text:
{We present a study of the intrinsic absorption lines in the
ultraviolet spectra of Seyfert 1 galaxies. The study is based on
spectra from the {\it Hubble Space Telescope}, and includes the
Seyfert 1 galaxies observed with the Faint Object Spectrograph and
Goddard High Resolution Spectrograph at spectral resolutions of
$\lambda$/$\Delta\lambda$ $\approx$ 1000 -- 20,000 with good
signal-to-noise ratios. We find that the fraction of Seyfert 1
galaxies that show intrinsic absorption associated with their active
nuclei is more than one-half (10/17), which is much higher than
previous estimates (3 -- 10\%) based on {\it IUE} data. There is a
one-to-one correspondence between Seyferts that show intrinsic UV
absorption and X-ray ``warm absorbers'', indicating that these two
phenomena are related. Although our sample is not complete, we
conclude that intrinsic absorption represents an important component
that needs to be integrated into our overall physical picture of
active galaxies.
The intrinsic UV absorption is generally characterized by
high-ionization: C~IV and N~V are seen in all 10 Seyferts with
detected absorption (in addition to L$\alpha$), whereas Si~IV is
present in only four of these Seyferts, and Mg~II absorption is only
detected in NGC~4151. The absorption lines are blueshifted (or in a
few cases at rest) with respect to the narrow emission lines,
indicating that the absorbing gas is undergoing net radial outflow. At
high resolution, the absorption often splits into distinct kinematic
components that show a wide range in widths (20 -- 400 km s$^{-1}$
FWHM), indicating macroscopic motions (e.g., radial velocity
subcomponents or turbulence) within a component. The strong absorption
components have cores that are much deeper than the continuum flux
levels, indicating that the regions responsible for these components
lie completely outside of the broad emission-line regions.
Additional information on the covering factors and column densities
can be derived from the absorption profiles in the high resolution
spectra. The covering factor of the absorbing gas in the line of
sight, relative to the total underlying emission, is C$_{los}$ $\geq$
0.86, on average. The global covering factor, which is the fraction
of emission intercepted by the absorber averaged over all lines of
sight, is C$_{global}$ $\geq$ 0.5. Thus, structures covering large
solid angles as seen by the central continuum source (e.g., spherical
shells, sheets, or cones with large opening angles) are required. The
individual absorption components show a wide range in C~IV column
densities (0.1 -- 14 x 10$^{14}$ cm$^{-2}$), and the ratio of N~V to
C~IV column density varies significantly from one absorption component
to the next, even in the same Seyfert galaxy. Thus, the intrinsic
absorption in a Seyfert 1 galaxy is typically comprised of distinct
kinematic components that are characterized by a range in physical
conditions (e.g., ionization parameter and hydrogen column density).
Finally, we show evidence for extreme variability in the intrinsic
absorption lines of NGC 3783. In addition to our earlier report of the
appearance of a C~IV absorption doublet at $-560$ km s$^{-1}$
(relative to the emission lines) over 11 months, we have detected the
appearance of another C~IV doublet at $-1420$ km s$^{-1}$ over 15
months. On the other hand, the C~IV absorption lines of NGC 3516 and
NGC 4151 were very stable over periods of 6 months and 4 years,
respectively. Monitoring observations of individual Seyferts at higher
time resolution are needed to distinguish between different sources of
variability (variable ionization, motion of gas across the line of
sight) and to determine the densities and radial locations of the
absorption components.
}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by The Astrophysical Journal }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],
\newline preprint available at
http://www.acad.cua.edu/iacs/crenshaw/crenshaw.html}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Physical Conditions in the Emission-Line Gas
in the Extremely Low-Luminosity Seyfert Nucleus of NGC 4395}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Steven B. Kraemer$^1$, Luis C. Ho$^2$,
D.Michael Crenshaw$^1$,
Joseph C. Shields$^3$,
\& Alexei V. Filippenko$^4$}}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Catholic University of America,
NASA's Goddard Space Flight Center, Code 681,
Greenbelt, MD 20771} \\
$^2$ {Carnegie Observatories, 813 Santa Barbara Street,
Pasedena, CA 91101-1292} \\
$^3$ {Department of Physics \& Astronomy, Ohio University,
Athens, OH 45701-2979} \\
$^4$ {Department of Astronomy, University of California, Berkeley,
CA 94720-3411} \\
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
\def\arcsecpoint{$''\!.$}
%% Within the following brackets you place your text:
{ We have combined {\it Hubble Space Telescope}/Faint Object Spectrograph,
ground-based, and {\it Infrared Space Observatory} spectra
of the nucleus of NGC 4395, the least luminous and nearest known type 1
Seyfert galaxy. The spectra show emission lines from a wide
range of ionization states and critical densities.
We have generated multicomponent photoionization models
of both the broad and narrow emission-line regions (BLR and NLR) to
investigate the physical conditions in the emission-line gas and
test the proposition that the source of ionization is the non-stellar
continuum radiation emitted by the central source. We show that, with
a minimum of free parameters, the model predictions match the observed
emission-line intensity ratios quite well. The elemental abundances
appear to be
be subsolar, with even greater underabundance of nitrogen.
From the size of the BLR
predicted by the models, we estimate a central mass of a few x
10$^{5}$ M$_\odot$, in reasonable agreement with estimates from the
stellar kinematics. Finally, our results suggest that the covering factor of
the emission-line gas is close to unity, and that the observed UV to X-ray
continuum is absorbed by intervening NLR gas. We argue that a
high covering factor is responsible for the apparent flattening of
the Baldwin relation
relation in low-luminosity active galactic nuclei.
}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by The Astrophysical Journal }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],
\newline preprint available at
http://www.acad.cua.edu/iacs/crenshaw/crenshaw.html}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Origin of MeV gamma ray emissions from blazars}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ K. K. Ghosh$^1,2$, B. D. Ramsey$^1$ \ and C. Sivaram$^3$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {NASA/Marshall Space Flight Center, Space Sciences Laboratory, ES84,
Huntsville, AL35812, USA} \\
$^2$ {On leave from Indian Institute of Astrophysics, Bangalore, India} \\
$^3$ {Indian Institute of Astrophysics, Bangalore, India}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We have developed a model for MeV emission from blazars that involves
the production of MeV $\gamma$\ -rays through Inverse Compton (IC)
scattering of electrons in the blob of a jet, with the UV photons of
the accretion disk. The OSSE and the COMPTEL spectra of PKS 0528 +
134 have been fitted with the computed MeV $\gamma$\ -ray fluxes of
the above model. A good fit was obtained with electrons of Lorentz
factor of $10^{1.5}$ to $10^3$ and a jet the viewing angle of $\leq$\
$15^o$ and an accretion disk temperature in the range of 2.0 to 6.0 x
$10^5$K.}
%% Here you write which journal which accepted your paper, for example:
{ Accepted by Journal of Astro-Particle Physics }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected]}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{ The HST Survey of BL Lac Objects:
Gravitational Lens Candidates and Other Unusual Sources }}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Riccardo Scarpa$^1$, C. Megan Urry$^1$, Renato Falomo$^2$, Joseph E. Pesce$^3$,
Rachel Webster$^4$, Matthew O'Dowd$^4$ \ and Aldo Treves$^5$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA} \\
$^2$ {Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy} \\
$^3$ {Eureka Scientific}\\
$^4$ {Melbourne University, Parkville, Victoria, Australia, 3052} \\
$^5$ {University of Insubria, Via Lucini 3, Como, Italy}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We present HST observations of seven unusual objects from the HST
``snapshot survey'' of BL Lac objects, of which four are gravitational
lens candidates. In three cases a double point sources is observed:
0033+595, with 1.58~arcsec separation, and 0502+675 and 1440+122, each
with $\sim 0.3$~arcsec separation. The last two also show one or more
galaxies, which could be either host or lensing galaxies. If any are
confirmed as lenses, these BL Lac objects are excellent candidates for
measuring H$_0$ via gravitational time delay because of their
characteristic rapid, high amplitude variability. An additional
advantage is that, like other blazars, they are likely superluminal
radio sources, in which case the source plane is mapped out over a
period of years, providing strong additional constraints on the
lensing mass distribution. The fourth gravitational lens candidate is
1517+656, which is surrounded by three arclets forming an almost
perfect ring of radius 2.4~arcsec. If this is indeed an Einstein ring,
it is most likely a background source gravitationally lensed by the BL
Lac object host galaxy and possibly a surrounding group or cluster. In
the extreme case that all four candidates are true lenses, the derived
frequency of gravitational lensing in this BL Lac sample would be an
order of magnitude higher than in comparable quasar samples.
We also report on three other remarkable BL Lac objects: 0138--097,
which is surrounded by a large number of close companion galaxies;
0806+524, whose host galaxy contains an uncommon arc-like structure;
and 1959+650, which is hosted by a gas rich elliptical galaxy with a
prominent dust lane of $\sim 5\times 10^5$ M$_\odot$. }
%% Here you write which journal which accepted your paper, for example:
{ Accepted by the Astrophysical Journal }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
astro-ph 9902333 }
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Strong optical line variability in Mkn 110}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ Karsten Bischoff and Wolfram Kollatschny }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
{Universit\"ats-Sternwarte G\"ottingen}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We present results of a long-term variability campaign on the
Seyfert 1 galaxy Markarian 110. Mkn 110 is a narrow-line Seyfert 1
object hosted in a morphological peculiar galaxy. We monitored the
optical continuum and the line intensities as well as their profiles
over a time interval of nearly ten years. The continuum and the
Balmer lines varied by a factor of 2 to 5 within two years. The
HeII4686 line showed exceptional intensity variations of a factor of
eight. We detected an additional independent very broad-line region
in high intensity stages of the Balmer and HeII lines. The CCF
analysis of the HeII line indicates that this very broad-line region
originates at a distance of 9 light days only from the central
ionizing source. }
%% Here you write which journal which accepted your paper, for example:
{ Accepted by A\&A }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at
http://www.uni-sw.gwdg.de/$\sim$bischoff/pub/Mkn110.html ~and~ astro-ph/9903012}
\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Broad band X-ray observations of the narrow line X-ray galaxy NGC 5506}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ T. Wang$^{1,2}$, T. Mihara$^1$, C. Otani$^1$, M. Matsuoka$^1$ \ and
H. Awaki$^{3}$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {The Institute of Physical and Chemical Research ({\it RIKEN}),
2-1, Hirosawa, Wako, Saitama, 351-0198, Japan} \\
$^2$ {Center for Astrophysics, University of Science and Technology o
f China, Anhui, 230026, China } \\
$^3$ {Department of Physics, Faculty of Science, Kyoto University, Sa
kyo-ku, Kyoto, 606-01, Japan}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{We present a detailed analysis of broad band X-ray data of the
Seyfert 2 galaxy NGC5506, obtained with the ASCA and ROSAT, to address
the nature of Fe K$\alpha$
line profile and the soft X-ray excess in this AGN. Variations up to
60\% in the 2-10 keV band are detected during a 1-day ASCA observation
performed in January 1997, while no significant change in the 2-10 keV
continuum shape is found. The ASCA spectrum consists of an absorbed
power-law, a 'soft excess' below 2 keV, and an Fe K$\alpha$ emission
line at 6.4 keV. The 'soft excess' can be well described by either
thermal emission from very low abundance material at a temperature
kT$\simeq$0.8 keV, or scattered/leaking flux from the primary
power-law plus a small amount of thermal emission. The luminosity of
the thermal emission in the former case is
1.2$\times$10$^{40}$~erg~s$^{-1}$ over the 0.5-2 keV band, while the
excess is $\sim$ 1\% of the intrinsic hard X-ray continuum in the
latter case. Analysis of ROSAT HRI data reveals that the soft X-ray
emission is extended on kpc scales in this object, and the extended
component may account for most of the soft X-ray excess observed by
the ASCA. The result suggests that in this type 2 AGN, the 'soft
excess' at least partly comes from an extended region, imposing
serious problem for the model in which the source is partially
covered. We argue that the generally low abundances are a drawback
for the thermal model, favoring a scattering dominated model. The
scatterer is likely to be relatively cold (kT $\ll$ 1 keV) in this
object.
Fe K$\alpha$ profile is complex and can not be satisfactorily modeled
by a single gaussian. Models of either double gaussians, or a narrow
gaussian plus a line from a relativistic accretion disk viewed at an
inclination of about 40$\pm$10$^\circ$ provide good fits to the
data. However, the inclination of the disk can be substantially larger
if there is a small amount of excessive Fe K edge absorption. The
intermediate inclinations for NLXGs are consistent with the ideas that
the inner accretion disk is aligned with the outer obscuring torus. }
%% Here you write which journal which accepted your paper, for example:
{ To appear in Astrophys. J. }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: wang@crab,riken,go,jp }
\begin{center}
\fboxrule0.02cm
\fboxsep0.4cm
\fbox{\rule[-0.9cm]{0.0cm}{1.8cm}{\parbox{14cm}
{
The Active Galaxies Newsletter is available on the World Wide Web.
You can access it via the University of Manchester home page :-
http://www.ast.man.ac.uk/$\sim$mpr/agn/
}}}
\end{center}
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% %%%
%%% LaTeX macro for the Active Galaxies Newsletter %%%
%%% Please use the following macro for your recently accepted paper %%%
%%% and return to [email protected] %%%
%%% %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentstyle{article}
\textwidth 18cm
\textheight 23cm
\oddsidemargin -1cm
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\parskip 0.15cm
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%\vspace*{0.6cm}
%% Between these brackets you write the title of your paper:
{\large\bf{Title of Paper}}
%% Here comes the author(s) of the paper, please indicate within $^...$
%% the number which corresponds to the institute of each author.
{\bf{ First Author$^1$, Second Author$^2$ \ and Third Author$^3$ }}
%% Here you write your institute name(s) and address(es),
%% the number in $^..$ indicates your author number, for example:
$^1$ {European Southern Observatory, Casilla 19001, Santiago 19, Chile} \\
$^2$ {Cerro Tololo Inter-American Observatory, National Optical Astronomy
Observatories, Casilla 603, La Serena, Chile} \\
$^3$ {Las Campanas Observatory, Carnegie Inst. of Washington, Casilla
601, La Serena, Chile}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Within the following brackets you place your text:
{This is the abstract of your paper}
%% Here you write which journal accepted your paper, for example:
{ Accepted by Astron. J. }
%% Here you may write the e-mail address of one or more of the authors
%% who will act as contact person for preprint requests and
%% details of availability of the paper via the World Wide Web. For example:
{E-mail contact: [email protected],\newline preprint available at http://axp2.ast.man.ac.uk:8000/Preprints.html}
\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% %%%
%%% LaTeX macro for DISSERTATION ABSTRACTS %%%
%%% Please use the following macro for your thesis abstract and return %%%
%%% to [email protected] %%%
%%% %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentstyle{article}
\textwidth 18cm
\textheight 23cm
\oddsidemargin -1cm
\topmargin 0cm
\parskip 0.15cm
\parindent 0pt
\small
\begin{document}
\begin{center}
%% If you use any personal Latex commands in your abstract, please include
%% their definitions here.
%% Between these brackets you write the title of your thesis:
{\Large\bf{Title of Thesis}}
\vspace*{0.5cm}
%% Here comes your name
{\bf{ Author }}
%% Here you write the institute where your thesis work was conducted, e.g.:
{Thesis work conducted at: Steward Observatory, University of Arizona, USA}
%% Here comes your present postal address (if you are about to move and know
%% your coming address give it as well) e.g.:
{Current address: European Southern Observatory, Casilla 19001,
Santiago 19, Chile}
%% (if you use this part, remove %%)
%% {Address as of XX XXX 1997: }
%% Here comes your e-mail address:
{Electronic mail: [email protected]}
%% Name of your adviser:
{Ph.D dissertation directed by: Galileo Galilei}
%% Month and Year of thesis:
{Ph.D degree awarded: Month Year}
\vspace*{0.8cm}
\end{center}
%% Within the following brackets you place your text:
{This is the abstract of your thesis}
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%
% [email protected] http://unilab.gbb60166.jp/prekou/prekou.htm
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\title{プレ高数学科}\author{gbb60166}
%■■■■■■■■■■■■■ テスト領域 ■■■■■■■■■■■■■■
%\end{document}
%■■■■■■■■■■■■■ 完成品 ■■■■■■■■■■■■■■
\begin{frame}[t]
\frametitle{白$7$\textcolor{red}{赤$3$}から$5$個取るとき白の数が多い確率？}
\pause
$5$個取るときは
\bigskip
\noindent（白$5$個\textcolor{red}{赤$0$個}）（白$4$個\textcolor{red}{赤$1$個}）（白$3$個\textcolor{red}{赤$2$個}）
（白$2$個\textcolor{red}{赤$3$個}）（白$1$個\textcolor{red}{赤$4$個}）（白$0$個\textcolor{red}{赤$5$個}）
\bigskip
の$6$パターンある。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{白$7$\textcolor{red}{赤$3$}から$5$個取るとき白の数が多い確率？}
このうち「白の個数が\textcolor{red}{赤の個数}より多い」のは
\bigskip
\noindent（白$5$個\textcolor{red}{赤$0$個}）（白$4$個\textcolor{red}{赤$1$個}）（白$3$個\textcolor{red}{赤$2$個}）
\bigskip
の$3$パターンだ。\pause
そこで、この$3$パターンの確率を計算する。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}[t]
\frametitle{白$7$\textcolor{red}{赤$3$}から$5$個取るとき白の数が多い確率？}
\vskip-5ex
\begin{eqnarray*}
& & \mbox{白$5$} + \mbox{白$4$\textcolor{red}{赤$1$}} + \mbox{白$3$\textcolor{red}{赤$2$}}\\[1ex]\pause
&=& { {}_{7} {\rm C}_5 \over {}_{10} {\rm C}_5} + {{}_{7} {\rm C}_4 \times \textcolor{red}{{}_{3} {\rm C}_1} \over {}_{10} {\rm C}_5} %
+ {{}_{7} {\rm C}_3 \times \textcolor{red}{{}_{3} {\rm C}_2} \over {}_{10} {\rm C}_5}\\[1ex]\pause
&=& { {}_{7} {\rm C}_5 \ + \ {}_{7} {\rm C}_4 \!\times\! \textcolor{red}{{}_{3} {\rm C}_1}\ + \ {}_{7} {\rm C}_3 \!\times\! \textcolor{red}{{}_{3} {\rm C}_2} %
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\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\frametitle{白$7$\textcolor{red}{赤$3$}から$5$個取るとき白の数が多い確率？}
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&=& { {}_{7} {\rm C}_5 \ + \ {}_{7} {\rm C}_4 \!\times\! \textcolor{red}{{}_{3} {\rm C}_1}\ + \ {}_{7} {\rm C}_3 \!\times\! \textcolor{red}{{}_{3} {\rm C}_2} %
\over {}_{10} {\rm C}_5}\\[1ex] \pause
&=& { 21 + 105 + 105\over 2\times9\times2\times7} \pause ={ 231 \over 2\times9\times2\times7} \\[1ex] \pause
&=& {33\over 2\times9\times2} ={11\over 2\times3\times2}={11\over 12} \\[1ex]
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
\textcolor{red}{
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%%
%% A DANTE-Edition example
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%% Copyright (C) 2011 Herbert Voss
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% -*- coding: utf-8 -*-
% example_fmr.tex, works with modern lualatex in TeX Live 2019.
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\section{Első}\label{f1}
\Aref{f2}.\ szakasz se érdekesebb ennél.
\section{Második}\label{f2}
\Aref{f1}.\ szakasz se érdekesebb ennél.
\end{document}
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\[\mathop{\mathbf{M}_{\nu}\/}\nolimits\!\left(\lambda\nu\right)\sim-\frac{(\frac%
{1}{2}\lambda\nu)^{\nu-1}}{\sqrt{\pi}\mathop{\Gamma\/}\nolimits\!\left(\nu+%
\frac{1}{2}\right)}\sum_{k=0}^{\infty}\frac{k!c_{k}(i\lambda)}{\nu^{k}},\]
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\documentclass{article}
\usepackage{ulem}
\usepackage{csquotes}
\begin{document}
\title{To the editors of la Huelga General in Barcelona}
\author{From: From : Anarchy Archives. }
\maketitle
\begin{abstract}
\end{abstract}
\section{To the editors of la Huelga General in Barcelona}
1901
\textbf{People :}
Author : Élisée Reclus
\textbf{Tags :} life, comrades, revolutionary, sacrifice, justice, solidarity, knowledge, ideas, poor, 1901.
\textbf{Text :}
Photo by duncan c,CC BY-NC License This letter was translated by John Clark and appears in Anarchy Archives with his permission
To the editors of la Huelga General in Barcelona. Brussels, Dec. 4, 1901. Corresp. III:238-240.
Dear comrades,
We have an ingrained habit of exaggerating both our strengths and our weakness. During revolutionary periods, it seems that our most minor actions have incalculably great consequences. On the other hand, during times of stagnation, though we may be totally dedicated to our work, our entire lives seem barren and useless, and we may even feel swept away by the winds of reaction.
What then should we do to maintain our intellectual vigor, our moral energy, and our faith in the good fight?
You come to me hoping to draw on my long experience of people and things. So, as an elderly person I give you the following advice:
Do not quarrel or deal in personalities. Listen to other people's arguments before you present your own. Learn how to remain silent and reflect. Don't try to get the better in an argument at the expense of your own sincerity.
Study with discretion and perseverance. Great enthusiasm and dedication to the point of risking one's life are not the only ways of serving a cause. It is easier to sacrifice one's life than to make one's whole life an education for others. The conscious revolutionary is not only a person only of feeling, but also one of reason, for whom every effort to promote justice and solidarity rests on precise knowledge and on a comprehensive understanding of history, sociology, and biology. Such a person can incorporate his personal ideas into the larger context of the human sciences, and is sustained in the struggle by the immense power he gains through his broad knowledge.
Avoid overspecialization. Side neither with nations nor with parties [\underline{ni aux patries ni aux partis}]. Be neither Russians, Poles nor Slavs. Rather, be men of truth, free from any thoughts of particular interests, and from speculative ideas concerning the nature of peoples, whether Chinese, Africans, or Europeans. The patriot always ends up hating the foreigner, and loses the sense of justice that once kindled his enthusiasm.
Away with all bosses, leaders, and those who treat language as if it were Sacred Scripture. Reject such idolatry and value the words even of your closest friend or the wisest professor only for the truth that you find in them. If, having listened, you still have some doubts, turn inward toward your own mind and reexamine the matter before making a final judgment.
So you should reject every authority, but also commit yourself to a deep respect for all sincere convictions. Live your own life, but also allow others the complete freedom to live theirs.
If you throw yourself into the conflict to sacrifice yourself on behalf of the humiliated and the downtrodden, that is a very good thing, my companions. Face death nobly. If you prefer to take on slow and patient work on behalf of a better future, that is an even better thing. Make it the goal of every instant of a generous life. But if you choose to remain poor among the poor, in complete solidarity with those who suffer, may your life shine forth as a beneficent light, a perfect example, a fruitful lesson for all!
Greetings, comrades. Elisee Reclus.
From : Anarchy Archives.
\textbf{Chronology :}
\begin{displayquote}
\textbf{December 04, 1901 :} To the editors of la Huelga General in Barcelona -- Publication.
\end{displayquote}
\begin{displayquote}
\textbf{February 01, 2017 :} To the editors of la Huelga General in Barcelona -- Added to http://www.RevoltLib.com.
\end{displayquote}
\begin{displayquote}
\textbf{April 13, 2019 :} To the editors of la Huelga General in Barcelona -- Last Updated on http://www.RevoltLib.com.
\end{displayquote}
file generated from :
\begin{displayquote}
\textbf{http://www.RevoltLib.com/}
\end{displayquote}\end{document}
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\begin{center}
\vskip 1cm{\LARGE\bf Infinite Sets of $b$-Additive and\\
\vskip .1in
$b$-Multiplicative Ramanujan-Hardy Numbers}
\vskip 1cm
\large
Viorel Ni\c tic\u a\\
Department of Mathematics\\
West Chester University of Pennsylvania\\
West Chester, PA 19383\\
USA\\
\href{mailto:[email protected]}{\tt [email protected]} \\
\end{center}
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\begin{abstract} Let $b$ a numeration base. A $b$-additive Ramanujan-Hardy
number $N$ is an integer for which there exists at least one integer $M$,
called the additive multiplier, such that the product of $M$ and the sum
of base-$b$ digits of $N$, added to the reversal of the product, gives
$N$. We show that for any $b$ there exist infinitely many $b$-additive
Ramanujan-Hardy numbers and infinitely many additive multipliers. A
$b$-multiplicative Ramanujan-Hardy number $N$ is an integer for which
there exists at least an integer $M$, called the multiplicative multiplier,
such that the product of $M$ and the sum of base-$b$ digits of $N$,
multiplied by the reversal of the product, gives $N$. We show that
for $b\equiv 4 \pmod {6}$, and for $b=2$, there exist infinitely many
$b$-multiplicative Ramanujan-Hardy numbers and infinitely many
multiplicative multipliers. If $b$ even, $b\equiv 0 \pmod {3}$ or
$b\equiv 2 \pmod {3},$ we show there exist
infinitely many numeration bases for which
there exist infinitely many $b$-multiplicative Ramanujan-Hardy numbers
and infinitely many multiplicative multipliers.
These results completely answer two questions and partially answer
two other questions asked in a previous paper of the author.
\end{abstract}
\section{Introduction}\label{sec:1}
Let $b\ge 2$ be a numeration base. In Ni\c tic\u a \cite{N}, motivated by some properties of the taxicab number, 1729, we introduce the classes of {\it $b$-additive Ramanujan-Hardy (or $b$-ARH) numbers} and {\it $b$-multiplicative Ramanujan-Hardy (or $b$-MRH) numbers}. The first class consists of numbers $N$ for which there exists at least an integer $M$, called the
\emph{additive multiplier}, such that the product of $M$ and the sum of base-$b$ digits of $N$, added to the reversal of the product, gives $N$. The second class consists of numbers $N$ for which there exists at least an integer $M$,
called the \emph{multiplicative multiplier}, such that the product of $M$ and the sum of base-$b$ digits of $N$, multiplied by the reversal of the product, gives $N$.
It is asked \cite[Question 6]{N} if the set of $b$-ARH numbers is infinite and it is asked \cite[Question 8]{N} if the set of additive multipliers is infinite. It is shown \cite[Theorems 12 and 15]{N} that the answer is positive if $b$
is even. The case $b$ odd is left open. It is asked \cite[Question 7]{N} if the set of $b$-MRH numbers is infinite and it is asked \cite[Question 9]{N} if the set of multiplicative multipliers is infinite. It is shown \cite[Theorem 30]{N} that the answer is positive if $b$ is odd. The case $b$ even is left open.
We recall that \emph{Niven (or Harshad) numbers} are numbers divisible by the sum of their decimal digits. Niven numbers have been extensively studied. See, for instance, Cai \cite{C}, Cooper and Kennedy \cite{CK}, De Koninck and Doyon \cite{KD}, and Grundman \cite{G}. Of interest are also $b$-Niven numbers, which are numbers divisible by the sum of their base-$b$ digits. See, for example, Fredricksen, Iona\c scu, Luca, and St\u anic\u a \cite{FILS}. A $b$-MRH-number is a $b$-Niven number. High degree $b$-Niven numbers are introduced in \cite{N2}.
The goal of this paper is to show that, for any numeration base, there
exist infinitely many $b$-ARH numbers and infinitely many distinct
additive multipliers. We also show that, for $b\equiv 4 \pmod {6}$,
and for $b=2$, there exist infinitely many $b$-MRH numbers, and
infinitely many distinct multiplicative multipliers. If $b$ even,
$b\equiv 0 \pmod {3}$ or $b\equiv 2 \pmod {3},$ we show there are
infinitely many numeration bases for which there exist infinitely
many $b$-multiplicative Ramanujan-Hardy numbers and infinitely many
multiplicative multipliers. These results completely answer the first
two questions from \cite{N} revisited above, and partially answer the
other two. We observe that a trivial example of infinitely many $b$-MRH
numbers is given by the powers of $10$. Our examples have at least two
digits different from zero. Finding infinitely many $b$-MRH numbers with
all digits different from zero remains an open question.
Our results about $b$-ARH numbers also give solutions to the Diophantine
equation $N\cdot M=\text{reversal}(N\cdot M)$. Motivated by this link,
we show that the Diophantine equation has solution for all integers $N$
not divisible by the numeration base $b$. We do not know how to answer
the following related question:
\begin{question} Does there exist, for any integer $N$, an integer $M$ such that $N\cdot M$ is a $b$-ARH number (or a $b$-MRH number, or a $b$-Niven number)?
\end{question}
Our final result shows that for any string of digits $I$ there exist
infinitely many $b$-Niven numbers that contain $I$ in their base-$b$ representation. We do not know a similar result for the classes of $b$-ARH and $b$-MRH numbers.
\section{Statements of the main results}\label{sec:1-main}
Let $s_b(N)$ denote the sum of base-$b$ digits of integer $N$. If $x$ is a string of digits, let $(x)^{\land k}$ denote the base-$10$ integer obtained by repeating $x$ $k$-times. Let $[x]_b$ denote the value of the string $x$ in base $b$.If $N$ is an integer, let $N^R$ denote the reversal of $N$, that is, the number obtained from $N$ writing its digits in reverse order. The operation of taking the reversal is dependent on the base. In the definition of a $b$-ARH-number/$b$-MRH number $N$ we take the reversal of the base-$b$ representation of $s_b(N)M$.
\begin{theorem}\label{thm:1} Let $\alpha\ge 1$ integer, $b\ge \alpha+1$ integer, and $k=(1+\alpha)^\ell, \ell\ge 0$.
Assume $b\equiv 2+\alpha \pmod{2+2\alpha}$. Define
\begin{equation*}
N_k=[(1\alpha)^{\land k}]_b.
\end{equation*}
Then there exists $M\ge 0$ integer such that
\begin{equation*}
s_b(N_k)\cdot M=(s_b(N_k)\cdot M)^R=\frac{N_k}{2}.
\end{equation*}
In particular, the numbers $N_k, k\ge 1,$ are $b$-ARH numbers and $b$-Niven numbers.
\end{theorem}
The proof of Theorem \ref{thm:1} is done in Section \ref{sec:2}.
\begin{remark} The particular case $b=10, \alpha=2,$ of Theorem \ref{thm:1}, which gives $N_k=(12)^{3^\ell}$, is covered by \cite[Example 10]{N}.
Theorem \ref{thm:1} does not give any information if $b=2$.
\end{remark}
The following proposition gives positive answers to \cite[Questions 5 and 6]{N}.
\begin{proposition}\label{prop:1} For any $b\ge 2$, there exist infinitely
many $b$-ARH numbers and infinitely many additive multipliers. The $b$-ARH numbers are also $b$-Niven numbers.
\end{proposition}
The proof of Proposition \ref{prop:1} is done in Section \ref{sec:3-pre}.
\begin{remark} Note that \cite[Theorems 12 and 15]{N} show, for all even bases, infinitely many $b$-ARH numbers that are not $b$-Niven numbers. The case of odd
base is open. The question of finding infinitely many $b$-Niven numbers that are not $b$-ARH numbers is also open. It is shown in \cite[Theorem 28]{N} that for any base there exist infinitely many numbers that are not $b$-ARH numbers.
\end{remark}
The result in Theorem \ref{thm:1} gives many base-$10$ solutions for the equation:
\begin{equation}\label{eq:star10}
N\cdot M=(N\cdot M)^R.
\end{equation}
One can try to solve the equation \eqref{eq:star10} ,where $(N\cdot M)^R$ is the reversal of $N\cdot M$ written in base $b$, for any numeration base $b$.
Observe that if $N$ is divisible by $b$, then $(N\cdot M)^R$ has less digits then $N\cdot M$, therefore $N$ is not a solution of \eqref{eq:star10}. Note also that if $N=N^R$ and $N$ has $k$ digits then \eqref{eq:star10} always has an infinite set of solutions with
\begin{equation*}
M=[(1(0)^{\land\ell})^{\land p}1]_b, \ell \ge k-1, p\ge 0.
\end{equation*}
Consequently, if $(N_0,M_0)$ is a solution of \eqref{eq:star10}, then \eqref{eq:star10} has infinite sets of solutions of types $(N_0,M)$ and $(N,M_0)$.
\begin{theorem}\label{thm:new} Let $b\ge 2$ and $N\ge 1$ integer such that $b\not \vert N$. Then $N$ is a solution of \eqref{eq:star10}.
\end{theorem}
The proof of Theorem \ref{thm:new} is done in Section \ref{sec:3}. For
base 10, a proof belonging to David Radcliffe can be found at \cite{Rat}. We learned about this reference from J. Shallit. We generalize the proof for an arbitrary numeration base. After our paper was written, we learned from J. Shallit \cite{S} that he also has a proof of Theorem \ref{thm:new}.
A \emph{$b$-numeric palindrome} is a base-$b$ integer $N$ such that $N=N^R$.
\begin{corollary} All integers, not divisible by $b$, are factors of $b$-numeric palindromes.
\end{corollary}
\begin{definition} The \emph{multiplicity} of a multiplicative multiplier $M$ is the number of $(N,M)$ solutions of \eqref{eq:star10}.
\end{definition}
It was observed above that for any solution $(N,M)$ of \eqref{eq:star10}, $M$ has infinite multiplicity. The following theorem shows infinitely many solutions of \eqref{eq:star10} independent of above.
\begin{theorem}\label{thm:33} Let $b\ge 2$ a numeration base. Then, for all $k\ge 0$, we have
\begin{equation*}
[1(b-1)]_b\cdot [(b-1)^{\land k}]_b=[1(b-2)(b-1)^{\land k-2}(b-2)1]_b.
\end{equation*}
\end{theorem}
The proof of Theorem \ref{thm:33} is done in Section \ref{sec:44}.
Our next results show, for $b$ even, more examples of infinite sets of of $b$-ARH.
\begin{theorem}\label{thm:final} Let $b\ge 2$ even.
Let $a\in\{1,2,\dots,b-1\}$ and let $k\ge 0$ be an integer.
\noindent (a) Let
\begin{equation*}
N_k=[a(0)^{\land k}a]_b.
\end{equation*}
Then $N_k$ is a $b$-ARH number, but not a $b$-Niven number.
\bigskip
\noindent (b) Let
\begin{equation*}
N_k=[\left ( 1(0)^{\land k} \right )^{\land b}0 \left ( (0)^{\land k} 1\right )^{\land b}]_b.
\end{equation*}
Then $N_k$ is a $b$-ARH number, but not a $b$-Niven number.
\bigskip
\noindent (c) Let
\begin{equation*}
N_k=[\left ( (0)^{\land k}1 \right )^{\land b}0 \left (1 (0)^{\land k} \right )^{\land b}]_b.
\end{equation*}
Then $N_k$ is a $b$-ARH number and a $b$-Niven number.
\end{theorem}
The proof of Theorem \ref{thm:final} is done in Section \ref{sec:final}.
The following theorem gives partial answers to \cite[Questions 7 and 8]{N}.
\begin{theorem}\label{thm:final2}
\leavevmode
\vphantom{x} \\
\noindent (a) Let $b\equiv 4\pmod{6}$. Let $k\ge 1$ integer such that $k\equiv 1\pmod{3}$. Define
\begin{equation*}
\alpha_k=[1(0)^{\land k}(b-2)]_b.
\end{equation*}
Then $N_k=\alpha_k\cdot(\alpha_k)^R$ is a $b$-MRH number.
\medskip
\noindent (b) Let $b=2$ and let $k\ge 1$ be an even integer. Define
\begin{equation*}
\alpha_k=[1(0)^{\land k}1]_2.
\end{equation*}
Then $N_k=\alpha_k\cdot(\alpha_k)^R$ is a $b$-MRH number.
In particular, for any numeration base $b$, $b\equiv 4\pmod{6},$ and for $b=2,$ there exist infinitely many $b$-MRH numbers and infinitely many multipliers.
\end{theorem}
The proof of Theorem \ref{thm:final2} is done in Section \ref{sec:final2}.
Our next result lists several infinite sequences of $10$-MRH-numbers.
\begin{proposition}\label{prop:examplesMRH} Assume $k\ge 1$ integer and define $N_k=\alpha_k\cdot (\alpha_k)^R$, where $\alpha_k$ is one of the following numbers:
\begin{itemize}
\item $[1(0)^{\land k} 8]_{10}, k\equiv 1\pmod{3}$,
\item $[7(0)^{\land k} 2]_{10},$
\item $[5(0)^{\land k} 4]_{10},$
\item $[4(0)^{\land k} 5]_{10}$
\end{itemize}
Then $N_k$ is a 10-MRH number.
\end{proposition}
The first item in Proposition \ref{prop:examplesMRH} follows as a corollary of Theorem \ref{thm:final2}. The other items can be proved using the same approach as in the proof of Theorem \ref{thm:final2}.
If $b$ even, $b\equiv 0 \pmod {3}$ or $b\equiv 2 \pmod {3}$, the
next theorem shows there are infinitely many numeration bases for which there exist infinitely many $b$-MRH numbers and infinitely many
multipliers.
\begin{theorem}\label{thm:3k0,2}
\leavevmode
\vphantom{x} \\
\noindent (a) Let $b\ge 18$, $b=6a$, and $ a\equiv 1\pmod {25}$. Let $\alpha_k=[1 (0)^{\land k}4]_b$ with $k\equiv 4\pmod 5$. Then $N_k=\alpha_k\cdot \alpha_k^R$ is a $b$-MRH number. The corresponding multipliers are distinct.
\bigskip
\noindent (b) Let $b\ge 18$, $b=8a$, $a\equiv 1\pmod {25}$, and $a\equiv 1 \pmod{3}$. Let $\alpha_k=[1 (0)^{\land k}4]_b$ with $k\equiv 4\pmod {20}$. Then $N_k=\alpha_k\cdot \alpha_k^R$ is a $b$-MRH number. The corresponding multipliers are distinct.
\end{theorem}
The proof of Theorem \ref{thm:3k0,2} is done in section \ref{sec:thm3k02}.
\begin{theorem}\label{thm:last-thm} For any base $b$ and for any string of base $b$ digits $I$ there exist infinitely many $b$-Niven numbers that contain the string $I$ in their base-$b$ representation.
\end{theorem}
\begin{proof} Let $I$ be a string of base-$b$ digits. There exist
infinitely many base-$b$ strings $J$ such that $s_b([IJ]_b)$ is a power of $b$, say $b^k, k\ge 1$. Then the number $N_J=[IJ(0)^{\land k}]_b$ is a $b$-Niven number.
\end{proof}
\section{Proof of Theorem \ref{thm:1}}\label{sec:2}
\begin{proof} The condition $b\equiv 2+\alpha \pmod{2+2\alpha}$ implies that $b+\alpha$ is even. The base-$b$ representation for $N_k/2$ is $N_k/2=\left [ \left ( 0\frac{b+\alpha}{2}\right )^{\land k}\right ]_b$. One has that:
\begin{equation}\label{eq:55}
s_b(N_k)=k\cdot(1+\alpha)=(1+\alpha)^{\ell+1}.
\end{equation}
The value of $N_k/2$ in base 10 is obtained summing a geometric series.
\begin{align}\label{eq:66}
\frac{N_k}{2}&=\frac{b+\alpha}{2}\cdot b^{2k-2}+\frac{b+\alpha}{2}\cdot b^{2k-4}+\cdots
+ \frac{b+\alpha}{2}\cdot b^{2}+\frac{b+\alpha}{2}=\frac{b+\alpha}{2}\cdot \frac{b^{2k}-1}{b^2-1} \nonumber \\
&=\frac{b+\alpha}{2}\cdot \frac{b^{2(1+\alpha)^{\ell}}-1}{b^2-1}.
\end{align}
Note that $N_k/2=(N_k/2)^R$. We finish the proof of the theorem if we show that:
\begin{equation}\label{eq:1}
(1+\alpha)^{\ell+1} \Big \vert \frac{b+\alpha}{2}\cdot \frac{b^{2(1+\alpha)^{\ell}}-1}{b^2-1}.
\end{equation}
We prove \eqref{eq:1} by induction on $\ell$. For $\ell=0$ equation \eqref{eq:1} becomes $1+\alpha \Big \vert \frac{b+\alpha}{2},$
which is true because $b\equiv 2+\alpha \pmod{2+2\alpha}$.
Now we assume that \eqref{eq:1} is true for $\ell$ and show that it is true for $\ell+1$.
\begin{equation}\label{eq:account}
\begin{gathered}
\frac{b+\alpha}{2}\cdot \frac{b^{2(1+\alpha)^{\ell+1}}-1}{b^2-1}=\frac{b+\alpha}{2}\cdot \frac{\left ( b^{2(1+\alpha)^{\ell}}\right )^{1+\alpha}-1}{b^2-1}\\
=\frac{b+\alpha}{2}\cdot \frac{b^{2(1+\alpha)^{\ell}}-1}{b^2-1}\left ( B^{\alpha}+B^{\alpha-1}+\cdots +B^2+B+1\right ),
\end{gathered}
\end{equation}
where
\begin{equation}\label{eq:B}
B=b^{2(1+\alpha)^{\ell}}.
\end{equation}
The congruence $b\equiv 2+\alpha \pmod{2+2\alpha}$ implies that
\begin{equation*}
b^2\equiv (2+\alpha)^2\equiv \alpha^2+4\alpha+4\equiv \alpha^2\equiv 1 \pmod{1+\alpha},
\end{equation*}
which implies that
\begin{equation}\label{eq:bsquare}
b^m\equiv 1 \pmod{1+\alpha}, \text{ $m$ even}.
\end{equation}
From \eqref{eq:B} and \eqref{eq:bsquare} follows that $B^p\equiv 1 \pmod{1+\alpha}, 1\le p\le \alpha$, so
\begin{equation}\label{eq:bigB}
1+\alpha\vert B^{\alpha}+B^{\alpha-1}+\cdots +B^2+B+1.
\end{equation}
Combining \eqref{eq:1} (for $\ell$) and \eqref{eq:bigB}, and using \eqref{eq:account}, it follows that \eqref{eq:1} is true for $\ell+1$.
\end{proof}
\section{Proof of Proposition \ref{prop:1}} \label{sec:3-pre}
\begin{proof} The case $b=2$ is covered by \cite[Theorem 12]{N}. If $b\ge 3$, choose $\alpha=b-2$ and apply Theorem \ref{thm:1}. We show that, for a fixed $b$, the multipliers appearing in the proof of Theorem \ref{thm:1} are all distinct. It follows from \eqref{eq:55} and \eqref{eq:66} that the multiplier for $N_k$ is given by:
\begin{equation}\label{eq:comp}
M=\frac{\frac{N_k}{2}}{s_b(N_k)}=\frac{\frac{b+\alpha}{2}\cdot\frac{b^{2(1+\alpha)^\ell}-1}{b^2-1}}{(1+\alpha)^{\ell+1}}.
\end{equation}
Note that $\alpha=b-2$. After algebraic manipulations, equation \eqref{eq:comp} becomes
\begin{equation*}
M=\frac{b^{2(1+\alpha)^{\ell}}-1}{(b-1)^{\ell}(b^2-1)}.
\end{equation*}
In order to show that the multipliers are distinct it is enough to show that the sequence of multipliers is strictly increasing as a function of $\ell$ That is, we need to show that:
\begin{equation}\label{eq:22}
\frac{b^{2(1+\alpha)^{\ell}}-1}{(b-1)^{\ell}(b^2-1)}<\frac{b^{2(1+\alpha)^{\ell+1}}-1}{(b-1)^{\ell+1}(b^2-1)}.
\end{equation}
After algebraic manipulations \eqref{eq:22} becomes
\begin{equation}\label{eq:33}
(b-1)(b^{2(1+\alpha)^{\ell}}-1)< b^{2(1+\alpha)^{\ell+1}}-1.
\end{equation}
After denoting
\begin{equation*}
B=b^{2(1+\alpha)^{\ell}}=b^{2(b-1)^{\ell}},
\end{equation*}
right hand side of \eqref{eq:33} factors as follows:
\begin{equation}\label{eq:131}
b^{2(1+\alpha)^{\ell+1}}-1=(b^{2(1+\alpha)^{\ell}}-1)(B^{\alpha}+B^{\alpha-1}+\cdots +B+1).
\end{equation}
Now \eqref{eq:33} follows from \eqref{eq:131} and the following inequality:
\begin{equation*}
b-1< b^{2(b-1)^{\ell}}, \ell\ge 0, \ell\ge 0, b\ge 3.
\end{equation*}
\end{proof}
\section{Proof of Theorem \ref{thm:new}}\label{sec:3}
\begin{proof} Let $b=p_1^{\alpha_1}p_2^{\alpha_2}\cdots p_k^{\alpha_k}, \alpha_i\ge 1$, $p_i$ prime, $1\le i\le k$. We recall that a base-$b$ integer $N$ is divisible by $p_i^{\gamma}$ if the last $\gamma$ digits of $N$ form a base-$b$ integer divisible by $p_i^{\gamma}$.
Let $N=p_1^{\beta_1}p_2^{\beta_2}\cdots p_k^{\beta_k}w$, where $\gcd(w,b)=1$. Let $m=\max(\beta_1, \beta_2, \cdots , \beta_k)$. Let $L$ be the base-$b$ integer equal to $p_1^{\beta_1}p_2^{\beta_2}\cdots p_k^{\beta_k}$. As $b\not\vert N$, the last digit of $L$ is not $0$. Let $\ell$ be the length of $L$. Consider the
base-$b$ palindrome $P=[L^R(0)^{\land {m-\ell}}L]_b$, where $L^R$ is the reversal of base-$b$ representation of $L$. As $P$ is divisible by $p_1^{\beta_1}p_2^{\beta_2}\cdots p_k^{\beta_k}$, this is the end of the proof if $w=1$.
Assume $w>1$. Let $\phi$ be Euler's totient function which counts the positive integers up to a given integer $n$ that are relatively prime to $n$. As $\gcd(w,b)=1$ Euler's theorem implies that $b^{\phi(w)} - 1\equiv 0 \pmod w$.
Let $r$ be an multiple of $\phi(w)$ which is greater than $l+m$, the length of $P$. Let $q\ge 1$ a multiple of $b^{\phi(w)}-1$.
Consider
the infinite family of integers given by
\begin{align}
\label{eq:newalpha}
Q_{r,q}&=\big[1\big((0)^{\land r-1}1\big)^{\land q}\big]_b=1+b^{r}+b^{2r}+\cdots+b^{qr}\nonumber\\
&=1+b^{r}+b^{2r}+\cdots+b^{qr}+q-q\\
&=\big (b^{r}-1\big )+\big (b^{2r}-1\big )+\big (b^{3r}-1\big )+\cdots + \big (b^{qr}-1\big )+q. \nonumber
\end{align}
All terms in the last part of \eqref{eq:newalpha} are divisible by $b^{\phi(w)}-1$, so $Q_{r,q}$ is divisible by $b^{\phi(w)}-1$ and by $w$.
We finish the proof observing that $P\cdot Q_{r,q}$ is a base-$b$ palindrome divisible by $N$.
\end{proof}
\section{Proof of Theorem \ref{thm:33}}\label{sec:44}
\begin{proof} Observe that:
\begin{equation}\label{eq:77}
\begin{gathered}
(b-1)\cdot (b-1)=b(b-2)+1=[(b-2)1]_b\\
(b-1)b^{k}+(b-1)b^{k}=b^k+(b-2)b^{k-1}=[1(b-2)0^{\land k}]_b.
\end{gathered}
\end{equation}
Using \eqref{eq:77} we get
\begin{align*}
\ [1(b-1)]_b\cdot[(b-1)^{\land k}]_b &=(b+b-1)\cdot \left ( \sum_{i=0}^{k-1}(b-1)b^i\right )\\
&=\sum_{i=0}^{k-1} \Big ( (b-1)b^{i+1}+ \left ( b(b-2)+1\right )b^i\Big )\\
&=\sum_{i=1}^{k}(b-1)b^i+\sum_{i=0}^{k-1} \left ( b(b-2)+1\right )b^i \\
&=(b-1)b^{k}+\sum_{i=1}^{k-1}\Big ((b-1)+b(b-2)+1\Big ) b^i+b(b-2)+1\\
&=(b-1)b^{k}+\sum_{i=1}^{k-1} (b-1)b^{i+1}+b(b-2)+1\\
&=(b-1)b^{k}+(b-1)b^{k}+\sum_{i=1}^{k-2} (b-1)b^{i+1}+b(b-2)+1
\end{align*}
\begin{align*}
&=b^k+(b-2)b^{k-1}+\sum_{i=1}^{k-2} (b-1)b^{i+1}+b(b-2)+1\\
&=[1(b-2)(b-1)^{\land k-2}(b-2)1]_b.
\end{align*}
\end{proof}
\section{Proof of Theorem \ref{thm:final}}\label{sec:final}
\begin{proof}
\noindent (a) Note that $s_b(N_k)=2a$. As $b$ is even, there exists an integer $M$ such that:
\begin{equation*}
2a\cdot M=[a(0)^{\land k+1}]_b.
\end{equation*}
The following computation shows that $N_k$ is a $b$-ARH number:
$$
s_b(N_k)\cdot M+(s_b(N_k)\cdot M)^R\\
=[a(0)^{\land k+1}]_b+[a]_b=[a(0)^{\land k}a]_b=N_k.
$$
To show that $N_k$ is not $b$-Niven observe that $N_k/a=[1(0)^{\land k}1]_b$ is odd.
\bigskip
\noindent (b) Note that $s_b(N_k)=2b$. As $b$ is even, the multiplier $M=[(1(0)^{\land k})^{\land b}(0)^{\land kb+b-1}]_b/2$ is an integer.
The following computation shows that $N_k$ is a $b$-ARH number:
\begin{equation*}
\begin{gathered}
s_b(N_k)\cdot M+(s_b(N_k)\cdot M)^R\\
=[(1(0)^{\land k})^{\land b}(0)^{\land kb+b}]_b+[((0)^{\land k}1)^{\land b}]_b=[(1(0)^{\land k})^{\land b}0 ((0)^{\land k}1)^{\land b}]_b=N_k.
\end{gathered}
\end{equation*}
To show that $N_k$ is not $b$-Niven observe that $N_k$ is not divisible by $b$.
\bigskip
\noindent (c) The proof is similar to that of b).
\end{proof}
\section{Proof of Theorem \ref{thm:final2}}\label{sec:final2}
\begin{proof}
\noindent (a) Using the fact that
\begin{equation*}
(b-2)^2=b^2-4b+4=b(b-4)+4=[(b-4)4]_b,
\end{equation*}
an equivalent base-$b$ representation for $N_k$ is given by
\begin{equation}
N_k =
\begin{cases}
[(b-2)(0)^{\land k-1}(b-4)5(0)^{\land k}(b-2)]_b, & \text {if }b\not = 4; \\
[2(0)^{\land k-1}11(0)^{\land k}2]_4, & \text {if }b = 4.
\end{cases}
\end{equation}
If $b\not = 4$ one has $s_b(N_k)=3(b-1)$ and if $b=4$ one has $s_4(N_k)=6$. To finish the proof of case a) it is enough to show that $\alpha_k$ is divisible by $s_b(N_k)$.
If $b\not = 4$ we get
$$
\alpha_k=b^{k+1}+b-2=b^{k+1}-1+b-1\\
=(b-1)\big (b^k+b^{k-1}+\dots +b^2+b+2 \big)
$$
and
$$b^k+b^{k-1}+\dots +b^2+b+2\\
\equiv k+2 \equiv 0\pmod{3}.
$$
For the first congruence we used $b\equiv 1\pmod{3}$ and for the second we used $k\equiv 1 \pmod{3}$.
If $b=4$, then clearly $\alpha_k$ is divisible by 2. Moreover
\begin{equation*}
\alpha_k=4^{k+1}+2=(3+1)^{k+1}+2\equiv 0\pmod{3},
\end{equation*}
which shows that $\alpha_k$ is divisible by 6.
\bigskip
\noindent (b) Now assume that $b=2$. Then an equivalent base-2 representation for $N_k$ is given by
\begin{equation*}
N_k=[1(0)^{\land k-1}10(0)^{\land k}1]_2,
\end{equation*}
so $s_2(N_k)=3$. To finish the proof, we use the fact that $k$ is even to show that $\alpha_k$ is divisible by 3:
\begin{equation*}
\alpha_k=2^{k+1}+1=(3-1)^{k+1}+1\equiv 0\pmod{3}.
\end{equation*}
To prove the last claim in the theorem, we show that the multipliers corresponding to various values of $k$ are distinct. This follows from the explicit formulas below. All sequences of multipliers are strictly increasing as functions of $k$.
If $b=2$ the sequence of multipliers is given by $M_k=\frac{2^{k+1}+1}{3}$.
If $b=4$ the sequence of multipliers is given by $M_k=\frac{4^{k+1}+2}{6}$.
If $b>4$ the sequence of multipliers is given by $M_k=\frac{b^{k+1}+b-2}{3(b-1)}$.
\end{proof}
\section{Proof of Theorem \ref{thm:3k0,2}}\label{sec:thm3k02}
\begin{proof}
\noindent (a) The base-$b$ representation for $N_k$ is
\begin{equation*}
N_k=[4(0)^{\land k-1}(17)(0)^{\land k}4]_b.
\end{equation*}
Therefore $s_b(N_k)=25$. If $k=5\ell+4$. one has that:
\begin{equation*}
\alpha_k=6^ka^k+4\equiv (6^5)^\ell6^4+4\equiv (7776)^\ell\cdot 296+4\equiv 0 \pmod {25}.
\end{equation*}
Hence $N_k$ is a $b$-MRH number with multiplier $\frac{\alpha_k}{25}=\frac{(6a)^k+4}{25}$.
\bigskip
\noindent (b) As above, $s_b(N_k)=25$. If $k=20\ell+4$, one has that:
\begin{equation*}
\alpha_k=8^ka^k+4\equiv (8^{20})^\ell8^4+4\equiv (76)^\ell\cdot 96+4\equiv 0 \pmod {25}.
\end{equation*}
Hence $N_k$ is a $b$-MRH number with multiplier $\frac{\alpha_k}{25}=\frac{(8a)^k+4}{25}$.
\end{proof}
\section{Acknowledgments} The author would like to thank the editor and the referee for valuable comments that helped him write a better paper.
\begin{thebibliography}{9}
\bibitem{C} T. Cai, On $2$-Niven numbers and $3$-Niven numbers, {\it
Fibonacci Quart.}, {\bf 34} (1996), 118--120.
\bibitem{CK} C. N. Cooper and R. E. Kennedy, On consecutive Niven numbers,
{\it Fibonacci Quart.}, {\bf 21} (1993), 146--151.
\bibitem{KD} J. M. De Koninck and N. Doyon, Large and small gaps
between consecutive Niven numbers, {\it J. Integer Sequences} {\bf 6}
(2003),
\href{https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.html}{Article 03.2.5}.
\bibitem{G} H. G. Grundman, Sequences of consecutive Niven numbers,
{\it Fibonacci Quart.}, {\bf 32} (1994), 174--175.
\bibitem{FILS} H. Fredricksen, E. J. Iona\c scu, F. Luca, and P. St\u
anic\u a, Remarks on a sequence of minimal Niven numbers, in
S. W. Golomb, G. Gong, T. Helleseth and H.-Y. Song, eds.,
{\it Sequences, Subsequences, and Consequences}, Lecture Notes in Comp. Sci.,
Vol.~4893, Springer, 2007, pp.~162--168.
\bibitem{N} V. Ni\c tic\u a, About some relatives of the
taxicab number, {\it J. Integer Sequences}, {\bf 21} (2018),
\href{https://cs.uwaterloo.ca/journals/JIS/VOL21/Nitica/nitica10.html}{Article
18.9.4}.
\bibitem{N2} V. Ni\c tic\u a, High degree $b$-Niven numbers,
to appear in {\em Integers}. Preprint available at
\url{http://arxiv.org/abs/1807.02573}, July 6 2018.
\bibitem{Rat} D. Radcliffe, World of numbers,
\url{http://www.worldofnumbers.com/em36.htm}.
\bibitem{S} J. Shallit, Palindromic multiples, preprint, 2018.
\end{thebibliography}
\bigskip
\hrule
\bigskip
\noindent 2010 {\it Mathematics Subject Classification}:
Primary 11B83; Secondary 11B99.
\noindent \emph{Keywords:} numeration base, $b$-Niven number, reversal, additive $b$-Ramanujan-Hardy number, multiplicative $b$-Ramanujan-Hardy number, palindrome.
\bigskip
\hrule
\bigskip
\noindent (Concerned with sequences
\seqnum{A005349},
\seqnum{A067030},
\seqnum{A305130}, and
\seqnum{A305131}.)
\bigskip
\hrule
\bigskip
\vspace*{+.1in}
\noindent
Received December 26 2018;
revised versions received March 14 2019; March 30 2019;
April 4 2019.
Published in {\it Journal of Integer Sequences}, May 24 2019.
\bigskip
\hrule
\bigskip
\noindent
Return to
\htmladdnormallink{Journal of Integer Sequences home page}{http://www.cs.uwaterloo.ca/journals/JIS/}.
\vskip .1in
\end{document}
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\title{Anarcho-syndicalists in the Mexican revolution}
\date{2010}
\author{Anarchist Federation}
\subtitle{the Casa del Obrero Mundial}
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{\usekomafont{title}{\huge Anarcho-syndicalists in the Mexican revolution\par}}%
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{\usekomafont{subtitle}{the Casa del Obrero Mundial\par}}%
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\par
During the first twenty years of the 20\textsuperscript{th} century Mexico was engulfed in revolutionary turmoil. Various ‘constitutionalist’ (i.e. democratic) capitalist factions vied for power whilst attempting to overthrow the dictatorship of General Porfirio Diaz . Meanwhile the Agrarian (landless peasant) movement of Emiliano Zapata and the emerging urban working class attempted to defend their own interests amidst the chaos. The Agrarians engaged in guerrilla activity against the various ‘revolutionary’ governments with the aim of reclaiming and defending the land of the indigenous population from the landowners. During the years 1906 to 1915 the Partido Liberal Mexicano (P.L.M.) played a leading in role in attempting to bring together Agrarian and proletarian revolt. Beginning from an advanced left liberal-democratic position the P.L.M., under the influence of the Magon brothers, developed into an anarchist communist organisation with its own guerrilla units involved in the expropriation of land in the Baja California region and leading strikes in Veracruz, amongst other areas. The P.L.M. called for “Tierra y Libertad” (Land and Freedom), the immediate expropriation of the landlords and bosses and the abolition of the state.
In 1912 the anarcho-syndicalist Casa del Obrero Mundial (House of the World Worker) was formed and rapidly attracted the urban workers of Mexico City to its ranks. Yet, within three years the anarcho-syndicalists were organising Red Battalions to fight in defence of the Mexican state! Although the Casa emerged with a typical anti-politicism and a desire to concentrate on economic struggle several factors led it to give support to one bourgeois faction, the Constitutionalist forces of Venustiano Carranza, against the Agrarians and their P.L.M. allies. Firstly, the anarcho-syndicalists viewed the industrial proletariat as the organised vanguard of the social revolution, in spite of the fact that they constituted a tiny minority of the Mexican working population. This vanguard, they argued, had to be developed and expanded as rapidly as possible and the anarcho-syndicalists sought what they hoped would be the best conditions for this. Secondly, the anarcho-syndicalists considered the Agrarian movement as an essentially reactionary one, committed to turning back the clock, and rejecting the ‘advances’ in technology and understanding that capitalism had brought. They pointed to the Zapatista’s “religiosity” and general ‘backwardness’ as proof of their danger to the ‘advanced’ sections of the working class. Finally, and most importantly, the anarcho-syndicalists believed that the progressive, democratic bourgeois state which was offering the Casa freedom to organise (and in fact was actually encouraging the Casa to organise!) should be defended against ‘reaction’, Agrarianist or anti-constitutionalist.
After the anarcho-syndicalist Red Battalions had played their part in ‘saving’ the Mexican state, the inevitable happened. In the spring of 1916 the Constitutionalist government turned on the Casa, disbanded the Red Battallions and forcibly closed down the syndicates following the second of two General Strikes that year. The failure of the anarcho-syndicalists to recognise the class nature of the state, despite all their verbal anti-statism, had led them to take sides against genuinely revolutionary movements.
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The Anarchist Library
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Anti-Copyright
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Anarchist Federation
Anarcho-syndicalists in the Mexican revolution
the Casa del Obrero Mundial
2010
\bigskip
\href{https://libcom.org/history/anarcho-syndicalists-mexican-revolution-casa-del-obrero-mundial}{libcom.org}
Excerpted from a longer article “The union makes us strong?”\forcelinebreak \forcelinebreak A critical account of the Mexican anarcho-syndicalist union the Casa del Obrero Mundial which took up arms against revolutionary peasants.
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\textbf{theanarchistlibrary.org}
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How to replicate data with Horde and your phone, PDA or OutlookGeneral informationInformation for syncing with Outlook or BlackberryInformation for syncing PDAs with the Synthesis clientInformation for syncing Horde with Evolution or KDE AkonadiSync clients being used succesfullyFAQIt's not working! I get a message like "Invalid response" on the phone or "Server returned error code -1" on Funambol clientsIt's not working! I get a "System Error!" on my mobile device when trying to synchronizeIt's not working with Funambol 7.0.8 (Windows Mobile) (first sync does not start)It's still not working! What can I do?I Want to test syncing on my PC, does some Palm or PocketPC emulator exist and how do i use it?Incorrect username or password
\part{How to replicate data with Horde and your phone, PDA or Outlook}
This is the Horde SyncML\footnote{http://example.com/index.php?page=SyncML} Howto page. It describes how to setup your phone, PDA, or Outlook to synchronize its data (calendar, events, tasks, notes) with Horde. You might also want to check out these pages:
\begin{itemize}
\item{SyncMLRoadmap\footnote{http://example.com/index.php?page=SyncMLRoadmap} describes planned, upcoming or currently missing features. }
\item{Once you managed to sync your phone with Horde, please check the SyncMLContributeTesting\footnote{http://example.com/index.php?page=SyncMLContributeTesting} page and provide a test case if there's none for your client yet. You'll help us to improve the stability for your client!}
\item{If you encounter problems with syncing and can't resolve them on your own or using the FAQ below, please follow the directions in SyncMLProblemReport\footnote{http://example.com/index.php?page=SyncMLProblemReport} for reporting problems.}
\end{itemize}
If you are here looking for information on how to sync your mobile device using Microsoft ActiveSync technology, see the ActiveSync project page\footnote{http://example.com/index.php?page=ActiveSync}.
\section{General information}
Syncing is beta quality code - to help fixing bugs and locating issues you need to be able to at least read logfiles! Testing is welcome; please report to the sync list ([email protected]), but please keep in mind that the code is still in development.
\begin{itemize}
\item{You have to use at least Horde 3.2 and x.2 versions of the Horde applications, or Horde Groupware (Webmail Edition) 1.1, or the CVS version or a CVS snapshot. Horde 3.1.x or Horde Groupware 1.0.x won't do. The newer the Horde (Groupware) version, the better. Please note that if you are using a CVS checkout or snapshot, you have to run \texttt{framework/install-packages.php} to install the required packages into your PEAR path.}
\item{Client configuration is as follows:}
\begin{itemize}
\item{The sync URL is http(s)://pathtoyourhordeinstall/rpc.php}
\begin{itemize}
\item{User name/password: your Horde account data}
\item{Databases (sometimes called remote settings or server path) should be calendar, tasks, notes, and contacts, but common default values from the various clients may work too. The default values in Funambol Client work just fine.}
\end{itemize}
\end{itemize}
\end{itemize}
\section{Information for syncing with Outlook or Blackberry}
\begin{itemize}
\item{You need the Funambol connector version 7.1.10 or later. Go to https://www.forge.funambol.org/download/\footnote{https://www.forge.funambol.org/download/} -> select your client software -> Download and install. (As of Jan 2012 the relevant application now appears to be the Funambol Windows Sync Client.)}
\item{Configure as mentioned above.}
\item{Make sure the server's certificate does validate when using https: Open the https://pathtoyourhordeinstall/rpc.php\footnote{https://pathtoyourhordeinstall/rpc.php} in Internet Explorer. If the server's certificate is not trusted or not valid, Funambol will not work!}
\item{Unfortunately, the Windows Mobile version 7.0.8 requires you to synchronize once with a Funambol server (such as http://my.funambol.com\footnote{http://my.funambol.com}) before you are allowed to change settings. (reference?)}
\item{With cPanel installations of Horde, the Funambol client may fail to authenticate because \texttt{rpc.php} is not accessible without first logging into cPanel's webmail system, making syncing impossible. See http://forums.cpanel.net/f43/horde-groupware-syncml-rpc-php-174551.html\footnote{http://forums.cpanel.net/f43/horde-groupware-syncml-rpc-php-174551.html}}
\end{itemize}
\section{Information for syncing PDAs with the Synthesis client}
\begin{itemize}
\item{The Synthesis client is a commercial SyncML\footnote{http://example.com/index.php?page=SyncML} client from http://www.synthesis.ch/\footnote{http://www.synthesis.ch/}. It is available for PocketPC, Windows Mobile, Smartphone and PalmOS. Stability and SyncML conformance is very good. There's a 30 days trial version. }
\item{Uncheck the "only from 30 days before until 90 after today" setting, it will be ignored by Horde anyway.}
\end{itemize}
\section{Information for syncing Horde with Evolution or KDE Akonadi}
How to configure Horde with SyncEvolution (based on Sync4j) : http://syncevolution.org/wiki/horde\footnote{http://syncevolution.org/wiki/horde}\newline
SyncEvolution uses the open source libsynthesis\footnote{http://www.synthesis.ch/indefero/index.php/p/libsynthesis/} library.
\section{Sync clients being used succesfully}
If you are using Horde 3.3.7 or later and a recent SyncML\footnote{http://example.com/index.php?page=SyncML} client, synchronisation generally work out of the box.\newline
Check the \textbf{compatibility table\footnote{http://example.com/index.php?page=SyncMLCompatTable}}, informations below can be incomplete and quite old.
\begin{itemize}
\item{Synthesis client}
\item{Sony Ericsson P800, P900, K800i, C902i, J105i (Naite)}
\item{Outlook with Funambol SyncClient PIM outlook 3.0.15}
\item{Nokia E51, E65, E60, E90, N70, N73, N80, N95, N97mini, E61, E61i, E71, 5800 XpressMusic, 6120 Classic, 9500 Communicator}
\item{Nokia N900 with Syncevolution}
\item{Samsung I8910 HD}
\item{Motorola RAZR v9 (only entries without non-ASCII characters)}
\item{Windows Mobile /w Funambol client 7.0.8 after some tinkering}
\item{Mozilla Thunderbird with Funambol Mozilla Sync Client https://mozilla-plugin.forge.funambol.org/\footnote{https://mozilla-plugin.forge.funambol.org/} (Linux only without page compression or Horde versions from September 2009 or later)}
\item{KAddressbook with Akonadi based data via Akunambol}
\item{KDE >= 4.6 Akonadi with SyncEvolution}
\item{Android phones via the funambol legacy client or forks, some experiences found here\footnote{http://www.hwahl.de/syncml\_horde\_android\_funambol-client.html} }
\end{itemize}
\section{FAQ}
\subsection{It's not working! I get a message like "Invalid response" on the phone or "Server returned error code -1" on Funambol clients}
There's a chance that SyncML\footnote{http://example.com/index.php?page=SyncML} processing stopped due some PHP error in the server. We try to catch these errors, but sometimes they are passed to the phone so the phone gets confused because it doesn't receive a valid XML message. To catch even those error message, you need to make PHP log errors to a file: edit your \texttt{php.ini} and include a line like \texttt{error\_log = /var/log/php.log}. Then try a sync and check if anything comes up in this log.
Another common pitfall is a bug in some older Funambol clients: The clients propagate that they are able to handle "deflate" encoded HTTP traffic while in fact they don't. This affects e.g. the 6.0.x series of the Outlook Plugin, probably others too. This has been fixed with later versions, i.e. the 6.5.x Outlook Plugins. Either upgrade to a newer Funambol client, or configure your web server to \textsl{not} send deflate encoded HTTP responses for the horde directory, even if the client tells to do so.
\subsection{It's not working! I get a "System Error!" on my mobile device when trying to synchronize}
Check the SyncML\footnote{http://example.com/index.php?page=SyncML} Version that the device is trying to use. Version 1.2 gave this error, Version 1.1 worked without problems (Nokia E71 Symbian).
\subsection{It's not working with Funambol 7.0.8 (Windows Mobile) (first sync does not start)}
Funambol tries to sync a folder 'configuration' when a new server is added - old versions of rpc.php ignore this request, newer versions abort the process\newline
Quick Fix: Do a first sync with an older server (I used eGroupware 1.4 - its interface seems to be based on Horde's) and afterwards change the sync URL with a registry editor to the one you intend to use.\newline
Or even better, help fixing this problem: http://bugs.horde.org/ticket/8621\footnote{http://bugs.horde.org/ticket/8621}
\subsection{It's still not working! What can I do?}
Please follow the directions in SyncMLProblemReport\footnote{http://example.com/index.php?page=SyncMLProblemReport} and report the problem to the sync mailing list.
\subsection{I Want to test syncing on my PC, does some Palm or PocketPC emulator exist and how do i use it?}
Please see the PdaEmulators\footnote{http://example.com/index.php?page=PdaEmulators} page for info.
\subsection{Incorrect username or password}
Try performing a complete factory reset (worked for Nokia E71)\newline
For me worked to change the authorization from horde to imap. After that it worked perfectly.
\end{document}
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https://www.zentralblatt-math.org/matheduc/en/?id=73064&type=tex
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zentralblatt-math.org
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\iteman{ZMATH 02361515}
\itemau{Mercier, Alain; Rouchier, Andr\'e; Lemoyne, Gis\`ele}
\itemti{The teaching engineering (uses and abuses of educational theories). (Le g\'enie didactique (Usages et m\'esusages des th\'eories de l'enseignement).)}
\itemso{De Boeck Universit\'e, Bruxelles (ISBN 2-8041-3540-3). 277 p. (2001).}
\itemab
Some of the articles will be reviewed individually in MathEduc.
\itemrv{~}
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http://dlmf.nist.gov/29.6.E60.tex
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\[\sum_{p=1}^{\infty}B_{2p}D_{2p}=\frac{4}{\pi}\int_{0}^{\!\mathop{K\/}\nolimits%
\!}\left(\mathop{\mathit{Es}^{2m+2}_{\nu}\/}\nolimits\!\left(x,k^{2}\right)%
\right)^{2}dx.\]
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%&LaTeX
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\begin{thebibliography}{1}
\bibitem{SanchezSanchez-Serrano2001} S{\'a}nchez S{\'a}nchez-Serrano, A. (2001). Otro punto de vista sobre el Manuscrito de Palacio Ms. 1520. En F. B. Pedraza Jim{\'e}nez, G. G{\'o}mez Rubio, \& R. Gonz{\'a}lez Ca{\~n}al (Eds.), \textit{{\textquotedblleft}La Celestina{\textquotedblright}, V centenario (1499-1999). Actas del Congreso Internacional (Salamanca, Talavera de la Reina, Toledo, La Puebla de Montalb{\'a}n, 27 de septiembre -- 1 de octubre de 1999)} (pp. 273--282). Cuenca: Ediciones de la Universidad de Castilla-La Mancha.
\end{thebibliography}
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http://theanarchistlibrary.org/library/ramor-ryan-anti-ulises-a-day-in-the-life-of-a-simmering-city.tex
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\title{Anti-Ulises}
\date{June 4, 2008}
\author{Ramor Ryan}
\subtitle{A Day In the Life of a Simmering City}
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\begin{quote}
“History is a nightmare from which I am trying to wake.”
\forcelinebreak
Stephen Daedalus, in Ulysses, James Joyce 1922
\end{quote}
Midnight in Oaxaca, and walking around the historic center, its almost as if nothing had ever happened here. The bourgeoisie sit around under the colonial arches in the long stretch of French-style outdoor cafes lining the central plaza. Aside from being beset by a small army of ambulant trinket vendors and beggars, the well-heeled citizens sipping cappuccinos seem very at ease with the world. A few late night tourists wander about the pleasant old streets under the starry sky, and the industrious hum of the sultry cosmopolitan city invokes an eternal calm.
It’s as if there had never been a riotous peoples’ insurrection in these same streets just 2 years ago. As if the rebel citizenry had never erected one thousand and one barricades to defend their city from the marauding police forces of the despised and despotic state government. And as if the tens of thousands of rebels and insurrectionists had not been this close to winning the great battle for Oaxaca in the heady summer days and nights at the barricades of 2006. The famous subversive graffiti that painted the whole town red and black is removed, whitewashed, as is the blood in the streets of the 26 fallen comrades shot down by the police and state paramilitaries.
“Since all of this, we will not be the same at all as before; we can’t be and we don’t want to be.” said a resident shortly after the quelled uprising.
But at this moment, to a visitor just having stepped off the bus from Chiapas, the strange normality of the place gives the appearance that everything has not changed, that everything remains the same as pre-2006.
Sometimes hope comes from the most unexpected quarters. Walking away from the sanitized Zocalo we chance upon a moribund vista. Shuffling around in the half shadows of a street corner, about a hundred tooled-up riot cops loiter with menace – as if itching for something to happen. The phalanx of troops, an ominous dark mass of helmets, riot shields and shiny black boots, clank their long metal sticks on the somewhat medieval flagstones. It is an incongruous sight at this time of night, amidst this placid ambiance, without the slightest disturbance to be ascertained of any kind anywhere.
Paradoxically, their presence signifies a welcome sign – where there are riot police there is generally trouble, and trouble in the Oaxaca context, means\dots{} resistance.
I have followed the movements of police riot squads with close interest for many years. So I approach the last cop in the line – a young indigenous man clad in state-of-the-art modern armor – with all the sweet innocence of a visiting tourist, and ask him as to why there are here. Is there a problem, officer?
He tenses up, grips his metal baton and stares at the distant wall, not at me.
“We are here for your protection” he says sternly – and somewhat comically.
We have heard that one before. Back in the day, during the war in Ireland, this is how the occupying British troops behaved – nervous, uncertain and trigger-happy. So this is it – as people had forewarned – this tremulous peace in the city is one overseen by riot cops lingering in the shadows. Like Oaxaca is a city under stealthy occupation.
\section{The March of the Umbrellas}
Around midday, under the glare of the blazing tropical sun, some 50,000 protesting teachers start flooding into downtown Oaxaca. Today, May 15 is Teachers Day, and the states educators have downed chalk on-mass, and declared a strike as they have done religiously every year for the last 25 years.
It’s a remarkable sight, the arrival of the teacher hordes. Teachers anywhere in the world are a most innocuous bunch of people, and the members of this particular branch of the national teachers union, known as Section 22, are the most unlikely street revolutionaries imaginable. Yet these same humble unionists were the solid backbone of the 2006 insurrection. Here they come, this sea of teachers under the midday sun, these revolutionary hordes and\dots{} they are not masked up, nor linking arms, nor pumping fists. No, they are strolling along gaily under a roof of colorful bobbing umbrellas, singing songs and being generally full of revelry and joy. Having marched for 3 hours one would expect a certain fatigue, but no, the teachers are boisterous and upbeat and the enticing chaos is more mad hatters tea party than militant discipline.
“The teachers struggling,” they sing, “celebrating their day of the teachers!”
But it would be a mistake to underestimate their militant resolve. Maria, an indigenous Zapotec teacher from the isthmus is carrying her one-year-old child Victoria in her arms as she marches.
“Victoria?,” I ask.
“Hasta la victoria siempre!” she laughs, towards victory always, quoting Che.
Maria had been part of the uprising in 2006.
“Wow, lots of tear gas and running,” she says, looking back, “but\dots{}we almost made it, we almost won.”
“Do you have fear,” I ask, “returning here two years later, to Oaxaca city center, after the brutal repression?”
“Not unless I don’t have a stone or a stick in my hand to protect myself, no, then I am not afraid,” she says with a laugh, this 20-something-year-old mother who defines herself as “a Christian teacher”.
From the central platform on the kiosk in the Zocalo, the teacher’s leaders spell out their demands for higher salaries, increased funding for rural schools and the resignation of the state governor Ulises Ruiz Ortiz.
“We wont negotiate with the government of Ulises,” says Domingo Cabera, secretary general of the Section 22 of the Teachers Union, “ because we don’t recognize the legitimacy of his government, we will only negotiate with the federal government.”
“Here today with this massive turnout,” says the speaker, “we demonstrate that the movement is more consolidated than ever.”
Sort of. It’s common knowledge that Section 22 of the Teacher Union is in a state of disarray. Maria, the rural teacher, doesn’t trust the words or intentions of her union leadership.
“While striking teachers were selling their cars and their houses in 2006 to support the strike, the corrupt leaders were accepting bribes and selling out the grassroots,” she tells me.“It is a tragedy, but now we are re-organizing.”
Flavio Sosa takes the microphone and it is a significant moment. Recently released from jail, he is one of the most recognized figures of the Oaxaca Peoples Popular Assembly (APPO). As the organizing body of the uprising, APPO brought together a myriad of social and political groupings and could mobilize hundreds of thousands at the height of the rebellion. Flavio is of the faction of the APPO state council who favors negotiation with the authorities and political participation in state and municipal elections – a very contentious issue within the rebel movement.
“We demand the release the remaining political prisoners,” says Flavio over the microphone, outlining the political demands of the movement, “[and] the cancellation of the outstanding arrest warrants (several hundred), punishment for those responsible for the deadly repression committed during 2006 and the resignation of state governor Ulises Ruiz Ortiz. Fuera Ulises – Ulises out!”
Ulises, Ulysses, is a most aptly named tyrant – whom Virgil refers to famously in the Aeneid, as “a cruel and deceitful man”. The much hated latter-day Ulises minor continues to be the focus of the protesters ire. Representing the PRI party who ruled Mexico for 70 years, he was elected in 2004 under very dubious circumstances, and marked the beginning of his tenure with a campaign of brutal repression against his opponents. While previous Governors had negotiated or tolerated the widespread and deeply ingrained opposition movement in Oaxaca, Ulises oversaw the criminalization of protest. But he underestimated the strength and determination of the opposition, who responded with the total takeover of Oaxaca. Exiled for most of 2006, his administration was only able to return after a bloody offensive by some 6,500 militarized cops against APPO on October 29 of that same year- leading to 200 arrests, hundreds hospitalized and the city center resembling a battlefield.
\section{A Cantina Full of Anarchists}
We – two Irish visitors – have come to Oaxaca to talk with the comrades from Oaxacan Voices Constructing Autonomy and Freedom (VOCAL), a sizable anti-authoritarian grouping that forms part of APPO. Anarchists and libertarians had played a prominent role in the defense of the city in 2006, and remain an important voice in the movement. In a traditional cantina, a group of grassroots teachers and Vocal-istas engage in a the post-march analysis.
A big march somewhat empty of content, appears to be the general agreement.
We meet with David Venegas Reyes, a 25-year-old local resident who emerged as one of the more charismatic and articulate young voices on the street in 2006. For his trouble, the state issued an arrest warrant and in April 2007 he was abducted from a city park, and thrown in jail. After a campaign for his release, in which even Amnesty International voiced concern for the manner of his detention, he walked in February 2007, all charges dropped.
“On the one hand here in the city,” explains David, “the government has been able to partially dismantle the Section 22 which was the largest of the unions and the center of the movement in 2006. But at the same time there is a lot of discontent in the ranks, and the leadership has been totally discredited by the base. So while the government has managed to corrupt the union leadership by buying them off, the base has become more conscientious and is therefore more difficult to cheat or hoodwink.”
First off, David is not a leader, nor a spokesperson for VOCAL. But it seems by general consensus of the various Vocal-istas here, that he will be the one to talk to us visitors – maybe because he is the affable and chatty one of the group.
The owner of the cantina overhears the table talk, and voicing support for the teachers and APPO, sends over a round of beers. I am impressed by how open and conspicuous are the activists despite the general atmosphere of repression in the city. Several of the people here have outstanding arrest warrants from 2006 still hanging over their heads, yet this does not stop them going out and joining the protests, or simply going about their lives unbowed.
“What about APPO?,” I ask. “Is it affected by the same kind of disarray as the Section 22?”
David responds carefully and comprehensively; I think its worth quoting him at length:
\begin{quote}
“APPO has basically being the unity of the different organizations of the peoples of Oaxaca. The interesting thing, the transcendental thing about APPO is that it has managed to bring together a broad representation of the various peoples of the state with a wide convergence of different ideologies and visions of the world – all under the one assembly. Then came the great wave of actions that took place in 2006, the great advance towards realizing our collective aspirations – first demanding the exit of Ulises, and much more than that, also demanding a radical and profound change in the society in which we live in .”
“So in 2006 our APPO assemblies reflected the assemblies of the indigenous communities in so much as that there were no leaders and it is the assembly which decides things. We tried to act like this but sadly there was a gap between how we acted in assembly and the verticalism practiced by some of the social organizations. So there was this tension within APPO as how people wanted to organize and how to practice.”
“The spontaneous combative spirit that arose in the streets was not the result of some bureaucratic orders from some leaders up on top; no, they came from the people in the streets themselves, and the spirit remains there.”
“When the brutal repression against us began, the mobilizations weakened, firstly because of fear at the ferocity of the repression. But alongside this, people felt dispirited and demoralized by the opportunistic actions at this critical moment of some of the considered leaders of a few social movements. The important point of this story is that in February 2007, some social movements decided that the movement couldn’t achieve the demand of removing Ulises from government and so proposed that APPO make an alliance with the supposed left-wing political parties in Oaxaca and to compete for power in the local municipal and congressional elections. During this discussion, an important group of companeros defined themselves by opposing this proposal and we managed to stop this attempt to institutionalize our movement. And so emerged strong divisions within the movement, provoked mainly by those whose aspirations for taking power were frustrated.”
“So a group of us libertarian companeros and those who didn’t believe in political parties and various ideologies, agreed that for the movement to enter into the electoral route was to merely play the states game in this context in Oaxaca and so we opposed it. VOCAL doesn’t aspire to become the leadership of APPO. VOCAL is a space of unity for those who think the autonomy of our diverse and multicultural peoples is a political proposal for our reality. We stayed with the APPO because the unity of the people is important. And its important to remain true to the words that were said in 2006 that the APPO is a movement of bases and not of leaders. Although it was said, many did not act like this and began to invest their confidence in false leaders.”
\end{quote}
Other voices around the table are more forthright in their criticism of the PRD (opposition political party) and Marxist-type elements which took control of the APPO, but David remains staunchly non-sectarian.
“So there are many of us, not just VOCAL, the Magonistas and some Marxists, but many of the base who believe that we have to re-organize the movement from below, not from the top down. Because the truth is that APPO is in the communities and in the union bases – not just in the leadership. In Mexico there is a long history of leaders becoming compromised – anybody who knows a little of the union history knows how often this has happened – the leadership always becomes compromised, recuperated by power. And the leadership in APPO has similar tendencies.”
So what are the lessons, I ask, that have been taken away from 2006.
As in, you almost had it, APPO was in control of the city like a modern day Paris Commune and Ulises was on his way out the door; victory was so close. And then after holding the city for eight long, glorious months, came the huge wave of repression and the movement was beaten off the streets. What went wrong? I ask.
“There are some who say we made tactical errors in 2006, but I don’t think it was an error or mistake to defend our territory in a physical form against the assassins of Ulises and the militarized Federal police of (Presidents) Vincente Fox and Felipe Calderon. For me that was not the error – to defend ourselves , no, the error that was made was when people started to believe in false leaders,” said David.
Another comrade chimes into the discussion. “And there are those who say that the movement brought repression upon themselves by upping the ante of resistance, that they got what they deserved! Nonsense!”
“The prisoners and the dead aren’t guilty!” says David. “The guilty are those who imprisoned and murdered them.”
It’s now late afternoon and everyone disperses for various meetings. The political energy is perceivable and the days’ march has got people upbeat. The spirit of resistance is simmering once more in the streets of Oaxaca.
\section{Of Police and Streets}
Sometime after dusk, we reunite with David under the portal of the great old central Cathedral in the Zocalo. Despite the days events, the police presence in the center is negligible – mostly undercover agents discreetly monitoring the proceedings. The authorities have decided upon a non-aggressive strategy and the city is teeming with teachers in repose. It must be surreal for them to be confronted with this veil of normality in the city they once occupied. One noticeable difference from even the night before is the clandestine presence of graffiti all over the place. The ubiquitous APPO slogans and Fuera Ulises! are back on the walls of the city again.
Walking the darkening city thoroughfare, a police car slowly passes by, and David involuntarily glances over his shoulder. I imagine he has his fears – after all, it was in these very streets that he was suddenly lifted by an undercover snatch squad in broad daylight, and abruptly removed to the nightmare of indefinite incarceration.
“Fear? Yeah,” he says, “of course we have fear. But fear should not impede us from moving forward. People continue to struggle just as they did in 2006 without stepping back, or wobbling. People are coming together again, to make sure that Ulises’s assassins or the abductions don’t continue.”
“I was a prisoner held for 11 months, just a caprice for the authorities. And then I was released for lack of evidence.” he added.
It wasn’t that justice was done, more that the pressure from outside meant it was politically untenable for the state to hold him hostage any longer. David recognizes the role national and international solidarity played in his release, and in the struggle in general.
“A really important part in detaining the repression was the level of national and international observation that took place from outside. If this hadn’t happened, I think that the repression would have been even much worse.”
“But it shouldn’t be thought that suddenly we live in a just state now,” emphasizes David. “We still live under a state of daily repression and harassment. It’s unbearable, and we can’t have some government telling us that we must accept living under this state of oppression, as if it was some kind of normalcy. We don’t accept it, because we are a free people, free we are born and free we were brought up. And since the resistance hasn’t stopped, so the repression continues. I think that whatever happens in Oaxaca in the next while it’s really important that people from outside don’t stop the vigilance, and continue pressurizing the government to limit their use of reactionary violence.”
A new Amnesty International report echoes his concerns, denouncing the repression on the social movement and the general impunity that exists for security forces in the country in general, and the abuse of citizen’s rights in Oaxaca in particular.
But this climate of fear engendered by the authorities doesn’t stop David traversing these streets which he has known all his life. Indeed, the going is slow as he meets and greets all and sundry along the way – like this middle-aged indigenous man who stops him randomly and wishes him well, knowing of his unjust imprisonment. It’s like the movement, even if it doesn’t hold the center, still has the street.
We are going to a social center where a bunch of musicians and activists are gathered for a night of Son Jarocho, a traditional popular song and dance. It’s an autonomous space, familiar to other cultural and political spaces in different parts of the globe – self-managed, a shebeen of sorts, where people come and go, and the mood is friendly. Between ardent musical performances, people give brief presentations, like this from a representative of the Universidad de la Tierra (UniTierra), a peoples’ university based here in the city. Another is a report back from the caravan of the isthmus region undertaken by a group of VOCAL activists, including David, who returned early this morning. The Trail of the Jaguar political tour of the rural isthmus consolidated links with indigenous communities under the theme “for the regeneration of our collective memory”.
In a quiet moment we drag David away for the gathering and continue with our interrogation. On the flat roof of the social center, the city stretches out far and wide, the lights shimmering across the vast valley. Oaxaca is a much bigger place than it seems when wandering around the historic center.
“What’s going on with the movement in the city, and in the countryside,” I ask, “Where do we stand now?”
“Here in the city, there has been a strong militarization and a heavy police presence to repress the movement. Meanwhile the government has somewhat ignored the indigenous communities and it is there, in the rural community that some very important organizing is happening. I’m not saying that the movement in the city has finished and now the movement is only in the countryside, no. It is more that the government, while focusing all their attention on defeating the movement in the city, has allowed discontent to flourish in the countryside,” says David.
While of course simultaneously letting the paramilitaries have a free hand to do their dirty work in the communities – including the April ambush murder of two women journalists working for La Voz que Rompe el Silencio (“The Voice that Breaks the Silence”), a community radio station serving the Trique indigenous community. But the kind of police and military saturation within the City has not occurred in the communities.
“And so today in Oaxaca City there is a tense calm. The councilors and officials of the APPO and Section 22 leadership are being conciliatory and opportunistic. Groups of Stalinists and PRD-istas of the electoral persuasion are making a pact with the business leaders to get permission to mobilize. But the others, like us in VOCAL and other groups, the majority of the movement, are in constant confrontation with the authorities because our mobilizations are not seen gladly by the state – and the line between repression and tolerance is barely visible,” says David.
\section{A Oaxaca Commune}
The Son Jarocho session is wrapping up and people are homeward bound. We pile into a van going out to the outskirts of town where a bunch of people are staying. There’s about a dozen of us in this beat up van, rattling along the highway out of town. There’s a certain spirit of abandonment about these people and its contagious. I’m thinking if the cops stop this thing, they will net a good dirty dozen desperadoes of veteran anarchists.
The van arrives at a feral warehouse on a sprawling lot, cluttered with machines, tools and a big old bus just back from the Trail of the Jaguar tour. The collective living space is populated by a group of weary and sonambulant activists. A tattered, faded image of the Virgin of the Barricades adorns a wall, the ironic patron saint who presided over those at the barricades in 2006. Her image, with her iconic gas mask and cloak of burning tires reminds me of Calamidad’s words, the last gringa on the last barricade on the last night of the Oaxaca commune.
“A lot of people have been fucked in the head ever since November 25, 2006, ” she lamented, “when it was all lost in a flurry of bullets–but damn was it a close fight for awhile. In a sense people are just as traumatized by the tragic implications of what victory might have been- and how close people were to it, so close they could taste it for the first time in their lives- as they were by the violence. When I returned to Oaxaca, I would walk into a party, and comrades would come up to me and say – ‘she remembers! We almost did it, we had the city! All the barricades! The city was ours!’ So its not only the repression that people remember, but also the memory of holding the streets for so long is a bitter one\dots{}..because they lost them.”
Here in this chaotic, creative space, among the barricadistas who have not given up, there is a palpable feeling that, despite the loss in 2006, there is still hope and people are now organizing harder than ever.
“And,” David Venegas reminds us, “as the Mexican saying goes – ‘There is no evil that can last a hundred years, and there’s no body that can’t resist it’, meaning that everything has its own time, and this straight-jacket of a state has come to its end. That the time has come.”
Up and down the country people are invoking the centennial memory of the first Mexican revolution – 1910 – to herald a new revolution in 2010. “What’s the feeling here,” I ask David, “about this quasi-mystical belief in revolutionary change on a sanctified date?”
“Well many Mexicans are resigned to the fatality of the idea of 2010,” he says with a smile, “ and as you know, Mexico is profound and millenarian. But for me, its not important that the deed happens on this very date, but more importantly that it occurs! And I can feel it in the air in Mexico – a longing for revolution. But revolutions don’t just occur on a certain date – they are prepared. And what I’m seeing is an growing insurgent spirit, alongside an increase in the brutality of the government. There is a great indignation felt by the communities and movements against whom the bad government has declared war.”
“I hope a revolutionary change occurs in this country because there can be no half solutions, reforms are not going to end the injustice and exploitation. A change from the bottom is necessary, a profound and truthful change. This is what millions are demanding, and this is what the government are trying to deny us. The government has failed to reform the state constitutionally, to comply to our aspirations. That is why it is we, the people who must make those changes – because the government has lost its opportunity. So now its our responsibility to make those changes.”
It’s midnight once more in Oaxaca, and this long plenteous day, May 15, 2008, is over. We bed down in the loft cosy with about 20 other companer@s and dreams come easily. History is a nightmare from which Oaxaca, like Mexico, is trying to wake up from and maybe 2006 was just a primer.
% begin final page
\clearpage
% if we are on an odd page, add another one, otherwise when imposing
% the page would be odd on an even one.
\ifthispageodd{\strut\thispagestyle{empty}\clearpage}{}
% new page for the colophon
\thispagestyle{empty}
\begin{center}
The Anarchist Library
\smallskip
Anti-Copyright
\bigskip
\includegraphics[width=0.25\textwidth]{logo-en}
\bigskip
\end{center}
\strut
\vfill
\begin{center}
Ramor Ryan
Anti-Ulises
A Day In the Life of a Simmering City
June 4, 2008
\bigskip
Retrieved on 29\textsuperscript{th} January 2021 from \href{https://anarchism.pageabode.com/?p=67}{anarchism.pageabode.com}
\bigskip
\textbf{theanarchistlibrary.org}
\end{center}
% end final page with colophon
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https://cheatography.com/timdalton/cheat-sheets/spiceworks-tickets-anywhere/latex/
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\vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Spiceworks Tickets Anywhere Cheat Sheet}}}} \\
\normalsize{by \textcolor{DarkBackground}{Tim Dalton (timdalton)} via \textcolor{DarkBackground}{\uline{cheatography.com/25948/cs/7058/}}}
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\vspace{-2pt}Published 8th February, 2016.\\
Updated 8th February, 2016.\\
Page {\thepage} of \pageref{LastPage}.
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Measure your website readability!\\
www.readability-score.com
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\begin{multicols*}{2}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Priority of a ticket:}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#priority high} \tn
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#priority low} \tn
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Accept a ticket}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#accept} \tn
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#assign to me} \tn
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Assign the ticket}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#assign to Bob} \tn
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#assign Bob Saget} \tn
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Note: With this command, you can enter the email address of the assignee (you don't have to enter the entire email address, just enough to distinguish what admin the ticket is getting assigned to). You can also enter the first name of the assignee if it is defined in the User Accounts Table. Optionally use the first and last name to distinguish duplicate first names, e.g. Bob Smith and Bob Saget.} \tn
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Time worked on a ticket}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#worked 10m} \tn
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#add 2h to [email protected]} \tn
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#worked 15m Ford} \tn
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#add 1h me} \tn
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Put a ticket in "Waiting on user" status}} \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{\#waiting} \tn
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Close a ticket}} \tn
% Row 0
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% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{CC a user}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#cc [email protected]} \tn
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Note: this command ONLY works with email addresses that have previously submitted tickets or are registered in Spiceworks. To add a completely new address, it will need to be added to the cc field of the ticket's email.} \tn
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
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% Row 0
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% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Note: this applies to the whole email; you can't make a specific comment within your email private.} \tn
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Set due dates}} \tn
% Row 0
\SetRowColor{LightBackground}
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% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#due tomorrow @5pm} \tn
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#due July 15, 2013 at noon} \tn
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{\#due 3 businessdays from today @ noon} \tn
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
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% Row Count 5 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{NOTE: You can also include terms like "weekdays", "businessdays", "fortnights", "first day of summer", etc.} \tn
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Create a ticket for someone else}} \tn
% Row 0
\SetRowColor{LightBackground}
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% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Set your custom attributes}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#set attribute name=attribute value (ex: \#set Floor Number=14)} \tn
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Categorize the ticket}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#category maintenance} \tn
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Reopen a closed ticket}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#reopen} \tn
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Unassign a ticket}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#unassign} \tn
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Relate the ticket to a machine}} \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{The \#relate command works as follows: \newline % Row Count 1 (+ 1)
- If the input looks like an IP address, lookup device by IP. \newline % Row Count 3 (+ 2)
- Otherwise, try to find the device by serial number or asset tag. \newline % Row Count 5 (+ 2)
- If nothing matched, try to find the device by its server / host name. \newline % Row Count 7 (+ 2)
- If still nothing matched, it tries each of these in order until something matches: \newline % Row Count 9 (+ 2)
- Device name \newline % Row Count 10 (+ 1)
- Software name \newline % Row Count 11 (+ 1)
- Service name \newline % Row Count 12 (+ 1)
- Hotfix name \newline % Row Count 13 (+ 1)
- Agreement name% Row Count 14 (+ 1)
} \tn
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Add a purchase}} \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{\#purchase {[}count{]} purchased-item {[}price{]} (ex: \#purchase 13 4gb USB Thumb Drive \$12.72)} \tn
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{Note: {[}count{]} and {[}price{]} are optional and can be edited later from your Spiceworks desktop if needed.} \tn
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}
% That's all folks
\end{multicols*}
\end{document}
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\hfill \huge{ \textbf{Mathématiques}} \hspace*{3cm} \newline
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\hfill \huge{ \textbf{Les Nombres Réels}} \hspace*{3cm} \newline
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\hfill \Large{ David Zancanaro \hspace*{3cm} \newline
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\section{Les nombres réels : définitions et généralités}
\subsection{Définitions et notations}
\begin{defi}
Un \underline{nombre réel} est un nombre qui peut être représenté par une partie entière et une liste finie ou infinie de décimales.\\
En particulier, chaque nombre réel correspond à un unique point sur une droite graduée (que l'on appelle abscisse du point) et réciproquement à chaque point d'une droite graduée correspond un unique nombre réel.
\end{defi}
\textbf{Notations} : L'ensemble de tous les nombres réels se note $\R$.
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\subsection{Exemples de nombres réels avec quelques unes de leurs particularités}
\begin{itemize}
\item[$\star$)] $0$ est le seul nombre à la fois positif et négatif ; il est le plus petit des entiers naturels. Il est encore l'élément neutre de l'addition c'est-à-dire quelque soit le nombre réel $x$ on a :
$$ x+0=0+x=x$$
Il sert de base pour définir l'opposé d'un nombre réel $x$ : tout nombre réel $x$ admet un unique opposé $-x$ qui vérifie :
$$ x+(-x)=0$$
C'est la propriété que l'on utilise pour équilibrer et résoudre les équations.
\item[$\star$)] $1$ est le plus petit entier naturel strictement positif ; il est aussi l'élément neutre de la multiplication c'est-à-dire :
$$ \forall x \in \R\qquad\text{on a } \qquad x\times 1=1\times x=x$$
Il sert de base pour définir l'inverse d'un nombre réel non nul $x$ : tout nombre réel $x$ distinct de $0$ admet un unique inverse $\dfrac{1}{x}$ qui vérifie :
$$ x\times \dfrac{1}{x}=1$$
Il s'agit de l'autre propriété que l'on utilise pour équilibrer et résoudre les équations.
\Expl{On cherche le nombre réel $x$ qui vérifie $3x+2=0$.\\
L'opposé de $2$ est $-2$ que l'on ajoute aux deux membres de l'équation ce qui donne :
$$ 3x+2-2=0-2 \quad\text{c'est-à-dire} \quad 3x=-2$$
Enfin l'inverse de $3$ est $\dfrac{1}{3}$ et l'on multiplie les deux membres de l'équation par $\dfrac{1}{3}$ ce qui donne :
$$ \dfrac{1}{3}\times 3x=-2\times \dfrac{1}{3} \quad\text{c'est-à-dire} \quad x=-\dfrac{2}{3}$$
L'équation admet une unique solution qui est le nombre réel $-\dfrac{2}{3}$ ; nous pouvons vérifier que ce nombre est bien solution :
$$ 3\times \left(-\dfrac{2}{3}\right)+2=-2+2=0$$}
\item[$\star$)] $11$ est un nombre entier naturel (c'est-à-dire un nombre entier positif). $11$ est aussi un nombre premier c'est-à-dire un nombre entier naturel qui admet exactement deux diviseurs positifs distincts de $1$ et de lui-même. $2$ est le plus petit des nombres premiers et est le seul nombre pair premier ; en effet tout autre nombre pair n'est pas premier puisqu'on peut le diviser par $2$ (ex : $4=2\times 2$ ou $6=2\times 3$). Voici une liste des plus petits nombres premiers :
$$ 2\quad 3\quad 5\quad 7\quad 11\quad 13\quad 17\quad 19\quad \dots$$
\item[$\star$)] $-2,75$ est un nombre décimal qui a la particularité d'être négatif. Comme tout nombre décimal son écriture \og décimale \fg{} admet un nombre de chiffre fini après la virgule. Par exemple le nombre $\dfrac{1}{3}$ dont l'écriture décimale comporte une infinité de $3$ après la virgule n'est pas un nombre décimal. On peut choisir d'écrire $-2,75$ sous forme de fraction :
$$ -2,75=\dfrac{-275}{100}=-\dfrac{11}{4}$$
et d'une manière générale un même nombre admet bien des écritures différentes$\dots$
\item[$\star$)] $-\dfrac{2}{3}$ est une fraction négative ; dès lors que l'on peut écrire un nombre sous forme de fraction on dit qu'il s'agit d'un nombre \textbf{rationnel}. Pendant longtemps l'homme pensait que tous les nombres réels étaient des nombres rationnels ; c'est-à-dire qu'il était possible de tous les écrire sous forme de fraction.
\item[$\star$)] $\sqrt{2}$ est un nombre qui ne peut pas être écrit sous forme de fraction. On dit qu'il est irrationnel. Pour avoir démontré ce résultat on raconte qu'Hippase de Métaponte fut jeté à la mer car contredisant la philosophie Pythagoricienne$\dots$
\\
Tous les nombres irrationnels ont une écriture décimale infini et non périodique, ainsi pour connaître les décimales de $\sqrt{2}$ les mathématiciens ont inventé des méthodes, des algorithmes, retenons que :
$$ \sqrt{2}\simeq 1,41$$
D'un point de vue géométrique la diagonale d'un carré de côté $1$ a pour longueur $\sqrt{2}$. Ce résultat est une conséquence du théorème de Pythagore.
\begin{center}
\includegraphics[scale=0.3]{racine.eps}
\end{center}
\item[$\star$)] Le nombre d'or : $\varphi=\dfrac{1+\sqrt{5}}{2}$. Le nombre d'or est un nombre mythique ; définissant une sorte de proportion idéal pour les figures géométriques ; certains le voient partout : dans les proportions de la pyramide de Khéops, Léonard de Vinci l'utilise pour quelques unes de ses peintures, dans la coquille d'un escargot, etc...
\\
Il s'agit d'un nombre irrationnel, comme $\sqrt{2}$.
\\
Approximativement le nombre d'or vaut :
$$ \varphi\simeq 1,618$$
En partant de la suite de nombre suivante (appelé suite de Fibonacci):
$$ 1\quad 1 \quad 2\quad 3 \quad 5\quad 8\quad 13 \quad 21 \quad 34\quad 55\quad \dots$$
(on obtient un nombre en additionnant les deux précédents)\\
le rapport de deux nombres successifs se rapproche de plus en plus du nombre d'or :
$$ \dfrac{8}{5}=1,6 \qquad \dfrac{13}{8}\simeq 1,625 \qquad \dfrac{21}{13}=1,615$$
En utilisant les termes de cette suite voici une construction de la \og spirale d'or\fg{} qui rappelle la coquille des escargots$\dots$
\begin{center}
\includegraphics[scale=0.8]{spiraledor.eps}
\end{center}
\pagebreak
\item[$\star$)] Le fameux nombre $\pi$. Si on double le diamètre d'un cercle alors on double son périmètre ; idem si on triple le diamètre, etc$\dots$ On a constaté que la circonférence d'un cercle est proportionnelle à son diamètre ; autrement dit il existe une constante qu'on appelle $\pi$ telle que le périmètre du cercle vaut :
$$ \pi\times d=2\pi r$$
avec $r$ la longueur du rayon et $d=2r$ celle du diamètre. Approximativement ce nombre vaut $\pi\simeq 3,14$. Précisément découvrir la valeur exacte de $\pi$ ou plutôt les décimales de $\pi$ a constitué un des défis majeurs des mathématiciens ; jusqu'en $1400$ on connaissait à peine $10$ décimales de $\pi$ ; vers $1700$ on en connaissait $100$ et en $2010$ en utilisant des ordinateurs on en connaissait aux alentours de $5000$ milliards$\dots$
Les formules utilisées pour découvrir de nouvelles décimales sont particulièrement complexes, citons par exemple l'une des formules du mathématicien indien Srinivasa Ramanujan :
$$ \dfrac{1}{\pi}=\dfrac{2\sqrt{2}}{9801}\sum_{k=0}^{\infty}\dfrac{(4k)!\left(1103+26390k\right)}{(k!)^4 396^{4k}}$$
\textbf{A retenir} : $\pi$ est un nombre irrationnel ; on ne peut donc pas l'écrire sous forme de fraction. Bien que $\pi$ paraisse très spécial, la plupart des nombres sont des nombres irrationnels tels que $\pi$ et c'est plutôt les nombres dont on a parlé plus tôt qui sont très spéciaux.
\textbf{Question non résolue} : On ne sait pas si $\pi$ est un nombre univers (un nombre univers est un nombre réel dans lequel on peut trouver n'importe quelle succession de chiffres de longueur finie).
\end{itemize}
\begin{exoi}\hfill \textbf{Des écritures différentes pour un même nombre}
Considérons $a=0,9999\dots=0,\underline{9}$. Le but de l'exercice est de démontrer que $a$ et $1$ sont \textbf{exactement} le même nombre. Ce résultat est particulièrement contre intuitif.
\begin{enumerate}
\item Démontrer que :
$$10a=9+a$$
\item Résoudre l'équation $10a=9+a$.
\item Conclure.
\end{enumerate}
\end{exoi}
\begin{exoi}
\begin{enumerate}
\item Effectuer les quatre opérations suivantes en moins de 20 secondes chacune :
$$3+\dfrac14 \qquad\qquad\qquad 5\times \dfrac23 \qquad \qquad\qquad \dfrac17 + \dfrac15 \qquad\qquad\qquad \dfrac34 \div \dfrac27$$
\item Compléter les égalités manquantes en moins de 30 secondes chacune.
$$4+ \hdots = 2 \times 6 \qquad \qquad\qquad 5- \hdots = -2 \times (-3)
\qquad\qquad\qquad 2+3\times \hdots = 4 \qquad \qquad \qquad 2x+5=x-2 + \hdots$$
\item Répondre à chaque problème posé en moins d'une minute chacun.
\begin{itemize}
\item Dans une classe de seconde, il y a 15 garçons et 20 filles. Les deux-tiers des garçons
et le quart des filles sont demi-pensionnaires. Combien y-a-t-il d'élèves de cette classe demi-pensionnaires ?
\item Dans un triangle rectangle en $C$, le côté $[AB]$ mesure 6 cm, le côté $[BC]$ mesure 5 cm.
Donner la valeur exacte de la longueur du côté $[AC]$.
\end{itemize}
\end{enumerate}
\end{exoi}
\begin{exoi}
\hfill \textbf{Somme et différence}\\
Trouver deux nombres entiers dont la somme vaut 281 et dont la diff\'erence vaut 111.
\end{exoi}
\begin{exoi}
\hfill \textbf{Division euclidienne}\\
La somme de deux entiers naturels $x$ et $y$ est 157. Dans la division euclidienne de $x$ par $y$,
le quotient vaut 6 et le reste 17. D\'eterminer $x$ et $y$.
\end{exoi}
\begin{exoi}
\begin{enumerate}
\item Écrire chacun des nombres suivants sous la forme d'une fraction irréductible :
\begin{multicols}{4}
\begin{enumerate}
\item $ \dfrac{1}{6}+\dfrac{1}{2}$
\item $ \dfrac{1}{\dfrac{1}{2}-\dfrac{1}{3} }$
\item $ \dfrac{1}{\dfrac{1}{3} }-\dfrac{1}{\dfrac{1}{5} }$
\item $ \dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+2} } }$
\end{enumerate}
\end{multicols}
\item \begin{enumerate}
\item La somme des inverses de deux nombres est-elle égale à l'inverse de la somme de ces deux nombres ?
\item La différence des inverses de deux nombres est-elle égale à l'inverse de la différence de ces deux nombres ?
\end{enumerate}
\end{enumerate}
\end{exoi}
\begin{exoi}
On donne $\sqrt{2}\simeq 1.41$ et $\sqrt{3}\simeq 1.73$. \hfill \textbf{Ordre de grandeur, sans calculatrice}
\begin{enumerate}
\item Pouvez-vous donner facilement (et sans calculatrice) un ordre de grandeur des valeurs suivantes ?
$$A=\sqrt{72}+\sqrt{32}-6\sqrt{8} \qquad \qquad B=\sqrt{\dfrac32} \qquad \qquad C=\dfrac{1}{1+\sqrt{3}}$$
\item \begin{enumerate}
\item Ecrire $A$ en fonction de $\sqrt{2}$. En déduire un ordre de grandeur de $A$.
\item Ecrire $B$ sous la forme d'une fraction de dénominateur $2$.
En déduire un ordre de grandeur de $B$.
\item Montrer que $C=\dfrac{\sqrt{3}-1}{2}$. En déduire un ordre de grandeur de $C$.
\end{enumerate}
% \item Donner alors un ordre de grandeur de $A$, $B$ et $C$.
\item Déterminer un ordre de grandeur des valeurs suivantes, après avoir changer leur écriture :
$$D=\sqrt{2}\times \sqrt{54} \qquad\qquad E=\sqrt{\dfrac43} \qquad\qquad
F=\dfrac{2}{1-\sqrt{3}} \qquad\qquad G=1+ \dfrac{1 }{ 1+ \dfrac{1}{1+\sqrt{3} } } $$
\item \textbf{Application} : Un triangle rectangle isocèle a son hypoténuse qui mesure 10 cm.\\
Déterminer un ordre de grandeur de la longueur des deux autres côtés
\end{enumerate}
\end{exoi}
\begin{exoi}
Tracer un segment d'une longueur quelconque, à l'aide uniquement de la règle non graduée et du compas, diviser ce segment en trois segments égaux. Expliquer votre démarche.
\end{exoi}
\begin{exoi}
\begin{enumerate}
\item Calculer $(3 \sqrt{5}-4)^2$ et $(2 \sqrt{6}-5)^2$
\item En déduire une autre écriture de $ \sqrt{61-24 \sqrt{5} } $ et $ \sqrt{49-20 \sqrt{6} }$
\end{enumerate}
\end{exoi}
\begin{exoi}
\hfill \textbf{Sans calculatrice}\\
Le but de cet exercice est de calculer le nombre suivant sans calculatrice :
$$A = 83\,875\,683\,470^2 – 83\,875\,683\,469 \times 83\,875\,683\,471 $$
\begin{enumerate}
\item On pose $a = 83\,875\,683\,470$. Exprimer $A$ en fonction de $a$, puis en simplifiant déterminer $A$.
\item Conclure.
\end{enumerate}
\end{exoi}
\begin{exoi}
Soit $p$ un nombre premier supérieur ou égal à $3$.\\
On pose :
$$ a=\dfrac{p+1}{2}\qquad \text{et}\qquad b=\dfrac{p-1}{2}$$
\begin{enumerate}
\item Donner la liste des $10$ plus petit nombres premiers.
\item Justifier que $a$ et $b$ sont des nombres entiers.
\item Calculer $a^2-b^2$ en fonction de $p$.
\item En déduire que tout nombre premier $p\geq 3$ peut s'écrire comme la différence de deux carrés d'entiers. \\
Donner cette différence pour $p=29$.
\end{enumerate}
\end{exoi}
\begin{exoi}
Démontrer que la somme de deux nombres rationnels est encore un nombre rationnel. Qu'en est-il de la somme de deux nombres irrationnels ?
\end{exoi}
\begin{exoi}
Un triangle a des côtés qui mesurent $x + 4$ cm, $x$ cm et $9$ cm.
Le côté de $x + 4$ cm est le côté le plus long.
Déterminer $x$ pour que ce triangle soit un triangle rectangle.
\end{exoi}
\begin{exoi}
La somme de cinq nombres entiers consécutifs vaut $1515$. Déterminer ces cinq nombres.
\end{exoi}
\begin{exoi}
Pour assister à un mach de foot, un groupe de 21 personnes a payé 90 $\euro$ de plus qu'un groupe de 12 personnes.
Sachant que toutes les places sont au même prix, quel est le prix, en euros, d'une place
\end{exoi}
\begin{exoi}
À ce jour, l'âge du capitaine est le double de celui de Fred. Dans 5 ans, ils auront à eux deux 70 ans. Quel est l'âge du capitaine ?
\end{exoi}
\begin{exoi}
La somme de trois nombres pairs consécutifs est égale à 378.\\
Quels sont ces trois nombres ?
\end{exoi}
\begin{exoi}
Dans une classe de 3e , deux septièmes des élèves apprennent l'allemand, la moitié des élèves apprennent l'espagnol, et les six restants apprennent l'italien.
Combien y a t-il d'élèves dans cette classe ?
\end{exoi}
\begin{exoi}
j'ai deux fois l'age que vous aviez lorsque j'avais l'age que vous avez. Lorsque vous aurez mon age, nous aurons à nous deux 63 ans. quel est mon age?
\end{exoi}
\pagebreak
\section{ Ensembles de nombres - Notations - Relations et Ensembles}
\subsection{Définition}
\begin{defi}
Un ensemble représente une collection d'objets. Les objets de la collection sont les éléments de l'ensemble. Un ensemble peut être constitué d'une infinité d'élements ou d'un nombre fini d'élément ou même d'aucun élément (c'est le cas de l'ensemble vide qui se note $\emptyset$).
\end{defi}
\Expl{Notons $E$ l'ensemble des trois derniers présidents de la république française.
On utilise les accolades pour écrire un ensemble ayant un nombre fini d'éléments ; ainsi :
$$ E=\{Hollande ; Sarkozy ; Chirac\}$$
Notons $F$ l'ensemble des deux derniers présidents (qui se revendiquent de droite) de la république française :
$$ F=\{Sarkozy ; Chirac\}$$
Enfin notons $G$ l'ensemble des deux derniers présidents (qui se revendiquent de gauche) de la république française :
$$ G=\{Mittérand ; Hollande\}$$
Pour signifier qu'un élément appartient ou non à un ensemble on utilise les symboles $\in$ et $\notin$.
Ainsi $Sarkozy \in E$ et $Sarkozy \notin G$ ou encore $Hollande \in E$ et $Hollande \notin F$.
}
\begin{defi}
Si tous les éléments d'un ensemble $E$ appartiennent aussi à un ensemble $F$ alors on dit que l'ensemble $E$ est contenu dans l'ensemble $F$, on écrit alors $E \subset F$. Dans le cas contraire on écrit $E\not\subset F$.
\end{defi}
\Expl{En reprenant l'exemple des présidents français on a par exemple $F\subset E$ et $G\not\subset E$.}
\subsection{Opération sur les ensembles}
\begin{defi}
Il est possible de réunir les ensembles $E$ et $F$ pour en former un nouveau $G$ ; on note alors :
$$ G = E\cup F$$
On lit $G$ est la réunion des ensembles $E$ et $F$.
\end{defi}
\Expl{En reprenant l'exemple des présidents français on a par exemple $E\cup G=\{Mittérand ; Hollande ; Sarkozy ; Chirac\}$.}
\begin{defi}
Les éléments commun à deux ensembles $E$ et $F$ forment un nouvel ensemble $G$ appelé intersection de $E$ et $F$ que l'on note :
$$E\cap G=F $$
\end{defi}
\Expl{En reprenant l'exemple des présidents français on a par exemple $E\cap G=\{Hollande \}$.}
\begin{defi}
Considérons l'ensemble $E$ et un ensemble $F$ contenu dans l'ensemble $E$, alors le contraire de l'ensemble $F$ dans $E$ est l'ensemble des éléments de $E$ qui ne sont pas dans $E$, on le note $\overline{F}$.
\end{defi}
\Expl{Soit $E$ l'ensemble des $32$ cartes d'un jeu classique ; $F$ l'ensemble des piques et $G$ l'ensemble des rois alors le contraire de $F$ dans $E$ est l'ensemble $\overline{F}$ des coeurs, des carreaux et des trèfles et le contraire de $G$ dans $E$ est l'ensemble $\overline{G}$ des $28$ cartes du paquet qui ne sont pas des rois.}
\begin{exoi}
On considère l'ensemble $E$ des nombres entiers naturels inférieur ou égal à $30$ et l'ensemble $F$ des nombre premier inférieur ou égaux à $30$.
\begin{enumerate}
\item Combien d'éléments contient $E$ ? Lister les éléments de $F$ et compléter $F\dots E$.
\item Soit $G$ l'ensemble des nombres pairs inférieurs ou égaux à $30$ ; donner le contraire de $G$ dans $E$.
\item Donner $G\cap F$ et $G\cup F$.
\end{enumerate}
\end{exoi}
\pagebreak
\subsection{Ensemble de nombre}
Pour noter les ensembles de nombres on utilise des lettres de l'alphabet que l'on écrit avec une double barre comme l'ensemble des nombres réels $\R$. Ces ensembles sont particuliers car ils possèdent une infinité d'éléments.
\Cadre{\textbf{Notations} : \newline
L'ensemble des nombres entiers positifs ou nuls se note $\N$. On a $\N=\{0;1;2;3;4;5;...\}$. Les \'el\'ements de $\N$ sont les entiers naturels. \newline
L'ensemble des entiers positifs et n\'egatifs se note $\Z$. On a $\Z=\{\dots; -4;-3;-2;0;1;2;3;\dots\}$.
Les \'el\'emlents de $\Z$ sont les entiers relatifs.\newline
L'ensemble des nombres pouvant s'\'ecrire comme le quotient de deux entiers se note $\Q$. On a
$\Q=\left\{\dfrac{a}{b} \, \textrm{ o\`u } \, a\in\Z \,et\, b\in \Z^*\right\}$. Les \'el\'ements de $\Q$ sont les nombres rationnels.\newline
L'ensemble des nombres connus en seconde (rationnels et irrationnels) s'appelle l'ensemble des nombres r\'eels. On note $\R$ cet ensemble.\newline
$$\N \subset \Z \subset \Q \subset \R$$
}
\subsection{Quantificateur}
Pour exprimer qu'une proposition est vraie quelque soit le nombre réel $x$ on utilise le quantificateur universel $\forall$ qui signifie pour tout ou quelque soit et on écrit :
$$ \forall x\in \R, \quad x+2>x$$
On lit : Quelque soit le nombre réel $x$ alors $x+2$ est strictement supérieur à $x$.
Pour exprimer qu'une proposition est vraie pour au moins un nombre réel $x$ on utilise le quantificateur existentiel $\exists$ qui signifie \og il existe au moins \fg.
$$\exists x \in \Q, 100\times x \in \N $$
Cette phrase se traduit par : \og Il existe au moins un nombre rationnel tel que multiplier par $100$ ce nombre soit un entier naturel \fg{}.
En effet c'est le cas de $x=2,51=\dfrac{251}{100}$ puisque $100\times 2,51=251$ est un entier naturel.
Une autre phrase qui mélange les deux quantificateurs :
$$ \exists x \in \R, \forall p\in \N \text{ et } \forall q\neq 0 \in \Z \text{on a }x\neq \dfrac{p}{q}$$
Une traduction : \og Il existe au moins un nombre réel qui ne pas être écrit sous forme de fraction d'entier.\fg{} C'est par exemple le cas de $\sqrt{2}$ ou de $\pi$.
\pagebreak
\begin{exoi}
Traduire les propositions mathématiques en français puis dire si elles sont vraies ou fausses :\\
$\forall$ signifie pour tout ou quelque soit ; $\exists$ signifie il existe.
\begin{enumerate}
\item $\forall x\in \Z$ alors $x>0$.
\item Soit $x\in \R$. Si $x^2 \in \N$ alors $x\in \N$.
\item Si $x\in \R$ alors $x^2\geq 0$.
\item $\forall x\in \Q$ et $\forall y \in \N$ alors $x+y\in \N$.
\end{enumerate}
\end{exoi}
\begin{exoi}
Traduire les propositions écrites en français en langage mathématiques dans le cas où elles sont vraies, dans le cas contraire corriger ses propositions et les écrire en langage mathématiques:
\begin{enumerate}
\item Quelque soit le nombre réel $x$ alors il existe un nombre réel $y$ tel que $x+y=0$.
\item Quelque soit le nombre réel $x$ alors il existe un nombre réel $y$ tel que $x\times y=1$.
\item Soit $x$ un nombre réel strictement supérieur à $2$ alors $2-x$ est strictement supérieur à $0$.
\item L'ensemble des nombres premiers $\P$ est contenu dans l'ensemble des nombres rationnels.
\end{enumerate}
\end{exoi}
\pagebreak
\section{Intervalle de $\R$}
\subsection{Définition}
\begin{defi}
Soient $a$ et $b$ deux r\'eels tels que $a<b$. \newline
L'ensemble des r\'eels $x$ tels que $a\leq x \leq b$ est appel\'e \textbf{intervalle ferm\'e} de $\R$. On le note $[a;b]$.\newline
$a$ et $b$ sont les bornes de l'intervalle $[a;b]$.
\end{defi}
\Rq{
On dit qu'un intervalle est born\'e si et seulement si ses deux bornes sont finies (ie r\'eels).
}\vspace*{-5mm}
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
In\'egalit\'e & Repr\'esentation graphique & Intervalle born\'e & D\'enomination \\ \hline
$a \leq x \leq b$ & & & \\ &&&\\\hline
& & & Intervalle ouvert \\&&&\\\hline
& & & Intervalle semi-ouvert \\
& & & \`a droite \\\hline
& & & Intervalle semi-ouvert \\
& & & \`a gauche \\\hline
\end{tabular}
\vspace{0.5cm}
\begin{tabular}{|c|c|c|c|}
\hline
In\'egalit\'e & Repr\'esentation graphique & Intervalle & D\'enomination \\ \hline
$x \geq a$ & & $[a;+\infty [$ & Intervalle ferm\'e \\&&&\\ \hline
& & $]a;+\infty [$ & \\&&&\\\hline
& & & \\&&&\\\hline
& & & \\&&&\\\hline
\end{tabular}
\end{center}
\Rq{ On note :\begin{multicols}{3}
\begin{itemize}
\item $\R^+=[0;+\infty[$
\item $\R^-=]-\infty;0]$
\item $\R^*=\R\smallsetminus {0}$
\item $\R^{+*}=]0;+\infty[$
\item $\R^{-*}=]-\infty;0[$
\item $\R=]-\infty;+\infty[$
\end{itemize}
\end{multicols}
}
\Expls{\begin{enumerate}
\item Donner les intervalles correspondant aux in\'egalit\'es suivantes:
$$-6\leq x \leq 7 \qquad\qquad -5<x \qquad\qquad x\leq 3 $$
\item Donner les in\'egalit\'es correspondant aux intervalles suivants :
$$\left] \dfrac{1}{3} ; \sqrt{7} \right] \qquad \qquad \left[ -\sqrt{5};+\infty\right[ $$
\end{enumerate}
}
\subsection{Manipulation d'inégalité}
\begin{exoi}\begin{enumerate}
\item Supposons que $x\in [1;5]$ et $y\in[2;7]$. Encadrer $xy$, $x+y$, $x-y$ et $\dfrac{x}{y}$.
\item Dans chacun des cas suivants donner l'intervalle dans lequel se situe le nombre $x$ :
\begin{multicols}{3}
\begin{enumerate}
\item $2\leq 2x+3\leq 7$
\item $-3x+1\leq 7$
\item $-4x+\dfrac{1}{2}>\dfrac{7}{3}$
\item $x(x+2)<x^2$
\item $-1\leq -x+1<8$
\item $x^2>4$
\end{enumerate}
\end{multicols}
\end{enumerate}
\end{exoi}
\end{document}
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https://alco.centre-mersenne.org/article/10.5802/alco.175/file/src/tex/ALCO_2021__4_4_683_0.tex
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\documentclass[ALCO,ThmDefs,Unicode,epreuves,published]{cedram}
\OneNumberAllTheorems
\usepackage{pict2e}
\usepackage{amscd,euscript,tikz}
\DeclareMathOperator{\Hom}{Hom}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%% a placer avant \begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand*{\Alphenumi}{\renewcommand*{\theenumi}{\Alph{enumi}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% Auteur
%%%1
\author{\firstname{Sergey} \lastname{Fomin}}
\address{Department of Mathematics\\
University of Michigan\\
Ann Arbor\\
MI 48109, USA
}
\email{[email protected]}
%%%2
\author
{\firstname{Kiyoshi} \lastname{Igusa}}
\address{Department of Mathematics\\
Brandeis University\\
Waltham\\
MA 02454, USA}
\email{[email protected]}
%%%%3
\author
{\firstname{Kyungyong} \lastname{Lee}}
\address{Department of Mathematics\\
University of Alabama\\
Tuscaloosa\\
AL 35487, USA;}
%School of Mathematics\\
\curraddr{Korea Institute for Advanced Study\\
Seoul \\
02455, Republic of Korea}
\email{[email protected]; [email protected]}
\thanks{Partially supported by NSF grants DMS-1664722 and DMS-1800207
as well as by the Simons Foundation.}
%%%%% Sujet
\keywords{Quiver mutation, universal quiver, cluster algebra.}
\subjclass{13F60, 05C25, 05E16, 16G20, 18G80}
%%%%% Gestion
\DOI{10.5802/alco.175}
\datereceived{2020-08-04}
\daterevised{2021-03-08}
\dateaccepted{2021-04-11}
%%%%% Titre et résumé
\title[Universal quivers]{Universal quivers}
\begin{abstract}
We show that for any positive integer $n$,
there exists a quiver $Q$ with $O(n^2)$ vertices and $O(n^2)$ edges
such that any quiver on $n$ vertices is a full subquiver
of a quiver mutation equivalent to $Q$.
We generalize this statement to skew-symmetrizable matrices,
and obtain other related results.
\end{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\datepublished{2021-08-17}
\begin{document}
\maketitle
\section{Introduction}
Quivers and their mutations play a fundamental role in the combinatorial theory of cluster algebras~\cite{FWZ, ca1}. Among the various properties that a quiver may possess, one is especially interested in those which are both \emph{mutation-invariant} and \emph{hereditary}, \ie preserved both by quiver mutations and by restriction to a full subquiver.
A quiver~$Q$ (without frozen vertices) is called
\emph{$n$-universal} if any quiver on $n$ vertices is a full subquiver of a quiver which is mutation equivalent to~$Q$.
Our interest in this notion stems from the following simple remark. Let $P$ be a mutation-invariant and hereditary property of quivers. Then, in order to prove that any $n$-vertex quiver possesses property~$P$, it is sufficient to establish~$P$ for a single $n$-universal quiver.
It is not at all obvious that $n$-universal quivers exist, even for small values of~$n$.
(For any $n\ge 2$, there are infinitely many mutation classes of $n$-vertex quivers.)
It~turns out that not only they do exist, but some of them are not too big.
Our main result, presented in~Section~\ref{sec:constructing-universal-quivers}, is an explicit combinatorial construction that produces, for any~$n$, an $n$-universal quiver with $2n^2-n$ vertices and $7n^2-7n$ arrows.
We demonstrate that some seemingly ``tame'' classes of quivers include universal quivers (which can be regarded as ``totally wild'').
For any~$n$, there is an $n$-universal quiver on $O(n^2)$ vertices in which each vertex is incident to at most three arrows.
We also construct a \emph{planar} $n$-universal quiver with $O(n^4)$ vertices and $O(n^4)$ arrows.
This enables us to show in Section~\ref{sec:quivers-plabic} that any quiver can be embedded
into a quiver mutation equivalent to a quiver of a \emph{plabic graph}.
We note that the analogue of this statement for \emph{reduced} plabic graphs is false,
see Remark~\ref{rem:reduced-plabic-not-universal}.
In Section~\ref{sec:universal-matrices}, we extend our main result to skew-symmetrizable matrices and their mutations. The construction is largely the same, with some technical adjustments.
Potential applications of these results and concepts are discussed
in the last two sections.
In Section~\ref{sec:hereditary+universal}, we clarify the relationship between hereditariness and universality,
and illustrate it using such hereditary properties as
Laurent positivity and sign-coherence of $c$-vectors.
In Section~\ref{sec:categorification},
we show that the $2$-universal quivers constructed in
Section~\ref{sec:constructing-universal-quivers}
do not allow any Hom-finite additive categorifications.
\section{Constructing universal quivers}
\label{sec:constructing-universal-quivers}
We begin by reviewing the relevant background on quiver mutations and mutation classes, generally following~\cite[Sections~2.1, 2.6, 4.1]{FWZ}.
Here and in Section~\ref{sec:universal-matrices},
we work with quivers without frozen vertices; so the definitions are slightly simpler than usual.
\begin{definition}
\label{def:quiver-mutation}
A \emph{quiver} is a finite oriented graph with no loops or oriented $2$-cycles. The oriented edges of a quiver are called \emph{arrows}. For any vertex $v$ in a quiver~$Q$, the (quiver) \emph{mutation} $\mu_v$ transforms $Q$ into another quiver $Q'=\mu_v(Q)$ on the same vertex set, by performing the following three steps:
\begin{itemize} %[leftmargin=.3in]
\item
for each oriented path $u\to v\to w$ passing through~$v$, add a new arrow
$u\to w$;
\item
reverse all arrows incident to~$v$;
\item
repeatedly remove oriented 2-cycles until there are none left.
\end{itemize}
\end{definition}
It is easy to see that quiver mutation is an involution: $\mu_v(\mu_v(Q))=Q$.
A simple example is shown in Figure~\ref{fig:quiver-mutation}.
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=1.2]
\coordinate (A) at (1.75,0);
\coordinate (A1) at (2.05,.08);
\coordinate (A2) at (2.05,-.08);
%
\coordinate (Ap) at (2,.25);
\coordinate (B) at (3.25,1.5);
\coordinate (B1) at (3.25,.3);
\coordinate (B2) at (3.25,-.3);
%
\coordinate (Bp) at (3.5,1.25);
\coordinate (Bl) at (3,1.25);
\coordinate (C) at (4.75,0);
\coordinate (C1) at (4.45,0.08);
\coordinate (C2) at (4.45,-.08);
%
\coordinate (Cl) at (4.5,.25);
\coordinate (L1) at (2.25,1);
\coordinate (L2) at (4.25,1);
%\node at (L1) {$1$};
%\node at (L2) {$1$};
\node at (A) {$u$};
\draw (A) circle [radius=0.2];
\draw[->](Ap)--(Bl);
\node at (B) {$v$};
\draw (B) circle [radius=0.2];
\draw[->](Bp)--(Cl);
%\draw[->](3.5,-0.1)--(4.5,-0.1);
\node at (C) {$w$};
\draw (C) circle [radius=0.2];
\draw[->](C1)--(A1);
\draw[->](C2)--(A2);
\end{tikzpicture}
\qquad\qquad
\begin{tikzpicture}
\coordinate (A) at (1.75,0);
\coordinate (A1) at (2.05,0);
\coordinate (A2) at (2.05,-.08);
%
\coordinate (Ap) at (2,.25);
\coordinate (B) at (3.25,1.5);
\coordinate (B1) at (3.25,.3);
\coordinate (B2) at (3.25,-.3);
%
\coordinate (Bp) at (3.5,1.25);
\coordinate (Bl) at (3,1.25);
\coordinate (C) at (4.75,0);
\coordinate (C1) at (4.45,0);
%
\coordinate (Cl) at (4.5,.25);
\coordinate (L1) at (2.25,1);
\coordinate (L2) at (4.25,1);
%\node at (L1) {$1$};
%\node at (L2) {$1$};
\node at (A) {$u$};
\draw (A) circle [radius=0.2];
\draw[<-](Ap)--(Bl);
\node at (B) {$v$};
\draw (B) circle [radius=0.2];
\draw[<-](Bp)--(Cl);
%\draw[->](3.5,-0.1)--(4.5,-0.1);
\node at (C) {$w$};
\draw (C) circle [radius=0.2];
\draw[->](C1)--(A1);
\end{tikzpicture}
\caption{Quiver mutation. Applying mutation $\mu_v$ to each of the two quivers shown above produces the other quiver.}
\label{fig:quiver-mutation}
\end{figure}
\begin{definition}
Two quivers $Q$ and $Q'$ are \emph{mutation equivalent} (denoted $Q\sim Q'$) if~$Q$ can be transformed into a quiver isomorphic to~$Q'$ by a sequence of mutations.
Mutation equivalence is an equivalence relation on the set of quivers (viewed up to isomorphism). Equivalence classes for this relation are called \emph{mutation classes}. We~denote by $[Q]$ the mutation class of a quiver~$Q$. Thus $[Q]$ consists of all (isomorphism types of) quivers mutation equivalent to~$Q$.
\end{definition}
\begin{remark}[{\cf \cite[Problem~2.6.14]{FWZ}}]
There is no known algorithm for detecting whether a given pair of quivers (with the same number of vertices) are mutation equivalent to each other. Note that exhaustive search of all possible mutation scenarios does not qualify, since there is no known \emph{a~priori} upper bound on the depth of a successful search.
\end{remark}
\begin{definition}
\label{def:full-subquiver}
Let $Q$ be a quiver, and $I$ a subset of the set of its vertices. The \emph{restriction} of $Q$ to~$I$, denoted~$Q_I$, is the induced subgraph of $Q$ supported on the vertex set~$I$. In other words, take $I$ as the new set of vertices, and keep all the arrows of~$Q$ which connect vertices in~$I$ to each other. Any quiver that can be obtained from~$Q$ by such a restriction is called a \emph{full subquiver} of~$Q$.
\end{definition}
%\pagebreak[3]
The following statement is well known, and easy to check.
\begin{lemma}
\label{lem:restriction-mutation}
Restriction commutes with mutation. More precisely, if $Q_I$ is a full sub\-quiver of~$Q$, and $v$ is a vertex in~$I$, then $\mu_v(Q_I)=(\mu_v(Q))_I$.
\end{lemma}
Lemma~\ref{lem:restriction-mutation} implies that any quiver in
$[Q_I]$ is a full subquiver of a quiver in~$[Q]$.
%\medskip
We are now ready to introduce the main new concept of this paper.
\begin{definition}
\label{def:n-universal}
Let $n\ge 2$ be an integer.
A~quiver $Q$ is called \emph{$n$-universal}
if every quiver on $n$ vertices is a full subquiver of a quiver mutation equivalent to~$Q$.
\end{definition}
If a quiver is $n$-universal, then it is also $m$-universal for any $m\le n$.
\begin{example}
The special case $n=2$ of Definition~\ref{def:n-universal} is the easiest one (but still important). A~quiver is $2$-universal if for any nonnegative integer~$k$, the given quiver can be mutated into a quiver containing two vertices connected by $k$ ``parallel'' arrows.
%
Figure~\ref{fig:2-universal-quiver} shows an example of a 2-universal quiver on $3$~vertices.
\end{example}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=1,line width=0.6pt]
\node at (1.75,0) {1};
\draw (1.75,0) circle [radius=0.25];
\draw[->](2.1,0)--(2.9,0);
\node at (3.25,0) {2};
\draw (3.25,0) circle [radius=0.25];
\draw[->](3.6,0.1)--(4.4,0.1);
\draw[->](3.6,-0.1)--(4.4,-0.1);
\node at (4.75,0) {3};
\draw (4.75,0) circle [radius=0.25];
\end{tikzpicture}
\caption{A $2$-universal quiver. The mutation sequence $\mu_2,\mu_3,\mu_2,\mu_3,...$ produces every quiver on 2~vertices as a full subquiver supported either on the vertices 1~and~2, or on the vertices 1 and~3.}\label{fig:2-universal-quiver}
\end{figure}
\begin{remark}
We are not aware of any algorithm for deciding whether a given quiver~$Q$ is $2$-universal, or whether $Q$ can be mutated to a quiver containing a pair of vertices connected by $k$ parallel arrows, \cf \cite[Remark~4.1.13]{FWZ}. For larger values of~$n$, the problem of detecting $n$-universality seems harder yet.
\end{remark}
A quiver~$Q$ has \emph{finite mutation type} if its mutation class $[Q]$ is finite; in other words, there are finitely many (pairwise non-isomorphic) quivers mutation equivalent~to~$Q$.
\begin{example}
\label{example:grid-quivers}
Any quiver of finite mutation type is \underbar{not} $2$-universal. One example of such a quiver is the \emph{grid quiver} $A_2\boxtimes A_5$, shown in Figure~\ref{fig:grid} on the left. On the other hand, the grid quiver $A_2\boxtimes A_6$ (see Figure~\ref{fig:grid} on the right) is $2$-universal, as it can be mutated to a quiver that restricts to the quiver from Figure~\ref{fig:2-universal-quiver}.
\end{example}
\begin{figure}[ht]\centering
\setlength{\unitlength}{3.2pt}
\begin{picture}(40,10)(0,0)
\multiput(0,0)(10,0){5}{\circle*{1.5}}
\multiput(0,10)(10,0){5}{\circle*{1.5}}
\thicklines
\multiput(2,0)(20,0){2}{\vector(1,0){6}}
\multiput(18,0)(20,0){2}{\vector(-1,0){6}}
\multiput(12,10)(20,0){2}{\vector(1,0){6}}
\multiput(8,10)(20,0){2}{\vector(-1,0){6}}
\multiput(10,2)(20,0){2}{\vector(0,1){6}}
\multiput(0,8)(20,0){3}{\vector(0,-1){6}}
\end{picture}
\qquad\qquad
\begin{picture}(50,10)(0,0)
\multiput(0,0)(10,0){6}{\circle*{1.5}}
\multiput(0,10)(10,0){6}{\circle*{1.5}}
\thicklines
\multiput(2,0)(20,0){3}{\vector(1,0){6}}
\multiput(18,0)(20,0){2}{\vector(-1,0){6}}
\multiput(12,10)(20,0){2}{\vector(1,0){6}}
\multiput(8,10)(20,0){3}{\vector(-1,0){6}}
\multiput(10,2)(20,0){3}{\vector(0,1){6}}
\multiput(0,8)(20,0){3}{\vector(0,-1){6}}
\end{picture}
\caption{The grid quivers $A_2\boxtimes A_5$ and $A_2\boxtimes A_6$.}
\label{fig:grid}
\end{figure}
\begin{remark}
\label{rem:grid-not-3-universal}
The grid quiver $A_k\boxtimes A_\ell$ is \underbar{not} $3$-universal for any $k$ and~$\ell$. The reasons will be explained in Proposition~\ref{prop:grid-no-markov}.
\end{remark}
A quiver is \emph{acyclic} if it does not contain oriented cycles.
A quiver is called \emph{mutation-acyclic} if it can be mutated to an acyclic quiver.
\begin{remark}
\label{rem:acyclic-not-3-universal}
Any mutation-acyclic quiver $Q$ is \underbar{not} $3$-universal, for the following reason. It has been shown in~\cite{BMR} that a full subquiver of a mutation-acyclic quiver is mutation-acyclic. If $Q$ were $3$-universal, then any $3$-vertex quiver would be a full subquiver of a quiver in~$[Q]$, and consequently would have to be mutation-acyclic. This contradicts the well known fact that some 3-vertex quivers are not mutation-acyclic. One easy example is the \emph{Markov quiver}, see Figure~\ref{fig:Markov-quiver}. %~\cite[Example~2.6.4]{FWZ}.
\end{remark}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=0.9,line width=0.6pt]
\draw (0,0) circle [radius=0.2];
\draw[->](0.4,0.09)--(1.6,0.09);
\draw[->](0.4,-0.09)--(1.6,-0.09);
\draw (2,0) circle [radius=0.2];
\draw (1,1.73) circle [radius=0.2];
%\draw[<-](1.2,1.38)--(1.8,0.35);
\draw[<-](1.12,1.33)--(1.72,0.30);
\draw[<-](1.28,1.43)--(1.88,0.40);
\draw[->](0.88,1.33)--(0.28,0.30);
\draw[->](0.72,1.43)--(0.12,0.40);
\end{tikzpicture}
\caption{The Markov quiver. }
\label{fig:Markov-quiver}
\end{figure}
The following is our main result.
\begin{theorem}
\label{thm:main-thm-quivers}
For any integer $n\ge 2$, there exists an $n$-universal quiver with $2n^2-n$ vertices and $7n^2-7n$ arrows.
\end{theorem}
The proof of Theorem~\ref{thm:main-thm-quivers} relies on two key lemmas.
\begin{lemma}
\label{lem:gluing}
Let $Q$ be a quiver with $k+2$ vertices, including vertices $u$ and~$v$, and $\ell$ arrows. Assume that for any nonnegative (resp., negative) integer~$m$, there exists a sequence of mutations, none of them at $u$ or~$v$, which transforms~$Q$ into a quiver that has exactly $m$ arrows directed from $u$ to~$v$ (resp., $|m|$ arrows directed from~$v$~to~$u$). %\linebreak
Then for any $n$, there is an $n$-universal quiver with $n+k\binom{n}{2}$ vertices and $\ell\binom{n}{2}$ arrows.
\end{lemma}
\begin{proof}
We construct the desired $n$-universal quiver $\overline Q$ by amalgamating (gluing) $\binom{n}{2}$ copies of the quiver~$Q$.
We start with a totally disconnected quiver $Q_\bullet$ with $n$ vertices and no arrows.
We then take $\binom{n}{2}$ disjoint copies of~$Q$, denoted $Q_{\{i,j\}}$, where $\{i,j\}$ runs over all $2$-element subsets of vertices in~$Q_\bullet$.
In each of these copies, we mark the two vertices corresponding to the special vertices $u$ and $v$ in the original quiver~$Q$.
Now, for each pair of vertices $i,j$ in~$Q_\bullet$, we glue $Q_{\{i,j\}}$ to~$Q_\bullet$ by identifying $i$ and~$j$ with the marked vertices in~$Q_{\{i,j\}}$. (Any of the two possible identifications would work: either glue $i$ to~$u$ and $j$ to~$v$, or the other way around.) The resulting quiver $\overline Q$ will have $n+k\binom{n}{2}$ vertices and $\ell\binom{n}{2}$ arrows. It is not hard to see that $\overline Q$ is \hbox{$n$-universal}; in fact, any $n$-vertex quiver can be obtained by restricting a quiver in $[\overline Q]$ to the vertex set of~$Q_\bullet$. To see that, note that for any pair $i,j$ of vertices in~$Q_\bullet$, we can achieve the desired number of arrows between $i$ and~$j$ (with the desired direction) by performing mutations at the unmarked vertices in~$Q_{\{i,j\}}$. Moreover these mutations will not interact across different copies~$Q_{\{i,j\}}$ because there are no arrows connecting unmarked vertices from different copies to each other.
\end{proof}
%\pagebreak[3]
\begin{lemma}
\label{lem:6-vertex-quivers}
Each of the two quivers shown in Figures~\ref{fig:extended-somos-4}
and~\ref{fig:double-4-cycle}
satisfies the conditions in Lemma~\ref{lem:gluing}, for the vertices $u$ and~$v$ indicated in the drawings.
\end{lemma}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=1,line width=0.6pt]
\node at (0,4) {$u$};
\draw (0,4) circle [radius=0.25];
\node at (2,4) {$v$};
\draw (2,4) circle [radius=0.25];
\node at (0,0) {1};
\draw (0,0) circle [radius=0.25];
\node at (0,2) {2};
\draw (0,2) circle [radius=0.25];
\node at (2,2) {3};
\draw (2,2) circle [radius=0.25];
\node at (2,0) {4};
\draw (2,0) circle [radius=0.25];
\draw[->](0,2.4)--(0,3.6);
\draw[->](2,2.4)--(2,3.6);
\draw[->](0.3,3.7)--(1.7,2.3);
\draw[<-](0.3,2.3)--(1.7,3.7);
\draw[<-](0,0.4)--(0,1.6);
\draw[->](2,0.4)--(2,1.6);
\draw[<-](0.4,0)--(1.6,0);
\draw[->](0.3,0.2)--(1.8,1.7);
\draw[->](0.2,0.3)--(1.7,1.8);
\draw[->](0.3,1.8)--(1.8,0.3);
\draw[->](0.2,1.7)--(1.7,0.2);
\draw[<-](0.4,2)--(1.6,2);
\draw[<-](0.4,2.13)--(1.6,2.13);
\draw[<-](0.4,1.87)--(1.6,1.87);
\end{tikzpicture}
\caption{The extended Somos-4 quiver.}
\label{fig:extended-somos-4}
\end{figure}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=1,line width=0.6pt]
\node at (1,2) {$u$};
\draw (1,2) circle [radius=0.25];
\node at (3,2) {$v$};
\draw (3,2) circle [radius=0.25];
\node at (0,0) {4};
\draw (0,0) circle [radius=0.25];
\node at (0,4) {1};
\draw (0,4) circle [radius=0.25];
\node at (4,4) {2};
\draw (4,4) circle [radius=0.25];
\node at (4,0) {3};
\draw (4,0) circle [radius=0.25];
\draw[->] (-0.08,0.4)--(-0.08,3.6);
\draw[->](0.08,0.4)--(0.08,3.6);
\draw[<-](3.92,0.4)--(3.92,3.6);
\draw[<-](4.08,0.4)--(4.08,3.6);
\draw[<-](0.4,-0.08)--(3.6,-0.08);
\draw[<-](0.4,0.08)--(3.6,0.08);
\draw[->](0.4,3.92)--(3.6,3.92);
\draw[->](0.4,4.08)--(3.6,4.08);
\draw[->](0.18,0.36)--(0.82,1.64);
\draw[<-](0.18,3.64)--(0.82,2.36);
\draw[->](3.82,0.36)--(3.18,1.64);
\draw[<-](3.82,3.64)--(3.18,2.36);
\draw[<-](0.3,0.2)--(2.7,1.8);
\draw[->](0.3,3.8)--(2.7,2.2);
\draw[->](3.7,3.8)--(1.3,2.2);
\draw[<-](3.7,0.2)--(1.3,1.8);
\end{tikzpicture}
\caption{Another quiver on 6 vertices satisfying the conditions in Lemma~\ref{lem:gluing}. }
\label{fig:double-4-cycle}
\end{figure}
\begin{proof}
The proof relies on straightworward but tedious calculations, preferably done using one of the widely available software packages for quiver mutations~\cite{keller-applet, musiker-stump}.
For the quiver shown in Figure~\ref{fig:extended-somos-4}, repeatedly apply the mutations~at the vertices labeled $1,2,3,4,1,2,3,4,1,2,3,4,\dots$
(in this order). Computations show that the resulting quivers have the following number of arrows directed from $v$ to~$u$:
\begin{equation}
\label{eq:0011111...}
0, 0, \underbrace{1,1,\dots,1,1}_{12},2,2,2,\underbrace{3,3,\dots,3,3}_{12},4,4,4,\underbrace{5,5,\dots,5,5}_{12},6,6,6,\dots
\end{equation}
(the leftmost entry corresponds to the original quiver).
After 60 mutations, we recover the original quiver, with additional 8~arrows directed from $v$ to~$u$, and the process continues. To get the opposite orientation, \ie arrows directed from $u$ to~$v$, take the original quiver and apply mutations at the vertices $4,3,2,1,4,3,2,1,4,3,2,1,\dots$ (in this order).
In the resulting quivers, the number~of arrows directed from $u$ to~$v$ will again be given by the sequence~\eqref{eq:0011111...}, and we are~done.
%\pagebreak[3]
For the quiver shown in Figure~\ref{fig:double-4-cycle}, repeatedly apply the mutations~at the vertices labeled $1,3,2,4,1,3,2,4,1,3,2,4,\dots$ (in this order). The resulting quivers have the following number of arrows directed from $u$ to~$v$:
\begin{equation}
\label{eq:00112334...}
%0,0,1,1,2,3,3,4,4,4,5,5,6,7,7,8,8,8,\dots
0,1,2,3,4,5,6,7,8,9,\dots
\end{equation}
(the first~0 corresponds to the original quiver).
The quiver obtained after the first 4~mutations differs from the original quiver by having extra 4~arrows $u\!\longrightarrow \!v$, so the pattern continues. To get the opposite orientation, with arrows directed from $v$ to~$u$, apply mutations at the vertices $4,2,3,1,4,2,3,1,4,2,3,1,\dots$ (in this order) to the original quiver.
In the resulting quivers, the number~of arrows $v\!\longrightarrow \!u$ will again be given by the sequence~\eqref{eq:00112334...}, and we are~done.
\end{proof}
%\pagebreak[3]
\begin{remark}
Restricting the quiver shown in Figure~\ref{fig:extended-somos-4} to the vertex set $\{1,2,3,4\}$ yields the \emph{Somos-4} quiver, see, \eg \cite[Section~7.1]{marsh-lectures}.
The same restriction applied to the quiver shown in Figure~\ref{fig:double-4-cycle} produces the product $A_1^{(1)}\boxtimes A_1^{(1)}$ of two Kronecker quivers of affine type~$A_1$. Both $4$-vertex quivers are closely related to discrete integrable systems. We~do not know whether this relationship is purely coincidental, or is a sign of some connection between universality and integrability.
\end{remark}
\begin{proof}[Proof of Theorem~\ref{thm:main-thm-quivers}]
The theorem directly follows from Lemmas~\ref{lem:gluing} and~\ref{lem:6-vertex-quivers}.
The quiver shown in Figure~\ref{fig:extended-somos-4} has $6$~vertices and $14$~arrows. Applying (the construction in) Lemma~\ref{lem:gluing} with $k=4$ and $\ell=14$, we obtain an $n$-universal quiver with $n+4\binom{n}{2}=2n^2-n$ vertices and $14\binom{n}{2}=7n^2-7n$ arrows.
An example for $n=3$ is shown in Figure~\ref{fig:3-universal}.
\end{proof}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=1,line width=0.6pt]
%\node at (0,4) {$u$};
\draw (0,4) circle [radius=0.15];
%\node at (2,4) {$v$};
\draw (2,4) circle [radius=0.25];
\node at (0,0) {1};
\draw (0,0) circle [radius=0.25];
\node at (0,2) {2};
\draw (0,2) circle [radius=0.25];
\node at (2,2) {3};
\draw (2,2) circle [radius=0.25];
\node at (2,0) {4};
\draw (2,0) circle [radius=0.25];
\draw[->](0,2.4)--(0,3.6);
\draw[->](2,2.4)--(2,3.6);
\draw[->](0.3,3.7)--(1.7,2.3);
\draw[<-](0.3,2.3)--(1.7,3.7);
\draw[<-](0,0.4)--(0,1.6);
\draw[->](2,0.4)--(2,1.6);
\draw[<-](0.4,0)--(1.6,0);
\draw[->](0.3,0.2)--(1.8,1.7);
\draw[->](0.2,0.3)--(1.7,1.8);
\draw[->](0.3,1.8)--(1.8,0.3);
\draw[->](0.2,1.7)--(1.7,0.2);
\draw[<-](0.4,2)--(1.6,2);
\draw[<-](0.4,2.13)--(1.6,2.13);
\draw[<-](0.4,1.87)--(1.6,1.87);
\draw[red] (2,4) circle [radius=0.15];
\draw[red] (3.73,5) circle [radius=0.25];
\draw[red] (5.46,6) circle [radius=0.25];
\draw[red] (1,5.73) circle [radius=0.25];
\draw[red] (2.73,6.73) circle [radius=0.25];
\draw[red] (4.46,7.73) circle [radius=0.25];
\node[red] at (3.73,5) {2};
\node[red] at (5.46,6) {1};
\node[red] at (2.73,6.73) {3};
\node[red] at (4.46,7.73) {4};
\draw[red,<-](2.346,4.2)--(3.384,4.8);
\draw[red,->](4.076,5.2)--(5.114,5.8);
\draw[red,<-](1.346,5.92)--(2.384,6.53);
\draw[red,<-](3.076,6.92)--(4.114,7.53);
\draw[red,->](2.1,4.36)--(2.63,6.37);
\draw[red,->](1.36,5.63)--(3.37,5.1);
\draw[red,->](2.93,6.39)--(3.53,5.346);
\draw[red,->](2.815,6.32)--(3.415,5.276);
\draw[red,->](3.045,6.46)--(3.645,5.416);
%\draw[red,->](3.83,5.36)--(4.36,7.37);
\draw[red,->](3.76,5.38)--(4.29,7.39);
\draw[red,->](3.90,5.34)--(4.43,7.35);
%\draw[red,<-](3.09,6.63)--(5.1,6.1);
\draw[red,<-](3.07,6.56)--(5.08,6.03);
\draw[red,<-](3.11,6.7)--(5.12,6.17);
%\draw[red,->](2.93,6.39)--(3.53,5.346);
\draw[red,->](4.66,7.39)--(5.26,6.346);
\draw[cyan] (0,4) circle [radius=0.25];
\draw[cyan] (1,5.73) circle [radius=0.15];
\draw[cyan] (-3.46,6) circle [radius=0.25];
\draw[cyan] (-0.73,6.73) circle [radius=0.25];
\draw[cyan] (-2.46,7.73) circle [radius=0.25];
\draw[cyan] (-1.73,5) circle [radius=0.25];
\node[cyan] at (-1.73,5) {2};
\node[cyan] at (-3.46,6) {1};
\node[cyan] at (-0.73,6.73) {3};
\node[cyan] at (-2.46,7.73) {4};
\draw[cyan,<-](-0.346,4.2)--(-1.384,4.8);
\draw[cyan,->](-2.076,5.2)--(-3.114,5.8);
\draw[cyan,<-](0.654,5.92)--(-0.384,6.53);
\draw[cyan,<-](-1.076,6.92)--(-2.114,7.53);
\draw[cyan,->](-0.1,4.36)--(-0.63,6.37);
\draw[cyan,->](0.64,5.63)--(-1.37,5.1);
\draw[cyan,->](-0.93,6.39)--(-1.53,5.346);
\draw[cyan,->](-0.815,6.32)--(-1.415,5.276);
\draw[cyan,->](-1.045,6.46)--(-1.645,5.416);
\draw[cyan,->](-1.76,5.38)--(-2.29,7.39);
\draw[cyan,->](-1.90,5.34)--(-2.43,7.35);
\draw[cyan,<-](-1.07,6.56)--(-3.08,6.03);
\draw[cyan,<-](-1.11,6.7)--(-3.12,6.17);
\draw[cyan,->](-2.66,7.39)--(-3.26,6.346);
\end{tikzpicture}
\caption{A $3$-universal quiver with 15 vertices and 42 arrows, obtained by gluing 3~copies of the extended Somos-4 quiver shown in Figure~\ref{fig:extended-somos-4}. Each copy can be affixed to the respective pair of vertices in two different ways.}
\label{fig:3-universal}
\end{figure}
\begin{proposition}
\label{main_prop}
Let $Q$ be a quiver with $r$ arrows and $n$ vertices, none of which is a source or a sink. Then there exists a quiver $\widetilde{Q}$ such that
\begin{itemize} %[leftmargin=.3in]
\item
$Q$ is a full subquiver of a quiver mutation equivalent to $\widetilde{Q}$;
\item
$\widetilde{Q}$ has $2r-n$ vertices;
\item
each vertex in $\widetilde{Q}$ is incident to at most 3 arrows.
\end{itemize}
\end{proposition}
\begin{proof}
Let us split each arrow $u \mathrel{\succ\hspace{-2pt}\rightarrow} v$ in~$Q$ into two halves
$u\lefthalfarrow{}$ and~${}\mapsto v$. This produces $n$ fragments~$F_v$, one for each vertex~$v$ in~$Q$. We then replace each $F_v$ by a new fragment~$\widetilde F_v$, constructed as follows. Let $p=\indeg (v)$ and $q=\outdeg(v)$. Since $v$ is neither a source nor a sink, we have $p,q\ge 1$.
The new fragment~$\widetilde F_v$ consists~of:
\begin{itemize} %[leftmargin=.3in]
\item
$p+q-1$ vertices, denoted
$u_{p},\dots,u_2,u_1=w_1,w_2,\dots,w_{q}\,$;
\item
$p+q-2$ arrows $u_{p}\longrightarrow \cdots \longrightarrow u_2\longrightarrow u_1=w_1\longrightarrow w_2 \longrightarrow\cdots\longrightarrow w_{q}\,$;
\item
$p$ incoming half-arrows: $\mapsto \!u_i$ for $2\le i\le p$, plus one extra half-arrow $\mapsto \!u_{p}\,$;
\item
$q$~outgoing half-arrows: $\,w_i\!\lefthalfarrow\,$ for $2\le i\le q$, plus one extra half-arrow $w_q\!\lefthalfarrow\,\,$.
\end{itemize}
We then piece together the fragments $\widetilde F_v$, using the original quiver as a template: for each arrow $v\longrightarrow v'$ in~$Q$, we stitch one outgoing half-arrow from~$\widetilde F_v$ to one incoming half-arrow from~$\widetilde F_v'$. (The choices of particular half-arrows are immaterial.)
The resulting quiver $\widetilde Q$ has
$\sum_v (\indeg(v)+\outdeg(v)-1)=2r-n$ vertices.
The total degree of each vertex in this quiver is either 2 or~3.
Let us now mutate $\widetilde Q$ as follows: for each fragment $\widetilde F_v$ as above, mutate once at each of the vertices $u_2,\dots,u_{p},w_2,\dots,w_q$. (Mutations at different fragments commute.)
After each mutation~$\mu_u$, remove the corresponding vertex~$u$, together with all arrows incident to~$u$. The resulting quiver is canonically isomorphic to~$Q$.
%
\iffalse
Let $Q'$ be the quiver obtained from $Q$ by replacing each arrow $\alpha:i\longrightarrow j$ with $i\longrightarrow v_\alpha \longrightarrow j$, where $v_\alpha$ is a new vertex corresponding to $\alpha$. It is easy to see that $Q$ is a full subquiver of a quiver mutation equivalent to $Q'$. In fact, we obtain $Q$ as a full subquiver given by old vertices, after mutating $Q'$ at every new vertex. By abuse of notation, let $Q_0$ be the set of old vertices and $Q_0'$ the set of all vertices on $Q'$. Note that $Q'$ has $n+r$ vertices and $2r$ arrows total.
Next we construct $\widetilde{Q}$ such that $Q'$ is a full subquiver of a quiver mutation equivalent to $\widetilde{Q}$.
Choose any vertex $v\in Q_0\subset Q_0'$. Suppose that there are $e$ arrows on $Q'$, say $\alpha_1,...,\alpha_e$, with $h(\alpha_i)=v$. Introduce $e$ new vertices $w_1,...,w_e$ and add $2e$ new arrows:
$$\aligned
&w_1\longrightarrow v,\\
&w_{i+1}\longrightarrow w_i\text{ for }i\in\{1,...,e-1\},\\
&t(\alpha_i)\longrightarrow w_i\text{ for }i\in\{1,...,e\}.
\endaligned$$
Delete $\alpha_1,...,\alpha_e$. Apply the same construction to the arrows $\beta$ with $t(\beta)=v$, with the direction of new arrows reversed. Repeat this procedure for all vertices in $Q_0$. Let $\widetilde{Q}$ be the resulting quiver, and $\widetilde{Q}_0$ be the set of all vertices on $\widetilde{Q}$. Note that $|\widetilde{Q}_0|=n+3r$. It is clear that $\widetilde{Q}$ is of degree at most 3 at each vertex. If we mutate $\widetilde{Q}$ at every vertex in $ \widetilde{Q}_0\setminus Q_0'$ exactly once in any order, then we obtain $Q'$ as a full subquiver given by $Q_0'$.
\fi
\end{proof}
\begin{corollary}
\label{main_thm2}
For any $n\ge 2$, there exists an $n$-universal quiver with fewer than $12n^2$ vertices, each of which is incident to at most 3 arrows.
\end{corollary}
\begin{proof}
Apply Proposition~\ref{main_prop} to the $n$-universal quiver constructed in the proof of Theorem~\ref{thm:main-thm-quivers}.
\end{proof}
\begin{theorem}
\label{thm:planar-universal}
For any integer $n\ge 2$, there exists a planar $n$-universal quiver with $O(n^4)$ vertices and $O(n^4)$ arrows.
\end{theorem}
\begin{proof}
As a warm-up, let us discuss the case $n=3$. %the cases $n=3$ and $n=4$.
The 3-universal~quiver shown in Figure~\ref{fig:3-universal} is planar.
To see that, replace each edge of a regular triangle by a copy of the planar embedding of the extended Somos-4 quiver shown in Figure~\ref{fig:flattened-Somos-4}.
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=0.9,line width=0.6pt]
\node at (-3.5,0) {$u$};
\draw (-3.5,0) circle [radius=0.25];
\node at (3,1) {$3$};
\draw (3,1) circle [radius=0.25];
\node at (3,-1) {$2$};
\draw (3,-1) circle [radius=0.25];
\node at (4,0) {$4$};
\draw (4,0) circle [radius=0.25];
\node at (9.5,0) {$v$};
\draw (9.5,0) circle [radius=0.25];
\node at (6,0) {$1$};
\draw (6,0) circle [radius=0.25];
\draw[->](-3.14,0.12)--(2.64,0.88);
\draw[<-](-3.14,-0.12)--(2.64,-0.88);
\draw[->](3.4,1)--(9.1,0.08);
\draw[<-](3.4,-1)--(9.1,-0.08);
\draw[->](3.3,-0.88)--(5.64,-0.12);
\draw[<-](3.3,0.88)--(5.64,0.2);
\draw[<-](3.3,0.75)--(5.64,0.07);
\draw[->](4.35,0)--(5.55,0);
\draw[->](3,0.6)--(3,-0.6);
\draw[->](3.15,0.6)--(3.15,-0.6);
\draw[->](2.85,0.6)--(2.85,-0.6);
\draw[->](3.75,0.25)--(3.3,0.6);
\draw[<-](3.7,-0.2)--(3.25,-0.65);
\draw[<-](3.8,-0.3)--(3.35,-0.75);
\end{tikzpicture}
\caption{A planar rendition of the extended Somos-4 quiver. }
\label{fig:flattened-Somos-4}
\end{figure}
%\pagebreak[3]
For general~$n$, we will need an additional trick.
\begin{lemma}
\label{lem:resolving-crossings}
Let $Q$ be a quiver with $k$ vertices and $\ell$ arrows.
Suppose $Q$ can be drawn on the plane so that its arrows cross at $m$ points, two arrows at each crossing. Then there exists a planar quiver $Q'$ with $k+5m$ vertices and $\ell+8m$ arrows which can be mutated into a quiver that has $Q$ as a full subquiver.
\end{lemma}
\begin{proof}
Let us replace each of the $m$ crossings by a (small) fragment of the kind shown in Figure~\ref{fig:replacing-a-crossing}.
This produces a planar quiver~$Q'$ with the required parameters. Now perform the following operations for each of the new fragments:
mutate at~$e$; remove~$e$;
mutate at $a$ and~$b$; remove $a$ and~$b$;
mutate at $c$ and~$d$; remove $c$ and~$d$.
This recovers the original quiver~$Q$.
\end{proof}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=1,line width=0.6pt]
\draw[->](-2.6,0)--(2.6,0);
\draw[->](0,-2.6)--(0,2.6);
\node at (4,0) {$\leadsto$};
\end{tikzpicture}
\qquad
\begin{tikzpicture}[scale=1,line width=0.6pt]
\node at (0,0) {$e$};
\draw (0,0) circle [radius=0.25];
\node at (1.5,0) {$c$};
\draw (1.5,0) circle [radius=0.25];
\node at (-1.5,0) {$a$};
\draw (-1.5,0) circle [radius=0.25];
\node at (0,1.5) {$b$};
\draw (0,1.5) circle [radius=0.25];
\node at (0,-1.5) {$d$};
\draw (0,-1.5) circle [radius=0.25];
\draw[<-](-1.25,0.25)--(-0.25,1.25);
\draw[<-](0.25,-1.25)--(1.25,-0.25);
\draw[->](-1.1,0)--(-0.4,0);
\draw[->](-2.6,0)--(-1.9,0);
\draw[->](0.4,0)--(1.1,0);
\draw[->](1.9,0)--(2.6,0);
\draw[->](0,-1.1)--(0,-0.4);
\draw[->](0,-2.6)--(0,-1.9);
\draw[->](0,0.4)--(0,1.1);
\draw[->](0,1.9)--(0,2.6);
\end{tikzpicture}
\caption{Replacing a crossing by a planar fragment. }
\label{fig:replacing-a-crossing}
\end{figure}
We are now ready to prove Theorem~\ref{thm:planar-universal}.
Let $v_1,\dots,v_n$ be the vertices of a convex $n$-gon on the real plane, chosen so that no three diagonals of it are concurrent.
As in the proof of Theorem~\ref{thm:main-thm-quivers}, we glue a copy $E_{ab}$ of the extended Somos-4 quiver between each pair of vertices $\{v_a, v_b\}$.
In doing so, we flatten each subquiver $E_{ab}$ as shown in Figure~\ref{fig:very-flattened-Somos-4}, making sure that for any $a<b<c<d$, the drawings of $E_{ac}$ and $E_{bd}$ cross at exactly four points. The resulting quiver~$Q$ is isomorphic to the quiver constructed in the proof of Theorem~\ref{thm:main-thm-quivers}, so is $n$-universal, with $k=2n^2-n$ vertices and $\ell=7n^2-7n$ arrows. The drawings of the arrows of~$Q$ intersect at $m=4\binom{n}{4}$ points.
Applying Lemma~\ref{lem:resolving-crossings}, we obtain a quiver with $2n^2-n+20\binom{n}{4}\sim\frac56 n^4$ vertices and $7n^2-7n+32\binom{n}{4}\sim \frac43 n^4$ arrows. This quiver is $n$-universal since it can be mutated into a quiver that restricts to~$Q$.
\end{proof}
\begin{figure}[ht]\centering
\begin{tikzpicture}[scale=0.36,line width=0.6pt]
%\node at (-3,0) {$u$};
\draw (-2,0) circle [radius=0.2];
%\node at (3,1) {$3$};
\draw (3,1) circle [radius=0.2];
%\node at (3,-1) {$2$};
\draw (3,-1) circle [radius=0.2];
%\node at (4,0) {$4$};
\draw (4,0) circle [radius=0.2];
%\node at (9,0) {$v$};
%\draw (9,0) circle [radius=0.2];
%\node at (6,0) {$1$};
\draw (6,0) circle [radius=0.2];
\draw[->](-1.64,0.12)--(2.64,0.88);
\draw[<-](-1.64,-0.12)--(2.64,-0.88);
%\draw[->](3.4,1)--(8.6,0.08);
%\draw[<-](3.4,-1)--(8.6,-0.08);
\draw[->](3.3,-0.88)--(5.64,-0.12);
\draw[<-](3.3,0.88)--(5.64,0.2);
\draw[<-](3.3,0.75)--(5.64,0.07);
\draw[->](4.35,0)--(5.55,0);
\draw[->](3,0.6)--(3,-0.6);
\draw[->](3.15,0.6)--(3.15,-0.6);
\draw[->](2.85,0.6)--(2.85,-0.6);
\draw[->](3.75,0.25)--(3.3,0.6);
\draw[<-](3.7,-0.2)--(3.25,-0.65);
\draw[<-](3.8,-0.3)--(3.35,-0.75);
\draw[<-](3.35,-1.1)--(32.6,-0.15);
\draw[->](3.35,1.1)--(32.6,0.15);
\draw (33,0) circle [radius=0.2];
\end{tikzpicture}
\caption{A deformation of the drawing in Figure~\ref{fig:flattened-Somos-4}.}
\label{fig:very-flattened-Somos-4}
\end{figure}
\begin{remark}
%\label{rem:}
The asymptotics obtained above can be improved to $\sim\frac5{16} n^4$ vertices and $\sim \frac12 n^4$ arrows by using the drawings of the complete graph~$K_n$ with the smallest known number of crossings; see, \eg \cite[Section~13.2]{szekely}.
\end{remark}
\section{Quivers of plabic graphs}
\label{sec:quivers-plabic}
Theorem~\ref{thm:planar-universal} has a corollary concerning quivers
associated with Postnikov's plabic graphs~\cite{postnikov}.
In order to~state this corollary, we recall the requisite background,
adapting it to our current purposes and borrowing examples from
\cite[Section~6]{FPST}.
\begin{definition}
\label{def:plabic}
Let $P$ be a finite connected planar graph~$P$ properly embedded
(as a $1$-dimensional cell complex) into a closed disk~$\Disk$.
We call $P$ a (trivalent) \emph{plabic} ($=$planar bicolored) \emph{graph}
if the following conditions are satisfied:
\begin{itemize} %[leftmargin=.3in]
\item
each interior vertex of~$P$ is colored in one of the two colors, either black or white;
\item
each vertex of $P$ lying in the interior of~$\Disk$ is trivalent
(\ie has degree~$3$);
\item
each vertex of $P$ lying on the boundary~$\partial\Disk$ is univalent
(\ie has degree~$1$).
\end{itemize}
Plabic graphs are viewed up to isotopy of the ambient disk~$\Disk$,
and up to simultaneous reversal of the colors of all vertices.
The \emph{move equivalence} is an equivalence relation on plabic graphs
generated by the following \emph{local moves}:
\begin{itemize} %[leftmargin=.3in]
\item The \emph{flip} move replaces two adjacent trivalent vertices of
the same color with two other vertices of the same color, connected
in a different way:
\[
%\begin{center}
\setlength{\unitlength}{0.8pt}
\begin{picture}(40,45)(0,0)
\thicklines
\put(0,0){\line(2,1){20}}
\put(20,30){\line(2,1){20}}
\put(0,40){\line(2,-1){20}}
\put(20,10){\line(2,-1){20}}
\put(20,10){\line(0,1){20}}
\put(20,10){\circle*{5}}
\put(20,30){\circle*{5}}
\end{picture}
\begin{picture}(40,40)(0,0)
\put(20,20){\makebox(0,0){$\longleftrightarrow$}}
\end{picture}
\begin{picture}(40,40)(0,0)
\thicklines
\put(0,0){\line(1,2){10}}
\put(30,20){\line(1,2){10}}
\put(40,0){\line(-1,2){10}}
\put(10,20){\line(-1,2){10}}
\put(10,20){\line(1,0){20}}
\put(10,20){\circle*{5}}
\put(30,20){\circle*{5}}
\end{picture}
\begin{picture}(60,40)(0,0)
\end{picture}
\begin{picture}(40,40)(0,0)
\thicklines
\put(0,0){\line(2,1){18}}
\put(40,40){\line(-2,-1){18}}
\put(0,40){\line(2,-1){18}}
\put(40,0){\line(-2,1){18}}
\put(20,12.5){\line(0,1){15}}
\put(20,10){\circle{5}}
\put(20,30){\circle{5}}
\end{picture}
\begin{picture}(40,40)(0,0)
\thicklines
\put(20,20){\makebox(0,0){$\longleftrightarrow$}}
\end{picture}
\begin{picture}(40,40)(0,0)
\thicklines
\put(0,0){\line(1,2){9}}
\put(40,40){\line(-1,-2){9}}
\put(40,0){\line(-1,2){9}}
\put(0,40){\line(1,-2){9}}
\put(12.5,20){\line(1,0){15}}
\put(10,20){\circle{5}}
\put(30,20){\circle{5}}
\put(42,20){.}
\end{picture}
%\vspace{.1in}
%\end{center}
\]
\item The \emph{square} move switches the colors on a 4-cycle of
vertices of alternating colors:
%\begin{center}
%\vspace{.1in}
\[
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%\vspace{.1in}
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\end{itemize}
(This move requires a seldom relevant restriction on the faces surrounding the square face,
\cf \cite[Restriction~6.3]{FPST}.)
\end{definition}
\begin{definition}
\label{def:Q(P)}
The quiver~$Q(P)$ associated with a plabic graph~$P$ is constructed as follows.
Place a vertex of~$Q(P)$ into each bounded face of~$P$.
For each edge~$e$ in~$P$ that connects vertices of different colors,
draw an arrow across~$e$ connecting the vertices of~$Q(P)$ located inside the faces
on the two sides of~$e$. (We assume that these faces are bounded and distinct.)
Orient this arrow so that the black endpoint of~$e$ appears on its right as one moves
in the chosen direction.
Then remove oriented cycles of length~2, if any.
%If this construction produces oriented cycles of length~2, then remove them, one by one.
See Figure~\ref{fig:quivers-plabic-graphs}.
\end{definition}
%We note that the colors of boundary vertices do not affect the quiver.
\begin{figure}[ht]\centering
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\caption{Quivers associated with plabic graphs.
Double arrows arise when two faces of a
plabic graph share two disconnected boundary segments.}
\label{fig:quivers-plabic-graphs}
\end{figure}
\begin{remark}
%\label{rem:}
There is a version of Definitions~\ref{def:plabic}--\ref{def:Q(P)}
in which the interior vertices of a plabic graph are not required to be trivalent.
The class of quivers associated with these more general plabic graphs
is exactly the same as in the trivalent setting.
\end{remark}
The following observation is implicit in Postnikov's original work~\cite{postnikov}.
\begin{proposition} %[{$\!\!$ \cite{postnikov}}]
\label{pr:plabic-vs-quivers}
If two plabic graphs are move equivalent to each other,
then their associated quivers are mutation equivalent.
%Cf.\ Figure~\ref{fig:plabic-moves-are-mutations}.
\end{proposition}
Proposition~\ref{pr:plabic-vs-quivers} is illustrated in
Figure~\ref{fig:plabic-moves-are-mutations}.
%\vspace{.1in}
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\caption{The first two plabic graphs are related by a square move; their quivers are obtained from each other by a single mutation.
The second and third plabic graphs are related by a flip move and have isomorphic quivers.
}
\label{fig:plabic-moves-are-mutations}
\end{figure}
\begin{remark}
\label{rem:q-not=>p}
The converse to Proposition~\ref{pr:plabic-vs-quivers} is false, see~\cite[Remark~6.10]{FPST}:
there exist plabic graphs which are not move equivalent even though
their quivers are isomorphic (hence mutation equivalent).
\end{remark}
It is natural to wonder whether the class of quivers (and by extension, cluster algebras)
arising from plabic graphs is substantially narrower than the class of all quivers.
The following result shows that in some sense, no generality is lost
by restricting the theory of quiver mutations to plabic graphs:
\begin{theorem}
\label{th:plabic-universal}
For any integer $n$, there exists a plabic graph with $O(n^4)$ edges and $O(n^4)$ faces
whose associated quiver is $n$-universal.
In particular, any quiver is a full subquiver of a quiver
mutation equivalent to a quiver of a plabic graph.
\end{theorem}
Theorem~\ref{th:plabic-universal}
can be regarded as a strengthening of Theorem~\ref{thm:planar-universal}
since the quiver of any plabic graph is planar.
The proof of Theorem~\ref{th:plabic-universal} will rely on a couple of lemmas.
\goodbreak
\begin{lemma}
\label{lem:quivers-from-plabic}
Let $Q$ be a planar quiver properly embedded in the plane.
Assume that
\begin{enumerate}[label=(\alph*)]
\item\label{lemma3.7_a} %[\rm{(a)}]
$Q$ is connected;
\item\label{lemma3.7_b} %[\rm{(b)}]
$Q$ has no univalent vertices;
\item\label{lemma3.7_c} %[\rm{(c)}]
%if an arrow of $Q$ separates two bounded faces, then those faces are distinct;
the closure of each bounded face of~$Q$ is simply connected; and
\item\label{lemma3.7_d} %[\rm{(d)}]
the boundary of each bounded face of~$Q$ is an oriented cycle.
\end{enumerate}
Then %$Q$ comes from a plabic graph, \ie
there exists a plabic graph $P$ such that $Q(P)$ is isomorphic to~$Q$.
\end{lemma}
\begin{proof}
Let $U$ denote the unique unbounded face of~$Q$.
We construct the plabic~graph $P$ as follows.
(Consult Figure~\ref{fig:quiver-to-plabic}.)
We begin by placing one black (resp., white) vertex of~$P$ inside each bounded face of~$Q$
whose boundary is oriented clockwise (resp., counter-clockwise).
For each arrow~$a$ of~$Q$ that lies on the boundary of the unbounded face~$U$,
let us place a vertex of~$P$ inside~$U$ next to~$a$.
(There will be many vertices of~$P$ inside~$U$, one for each boundary segment of~$U$.)
Color that vertex black (resp., white) if $U$ lies on the right (resp., left) of~$a$ as we move along~$a$.
If $a$ has $U$ on both sides of it, place a black vertex on its right and a white vertex on its~left.
We now describe the edges of~$P$.
For each arrow~$a$ of~$Q$ separating two bounded (necessarily distinct) faces of~$Q$,
connect the vertices of~$P$ placed in those faces with an edge of~$P$ going across~$a$.
If one or both faces bordering an arrow~$a$ are unbounded, then use instead
the vertices of~$P$ located near~$a$.
We then walk around the boundary of the unbounded face~$U$
and cyclically connect all the vertices of~$P$ located~there.
%
Finally, we make our plabic graph trivalent by ``uncontracting'' each vertex of degree $\ge 4$ into a trivalent tree,
see the paragraph preceding Corollary~12.4 in~\cite{postnikov}; \cf also Figure~\ref{fig:quiver-to-plabic}.
%
It is straightforward to verify that the quiver associated with the resulting plabic graph~$P$
is the original quiver~$Q$.
\end{proof}
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}
\end{picture}
\caption{Constructing a plabic graph from a planar quiver
satisfying the conditions in Lemma~\ref{lem:quivers-from-plabic}.
The graph on the right is obtained from the one on the left by ``uncontracting'' three vertices of degree~4.}
\label{fig:quiver-to-plabic}
\end{figure}
\begin{lemma}
\label{lem:oriented-faces}
Any planar quiver can be embedded (as a full subquiver) into a planar quiver satisfying
conditions~\ref{lemma3.7_a}--\ref{lemma3.7_d} in Lemma~\ref{lem:quivers-from-plabic}.
\end{lemma}
\begin{proof}
We first add pairs of arrows $\,\red{\bullet\!\to\!\bullet\!\to\!\bullet}\,$ to the quiver
(here the vertex in the middle is new)
to make it connected, to get rid of univalent vertices,
and to cut up each bounded face that is not simply connected
%that violates condition~(c) in Lemma~\ref{lem:quivers-from-plabic} into faces satisfying that condition.
into pieces that are.
(To convince yourself that the latter can always be accomplished,
recall that a quiver cannot contain loops, \ie arrows connecting a vertex to itself.)
It remains to take care of condition~\ref{lemma3.7_d}. Let $F$ be a bounded face of the resulting quiver.
Suppose that $F$ is not oriented.
Let $Q_F$ denote the quiver formed by the vertices and arrows of~$Q$
lying on the boundary of~$F$.
(There might exist arrows which connect some of those vertices to each other
but do not lie on~$\partial F$;
those arrows are not included in~$Q_F$.)
We now augment $Q$ by adding an extra vertex~$v_F$ lying inside~$F$,
and by adding new arrows to~$Q$ as follows:
\begin{itemize}%[leftmargin=.2in]
\item for every sink~$u$ of~$Q_F$, draw an arrow $u\color{cyan}\to\color{black} v_F$;
\item for every source~$u$ of~$Q_F$, draw an arrow $v_F\color{cyan}\to\color{black} u$.
\end{itemize}
Once this is done for all such faces~$F$, we obtain a quiver all of whose bounded faces are oriented.
See Figure~\ref{fig:making-faces-oriented}.
\end{proof}
\begin{figure}[ht]\centering
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\put(39,19){\vector(-1,-1){8}}
\color{black}
\end{picture}
\caption{Embedding a planar quiver into a quiver with oriented bounded~faces.}
\label{fig:making-faces-oriented}
\end{figure}
%\pagebreak[3]
\begin{proof}[Proof of Theorem~\ref{th:plabic-universal}]
Lemmas~\ref{lem:quivers-from-plabic} and~\ref{lem:oriented-faces} imply that
any planar quiver~$Q$ can be embedded (as a full subquiver)
into a quiver $Q(P)$ coming from a plabic graph~$P$.
This embedding is illustrated in Figure~\ref{fig:extended-Somos-into-plabic}
for the case of the extended Somos quiver.
Taking account of the number of vertices and arrows added in the course of such embedding
(\cf the proofs of Lemmas~\ref{lem:quivers-from-plabic} and~\ref{lem:oriented-faces}),
we conclude that if a planar quiver~$Q$ has $k$ vertices and $\ell$ arrows,
then the number of vertices (resp., arrows) of the ambient quiver $Q(P)$ are both bounded by $O(k+\ell)$.
Letting $Q$ be an $n$-universal planar quiver
from Theorem~\ref{thm:planar-universal}, we obtain the statement of Theorem~\ref{th:plabic-universal}.
\end{proof}
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\begin{figure}[ht]\centering
%\begin{picture}(130,150)(12,-15)
\begin{picture}(130,120)(12,-0)
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\put(40,60){{\usebox{\wb}}}
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%\put(0,0){\makebox(0,0){\usebox{\digon}}}
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\end{picture}
\caption{Embedding the extended Somos quiver~$Q$ (see Figure~\ref{fig:flattened-Somos-4})
into a quiver of a plabic graph~$P$.
Removing the vertices of the latter quiver
corresponding to the bigon faces of~$P$, we obtain~$Q$ (shown in the picture).
}
\label{fig:extended-Somos-into-plabic}
\end{figure}
\begin{remark}
\label{rem:reduced-plabic-not-universal}
There is a large body of research focusing on the important subclass of
\emph{reduced} plabic graphs. Reduced plabic graphs describe cluster structures in
Grassmannians, basic affine spaces, and most generally, arbitrary positroid varieties~\cite{Galashin-Lam}. %\linebreak[3]
Remarkably, the analogue of Theorem~\ref{th:plabic-universal} fails for reduced plabic graphs,
for the following reason.
As shown by N.~Ford and K.~Serhiyenko~\cite[Theorem~1.2]{ford-serhiyenko},
the quiver associated with any reduced plabic graph has a \emph{reddening sequence}.
This property is preserved by quiver mutations and by passing to a full subquiver,
see G.~Muller~\cite[Theorem~17, Corollary~19]{muller-max-green}.
Consequently any quiver without a reddening sequence
(\eg the Markov quiver, \cf Figure~\ref{fig:Markov-quiver})
cannot be embedded into a quiver of a reduced plabic graph.
Thus, restricting the study of plabic graphs to the reduced %\linebreak[3]
case limits the theory
to a proper subclass of ``nice'' quivers (and associated cluster structures)
whereas general plabic graphs contain arbitrarily ``nasty'' cluster types.
\end{remark}
%\newpage
\section{Universal skew-symmetrizable matrices}
\label{sec:universal-matrices}
In this section, we extend Theorem~\ref{thm:main-thm-quivers} to the wider generality of skew-sym\-met\-rizable matrices.
We start by recalling the basic background, \cf \eg \cite[Section~2.7]{FWZ}.
\begin{definition}
An $n \times n$ matrix $B = (b_{ij})$ with integer entries is called
\emph{skew-symmetrizable} if there exist positive integers $d_1,..., d_n$ such that $d_ib_{ij} = -d_j b_{ji}$ for all $i,j\in\{1,\dots,n\}$.
Equivalently, there exists a diagonal matrix $D=\diag(d_1,\dots,d_n)$ with positive diagonal entries $d_1,...,d_n$ such that the matrix $DB$ is skew-symmetric. Such a matrix $D$ is called a \emph{symmetrizer} for~$B$.
\end{definition}
\begin{definition}
\label{def:matrix-mutation}
Let $B$ be an $n \times n$ skew-symmetrizable
integer matrix.
For $k\in\{1,...,n\}$, the \emph{matrix mutation $\mu_k$ in direction $k$} transforms $B$ into
the $n \times n$ matrix $\mu_k(B)=(b_{ij}')$ whose entries are given as follows:
\begin{equation}
\label{eq:matrix-mutation}
b_{ij}'=
\begin{cases} -b_{ij} &\text{ if }i=k\text{ or }j=k, \\
b_{ij}+b_{ik}b_{kj} &\text{ if }b_{ik}>0\text{ and }b_{kj}>0,\\
b_{ij}-b_{ik}b_{kj} &\text{ if }b_{ik}<0\text{ and }b_{kj}<0,\\
b_{ij} &\text{ otherwise.}
\end{cases}
\end{equation}
Two skew-symmetrizable matrices $B$ and $B'$ are called \emph{mutation
equivalent} (denoted \hbox{$B\sim B'$}) if one can get from $B$ to $B'$ by a sequence of mutations.
\end{definition}
\begin{remark}
To any quiver~$Q$ with vertices $1,\dots,n$, we can associate a skew-symmetric matrix $B=B(Q)=(b_{ij})$ by setting
\[
b_{ij}=\begin{cases}
\quad \, \text{number of arrows pointing from $i$ to~$j$} &\text{if there are any,}\\
-(\text{number of arrows pointing from $j$ to~$i$}) &\text{otherwise.}
\end{cases}
\]
Under this correspondence, mutations of quivers translate into mutations of associated matrices. Thus, Definition~\ref{def:matrix-mutation} is a generalization of Definition~\ref{def:quiver-mutation}.
\end{remark}
It is easy to see that if $D$ is a symmetrizer for~$B$, and $B\sim B'$, then $D$ is also a symmetrizer for~$B'$.
\begin{definition}
Let $B$ be a skew-symmetrizable $n\times n$ matrix, and $I$ a subset of $\{1,\dots,n\}$. We denote by $B_I$ the \emph{principal submatrix} of~$B$ supported on~$I$, \ie the matrix obtained from~$B$ by selecting the rows and columns belonging to~$I$.
\end{definition}
\begin{remark}
The notion of a principal submatrix is a straightworward extension of the notion of a full subquiver, see Definition~\ref{def:full-subquiver}: for a matrix $B(Q)$ associated with a quiver~$Q$, we have $B(Q)_I=B(Q_I)$.
Lemma~\ref{lem:restriction-mutation} extends to this generality: for $k\in I$, we have $\mu_k(B_I)=(\mu_k(B))_I$.
\end{remark}
%\pagebreak[3]
We can now extend Definition~\ref{def:n-universal}.
\begin{definition}
Let $D=\diag (d_1,\dots,d_n)$ be a diagonal matrix with positive integer diagonal entries $d_1,...,d_n$.
A skew-symmetrizable matrix $B$ is called $D$-\emph{universal} if every $n\times n$ skew-symmetrizable matrix with symmetrizer $D$ is a principal submatrix of a matrix mutation equivalent to $B$.
\end{definition}
Our main result (Theorem~\ref{thm:main-thm-quivers}) directly extends to the skew-symmetrizable case.
\begin{theorem}
\label{main_thm1}
For any $n\times n$ diagonal matrix $D$ with positive integer entries, there exists a $D$-universal matrix of size $(2n^2\!-\!n)\!\times\!(2n^2\!-\!n)$ with $2(7n^2\!-\!7n)$ nonzero~entries.
\end{theorem}
To prove Theorem~\ref{main_thm1}, we will need a couple of lemmas.
\begin{lemma}
\label{lem:mu-BD}
Let $B$ be an $n\times n$ skew-symmetric matrix, and $H=\diag (h_1,\dots,h_n)$ a diagonal matrix with positive integer entries. If $h_k=1$, then $\mu_k(BH)=\mu_k(B)H$.
\end{lemma}
\begin{proof}
Let $B=(b_{ij})$. Then we have, for any $i,j\in\{1,\dots,n\}$ (cf.~\eqref{eq:matrix-mutation}):
\[
(\mu_k(BH))_{ij}=\begin{cases} -b_{ij}h_j &\text{ if }i=k\text{ or }j=k, \\
b_{ij}h_j+b_{ik}h_k b_{kj} h_j &\text{ if }b_{ik}>0\text{ and }b_{kj}>0,\\
b_{ij}h_j-b_{ik}h_k b_{kj} h_j&\text{ if }b_{ik}<0\text{ and }b_{kj}<0,\\
b_{ij}h_j &\text{ otherwise.}
\end{cases}
\]
Since $h_k=1$, it follows that $(\mu_k(BH))_{ij}=(\mu_k(B))_{ij}h_j=(\mu_k(B)H)_{ij}$.
\end{proof}
\begin{lemma}
\label{lem:bij-divisible}
Let $B=(b_{ij})$ be a skew-symmetrizable $n\times n$ matrix with symmetrizer $D=\diag (d_1,\dots,d_n)$.
For $i,j\in\{1,\dots,n\}$, denote
\begin{equation}
\label{eq:hij}
h_{ij}=\frac{d_j}{\gcd(d_i,d_j)} .
\end{equation}
Then %$b_{ij}\equiv 0\bmod h_{ij}$, and similarly $b_{ji}\equiv 0\bmod h_{ji}$. Moreover
there exists an integer $k$ such that
\[
\begin{bmatrix}
0 & b_{ij} \\
b_{ji} & 0
\end{bmatrix}
= \begin{bmatrix}
0 & kh_{ij} \\
-kh_{ji} & 0
\end{bmatrix} .
\]
\end{lemma}
\begin{proof}
By the definition of a symmetrizer, we have $d_i b_{ij}=-d_j b_{ji}$. Dividing by $\gcd(d_i,d_j)$, we get $h_{ji} b_{ij}=-h_{ij} b_{ji}$.
It remains to observe that $\gcd(h_{ij},h_{ji})=1$, and therefore the number
$k=\frac{b_{ij}}{h_{ij}}=-\frac{b_{ji}}{h_{ji}}$
is an integer.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{main_thm1}]
As explained below, the requisite $D$-universal matrix is constructed in the same way as the $n$-universal quiver~$\overline Q$ in Theorem~\ref{thm:main-thm-quivers}, with slight modifications.
We continue to use the notation from the proof of Theorem~\ref{thm:main-thm-quivers}.
Let $\overline B=B(\overline Q)$ be the skew-symmetric matrix corresponding to the quiver~$\overline Q$. All nonzero entries of~$\overline B$ are located inside $\binom{n}{2}$ blocks $\overline B_{ij}$ of size $6\times 6$, labeled by the pairs $i,j\in\{1,\dots,n\}$ of vertices in~$Q_\bullet$. Each block $\overline B_{ij}$ has the same form, and corresponds to a copy (here denoted~$Q_{ij}$) of the extended Somos-4 quiver. The marked vertices of~$Q_{ij}$ (those labeled $u$ and~$v$ in Figures~\ref{fig:extended-somos-4} and~\ref{fig:flattened-Somos-4}) are the vertices $i$ and~$j$ of~$Q_\bullet$. We label the remaining four vertices by the triples $(i,j,1)$, $(i,j,2)$, $(i,j,3)$, $(i,j,4)$. With this notation, the block $\overline B_{ij}$ is represented as follows:
\begin{equation}
\label{eq:overline-Bij}
\renewcommand{\arraystretch}{1.2}
\begin{array}{c||cc|cccc}
& i & j & (i,j,1) & (i,j,2) & (i,j,3) & (i,j,4) \\[1pt]
\hline
\hline
\\[-12pt]
i & 0 & 0 & 0 & -1 & 1 & 0 \\
j & 0 & 0 & 0 & 1 & -1 & 0 \\
\hline
\\[-11pt]
(i,j,1) & 0 & 0 & 0 & -1 & 2 & -1 \\
(i,j,2) & 1 & -1 & 1 & 0 & -3 & 2 \\
(i,j,3) & -1 &1 &-2 & 3 & 0 & -1 \\
(i,j,4) & 0 & 0 & 1 & -2 & 1 &0
\end{array}\,.
\end{equation}
%Here $i,j\in\{1,\dots,n\}$ are the labels of two vertices in~$Q_\bullet$ which are identified with the marked vertices $u$ and $v$ of this particular copy of the extended Somos-4 quiver. We label the remaining four vertices of the latter copy by the triples $(i,j,1)$, $(i,j,2)$, $(i,j,3)$, $(i,j,4)$, \cf Figure~\ref{fig:6-vertex-quivers} or Figure~\ref{fig:flattened-Somos-4}.
Let $D=\diag (d_1,\dots,d_n)$. For $i,j\in\{1,\dots,n\}$, we denote
\[
H_{ij}=\diag (h_{ji},h_{ij},1,1,1,1),
\]
where we use the notation~\eqref{eq:hij}.
To construct the desired $D$-universal matrix~$\overline B_D$, we replace each block $\overline B_{ij}$ in~$\overline B$ by the product~$\overline B_{ij} H_{ij}$. In other words, we replace~\eqref{eq:overline-Bij} by the $6\times 6$ block
\begin{equation}
\label{eq:overline-BijH}
\renewcommand{\arraystretch}{1.2}
\begin{array}{c||cc|cccc}
& i & j & (i,j,1) & (i,j,2) & (i,j,3) & (i,j,4) \\[1pt]
\hline
\hline
\\[-12pt]
i & 0 & 0 & 0 & -1 & 1 & 0 \\
j & 0 & 0 & 0 & 1 & -1 & 0 \\
\hline
\\[-11pt]
(i,j,1) & 0 & 0 & 0 & -1 & 2 & -1 \\
(i,j,2) & h_{ji} & -h_{ij} & 1 & 0 & -3 & 2 \\
(i,j,3) & -h_{ji} &h_{ij} &-2 & 3 & 0 & -1 \\
(i,j,4) & 0 & 0 & 1 & -2 & 1 &0
\end{array}\,.
\end{equation}
The resulting $(2n^2-n)\times(2n^2-n)$ matrix~$\overline B_D$ is skew-symmetrizable: its symmetrizer has diagonal entry $d_i$ corresponding to each vertex $i$ in~$Q_\bullet$, and diagonal entry~$\gcd(d_i,d_j)$ for each vertex labeled $(i,j,1)$, $(i,j,2)$, $(i,j,3)$, or $(i,j,4)$.
It remains to show that the matrix $\overline B_D$ is $D$-universal. The general shape of the argument is the same as in the quiver case: we mutate each block separately; these~mutations do not interfere with each other; and at the end, we restrict to the principal submatrix supported on the indexing set $\{1,\dots,n\}$.
Since the mutated matrix has the same symmetrizer as~$\overline B_D$, the restricted matrix will have symmetrizer~$D$.
We now need to prove that for any skew-symmetrizable matrix $B=(b_{ij})$ with symmetrizer~$D$, and any $i,j\in\{1,\dots,n\}$, there exists a sequence of mutations, using only the indices $(i,j,1)$, $(i,j,2)$, $(i,j,3)$, or~$(i,j,4)$, which transform the $6\times 6$ matrix $\overline B_{ij} H_{ij}$ shown in~\eqref{eq:overline-BijH} into a matrix whose upper-left $2\times 2$ block is $\Bigl[\begin{array}{cc} 0 & b_{ij}\\ b_{ji} & 0 \end{array}\Bigr]$.
By Lemma~\ref{lem:bij-divisible}, this $2\times 2$ block has the form $ \Bigl[\begin{array}{cc}
0 & kh_{ij} \\
-kh_{ji} & 0
\end{array}\Bigr]$, for some $k\in\mathbb{Z}$.
Let us take a sequence of mutations whose indices replicate the mutation sequence required to obtain the desired outcome in the quiver case, \ie
to transform $\overline B_{ij}$ into a matrix with the upper-left block $\Bigl[\begin{array}{cc}
0 & k \\
-k & 0
\end{array}\Bigr]$.
By Lemma~\ref{lem:mu-BD} (which applies since the corresponding components of $H_{ij}$ are equal to~1), each of these mutations commutes with multiplication by $H_{ij}$ on the right, and we are done.
\end{proof}
\section{Hereditary properties and universal collections}
\label{sec:hereditary+universal}
We begin by reviewing the concept of hereditary properties, \cf \cite[Section~4.1]{FWZ}. We will then explain the connection between this concept and the notion of universality.
\begin{definition}[{\cite[Definition~4.1.3]{FWZ}}]
\label{def:hereditary}
A property of quivers (or more generally skew-symmetrizable matrices) is called \emph{hereditary} if it is preserved under restriction to a full subquiver (resp., a principal submatrix).
Of particular importance are the properties of quivers (resp., skew-symmetrizable matrices) which are both hereditary and \emph{mutation-invariant}, \ie preserved under mutations.
Equivalently, one can talk about properties of mutation classes (or the corresponding cluster algebras) which are preserved under restriction, \ie taking any quiver in a mutation class, restricting to its full subquiver, then taking the mutation class of the latter.
%Since mutation classes are in one-to-one correspondence with cluster algebras with trivial coefficients, one can also translate the notion of a hereditary property into the language of cluster algebras.
\end{definition}
\begin{example}
The following properties of a quiver~$Q$ are hereditary and mutation-invariant (see~\cite[Section~4.1]{FWZ}, \cite[Section~5.2]{keller-survey}, and~\cite[Section~3]{muller-max-green} for details and further references):
\begin{itemize}%[leftmargin=.3in]
\item
$Q$ has \emph{finite type}, \cf \cite{ca2}, \cite[Remark~5.10.9]{FWZ}; %It follows from the finite type classification~\cite{ca2} that a full subquiver of a quiver of finite type (or a principal submatrix of a matrix of finite type) also has finite type. See \cite[Remark~5.10.9]{FWZ}
%\item Tameness. %SF: This is very close to finite mutation type
\item
$Q$ has \emph{finite mutation type}, \cf \cite[Proposition~4.1.4]{FWZ};
\item
$Q$ is a full subquiver of a particular (very special) infinite quiver, \cf \eg \cite{Henrich};
\item
$Q$ has \emph{finite/tame representation type}, \cf \cite[Theorem~5.5]{keller-survey};
\item
any quiver in $[Q]$ has arrow multiplicities $\le k$ (for some $k\in\ZZ_{>0}$), \cf \emph{loc.\ cit.};
\item
$Q$ is \emph{mutation acyclic}, see Remark~\ref{rem:acyclic-not-3-universal} above;
%See \cite[Example~4.1.5]{FWZ}, \cite{BMR}, .
\item
$Q$ is \emph{embeddable} into a given mutation class, see~\cite[Definition~4.1.8]{FWZ}; %or more generally into some mutation class from a given collection.
\item
$Q$ admits a \emph{reddening} (``green-to-red'') \emph{sequence}
\cite[Theorem~17, Corollary~19]{muller-max-green}.
\end{itemize}
We note that while the existence of a \emph{maximal green sequence} is a hereditary property, it is \underbar{not} mutation-invariant, see~\cite[Theorem~9, Corollary~14]{muller-max-green}.
%\medskip
None of the above properties holds for all quivers.
\end{example}
To illustrate the concepts introduced in Definition~\ref{def:hereditary},
we provide a curious application, \cf Remark~\ref{rem:grid-not-3-universal}.
\begin{proposition}
\label{prop:grid-no-markov}
Let $Q$ be a quiver mutation equivalent to a grid quiver $A_k\boxtimes A_\ell$, for some $k$ and~$\ell$ (\cf Example~\ref{example:grid-quivers}). Then $Q$ cannot have a full subquiver isomorphic to the Markov quiver, see Figure~\ref{fig:Markov-quiver}. In particular, every grid quiver is not $3$-universal.
\end{proposition}
\begin{proof}
It is well known (\cf \cite[Section~1]{marsh-scott}, \cite[Section~5]{keller-maxgreen}) that any grid quiver possesses a maximal green sequence, and therefore a reddening sequence. As mentioned above, the property of having a reddening sequence is both mutation invariant and hereditary~\cite[\emph{loc.\ cit.}]{muller-max-green}. Since the Markov quiver does not have this property, the claim follows.
\end{proof}
The following simple observation relates hereditary properties to the notion of $n$-universality.
%\pagebreak[3]
\begin{remark}
\label{rem:enough-n-universal}
Let $P$ be a mutation-invariant hereditary property of quivers.
If~some $n$-universal quiver has property~$P$, then any quiver on $\le n$~vertices has this property.
\end{remark}
In most applications, the number of vertices in a quiver is not fixed \emph{a~priori}. With this in mind, we introduce the following adaptation of the concept of universality:
\begin{definition}
\label{def:universal-collection}
Let $\mathcal{Q}$ be a collection of quivers. We call $\mathcal{Q}$ a \emph{universal collection} if any quiver is a full subquiver of a quiver mutation equivalent to a quiver in~$\mathcal{Q}$.
\end{definition}
%One is of course interested in constructing universal collections containing a rather limited---and manageable---subset of quivers.
\begin{remark}
\label{rem:universal-from-n-universal}
Let $Q_2, Q_3,\dots$ be a sequence of quivers such that each quiver $Q_n$~is \hbox{$n$-universal}. (For instance, let $Q_n$ be the $n$-universal quiver constructed in the proof of Theorem~\ref{thm:main-thm-quivers}.) Then $(Q_n)$ is a universal collection.
\end{remark}
%We make a simple but potentially useful observation:
\begin{proposition}
\label{prop:universal-hereditary-alternative}
Let $\mathcal{Q}$ be a collection of quivers. Then exactly one of the following two possibilities holds:
\begin{itemize}%[leftmargin=.3in]
\item
$\mathcal{Q}$ is a universal collection;
\item
all the quivers in $\mathcal{Q}$ share a nontrivial mutation-invariant hereditary property.
\end{itemize}
(Here ``nontrivial'' means that not every quiver has this property.)
\end{proposition}
\begin{proof}
Let us call a quiver $Q$ \emph{embeddable} into $\mathcal{Q}$ if $Q$ is a subquiver of a quiver mutation equivalent to a quiver in~$\mathcal{Q}$. There are two mutually exclusive possibilities.
\begin{enonce*}[remark]{Case~1} Any quiver is embeddable into~$\mathcal{Q}$. Then $\mathcal{Q}$ is universal, \cf Definition~\ref{def:universal-collection}. Furthermore, if the quivers in $\mathcal{Q}$ share a mutation-invariant hereditary property, then by Lemma~\ref{lem:enough-universal-collection}, any quiver has that property, so the property is trivial.
\end{enonce*}
%\emph{Case~2}:
\begin{enonce*}[remark]{Case~2} Some quiver~$Q$ is not embeddable into~$\mathcal{Q}$. Then $\mathcal{Q}$ is not universal. Furthermore, embeddability into~$\mathcal{Q}$ is a mutation-invariant and hereditary property which is both nontrivial (since $Q$ does not have it) and shared by all quivers~in~$\mathcal{Q}$. \qedhere
\end{enonce*}
\end{proof}
\iffalse
\begin{remark}
Let $\mathcal{Q}$ be a collection of quivers which are in some sense ``manageable,'' \ie amenable to techniques which are not available for arbitrary quivers. Suppose that we do not know whether $\mathcal{Q}$ is universal or not.
Proposition~\ref{prop:universal-hereditary-alternative} offers two alternatives, each of which is potentially exciting:
\begin{enumerate}[label=(\alph*)]
\item %[(a)]
$\mathcal{Q}$ is a universal collection; in this case, many problems concerning arbitrary quivers are immediately reduced to the case of the quivers in~$\mathcal{Q}$;
\item %[(b)]
all quivers in $\mathcal{Q}$ share some nontrivial mutation-invariant hereditary property;
if that is the case, then which property is it?
\end{enumerate}
\end{remark}
\fi
%In the spirit of Remark~\ref{rem:enough-n-universal}, we make the following easy observation:
\begin{lemma}
\label{lem:enough-universal-collection}
Let $P$ be a hereditary property of quivers,
and let $\mathcal{Q}$ be a universal collection of quivers.
Then:
\begin{itemize}%[leftmargin=.3in]
\item
If any quiver mutation equivalent to a quiver in~$\mathcal{Q}$ has property~$P$,
then any quiver has property~$P$.
\item
In particular, if $P$ is mutation-invariant, and all quivers in $\mathcal{Q}$ have property~$P$,
then any quiver has property~$P$.
\end{itemize}
\end{lemma}
\begin{proof}
Since $\mathcal{Q}$ is universal,
any quiver $Q$ is a full subquiver of a quiver~$Q'$
mutation equivalent to a quiver $Q''\in\mathcal{Q}$.
Since $Q'$ has property~$P$, and $P$ is hereditary, it follows that $Q$ has property~$P$.
\end{proof}
Suppose that we want to prove that a certain mutation-invariant hereditary property holds for all quivers. By Lemma~\ref{lem:enough-universal-collection}, it is enough to establish it for the quivers in some universal collection.
Since the quivers in this collection may be fairly special, the latter claim may be amenable to proof techniques which are not available for arbitrary quivers.
We illustrate this idea by proposing a hypothetical strategy for the proof of \emph{Laurent positivity} for cluster algebras.
Let $Q$ be a quiver without frozen vertices, and $\mathcal{A}(Q)$ the associated cluster algebra. (We refer the reader to~\cite{FWZ} for basic background on cluster algebras.)
The following strengthening of the Laurent Phenomenon for cluster algebras
was conjectured in~\cite{ca1} and proved in~\cite{GHKK,lee-schiffler}:
\begin{enumerate}[label=(LP+)]
\item\label{LP+} %[{\rm (LP+)}]
any cluster variable~$z$ in~$\mathcal{A}(Q)$ is expressed in terms of any cluster~$\mathbf{x}$ of this cluster algebra as a Laurent polynomial with positive coefficients.
\end{enumerate}
No~simple proof of this result is known. As a potential alternative to the highly technical proofs given in~\cite{GHKK} and~\cite{lee-schiffler}, we suggest an approach based on the following elementary result (which does not rely on~\cite{GHKK,lee-schiffler}).
\begin{lemma}
\label{lem:laurent-positivity-is-hereditary}
The statement~\ref{LP+} above, viewed as a property of a quiver~$Q$, is both mutation-invariant and hereditary.
\end{lemma}
\begin{proof}
Mutation invariance is immediate by construction. Let us prove that~\ref{LP+} is hereditary. Given a subset of indices~$I$, consider the restricted quiver~$Q_I$ and the corresponding cluster algebra~$\mathcal{A}(Q_I)$. We need to verify that if~\ref{LP+} holds for~$\mathcal{A}(Q)$, then it also holds for~$\mathcal{A}(Q_I)$.
Let $\overline I$ denote the complement of~$I$ in the set of all indices. The labeled seed pattern for~$\mathcal{A}(Q_I)$ is obtained from the labeled seed pattern for~$\mathcal{A}(Q)$ as follows:
\begin{enumerate}[label=(\alph*)]
\item\label{proof_lemma5.9_a} %[(a)]
freeze all indices in~$\overline I$, thereby allowing only mutations~$\mu_i$ in directions $i\in I$; this restricts the seed pattern to a subpattern supported on a smaller regular tree;
\item\label{proof_lemma5.9_b} %[(b)]
trivialize all coefficient variables~$x_i$ ($i\in\overline I$), \ie specialize $x_i=1$;
\item\label{proof_lemma5.9_c} %[(c)]
apply the same specialization as in~\ref{proof_lemma5.9_b} to each cluster variable in the pattern, viewed as a rational function in some base cluster; the result is well defined, and does not depend on which base cluster we use.
\end{enumerate}
Let $z$ be a cluster variable in the labeled seed pattern for~$\mathcal{A}(Q_I)$, and let $\tilde z$ be the corresponding cluster variable in~$\mathcal{A}(Q)$. Similarly, let~$\mathbf{x}$ be a cluster for~$\mathcal{A}(Q_I)$, and let~$\mathbf{\tilde x}$ be the corresponding cluster for~$\mathcal{A}(Q)$.
Then~$z$ (resp.,~$\mathbf{x}$) is obtained from~$\tilde z$ (resp.,~$\mathbf{\tilde x}$) via the specialization described in~\ref{proof_lemma5.9_b} above.
Hence the rational function that expresses $z$ in terms of~$\mathbf{x}$ is obtained from the rational expression for $\tilde z$ in terms of~$\mathbf{\tilde x}$ via the same specialization. If the latter expression is a Laurent polynomial with positive coefficients, then so is the former. Thus the property~\ref{LP+} is hereditary.
\end{proof}
\begin{observation}
{%\rm
By Lemma~\ref{lem:laurent-positivity-is-hereditary}, once we establish the Laurent positivity property~\ref{LP+} for a particular universal collection of quivers (say a certain sequence of $n$-universal quivers, \cf Remark~\ref{rem:universal-from-n-universal}), \ref{LP+}~in full generality follows.
%It~is not unreasonable to expect that for some universal collection, one can give explicit formulas for the corresponding Laurent expansions, as generating functions for some families of combinatorial objects. Such formulas would immediately imply Laurent positivity for all quivers.
}
\end{observation}
%\comment{Is there a similar argument for strong positivity? Seems tricky.}
Another important %mutation-invariant
hereditary property is the sign-coherence of $c$-vectors.
Let us quickly recall the relevant definitions.
(See~\cite{nakanishi-zelevinsky} and~\cite{ca4, keller-fpsac13} for additional details.)
\begin{definition}
Let $Q$ be a quiver on an $n$-element vertex set~$V$.
The corresponding \emph{framed quiver} $\widetilde Q$ is a quiver on $2n$ vertices
obtained from $Q$ as follows.
The vertex set of $\widetilde Q$ is the set $V\sqcup \overline V$ where
$\overline V=\{\bar v:v\in V\}$. The arrows in $\widetilde Q$ are the ones in~$Q$ plus
$n$ new arrows of the form $v\to \bar v$, for $v\in V$.
See Figure~\ref{fig:2-universal-quiver-framed}.
\end{definition}
\begin{figure}[ht]\centering
%\vspace{-.1in}
\begin{tikzpicture}[scale=1,line width=0.6pt]
\node at (1.75,0) {1};
\draw (1.75,0) circle [radius=0.25];
\draw[->](2.1,0)--(2.9,0);
\node at (3.25,0) {2};
\draw (3.25,0) circle [radius=0.25];
\draw[->](3.6,0.1)--(4.4,0.1);
\draw[->](3.6,-0.1)--(4.4,-0.1);
\node at (4.75,0) {3};
\draw (4.75,0) circle [radius=0.25];
\node at (1.75,-1.5) {$\bar 1$};
\draw (1.75,-1.5) circle [radius=0.25];
\draw[<-](1.75,-1.1)--(1.75,-0.4);
\node at (3.25,-1.5) {$\bar 2$};
\draw (3.25,-1.5) circle [radius=0.25];
\draw[<-](3.25,-1.1)--(3.25,-0.4);
\node at (4.75,-1.5) {$\bar 3$};
\draw (4.75,-1.5) circle [radius=0.25];
\draw[<-](4.75,-1.1)--(4.75,-0.4);
\end{tikzpicture}
\caption{The framed quiver $\widetilde Q$ for the $2$-universal quiver~$Q$ in Figure~\ref{fig:2-universal-quiver}. }
\label{fig:2-universal-quiver-framed}
\end{figure}
The following \emph{sign coherence} property was implicitly conjectured in~\cite{ca4}, and proved in~\cite{DWZ2}
(other proofs have been given in~\cite{GHKK, Nagao}):
\begin{enumerate}[label=(SC)]
\item\label{SC} %[{\rm (SC)}]
in any quiver $\widetilde Q'$ obtained from~$\widetilde Q$ by a sequence of mutations
at the vertices in~$V$,
no two vertices from the set $\overline V$ are connected by an arrow.
\end{enumerate}
%\pagebreak[3]
\begin{remark}
The conventional version of~\ref{SC} asserts that $\widetilde Q'$ does not contain any
arrows of the form $\bar u\to v\to \bar w$.
(Also, the vertices in~$\overline V$ are declared frozen.)
These two versions are equivalent to each~other:
if $\widetilde Q'$ contains a configuration $\bar u\to v\to \bar w$,
then $\mu_v(\widetilde Q')$ has an arrow $\bar u\to \bar w$; conversely,
the only way such an arrow could arise is via a configuration of this kind.
\end{remark}
\begin{remark}
The statement~\ref{SC} is usually called ``sign coherence of $c$-vectors.''
There is a companion (arguably more important) statement called
``sign coherence of $\mathbf{g}$-vectors''~\cite{ca4}.
As observed in~\cite{nakanishi-zelevinsky}, the latter easily follows from the former.
\end{remark}
In spite of its elementary formulation, no simple proof of sign-coherence is presently known.
All known proofs are highly nontrivial,
and go far beyond the elementary combinatorics of quiver mutations.
(The proof in~\cite{DWZ2} relies on the existence of a nondegenerate potential for any quiver,
whereas the proof in~\cite{GHKK} involves (coherent) scattering diagrams.)
By contrast, the following fact is very easy to verify.
\begin{lemma}
\label{lem:sc-hereditary}
The statement~\ref{SC}, viewed as a property of a quiver~$Q$, is hereditary.
\end{lemma}
\begin{proof}
Let $Q_2$ be a full subquiver of a quiver~$Q_1$.
Then the framed quiver $\widetilde Q_2$ is a full subquiver of~$\widetilde Q_1$.
Furthermore, any quiver~$\widetilde Q'_2$ obtained from $\widetilde Q_2$
via mutations at the vertices of~$Q_2$
is a full subquiver of the quiver~$\widetilde Q'_1$ obtained from $\widetilde Q_1$ via the same sequence of mutations.
Thus, if $\widetilde Q'_1$ does not contain arrows of the form $\bar u\to \bar v$,
then the same holds for~$\widetilde Q'_2$.
\end{proof}
$\!$Lemma~\ref{lem:sc-hereditary} suggests a potential strategy
towards a simpler proof of sign-coherence:
\begin{enumerate}[label=(\alph*)]
\item\label{sect5_i} %[(i)]
show (ideally, by a direct combinatorial argument) that the sign-coherence property~\ref{SC},
or some hereditary %\linebreak[3]
strengthening thereof, is mutation inva\-riant;
\item\label{sect5_ii} %[(ii)]
show that this property holds for a particular universal collection of quivers.
\end{enumerate}
Unfortunately, we have been unable to successfully implement this strategy.
%\bigskip
\section{Additive categorification}
\label{sec:categorification}
Roughly speaking, an \emph{(additive) categorification} of a quiver
$Q$ is a diagram in the shape of $Q$ in an abelian or triangulated category together with a rule for mutating the diagram as the quiver undergoes a mutation.
There is extensive literature on this popular topic, mostly in the case when the quivers are acyclic.
(There is also an alternative notion of a \emph{monoidal categorification}~\cite{leclerc-hernandez}
which we do not discuss here.)
Existence of a categorification is a hereditary property: a categorification of~$Q$ gives rise to a categorification of any subquiver of a quiver mutation equivalent~to~$Q$.
There are known examples of quivers which cannot be categorified in the traditional sense.
Consequently, any $n$-universal quiver (for sufficiently large~$n$) cannot be categorified.
In this section, we give a simple direct argument showing why universal quivers admit no Hom-finite categorification. We also note that universal quivers serve as a natural test case for any attempt to generalize the notion of categorification using Hom-infinite Jacobian algebras, as suggested by P.-G.~Plamondon~\cite{plamondon}.
Let us quickly review the basic ideas, sticking to the triangulated category setting.
We will need a more general notion of a quiver which involves designating some of its vertices as \emph{frozen}. (Mutations at those vertices are forbidden.)
From now on, we fix a field $K$ and work with $K$-categories. These are categories $\mathcal C$ in which $\Hom(X,Y)$ is a vector space over~$K$ for any objects $X,Y\in \mathcal C$, and composition is $K$-bilinear. We say that $\mathcal C$ is \emph{Hom-finite} if $\Hom(X,Y)$ is finite dimensional for any $X,Y\in \mathcal C$.
%
Any object $X=\bigoplus_{i=1}^nX_i$ in a $\Hom $-finite Krull--Schmidt category defines a finite-dimensional algebra $\End (X)$.
\begin{definition}[{\cite[Section~II.1]{BIRSc}}]
\label{def:BIRSc}
Let $\mathcal C$ be a $\Hom$-finite, Krull--Schmidt, 2-Calabi--Yau triangulated $K$-category.
That is, all objects are direct sums of indecomposables, with canonical isomorphisms
$\Hom(X,Y)\cong D\!\Hom (Y,X[2])$
where $D\!=\!\Hom _K(-,K)$ denotes the vector space dual.
A \emph{cluster structure} on~$\mathcal C$ is a collection of
objects, called \emph{extended clusters}, some of whose components are designated \emph{frozen}; this collection must satisfy the following conditions:
\begin{enumerate}[label=(\alph*)]
\item\label{defi6.1_a}
For every nonfrozen component $T_k$ of an extended cluster $T$, there is a unique, up to isomorphism, indecomposable object $T_k'$ such that $T'=T/T_k\oplus T_k'$ is another extended cluster.
%\item[(b)]
Moreover $T_k$ and $T_k'$ are related by two distinguished triangles
\[
\begin{aligned}
T_k[-1]\to T_k'\to B\to &T_k \,, \\
&T_k\to B'\to T_k'\to T_k[1] \,;
\end{aligned}
\]
here $B$ (resp.~$B'$) is the minimal right (resp.~left) $\add (T/T_k)$-approximation of~$T_k$.
We say that $T'$ is obtained from $T$ by a \emph{mutation} at~$T_k$.
\item\label{defi6.1_b}
For every extended cluster $T$, define the quiver $Q_T$ as follows.
The vertices~$v_k$ of $Q_T$ are in bijection with the components~$T_k$ of~$T$.
For each pair of vertices $v_i$ and~$v_j$,
at least one of them nonfrozen,
draw $\dim(\Hom(T_i,T_j)/I_{ij})$ arrows $v_i\to v_j$
where $I_{ij}$ is generated by the morphisms which factor through the remaining objects~$T_k$,
for $k\notin\{i,j\}$.
The quiver $Q_T$ constructed in this way should have no loops and no 2-cycles.
\item\label{defi6.1_c}
The quiver $Q_{T'}$ of $T'=T/T_k\oplus T_k'$ is obtained from $Q_T$ by mutating at~$v_k$.
\end{enumerate}
When conditions~\ref{defi6.1_a}--\ref{defi6.1_c} are satisfied, the resulting cluster structure on the category~$\mathcal{C}$
is called a (Hom-finite, additive) \emph{categorification} of any of the quivers~$Q_T$.
Any such categorification can be restricted to the set of extended clusters which are \emph{reachable} from a given extended cluster~$T$ by a sequence of mutations.
These reachable clusters naturally correspond to the seeds of the cluster algebra defined by the quiver~$Q_T$, and
the quivers appearing in the restricted categorification
are precisely the quivers mutation equivalent to~$Q_T$.
\end{definition}
%\pagebreak[3]
%Usually we need to assume that our triangulated category is Hom-finite.
\begin{theorem}
\label{th:universal-no-categorification}
Let $Q$ be one of the quivers shown in Figures~\ref{fig:extended-somos-4}--\ref{fig:double-4-cycle}.
Then:
\begin{itemize}%[leftmargin=.3in]
\item
the quiver $Q$ does not allow a Hom-finite categorification;
\item
for any potential $S$ for $Q$, the Jacobian algebra $J(Q,S)$ is infinite-dimensional.
\end{itemize}
\end{theorem}
\begin{proof}
In a categorification of~$Q$, the initial cluster consists of objects corresponding to the vertices of~$Q$. When we mutate at the vertices other than $u$ and~$v$ (see Figures~\ref{fig:extended-somos-4}--\ref{fig:double-4-cycle}), the objects $T_u$ and $T_v$ corresponding to $u$ and~$v$ remain unchanged. After any such sequence of mutations, the number of arrows from $u$ to $v$ equals the dimension of a certain quotient of $\Hom(T_u,T_v)$, see Definition~\ref{def:BIRSc}\ref{defi6.1_b}.
In particular, this number (which depends on the mutation sequence) cannot exceed $\dim\Hom(T_u,T_v)$.
Since this number is unbounded, $\Hom(T_u,T_v)$ must be infinite-dimensional, so the categorification is not Hom-finite.
Suppose $J(Q,S)$ is finite-dimensional. Under this condition,
C.~Amiot~\cite{amiot} constructed a cluster category~$\mathcal C(Q,S)$,
and showed that $\mathcal C(Q,S)$ is a Hom-finite categorification of the cluster algebra corresponding to~$Q$.
Since such a Hom-finite categorification does not exist, we conclude that $\dim J(Q,S)=\infty$.
\end{proof}
The conclusions of Theorem~\ref{th:universal-no-categorification} hold for any quiver~$Q$ satisfying the conditions in Lemma~\ref{lem:gluing}, and for any quiver which is mutation equivalent to a quiver containing such~$Q$ as a full subquiver.
\bibliographystyle{amsplain-ac}
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{Dragon continuum}
\e{dragon continuum}
\FIGURE{A}{dragon continuum}
\FIGURE{B}{dragon continuum}
\GIF{BB}{dragon continuum}
L. Fearnley, D. G. Wright : Geometric realization of a
Bellamy Continuum, BUll. London Math. Soc. 15(1993),
177-183.
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\documentclass[main.tex]{subfiles}
\begin{document}
\section{Hypothèses}
\begin{itemize}
\item la non-linéarité est statique et n'évolue pas dans le temps. On peut la séparer de la dynamique du système. Par exemple, la saturation (ou la zone morte) est une non-linéarité statique.
\item la partie dynamique (linéaire) est un filtre passe-bas \emph{suffisamment efficace} pour négliger les harmoniques d'ordre supérieur à 1. Plus précisément, l'ordre relatif du filtre doit être supérieur strict à 1.
\end{itemize}
\section{Schéma-blocs}
\[ x \longrightarrow \boxed{
\begin{array}{c}
\text{Non} \\
\text{Linéarité}
\end{array}
} \longrightarrow y \longrightarrow \boxed{H(p)} \longrightarrow z \]
La fonction de transfert $H(p)$ (fraction rationnelle) correspond à un filtre passe-bas de degré relatif $\geq 2$.\\
On prend $x=X\sin \omega t$. Dans le cas linéaire, seule la valeur de $\omega$ influe sur le tracé de la diagramme de Bode du système. Dans le cas non-linéaire, on a plusieurs tracés de réponses fréquentielles. Par exemple, avec une saturation, on obtient des réponses fréquentielles qui dépendent de l'amplitude d'entrée de $X$ dès qu'elle devient trop élevée.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.4]{2/424-1.png}
\end{figure}
Puisque $H(p)$ rejette les harmoniques d'ordre supérieur à 1, on peut donc décomposer \[y(t)=P \sin \omega t + Q \cos \omega t\]
Dans le cas d'une NL symétrique, on a
\begin{align*}
P& =\frac{2}{T} \int_{[T]} y(t) \sin \omega t dt\\
Q& =\frac{2}{T} \int_{[T]} y(t) \cos \omega t dt \quad \text{ avec } \omega T = 2\pi
\end{align*}
\begin{rem}
Si la NL est non-symétrique, $y(t) = Y+P\sin \omega t + Q \cos \omega t$ avec $Y=\frac{1}{T}\int_{[T]} y(t) dt$. La composante continue $Y$ peut être négligée pour l'analyse de stabilité et modélisée par une perturbation constante à l'entrée de $H(p)$.
\end{rem}
On définit le gain complexe équivalent :
\[ N(X) = \frac{P+jQ}{X} \text{ qu'on note } N(x) = N_P(X) + jN_Q(X) \]
\begin{itemize}
\item $N_P(X)=\frac{P}{X}$ est la gain en phase,
\item $N_Q(X)=\frac{Q}{X}$ est la gain en quadrature.
\end{itemize}
\begin{rem}
\begin{itemize}
\item À la différence du système linéaire, pour une même pulsation, on a plusieurs réponses fréquentielles qui dépendent de l'amplitude de l'entrée $X$. L'analyse de stabilité doit donc se faire par rapport à tous les tracés.
% Inclure le nyquist du génie
\item Les manipulations de schéma-blocs doivent satisfaire les règles connues (principe de superposition) et s'assurer que le signal en amont du bloc NL est le même, et en aval, qu'il est suffisamment filtré pour ne garer que le 1er harmonique.
\begin{example}
\begin{figure}[h!]
\centering
\begin{tikzpicture}
\sbEntree{E}
\sbComp[3]{comp}{E}
\sbRelier[$e$]{E}{comp}
\sbBloc[2]{C}{$C(p)$}{comp}
\sbRelier{comp}{C}
\sbBloc[2]{NL}{Non-linéarité}{C}
\sbRelier[$x$]{C}{NL}
\sbBloc[2]{sys}{$H(p)$}{NL}
\sbRelier{NL}{sys}
\sbSortie[2]{S}{sys}
\sbRelier{sys}{S}
\sbRenvoi{sys-S}{comp}{}
\end{tikzpicture}
\vspace{5mm}
équivalent à
\vspace{5mm}
\begin{tikzpicture}
\sbEntree{E}
\sbBloc[3]{C}{$C(p)$}{E}
\sbRelier[$e$]{E}{C}
\sbComp[4]{comp}{C}
\sbRelier{C}{comp}
\sbBloc[2]{NL}{Non-linéarité}{comp}
\sbRelier[$x$]{comp}{NL}
\sbBloc[2]{sys}{$H(p)$}{NL}
\sbRelier{NL}{sys}
\sbSortie[2]{S}{sys}
\sbRelier{sys}{S}
\sbDecaleNoeudy[4]{S}{R}
\sbBlocr[8]{Cr}{$C(p)$}{R}
\sbRelieryx{sys-S}{Cr}
\sbRelierxy{Cr}{comp}
\end{tikzpicture}
\vspace{5mm}
non équivalent à
\vspace{5mm}
\begin{tikzpicture}
\sbEntree{E}
\sbComp[3]{comp}{E}
\sbRelier[$e$]{E}{comp}
\sbBloc[4]{NL}{Non-linéarité}{comp}
\sbRelier[$\hat{x}\neq x$]{comp}{NL}
\sbBloc[2]{sys}{$H(p)C(p)$}{NL}
\sbRelier{NL}{sys}
\sbSortie[2]{S}{sys}
\sbRelier{sys}{S}
\sbRenvoi{sys-S}{comp}{}
\end{tikzpicture}
\caption{Transformations de schéma-blocs}
\end{figure}
\end{example}
\end{itemize}
\end{rem}
\newpage
\section{Analyse de la stabilité.}
Système NL bouclé à retour unitaire
\begin{figure}[h!]
\centering
\begin{tikzpicture}
\sbEntree{E}
\sbComp[4]{comp}{E}
\sbRelier[$e$]{E}{comp}
\sbBloc[4]{NL}{$N(X)$}{comp}
\sbRelier[$x$]{comp}{NL}
\sbBloc[4]{sys}{$T_{BO}(p)$}{NL}
\sbRelier{NL}{sys}
\sbSortie[4]{S}{sys}
\sbRelier{sys}{S}
\sbRenvoi{sys-S}{comp}{}
\end{tikzpicture}
\end{figure}
Dans l'analyse harmonique, la NL est modélisée par $N(X)$. Ainsi, il faut trouver l'expression de $N(X)$ en fonction de la NL :
\begin{example}[Saturation]
\begin{figure}[h!]
\centering
\includegraphics[scale=0.4]{2/424-4.png}
\end{figure}
Calcul de $N(X)$ :
Pour $0 \leq t \leq t_1$ : $y(t) = X\sin \omega t$
$t_1 \leq t \leq \frac{\pi}{\omega}-t_1$ : $y(t) = X_m = X\sin \omega t_1$
\begin{align*}
P & = \frac{4\omega}{\pi} \int_0^{\frac{\pi}{2\omega}} y(t) \sin \omega t dt \\
& = \frac{4\omega}{\pi} [ \int_0^{t_1} X \sin^2 \omega t dt + \int_{t_1}^{\frac{\pi}{2\omega}} X \sin \omega t_1 \sin \omega t dt ] \\
& = \frac{2X}{\pi}[ \omega t_1 + \frac{\sin 2\omega t_1}{2} ] \\
\intertext{ $t_1=\arcsin(\frac{X_m}{X})$ et $Q=0$}
\intertext{Ainsi}
N(x) & =
\begin{cases}
1 & \si X << X_m\\
\frac{2}{\pi}[\arcsin\frac{X_m}{X}+\frac{X_m}{X}\sqrt{1-\frac{X_m^2}{X^2}}] & \si X > X_m
\end{cases}
\end{align*}
Le dénominateur de la BF, $1+N(X)T_{BO}(p)$, donne la limite de stabilité : $T_{BO}(j\omega) = - \frac{1}{N(X)}$.
On a donc pour notre exemple de saturation
\begin{figure}[h!]
\centering
\includegraphics[scale=0.2]{2/424-5.png}
\end{figure}
\end{example}
Ainsi dans le cas NL, on remplace le point critique $-1$ par le lieu critique $\frac{-1}{N(X)}$. Par conséquent, l'analyse de stabilité est réalisée par rapport à $\frac{-1}{N(X)}$.
Dans le cas où le tracé de Nyquist ne présente pas d'intersection avec le lieu critique, on applique le critère de Nyquist pour la stabilité ou celui du revers sur la FT, qui est alors stable, strictement propre et à déphasage minimal.
Si on a une ou plusieurs intersections, on a un régime auto-oscillant (cycle limite).
\section{Étude de la stabilité du cycle limite}
Soit $(X_0,\omega_0)$ solution de $T_{B0}(j\omega_0)=-\frac{1}{N(X_0)}$.\\\
\subsection*{Critère analytique}
\begin{multicols}{2}
On décompose \[1+T_{B0}(j\omega)N(X)=R(\omega,X)+jI(\omega,X)\]
Ainsi, on a \[R(\omega_0,X_0)=0 \text{ et }I(\omega_0,X_0)=0\]
\end{multicols}
Par conséquent, l'entrée de la NL $x(t)=X_0e^{j\omega_0t}$\\
À $t_0$ appliquons une perturbation :
\[X_1 = X_0 + \delta X \text{ et }\omega_1 = \omega_0+\delta \omega \quad \text{ avec } |\frac{\delta X}{X_0}|<<1 \text{ et }|\frac{\delta \omega}{\omega_0}|<<1 \]
$x(t)$ n'est plus périodique et présente ainsi un amortissement $m>0$ (stable) ou $<0$ (instable).
\[ x(t) = (X_0 + \delta X) e^{-mt} e^{j(\omega_0 + \delta \omega) t} =(X_0 + \delta X) e^{j(\omega_0 + \delta \omega + jm) t} \]
Ainsi la perturbation nous donne un régime auto-oscillant avec une amplitude $X_0+\delta X$ et une pulsation complexe $\omega_0 + \delta \omega + jm$.
\[ R(\omega_0+\delta \omega + jm, X_0 + \delta X) + jI(\omega_0 + \delta \omega + jm,X_0 + \delta X) = 0 \]
\newcommand{\zero}{(\omega_0,X_0)}
On applique un DL du 1er ordre autour de $\zero$ :
\[ \left(\derivp[R]{X}|_{\zero} + j \derivp[I]{X}|_{\zero}\right) \delta X + \left(\derivp[R]{\omega}|_{\zero} + j \derivp[I]{\omega}|_{\zero}\right)(\delta \omega + jm)\approx 0 \]
i.e. en notant $\derivp[]{X}|_{\zero}=\derivp[]{X}|_0$
\begin{align*}
\derivp[R]{\omega}|_0 .\delta \omega + \derivp[R]{X}|_0 .\delta X - \derivp[I]{\omega}|_0 .m & = 0 \\
\text{ et }\quad \derivp[I]{\omega}|_0 .\delta \omega + \derivp[I]{X}|_0 .\delta X + \derivp[R]{\omega}|_0 .m & = 0
\end{align*}
Élimination de $\delta \omega$ :
\[ \left( (\derivp[R]{\omega}|_0)^2 + (\derivp[I]{\omega}|_0)^2 \right) m = \left( \derivp[R]{X}|_0.\derivp[I]{\omega}|_0 - \derivp[R]{\omega}|_0.\derivp[I]{X}|_0 \right) \delta X \]
\newpage
\noindent Différents types de perturbation
\begin{figure}[h!]
\centering
\includegraphics[scale=0.4]{2/424-61.png}
\end{figure}
$m > 0$ et $\delta X > 0$ : CL est stable
$m < 0$ et $\delta X > 0$ : CL est instable
\begin{figure}[h!]
\centering
\includegraphics[scale=0.4]{2/424-62.png}
\end{figure}
$\delta X < 0$ et $m < 0$ : CL est stable
$\delta X < 0$ et $m > 0$ : CL est instable
Donc le cycle limite est stable si et seulement si $\delta X . m >0$\\
Pour que $\delta X . m >0$ :
\[\boxed{ \derivp[R]{X}|_0.\derivp[I]{\omega}|_0 - \derivp[R]{\omega}|_0.\derivp[I]{X}|_0 > 0 }\]
\begin{center}
\emph{Condition de stabilité du cycle limite dans le plan de Nyquist}
\end{center}
On pose $T_{B0}(j\omega) = U(\omega) + jV(\omega)$ et $-\frac{1}{N(X)} = L(X) + jM(X)$
On a un cycle limite si
\[ T_{B0}(j\omega_0) = -\frac{1}{N(x)} \quad \Rightarrow \quad
\begin{cases}
R(\omega,X) & = U(\omega) - L(X)\\I(\omega,X) & = V(\omega) - M(X)
\end{cases}
\]
d'où d'après la condition de stabilité du cycle limite :
\[\boxed{-\derivp[L]{X}|_0.\derivp[V]{\omega}|_0 + \derivp[U]{\omega}|_0.\derivp[M]{X}|_0 > 0}\]
\subsection*{Détermination graphique}
Si on se place dans $\R^3$, on a 2 vecteurs : $\vect{U\\V\\0}$ et $\vect{L\\M\\0}$ qui décrivent respectivement $T_{BO}$ et $-\frac{1}{N}$.
Les tangentes aux courbes $T_{BO}$ et $-\frac{1}{N}$ sont colinéaires aux vecteurs $\vec{v_T} = \derivp[]{\omega}\vect{U\\V\\0}$ et $\vec{u_N}=\derivp[]{X}\vect{L\\M\\0}$.
\[\vec{v_T}\wedge\vec{u_N} = \vect{0\\0\\-\derivp[L]{X}.\derivp[V]{\omega} + \derivp[U]{\omega}.\derivp[M]{X}}\]
Ainsi, la condition $-\derivp[L]{X}.\derivp[V]{\omega} + \derivp[U]{\omega}.\derivp[M]{X}>0 \Rightarrow (\vec{v_T},\vec{u_N})$ dans le sens direct.
\begin{thm}[Critère de Loeb]
Le cycle limite est stable si l'intersection de $T_{BO}(j\omega)$ et de $-\frac{1}{N(X)}$ est telle qu'en parcourant le lieu de Nyquist $T_{BO}(j\omega)$ dans le sens des $\omega$ croissants, on laisse à gauche la direction des $X$ croissant sur le lieu critique.
\end{thm}
\begin{figure}[h!]
\centering
\includegraphics[scale=0.4]{2/424-7.png}
\end{figure}
\end{document}
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\begin{thebibliography}{1}
\bibitem{Deyermond2008} Deyermond, A. D. (2008). Fernando de Rojas de 1499 a 1502: {\textquestiondown}Cristiano nuevo? \textit{Medievalia}, 40, 130--141.
\end{thebibliography}
\end{document}
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\clan {Marko Razpet}
\begin{skupina}{G}
\konferenca
{Trije znameniti anti\v{c}ni geometrijski problemi in GeoGebra}
{Posvet Partnerstvo Pedago\v{s}ke fakultete Univerze v Ljubljani in vzgojno-izo\-bra\-\v{z}e\-val\-nih in\v{s}titucij}
{Ljubljana} {} {januar} {2014}
\konferenca
{Hipopeda na rogatem torusu}
{Mednarodna konferenca InfoKomTeh}
{Ljubljana} {} {april} {2014}
\konferenca
{Matematika v Mo\v{c}nikovem \v{c}asu}
{Strokovno sre\v{c}anje in 66. ob\v{c}ni zbor DMFA}
{Cerkno} {} {oktober} {2014}
\end{skupina}
\begin{skupina}{H}
\clanekRevijaIs
{}
{Franc Vitez Mo\v{c}nik: ob 200-letnici njegovega rojstva}
{Obzornik Mat.\ Fiz.} {61} {2014} {6} {2{2}0--2{2}9}
\clanekRevijaIs
{}
{Kro\v{z}na konstanta in skrivnostni rokopis}
{Presek} {41} {2013/2014} {5} {4--9}
\clanekRevijaIs
{}
{Naloga}
{Presek} {41} {2013/2014} {6} {7}
\clanekRevija
{}
{Re\v{s}itev naloge iz 6. \v{s}tevilke 41. letnika}
{Presek} {42} {2014/2015} {3} {9}
\clanekZbornik
{}
{Hipopeda na rogatem torusu}
{Mednarodna konferenca InfoKomTeh}
{Ljubljana} {} {april} {2014}
{Nova vizija tehnologij prihodnosti : zbornik referatov} {248--257}
\clanekZbornik
{}
{Trije znameniti anti\v{c}ni geometrijski problemi in GeoGebra}
{Posvet Partnerstvo Pedago\v{s}ke fakultete Univerze v Ljubljani in vzgojno-izo\-bra\-\v{z}e\-val\-nih in\v{s}titucij}
{Ljubljana} {} {januar} {2014}
{Sodobni pedagoški izzivi v teoriji in praksi : zbornik povzetkov} {1{1}7-130}
\end{skupina}
\begin{skupina}{I}
\razno
{Mentorstvo pri štirih diplomskih delih.}
\razno
{Mentorstvo pri enem magistrskem delu.}
\razno
{Dva opisa novih knjig v Obzorniku Mat. Fiz.}
\end{skupina}
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\title{Kula Shells and Zombies: Notes on Value}
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\par
Power relations are played out on the stage of desire. A valued object is a desired object. Value is a means through which culture effects desire. Ideology and culture effect power relations through the medium of value, whereas raw coercion is the simple imposition of the desire of one body on another, against the grain of the latter’s desire.
Culture and capitalism have become interpenetrating value systems. For capitalism to function it must penetrate culture; it must overcome value systems that contradict it. Previously, the immaterial was outside the domain of capital, however as capital’s domain grows and technology changes, it inches further and further into the immaterial. Images and information are now valuable commodities. The range of objects, emotions and concepts that are reduced to a monetary value becomes greater as capital’s penetration into culture grows. Our own cultural limitations on capital are shrinking. Justice as an “eye for an eye” is a moral equation which preceded capitalism. Justice is a value system that has yet to be completely subsumed by capitalist logic, but it has become adapted to capital’s needs. The blood lust for punishment sold on TV cop shows may function for the benefit of capital but its driving force is distinct from profit. Capitalism was once just one value system among many; now it is the system which attempts to transform all other systems into itself.
When the British and German banana plantation owners first tried to get the Bakweri of West Cameroon to work for them, few Bakweri would submit. Those that avoided plantation work thought that workers were members of a witchcraft association. They believed that the workers killed their relatives and children by turning them into zombies and making them work on some far away mountain, where the witch masters had a modern town. In the 1950s the Bakweri cultivated bananas collectively, and the witchcraft stopped. In the 1960s when the price of bananas fell the witches came back. The elders said that no one should pick money off the ground because money was being scattered by Frenchmen to draw men to the waterside where they would be employed as zombies to construct a new harbor. These stories of zombies and witchcraft must have discouraged not a few Bakweri from engaging in wage labor and for a good reason: they are in a sense true stories. Zombies are dead and wage labor sucks the life-blood out of workers. For those that have a non-capitalist system of value circulation and production, wage labor is often incomprehensible and unnecessary. The need for money must be imposed. People only submit to wage labor when they are no longer self sufficient, the theft of peasant lands is often the only thing that will turn peasants into workers. Bakweris that refused to work on plantations continued to understand wage labor from the perspective of their own cultural logic and not that of capital.
Cultures that still consider that certain objects can never be sold and thus have exclusively qualitative value, reveal to us the brutal indiscriminacy of the general equivalent, by stark contrast. Money is after all the most indiscriminate of whores. In the New Guinea region, \emph{Kula} arm shells and necklaces circulate among many islands and eventually return to their origin through a series of gift donations. The only time that they are traded is when a young man receives his first \emph{kula} shell. On that occasion the shell can only be traded for specific restricted types of goods and services. \emph{Kula} shells are gifts that cement trade partnerships, but they must eventually be reciprocated if a trade partnership is to continue. \emph{Kula} shells are given names and are said to not ever die, their origin and path is remembered; they therefore bring fame to kula givers. The giving and receiving of \emph{kula} shells structures a trade network but kula shells are not merely a means to acquire goods, they also generate prestige for the donor. Thus this trade network does not only produce economic value but also social value. The prestige gained by giving \emph{kula} shells cannot be compared with the status acquired with the purchase of a consumer item. In New Guinea prestige is gained slowly, through a complex of relationships, it has nothing in common with status that can be immediately bought. The day the \emph{kula} shell is traded for money the entire value system and trade network regulated by the \emph{kula} shell will begin to travel down the path of its own destruction.
The Tiv of central Nigeria had 3 categories of flows: consumer goods, prestige goods, and women and children. When the money economy intervened in the Tiv economy, money was categorized as an object of prestige. Money crossed over the traditional boundaries between categories because it began to be used to buy consumer goods by male merchants when previously only women dealt in consumer goods. This is just one of innumerable examples in which money has inserted itself into a non-capitalist economy and broken down its categories of value.
Capitalism becomes hegemonic by bending other systems of value to its logic. Capitalism is a virus but this does not mean that there aren’t those who produce its antibodies. To Kill King Abacus is to destroy the capitalist equation, the mechanism of value that is trying to reduce life itself to a mere quantity. There are moments in which culture slows the spread of capital, where cultural systems of value resist their own transformation into capitalist value. But this does not mean that non-capitalist forms of value are therefore liberatory. Culture is an ineffective weapon against authority. Culture codifies relationships and is a means through which authority is constructed. Culture, capital, justice and law all have their own scales to weigh behavior. They measure, judge and channel human action; they are all coercive. In the absence of value systems desire shoots in new directions. Insurrection is desire rebelling against value.
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The Anarchist Library
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Anti-Copyright
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Anonymous
Kula Shells and Zombies: Notes on Value
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Retrieved on April 6\textsuperscript{th}, 2009 from \href{http://www.geocities.com/kk\_abacus/VALUEART.html}{www.geocities.com}
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\bib{2003/de-jonge-thesis}
\yr 2003
\by Merijn de Jonge
\book To reuse or to be reused: techniques for component composition and construction
\publ Faculty of Natural Sciences, Mathematics, and Computer Science, University of Amsterdam
\phdthesis
\url http://homepages.cwi.nl/~paulk/dissertations/DeJonge.pdf
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\bibitem{Adamczyk-Garbowska1993} Adamczyk-Garbowska Monika, \textit{I. B. Singer {\textendash} portret artysty w kraju m{\l}odo{\'s}ci}, "ExLibris", 1993, nr 31, s. 12--13.
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% \iffalse meta-comment
%
% Copyright (C) 1993-2022
% The LaTeX Project and any individual authors listed elsewhere
% in this file.
%
% This file is part of the LaTeX base system.
% -------------------------------------------
%
% It may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3c
% of this license or (at your option) any later version.
% The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of LaTeX
% version 2008 or later.
%
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% and covered by LPPL is defined by the unpacking scripts (with
% extension .ins) which are part of the distribution.
%
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% Filename: clsguide.tex
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\documentclass{ltxguide}[1995/11/28]
\title{\LaTeXe~for class and package writers}
\author{Copyright \copyright~1995--2006 The \LaTeX\ Project\\
All rights reserved}
\date{15 February 2006}
\begin{document}
\maketitle
\tableofcontents
\section{Introduction}
This document is an introduction to writing classes and packages for
\LaTeX{}, with special attention given to upgrading existing
\LaTeX~2.09 packages to \LaTeXe{}. The latter subject is also
covered in an article by Johannes Braams published in TUGboat~15.3.
\subsection{Writing classes and packages for \LaTeXe}
\LaTeX{} is a document preparation system that enables the document
writer to concentrate on the contents of their text, without bothering
too much about the formatting of it. For example, chapters are
indicated by |\chapter{<title>}| rather than by selecting 18pt bold.
The file that contains the information about how to turn logical
structure (like `|\chapter|') into formatting (like `18pt bold ragged
right') is a \emph{document class}. In addition, some features (such
as colour or included graphics) are independent of the document class
and these are contained in \emph{packages}.
One of the largest differences between \LaTeX~2.09 and \LaTeXe{} is in
the commands used to write packages and classes. In \LaTeX~2.09,
there was very little support for writing |.sty| files, and so writers
had to resort to using low-level commands.
\LaTeXe{} provides high-level commands for structuring packages.
It is also much easier to build classes and packages on top of each
other, for example writing a local technical report class |cetechr|
(for the Chemical Engineering department) based on |article|.
\subsection{Overview}
This document contains an overview of how to write classes and
packages for \LaTeX{}. It does \emph{not} introduce all of the
commands necessary to write packages: these can be found in either
\emph{\LaTeXbook} or \emph{\LaTeXcomp}. But it does describe the new
commands for structuring classes and packages.
\begin{description}
\item[Section~\ref{Sec:general}] contains some general advice about
writing classes and packages. It describes the difference between
classes and packages, the command naming conventions, the use of
|doc| and |docstrip|, how \TeX's primitive file and box commands
interact with \LaTeX{}. It also contains some hints about general
\LaTeX{} style.
\item[Section~\ref{Sec:structure}] describes the structure of classes
and packages. This includes building classes and packages on top of
other classes and packages, declaring options and declaring
commands. It also contains example classes.
\item[Section~\ref{Sec:commands}] lists the new class and package
commands.
\item[Section~\ref{Sec:upgrade}] gives detailed advice on how to
upgrade existing \LaTeX~2.09 classes and packages to \LaTeXe{}.
\end{description}
\subsection{Further information}
For a general introduction to \LaTeX{}, including the new features of
\LaTeXe{}, you should read \emph{\LaTeXbook}
by Leslie Lamport~\cite{A-W:LLa94}.
A more detailed description of the new features of \LaTeX, including an
overview of more than 200 packages and nearly 1000 ready to run examples, is
to be found in \emph{\LaTeXcomp\ second edition} by Frank Mittelbach and
Michel Goossens~\cite{A-W:MG2004}.
The \LaTeX{} system is based on \TeX{}, which is
described in \emph{The \TeX book} by Donald E.~Knuth~\cite{A-W:DEK91}.
There are a number of documentation files which accompany every copy
of \LaTeX{}. A copy of \emph{\LaTeX{} News} will come out with each
six-monthly release of \LaTeX{}, and is found in the files
|ltnews*.tex|. The author's guide \emph{\usrguide} describes the new
\LaTeX{} document features; it is in |usrguide.tex|. The guide
\emph{\fntguide} describes the \LaTeX{} font selection scheme for
class- and package-writers; it is in |fntguide.tex|. Configuring
\LaTeX{} is covered by the guide \emph{\cfgguide} in
\texttt{cfgguide.tex} whilst the philosophy behind our policy on
modifying \LaTeX{} is described in \emph{\modguide} in
\texttt{modguide.tex}.
The documented source code (from the files used to produce the kernel
format via |latex.ltx|) is now available as
\emph{The \LaTeXe\ Sources}.
This very large document also includes an index of
\LaTeX{} commands. It can be typeset from the \LaTeX{} file
|source2e.tex| in the |base| directory, using the source files and
the class file |ltxdoc.cls| from this directory.
For more information about \TeX{} and \LaTeX{}, please contact your
local \TeX{} Users Group, or the international \TeX{} Users Group.
Addresses and other details can be found at:
\begin{quote}\small\label{addrs}
\texttt{http://www.tug.org/lugs.html}
\end{quote}
\subsection{Policy on standard classes}
Many of the problem reports we receive concerning the standard classes
are not concerned with bugs but are suggesting, more or less politely,
that the design decisions embodied in them are `not optimal' and
asking us to modify them.
There are several reasons why we should not make such changes to these
files.
\begin{itemize}
\item
However misguided, the current behaviour is clearly what was
intended when these classes were designed.
\item
It is not good practice to change such aspects of `standard classes'
because many people will be relying on them.
\end{itemize}
We have therefore decided not to even consider making such
modifications, nor to spend time justifying that decision. This does
not mean that we do not agree that there are many deficiencies in the
design of these classes, but we have many tasks with higher priority
than continually explaining why the standard classes for \LaTeX{}
cannot be changed.
We would, of course, welcome the production of better classes, or of
packages that can be used to enhance these classes. So your first
thought when you consider such a deficiency will, we hope, be ``what
can I do to improve this?''
Similar considerations apply to those parts of the kernel that are
implementing design decisions, many of which should be left to the
class file but are not in the current system. We realise that in such
cases it is much more difficult for you to rectify the problem
yourself but it is also the case that making such changes in the
kernel would probably be a major project for us; therefore such
enhancements will have to wait for \LaTeX3.
\section{Writing classes and packages}
\label{Sec:writing}
This section covers some general points concerned with writing
\LaTeX{} classes and packages.
\subsection{Old versions}
If you are upgrading an existing \LaTeX~2.09 style file then we
recommend freezing the 2.09 version and no longer maintaining it.
Experience with the various dialects of \LaTeX{} which existed in the
early 1990's suggests that maintaining packages for different versions
of \LaTeX{} is almost impossible. It will, of course, be necessary
for some organisations to maintain both versions in parallel for some
time but this is not essential for those packages and classes
supported by individuals: they should support only the new standard
\LaTeXe{}, not obsolete versions of \LaTeX{}.
\subsection{Using `docstrip' and `doc'}
If you are going to write a large class or package for \LaTeX{} then
you should consider using the |doc| software which comes with
\LaTeX{}.
\LaTeX{} classes and packages written using this can be
processed in two ways: they can be run through \LaTeX{}, to produce
documentation; and they can be processed with |docstrip|, to produce
the |.cls| or |.sty| file.
The |doc| software can automatically generate indexes of definitions,
indexes of command use, and change-log lists. It is very useful for
maintaining and documenting large \TeX{} sources.
The documented sources of the \LaTeX{} kernel itself, and of the
standard classes, etc, are |doc| documents; they are in the |.dtx|
files in the distribution. You can, in fact, typeset the source code
of the kernel as one long document, complete with index, by running
\LaTeX{} on |source2e.tex|. Typesetting these documents uses the
class file |ltxdoc.cls|.
For more information on |doc| and |docstrip|, consult the files
|docstrip.dtx|, |doc.dtx|, and \emph{\LaTeXcomp}. For examples of its
use, look at the |.dtx| files.
\subsection{Is it a class or a package?}
\label{Sec:classorpkg}
The first thing to do when you want to put some new \LaTeX{} commands
in a file is to decide whether it should be a \emph{document class} or a
\emph{package}. The rule of thumb is:
\begin{quote}
If the commands could be used with any document class, then make
them a package; and if not, then make them a class.
\end{quote}
There are two major types of class: those like |article|, |report| or
|letter|, which are free-standing; and those which are extensions or
variations of other classes---for example, the |proc| document class,
which is built on the |article| document class.
Thus, a company might have a local |ownlet| class for printing letters
with their own headed note-paper. Such a class would build on top of
the existing |letter| class but it cannot be used with any other
document class, so we have |ownlet.cls| rather than |ownlet.sty|.
The |graphics| package, in contrast, provides commands for including
images into a \LaTeX{} document. Since these commands can be used
with any document class, we have |graphics.sty| rather than
|graphics.cls|.
\subsection{Command names}
\LaTeX{} has three types of command.
There are the author commands, such as |\section|, |\emph| and
|\times|: most of these have short names, all in lower case.
There are also the class and package writer commands:
most of these have long mixed-case names such as the following.
\begin{verbatim}
\InputIfFileExists \RequirePackage \PassOptionsToClass
\end{verbatim}
Finally, there are the internal commands used in the \LaTeX{}
implementation, such as |\@tempcnta|, |\@ifnextchar| and |\@eha|:
most of these commands contain |@| in their name, which means they
cannot be used in documents, only in class and package files.
Unfortunately, for historical reasons the distinction between these
commands is often blurred. For example, |\hbox| is an internal
command which should only be used in the \LaTeX{} kernel, whereas
|\m@ne| is the constant $-1$ and could have been |\MinusOne|.
However, this rule of thumb is still useful: if a command has |@| in
its name then it is not part of the supported \LaTeX{} language---and
its behaviour may change in future releases! If a command is
mixed-case, or is described in \emph{\LaTeXbook}, then you can rely on
future releases of \LaTeXe{} supporting the command.
\subsection{Box commands and colour}
\label{Sec:colour}
Even if you do not intend to use colour in your own documents, by
taking note of the points in this section you can ensure that your
class or package is compatible with the |color| package. This may
benefit people using your class or package who have access to colour
printers.
The simplest way to ensure `colour safety' is to always use \LaTeX{}
box commands rather than \TeX{} primitives, that is use |\sbox| rather
than |\setbox|, |\mbox| rather than |\hbox| and |\parbox| or
the |minipage| environment rather than |\vbox|.
The \LaTeX{} box commands have new options which mean that they are now
as powerful as the \TeX{} primitives.
As an example of what can go wrong, consider that in
|{\ttfamily <text>}|
the font is restored just \emph{before} the |}|, whereas in the
similar looking construction
|{\color{green} <text>}|
the colour is restored just \emph{after} the final |}|. Normally this
distinction does not matter at all; but consider a primitive \TeX{}
box assignment such as:
\begin{verbatim}
\setbox0=\hbox{\color{green} <text>}
\end{verbatim}
Now the colour-restore occurs after the |}| and so is \emph{not}
stored in the box. Exactly what bad effects this can have depends on
how colour is implemented: it can range from getting the wrong
colours in the rest of the document, to causing errors in the
dvi-driver used to print the document.
Also of interest is the command |\normalcolor|. This is
normally just |\relax| (i.e., does nothing)
but you can use it rather like |\normalfont| to
set regions of the page such as captions or section headings to the
`main document colour'.
\subsection{Defining text and math characters}
\label{Sec:chars}
Because \LaTeXe{} supports different encodings, definitions of commands
for producing symbols, accents, composite glyphs, etc.\ must be
defined using the commands provided for this purpose and described in
\emph{\fntguide}. This part of the system is still under development
so such tasks should be undertaken with great caution.
Also, |\DeclareRobustCommand| should be used for encoding-independent
commands of this type.
Note that it is no longer possible to refer to the math font set-up
outside math mode: for example, neither |\textfont 1| nor
|\scriptfont 2| are guaranteed to be defined in other modes.
\subsection{General style}
\label{Sec:general}
The new system provides many commands designed to help you produce
well-structured class and package files that are both robust and
portable. This section outlines some ways to make intelligent use of
these.
\subsubsection{Loading other files}
\label{Sec:loading}
\NEWdescription{1995/12/01}
\LaTeX{} provides these commands:
\begin{verbatim}
\LoadClass \LoadClassWithOptions
\RequirePackage \RequirePackageWithOptions
\end{verbatim}
for using classes or packages inside other classes or packages. We
recommend strongly that you use them, rather than the primitive
|\input| command, for a number of reasons.
Files loaded with |\input <filename>| will not be listed in the
|\listfiles| list.
If a package is always loaded with |\RequirePackage...| or |\usepackage|
then, even if its loading is requested several times, it will be
loaded only once. By contrast, if it is loaded with |\input| then it
can be loaded more than once; such an extra loading may waste time and
memory and it may produce strange results.
If a package provides option-processing then, again, strange results
are possible if the package is |\input| rather than loaded by means of
|\usepackage| or |\RequirePackage...|.
If the package |foo.sty| loads the package |baz.sty| by use of
|\input baz.sty| then the user will get a warning:
\begin{verbatim}
LaTeX Warning: You have requested package `foo',
but the package provides `baz'.
\end{verbatim}
Thus, for several reasons, using |\input| to load packages is not a
good idea.
Unfortunately, if you are upgrading the file |myclass.sty| to a class
file then you have to make sure that any old files which contain
|\input myclass.sty| still work.
This was also true for the standard classes (|article|, |book| and
|report|), since a lot of existing \LaTeX~2.09 document styles contain
|\input article.sty|. The approach which we use to solve this is
to provide minimal files |article.sty|, |book.sty| and |report.sty|,
which simply load the appropriate class files.
For example, |article.sty| contains just the following lines:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\@obsoletefile{article.cls}{article.sty}
\LoadClass{article}
\end{verbatim}
You may wish to do the same or, if you think that it is safe to do so,
you may decide to just remove |myclass.sty|.
\subsubsection{Make it robust}
We consider it good practice, when writing packages and classes, to use
\LaTeX{} commands as much as possible.
Thus, instead of using |\def...| we recommend using one of
|\newcommand|, |\renewcommand| or |\providecommand|; |\CheckCommand| is
also useful. Doing this makes
it less likely that you will inadvertently redefine a command, giving
unexpected results.
When you define an environment, use |\newenvironment| or
|\renewenvironment| instead |\def\foo{...}| and |\def\endfoo{...}|.
If you need to set or change the value of a \m{dimen} or \m{skip}
register, use |\setlength|.
To manipulate boxes, use \LaTeX{} commands such as |\sbox|,
|\mbox| and |\parbox| rather than |\setbox|, |\hbox| and |\vbox|.
Use |\PackageError|, |\PackageWarning| or |\PackageInfo| (or the
equivalent class commands) rather than |\@latexerr|, |\@warning| or
|\wlog|.
It is still possible to declare options by defining |\ds@<option>| and
calling |\@options|; but we recommend the |\DeclareOption| and
|\ProcessOptions| commands instead. These are more powerful and use
less memory. So rather than using:
\begin{verbatim}
\def\ds@draft{\overfullrule 5pt}
\@options
\end{verbatim}
you should use:
\begin{verbatim}
\DeclareOption{draft}{\setlength{\overfullrule}{5pt}}
\ProcessOptions\relax
\end{verbatim}
The advantage of this kind of practice is that your code is more
readable and, more important, that it is less likely to break when
used with future versions of \LaTeX{}.
\subsubsection{Make it portable}
It is also sensible to make your files are as portable as possible. To
ensure this; they should contain only visible 7-bit text; and the
filenames should contain at most eight characters (plus the three
letter extension). Also, of course, it \textbf{must not} have the
same name as a file in the standard \LaTeX{} distribution, however
similar its contents may be to one of these files.
It is also useful if local classes or packages have a common prefix,
for example the University of Nowhere classes might begin with |unw|.
This helps to avoid every University having its own thesis class, all
called |thesis.cls|.
If you rely on some features of the \LaTeX{} kernel, or on a package,
please specify the release-date you need. For example, the package
error commands were introduced in the June 1994 release so, if you use
them then you should put:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}[1994/06/01]
\end{verbatim}
\subsubsection{Useful hooks}
Some packages and document styles had to redefine the command
|\document| or |\enddocument| to achieve their goal. This is no
longer necessary. You can now use the `hooks' |\AtBeginDocument| and
|\AtEndDocument| (see Section~\ref{Sec:delays}). Again, using these
hooks makes it less likely that your code breaks with future versions
of \LaTeX{}. It also makes it more likely that your package can work
together with someone else's.
\NEWdescription{1996/12/01}
However, note that code in the |\AtBeginDocument| hook is part of the
preamble. Thus there are restrictions on what can be put there; in
particular, no typesetting can be done.
\section{The structure of a class or package}
\label{Sec:structure}
\LaTeXe{} classes and packages have more structure than \LaTeX~2.09
style files did. The outline of a class or package file is:
\begin{description}
\item[Identification] The file says that it is a \LaTeXe{} package or
class, and gives a short description of itself.
\item[Preliminary declarations]
Here the file declares some commands and can also load
other files. Usually these commands will be just those needed for
the code used in the declared options.
\item[Options] The file declares and processes its options.
\item[More declarations] This is where the file does most of its work:
declaring new variables, commands and fonts; and loading other files.
\end{description}
\subsection{Identification}
The first thing a class or package file does is identify itself.
Package files do this as follows:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{<package>}[<date> <other information>]
\end{verbatim}
For example:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{latexsym}[1994/06/01 Standard LaTeX package]
\end{verbatim}
Class files do this as follows:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{<class-name>}[<date> <other information>]
\end{verbatim}
For example:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{article}[1994/06/01 Standard LaTeX class]
\end{verbatim}
\NEWdescription{1998/06/19}
The \m{date} should be given in the form `\textsc{yyyy/mm/dd}' and
must be present if the optional argument is used (this is also true
for the |\NeedsTeXFormat| command).
Any derivation from this syntax will result in low-level \TeX{}
errors---the commands expect a valid syntax to speed up the daily
usage of the package or class and make no provision for the case that
the developer made a mistake!
This date is checked whenever a user specifies a date in their
|\documentclass| or |\usepackage| command. For example, if you wrote:
\begin{verbatim}
\documentclass{article}[1995/12/23]
\end{verbatim}
then users at a different location
would get a warning that their copy of |article| was out of
date.
The description of a class is displayed when the class is used. The
description of a package is put into the log file. These descriptions
are also displayed by the |\listfiles| command. The phrase
\texttt{Standard LaTeX} \textbf{must not} be used in the identification
banner of any file other than those in the standard \LaTeX{}
distribution.
\subsection{Using classes and packages}
The first major difference between \LaTeX~2.09 style files and
\LaTeXe{} packages and classes is that \LaTeXe{} supports
\emph{modularity}, in the sense of building files from small
building-blocks rather than using large single files.
A \LaTeX{} package or class can load a package as follows:
\begin{verbatim}
\RequirePackage[<options>]{<package>}[<date>]
\end{verbatim}
For example:
\begin{verbatim}
\RequirePackage{ifthen}[1994/06/01]
\end{verbatim}
This command has the same syntax as the author command |\usepackage|.
It allows packages or classes to use features provided by other
packages. For example, by loading the |ifthen| package, a package
writer can use the `if\dots then\dots else\dots' commands provided
by that package.
A \LaTeX{} class can load one other class as follows:
\begin{verbatim}
\LoadClass[<options>]{<class-name>}[<date>]
\end{verbatim}
For example:
\begin{verbatim}
\LoadClass[twocolumn]{article}
\end{verbatim}
This command has the same syntax as the author command |\documentclass|.
It allows classes to be based on the syntax and appearance of another
class. For example, by loading the |article| class, a class writer
only has to change the bits of |article| they don't like, rather than
writing a new class from scratch.
\NEWfeature{1995/12/01}
The following commands can be used in the common case that you want to
simply load a class or package file with exactly those options that
are being used by the current class.
\begin{verbatim}
\LoadClassWithOptions{<class-name>}[<date>]
\RequirePackageWithOptions{<package>}[<date>]
\end{verbatim}
For example:
\begin{verbatim}
\LoadClassWithOptions{article}
\RequirePackageWithOptions{graphics}[1995/12/01]
\end{verbatim}
\subsection{Declaring options}
\NEWdescription{1998/12/01}
The other major difference between \LaTeX~2.09 styles and \LaTeXe{}
packages and classes is in option handling. Packages and classes can
now declare options and these can be specified by authors; for
example, the |twocolumn| option is declared by the |article| class.
Note that the name of an option should contain only those characters
allowed in a `\LaTeX{} name'; in particular it must not contain any
control sequences.
An option is declared as follows:
\begin{verbatim}
\DeclareOption{<option>}{<code>}
\end{verbatim}
For example, the |dvips| option (slightly simplified)
to the |graphics| package is implemented as:
\begin{verbatim}
\DeclareOption{dvips}{\input{dvips.def}}
\end{verbatim}
This means that when an author writes |\usepackage[dvips]{graphics}|,
the file |dvips.def| is loaded. As another example, the |a4paper|
option is declared in the |article| class to set the |\paperheight|
and |\paperwidth| lengths:
\begin{verbatim}
\DeclareOption{a4paper}{%
\setlength{\paperheight}{297mm}%
\setlength{\paperwidth}{210mm}%
}
\end{verbatim}
Sometimes a user will request an option which the class
or package has not explicitly declared. By default this will produce
a warning (for classes) or error (for packages); this behaviour
can be altered as follows:
\begin{verbatim}
\DeclareOption*{<code>}
\end{verbatim}
For example, to make the package |fred| produce a warning rather than
an error for unknown options, you could specify:
\begin{verbatim}
\DeclareOption*{%
\PackageWarning{fred}{Unknown option `\CurrentOption'}%
}
\end{verbatim}
Then, if an author writes |\usepackage[foo]{fred}|, they will get a
warning \texttt{Package fred Warning: Unknown option `foo'.} As
another example, the |fontenc| package tries to load a file
|<ENC>enc.def| whenever the \m{ENC} option is used. This
can be done by writing:
\begin{verbatim}
\DeclareOption*{%
\input{\CurrentOption enc.def}%
}
\end{verbatim}
\NEWdescription{1998/12/01}
It is possible to pass options on to another package or class, using
the command |\PassOptionsToPackage| or |\PassOptionsToClass| (note
that this is a specialised operation that works only for option
names). For example, to pass every unknown option on to the |article|
class, you can use:
\begin{verbatim}
\DeclareOption*{%
\PassOptionsToClass{\CurrentOption}{article}%
}
\end{verbatim}
If you do this then you should make sure you load the class at some
later point, otherwise the options will never be processed!
So far, we have explained only how to declare options, not how to
execute them. To process the options with which the file was called,
you should use:
\begin{verbatim}
\ProcessOptions\relax
\end{verbatim}
This executes the \m{code} for each option that was both specified and
declared (see Section~\ref{Sec:commands.options} for details of how
this is done).
For example, if the |jane| package file contains:
\begin{verbatim}
\DeclareOption{foo}{\typeout{Saw foo.}}
\DeclareOption{baz}{\typeout{Saw baz.}}
\DeclareOption*{\typeout{What's \CurrentOption?}}
\ProcessOptions\relax
\end{verbatim}
and an author writes |\usepackage[foo,bar]{jane}|, then they will see
the messages \texttt{Saw foo.} and \texttt{What's bar?}
\subsection{A minimal class file}
Most of the work of a class or package is in defining new commands, or
changing the appearance of documents. This is done in the body of the
package, using commands such as |\newcommand| or |\setlength|.
\LaTeXe{} provides several new commands to help class and package
writers; these are described in detail in Section~\ref{Sec:commands}.
There are four things that every class file \emph{must} contain: these
are a definition of |\normalsize|, values for |\textwidth| and
|\textheight| and a specification for page-numbering. So a minimal
document class file\footnote {This class is now in the standard
distribution, as \texttt{minimal.cls}.} looks like this:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{minimal}[1995/10/30 Standard LaTeX minimal class]
\renewcommand{\normalsize}{\fontsize{10pt}{12pt}\selectfont}
\setlength{\textwidth}{6.5in}
\setlength{\textheight}{8in}
\pagenumbering{arabic} % needed even though this class will
% not show page numbers
\end{verbatim}
However, this class file will not support footnotes, marginals,
floats, etc., nor will it provide any of the 2-letter font commands
such as |\rm|; thus most classes will contain more than this minimum!
\subsection{Example: a local letter class}
A company may have its own letter class, for setting letters in the
company style. This section shows a simple implementation of such a
class, although a real class would need more structure.
The class begins by announcing itself as |neplet.cls|.
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{neplet}[1995/04/01 NonExistent Press letter class]
\end{verbatim}
Then this next bit passes any options on to the |letter| class, which
is loaded with the |a4paper| option.
\begin{verbatim}
\DeclareOption*{\PassOptionsToClass{\CurrentOption}{letter}}
\ProcessOptions\relax
\LoadClass[a4paper]{letter}
\end{verbatim}
In order to use the company letter head, it redefines the
|firstpage| page style: this is the page style that is used on
the first page of letters.
\begin{verbatim}
\renewcommand{\ps@firstpage}{%
\renewcommand{\@oddhead}{<letterhead goes here>}%
\renewcommand{\@oddfoot}{<letterfoot goes here>}%
}
\end{verbatim}
And that's it!
\subsection{Example: a newsletter class}
A simple newsletter can be typeset with \LaTeX{}, using a variant of the
|article| class.
The class begins by announcing itself as |smplnews.cls|.
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{smplnews}[1995/04/01 The Simple News newsletter class]
\newcommand{\headlinecolor}{\normalcolor}
\end{verbatim}
It passes most specified options on to the |article| class: apart from
the |onecolumn| option, which is switched off, and the |green| option,
which sets the headline in green.
\begin{verbatim}
\DeclareOption{onecolumn}{\OptionNotUsed}
\DeclareOption{green}{\renewcommand{\headlinecolor}{\color{green}}}
\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
\ProcessOptions\relax
\end{verbatim}
It then loads the class |article| with the option |twocolumn|.
\begin{verbatim}
\LoadClass[twocolumn]{article}
\end{verbatim}
Since the newsletter is to be printed in colour, it now loads the
|color| package. The class does not specify a device driver option
since this should be specified by the user of the |smplnews| class.
\begin{verbatim}
\RequirePackage{color}
\end{verbatim}
The class then redefines |\maketitle| to produce the title in 72pt
Helvetica bold oblique, in the appropriate colour.
\begin{verbatim}
\renewcommand{\maketitle}{%
\twocolumn[%
\fontsize{72}{80}\fontfamily{phv}\fontseries{b}%
\fontshape{sl}\selectfont\headlinecolor
\@title
]%
}
\end{verbatim}
It redefines |\section| and switches off section numbering.
\begin{verbatim}
\renewcommand{\section}{%
\@startsection
{section}{1}{0pt}{-1.5ex plus -1ex minus -.2ex}%
{1ex plus .2ex}{\large\sffamily\slshape\headlinecolor}%
}
\setcounter{secnumdepth}{0}
\end{verbatim}
It also sets the three essential things.
\begin{verbatim}
\renewcommand{\normalsize}{\fontsize{9}{10}\selectfont}
\setlength{\textwidth}{17.5cm}
\setlength{\textheight}{25cm}
\end{verbatim}
In practice, a class would need more than this: it would provide
commands for issue numbers, authors of articles, page styles and so
on; but this skeleton gives a start. The |ltnews| class file is not
much more complex than this one.
\section{Commands for class and package writers}
\label{Sec:commands}
This section describes briefly each of the new commands for class and
package writers. To find out about other aspects of the new system,
you should also read \emph{\LaTeXbook}, \emph{\LaTeXcomp} and
\emph{\usrguide}.
\subsection{Identification}
The first group of commands discussed here are those used
to identify your class or package file.
\begin{decl}
|\NeedsTeXFormat| \arg{format-name} \oarg{release-date}
\end{decl}
This command tells \TeX{} that this file should be processed using a
format with name \m{format-name}. You can use the optional argument
\m{release-date} to further specify the earliest release date of the
format that is needed. When the release date of the format is older
than the one specified a warning will be generated. The standard
\m{format-name} is \texttt{LaTeX2e}. The date, if present, must be in
the form \textsc{yyyy/mm/dd}.
Example:
\begin{verbatim}
\NeedsTeXFormat{LaTeX2e}[1994/06/01]
\end{verbatim}
\begin{decl}
|\ProvidesClass| \arg{class-name} \oarg{release-info} \\
|\ProvidesPackage| \arg{package-name} \oarg{release-info}
\end{decl}
This declares that the current file contains the definitions for the
document class \m{class-name} or package \m{package-name}.
The optional \m{release-info}, if used, must contain:
\begin{itemize}
\item the release date of
this version of the file, in the form \textsc{yyyy/mm/dd};
\item optionally followed by a space and a short description, possibly
including a version number.
\end{itemize}
The above syntax must be followed exactly so that this information
can be used by |\LoadClass| or |\documentclass| (for classes) or
|\RequirePackage| or |\usepackage| (for packages) to test that the
release is not too old.
The whole of this \m{release-info} information is displayed by
|\listfiles| and should therefore not be too long.
Example:
\begin{verbatim}
\ProvidesClass{article}[1994/06/01 v1.0 Standard LaTeX class]
\ProvidesPackage{ifthen}[1994/06/01 v1.0 Standard LaTeX package]
\end{verbatim}
\begin{decl}
|\ProvidesFile| \arg{file-name} \oarg{release-info}
\end{decl}
This is similar to the two previous commands except that here the full
filename, including the extension, must be given. It is used for
declaring any files other than main class and package files.
Example:
\begin{verbatim}
\ProvidesFile{T1enc.def}[1994/06/01 v1.0 Standard LaTeX file]
\end{verbatim}
Note that the phrase \texttt{Standard LaTeX} \textbf{must not} be used
in the identification banner of any file other than those in the
standard \LaTeX{} distribution.
\subsection{Loading files}
\label{Sec:loadf}
\NEWfeature{1995/12/01}
This group of commands can be used to create your own document class or
package by building on existing classes or packages.
\begin{decl}
|\RequirePackage| \oarg{options-list} \arg{package-name}
\oarg{release-info}\\
|\RequirePackageWithOptions| \arg{package-name}
\oarg{release-info}
\end{decl}
Packages and classes should use these commands to load other packages.
The use of |\RequirePackage| is the same as the author command
|\usepackage|.
Examples:
\begin{verbatim}
\RequirePackage{ifthen}[1994/06/01]
\RequirePackageWithOptions{graphics}[1995/12/01]
\end{verbatim}
\begin{decl}
|\LoadClass| \oarg{options-list} \arg{class-name}
\oarg{release-info}\\
|\LoadClassWithOptions| \arg{class-name}
\oarg{release-info}
\end{decl}
\NEWfeature{1995/12/01}
These commands are for use \emph{only} in class files, they cannot be
used in packages files;
they can be used at most once within a class file.
The use of |\LoadClass| is the same as
the use of |\documentclass| to load a class file.
Examples:
\begin{verbatim}
\LoadClass{article}[1994/06/01]
\LoadClassWithOptions{article}[1995/12/01]
\end{verbatim}
\NEWfeature{1995/12/01}
The two |WithOptions| versions simply load the class (or package) file
with exactly those options that are being used by the current file
(class or package). See below, in \ref{Sec:opmove}, for further
discussion of their use.
\subsection{Option declaration}
\label{Sec:commands.options.dec}
\NEWdescription{1998/12/01}
The following commands deal with the declaration and handling of
options to document classes and packages. Every option name must be a
`\LaTeX{} name'.
There are some commands designed especially for use within the
\m{code} argument of these commands (see below).
\begin{decl}
|\DeclareOption| \arg{option-name} \arg{code}
\end{decl}
This makes \m{option-name} a `declared option' of the class or package
in which it is put.
The \m{code} argument contains the code to be executed if that option
is specified for the class or package; it can contain any valid
\LaTeXe{} construct.
Example:
\begin{verbatim}
\DeclareOption{twoside}{\@twosidetrue}
\end{verbatim}
\begin{decl}
|\DeclareOption*| \arg{code}
\end{decl}
This declares the \m{code} to be executed for every option which is
specified for, but otherwise not explicitly declared by, the class or
package; this code is called the `default option code' and it can
contain any valid \LaTeXe{} construct.
If a class file contains no |\DeclareOption*| then, by default, all
specified but undeclared options for that class will be silently
passed to all packages (as will the specified and declared options for
that class).
If a package file contains no |\DeclareOption*| then, by default, each
specified but undeclared option for that package will produce an error.
\subsection{Commands within option code}
\label{Sec:within.code}
These two commands can be used only within the \m{code} argument of
either |\DeclareOption| or |\DeclareOption*|. Other commands commonly
used within these arguments can be found in the next few subsections.
\begin{decl}
|\CurrentOption|
\end{decl}
This expands to the name of the current option.
\begin{decl}
|\OptionNotUsed|
\end{decl}
This causes the current option to
be added to the list of `unused options'.
\NEWfeature{1995/06/01}
You can now include hash marks (\texttt{\#}) within these \m{code}
arguments without special treatment (formerly, it had been
necessary to double them).
\subsection{Moving options around}
\label{Sec:opmove}
These two commands are also very useful within the \m{code} argument
of |\DeclareOption| or |\DeclareOption*|:
\begin{decl}
|\PassOptionsToPackage| \arg{options-list} \arg{package-name}\\
|\PassOptionsToClass| \arg{options-list} \arg{class-name}
\end{decl}
The command |\PassOptionsToPackage| passes the option names in
\m{options-list} to package \m{package-name}.
This means that it adds the \m{option-list} to the
list of options used by any future |\RequirePackage| or |\usepackage|
command for package \m{package-name}.
Example:
\begin{verbatim}
\PassOptionsToPackage{foo,bar}{fred}
\RequirePackage[baz]{fred}
\end{verbatim}
is the same as:
\begin{verbatim}
\RequirePackage[foo,bar,baz]{fred}
\end{verbatim}
Similarly, |\PassOptionsToClass| may be used in a class file to pass
options to another class to be loaded with |\LoadClass|.
\NEWdescription{1995/12/01}
The effects and use of these two commands should be contrasted with
those of the following two (documented above, in \ref{Sec:loadf}):
\begin{verbatim}
\LoadClassWithOptions
\RequirePackageWithOptions
\end{verbatim}
The command |\RequirePackageWithOptions| is similar to
|\RequirePackage|, but it always loads the required package with
exactly the same option list as that being used by the current class
or package, rather than with any option explicitly supplied or passed
on by |\PassOptionsToPackage|.
The main purpose of |\LoadClassWithOptions| is to allow one class to
simply build on another, for example:
\begin{verbatim}
\LoadClassWithOptions{article}
\end{verbatim}
This should be compared with the slightly different construction
\begin{verbatim}
\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
\ProcessOptions\relax
\LoadClass{article}
\end{verbatim}
As used above, the effects are more or less the same, but the first is
a lot less to type; also the |\LoadClassWithOptions| method runs
slightly quicker.
If, however, the class declares options of its own then
the two constructions are different. Compare, for example:
\begin{verbatim}
\DeclareOption{landscape}{\@landscapetrue}
\ProcessOptions\relax
\LoadClassWithOptions{article}
\end{verbatim}
with:
\begin{verbatim}
\DeclareOption{landscape}{\@landscapetrue}
\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
\ProcessOptions\relax
\LoadClass{article}
\end{verbatim}
In the first example, the \textsf{article} class will be loaded with
option |landscape| precisely when the current class is called with
this option. By contrast, in the second example it will never be
called with option \texttt{landscape} as in that case \textsf{article}
is passed options only by the default option handler, but this handler
is not used for |landscape| because that option is explicitly
declared.
\subsection{Delaying code}
\label{Sec:delays}
These first two commands are also intended primarily for use within
the \m{code} argument of |\DeclareOption| or |\DeclareOption*|.
\begin{decl}
|\AtEndOfClass| \arg{code}\\
|\AtEndOfPackage| \arg{code}
\end{decl}
These commands declare \m{code} that is saved away internally and then
executed after processing the whole of the current class or package
file.
Repeated use of these commands is permitted: the code in the
arguments is stored (and later executed) in the order of their
declarations.
\begin{decl}
|\AtBeginDocument| \arg{code}\\
|\AtEndDocument| \arg{code}
\end{decl}
These commands declare \m{code} to be saved internally and executed
while \LaTeX{} is executing |\begin{document}| or |\end{document}|.
The \m{code} specified in the argument to |\AtBeginDocument| is
executed near the end of the |\begin{document}| code, \emph{after} the
font selection tables have been set up. It is therefore a useful
place to put code which needs to be executed after everything has been
prepared for typesetting and when the normal font for the document is
the current font.
\NEWdescription{1995/12/01}
The |\AtBeginDocument| hook should not be used for code that does any
typesetting since the typeset result would be unpredictable.
The \m{code} specified in the argument to |\AtEndDocument| is
executed at the beginning of the |\end{document}| code,
\emph{before} the final page is finished and before any leftover
floating environments are processed. If some of the \m{code} is to be
executed after these two processes, you should include a |\clearpage|
at the appropriate point in \m{code}.
Repeated use of these commands is permitted: the code in the
arguments is stored (and later executed) in the order of their
declarations.
\begin{decl}[1994/12/01]
|\AtBeginDvi| \arg{specials}
\end{decl}
These commands save in a box register things which are written to the
|.dvi| file at the beginning of the `shipout' of the first page of the
document.
This should not be used for anything that will add any typeset
material to the |.dvi| file.
Repeated use of this command is permitted.
\subsection{Option processing}
\label{Sec:commands.options}
\begin{decl}
|\ProcessOptions|
\end{decl}
This command executes the \m{code} for each selected option.
We shall first describe how |\ProcessOptions| works in a package file,
and then how this differs in a class file.
To understand in detail what |\ProcessOptions| does in a package file,
you have to know the difference between \emph{local} and \emph{global}
options.
\begin{itemize}
\item \textbf{Local options} are those which have been explicitly
specified for this particular package in the \m{options} argument of
any of these:
\begin{quote}
|\PassOptionsToPackage{<options>}| \ |\usepackage[<options>]|\\
|\RequirePackage[<options>]|
\end{quote}
\item \textbf{Global options} are any other options that are specified
by the author in the \m{options} argument of
|\documentclass[<options>]|.
\end{itemize}
For example, suppose that a document begins:
\begin{verbatim}
\documentclass[german,twocolumn]{article}
\usepackage{gerhardt}
\end{verbatim}
whilst package |gerhardt| calls package |fred| with:
\begin{verbatim}
\PassOptionsToPackage{german,dvips,a4paper}{fred}
\RequirePackage[errorshow]{fred}
\end{verbatim}
then:
\begin{itemize}
\item |fred|'s local options are |german|, |dvips|, |a4paper|
and |errorshow|;
\item |fred|'s only global option is |twocolumn|.
\end{itemize}
When |\ProcessOptions| is called, the following happen.
\begin{itemize}
\item \emph{First}, for each option so far declared in |fred.sty|
by |\DeclareOption|, it looks to see if that option is either a
global or a local option for |fred|: if it is then the corresponding
code is executed.
This is done in the order in which these options
were declared in |fred.sty|.
\item \emph{Then}, for each remaining \emph{local} option, the command
|\ds@<option>| is executed if it has been defined somewhere (other
than by a |\DeclareOption|); otherwise, the `default option code' is
executed. If no default option code has been declared then an error
message is produced.
This is done in the order in which these
options were specified.
\end{itemize}
Throughout this process, the system ensures that the code declared for
an option is executed at most once.
Returning to the example, if |fred.sty| contains:
\begin{verbatim}
\DeclareOption{dvips}{\typeout{DVIPS}}
\DeclareOption{german}{\typeout{GERMAN}}
\DeclareOption{french}{\typeout{FRENCH}}
\DeclareOption*{\PackageWarning{fred}{Unknown `\CurrentOption'}}
\ProcessOptions\relax
\end{verbatim}
then the result of processing this document will be:
\begin{verbatim}
DVIPS
GERMAN
Package fred Warning: Unknown `a4paper'.
Package fred Warning: Unknown `errorshow'.
\end{verbatim}
Note the following:
\begin{itemize}
\item the code for the |dvips| option is executed before that for the
|german| option, because that is the order in which they are declared
in |fred.sty|;
\item the code for the |german| option is executed only once, when the
declared options are being processed;
\item the |a4paper| and |errorshow| options produce the warning from
the code declared by |\DeclareOption*| (in the order in which they
were specified), whilst the |twocolumn| option does not: this is
because |twocolumn| is a global option.
\end{itemize}
In a class file, |\ProcessOptions| works in the same way, except
that: \emph{all} options are local; and the default value for
|\DeclareOption*| is |\OptionNotUsed| rather than an error.
\NEWdescription{1995/12/01}
Note that, because |\ProcessOptions| has a |*|-form, it is wise to
follow the non-star form with |\relax|, as in the previous examples,
since this prevents unnecessary look ahead and possibly misleading
error messages being issued.
\begin{decl}
|\ProcessOptions*| \\
|\@options|
\end{decl}
This is like |\ProcessOptions| but it executes the options in the
order specified in the calling commands, rather than in the order of
declaration in the class or package. For a package this means that the
global options are processed first.
The |\@options| command from \LaTeX~2.09 has been made equivalent to
this in order to ease the task of updating old document styles to
\LaTeXe{} class files.
\begin{decl}
|\ExecuteOptions| \arg{options-list}
\end{decl}
For each option in the \m{options-list}, in order,
this command simply executes the command
|\ds@<option>| (if this command is not defined, then that option is
silently ignored).
It can be used to provide a `default option list' just before
|\ProcessOptions|. For example, suppose that in a class file you want
to set up the default design to be: two-sided printing; 11pt fonts;
in two columns. Then it could specify:
\begin{verbatim}
\ExecuteOptions{11pt,twoside,twocolumn}
\end{verbatim}
\subsection{Safe file commands}
These commands deal with file input; they ensure that the non-existence
of a requested file can be handled in a user-friendly way.
\begin{decl}
|\IfFileExists| \arg{file-name} \arg{true} \arg{false}
\end{decl}
If the file exists then the code specified in \m{true} is
executed.
If the file does not exist then the code specified in \m{false} is
executed.
This command does \emph{not} input the file.
\begin{decl}
|\InputIfFileExists| \arg{file-name} \arg{true} \arg{false}
\end{decl}
This inputs the file \m{file-name} if it exists and, immediately
before the input, the code specified in \m{true} is executed.
If the file does not exist then the code specified in \m{false} is
executed.
It is implemented using |\IfFileExists|.
\subsection{Reporting errors, etc}
These commands should be used by third party classes and packages to
report errors, or to provide information to authors.
\begin{decl}
|\ClassError| \arg{class-name} \arg{error-text} \arg{help-text}\\
|\PackageError| \arg{package-name} \arg{error-text} \arg{help-text}
\end{decl}
These produce an error message. The \m{error-text} is displayed and the
|?| error prompt is shown. If the user types |h|, they will be shown
the \m{help-text}.
Within the \m{error-text} and \m{help-text}: |\protect| can be used to
stop a command from expanding; |\MessageBreak| causes a line-break;
and |\space| prints a space.
Note that the \m{error-text} will have a full stop added to it, so do
not put one into the argument.
For example:
\begin{verbatim}
\newcommand{\foo}{FOO}
\PackageError{ethel}{%
Your hovercraft is full of eels,\MessageBreak
and \protect\foo\space is \foo
}{%
Oh dear! Something's gone wrong.\MessageBreak
\space \space Try typing \space <<return>>
\space to proceed, ignoring \protect\foo.
}
\end{verbatim}
produces this display:
\begin{verbatim}
! Package ethel Error: Your hovercraft is full of eels,
(ethel) and \foo is FOO.
See the ethel package documentation for explanation.
\end{verbatim}
If the user types |h|, this will be shown:
\begin{verbatim}
Oh dear! Something's gone wrong.
Try typing <<return>> to proceed, ignoring \foo.
\end{verbatim}
\begin{decl}
|\ClassWarning| \arg{class-name} \arg{warning-text}\\
|\PackageWarning| \arg{package-name} \arg{warning-text}\\
|\ClassWarningNoLine| \arg{class-name} \arg{warning-text}\\
|\PackageWarningNoLine| \arg{package-name} \arg{warning-text}\\
|\ClassInfo| \arg{class-name} \arg{info-text}\\
|\PackageInfo| \arg{package-name} \arg{info-text}
\end{decl}
The four |Warning| commands are similar to the error commands, except
that they produce only a warning on the screen, with no error prompt.
The first two, |Warning| versions, also show the line number where the
warning occurred, whilst the second two, |WarningNoLine| versions, do
not.
The two |Info| commands are similar except that they log the
information only in the transcript file, including the line number.
There are no |NoLine| versions of these two.
Within the \m{warning-text} and \m{info-text}: |\protect| can be used to
stop a command from expanding; |\MessageBreak| causes a line-break;
and |\space| prints a space.
Also, these should not end with a full stop as one is
automatically added.
\subsection{Defining commands}
\label{Sec:commands.define}
\LaTeXe{} provides some extra methods of (re)defining commands that are
intended for use in class and package files.
\NEWfeature{1994/12/01}
The \texttt{*}-forms of these commands should be used to define
commands that are not, in \TeX{} terms, long. This can be useful for
error-trapping with commands whose arguments are not intended to
contain whole paragraphs of text.
\begin{decl}
|\DeclareRobustCommand| \arg{cmd} \oarg{num} \oarg{default}
\arg{definition}\\
|\DeclareRobustCommand*| \arg{cmd} \oarg{num} \oarg{default}
\arg{definition}
\end{decl}
This command takes the same arguments as |\newcommand| but it declares
a robust command, even if some code within the \m{definition} is
fragile. You can use this command to define new robust commands, or
to redefine existing commands and make them robust. A log is put into
the transcript file if a command is redefined.
For example, if |\seq| is defined as follows:
\begin{verbatim}
\DeclareRobustCommand{\seq}[2][n]{%
\ifmmode
#1_{1}\ldots#1_{#2}%
\else
\PackageWarning{fred}{You can't use \protect\seq\space in text}%
\fi
}
\end{verbatim}
Then the command |\seq| can be used in moving arguments, even though
|\ifmmode| cannot, for example:
\begin{verbatim}
\section{Stuff about sequences $\seq{x}$}
\end{verbatim}
Note also that there is no need to put a |\relax| before the
|\ifmmode| at the beginning of the definition; this is because the
protection given by this |\relax| against expansion at the wrong time
will be provided internally.
\begin{decl}
|\CheckCommand| \arg{cmd} \oarg{num} \oarg{default}
\arg{definition}\\
|\CheckCommand*| \arg{cmd} \oarg{num} \oarg{default}
\arg{definition}
\end{decl}
This takes the same arguments as |\newcommand| but, rather than define
\m{cmd}, it just checks that the current definition of \m{cmd} is
exactly as given by \m{definition}. An error is raised if these
definitions differ.
This command is useful for checking the state of the system before
your package starts altering the definitions of commands. It allows
you to check, in particular, that no other package has redefined the
same command.
\subsection{Moving arguments}
\NEWdescription{1994/12/01}
The setting of protect whilst processing (i.e.~moving) moving arguments
has been reimplemented, as has the method of writing information from
the |.aux| file to other files such as the |.toc| file. Details can
be found in the file |ltdefns.dtx|.
We hope that these changes will not affect many packages.
\section{Miscellaneous commands, etc}
\label{Sec:commands.misc}
\subsection{Layout parameters}
\begin{decl}
|\paperheight|\\
|\paperwidth|
\end{decl}
These two parameters are usually set by the class to be the size of
the paper being used. This should be actual paper size, unlike
|\textwidth| and |\textheight| which are the size of the main text
body within the margins.
\subsection{Case changing}
\label{sec:case}
\begin{decl}
|\MakeUppercase| \arg{text} \\
|\MakeLowercase| \arg{text}
\end{decl}
\NEWfeature{1995/06/01}
\TeX{} provides two primitives |\uppercase| and |\lowercase| for
changing the case of text. These are sometimes used in document
classes, for example to set information in running heads in all
capitals.
Unfortunately, these \TeX{} primitives do not change the case of
characters accessed by commands like |\ae| or |\aa|. To overcome this
problem, \LaTeX{} provides two new commands |\MakeUppercase| and
|\MakeLowercase| to do this.
For example:
\begin{quotation}
\begin{tabular}{rl}
|\uppercase{aBcD\ae\AA\ss\OE}| & \uppercase{aBcD\ae\AA\ss\OE}\\
|\lowercase{aBcD\ae\AA\ss\OE}| & \lowercase{aBcD\ae\AA\ss\OE}\\
|\MakeUppercase{aBcD\ae\AA\ss\OE}| &
\MakeUppercase{aBcD\ae\AA\ss\OE}\\
|\MakeLowercase{aBcD\ae\AA\ss\OE}| & \MakeLowercase{aBcD\ae\AA\ss\OE}
\end{tabular}
\end{quotation}
The commands |\MakeUppercase| and |\MakeLowercase| themselves are
robust, but they have moving arguments.
The commands use the \TeX{} primitives |\uppercase| and |\lowercase|,
and so have a number of unexpected `features'. In particular, they
change the case of everything (except characters in the names of
control-sequences) in their text argument: this includes mathematics,
environment names, and label names.
For example:
\begin{verbatim}
\MakeUppercase{$x+y$ in \ref{foo}}
\end{verbatim}
produces $X+Y$ and the warning:
\begin{verbatim}
LaTeX Warning: Reference `FOO' on page ... undefined on ...
\end{verbatim}
In the long run, we would like to use all-caps fonts rather than any
command like |\MakeUppercase| but this is not possible at the moment
because such fonts do not exist.
\NEWdescription{1995/12/01}
In order that upper/lower-casing will work reasonably well, and in
order to provide any correct hyphenation, \LaTeXe{} \emph{must} use,
throughout a document, the same fixed table for changing case.
The table used is designed for the font encoding |T1|; this works well
with the standard \TeX{} fonts for all Latin alphabets but will cause
problems when using other alphabets.
\subsection{The `openany' option in the `book' class}
\NEWdescription{1996/06/01}
The |openany| option allows chapter and similar openings to
occur on left hand pages. Previously this option affected only
|\chapter| and |\backmatter|. It now also affects
|\part|, |\frontmatter| and |\mainmatter|.
\subsection{Better user-defined math display environments}
\begin{decl}
|\ignorespacesafterend|
\end{decl}
\NEWfeature{1996/12/01}
\NEWdescription{2003/12/01}
Suppose that you want to define an environment for displaying text
that is numbered as an equation. A straightforward way to do this is
as follows:
\begin{verbatim}
\newenvironment{texteqn}
{\begin{equation}
\begin{minipage}{0.9\linewidth}}
{\end{minipage}
\end{equation}}
\end{verbatim}
However, if you have tried this then you will probably have noticed
that it does not work perfectly when used in the middle of a paragraph
because an inter-word space appears at the beginning of the first
line after the environment.
There is now an extra command (with a very long name) available that
you can use to avoid this problem; it should be inserted as shown here:
\begin{verbatim}
\newenvironment{texteqn}
{\begin{equation}
\begin{minipage}{0.9\linewidth}}
{\end{minipage}
\end{equation}
\ignorespacesafterend}
\end{verbatim}
This command may also have other uses.
\subsection{Normalising spacing}
\begin{decl}
|\normalsfcodes|
\end{decl}
\NEWfeature{1997/06/01}
This command should be used to restore the normal settings of the
parameters that affect spacing between words, sentences, etc.
An important use of this feature is to correct a problem, reported by
Donald Arseneau, that punctuation in page headers has always (in all
known \TeX{} formats) been potentially wrong whenever a page break
happens while a local setting of the space codes is in effect. These
space codes are changed by, for example, the command
\verb|\frenchspacing|) and the \textsf{verbatim} environment.
It is normally given the correct definition automatically in
|\begin{document}| and so need not be explicitly set; however, if it
is explicitly made nonempty in a class file then automatic
default setting will be over-ridden.
\section{Upgrading \LaTeX~2.09 classes and packages}
\label{Sec:upgrade}
This section describes the changes you may need to make when you
upgrade an existing \LaTeX{} style to a package or class but we shall
start in optimistic mode.
Many existing style files will run with \LaTeXe{} without any
modification to the file itself. When everything is running OK,
please put a note in the newly created package or class file to record
that it runs with the new standard \LaTeX{}; then distribute it to
your users.
\subsection{Try it first!}
\label{Sec:try-it}
The first thing you should do is to test your style in `compatibility
mode'. The only change you need to make in order to do this is,
possibly, to change the extension of the file to |.cls|: you should
make this change only if your file was used as a main document style.
Now, without any other modifications, run \LaTeXe{} on a document that
uses your file. This assumes that you have a suitable collection of
files that tests all the functionality provided by your style file.
(If you haven't, now is the time to make one!)
You now need to change the test document files so that they are
\LaTeXe{} documents: see \emph{\usrguide} for details of how to do
this and then try them again. You have now tried the test documents
in both \LaTeXe{} native mode and \LaTeX~2.09 compatibility mode.
\subsection{Troubleshooting}
\label{Sec:trouble}
If your file does not work with \LaTeXe{}, there are two likely
reasons.
\begin{itemize}
\item \LaTeX{} now has a robust, well-defined designer's interface for
selecting fonts, which is very different from the \LaTeX~2.09
internals.
\item Your style file may have used some \LaTeX~2.09 internal commands
which have changed, or which have been removed.
\end{itemize}
When you are debugging your file, you will probably need more
information than is normally displayed by \LaTeXe. This is achieved
by resetting the counter |errorcontextlines| from its default value of
$-1$ to a much higher value, e.g.~999.
\subsection{Accommodating compatibility mode}
Sometimes an existing collection of \LaTeX~2.09 documents makes it
inconvenient or impossible to abandon the old commands entirely.
If this is the case, then it is possible to accommodate both conventions
by making special provision for documents processed in compatibility
mode.
\begin{decl}
|\if@compatibility|
\end{decl}
This switch is set when a document begins with |\documentstyle| rather
than |\documentclass|. Appropriate code can be supplied for either
condition, as follows:
\begin{verbatim}
\if@compatibility
<code emulating LaTeX 2.09 behavior>
\else
<code suitable for LaTeX2e>
\fi
\end{verbatim}
\subsection{Font commands}
Some font and size commands are now defined by the document class
rather than by the \LaTeX{} kernel. If you are upgrading a
\LaTeX~2.09 document style to a class that does not load one of the
standard classes, then you will probably need to add definitions for
these commands.
\begin{decl}
|\rm| |\sf| |\tt| |\bf| |\it| |\sl| |\sc|
\end{decl}
None of these short-form font selection commands are defined in the
\LaTeXe{} kernel. They are defined by all the standard class files.
If you want to define them in your class file, there are several
reasonable ways to do this.
One possible definition is:
\begin{verbatim}
\newcommand{\rm}{\rmfamily}
...
\newcommand{\sc}{\scshape}
\end{verbatim}
This would make the font commands orthogonal; for example
|{\bf\it text}| would produce bold italic, thus: \textbf{\textit{text}}.
It will also make them produce an error if used in math mode.
Another possible definition is:
\begin{verbatim}
\DeclareOldFontCommand{\rm}{\rmfamily}{\mathrm}
...
\DeclareOldFontCommand{\sc}{\scshape}{\mathsc}
\end{verbatim}
This will make |\rm| act like |\rmfamily| in text mode (see above) and
it will make |\rm| select the |\mathrm| math alphabet in math mode.
Thus |${\rm math} = X + 1$| will produce `${\rm math} = X + 1$'.
If you do not want font selection to be orthogonal then you can
follow the standard classes and define:
\begin{verbatim}
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
...
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\mathsc}
\end{verbatim}
This means, for example, that |{\bf\it text}| will produce medium
weight (rather than bold) italic, thus: \textit{text}.
\begin{decl}
|\normalsize| \\
|\@normalsize|
\end{decl}
The command |\@normalsize| is retained for compatibility with
\LaTeX~2.09 packages which may have used its value; but redefining it
in a class file will have no effect since it is always reset to have
the same meaning as |\normalsize|.
This means that classes \emph{must} now redefine |\normalsize| rather
than redefining |\@normalsize|; for example (a rather incomplete one):
\begin{verbatim}
\renewcommand{\normalsize}{\fontsize{10}{12}\selectfont}
\end{verbatim}
Note that |\normalsize| is defined by the \LaTeX{} kernel to be an
error message.
\begin{decl}
|\tiny| |\footnotesize| |\small| |\large|\\
|\Large| |\LARGE| |\huge| |\Huge|
\end{decl}
None of these other `standard' size-changing commands are defined in
the kernel: each needs to be defined in a class file if you need it.
They are all defined by the standard classes.
This means you should use |\renewcommand| for |\normalsize| and
|\newcommand| for the other size-changing commands.
\subsection{Obsolete commands}
Some packages will not work with \LaTeXe{}, normally because they relied
on an internal \LaTeX{} command which was never supported and has now
changed, or been removed.
In many cases there will now be a robust, high-level means of
achieving what previously required low-level commands. Please consult
Section~\ref{Sec:commands} to see if you can now use the \LaTeXe{}
class and package writers commands.
Also, of course, if your package or class redefined any of the kernel
commands (i.e.~those defined in the files |latex.tex|, |slitex.tex|,
|lfonts.tex|, |sfonts.tex|) then you will need to check it very
carefully against the new kernel in case the implementation has
changed or the command no longer exists in the \LaTeX2e{} kernel.
Too many of the internal commands of \LaTeX~2.09 have been
re-implemented or removed to be able to list them all here. You must
check any that you have used or changed.
We shall, however, list some of the more important commands which are
no longer supported.
\begin{decl}
|\tenrm| |\elvrm| |\twlrm| \dots\\
|\tenbf| |\elvbf| |\twlbf| \dots\\
|\tensf| |\elvsf| |\twlsf| \dots\\
\qquad$\vdots$
\end{decl}
The (approximately) seventy internal commands of this form are no longer
defined. If your class or package uses them then \emph{please}
replace them with new font commands described in \emph{\fntguide}.
For example, the command |\twlsf| should be replaced by:
\begin{verbatim}
\fontsize{12}{14}\normalfont\sffamily\selectfont
\end{verbatim}
Another possibility is to use the |rawfonts| package, described in
\emph{\usrguide}.
Also, remember that many of the fonts preloaded by \LaTeX~2.09
are no longer preloaded.
\begin{decl}
|\vpt| |\vipt| |\viipt| \dots
\end{decl}
These were the internal size-selecting commands in \LaTeX~2.09.
(They can still be used in \LaTeX~2.09 compatibility mode.)
Please use the command |\fontsize| instead: see \emph{\fntguide} for
details.
For example, |\vpt| should be replaced by:
\begin{verbatim}
\fontsize{5}{6}\normalfont\selectfont
\end{verbatim}
\begin{decl}
|\prm|, |\pbf|, |\ppounds|, |\pLaTeX| \dots
\end{decl}
\LaTeX~2.09 used several commands beginning with |\p| in order to
provide `protected' commands. For example, |\LaTeX| was defined to be
|\protect\pLaTeX|, and |\pLaTeX| was defined to produce the \LaTeX{}
logo. This made |\LaTeX| robust, even though |\pLaTeX| was not.
These commands have now been reimplemented using
|\DeclareRobustCommand|
(described in Section~\ref{Sec:commands.define}).
If your package redefined one of the |\p|-commands then you must
remove the redefinition and use |\DeclareRobustCommand| to redefine the
non-|\p| command.
\begin{decl}
|\footheight|\\
|\@maxsep|\\
|\@dblmaxsep|
\end{decl}
These parameters are not used by \LaTeXe{} so they have been removed,
except in \LaTeX~2.09 compatibility mode. Classes should no longer
set them.
\begin{thebibliography}{1}
\bibitem{A-W:DEK91}
Donald~E. Knuth.
\newblock {\em The \TeX book}.
\newblock Addison-Wesley, Reading, Massachusetts, 1986.
\newblock Revised to cover \TeX3, 1991.
\bibitem{A-W:LLa94}
Leslie Lamport.
\newblock {\em {\LaTeX:} A Document Preparation System}.
\newblock Addison-Wesley, Reading, Massachusetts, second edition, 1994.
\bibitem{A-W:MG2004}
Frank Mittelbach and Michel Goossens.
\newblock {\em The {\LaTeX} Companion second edition}.
\newblock With Johannes Braams, David Carlisle, and Chris Rowley.
\newblock Addison-Wesley, Reading, Massachusetts, 2004.
\end{thebibliography}
\newpage
\thispagestyle{empty}
\section*{\LaTeXe{} Summary sheet: updating old styles}
Section references below are to \emph{\clsguide}.
\begin{enumerate}
\item Should it become a class or a package?
See Section~\ref{Sec:classorpkg} for how to answer this question.
\item If it uses another style file, then you will need to obtain an
updated version of this other file. Look at Section~\ref{Sec:loading}
for information on how to load other class and package files.
\item Try it: see Section~\ref{Sec:try-it}.
\item It worked? Excellent, but there are probably still some things
you should change in order to make your file into a well-structured
\LaTeXe{} file that is both robust and portable. So you should now
read Section~\ref{Sec:writing}, especially~\ref{Sec:general}. You
will also find some useful examples in Section~\ref{Sec:structure}.
If your file sets up new fonts, font-changing commands or symbols,
you should also read \emph{\fntguide}.
\item It did not work? There are three possibilities here:
\begin{itemize}
\item error messages are produced whilst reading your file;
\item error messages are produced whilst processing test documents;
\item there are no errors but the output is not as it should be.
\end{itemize}
Don't forget to check carefully for this last possibility.
If you have got to this stage then you will need to read
Section~\ref{Sec:upgrade} to find the solutions that will make your
file work.
\end{enumerate}
\end{document}
|
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%%
% * ----------------------------------------------------------------
% * "THE BEER-WARE LICENSE" (Revision 42/023):
% * Ronny Bergmann <[email protected]> wrote this file. As long as
% * you retain this notice you can do whatever you want with this
% * stuff. If we meet some day and you think this stuff is worth it,
% * you can buy me a beer or a coffee in return.
% * ----------------------------------------------------------------
%
%
% A german example using the Kartei.cls - including print and toc as
% options, hence all pages are Din A4.
%
% Last Change: Kartei 1.9, 2012/01/04
% SKS Fragen vom Wasserstraßen- und Schifffahrtsverwaltung des Bundes Stand: 18. August 2017
%
% zusammengestellt von Thomas Wittmann <[email protected]>
%
%
\documentclass[a7paper,print,both,10pt]{kartei}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[greek,ngerman]{babel}
\usepackage{textcomp}
\usepackage{graphicx}
\usepackage{textgreek}
\setlength{\parindent}{6pt}
\setlength{\parskip}{0pt}
\usepackage{hyperref}
\begin{document}
\setcardpagelayout
\begin{karte}[Navigation]{Worauf müssen Sie als Schiffsführer vor Reiseantritt hinsichtlich der Seekarten und Seebücher achten?}[1]
Auf Vollständigkeit der Unterlagen und deren Berichtigung auf den neuesten Stand.
\end{karte}
\begin{karte}[Navigation]{Warum muss in der GPS-Navigation das jeweilige Kartendatum unbedingt berücksichtigt werden?}[2]
Weil sich das von GPS verwendete Bezugssystem WGS 84 (World Geodetic System 1984) von anderen verwendeten Bezugssystemen (Kartendatum) unterscheiden kann.
\end{karte}
\begin{karte}[Navigation]{Welche Differenzen können zwischen WGS 84 und anderen Bezugssystemen auftreten? }[3]
Die Differenzen von φ (Phi; Breite) und λ (Lambda; Länge) liegen im Allgemeinen in der Größenordnung von 0,1 kbl (Kabel (10ter Teil einer Seemeile) bis 1 kbl, also etwa von 20 bis 200 m. Es können größere Unterschiede auftreten.
\end{karte}
\begin{karte}[Navigation]{Wo finden Sie in der Seekarte Angaben über das benutzte Bezugssystem und ggf. entsprechende Korrekturhinweise?}[4]
Am Kartenrand unter dem Titel.
\end{karte}
\begin{karte}[Navigation]{Wie lautet ggf. der Korrekturhinweis bezüglich GPS in der Seekarte, wenn das benutzte Kartendatum (z.B. ED 50) und WGS 84 nicht übereinstimmen?}[5]
Durch Satellitennavigation (z. B. GPS) erhaltene Positionen im WGS 84 sind 0, ... Minuten nordwärts/südwärts und 0, ... Minuten westwärts/ostwärts zu verlegen, um mit dieser Karte übereinzustimmen.
\end{karte}
\begin{karte}[Navigation]{Woran erkennen Sie, bis wann eine deutsche Seekarte \glqq amtlich\grqq{} berichtigt ist?}[6]
Am Berichtigungsstempel des BSH oder einer amtlichen Seekartenberichtigungsstelle.
\end{karte}
\begin{karte}[Navigation]{Woran erkennen Sie, bis wann eine britische Seekarte \glqq amtlich\grqq{} berichtigt ist? }[7]
Am Berichtigungsstempel auf der Rückseite der Seekarte.
\end{karte}
\begin{karte}[Navigation]{Was bedeutet der Stempel auf der britischen Seekarte: Corrected up to N.T.M. 3595 1998?}[8]
Seekarte ist berichtigt bis zur Mitteilung Nummer 3595 der Admiralty Notices to Mariners (N.T.M.) in 1998.
\end{karte}
\begin{karte}[Navigation]{Welche Angaben enthalten die Nachrichten für Seefahrer (NfS)?}[9]
In den NfS werden für die sichere Schiffsführung wichtige Maßnahmen, Ereignisse und Veränderungen auf den Seeschifffahrtsstraßen, auf der Hohen See sowie in den Hoheitsgewässern anderer Staaten im europäischen und angrenzenden Bereich bekannt gegeben.
\end{karte}
\begin{karte}[Navigation]{In welcher Sprache werden die Nachrichten für Seefahrer (NfS) verfasst?}[10]
Die Angaben erfolgen in deutscher und in englischer Sprache.
\end{karte}
\begin{karte}[Navigation]{Welche Angaben enthalten deutsche und britische Leuchtfeuerverzeichnisse?}[11]
Beschreibung der Leuchtfeuer, Feuerschiffe und Großtonnen sowie deren geographische Lage.
\end{karte}
\begin{karte}[Navigation]{Welche schwimmenden Schifffahrtszeichen werden in der britischen List of Lights und in deutschen Leuchtfeuerverzeichnissen nicht angegeben?}[12]
Tonnen kleiner als 8 m Höhe.
\end{karte}
\begin{karte}[Navigation]{Wo finden Sie Angaben über die Merkmale der Schifffahrtszeichen?}[13]
\begin{enumerate}
\item In den Leuchtfeuerverzeichnissen bzw. in der List of Lights sowie auszugsweise in den Seekarten.
\item In der Karte 1/INTInternational Hydrographic Organisation für die Gestaltung von Seekarten 1 des BSH.
\item Schwimmende Schifffahrtszeichen zusätzlich in der Anlage I zur SeeSchStrO (z. B. Tonnen des Lateral- bzw. Kardinalsystems).
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Worauf beziehen sich die Höhenangaben der Leuchtfeuer in Leuchtfeuerverzeichnissen in der Nord und Ostsee?}[14]
In Gewässern mit Gezeiten (z. B. Nordsee) auf mittleres Hochwasser, in gezeitenlosen Gewässern (z. B. Ostsee) auf mittleren Wasserstand.
\end{karte}
\begin{karte}[Navigation]{Wo finden Sie Angaben über Brückensignale?}[15]
In den See- und Hafenhandbüchern und in den Seekarten.
\end{karte}
\begin{karte}[Navigation]{Welche Themen (Grobgliederung) enthalten die Seehandbücher des BSH?}[16]
\begin{enumerate}
\item Schifffahrtsangelegenheiten,
\item Naturverhältnisse,
\item Küstenkunde und Segelanweisungen.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie werden Richtungsangaben in nautischen Veröffentlichungen gemacht?}[17]
\begin{enumerate}
\item Rechtweisend in Grad,
\item im Uhrzeigersinn (rechtsherum) zählend.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{In welchem Quadranten liegt der rote Warnsektor eines Leitfeuers mit der Angabe rot 030°-042° (Begründung!) }[18]
Im Südwest-Quadranten. Angegeben sind die Peilungen zum Leuchtfeuer.
\end{karte}
\begin{karte}[Navigation]{Was sind Leitfeuer (direction lights)?}[19]
Leitfeuer sind Einzelfeuer, die durch Sektoren verschiedener Farbe oder Kennung (Leit- oder Warnsektoren) im Allgemeinen ein
Fahrwasser, eine Hafeneinfahrt oder einen freien Seeraum zwischen Untiefen bezeichnen.
\end{karte}
\begin{karte}[Navigation]{
\begin{enumerate}
\item Was sind Richtfeuer (leading lights)?
\item Wann befindet man sich in einer Richtlinie eines Richtfeuers?
\end{enumerate}
}[20]
\begin{enumerate}
\item Richtfeuer sind Feuer, die als Unter- und Oberfeuer in Deckpeilung als Richtlinie beispielsweise einen Kurs im Fahrwasser, durch eine Hafeneinfahrt oder im freien Seeraum zwischen Untiefen bezeichnen.
\item Ein Schiff befindet sich in der Richtlinie, wenn Unter- und Oberfeuer senkrecht unter-/übereinander erscheinen.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was ist ein Torfeuer?}[21]
Ein Torfeuer besteht aus zwei Feuern gleicher Höhe, gleicher Lichtstärke und gleicher Kennung, die zu beiden Seiten der
Fahrwasserachse einander genau gegenüber (rechtwinklig zur Fahrwasserachse) und von der Fahrwasserachse gleich weit
entfernt angeordnet sind.
\end{karte}
\begin{karte}[Navigation]{Was ist die \glqq Tragweite\grqq{} eines Feuers?}[22]
Unter Tragweite versteht man denjenigen Abstand, in dem ein Feuer einen eben noch deutlichen Lichteindruck im Auge des
Beobachters hervorruft.
\end{karte}
\begin{karte}[Navigation]{Was ist die \glqq Nenntragweite\grqq{} eines Feuers?}[23]
Nenntragweite ist die Tragweite eines Feuers für einen definierten Wert bei einer meteorologischen Sichtweite am Tage von 10sm.
\end{karte}
\begin{karte}[Navigation]{Wovon hängt die \glqq Tragweite\grqq{} eines Feuers ab?}[24]
Sie hängt u. a. ab
\begin{enumerate}
\item von der Lichtstärke (Helligkeit) des Feuers und
\item vom Sichtwert (Lichtdurchlässigkeit der Atmosphäre).
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{In der Seekarte finden Sie bei einem Leuchtfeuer die Eintragung: 18 M. Was bedeutet diese Angabe?}[25]
Es ist die Nenntragweite, hier 18 Seemeilen.
\end{karte}
\begin{karte}[Navigation]{Was ist die \glqq Sichtweite\grqq{} eines Feuers? Wovon hängt sie ab?}[26]
Sichtweite ist die Entfernung, auf die ein Leuchtfeuer über die Erdkrümmung (Kimm) hinweg vom Beobachter gesehen werden kann. Sie hängt ab
\begin{enumerate}
\item von der Feuerhöhe und
\item von der Augeshöhe des Beobachters.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie müssen sich Tragweite und Sichtweite zueinander verhalten, damit das Verfahren zur Ortsbestimmung \glqq Feuer in der Kimm\grqq{} angewandt werden kann? }[27]
Die Tragweite muss mindestens gleich der Sichtweite sein.
\end{karte}
\begin{karte}[Navigation]{Wo findet man Tabellen zur Ermittlung des Abstandes eines Feuers in der Kimm?}[28]
In deutschen und britischen Leuchtfeuerverzeichnissen.
\end{karte}
\begin{karte}[Navigation]{Wo sind die in Seekarten verwendeten Symbole und Abkürzungen erklärt?}[29]
In der Karte 1/INT des BSH.
\end{karte}
\begin{karte}[Navigation]{Wer veröffentlicht die Bekanntmachungen für Seefahrer (BfS) und was umfassen diese Veröffentlichungen?}[30]
\begin{enumerate}
\item Die BfS werden von den jeweils zuständigen Behörden der Wasser- und Schifffahrtsverwaltung des Bundes bzw. der Länder veröffentlicht.
\item Sie enthalten alle wichtigen Maßnahmen und Ereignisse auf den Seeschifffahrtsstraßen und der ausschließlichen Wirtschaftszone Deutschlands.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie werden die Bekanntmachungen für Seefahrer (BfS) der Sportschifffahrt zur Kenntnis gebracht?}[31]
Die BfS werden an den amtlichen Aushangstellen (z. B. bei Wasser- und Schifffahrtsämtern, Hafenverwaltungen, WSPDienststellen, Schleusen, Yachthäfen) für das betreffende Seegebiet, in dem die Aushangstelle liegt, und für die angrenzenden Reviere und Gebiete sowie im Internet unter www.elwis.de zur Kenntnis gebracht.
\end{karte}
\begin{karte}[Navigation]{Zählen Sie die am häufigsten vorkommenden Ereignisse und Maßnahmen auf, über die die Bekanntmachungen für Seefahrer (BfS) unterrichten.}[32]
\begin{enumerate}
\item Änderungen an Befeuerung, Betonnung und Landmarken,
\item veränderte Wassertiefen,
\item Wracke, Schifffahrtshindernisse, Rohrleitungen usw.,
\item Bauarbeiten, Baggerarbeiten, militärische Übungen und damit zusammenhängende Sperrungen oder Behinderungen.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wer gibt die nautischen Warnnachrichten (NWN) heraus und von wem werden sie verbreitet?}[33]
Nautische Warnnachrichten (NWN) werden von den Verkehrszentralen für deren Zuständigkeitsbereich und von dem ständig besetzten Seewarndienst Emden für das gesamte deutsche Warngebiet zur Verbreitung über Funk herausgegeben. Der Rundfunksender Deutschlandfunk verbreitet alle über Funk abgegebenen NWN.
\end{karte}
\begin{karte}[Navigation]{Was bedeutet der Zusatz \glqq vital\grqq{} bei einer nautischen Warnnachricht (NWN)?}[34]
Die NWN erhält den Zusatz \glqq vital\grqq{}, wenn die Warnung auf eine lebensbedrohende Gefahr hinweist.
\end{karte}
\begin{karte}[Navigation]{Welche Besonderheit bezüglich des Zusatzes \glqq vital\grqq{} bei einer nautischen Warnnachricht (NWN) gibt es für die Sportschifffahrt?}[35]
Vitale nautische Warnnachrichten für die Sportschifffahrt werden während der Zeit vom 1. April bis zum 31. Oktober zur Verbreitung über ausgewählte private und öffentlich-rechtliche Rundfunkanstalten weitergeleitet.
\end{karte}
\begin{karte}[Navigation]{Wer gibt die Nachrichten für Seefahrer (NfS) heraus und wie und wie oft erfolgt die Herausgabe?}[36]
Die NfS werden vom BSH in Heftform und im Internet herausgegeben und erscheinen einmal wöchentlich.
\end{karte}
\begin{karte}[Navigation]{Welche Unterlage steht Ihnen zur Verfügung zur Berichtigung von britischen Seekarten, die nicht von den NfS erfasst werden?}[37]
Die britischen Notices to Mariners.
\end{karte}
\begin{karte}[Navigation]{
\begin{enumerate}
\item Was sind P-Nachrichten?
\item Wie verfährt man mit diesen Nachrichten im Berichtigungsverfahren? (Begründung!)
\end{enumerate}
}[38]
\begin{enumerate}
\item P-Nachrichten sind solche, die eine bevorstehende (preliminary) Maßnahme ankündigen.
\item Wegen der begrenzten Geltungsdauer werden keine Berichtigungen auf der Grundlage von P-Nachrichten vom BSH bzw. von amtlichen Seekartenberichtigungsstellen durchgeführt. Deshalb müssen vor Gebrauch jeder Seekarte die noch gültigen P-Nachrichten erfasst und in der Karte vermerkt werden.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{
\begin{enumerate}
\item Was sind T-Nachrichten?
\item Wie verfährt man mit diesen Nachrichten im Berichtigungsverfahren? (Begründung!)
\end{enumerate}
}[39]
\begin{enumerate}
\item T-Nachrichten sind solche, die über einen zeitweiligen (temporary) Zustand unterrichten.
\item Wegen der begrenzten Geltungsdauer werden keine Berichtigungen auf der Grundlage von T-Nachrichten vom BSH bzw. amtlichen Seekartenberichtigungsstellen durchgeführt. Deshalb müssen vor Gebrauch jeder Seekarte die noch gültigen T-Nachrichten erfasst und in der Karte vermerkt werden.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Worauf muss beim Ansteuern einer Küste bei der Auswahl von Seekarten geachtet werden? Begründen Sie Ihre Antwort.}[40]
Seekarten mit größtmöglichem Maßstab verwenden. Nur in diesen Karten sind alle Schifffahrtszeichen und weitere für die Navigation wichtigen Informationen eingetragen.
\end{karte}
\begin{karte}[Navigation]{Was müssen Sie bei Kursberechnungen hinsichtlich der in der Seekarte angegebenen Ortsmissweisungen beachten?}[41]
Die für ein bestimmtes Jahr angegebene Missweisung muss mittels der in der Seekarte angegebenen jährlichen Änderung für das aktuelle Jahr berichtigt werden.
\end{karte}
\begin{karte}[Navigation]{Was müssen Sie bei der Benutzung von deutschen \glqq Sportbootkarten\grqq{} beachten?}[42]
Sie werden nach dem Druck weder vom BSH noch von den Seekartenvertriebsstellen berichtigt. Sie müssen also vom Nutzer nach dem Kauf vor Benutzung über die NfS auf den aktuellen Stand berichtigt werden.
\end{karte}
\begin{karte}[Navigation]{Nach welcher Faustregel können Sie m/s in Knoten umrechnen?}[43]
\glqq Doppelt so viele Knoten (kn) wie m/s\grqq{} oder \glqq m/s multipliziert mit 2 = kn\grqq{}.
\end{karte}
\begin{karte}[Navigation]{Was müssen Sie beachten, wenn Sie die mit Loggen ermittelte Fahrt z. B. für das Arbeiten in Seekarten berücksichtigen wollen?}[44]
Die üblichen Logmethoden liefern ausschließlich die \glqq Fahrt durchs Wasser (FdW)\grqq{}. Um die \glqq Fahrt über Grund (FüG)\grqq{} zu ermitteln, müssen Stromrichtung und Stromgeschwindigkeit berücksichtigt werden.
\end{karte}
\begin{karte}[Navigation]{Welche Fahrt zeigen GPS-Geräte an?}[45]
Die Fahrt über Grund (FüG).
\end{karte}
\begin{karte}[Navigation]{Welchen Kurs zeigen GPS-Geräte an?}[46]
Den Kurs über Grund (KüG).
\end{karte}
\begin{karte}[Navigation]{Warum müssen Sie Ihre Position regelmäßig in die Seekarte eintragen?}[47]
Um Abweichungen von der Kurslinie frühzeitig und sicher zu erkennen und um ggf. den Kurs zu berichtigen.
\end{karte}
\begin{karte}[Navigation]{Was ist die Besteckversetzung (BV)?}[48]
Richtung (rw) und Entfernung (in sm) vom Koppelort (O\textsubscript{k}) zum beobachteten Ort (O\textsubscript{b}), bezogen auf den gleichen Zeitpunkt.
\end{karte}
\begin{karte}[Navigation]{Welche Ursachen kann die Besteckversetzung (BV) haben?}[49]
Die BV kann folgende Ursachen haben:
\begin{enumerate}
\item ungenaues Steuern und Koppeln,
\item Kursfehler (z. B. ungenaue Steuertafel) und
\item fehlende oder unvollständige Berücksichtigung von Strom und Wind.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Warum sollte der Winkel zwischen zwei Peilungen nicht kleiner als 30° und nicht größer als 150° sein?}[50]
Damit der gefundene Standort eine ausreichend sichere Positionsbestimmung ergibt.
\end{karte}
\begin{karte}[Navigation]{Warum sind regelmäßige Kompasskontrollen erforderlich?}[51]
Zur Überprüfung der Funktionsfähigkeit des Kompasses und der Werte in der Ablenkungstabelle.
\end{karte}
\begin{karte}[Navigation]{Wodurch können auch in gezeitenlosen Revieren erhebliche Wasserstandsschwankungen und Strömungen (z. B. Triftstrom) hervorgerufen werden?}[52]
Durch Stärke, Dauer und Richtung des Windes oder \glqq Zurückschwappen\grqq{} aufgestauter Wassermassen (z. B. Ostsee).
\end{karte}
\begin{karte}[Navigation]{Welche navigatorischen Vorbereitungen treffen Sie vor einer Fahrt in Dunkelheit?}[53]
\begin{enumerate}
\item Kurse und Kursänderungspunkte möglichst vorausbestimmen,
\item Untiefen und Hindernisse in der Karte besonders kennzeichnen,
\item in der Seekarte markieren, welche Leuchtfeuer wann und wo in der Kimm erscheinen und
\item Wegstrecke nach unbefeuerten Tonnen absuchen.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Welche Möglichkeiten der terrestrischen Ortsbestimmung muss man kennen?}[54]
\begin{enumerate}
\item Kreuzpeilung,
\item Peilung und Abstand (Feuer in der Kimm, Radarabstand),
\item Peilung und Lotung.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Nennen Sie zwei Möglichkeiten der Ortsbestimmung, wenn Sie nur ein Objekt mit bekannten Merkmalen (z. B. Leuchtturm) in Sicht haben.}[55]
\begin{enumerate}
\item Peilung und Abstand (Feuer in der Kimm, Radarabstand),
\item Peilung und Lotung.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Welche Nordrichtungen werden in der Navigation unterschieden? Erläutern Sie diese kurz.}[56]
\begin{enumerate}
\item rwN: rechtweisend Nord ist die Richtung eines Meridians zum geographischen Nordpol.
\item mwN: missweisend Nord ist die Richtung des erdmagnetischen Feldes zum magnetischen Nordpol, abhängig von Schiffsort und Datum (Jahr). In diese Richtung stellt sich eine ungestörte Magnet-(Kompass-)nadel ein.
\item MgN: ist die Richtung zu Magnetkompass-Nord. In diese Richtung zeigt die durch das schiffsmagnetische Feld beeinflusste Kompassnadel an Bord.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Nennen Sie die Winkel zwischen den Nordrichtungen rechtweisend Nord (rwN), missweisend Nord (mwN) und Magnetkompass-Nord (MgN).}[57]
\begin{enumerate}
\item Mw: Missweisung ist der Winkel von rwN nach mwN.
\item Abl: Ablenkung (Abl) oder Deviation (Dev) ist der Winkel von mwN nach MgN.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Nennen Sie den Winkel zwischen den Nordrichtungen rwN und MgN.}[58]
Der Winkel von rwN nach MgN ist die Fehlweisung (Fw; Abl + Mw = Fw).
\end{karte}
\begin{karte}[Navigation]{Wo finden Sie die erforderlichen Werte der Missweisung? Worauf ist dabei zu achten?}[59]
\begin{enumerate}
\item Die Missweisung findet sich in der Seekarte eingedruckt für ein bestimmtes Jahr.
\item Dieser Wert muss mit der ebenfalls in der Seekarte angegebenen jährlichen Änderung auf das Jahr der Benutzung berichtigtwerden.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wo finden Sie die erforderlichen Werte der Ablenkung (Abl)? Worauf ist dabei zu achten?}[60]
\begin{enumerate}
\item Die Abl wird einer Ablenkungstabelle entnommen.
\item Die Abl ist abhängig vom anliegenden Kurs.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Warum muss für jedes Fahrzeug eine eigene Ablenkungstabelle (Steuertafel) erstellt werden?}[61]
Die Ablenkungstabelle kann auf jedem Schiff andere Werte haben.
\end{karte}
\begin{karte}[Navigation]{Worauf müssen Sie achten, wenn eine Magnetkompasspeilung (MgP) auf eine rechtweisende Peilung (rwP) beschickt werden soll?}[62]
Abl für den anliegenden MgK (Magnetkompasskurs) aus der Steuertafel (Ablenkungstabelle) entnehmen; an den so erhaltenen mwK (missweisenden Kurs) die für das laufende Jahr der Seekarte entnommene Mw anbringen.
\end{karte}
\begin{karte}[Navigation]{Unter welchen Voraussetzungen ergibt sich eine brauchbare Standlinie aus einer Lotung?}[63]
Der Meeresgrund muss ausreichend regelmäßig und ausreichend steil ansteigen/abfallen.
\end{karte}
\begin{karte}[Navigation]{Neben den Fahrwassertonnen liegen auf den Seeschifffahrtsstraßen weitere Tonnen aus, die für die Sportschifffahrt besonders wichtig sind. Welche Schifffahrtszeichen sind das?}[64]
Sonderzeichen zur Bezeichnung von Sperrgebieten und Kardinalzeichen für allgemeine Gefahrenstellen.
\end{karte}
\begin{karte}[Navigation]{Aus welchen nautischen Publikationen können Sie Sperr- und Verbotsgebiete mit ihren Grenzen ersehen?}[65]
Aus den Seekarten, Bekanntmachungen für Seefahrer (BfS) und Nautischen Warnnachrichten (NWN).
\end{karte}
\begin{karte}[Navigation]{Welche Sonderzeichen kennzeichnen Reeden, besondere Gebiete oder Stellen, z. B. Warngebiete?}[66]
Gelbe Fasstonnen, Leuchttonnen, Spierentonnen oder Stangen.
\end{karte}
\begin{karte}[Navigation]{Welche Sonderzeichen kennzeichnen Sperrgebiete?}[67]
Gelbe Fasstonnen, Leuchttonnen, Spierentonnen oder Stangen mit einem breiten roten Band. Beschriftung auf Fasstonne oder Leuchttonne mit schwarzen Buchstaben: \glqq Sperrgebiet\grqq{} oder \glqq Sperr-G\grqq{}.
\end{karte}
\begin{karte}[Navigation]{Welche Farbe haben Feuer auf Sonderzeichen, wenn vorhanden?}[68]
Farbe gelb.
\end{karte}
\begin{karte}[Navigation]{Was bedeutet das Ausliegen der folgenden Schifffahrtszeichen: weiße Fasstonne, Kugeltonne oder Stange mit einem - von oben gesehen - rechtwinkligen gelben Kreuz bzw. bei Stangen mit einem breiten gelben Band?}[69]
Fahrverbot für Maschinenfahrzeuge und Wassermotorräder auf wegen Badebetrieb gesperrten Wasserflächen.
\end{karte}
\begin{karte}[Navigation]{Wie stehen Sonne und Mond winkelmäßig zur Erde bei Springzeit und bei Nippzeit (die Springverspätung soll hier unberücksichtigt bleiben)?}[70]
Bei Springzeit befinden sich Mond und Sonne in einer Ebene mit der Erde, bei Nippzeit stehen die Verbindungslinien Erde/Sonne und Erde/Mond im rechten Winkel zueinander.
\end{karte}
\begin{karte}[Navigation]{Erklären Sie den Begriff \glqq Alter der Gezeit\grqq{}.}[71]
Das Alter der Gezeit gibt an, in welcher Phase (Nippzeit, Mittzeit, Springzeit) sich das aktuelle Tidengeschehen befindet.
\end{karte}
\begin{karte}[Navigation]{Warum findet man z. B. bei Bezugsorten in der Nordsee bzw. im Englischen Kanal zeitweise nur ein Hoch- bzw. Niedrigwasser pro Tag?}[72]
Die Umlaufzeit des Mondes um die Erde dauert im Mittel 24 h 50 min. (Mondtag) gegenüber dem Sonnentag (= 24 h). Deshalb \glqq rutscht\grqq{} das letzte HW oder NW zeitweise in den nächsten Tag.
\end{karte}
\begin{karte}[Navigation]{Weshalb und wie können die tatsächlichen Wasserstände von den Angaben in den Gezeitentafeln teilweise erheblich abweichen?}[73]
Durch Wind und/oder durch sehr hohen bzw. sehr niedrigen Luftdruck können erhebliche Wasserstandsänderungen entstehen. HWH bzw. NWH können höher oder niedriger sein als angegeben, die Hoch- und Niedrigwasserzeit kann füher oder später eintreten als angegeben.
\end{karte}
\begin{karte}[Navigation]{Worauf beziehen sich die Tiefenangaben in Seekarten in den deutschen Gewässern der Ost- und Nordsee?}[74]
Auf Kartennull (KN).
\end{karte}
\begin{karte}[Navigation]{Was ist Kartennull?}[75]
Kartennull (KN) ist die Bezugsfläche für die Tiefenangaben in einer Seekarte.
\end{karte}
\begin{karte}[Navigation]{Wie ist Kartennull (KN) in der Ost- und Nordsee und im Englischen Kanal definiert? Wo finden Sie die entsprechenden Angaben zur Kartennullebene?}[76]
\begin{itemize}
\item In der Ostsee entspricht KN dem mittleren Wasserstand.
\item In der Nordsee und im Englischen Kanal entspricht KN dem niedrigstmöglichen Gezeitenwasserstand (LAT = Lowest Astronomical Tide).
\item In der jeweiligen Seekarte ist die Kartennullebene beschrieben.
\end{itemize}
\end{karte}
\begin{karte}[Navigation]{Was müssen Sie bedenken, wenn Sie die Wassertiefe außerhalb der Niedrigwasserzeit loten?}[77]
Beim folgenden Niedrigwasser wird die Wassertiefe geringer sein als zum Zeitpunkt der Lotung.
\end{karte}
\begin{karte}[Navigation]{Was ist die Kartentiefe?}[78]
Die Kartentiefe (KT) ist die auf Kartennull bezogene Wassertiefe. Kartentiefe ist Wassertiefe abzüglich Höhe der Gezeit.
\end{karte}
\begin{karte}[Navigation]{Mit welcher Wassertiefe können Sie bei einer Lotung normalerweise mindestens rechnen?}[79]
Mit der Kartentiefe.
\end{karte}
\begin{karte}[Navigation]{Welche Bedeutung hat die Angabe \glqq Springzeit\grqq{} für die Wasserstände in Gezeitengebieten?}[80]
Zur Springzeit sind besonders hohe Hochwasser und besonders niedrige Niedrigwasser zu erwarten.
\end{karte}
\begin{karte}[Navigation]{Welche Bedeutung hat die Angabe \glqq Nippzeit\grqq{} für die Wasserstände in Gezeitengebieten?}[81]
Zur Nippzeit sind besonders niedrige Hochwasser und besonders hohe Niedrigwasser zu erwarten.
\end{karte}
\begin{karte}[Navigation]{Welche Bedeutung haben die Angaben \glqq Nippzeit\grqq{} bzw. \glqq Springzeit\grqq{} für die Gezeitenströme?}[82]
Zur Springzeit setzen die Gezeitenströme z. T. deutlich stärker als zur Nippzeit.
\end{karte}
\begin{karte}[Navigation]{Wo können Sie Informationen über Gezeitenströme in Küstengewässern finden?}[83]
\begin{enumerate}
\item In Gezeitenstromatlanten, Seehandbüchern,
\item in Seekarten aus Gezeitenstromtabellen, die bezogen sind auf die Hochwasserzeiten des dort genannten Bezugsortes.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Auf einer Seekarte finden Sie in Küstennähe die Tiefenangabe \underline{2}$_{3}$. Was bedeutet das?}[84]
Der Ort der Zahl liegt 2,3 m über Kartennull und kann trockenfallen.
\end{karte}
\begin{karte}[Navigation]{In welchem Zusammenhang stehen Kartentiefe (KT), Wassertiefe (WT) und Höhe der Gezeit (H)?}[85]
WT - H = KT oder KT + H = WT (Lösung auch als Skizze möglich).
\end{karte}
\begin{karte}[Navigation]{Warum ist es in Tidengewässern wichtig, die Uhrzeit einer Lotung festzuhalten?}[86]
Um anhand der Gezeitentafel feststellen zu können, ob das Wasser steigt oder fällt.
\end{karte}
\begin{karte}[Navigation]{Was ist ein Pegel?}[87]
Eine Skala zur Anzeige des Wasserstandes.
\end{karte}
\begin{karte}[Navigation]{Welchen Einfluss kann der Wind auf die Gezeiten haben?}[88]
Der Wind kann Strömungen und Wasserstandsänderungen hervorrufen, die zu den Gezeitenströmen und den Gezeiten hinzutreten.
\end{karte}
\begin{karte}[Navigation]{Nennen Sie drei wichtige Vorzüge von GPS.}[89]
\begin{enumerate}
\item GPS arbeitet weltweit.
\item Die Positionsanzeige ist jederzeit verfügbar.
\item Der Positionsfehler ist gering.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie groß ist die typische und realistische Genauigkeit von Positionen, die mit GPS und DGPS ermittelt werden?}[90]
\begin{enumerate}
\item GPS: 10 - 20 m bei einer Wahrscheinlichkeit von etwa 95\%.
\item DGPS: 1 - 10 m bei einer Wahrscheinlichkeit von etwa 95\%.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wo muss man mit ungenauen Anzeigen des GPS rechnen?}[91]
\begin{enumerate}
\item Bei Abschattung der GPS-Antenne.
\item In der Nähe von Flughäfen und in der Nähe von Fernsehsendern.
\item In der Nähe von Marineeinrichtungen.
\item Bei Nutzung von UKW-Geräten und anderen elektronischen/elektrischen Geräten an Bord.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was bedeutet die Abkürzung GPS?}[92]
Global Positioning System.
\end{karte}
\begin{karte}[Navigation]{Was ist das Grundprinzip von GPS?}[93]
Durch Laufzeitmessungen von GPS-Signalen vom Satelliten zum Empfänger und damit durch Abstandsmessungen zu den Satelliten wird die Ortsbestimmung ermöglicht.
\end{karte}
\begin{karte}[Navigation]{Was bedeutet die Abkürzung DGPS und nach welchem Prinzip arbeitet DGPS?}[94]
DGPS = Differential Global Positioning System.
Hierbei handelt es sich um eine regionale Verbesserung der Ortsbestimmung. Dabei werden von Referenzstationen über Funk Korrekturwerte für die GPS-Messwerte an die Schiffe übertragen.
\end{karte}
\begin{karte}[Navigation]{Was ist bei Anbringung einer GPS-Antenne zu beachten?}[95]
\begin{enumerate}
\item Sie muss ringsum freie Sicht (ohne Abschattungen) haben.
\item Einwandfreie Erdung.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was bewirkt die Bedienung der MOB-Taste bei GPS-Geräten?}[96]
\begin{enumerate}
\item Die Position zur Zeit des Tastendrucks wird gespeichert.
\item Rechtweisende Peilung (rwP) und Distanz zu diesem Punkt werden angezeigt.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was bedeutet die Aussage:\\ \glqq Die Ortsgenauigkeit beträgt 100 m mit einer Wahrscheinlichkeit von 95 \%\grqq?}[97]
Das Schiff befindet sich mit einer Wahrscheinlichkeit von 95 \% in einem Fehlerkreis von 100 m Radius um den beobachteten Ort. Also: jede 20. Ortsbestimmung (5 \%) ist ungenauer als ca. 100 m.
\end{karte}
\begin{karte}[Navigation]{Wie kann man feststellen, ob die GPS-Position genau bzw. zuverlässig ist?}[98]
\begin{enumerate}
\item Durch den vom Empfänger angezeigten HDOP (horizontal dilution of precision = Satellitenverteilung).
\item Durch die vom Empfänger angezeigte Anzahl der getrackten Satelliten.
\item Durch Vergleich mit anderen Navigationssystemen und der Koppelposition.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was ist bei Eintragung eines GPS-Ortes in eine Seekarte zu beachten?}[99]
Das Bezugssystem muss übereinstimmen. Dieses kann geschehen durch:
\begin{enumerate}
\item Auswahl und Einstellung des Kartenbezugssystems im Empfänger.
\item Manuelle Verschiebung des GPS-Ortes um die in der Seekarte angegebenen N/S- und E/W-Korrektur.
\item Verwendung von Seekarten, die auf dem System WGS 84 beruhen.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was ist ein Wegpunkt?}[100]
Geographische Koordination eines anzusteuernden Punktes.
\end{karte}
\begin{karte}[Navigation]{Was bedeutet WGS 84 und was wird damit erreicht?}[101]
\begin{enumerate}
\item Globales Bezugssystem \glqq World Geodetic System 1984\grqq.
\item Mit diesem System (= Referenzellipsoid bei GPS) wird weltweit eine optimale Anpassung an die reale Form des gesamten Erdkörpers erreicht.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wodurch können Radarechos von kleinen Fahrzeugen und Tonnen auf den Sichtschirmen von Radargeräten \glqq verschwinden\grqq?}[102]
\begin{enumerate}
\item Durch Seegang und/oder Niederschlag,
\item durch falsche Bedienung,
\item durch zu große Entfernung,
\item durch Gieren des eigenen Fahrzeugs bei relativ vorausorientierter Radarstellung (head up).
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie kann man mit Radar den eigenen Schiffsort bestimmen?}[103]
\begin{enumerate}
\item Peilung des Objektes gibt einen Peilstrahl als Standlinie.
\item Abstandsmessung mit dem VRM (Variable Range Marker) gibt einen Abstandskreis als Standlinie.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie kann man gegebenenfalls verhindern, dass sich Echoanzeigen von Zielen (z. B. 2 Tonnen, 2 Molenköpfe) überlappen?}[104]
\begin{enumerate}
\item Kurze Impulslänge wählen.
\item Messbereich verkleinern.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was bedeutet der Begriff AIS auf See?}[105]
AIS bezeichnet das automatische Identifizierungssystem (Automatic Identification System).
\end{karte}
\begin{karte}[Navigation]{Welche Aufgaben hat AIS?}[106]
Alle ausgerüsteten Schiffe senden automatisch (also ohne Aufforderung und menschliches Eingreifen) in regelmäßigen kurzen Abständen ihre Identität und einen schiffsbezogenen Datensatz. Außerdem können bei Bedarf sicherheitsrelevante Nachrichten (\glqq safety related messages\grqq) von Bord oder von Landstationen gesendet werden.
\end{karte}
\begin{karte}[Navigation]{Welche Reichweite hat ein AIS-Bordgerät und wovon ist sie abhängig?}[107]
Die Reichweite und Ausbreitungsbedingungen entsprechen denen von UKW. Bei Handelsschiffen kann man von 20 bis 30 sm ausgehen. Die Reichweite ist abhängig von der Antennenhöhe.
\end{karte}
\begin{karte}[Navigation]{Wie kann die Reichweite eines AIS-Bordgerätes landseitig erhöht werden und wie wirken sich dabei Hindernisse (z. B. Berge) aus?}[108]
Unter bestimmten Umständen kann die Reichweite heraufgesetzt werden (z. B. mit Hilfe von "Relaisstationen"), wobei ggf. auch abschattende Hindernisse umgangen werden können.
\end{karte}
\begin{karte}[Navigation]{Welche AIS-Daten werden von Schiffen aus der Berufsschifffahrt gesendet?}[109]
\begin{itemize}
\item Statische Daten: ID, Rufzeichen, Länge und Breite des Schiffes u. a.
\item Dynamische Daten (i. W. Sensordaten): UTC, Position, Heading, Kurs und Fahrt über Grund, ggf. Rate-of-turn, Fahrtstatus (z. B. Maschinenfahrzeug mit Fahrt durchs Wasser, Ankerlieger, manövrierbehindertes Fahrzeug).
\item Reisebezogene Daten: Tiefgang, Zielort (Destinaton), ETA u. a.
\end{itemize}
\end{karte}
\begin{karte}[Navigation]{Wann kann man sich auf die Verfügbarkeit und Anzeige von AIS-Signalen anderer Fahrzeuge verlassen? Nennen Sie die wesentlichen Voraussetzungen!}[110]
Andere Fahrzeuge werden nur angezeigt, wenn das Fahrzeug auch sendet, d. h., wenn
\begin{enumerate}
\item das Fahrzeug mit AIS ausgerüstet ist,
\item das sendende Fahrzeug AIS nicht abgeschaltet hat (darf der Kapitän allerdings nur bei bestimmten zwingenden Gründen),
\item GPS aktiv ist und
\item aus Kapazitätsgründen (z. B. durch zu viele Schiffe in einem Seegebiet = "target overflow") keine Fahrzeuge ausgeschlossen werden.
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Wie ist die Genauigkeit von AIS-Daten zu beurteilen (Position und manuell eingegebene Daten)?}[111]
\begin{itemize}
\item Position: Mit AIS wird zusätzlich zur GPS-Position eines Schiffes die Information übertragen, ob es sich um einen GPS- oder DGPSOrt handelt. Ist die GPS-Position eines Schiffes falsch, wird diese falsche Position auf allen anderen Schiffen angezeigt.
\item Manuell eingegebene Daten: Es muss damit gerechnet werden, dass Zielort, Tiefgang, Fahrtstatus u. a. falsch sind, wenn sie - z. B. aus Nachlässigkeit - nicht von der Schiffsführung aufdatiert werden.
\end{itemize}
\end{karte}
\begin{karte}[Navigation]{Welche besondere Bedeutung hat AIS für die Sportschifffahrt im Vergleich mit der Radaranzeige auf anderen Schiffen?}[112]
Sportfahrzeuge werden häufig auf den Radargeräten anderer Schiffe nicht sicher angezeigt bzw. die Anzeigen gehen im Seegangsclutter oder in der Informationsfülle unter. Da jetzt auf vielen Schiffen die AIS-Daten zusätzlich im Radar dargestellt werden, besteht die Gefahr, dass Sportfahrzeuge noch weniger auffällig sind, wenn sie nicht selbst mit AIS ausgerüstet sind.
\end{karte}
\begin{karte}[Navigation]{Welche Navigationsgeräte sollten Sie auf einer Yacht auch bei Kurzfahrten nahe der Küste mindestens an Bord haben? }[113]
Steuerkompass, Peilkompass, Lot, Log, Uhr.
\end{karte}
\begin{karte}[Navigation]{Was gehört zur navigatorischen Mindestausrüstung einer Yacht in Küstengewässern? Nennen Sie mindestens 6 Beispiele. }[114]
{\small \begin{enumerate}
\item Steuerkompass,
\item Peileinrichtung,
\item terrestrisches oder satellitengestütztes Funknavigationsgerät,
\item Log,
\item Lot,
\item Fernglas,
\item Barometer,
\item Weltempfänger für Rundfunk,
\item Seebücher und auf den neuesten Stand berichtigte Seekarten für das zu befahrende Seegebiet,
\item Logbuch,
\item Uhr/Zeitmesser.
\end{enumerate}\par}
\end{karte}
\begin{karte}[Navigation]{Welchen Vorteil hat ein Kugelkompass gegenüber einem Fernglaskompass?}[115]
\begin{enumerate}
\item Der Kugelkompass kann auch bei größerer Krängung noch als Messinstrument benutzt werden.
\item Die Kugelform verbessert die Ablesbarkeit der Kompassrose (Vergrößerungseffekt).
\end{enumerate}
\end{karte}
\begin{karte}[Navigation]{Was beeinflusst die Ablenkung eines Kompasses dauerhaft?}[116]
Veränderung des magnetischen Zustandes an Bord, z. B. Einbauten und Lageänderung von Ausrüstungsgegenständen.
\end{karte}
\begin{karte}[Navigation]{Was beeinflusst die Ablenkung eines Kompasses vorübergehend?}[117]
Elektronische Geräte (z. B. Radio, Handy), magnetisierte Gegenstände (z. B. Werkzeug, Peilkompass) und Gleichstromleitungen in der Nähe des Kompasses.
\end{karte}
\begin{karte}[Navigation]{Welchen Abstand muss magnetisierbares Material vom Magnetkompass haben?}[118]
Mindestens 1 Meter.
\end{karte}
\end{document}
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\begin{thebibliography}{1}
\bibitem{MahendraKumarTrivedi2017} Mahendra Kumar Trivedi, A. B., Dahryn Trivedi, Gopal Nayak, Cathryn Dawn Nykvist, Celine Lavelle, Daniel Paul Przybylski, Dianne Heather Vincent, Dorothy Felger, Douglas Jay Konersman, Elizabeth Ann Feeney, Jay Anthony Prague, Joanne Lydia Starodub, Karan Rasdan, Karen Mie Strassman, Leonid Soboleff, Maire Mayne, Mary M. Keesee, Padmanabha Narayana Pillai, Pamela Clarkson Ansley, Ronald David Schmitz, Sharyn Marie Sodomora, Sambhu Charan Mondal, Snehasis Jana. (2017). Potential Role of the Trivedi Effect{\textregistered}~- Biofield Energy Healing on Immunomodulatory Response of Herbomineral Formulation in Male~Sprague Dawley~Rats. \textit{International Journal of Biomedical Science and Engineering}, \textit{5}(5). Retrieved May 22, 2018, from http://dx.doi.org/10.11648/j.ijbse.20170505.12
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\bib{1999/murphy}
\yr 1999
\by Brian Murphy
\book Polynomial selection for the number field sieve integer factorisation algorithm
\phdthesis
\url http://web.comlab.ox.ac.uk/oucl/work/richard.brent/students.html
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\documentclass{report}
\usepackage{graphicx}
\begin{document}
\title{Calculating the work function of a metallic surface with ABINIT}
\author{Matthieu Verstraete, Univeristy of Li\`ege, Belgium}
\maketitle
Copyright (C) 2014-2018 ABINIT group (MV)
This file is distributed under the terms of the
GNU General Public License, see ~abinit/COPYING
or http://www.gnu.org/copyleft/gpl.txt.
For the initials of contributors, see ~abinit/doc/developers/contributors.txt
This brief tutorial should teach you how to calculate a work function $\phi$ for a (metallic) surface, using the ABINIT code. We will presume you know how to calculate a ground state, and have done the first 4 tutorials of ABINIT.
The experimental work function of the Gold (111) surface is 5.2 eV (habitual for metal surfaces which are between 3.5 and 7 eV habitually), and corresponds to the minimal energy required to extract an electron from the surface and bring it to a detector, which is a macroscopic distance away in the vacuum above the surface. The work function in DFT is estimated as the difference between $V(\infty)$, the value of the electronic potential in the vacuum, and the Fermi level $E_F$, which is the energy of the highest lying electron, which is the easiest to extract. The electron density at the surface will spill out some and re-arrange self-consistently when we obtain the ground state. The resulting surface dipole determines the potential step which is experienced between the center of the slab and the vacuum region.
\section{Slab calculation}
We will now perform a straight slab calculation. All of this is severely unconverged in number of k-points, kinetic energy cutoff, slab thickness and vacuum thicknesses. The input file i.au describes a slab of 3 layers of gold, stacked along the (111) direction (ABC stacking). The full height of the supercell is 10 times the inter-layer distance, such that the fractional coordinates of the layers are easy to calculate, and there are 10-3=7 ``layers'' of vacuum (which corresponds to 21 Angstrom). Another thing we will not converge is the atomic positions: there should be some relaxation of the interlayer distances at the surface, and you should do a structural relaxation to get an accurate result.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.8\linewidth]{workfunction_image0}
\caption{Potential and $E_F$ for a slab of 3 layers of (111) Gold}
\label{fig1}
\end{center}
\end{figure}
The important new input variable is \texttt{prt1dm} which triggers the output of the projected potential and density, along the 3 axes of the unit cell. These quantities are (in the case of the $z$ direction we are interested in):
\begin{eqnarray}
\bar{V}(z) &=& \int dx dy V(x,y,z) \\
\bar{\rho}(z) &=& \int dx dy \rho(x,y,z)
\end{eqnarray}
where $V$ is the electrostatic+xc (local) part of the potential (in Hartree), whereas $\rho$ is the electron density (in number of electrons / bohr$^3$).
Run the input file, using the pseudopotential 79au.pspnc - it should take less than a minute. The resulting output files are the usual ones (EIG, DEN, WFK) plus a new one, with a suffix 1DM, containing the projected density and potential. The file is ascii text, and organised into blocks, for projection on the first, then second, then third axis of the unit cell. The projection is along planes of points on the FFT grid - if your box is not orthogonal, the projection will not correspond to the cartesian projection! In our case the c axis is perpendicular to the other two, so we are fine. The first two columns of the file data contain the FFT index in the grid, and the fractional (reduced) coordinate of the plane for averaging. Then come the averaged potential, and the density. If you are a user of xmgrace or gnuplot, and have commented or chopped out the header and auxiliary information lines (this will be automatic from abinit v7.8), you can read in the data directly. The resulting plot for the z-projection is shown in Fig.~\ref{fig1}
You can see the potential goes up and has a plateau in the middle of the vacuum. One test of vacuum thickness convergence is that the plateau is indeed flat. Note that the potential does not go to 0 - the convention in abinit is that the electrostatic potential average over the \emph{whole} cell is 0, such that the vacuum part has to compensate the rest. Also shown is the Fermi energy of the slab, extracted from the output file. A first estimate of the work function is simply the difference between the potential plateau value and the Fermi level.
\section{Refinement of the Fermi level}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.48\linewidth]{workfunction_image1}
\includegraphics[width=0.48\linewidth]{workfunction_image2}
\caption{Potential and $E_F$ for a slab and a bulk, of 3 layers of (111) Gold. left: as produced by ABINIT; right: with the bulk quantities aligned to the potential in the center of the slab.}
\label{fig2}
\end{center}
\end{figure}
There is an additional correction which should be taken into account, due to the finite thickness of the slab. The total energy and surface relaxations can usually be converged with slabs of the order of 5-10 layers or a bit more (metals tend to screen well and converge a bit faster). However, if you consider the k-point sampling, this is equivalent to 5-10 k-points and is woefully insufficient in a metal. To compensate this we will do a supplementary correction of the position of $E_F$, taking it from a well converged continuous bulk calculation (with as many k-points as needed). To translate the bulk $E_F$ to the slab, we will need a common reference energy, which can not be the vacuum of course - there is none in the bulk. If your slab is thick enough, a local quantity we can compare is the potential, and it should be quite similar in the bulk and in the center of the slab.
You should now run the second input file, for the bulk system, and it should run even faster than the first. In principle you can use a primitive unit cell to get $E_F$, and this will also be the most efficient calculation. However, to get the planar averaged potential, you would need to do a little geometry and extract the real cartesian projection, which ABINIT does not do for you... For simplicity, we have replicated the same atoms as in the slab (same c direction) but removed the vacuum. As this cell is not primitive we set chkprim to 0 to force ABINIT to calculate it anyway. prt1dm is still turned on so we can get averaged $\bar{V}(z)$ to compare. The result is shown in Fig~\ref{fig2}(left): as you can see the potentials in the slab are very similar. If you shift the bulk potential and $E_F$ to align with the potential in the center of the slab (Fig~\ref{fig2}(right)) you can see a small difference in the $E_F$ values, which is the (quite small) correction for an infinitely thick slab.
The final result is shown in Fig~\ref{fig3}, converted to electron-volts. The resulting value is 5.82 eV, which is ridiculously close to the experimental 5.2 given how badly we are converged. This rough estimation often holds, as the work function for simple metals is mainly due to atomic properties and densities, but do not bet on it... In practical calculations, you do not necessarily need to plot things, but it is easier. Find the plateau value of $\bar{V}$ at position $z_1$, compare the potentials in bulk and slab inside the slab - position $z_0$ - (this is easier done graphically, but does not give you good numerical precision), and shift $E_F$ for the bulk by this difference, to get
\begin{eqnarray}
\phi = \bar{V}_{slab}(z_1) - E_{F,bulk} - \bar{V}_{slab}(z_0) + \bar{V}_{bulk}(z_0)
\end{eqnarray}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.8\linewidth]{workfunction_image3}
\caption{Potential and $E_F$ in eV for a slab and a bulk, of 3 layers of (111) Gold.}
\label{fig3}
\end{center}
\end{figure}
\section{Slab input file}
\begin{verbatim}
# bulk calculation for the z along 111 orientation of gold
prt1dm 1
ngkpt 4 4 1
# 4.07 cubic lattice parameter,
# 5.76 in-plane 111 lattice parameter, and
# 2.3498 interlayer distance -> 10 layers, 3 filled 7 vacuum
acell 2*5.76 23.498 Angstr
angdeg 90 90 120
ntypat 1
znucl 79
natom 3
typat 1 1 1
# z coordinate in tenths here!
xred
0 0 0
1/3 2/3 1/10
2/3 1/3 2/10
tolvrs 1.e-9
occopt 7
tsmear 0.0001
ecut 6
shiftk 0 0 0
\end{verbatim}
\section{Bulk input file}
\begin{verbatim}
# slab calculation for the 111 surface of gold
prt1dm 1
chkprim 0
ngkpt 4 4 4
# 4.07 cubic lattice parameter,
# 5.76 in-plane 111 lattice parameter, and
# 2.3498 interlayer distance -> 3 layers 0 vacuum
acell 2*5.76 7.0494 Angstr
angdeg 90 90 120
ntypat 1
znucl 79
natom 3
typat 1 1 1
# z coordinate in thirds here!
xred
0 0 0
1/3 2/3 1/3
2/3 1/3 2/3
tolvrs 1.e-9
occopt 7
tsmear 0.0001
ecut 6
shiftk 0 0 0
\end{verbatim}
\end{document}
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\documentclass{article}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{tabularx}
\usepackage{fancyvrb}
\usepackage{booktabs}
\usepackage{semantic-markup}
\frenchspacing
\usepackage
[pdftitle={The semantic-markup Package for Meaningful Markup},
pdfauthor={Andrew A. Cashner},
pdfsubject={LaTeX package},
pdfkeywords={LaTeX, semantic markup, TEI, humanities}]{hyperref}
\title{The \texttt{semantic-markup} Package for Meaningful Markup}
\author{Andrew A. Cashner%
\thanks{\href{mailto:[email protected]}{\nolinkurl{[email protected]}}}%
}
\begin{document}
\maketitle
The \texttt{semantic-markup} package provides a set of simple commands to allow for semantic markup.
The commands are inspired by the XML elements of the Text Encoding Initiative (\url{http://www.tei-c.org}).
They are intended especially for scholarly writing in the humanities, including about music.
The goal is simply to allow scholars to write with attention to meaning and content rather than to formatting.
\tableofcontents
\section{Package Options}
\subsection{\texttt{defaultquotes}}
The package configures \texttt{csquotes} to place end punctuation inside quotation marks, according to United States usage.
Use the \texttt{defaultquotes} package option to restore the default behavior of \texttt{csquotes}.
\subsection{\texttt{endnotes}}
The \texttt{endnotes} option converts footnotes to endnotes, including footnotes created with this package's \texttt{Footnote} environment.
On its own, this option loads the \texttt{endnotes} package and does everything
necessary for endnotes.
You can define the following commands to adjust the behavior:
\begin{center}
\begin{tabular}{ll}
Command & Default value \\ \hline
\verb|\DoBeforeEndnotes| & \verb|\clearpage| \\
\verb|\EndnoteFont| & Empty (normal font) \\
\end{tabular}
\end{center}
If you want to setup the endnotes in a completely different way or avoid
conflicts with another package, you can do
\verb|\renewcommand{\SetupEndnotes}{}| to eliminate all of this or you can renew
the command to do something else.
\section{Semantic Commands Defined Without Arguments}
The following commands are defined (using \texttt{xparse}) as aliases to standard \LaTeX{} commands or \verb|\textquote| from the \texttt{csquotes} package.
In other words, they are not defined with an argument.
For example, the command for a technical term, typically set in italics is defined this way:
\begin{verbatim}
\NewDocumentCommand{\term}{}{\emph}
\end{verbatim}
To redefine it to be set in bold, for example, you can use the basic \LaTeX{} command \verb|\renewcommand{\term}{\textbf}|.
The \verb|\strong| command is already defined in the \texttt{fontspec} package;
if that package is loaded, this package will not redefine its command.
\begin{center}
\begin{tabularx}{\linewidth}{llX}
\toprule
Package Command & Alias & Use\\
\midrule
\verb|\quoted| & \verb|\textquote| & Quoted material, taking care of end punctuation: instead of \verb|``word,''| write \verb|\quoted{word},|\\
\verb|\soCalled| & \verb|\textquote| & Scare quotes\\
\verb|\strong| & \verb|\textbf| & Highlight emphasis just as in HTML\\
\verb|\code| & \verb|\texttt| & Computer code in teletype font (not verbatim)\\
\verb|\term| & \verb|\emph| & Technical terms, set in italics\\
\verb|\mentioned| & \verb|\emph| & Referring to a word as a word rather than to its meaning, as in philological discussion\\
\verb|\foreign| & \verb|\emph| & Foreign term\\
\verb|\worktitle| & \verb|\emph| & Title of a complete work (of literature, art, music), set in italics; use for books, journal titles\\
\verb|\parttitle| & \verb|\textquote| & Title of a portion of a work, set in quotation marks, such as a journal article, song on an album\\
\bottomrule
\end{tabularx}
\end{center}
\section{Semantic Commands With Arguments}
These commands have slightly more complex definitions, but can still be easily redefined.
See the \texttt{xparse} documentation on the syntax of these commands.
\begin{center}
\begin{tabularx}{\linewidth}{lXX}
\toprule
Command & Definition & Usage\\
\midrule
\verb|\add| & One argument: Put square brackets around argument & For editorial additions\\
\verb|\Dots| & Put ellipsis in square brackets & For editorial omissions from quotations\\
\verb|\gloss| & Two arguments: Put first in italics and second in parentheses & Use a technical or foreign term and give its definition\\
\verb|\quotedgloss| & Two arguments: Put first in quotation marks and second in parentheses & Same as \verb|\gloss| but using \verb|\quoted| for the first argument instead of \verb|\mentioned|\\
\verb|\XXX| & One optional argument with default value of \verb|\add{FIX}| & Identify problem spot in draft\\
\verb|\citXXX| & One optional argument & Make footnote indicating a missing citation; optional argument may be used for reminder of the citation name or description\\
\bottomrule
\end{tabularx}
\end{center}
\section{Footnote Environment}
When writing many long footnotes it can be useful to have an environment for footnotes.
Here one is defined using the \texttt{environ} package.
You still have to escape the end of the line before the footnote begins.
Use like so:
\begin{verbatim}
Body text.%
\begin{Footnote}
Footnote text.
More footnote text.
\end{Footnote}
Continuation of body text.
\end{verbatim}
\section{Musical Symbols}
Shorthands are defined for musical accidentals, using \LaTeX{} math-mode symbols.
These could be redefined to use Unicode symbols if the font contains them, or with commands from the \texttt{lilyglyphs} package.
Remember that like all commands without arguments, \LaTeX{} will ignore the space after the command-name, so you will need to write \verb|\fl{}| or \verb|\fl\ |.
There is also a command for octave numbers, for the system in which middle C begins the fourth octave.
If the \texttt{musicography} package is loaded, it will redefine the commands
\verb|\fl|, \verb|\sh|, and \verb|\na| to use nicer symbols from the MusiX\TeX{}
fonts.
\begin{center}
\begin{tabular}{ll}
\toprule
Command & Alias\\
\midrule
\verb|\fl| & \verb|$\flat$|\\
\verb|\na| & \verb|$\natural$|\\
\verb|\sh| & \verb|$\sharp$|\\
\verb|\octave| & \verb|\textsubscript|\\
\bottomrule
\end{tabular}
\end{center}
For stacked numerals, as in meter signatures or figured bass, we provide two simple options, \verb|\musfig| using \verb|\genfrac| from \texttt{amsmath}, and \verb|\meter|, which uses \verb|\Takt| from the \texttt{harmony} package, which spaces the numerals more closely.
Both commands take two arguments, one for the top numeral and the second for the bottom numeral.
You could write, for example:
\begin{verbatim}
There is a \musfig{6--5}{4--3} cadential pattern
before the shift to \meter{3}{4} time.
The melody begins on F\sh\octave{4}.
\end{verbatim}
\begin{center}
\fbox{\parbox{\textwidth}{%
There is a \musfig{6--5}{4--3} cadential pattern
before the shift to \meter{3}{4} time.
The melody begins on F\sh\octave{4}.
}}
\end{center}
For more complex notation, such as three-level numerals, or stacked figured-bass symbols with accidentals or slashes, you will have to devise your own solution.
\section{Code}
\VerbatimInput{semantic-markup.sty}
\end{document}
|
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authorea.com
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| 317,244,075
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\documentclass{article}
\usepackage{fullpage}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage{xcolor}
\usepackage[colorlinks = true,
linkcolor = blue,
urlcolor = blue,
citecolor = blue,
anchorcolor = blue]{hyperref}
\usepackage[natbibapa]{apacite}
\usepackage{eso-pic}
\AddToShipoutPictureBG{\AtPageLowerLeft{\includegraphics[scale=0.7]{powered-by-Authorea-watermark.png}}}
\renewenvironment{abstract}
{{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
{\bigskip}
\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}
\usepackage{authblk}
\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
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% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\begin{document}
\title{Authorea Spotlight: Viputheshwar Sitaraman (Draw Science)\\}
\author{The Authorea Team}
\date{}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
Who is the youngest person in the U.S. to ever raise venture capital
funding? \textbf{Vip Sitaraman}.\\
Vip---no relation to Very Important Person, although he is pretty damn
cool---is a 3-time entrepreneur, scientist, and designer extraordinaire.
He is at the helm of \href{http://www.gmtry.co/}{GMTRY}~(parent company
of~\href{http://pubdraw.org/}{Draw
Science},~\href{http://rxnscience.com/}{RXN},
and~\href{http://explica.co/}{Explica}), an open access publishing
platform that turns academic papers into infographics. Did we mention
he's 18 years old?\\\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/vip-2/vip-2}
\caption{{\textbf{\href{http://www.viputheshwar.com/}{Viputheshwar Sitaraman}},
CEO and Founder of \textbf{GMTRY}%
}}
\end{center}
\end{figure}
We interviewed Vip while he is in the midst of
the~\href{http://www.seedsumo.com/}{Seed Sumo}~(early-stage startup
accelerator) summer program in Texas.\\
\textbf{What inspired you at the age of 16 and continues to inspire you
today?}\\
I believe that anybody can do anything with access to knowledge.
\href{https://twitter.com/drawscience}{Draw Science} is my way of
helping open the gates to knowledge, by making cutting edge research
accessible to anyone.\\
When I was 13, I was handed my first academic paper. I spent weeks
trying to understand it, searching almost every other word on Wikipedia.
After two more years of that, I landed my first lab position. Soon
after, I published in the World Forum in Biology. But since day 1, I've
had an acute hatred for jargon as a barrier to knowledge
dissemination.\\
\textbf{What does being a scientist and artist mean to you? How does art
promote open science?}\\
We can break down paywalls and publishing fees, but the biggest hurdle
in open science is language. Jargon prevents even scientists from
communicating with each other, let alone the remaining 99.98\% of the
world. My goal is to translate science through art.~\\
Written language used to be in the form of cuneiform and hieroglyphics:
symbols that resembled the items they represented.
\href{https://www.authorea.com/users/96042/articles/115395/_show_article}{Infographics}
are merely a revival of such illustrative modes of communication: more
tedious to create, but more rapidly understood.\\
\textbf{What are some
not-so-intuitive~\href{https://www.authorea.com/users/96042/articles/115550/_show_article}{tips}~you
have for telling the most compelling story via design?}\\
\begin{itemize}
\tightlist
\item
Avoid being chronological: instead go from big idea to specific
conclusion.\\
\item
Conclusion first, story second: catch your reader's attention with the
impact of your work--then explain it.\\
\end{itemize}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.91\columnwidth]{figures/j-biocon-2016-01-006/j-biocon-2016-01-006}
\caption{{\hypertarget{auto-label-caption-844697}{}
Graphic abstract of
"\href{http://www.sciencedirect.com/science/article/pii/S0006320716300064}{To
what extent could edge effects and habitat fragmentation diminish the
potential benefits of land sparing?}" (\protect\cite{Lamb_2016}) by Draw
Science.~%
}}
\end{center}
\end{figure}
\textbf{Why should scientists care? Why are graphics important to
science communication?}\\
Academic research is, in business terms, a battle of branding.
Scientists seldom realize it but much like publishers, they're trying to
brand themselves as the authority in a certain niche in science.
Graphics are a really easy way to
\href{https://www.authorea.com/users/3/articles/149}{stand out from the
crowd}: that's why authors using Draw Science are cited and viewed
more.\textbf{}\\
\textbf{What would you be doing if you weren't running GMTRY?}\\
\textbf{}If I wasn't running some other startup, I'd be working on a
career in music.\textbf{}
\selectlanguage{english}
\FloatBarrier
\end{document}
|
https://mirror.anarhija.net/anarhisticka-biblioteka.net/mirror/j/jd/jane-doe-anarhisticka-farma.tex
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\documentclass[DIV=12,%
BCOR=10mm,%
headinclude=false,%
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fontsize=11pt,%
twoside,%
paper=a4]%
{scrbook}
\usepackage{fontspec}
\usepackage{polyglossia}
\setmainfont{Linux Libertine O}
% these are not used but prevents XeTeX to barf
\setsansfont[Scale=MatchLowercase]{CMU Sans Serif}
\setmonofont[Scale=MatchLowercase]{CMU Typewriter Text}
\setmainlanguage{croatian}
% global style
\pagestyle{plain}
\usepackage{microtype} % you need an *updated* texlive 2012, but harmless
\usepackage{graphicx}
\usepackage{alltt}
\usepackage{verbatim}
% http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url
\PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref}
\usepackage{bookmark}
% footnote handling
\usepackage[fragile]{bigfoot}
\usepackage{perpage}
\DeclareNewFootnote{default}
\DeclareNewFootnote{B}
\MakeSorted{footnoteB}
\renewcommand*\thefootnoteB{(\arabic{footnoteB})}
\deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~}
% continuous numbering across the document. Defaults to resetting at chapter. Unclear
% \usepackage{chngcntr}
% \counterwithout{footnote}{chapter}
\usepackage[shortlabels]{enumitem}
\usepackage{tabularx}
\usepackage[normalem]{ulem}
\def\hsout{\bgroup \ULdepth=-.55ex \ULset}
% https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title
% Unclear if \protect \hsout is needed. Doesn't looks so
\DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}}
\usepackage{wrapfig}
\usepackage{indentfirst}
% remove the numbering
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% remove labels from the captions
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\renewcommand*{\figureformat}{}
\renewcommand*{\tableformat}{}
\KOMAoption{captions}{belowfigure,nooneline}
\addtokomafont{caption}{\centering}
% avoid breakage on multiple <br><br> and avoid the next [] to be eaten
\newcommand*{\forcelinebreak}{\strut\\*{}}
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\bigskip%
\noindent \hrulefill%
\bigskip%
}
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% forbid widows/orphans
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% http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph
\finalhyphendemerits=10000
% given that we said footinclude=false, this should be safe
\setlength{\footskip}{2\baselineskip}
\title{Anarhistička farma}
\date{}
\author{Jane Doe}
\subtitle{}
% https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion
\hypersetup{%
pdfencoding=auto,
pdftitle={Anarhistička farma},%
pdfauthor={Jane Doe},%
pdfsubject={},%
pdfkeywords={Književnost; anarhizam; ekologija; pobuna}%
}
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\begin{center}
{\usekomafont{title}{\huge Anarhistička farma\par}}%
\vskip 1em
\vskip 2em
{\usekomafont{author}{Jane Doe\par}}%
\vskip 1.5em
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\cleardoublepage
\tableofcontents
% start a new right-handed page
\cleardoublepage
Anarhistima i anarhistkinjama u Hrvatskoj\dots{}
Svijet je doživio puno patnje tijekom godina proteklih od kad je „Anarhistička farma” prvi put objavljena. Puno te patnje se dogodilo u vašoj zemlji. Iz relativne sigurnosti sjeverne Kalifornije smo promatrali kako proživljavate utjecaj najgoreg oblika hijerarhijske i autoritarne moći, iz čega ste izašli, a vaši snovi i vrijednosti su ostali netaknuti. Proživjeli se lekcije koje ne možeš naučiti iz knjiga.
Međutim, bilo je i nekih znakova nade. U Americi, riječ „anarhizam” je od riječi koju zna tek nekolicina ljudi došla na naslovnice svih novina. Unutar američke ljevice, anarhizam je brzo postao izrazito prihvatljiv politički stav, prvenstveno zbog svojih organizacijskih modela koji se uvelike prakticiraju. To putovanje je tek počelo, no idemo naprijed, a puno inspiracije dolazi od vas, naših europskih suputnika i suputnica.
George Orwell je napisao „Životinjsku farmu” u Engleskoj da bi objasnio svoj pogled na političke filozofije svog vremena. „Anarhistička farma” je napisana u Americi kao plod istraživanja onoga što anarhizam jest i što bi mogao biti. Možda će sljedeća verzija ove priče doći iz Hrvatske. Možda će ovaj put priča biti istinita, što će vam omogućiti da pokažete svijetu kako je anarhizam puno više od utopijskog sna, kako je to model koji bi ljudi trebali koristiti u međuljudskim odnosima i svom odnosu prema planetu.
Nadam se da će vam se knjiga svidjeti.
U prijateljstvu i solidarnosti,
Jane Doe
lipanj 2002.
\chapter{1}
„Margaret je još bolesna” zlatni je ptičar obavijestio zabrinute životinje okupljene pred kuhinjskim vratima. Očaj i razočaranje zavladaju mnoštvom. Nitko od njih nije znao što je bilo prije Margaret. Ona je uvijek bila tu, hranila ih, brinula se za njih kada bi se ozlijedili, muzla ih, organizirala, stavljala na spavanje. Vjerovali su joj, štoviše, ovisili su o njoj.
„Tko će nas hraniti?”, upitaše kokoši.
„Mene treba pomusti”. Rosy je bila sasvim u pravu. Činilo se da će joj vimena eksplodirati.
„Staja je u neredu. Trebalo bi ju očistiti”. Mazga se navikla na čišćenje sijena u svojoj štali.
„Goldie, kada će Margaret ozdraviti?”
Ptičar uzdahne i odmahne glavom. „Margaret je vrlo stara. Nitko ne zna koliko stara, a ona se baš ne čini kao da će ozdraviti. Ne znam što možemo učiniti.” Sjedne je na stražnji trijem i stade čekati. Ostale su životinje ili stajale ili sjedile ili pak ležale po dvorištu ispod praznog užeta za vješanje rublja, također čekajući.
Malo se njih sjećalo vremena kada je Margaretin muž bio živ i kada je farma bila življe mjesto. Ed je imao velike planove, uvijek je sadio neke egzotične biljke i isprobavao najnovije teorije o kontroli pesticida. On je bio taj koji je Juanitu i Carlosa iz neke daleke zemlje doveo na farmu.
Ljame su još uvijek bile tu, ali je Ed već godinama bio mrtav. Margaret je sama vodila farmu, ulažući u taj posao svo svoje srce. Sadašnji su planovi bili skromniji, no već je tu bio i prekrasan voćnjak, a livade su bile spremne za ljetnu ispašu. Margaret je već ranije bila napravila ogroman vrt pred vratima kuhinje kojeg su sad životinje gledale kako na ovom ljetnom suncu očajnički žudi za vodom.
„Biljke će umrijeti ako ih netko ne zalije”, reče mlada svinja Susie, „I što ćemo onda mi jesti?”
„Ja sam stvarno gladan”, požalilo se mladunče.
„Voliš mlijeko?”, upita ga Rosy.
„Naravno da volim!”, odgovori mladunče, na što ga Rosy nasloni na svoje naduto vime.
„Mislim da to baš nije u redu, zar ne Goldie?”, ljutita guska upita psa.
„Zašto bi trebalo pitati Goldie? To je moje vime i osim ako ti nemaš pametniju ideju, ovo je sasvim u redu”. Mladunče se iz sve snage trudilo nadojiti se iz kravine bradavice, iako je već neko vrijeme bio odviknuto od dojenja.
„Što god upali”, reče Goldie, „Teška su vremena.”
„I mi smo gladni”, cvrčali su pilići, „ali mi ne volimo mlijeko”.
„Znam”, kaže kokoš, „no moramo čekati da Margaret ozdravi i da nas nahrani”.
Goldie pogleda gladne piliće i shvati da čekanje na nju nije nikako bio dobar plan. „Mislim da ne možemo više čekati Margaret. Jako je bolesna, a mi joj možemo pomoći tako da joj obavimo neke kućanske poslove. To će je razveseliti. Spast će joj teret s leđa. Svi znamo gdje se drži hrana i mislim da bi se trebali sami nahraniti.”
Bila je to dosta radikalna ideja, no bili su pregladni da ne bi bili spremni da je probaju sprovesti. Kokoš povede piliće u kokošinjac i polagano otvori vreću s kukuruzom. Za tu je vreću znala cijeli život, a ipak se nikad nije usudila pogledati unutra. Bila je gotovo puna, a navrh nje bio je i tanjur na kojem je Margaret običavala služiti doručak. Penny uzme tanjur svojim krilom i zagrabi u vreću. Druge se životinje okupe oko nje gledajući je kako radi ono što do tada nisu mogli ni zamisliti. Kokoš odnese tanjur kukuruza u dvorište i pospe ga pred piliće koji su se borili da zgrabe što više. S osmijehom na kljunu, mašući tanjurom po zraku okrene se prema drugima i uzvikne „Mi to možemo!”
Sve životinje pohrle tamo gdje se držala njihova hrana. Zob, sijeno i kukuruz: svi su se najeli do sitosti. Hrana je taj dan imala posebno sladak okus. Svi su pazili da vrate sve tamo gdje je Margaret to držala. „Nadam se da nije ljuta što mi sami sebe hranimo”, reče Rosy, osjećajući se mnogo bolje nakon što su je pomuzli i nakon što je jela.
„Naravno da neće biti ljuta”, uvjeravala ih je Goldie, koja je najbolje poznavala Margaret pošto je njoj bio dopušten ulazak u kuću. „Bit će joj drago što ste ovo napravili umjesto nje, što ste joj pomogli da vodi farmu.”
Nakon što je pojela svoju kašu, Susie prasica, ponovo pogleda žedan vrt. „Ja ću zaliti vrt umjesto Margaret”, reče ostalima.
„Ne znam\dots{}”, reče guska, „Margaret nam ne dopušta da ulazimo u vrt”. Istina, vrt je bio ograđen kako životinje ne bi ulazile.
„Margaret ne želi da vrt umre. Bit će vrlo sretna ako ga ja zalijem, zar ne Goldie?”, okrene se Susie psu koji je bio stručnjak u vezi Margaret.
Goldie razmisli. Margaret nije dopuštala da životinje ulaze u vrt, no ubrzo neće biti nikakvog vrta ukoliko ga životinje ne zaliju. „Susie, Margaret će biti sretna ako joj zaliješ vrt”. Pas je rekao svoje.
Ubrzo su svi razmišljali o tome kako pomoći Margaret. Mazga umjesto Margaret pomete staju. Svinje pokupe jabuke umjesto Margaret. Patke čak pojedu crve. Sve se životinje rasporediše po farmi i obave sve kućanske poslove, i one potrebne i one nepotrebne, samo da bi pomogle jadnoj, ostarjeloj Margaret.
Prolazili su dani i tjedni, a Margaret je još uvijek ležala u krevetu bivajući s vremenom sve bolesnija. Goldie joj je nosila hranu iz vrta i voćnjaka. Margaret se smiješila i gladila njenu zlatnu dlaku. Kako je Margaret slabila, tako je farma jačala. Životinje su otkrile način na koji farma opstaje i iz dana u dan bivale sve bolje i bolje u poslovima. Zajedno su donijele urod na farmu i spremile sve za zimu, sve umjesto Margaret. Za Margaret su posadile vrt sa zimskim povrćem i podrezali ruže.
Tijekom zime, životinje su radile planove za proljeće, što će zasaditi na poljima, kako će izgledati kuhinjski vrt, imajući čak ideju da prošire staju, naravno, sve kako bi pomogle Margaret.
S proljećem skoro na vratima i suncem nad farmom, Margaret umre. Za Goldie je to bio osobni gubitak. Ona je bila pored Margaretinog uzglavlja pri njezinim posljednjim trenucima i hranila je tijekom svih ovih posljednjih mjeseci. Margaret joj je bila prijateljica. Ostalima je, međutim, Margaretina smrt bila apstraktna. Nikad nisu poznavali Margaret na način na koji ju je Goldie poznavala, no ipak se njezina smrt nadvila nad farmom poput lešinara. Njena je bolest bila početna točka borbe. Ona je natjerala sve životinje da pokušaju i da rade stvari za koje su mislile da ih nikada ne bi mogle napraviti. Farma je bila življa nego ikad, ali sada je Margaret bila mrtva. Kako joj sada mogu pomoći?
Pokopaju je pored Eda na sjevernoj strani kuće, tamo ispod hrasta. Životinje polagano okruže oko grobova plačući za voljenom Margaret. Pričali su priče o Margaretinoj ljubaznosti i ljubavi prema životinjama. Goldie im reče kako će Margaretin duh uvijek biti uz njih jer su je pokopali na farmi. Mogli su nastaviti raditi za Margaret da bi pomogli ostvariti njen san o prekrasnoj farmi. Životinje su voljele Margaret još više sada kada više nije bila živa. Preklinjali su Goldie da im priča o Margaret, što je nju posebno dirnulo.
„Reći ću vam što je Margaret običavala govoriti, što je bilo njezino pravilo”. Goldie zatvori oči i ponovi onako kako se sjećala „Uvijek postupaj s drugima onako kako bi želio da s tobom postupaju”. Životinje upiše tu rečenicu. Goldino pravilo postade moto farme koju su zvali Krug H.
\chapter{2}
\emph{Mnogo kasnije, na drugoj farmi, tamo daleko iza šume\dots{}}
Mozak mu je radio istom brzinom kao i srce; kad bi mu bar tako radile i noge! Pao je na zemlju trčeći svom snagom iz straha, probijajući se kroz blatnjav pašnjak s bijesnim psima par metara iza sebe. Grude blata koje su se otkidale od njegovih cipela završavale su u psećim slinavim ustima. „Što trebam učiniti? Farma je ograđena. U zamci sam,” pomisli.
Zakorači u neku lokvu i nađe se odjednom kako kliže kroz blato i udara o drvenu ogradu. Pomalo zbunjen, puzao je duž ograde.
„Uh, to je bilo gusto! Ne mogu vjerovati da me nisu uhvatili.” Osvrnuo se nakratko iza sebe.
Izgleda da su dobermani malo zastali, iako su i dalje lajali istom jačinom kao i ranije. Došao je do kuta, okrenuo se za devedeset stupnjeva duž živice sjetivši se najednom da postoji rupa u ogradi koju su radnici trebali sutradan popraviti i za koju se nadao da će je sada moći naći.
Usporio je korak kako bi pronašao rupu. Čudno, ali i psi su usporili. „Evo je, samo da se mogu provući kroz nju”. Rupa, koju je vjerojatno napravila neka manja životinja, možda zec, bila je taman toliko velika da može proći. Nakon što je ugurao gornju polovicu tijela, zapela mu je stražnjica. Psi su se nakon klizanja zaustavili i stali pred iskopanom rupom u ogradi. Dok su ga svi sarkastično podbadali, jedan ga snažno ugrize za bijeli kovrčavi rep, što se ispostavilo kao prava inspiracija da se potpuno provuče kroz ogradu.
Nakon što se izvukao, novi adrenalin potaknut psećim ugrizom natjerao je jadnu svinju doslovno na let preko susjedovog polja kukuruza sve do šume koja se nalazila preko. Zaustavio se tek kad je zapeo nogom o korijen nekog drveta. Skrivajući se iza grmlja, virio je da se uvjeri kako ga nitko ne prati.
Sjedne iza bora da uhvati dah i pregleda ugriženi rep. Bolio ga je, no nije bilo previše strašno.
„Taj ga je pas mogao slobodno potpuno odgristi.” Osjećao se sretnim, ali zašto? Tad mu sine. Psi su slušali naredbe. Trebali su me potjerati, ali ne i ubiti. Naravno, kako su me mogli ubiti pred ostalim životinjama. One me vole, ja sam im vođa. Vjerojatno me sada traže da me vrate kući”. No na vidiku nije bilo nikoga. Tad počne razmišljati drugačije. Stvari na farmi su se bitno promijenile. U početku je osjećao ljubav i potporu drugih životinja, no sada? Provodio je manje vremena s ovcama i kravama i kokošima. Uvijek je bio sa svinjama. „I sada su se ostale svinje okrenule protiv mene, a ostale životinje uopće ne mare da ih spriječe. Nakon svega što sam učinio u njihovu korist\dots{}”
Nasloni se na grubu koru drveta, dok su mu suze klizile niz obraze sjećajući se starih vremena. Revolucija, ah, to je bilo veličanstveno. On je bio heroj, s medaljom koja je to mogla potvrditi. Bio je predivan uspjeh otjerati pohlepnog farmera sa zemlje i dati farmu životinjama koje su radile za dobro svih. Izvukao mu se osmijeh na licu dok je razmišljao o paradama koje je vodio i o burnim govorima koje je držao zahvalnim životinjama u danima nakon revolucije.
Kao svinja, prirodno je bio više stvoren za vodstvo od, recimo, ovaca i pataka. Zar je bila njegova pogreška što se ispostavilo da nisu sve svinje tako ljubazne i poštene? Oči mu se skupe dok je mislio na svinju koja je od štenadi dobermana napravila zle ubojice koji su ga maloprije jurili po njegovoj vlastitoj farmi. Na farmi gdje se rodio i gdje je proveo čitav svoj život. Ustvari, farma je i bila čitav njegov život; stvaranje planova za farmu, organiziranje životinja, poticanje ostalih tijekom teških vremena\dots{} „I ovo je hvala za sve”, brisao je suze istovremeno trljajući bolni rep.
Sjećanje na prošlu moć i neviđeno padanje u nemilost prouzročilo mu je tupu bol u trbuhu. Ili je možda samo bio gladan.
Svinja pogleda uokolo. Drveće. Nikad u svom životu nije kročio van farme. Sada je bio bez hrane, bez prijatelja, bez prenoćišta i bez plana. Ovo potonje je bilo najstrašnije. Uvijek je imao neki plan. No sada se u nepoznatoj šumi spuštao mrak, a on je sjedio posve sam bez plana.
Uzme štap sa poda i uhvati se posla. Iz grmlja, deseci očiju promatrali su blatnjavu bijelu svinju sa štapom kako radi čudne crte u prljavštini:
\begin{quote}
1. Pronaći hranu
a. Jabuke i po mogućnosti drugo voće
b. Izvor dobre pitke vode
2. Pronaći mjesto za spavanje
a. Mora biti sigurno
b. Toplo i mekano
Oči su bile sve bliže kako bi uspješno dešifrirale škrabotine.
3. Pronaći
\end{quote}
Svinja se još više nagne prema zemlji jer se na zalazećem svjetlu škrabotine nisu baš dobro vidjele. Nakon par minuta razmišljanja o 3. točci, odluči je izbrisati. „Pa da, 1 i 2 su bitan dio plana,” reče sam sebi odmičući se dalje kako bi se divio svom uratku.
Oči su se gotovo nečujno povukle u grmlje. Uspravi se i podvije rep nakon što je shvatio da nije sam. Mozak mu je radio svom snagom, a oči tražile da nešto vide kroz mrak. Pun nade izusti: „Prijatelji?”
Trenutak tišine i zatim zvukovi natezanja i prigušenog hihotanja.
Svaka svinja posjeduje istančano osjetilo mirisa. Čak i svinja poput ove, udaljena od svoje prirodne sredine, može znati mnoge stvari samo po mirisu. Mogao je znati tko nije bio u mraku: svinja, krava, ovca, čovjek ili pas. Ustvari, nije mirisalo na nijednu životinju koju je ikad ranije susreo. Pošto je miris bio dosta jak i nepoznat, počne u glavi nabrajati sve mogućnosti.
„Tko živi u šumi? Medvjedi! Vukovi! Tigrovi? Ne, ne tu. Ima još i jelena i zečeva.” Upita na glas: „Jeste li vi zečevi?” Odgovor: još hihotanja. „Ne bojte se, prijatelji zečevi, neću vas ozlijediti.”
Ovo ih je očito pogodilo u žicu. Smijeh je bivao sve jači i sve više prijeteći da bi se nakon toga dva odrasla rakuna dokotrljala iz grmlja i okružila svinju. Rakuni su se kretali tiho, polako kružeći oko svinje. Svinja se sabere i pokuša s prijateljskom taktikom. „Hm, čini se da sam bio u krivu. Oprostite, vidim da niste zečevi već vjeverice.”
„Vjeverice!” Jedan od većih rakuna skoči na njega. Iz takve je blizine svinja mogla i u ovakvom mraku jasno vidjeti da je pogriješila. „Koga ti nazivaš vjevericom?”
Svinja pomiriše životinju pred sobom i dalje ne znajući što je to. „Vi niste medvjedi, zar ne?” Sve su životinje na farmi čule za medvjede, no malo ih je tko imao priliku vidjeti. Međutim, navečer u staji pričale su se priče o njihovoj silovitosti i snazi kako bi zabavili i ustrašili mlade svinje da im ne padne na pamet odlutati van granica farme.
„Pa, nismo baš medvjedi”, prizna jedan rakun, „Odakle si ti uopće?”
„S one farme tamo preko\dots{}ili možda tamo\dots{}”. Okretao je svoju svinjsku nožicu ukrug sve dok nije shvatio da nema pojma odakle je došao.„Lijepa farma koju vode isključivo životinje. Ja sam bio njihov omiljeni vođa sve do danas kada su me otjerali zli dobermani.”
„Dobermani!” Čoporom rakuna zavlada drhtanje. „Mi zaista mrzimo dobermane. Mene zovu Riff Raff, a mi smo svi rakuni.” Govorio je sporo kako bi izbjegao ponovni nesporazum sa svinjom. „Ovo su Bandit, Bitanga, Vragolan, Odrpanac i Rasparač. A kako je tebi ime?”
Svinja izusti samo „S” prije nego se sjeti da je postao bjegunac, pobunjenik, koji se sada skrivao u bijegu. Ne bi bilo nikako dobro da im kaže svoje pravo ime. Uostalom, uvijek je mrzio to ime. Nije u njemu bilo ni ponosa ni romantike. A i nije bilo ime za jednog pobunjenika. Trebao je ime koje će inspirirati legende i zahtijevati poštovanje. Znao je samo ime. Uvijek je zamišljao sebe kao\dots{}
„Pancho”, reče svinja, „ime mi je Pancho” i udari o Riff Rafffovu podignutu šapu svojom nogom, „Drago mi je što sam vas sve upoznao.”
Pancho nije bio baš siguran da mu je drago što ih je sreo, jer su rakuni imali prilično lošu reputaciju među životinjama na farmi. No pošto nikad ranije nije sreo nijednog rakuna, odluči da će biti otvorenih pogleda.
„Gledali smo te kako šaraš sa štapom,” reče Bitanga.
„Ah, da,” odgovori Pancho. „Radio sam planove”. Bilo je poprilično mračno i obrisi u prljavštini su bili gotovo nevidljivi, no rakuni s tim nisu imali problema. „Da ti pročitam to?” Uvijek je bio zadovoljan kad je imao nešto za objasniti.
Rakuni se okupe oko plana i stanu zuriti u prljavštinu, no bili su toliko blizu da su sami sebi zaklonili svjetlo. Panchu to nije ni bilo bitno jer je plan znao napamet. „Na vrhu piše „Plan za preživljavanje u šumi”. Na to se začu žamor impresioniranih rakuna. „Zatim piše pod 1. Naći hranu, a pod 2. Naći mjesto za spavanje”, objasni im svima.
Uslijedio je trenutak šutnje kojeg prekine Riff Raffovo pitanje: „Je li to sve?”
„Pa izostavio sam neke točke A i B, no u principu jest, to je to.” Pancho ušuti, misleći da je možda izostavio neke bitne točke za preživljavanje. Točka broj 3 mu padne na pamet: Izbjegavati rakune.
Naposljetku Odrpanac ustvrdi kako, unatoč što je omirisao i razmazao većinu napisanog, ne shvaća čemu sve to.
„Ne shvaćaš? Koji dio ne shvaćaš?”, upita ga svinja pokroviteljskim tonom. Prije mu je trebalo manje vremena da objasni složenije planove životinjama s puno manje inteligencije. Izgleda da bi i rakuni spadali u ovu kategoriju.
Odrpanac nije mario za Panchov ton. „Ne shvaćam”, naglasi ponovo, „Zašto bi itko gubio vrijeme pišući „Naći hranu” po blatu. Ako želiš naći hranu, zašto je jednostavno ne nađeš!?” te kazavši to u potpunosti razmaže nogom ono što je ostalo od plana. Drugim se rakunima ovo učini vrlo zabavno. Međutim, usred smijeha i šaljivog međusobnog gurkanja, Bandit reče: „Idemo odavde.”
„Čekajte”, povikne Pancho, „gdje ćete?”
Svi se rakuni okrenuše licem prema svinji. Pogledaše se i u isti čas rekoše „Naći hranu” te nestadoše. Svinji je trebao samo trenutak da se dosjeti što dalje. Od očiju po mraku nije imao puno koristi, no miris šest rakuna nije bilo teško za slijediti. Osim toga, smijeh i vika mnogo su mu olakšali posao praćenja. Bili su mladi i brzi. Pancho je zapinjao, udario o neko drvo, naletio na kupinu i pokupio nemalo trnja s nje, da bi se na kraju poskliznuo i pao u potok pokušavajući imitirati rakune koji su skakali sa stijene na stijenu. Bilo je to puno više vježbe nego što je svinja na to navikla tijekom čitave godine. Kakav dan! Kakva noć! Odjednom prestane smijeh, prestanu šale i općenito svi zvukovi. Rakuni su se kretali sve tiše i sve sporije kako su prilazili drvenoj ogradi. Pošto su dolazili iz tame mjesečina mu je pomogla da razazna oblike. „Pa to je farma!”, uzvikne.
„Š-š-š-š”, šest se glava okrene i ukori ga, „ako ideš s nama barem budi tih.”
Svinja klimne i svi se zajedno provuku ispod ograde.
Riff Raff dade Panchu znak da ostane na distanci te Pancho posluša. Ostane u pozadini i stane promatrati kako šest malenih figura klizi kroz blato. Što se više približavao staji, sve je jasnije razaznavao poznati miris: svinje. Njuškajući oko svinjca, ugleda rakune kako kruže oko kokošinjca. Dakle, glasine koje je ranije čuo na farmi su bile istinite.
Pancho zapazi u kutu svinjca nekoliko odraslih i mladih svinja koje su tamo spavale. Provuče se ispod vrata i na prstima dođe do korita za hranu. Hura! Kukuruz koji je ostao svinjama od ručka. Pancho počne žderati onako kako to samo prava svinja može. Pokuša istodobno biti i jako tih i jako brzo jesti, što baš i nije zahvalna kombinacija, pogotovo za jednu svinju. Pretpostavi da bi se to čak, formalno gledajući, moglo nazvati i krađom. Dakle, nije bilo u redu. No ostale su se svinje najele i ostavile mu to da mu pomognu kao pobunjeniku. „Kad bi bile budne”, pomisli, „ siguran sam da bi im bilo drago da ga podijele sa mnom i da bi zbog toga bile ponosne.” Ipak, trudio se da nikog ne probudi. Rakuni nisu bili baš toliko pažljivi.
U kokošinjcu je prštalo perje. Uhvaćene u zamku šest rakuna, kokoši su vapile za pomoći. Panchu se sledi krv u žilama od strave koja se čula u njihovim glasovima. Ovčar potrči u pomoć lajući toliko glasno da je uspio probuditi čitavu farmu. U kući se upale svjetla i polugoli farmer istrči van vičući i pucajući iz sačmarice. Pancho zaroni u mekano blato svinjca misleći da bi mogao tamo ostati zauvijek. Možda bi se mogao prilagoditi ovim svinjama i jednom na ovoj farmi započeti novu revoluciju.
Rakuna više nije bilo. Na livadi se još se čulo lajanje pasa i pucanje farmera.
„Ostat ću ovdje”, pomisli svinja. Dok se okretao unaokolo da se upozna sa svojim novim domom, primijeti ogromnog vepra kojeg je probudila sva ova strka i koji je upravo zurio u njega.
„Novi plan”, bilo je sve što je Pancho stigao pomisliti dok se provlačio ispod vrata i počeo bježati prema šumi, no ne u pravcu rakuna.
Usporio je tek kad je stigao u gustu šumu. Bilo je suviše mračno za trčanje, a i on je bio poprilično umoran. „Moram zaći još dublje u šumu kako bi bio doista siguran”, pomisli, „no koliko duboko i koliko će to uopće biti sigurno?” Vrteći to pitanje po glavi, otpuže u gustu kupinu. Zaspi mrmljajući „Moram imati plan.”
\chapter{3}
Sunce je već odavno bilo izašlo kad je Pancho otvorio oči. Sunce je jedva prodiralo kroz tu gustu kupinu ispod bora. Probudi se iz dugog i nemirnog sna o psima koji su ga naganjali i o masakru u kokošinjcu. No kada ugleda pred svojim malim ružičastim očima trnje kupine shvati da ono što je sanjao nije bio san.
Stenjao je mučeći se da ustane. Svaki ga je mišić bolio, a svaki korak podsjećao na jučerašnji dan. Dok je puzao iz gustiša da vidi gdje se nalazi, Pancho shvati da nema pojma kako je stigao na ovo mjesto. Kružio je oko grmlja i njuškao obližnja stabla ne bi li našao nešto što bi mu pokazalo put. „Ne znam kako sam došao tu, ne znam gdje sam i ne znam gdje bi išao, dakle\dots{}” Možda i nije bitno. Bila je ovo izvrsna vježba za mozak. „Ono što jest bitno je da sam gladan.”
Znajući sasvim jasno što prvo treba učiniti, onjuši zrak. U šumi je bilo obilje nepoznatih mirisa, no ništa od mirisa kukuruza ili jabuka ili čak mrkve. Ipak, osjeti nešto. Vlagu, možda vodu. Bio je prilično ponosan što je uspio otkriti izvor mirisa pa krene na sjever. No možda ipak na istok? U bilo kojem slučaju, išao je prema vodi.
Šuma se danju nije činila toliko opasnom i nitko ga nije hvatao te se Pancho opusti u jutarnjoj šetnjici. Svakih nekoliko minuta bi stao da njuhom provjeri smjer. Bio je prilično brz s obzirom na bol u mišićima. „Bilo bi vrlo dobro kada bih našao vodu,” promisli, „to je i bio moj prvotni plan. Možda će na rubovima tog potoka ili jezera biti biljaka koje će mi dobro poslužiti kao doručak.”
U nekom žbunju sa svoje lijeve strane začu glasno pucanje grana. Odjednom na oprezu, Pancho se usmjeri na zvuk i onjuši. Taj miris nije mogao promašiti. Rakuni. „Idem desno i zaobići ću ih” Samo nekoliko koraka dalje začu hihotanje iza drveta s desne strane. Pomisli se vratiti i zaobići ih u širokom luku, no iza sebe već ugleda dva rakuna koji su kopali ispod debla. Ako je želio izbjeći susret bio je samo jedan izlaz: onaj naprijed. Posvuda je mogao namirisati svoje prijatelje, ponekad ih čak i čuti, no uglavnom ih nije vidio. Međutim, svaki put kad bi se uputio udesno u smjeru vode shvatio bi da mu je put blokiran.
„Pitam se da li rakuni možda paze vodu kako je nitko drugi ne bi mogao koristiti.” Polako, ali sigurno Pancho se nađe kako korača uzbrdo u suprotnom smjeru od vode. Ubrzo dođe na uski puteljak kroz nepokošenu livadu. „Mnogo je životinja prošlo ovuda,” pomisli. Budući da je bio na dobro ugaženom putu osjećao se manje izgubljenim ubrzo zaboravivši da je krenuo ka vodi. Iako mu više nisu bili sa svih strana, rakuni su ga ipak pratili na pristojnoj udaljenosti. Teren je bio sve strmiji i cesta je bila sve uža dok nije nestala te mu je jedino preostalo penjanje. Pancho je bio prisiljen slijediti put pošto je s jedne strane bila planina, s druge oštra strmina. Uostalom, tu mu je bilo dobro i očito je put vodio nekamo, iako doduše on nije znao gdje.
Put je nekoliko puta naglo skretao i bivao je sve strmiji. Želudac mu počne kruliti, a i noge se počnu žaliti. Pancho sjedne na trenutak da se odmori, no primijeti kako su rakuni bili samo jedan zavoj iza. „Kuda idemo?”, razbjesni se nakon što je još jednom skrenuo i dobio odgovor na svoje pitanje. Put je tu završavao. Pred njim je stajao ulaz u ogromnu mračnu špilju.
„Predivno!”, vrisne, „U zamci sam!” Oprezno zakorači u špilju. Ništa nije vidio, ali mu je nos govorio sve. Koji miris! „Nemam pojma što je tamo unutra, ali ću se radije suočiti s rakunima,” pomisli dok se okretao i krenuo natrag.
Tad začu poznat zvuk: „Ej, ja sam!”
Prvo je mogao vidjeti samo par žutih očiju, a zatim i obris crne mačke u crnoj špilji. „Sabo?”, šapne. Bila je to mačka s njegove farme.
„U redu je,” zaprede. „Pođi za mnom.”
Pancho baci letimičan pogled unatrag i ugleda rakune kako ulaze u špilju. Požuri se da sustigne mačku koja nije imala problema s kretanjem u mraku. „Mačke vide u mraku, rakuni vide u mraku. Samo ja — samo ja ne mogu,” promrmlja te se spotakne o kamen. Smrad je u špilji bio jak; toliko mirisa koji su se preklapali i napravili zbrku u njegovom nosu. Mačka je hodala ispred njega, rakuni odmah iza. „Sabo, kuda idemo?”, upita Pancho trudeći se zvučati kao da mu je svejedno. Je li to bila zamka koju su mu postavili neprijatelji s farme?
„Želim da upoznaš neke moje prijatelje”, reče mačka.
„Zašto nisi sama došla po mene?” upita svinja sumnjičavo.
„Rakuni su se javili dobrovoljno”, mačka slegne ramenima.
Iz pozadine se začu hihotanje, no kad se Pancho okrenuo na licu im je mogao vidjeti samo sladak osmijeh.
„Evo nas,” reče mačka. Skrenuli su iza ugla i ušli u trbuh spilje. Zraka sunca koja je prodirala izvana davala im je svjetlo i blaženi kisik. Životinja je bilo posvuda, među ostalima naravno i rakuna, vjeverica i jelena. Tada na rubu golemog kruga životinja Pancho ugleda pet ogromnih obrisa tako veličan-stvenih i zastrašujućih da je odmah znao:„Medvjedi!”
Odmakne se i na leđima osjeti hladnoću stijena. Mačka odlunja te se smjesti u podnožje manjeg medvjeda koji je sjedio u sredini, na što joj Pancho uputi par prodornih pogleda.
„Dobrodošao,” reče mali medvjed.
Pancho se osjećao slabo. Koljena mu počnu klecati, a lice problijedi. (Ovo je bilo posebno dojmljivo s obzirom da je bio bijela životinja). Srebrna se vjeverica stvori s drvenom posudom kraj njega gotovo u sekundi.
„Hoćeš malo vode?”, upita svinju. Pancho potvrdno klimne glavom i posegne za vodom. „Smiri se, sve je dobro. Među prijateljima si,” šapne mu vjeverica te odjuri natrag s praznom zdjelom.
Sve su oči bile uperene u svinju. Osjećao je kako mu ponos govori da pokaže malo hrabrosti. Prisilio se da dođe među životinje te kaže: „Hvala vam za vodu. Bio sam toliko žedan da sam mislio da ću se onesvijestiti!”
Ta je rečenica urodila plodom, iako nije bio siguran da li su mu vjerovali.
„Vjerojatno si gladan. Ubrzo će ručak. Ja sam Judi”, kaže medvjedica.
„Ja sam
„ usne mu još ne navikoše na novo ime. „Ja sam Pancho”, reče svinja pogledavši Sabo koja je samo zavrtjela očima, ne rekavši ništa.
Štoviše, nitko ne reče ništa, pa je Pancho pitao što ima za ručak, čisto da probije led i započne razgovor. Nadao se da odgovor neće biti svinjetina.
„Rekla sam im što se ti se jučer dogodilo na farmi. Mislili smo da bi nam se možda htio pridružiti.” reče Sabo.
Nama? Pancho je mislio da je mačka bila životinja s farme, ali je očito vodila dvostruki život.
Pancho se smrzne kad je ogroman naboran smeđi medvjed prozborio svojim dubokim glasom „Sabo nam je rekla da znaš čitati. Što još znaš?”
„Pa,” zamukne Pancho, „znam pisati i pomalo zbrajati. Radim planove, nadzirem i organiziram ostale životinje.”
Po šaputanju među životinjama Pancho zaključi da ih je razočarao.
Riff Raff ga upita da li zna pronaći drva u šumi. Još jedna nova životinja pomoli glavu iz gomile, dođe do Pancha i zarine mu svoje smiješno lice u njušku. „Znaš li graditi?”
Svinja upije miris čudne životinje pred sobom\dots{} Okretna i brza, sitna životinja odskoči unatrag i skoči na rame velikog medvjeda gdje ostane sjediti.
„Graditi baš i ne znam”, reče Pancho, „ali mi vrlo dobro ide nadziranje drugih dok to rade.”
„Pa, zar to ne ide svima nama!”, prozbori čudnovata životinja te pokrene lavinu smijeha koja se kao divlja vatra širila među rakunima.
Sabo se nagne prema Panchu i reče „To je Bonkers. On je majmun. I to odbjegli majmun!”
Smijeh prestane kad prozbori medvjedica Judi: „Ako ne znaš ništa raditi, kako znaš nadzirati druge dok rade? I ako oni mogu sami nešto raditi, zašto si im ti potreban?”
Pancho ostane zabezeknut. Već umoran od ismijavanja, preokrene priču. „Što to točno vi radite? Imate farmu?” Bilo je to dobro pitanje s obzirom da je ovo bio čudan sastav životinja.
„Nema nikakve farme”, odgovori mu Judi, „Živimo u šumi i radimo kako bi je zaštitili.”
„I živite i radite zajedno?”
„Svi živimo u blizini i ponekad radimo stvari zajedno, no ne nužno”, reče Judi.
„Ti si vođa?” Svinja upita iskreno, ne misleći ništa ružno time, no uzdasi koji su se čuli među životinjama rekoše mu da je napravio gadnu pogrešku time što je to pitao.
„Nemamo vođa!”, odbrusi mu Bonkers, „Nema vođa, nema sljedbenika.”
Neugodnost razbije tek piskutav glas vjeverice: „Idemo jesti!” Na to sve životinje pohrle prema ulazu u špilju.
Judi se kretala znatno sporije od ostalih. Nedavno je upala u zamku lovaca i ozlijedila se, te se sada još uvijek oporavljala. „Ne brini se, ima dosta hrane,” reče Judi. Sabo i Pancho uspore kako bi joj pravili društvo.
Hrana se dijelila ispod stabala u blizini špilje. Pancho primijeti i neke životinje koje nisu bile na sastanku u špilji. Vjeverice su pripremile jelo od žireva i iako nije baš bilo privlačno, bilo je zasitno i gladnoj je svinji imalo dobar okus. Nad hranom se vijorila zastava na kojoj je pisalo „Orasi za sve”. Tako su se zvale vjeverice koje su na sebe preuzele hrabar zadatak da se brinu za prehranu tako velikog i šarenog skupa životinja.
Pancho sjedne između Judi i Sabe.
„Sabo mi je dosta pričala o tvojoj farmi”, reče Judi. „Čini se da je sve počelo s uspješnim ustankom. Prava je šteta što su neke životinje postale poput ljudi.” Pancho zine u čudu. Je li to način na koji je Sabo vidjela trud i napore na farmi? Kad bolje promisli o tome, pomisli Pancho gledajući mačku, gdje je ona bila kad se trebalo raditi? Ovdje, bez ikakve sumnje. Pancho ne reče ništa te Judi nastavi: „Uvijek sam se pitala zašto si ostao na farmi nakon što si postao neovisan, radeći i dalje kao rob? Zašto nisi pobjegao u šumu i postao uistinu slobodan?”
Nikad nije o tome razmišljao, a koliko je znao ni druge životinje nisu mislile na to. Odmahne glavom i jednostavno reče: „Ne znam.” I zaista nije znao.
Svinja pogleda prema gore i primijeti dvojicu rakuna od sinoć, Vragolana i vjerojatno Bitangu, kako iznova staju u red. „Vidio sam sinoć kako ti rakuni napadaju kokošinjac,” izbrblja se Pancho. „To je bilo užasno za gledati, no opravdao sam to njihovom glađu. Sada vidim da su mogli tu jesti, a da su tamo samo radili nevolje.”
Judi i Sabo se zadovoljno nasmiju. Sabo promrmlja kroz zube kako je vjeverice kuharice ne bi čule: „Zlo nam je od žireva.”
„To i nije neki izgovor,” pomisli Pancho i primijeti da je on bio jedini koji je pojeo čitav tanjur. Većina ostalih životinja nisu svoj ni takle.
Sabo pruži svoj tanjur Panchu i reče „Posluži se. Nisam gladna kao što sam mislila.”, sretna što se uspjela osloboditi tog jela.
„Hvala”, progunđa Pancho primivši se zdjele.
„Imaš pravo Pancho,” reče medvjedica. „Ovo je sasvim zdrava hrana i vjeverice naporno rade da bi je spravile”, te rekavši to počne jesti, ali ne s onakvim užitkom kao svinja.
Pancho je bio gotov vrlo brzo. Želudac mu je bio pun, te mu se mozak mogao usredotočiti na druge stvari. „Rekla si da radite kako bi zaštitili šumu. Što radite?”, upita medvjedicu.
„Radimo u korist šume,” odgovori, „i šuma nam vraća tako što nas hrani i štiti.” Pancho sjedne i ne prozbori ništa nekoliko minuta te Judi nastavi. „Ljudi sijeku previše stabala i na taj način uništavaju mnoge životinjske domove. Životinje se stoga trebaju udružiti kako bi spasile i sebe i drveće i potoke.” Sada je govorila o svojoj omiljenoj temi, a pritom je imala i pozornog slušatelja. Judi mu je potanko ispričala sve o ekološkim katastrofama sve dok Pancho nije postao potpuno svjestan općih posljedica.
To ga toliko dirne da počne plakati. Osjećao je da je zadatak životinja od iznimne važnosti.
„Pomoći ću koliko god mogu”, obeća, „no nemam nikakav plan.”
„Nema veze”, Judi kaže, „mnogi od nas imaju planove”. Pancho se nasmiješi i pogleda oko sebe svoje nove prijatelje. Samo se nadao da ti planovi nisu bili Bonkersovi ili možda od rakuna.
U slijedećih je nekoliko dana Pancho upoznao čitavu družinu. Nisu ih baš zanimali planovi ili organizacija, no bili su prilično pametni i vrlo dobro obaviješteni. Svinja se pitala kako li će se uklopiti u sve to i što će im imati za ponuditi. „Barem me sve ovo zanima,” promisli dok je pokušavao naučiti kako se pali logorska vatra.
Pancho je uvijek volio nešto raditi te su ga bezbrižni dani u Špiljskom kampu pomalo umarali. Ostatak životinja većinom je uživala u dokolici, drijemajući na suncu, igrajući kojekakve igre i pričajući o ekološkoj revoluciji, no bez konkretnih poteza po tom pitanju. Samo bi se pojavljivale na ručku i večeri te svirale bubnjeve u večernjim satima. Nakon nekoliko dana besposličarenja, Pancho se dobrovoljno javio za pomoć vjevericama kuharicama. One su se kroz šumu kretale brzinom munje skupljajući sve što je bilo jestivo, posebice žireve, a Pancho je samo bezuspješno kaskao za njima. Nakon toga se okušao u kuhanju. Recept „Orasi za sve” bio je uvijek isti: uzeti sve što se tog dana uspjelo skupiti i baciti u ogroman lonac. Nakon par sati kuhanja, trebalo je samo smisliti novo ime za jelo i servirati ga.
Ovo je svinji bilo jako zabavno s obzirom da se volio igrati s hranom, ali ga to nije mentalno razvijalo. Međutim, počeo je jako cijeniti vjeverice. Štoviše, divio im se. Do tada nije nikada ni upoznao neku vjevericu. Prije je pretpostavljao da vjeverice nisu sposobne kao većina ostalih životinja, no kod nikoga nije nikada vidio takvu predanost, energičnost, pamet i samo-dostatnost kao kod njih. I to sve bez nadzora. One su bile nečujni otkucaj srca koji je održavao živom ovu skupinu životinja.
Na povremenim je sastancima Pancho uglavnom slušao, a ako mu nešto ne bi bilo jasno poslije bi nasamo zamolio Judi da mu to objasni.
„Korporacije,” pitala se svinja, „Jesu li one novi neprijatelj ili je to tek druga riječ za ljude?”
„To je isti neprijatelj, samo zamaskiran,” reče mu Judi, „Vrlo lukav i težak za poraziti.”
„Zašto jednostavno ne skinemo tu masku?”, upita svinja.
„Baš je to ono što pokušavamo,” reče medvjedica, klimajući glavom, „no teže je nego što se čini.”
Judi duboko uzdahne te počne s objašnjavanjem. „Recimo, što je i točno, da je jedini razlog postojanja tih korporacija da svojim dioničarima, odnosno sebi, donesu profit.”
Pancho klimne i doda: „Znao sam. Nije ni čudo da ne mare za životinje koji im osiguravaju taj profit ili pak za okoliš.”
Judi podigne šapu kako bi naglasila slijedeće pitanje upućeno Panchu. „No zašto postoje korporacije? Zašto jednostavno ne postoji mnoštvo zasebnih tvrtki i poslova?”
Pancho se počeše po glavi. Znao je da bi trebao znati odgovor
ali nije. I mrzio se zbog toga.
Medvjedica nastavi: „Zakon štiti korporacije tako da one nemaju pojedinačnu odgovornost. A znaš što svi mislimo o pojedinačnoj odgovornosti!”
„Pa da!”, odgovori Pancho u sekundi. Mnogo je naučio o toj temi otkad je došao u Špiljski kamp. Kada nema vođa ili pravila, najvažnija je pojedinačna odgovornost. „Zar na taj način uspijevaju iskoristiti šumu bez ikakvih posljedica?”
„Tako i na milijun ostalih ilegalnih načina.” Judi od gadosti prodrhti. „Dakle, mi se borimo protiv njih svim raspoloživim sredstvima, ali karte idu njima u korist.”
Pancho također prodrhti. Korporacije treba zaustaviti i osuditi ih za zločine. Svinja, koja je ne tako davno imala svojevrsnu moć na svojoj farmi, osjeti ljutnju zbog svoje bespomoćnosti. Što može napraviti?
„Kada ćemo napraviti nešto da sačuvamo šumu?, upita svinja.
„Ubrzo,” dobije odgovor. „Kada se gavran Quoth vrati.” Judi uzdahne. „Uživaj u tišini dok još možeš.”
No, Pancho je žudio za akcijom. Tog poslijepodneva, dok je punog trbuha ležao na slatkoj travi i gledao kako oblaci prolaze, promrmlja prema nebu: „Kad bi barem došao gavran.” Želja mu se ispuni koji trenutak kasnije kad kroz oblake bane velika crna ptica. Nekoliko puta okruži livadu na kojoj je Pancho ležao, te se spusti na stijenu u blizini privremene kuhinje. Sve se životinje okupe oko njega. Pancho također potrči da zauzme dobro mjesto.
Gavran se kretao naprijed-nazad sve dok sve životinje nisu bile na okupu. Imao je važne vijesti i znao je da je bitno da ih što prije čuju. „Korporacija namjerava povući još jedan radikalan potez”, zagrakće, „Par dolina dalje već postoji cesta!”
Čuvari šuma počnu zviždati i gunđati.
„Ne smijemo gubiti vrijeme!” poviče Bandit. „Moramo odmah krenuti.”
No, ostali odluče kako će pričekati do sutradan ujutro. Večeras će obaviti sve pripreme. Uzbuđeni je Pancho preklinjao da bude u odboru za sabotažu. To je od svega ostalog zvučalo najvažnije i najuzbu-dljivije. U odboru je još bilo nekoliko medvjeda, svi rakuni, majmun Bonkers i lasica.
„Koji nam je onda plan?”, zapitkivala je svinja sabotere koji su se raspršili po šumi i skupljali alat i ostali materijal potreban za akciju. „Hoćemo li našiljiti kolce, uništiti im opremu, blokirati im put?”
„Prestani postavljati ta svinjska pitanja”, odbrusi mu majmun, „Kako ćemo znati što ćemo raditi dok ne dođemo tamo?” Bonkers zakoluta očima kao da bi se svi trebali složiti s njim.
Crveni stavi šapu na Panchovo rame. „U redu je,” reče, „Uzet ćemo sve što trebamo da napravimo sve što se može.” Crveni namigne svom otrcanom kolegi medvjedu čija je šapa još uvijek bila na Panchovom ramenu i doda: „Ja i Arthur smo uvijek spremni za lov na ljude.” Dva se medvjeda zločesto nasmijaše.
Pancho se iznova osjetio sigurnim. „Plan je”, reče sam sebi, „da budemo spremni na sve,” te prizna kako je ovo zvučalo vrlo mudro.
Od spaljenog debla naprave sanduk, kojeg u čas napune raznim materijalima koji bi im mogli poslužiti pri sabotaži. Sanduk je bio toliko pun da se dobar dio toga prosuo i po podu. Saboteri su bili vrlo sretni što su uspjeli toliko toga skupiti, ali odluče kako bi ipak bilo pametnije da na tako dug put ne nose sav taj teret. „Ova žica i ovaj konopac su dobri”, reče Bitanga, koji je zaista radije vezivao drveće nego šiljio kolce.
„Treba uzeti i ovaj čekić, duge čavle i odvijač. Jest da su teški, no dobro će nam poslužiti,” doda Bonkers.
„Ovaj kamen i drvenu palicu ćemo ostaviti tu, već ćemo ih negdje naći. No moramo ponijeti hranu, vodu i zavoje,” preporuči Crveni. Panchu se to nije dopalo.
„Čujem li bubanj za jelo?” upita gladna svinja.
Bilo je malo rano, no sve se životinje odazovu pozivu i ostave svoje poslove. Po mirisu je Pancho mogao zaključiti kako je hrana skoro gotova, ali pored toga nanjuši nešto posve drugo.
„Hej, pa to su Tex i Mex!”, povikne Riff Raff, na što svi rakuni potrče u pravcu dvoje pohabanih starih kojota koji su čučali kraj bubnja s gitarama na leđima. Novi su posjetitelji bili pravi brbljavci. Životinje iz kampa dočekaju kojote s takvim zadovoljstvom da je Pancho odlučio ne pokleknuti pred starim predrasudama o njima.
„Prijatelji vam imaju odličan smisao za vrijeme, ne samo da su došli baš na vrijeme za večeru, nego i za sutrašnju akciju u šumi,” reče Vragolan i prezirno pogleda Texa i Mexa.
„Bili bi vam jako zahvalni na večeri, ali vašu ćemo avanturu morati preskočiti. Prestari smo mi za to,” odgovori Tex.
Pancho nekako posumnja u to, no njihova mu se priča učinila zanimljivom pa je za večerom sjedio s rakunima u podnožju kojota.
„Znate li gdje smo sinoć bili?”, upita Mex rakune. „Znate onu farmu s ogromnim kokošinjcem?”
„Naravno da znamo. Baš smo je napali prošli tjedan, zar ne Pancho?” reče Vragolan.
„Ja nisam napao nikakav kokošinjac,” objasni Pancho svima koji su slušali, „Ne bih nikada tako napao kokoši.”
„Nije nas bilo briga za kokoši. Uzeli smo samo jaja.”
„Mi također”, doda Tex.
„Pa, zar je to bolje?” Pancho upita s visoka, „Jaja su samo djeca kokoši koja se nisu iznesla.”
„Ne, ne, ova nisu plodna,” reče Vragolan.
„Čak i da jesu, ne vjerujem da se prije izlaska iz ljuske mogu smatrati kokošima”, objasni Mex.
„Uostalom, ako ih ne bi mi uzeli, uzeli bi ih ljudi”, doda Tex, „Nemojte me krivo shvatiti, nemam ja ništa protiv kokoši.”
„On obožava kokoši,” nasmije se Mex, „Nego, znate tu farmu? E, pa nema je više.”
„Nema?”, uzvikne Pancho, „Kako to?”
„Mislim, zemlja je naravno još uvijek tamo, ali farme nema. Govore da ju je korporacija kupila i zatvorila. Još se ne zna što će se tamo graditi, ali životinja i farmera tamo više nema.”
„Nema više jaja,” uzdahne Vragolan.
„Samo tako?” Pancho nije mogao vjerovati.
„Samo tako. Mislim da ću uzeti još malo složenca od žireva”, reče Tex i krene prema kuhinjskom stolu. „Mislim da ovakvo jelo nisam jeo od prošlog puta kada smo bili tu.”
Pancho je razmišljao o onoj kokošjoj farmi. Da nije bilo onog vepra, bio bi tamo i ostao. „Sva sreća što nisam”, pomisli, „Tko zna gdje bi sad bio?”
Nakon večere, mladunčad sakupi štapove i komadiće drveća za logorsku vatru koja je gorjela čitavu noć. Čitav se kamp okupio oko kojota koji su se podešavali i prebirali po svojim razlupanim instrumentima. Pjevanje započne s tužnim zavijanjem. Tex i Mex su pjevali stihove, no kada bi na red došao refren, moglo se čuti svakojako tuljenje, zavijanje i lajanje. Iako je čuo i ljepše pjevanje, Pancho nikada nije čuo tako tužne pjesme. Kojoti su pjevali o samotnim, lutalačkim životima beskućnih skitnica. Ako se i ne bi prepoznao u stihovima, u želucu bi osjetio nostalgiju za domom. Da mu prijatelji nisu bili tu, Pancho bi sigurno zaplakao. Pogledom je tražio Sabu, svoju staru prijateljicu s farme. Bila je tako dirnuta da je morala pokriti uši. Jurne do nje i sjedne kako bi se zajedno prisjetili starih dana.
Mačka se popne na prste i šapne Panchu: „Toliko mi je oštra bol u ušima.”
„Moji osjećaji također,” uzdahne Pancho dok je slušao tužne zvukove gitare.
„Ispričaj nam priču,” poviče netko od mladih.
„Priča, priča!” poviknu svi.
„U redu, u redu,” zadovoljno reče Tex svojim mladim obožavateljima koji su se okupili u njegovom podnožju. „Kakvu priču hoćete? Dugu i iscrpnu priču o lisici? Ili pak kratku i jednostavnu priču o medvjedu? Ili onu o biču s devet krajeva?”
„O biču s devet krajeva!” povikne mlada ovca. Sve se životinje slože.
„Neka onda bude ta priča,” iskesi se Tex i položi gitaru na zemlju. „Priča o biču s devet krajeva je priča o hrabrosti, herojstvu i žrtvi. No, iskrena je i istinita: prava priča.”
I Tex počne: „Ne tako davno, preko mora, mačke u Cataloniji živjele su pod tiranskom vladom čovjeka koji se nazivao kraljem. Vi mačke morate raditi ovo, ne smijete raditi ono, morate poštovati ovo, morate vjerovati u ono! Moć može biti zla stvar, a o moći vlade pak svi znamo sve. Mačkama u Cataloniji je bilo dosta svega. Bile su umorne od toga da im se naređuje i da ih se ugnjetava. Pričalo se o ustanku i svrgavanju kralja s trona. Mačke u Cataloniji nisu htjele više ono -alonija!”
Tex se smijao vlastitoj igri riječi. „No uvijek gladna vlada nije mogla to dopustiti. Rekoše im: Vi mačke ne možete same upravljati stvarima. Trebate našu pomoć. Niste dovoljno obrazovane. Za ovakav posao su potrebni stručnjaci, profesi-onalci. Vi mačke niste dovoljno jake da se same zaštitite od neprijatelja. Ubrzo su se neke mačke počele bojati. Možda vlada ima pravo. Možda se ne možemo same zaštititi. Druge su mačke bile bijesne.Mi se možemo brinuti jedni za druge. Bit će nam sasvim u redu. A tko nam je neprijatelj? Vlada, tko drugi!?”
„Ne brinite”, reče im korporacija, „Nitko vas neće tjerati. Vidite, imate mogućnost. Možete glasati za bilo kojeg vladara”. Mačke se slože. „Izabrat ćemo najboljeg. Glasovat ćemo za onog vladara koji će biti na strani mačaka.” I to učiniše.
„Ne”, povikne vojska, „Vi mačke ste izabrale krivo. To samo pokazuje da ne možete same upravljati stvarima. Od sada će general Skanko2 biti glavni. Pokazat će vam kako se stvari trebaju uređivati.”
„General Skanko bijaše veoma okrutan. Bio je i korporacijski i vladin, no ponajviše vojni čovjek. Imao je na raspolaganju sve vojnike i svo oružje. Što je jadna Catalonija mogla učiniti?” Tex zastane i potraži odgovor među svojom publikom.
„Boriti se!” uzviknu čuvari šume.
„Tako je,” potvrdi Tex, „I to je baš ono i što su i učinili: borili su se! Skanko je imao moćno oružje, ali mačke nisu bile same. Medvjedi iz Bearcelone istjeraju vojsku iz grada i preuzmu njihovo oružje.”
Medvjedi u publici glasno pohvale taj čin.
„Dok su se najsnažnije životinje i dalje borile na Skankovoj strani, držeći ostale dijelove zemlje još uvijek pod kontrolom, druge su životinje napravile nešto još nevjerojatnije. Započele su nov način suživota. Dijelile su hranu, međusobno razmje-njivale stvari umjesto da koriste vladin novac i odbacile vladare i vođe. Životinje diljem svijeta gledaše ih u čudu, ne zbog njihove borbe, već zbog njihovog novog načina života. Neke su došle iz dalekih zemalja kako bi im pomogle da očuvaju taj nov način življenja.”
„No, Skanko bijaše nemilosrdan. Njegova je vojska sve više jačala pod potporom stranih vlada koje su ulagale novac u mašineriju Skankovog rata. Brojčano i oružano nadjačane, mnoge su životinje ili izgubile život ili prestale s borbom. Neke su se čak pridružile Skanku kako bi bile na pobjedničkoj strani. Catalonija je bila poražena, a nov način života uništen.”
Tex uzdahne i pogleda tužna životinjska lica oko sebe.
„Catalonija i životinje u njoj patile su i još uvijek pate, ali su pokazale svijetu nešto zaista važno. Zbog njih životinje diljem svijeta imaju nade. Otkrili su i živjeli novim načinom života i iako je on trajao samo malo vremena, svijet je bio svjedokom njegove funkcionalnosti. Vlade su ga se bojale, korporacije su ga mrzile, vojsku je sigurno razbjesnio, no rep Catalonije ostaje inspiracija životinjama, ma gdje bile.”
Tex završi priču.
Sabo je, čini se, uronila duboko u misli. „Jesu li mačke zaista to napravile? Da li se to doista tako dogodilo?”, upita kojota.
„Da, Sabo, stvarno je bilo tako,” odgovori Tex.
„Vau, to su bile prave mačke,” reče ponosno.
\chapter{4}
Kada je Pancho otvorio oči, kamp je već bio u nizu akcija. Razni su se odbori okupili oko svojih zdjela s kašom od žireva i raspravljali o organizaciji. Vjeverice iz „Oraha za sve” letjele su unaokolo kako bi svi dobili svoju porciju jela. Jedna od njih stavi posudu s jelom pod Panchov nos čim se probudio, i poznavajući njegove manire za stolom, pričeka trideset sekundi koliko mu je trebalo da to srkne, zgrabi posudu i odjuri natrag tamo gdje je bila gužva. Judi je sjedila okružena raznim pticama, zečevima, jelenima i ostalim tihim i brzim kuririma. Oni su bili grupa za medije i informacije; u njoj je trebala biti i Sabo.
„Gdje je mačka Sabo?” upita Pancho nakon što svima zaželi dobro jutro. „Zar ovo nije njezina interesna grupa?”
„Sabo se jutros vratila na farmu. Tamo će raširiti vijesti i vratiti se natrag sa svježim vijestima.”
„Uostalom,” šapne mu Judi, „Kad je pod stresom, nije baš od koristi.”
Sabo se, naravno, vratila na farmu, pomisli Pancho. Tamo treba nešto napraviti: dobiti na vremenu da nestane. Nije se sjećao da je ona ikada na farmi širila ikakve vijesti. Možda i jest, samo ne među svinjama. Nije znao.
Pancho pogleda uokolo ne bi li pronašao svoje sabotere. Ugleda ih pokraj debla s materijalom kako se svađaju tko će prvi uzeti koji alat. Samo su čekić i odvijač zapravo bili alat, a od to dvoje i Riff Raff i Bonkers su htjeli odvijač, nudeći jedan drugom čekić kao nagodbu. Dogovor je riješio pohabani medvjed s hrapavim glasom jednostavno rekavši kako će on ponijeti oboje, a svi ostali će se po potrebi moći njima služiti. Tom se rješenju nije nitko protivio; alat je bio težak, a medvjed dovoljno velik. Pancho je nosio mali paket s užetom i čavlima kojeg je pričvrstio oko trbuha. Tada primijeti da je bio vitkiji nego ikad, sve to zahvaljujući žirevima i redovnoj vježbi. Spakirani i spremni, svi su stajali u krugu gledajući jedan drugoga. Sve su životinje imale oko sebe natovareno oružje i nakon što netko reče „Spremni?” svi povikaše „Spremni!” te se krug razbije u liniju koju je kroz dolinu predvodio gavran Quoth.
Koračajući tako duž planinskog puteljka u jednoj liniji, Pancho odvoji nekoliko minuta da se pribere od svog prvog medvjeđeg zagrljaja. „Kad samo pomislim, do prije tjedan dana nikad nisam ni vidio medvjeda, majmuna ili pak rakuna.”
Pogleda svoje nove prijatelje kako koračaju u jednoj liniji. „Trenutno najradije pričam s Judi, najbolje rasprave su s Riff Raffom, a Bonkers je, moram priznati, najzabavniji. Bio je toliko sretan da se ubrzo našao kako pjevuši neku ratnu pjesmicu dok su silazili u borovu šumu.
Na kraju reda su bile „Orasi za sve”, a nekoliko običnih i dvije prugaste vjeverice su nosile ogroman lonac u kojem su bez problema sve mogle spavati. Kad je teren postao bolji, bacile su ga na pod i kotrljale tako što su iznutra trčale po njemu. Pancho se nasmijao njihovoj dosjetljivosti, no gledajući ih što rade, slučajno naleti na nisku granu. Lasica iza njega se slatko nasmije, a svinja skupi ono malo dostojanstva što mu je ostalo, ubrza korak i stigne medvjeda ispred sebe.
Izađu iz šume i nastave hodati preko tako visoke trave da su se čak i medvjedi trebali popeti na stražnje noge kako bi vidjeli kuda idu. Gavran Quoth je letio iznad njihovih glava tako da ga svi mogu vidjeti, a i jelen je na početku kolone, poznat kao dobar vodič, savršeno dobro znao kuda idu. Drugi su samo trebali slijediti uski ugaženi puteljak. Činilo se da hodanju kroz travnati tunel s nikakvim oznakama, koje bi im pokazivale koliko su napredovali, nije bilo kraja. Manje su se životinje počele umarati, a Panchu je trbuh već krulio kad se najednom ukaže čistina s par stabala i potočićem. Životinje se tu okupe i polože na zemlju svoje terete. Svi nahrupe na potok da se napiju, a vjeverice počnu dijeliti kolače od žireva. „Nešto poput terenskih porcija u vojsci”, pomisli Pancho, koji je čitao ponešto o vojnim temama. Potom prožvaka tvrdi kolač. Hodali su sve do dugo u poslijepodne, tako da bi bilo što imalo dobar okus.
Gavran napokon sleti na deblo na podu i počne odgovarati na silna pitanja.
„Koliko još?”
„Još samo preko ovog brežuljka,” odgovori.
„Ima li ljudi naokolo?” Gavran nije znao pa odleti izvidjeti ima li kakvih opasnosti.
Zatim progovori jelen s početka reda. „Dobro znam ovo područje. Zimi se tu ponekad hranim. Mislim da je ovo najbolje mjesto za kamp. Skrovito je i ima vode. Možda bi se vjeverice trebale tu smjestiti.”
„Zvuči dobro,” zacvrkuću vjeverice te krenu u potragu za hranom. Među životinjama je bilo i onih kojima je trebalo mnogo hrane, a nov im je teren bio u potpunosti nepoznat. Bilo bi dobro da se što prije prime posla. Plava šojka odleti natrag u Špiljski kamp da obavijesti Judi (koja je tamo ostala zbog ozljede) i druge kako su uspjeli doći do čistine gdje će napraviti kamp.
Saboterska se grupa okupi pored potoka da raspravi svoj ne-plan. Uzbuđeni su rakuni htjeli krenuti što prije, no ipak odluče pričekati gavranov izvještaj. Ljudsko bi društvo zah-tijevalo promjenu taktike. Medvjedi su se, međutim, nadali nekom lovu. Pancho pak nije bio siguran kako će sve ovo funkcionirati. Nikad nije proveo mnogo vremena planirajući uništavanje; njegovo je područje bilo stvaranje. „Ovi ostali sigurno znaju što rade i činjenica da se Bonkers uhvatio repom o hrastovu granu i da se ljulja ne bi se trebala protumačiti kao manjak namjera.” Pancho sjedne uz rub potoka te se vrućim i bolnim nogama od dugog hodanja počne igrati s vodom. Promatrao je kako odbor za hranu šalje nekoliko zečeva zaduženih za medije da u široj okolici potraže nešto jestivo. Ptice su i dalje kružile po zraku i nadzirale čitavu situaciju.
Odjednom se ogroman crni gavran obruši među njih. Upao je u kamp poput bombe, skrenuvši malo u stranu da ščepa majmuna za stražnjicu, od čega on padne na zemlju. Nakon što je sletio na deblo, sve se životinje požure do tamo da čuju vijesti.
Nakon što nekoliko puta pročisti grlo, počne. Kako bi povećao napetost, provede par sekundi gladeći si raščupano perje dok su životinje pratile svaki njegov pokret i čekale da nešto kaže. Gavran Quoth rastegne što je duže mogao. Napokon, kada su napetost i očekivanje dosegli svoj vrhunac, i taman prije nego se sve to pretvorilo u razočaranje i ljutnju, gavran započne.
„Upravo sam se vratio s izviđanja neprijateljskog uporišta.” Šaputao je glasno kako bi priča dobila na dramatičnosti. „Na jednoj od čistina su četiri velika stroja, jedan mali spremnik i jedan veći na kotačima.”
„Ooo,” zine impresionirana gomila slušatelja.
Tad nastavi, „Mislim da je tamo jedan čovjek; no nisam uspio vidjeti ima li koga u manjem spremniku.”
„Da!” Dva se medvjeda lupnu šapom o šapu, a veliki se pohabani medvjed Arthur i manji zlatni (neobjašnjivo prozvan Crveni) znalački nasmiju jedan drugom.
„Ako sad krenemo, mogli bi tamo stići do mraka. Izgleda da će nam biti jako zabavno!” šapne ptica.
Saboterska grupa započne pakiranje svojih vreća s triča-rijama. I Bonkers i Riff Raff provjere da li je odvijač sigurno tu negdje pri ruci.
Kada su se rakuni i lasica počeli penjati uz brdo, Pancho je još uvijek pakirao svoj teret. „Čekajte, ja ću vas voditi!”, vikne jelen svojim mekim glasom tako da se to jedva i moglo nazvati vikom. Životinje ga pričekaju te se on popne i stane na početak, dajući tako Panchu šansu da ih stigne uhvatiti. Ptice koje su bile zadužene za informacije letjele su ispred svih, a jeleni i zečevi se neprimjetno rasprše na sve strane. Trebalo im je otprilike pet minuta da stignu na vrh brda, gdje su se rasporedili u liniju i stali viriti iza ogromnih stijena. S ovog im se povoljnog položaja čitava dolina pružala kao na dlanu. Od svjetlosti zalazećeg sunca mogli su vidjeti svježe napravljeni put za prenošenje posječenih stabala i čistinu na kojoj su bili spremnici i strojevi.
Pancho zamoli rakune sa svoje lijeve strane da mu objasne što to ljudi planiraju. „Posjeći će sva stabla u dolini,” reče Bandit s izrazom gađenja, „i vući ih duž puta kojeg su posjekli. Planinske će obronke silovati i opustošiti, a kiša će zatim isprati gornje slojeve zemlje i napuniti potoke u nizini blatom. Nova stabla neće moći rasti jer će ih uvijek voda odnijeti. Ti mesari
„
Crveni medvjed stavi šapu na Banditovo rame da smiri rakuna. „On se jako uzbudi kad priča o tome,” progunđa Crveni. „Mi također. No sada je vrijeme kada trebamo biti smireni i razumni.” Pancho je osjećao tjeskobu pri pogledu na dolinu razmišljajući o njezinom skorom uništenju. Ljudi su zaista zla stvorenja. Tu je lekciju naučio još za života na farmi, no nikad nije vidio koliku štetu oni zaista mogu učiniti.
„Uskoro će mrak,” zakuka lasica, „Idemo.”
Negdje u liniji jedan od medvjeda progunđa „U redu, idemo” te se odrpani saboteri kroz grmlje spuste niz brdo do čistine. Zaustave se iza grma koji je bio tek malo udaljen od velikog žutog stroja. Pancho nije znao koji je to stroj, no potajno zažali što ga nije imao na svojoj staroj farmi. „On pravi put,” reče Bandit, „Loš je to stroj, svi su oni loši.”
Bandit je bio vrlo uzbuđen pa se Pancho nije htio miješati. Ipak, pomisli, nije stroj taj koji je loš, već onaj koji ga rabi.
Panchov oprost ne bi poštedio žuto čudovište od bijesnih ljudi koji se brinu za očuvanje okoline. Svi su se potom raspa-kirali i položili svoj alat i ostali pribor. Iznenađujuće je bilo to što se Riff Raff nije bunio kada je Bonkers uzeo odvijač, a njemu ostavio čekić. Rakuni su u paru zabadali kolce u drveće: dok je jedan držao čavao, drugi ga je zabijao u drvo.
Druge su životinje zamotavale užad o debla drveća, praveći prilično zamršenu mrežu koja će donekle poslužiti pri uništa-vanju lanaca na pilama i malo ih zabaviti. Odvijač je mukotrpno radio na vijcima žutog buldožera. Bonkers se dokazao kao vrlo brz u rastavljanju stroja. Medvjedi i lasica Walter (što je prilično ozbiljno ime za takvu životinju) krenu za čovjekom. Nađoše ga dolje zaključanog u malom spremniku prodornog mirisa, no prije nego što su išta napravili odu po Pancha da im pročita natpis na vratima.
„Polj-ski w-c”, pročita na glas, odmahujući glavom. „Ne znam što znači, no barem ne piše opasnost ili eksploziv”
„Ajmo ga napasti,” rekoše medvjedi i, stojeći jedan do drugoga, počnu njihati mali spremnik. Isprva su čuli su kako unutar Polj-skog w-c-a netko viče, no poslije nekoliko teških prijetnji, nije bilo ničeg osim tišine. S obzirom da ljudi nisu htjeli izaći, medvjedi još jače poguraju spremnik te ga prevrnu. Počnu ga kotrljati i onog tko je bio unutra, niz svježe napravljeni put od posječenih stabala poput dvoje djece koja se igraju udaranja limenke nogom. U međuvremenu se Walter ušuljao u veliki spremnik. Bila je to relativno nova metalna prikolica s prilično malo rupa na podu, ali lasicama zaista nije problem ući bilo gdje ako im je to namjera. Otkrio je na krovu otvore s pokretnom mrežom od kojih je jedna bila samo malo pritvo-rena. To je bilo sasvim dovoljno. Pancho je u čudu gledao lasicu koja se provukla kroz pukotinu i neprimjetno upala unutra. Lasica iznutra s lakoćom otvori vrata nakon čega su Pancho i ona porazbijali prikolicu. Pancho je imao više iskustva s ljudskim stvarima tako da je bio svjestan da neke papire treba pročitati prije nego li se unište. Dokumente koji su izgledali bitni počne naguravati u vrećicu za kupovanje koju je našao u ormariću.
Walter počne prekapati po ladicama stola kiteći se svim što mu je bilo zanimljivo. Prebaci se preko da vidi što je Pancho stavljao u vrećicu. Lasica je na ušima imala ziherice, oko ruku narukvice od gumenih traka te oko vrata obješen ključ s natpisom „Auto za dostavu”. Pancho posegne za ključem na što lasica povikne „Hej, ovo je moje. Tamo ti toga ima još,” pokazujući na gornju ladicu stola. Pancho pregleda ključeve označene s „Bager”, „Grabilica”, „Teretni K.” i „Kutija za alat”. Ovo zadnje je jedino imalo smisla.
„Walter, ljudi zaključavaju važne stvari. Pronađi veliku kutiju s bravom.”
Walter otkliže iz prikolice i počne tražiti. Pancho zgrabi ostale spise i sve ključeve koje je uspio pronaći te stavi sve u torbu. Ostali su se posvetili rastavljanju strojeva. Rakunima je ponestalo užeta i čavala, a medvjedi se vrate s mjesta gdje su otkotrljali onog čovjeka.
„Gledajte svi!” pokaže Pancho ključeve. Kao odgovor dobije samo nekoliko zbunjenih pogleda. Svinja shvati da oni nemaju pojma o čaroliji ključeva.
Tad se javi Walter: „Pancho, možda u ovoj kutiji!” Svi pohrle iza prikolice i ugledaju jako veliku, bijelu, metalnu kutiju s lokotom. Svi se naguraju što su bliže mogli, tako da je Pancho jedva uspio zavrtjeti ključ. Škljocaj i lokot se otvori. Tucet šapa naglo digne poklopac i svi osjete nekakvo strahopoštovanje prema onom što su vidjeli; alat koji su mogli samo sanjati. Ključevi svih veličina za sve njih, čekići, odvijači i svakojake druge stvari za koje nisu imali nazive. U to se rakuni započnu boriti oko alata i trčati do već djelomično rastavljenog buldožera.
Bonkers gotovo u transu došeta do Pancha i pogleda ključeve. „Što oni otvaraju?”, upita glasom punim tajanstvenosti.
„Ne znam,” reče Pancho, „no možda pokrenu strojeve.”
Majmun stade širom otvorenih očiju zuriti u Panchove skupljene svinjske oči. „Napravimo to!”
Pancho položi ključeve na zemlju. „Walter! Dođi, trebamo tvoj ključ,” povikne Pancho.
Walter im dobaci ključ vičući kako voli taj ključ jer ima crveni privjesak. Zatim se vrati poslu na bageru.
Pancho pročita Bonkersu napise na ključevima. „Bager, Grabilica, Teretni K. i Kamionet. Znaš li što ijedno od ovoga znači?” Bonkers odmahne glavom; Pancho pokupi ključeve i odšeta do najmanjeg kamiona. Pregledaju čitav stroj ne bi li našli nešto što će odgovarati ključevima i ubrzo otkriju kako „Kamionet” odgovara rupi na vratima. Okrene ključ ne znajući što može očekivati.
Vrata se odškrinu te se ukaže malo svjetla, na što oni gurnu unutra glave. Nakon što je Bonkers skočio i zauzeo mjesto za volanom te počeo mahnito prebirati po dugmadi, Pancho u razini svojih očiju ugleda upute za korištenje stroja koje su stajale u pretincu na vozačevim vratima. Listajući zaprljanu knjigu pronađe stranicu koja je opisivala instrument tablu. Gurajući njušku preko Bonkersa, gurne stopalo u malu rupu za ključ. Bonkers se zaigra par minuta s ključem da bi ga nakon toga zaokrenuo u smjeru kazaljke na satu i upalio motor. Obje životinje odskoče unatrag, te motor prestane raditi. Nadahnuti Pancho pročita Bonkersu većinu uputa za rad koji je izgleda sve to trenutačno naučio napamet. Svinja je znala čitati, no Bonkers je bio taj koji je shvatio čitav postupak. „Walter!”, zakrešti Bonkers, „Dolazi ovamo, trebaš nam!”
Walter dotrči te mu Bonkers stade objašnjavati kako upotre-bljavati gas, kočnicu i kvačilo. „Ako ćeš ti znati upravljati papučicama, ja ću obaviti ostalo. Pancho, gubi se s puta!”
I tako nakon što su nekoliko puta krivo startali zahvaljujući lošoj koordinaciji, napokon krenu. Rakuni i medvjedi proma-traše u čudu kako Bonkers i Walter pomiču kamion naprijed-natrag, lijevo-desno, pokušavajući dokučiti kako što ide. Jurili su po čitavoj čistini i prebrzo ulazili u zavoje. Tad Bonkersu padne na pamet nešto ne baš suviše pametno. Usmjeri mali kamion u pravcu velikog i krene se zabiti u njega. „Čekaj, stani!” Nije samo Pancho uvidio problem; medvjedi pohrle naprijed i na vrijeme zaustave Bonkersa te ga spriječe u njegovoj namjeri.
„Upotrijebi veliki kamion da razbiješ male stvari. To je pravi način,” reče Crveni, „Ovako bi ozlijedio samo sebe.”
„Namjeravao sam iskočiti iz kamiona prije nego što udari,” objasni Bonkers.
„A što sa mnom?” poviče Walter, „Ja nisam ni znao što namjeravamo.”
No Bonkers se već bio uhvatio većeg kamiona, odlučivši da je vožnja ipak mnogo zabavnija od razbijanja. „Požuri se Walter, skoro je isto!”
Majmun pronađe odgovarajući ključ, i s ne tako oduševljenom lasicom na svom mjestu, počne pomicati veliki kamion. Jedino što im je stvaralo probleme bio je krut i temperamentan mjenjač. Mali je kamionet Bonkers mogao svladati svojim repom, no za upravljanje ovim kamionom trebao je pomoć i stražnjih nogu. Bonkers je bio obuzet poput pravog majmuna i ništa ga nije moglo zaustaviti. Pancho zgrabi svoju vrećicu i zajedno s ostalim životinjama potrči prema višim dijelovima kako ih kamion ne bi zgazio.
Bonkers se dao natrag što je više mogao te se svom brzinom zaleti u kamionet. Sudar napravi ogromnu buku. Bonkers se opet udalji te se još triput zaleti u kamionet. Treći ga je put uspio preletjeti. Kamionet je sada bio samo gomila metala. Velikom kamionu nije nimalo štetilo ovo nasilje nad njegovim mlađim bratom. Bonkers se stade pripremati za udar u prikolicu. Udarac zahvati kraj prikolice, baci je s blokova na kojima je stajala te se prikolica otkotrlja u tjesnac na kraju čistine.
Ovo neizmjerno razveseli sve životinje. Vičući i skačući na pristojno sigurnoj udaljenosti, životinje ugledaju Bonkersa kako se usmjerava prema onom što je Pancho zaključio da je grabilica (jer je ključ s napisom „Bager” pristajao drugoj rupi). Stroj koji je plašio svojim ogromnim metalnim čeljustima nije bio dorastao majmunu i lasici u teretnom kamionu. Zgnječen i nekoliko puta udaren pretvori se u hrpu metala koja je završila u istom tjesnacu kao i kamionet. Ostao je još samo bager, i iako je trenutno bio u par dijelova, Bonkers je bio na putu ka još jednom uspjehu. Prešli su preko pojedinačnih dijelova čisto da bi se osigurali da više neće poslužiti.
Nikad prije životnije nisu prouzročile toliku štetu. Kao novi junaci, Bonkers i Walter siđu s kamiona zaplesati pobjednički ples.
Pancho se popne u kabinu teretnog kamiona. Nije uspio pronaći unutra nikakvu knjigu pa počne pritiskati dugmad i vući poluge. Odjednom se stražnji dio kamiona podigne i svakojake teške stvari padnu na pod, skoro poklopivši neke od životinja koje su bile najbliže kamionu. Prestrašeni Pancho iskoči iz kabine i pojuri provjeriti je li se sve u redu s njegovim prijateljima koji su, s obzirom da nitko nije bio ozlijeđen, bili zauzeti pregledavanjem lanaca na pili.
Bandit je bio izvan sebe. „Iako su maleni, ovo su najstrašniji strojevi. Krv ti se sledi od samog zvuka kojeg proizvodi.”
„U redu, Bandit,” reče Crveni, „Ubit ćemo ih. Ti reci kako.”
Bandit sjedne malo i razmisli, no jedino što je uspio smisliti bilo je uništiti ih teretnim kamionom. Tad predloži: „Znam jedno mjesto uz put gdje je litica toliko visoka da će se strojevi uništiti ako ih bacimo niz nju.” Ovo je zvučalo dobro i Banditu i Bon-kersu, kojem bi svako društvo zabranilo vožnju, te kamionom počnu gaziti motorne pile sve dok ih nisu potpuno uništili i dok nisu pustile ulje. Tad ih ponovo ukrcaju na kamion i s gavranom Quothom na čelu odvezu do litice. Ostale životinje ostanu na čistini sakupljati najbolji alat i pripremati se za odlazak kući na večeru.
Strašan prasak potrese šumu i na nekoliko je sekundi obasja svjetlo. Životinje se ukipe od straha zureći u nebo sve dok se svjetlo ponovo ne pretvori u mrak. Polako se okrenu i počnu s penjanjem uz brdo; uzbuđenje se pretvorilo u jezu dok su se vukli preko brda hodajući natrag prema kampu.
Nakon što su prešli potok na rubu kampa začuju gavrana koji stade pričati priču na najdramatičniji mogući način. Kad su se približili, ugledaju Bonkersa koji je visio o hrastovoj grani i Waltera koji se nije prestao hvaliti svojim novim nakitom.
Bonkers i Walter ugledaju svoje umorne prijatelje sabotere te im pohrle ususret. „Bilo je odlično, trebali ste vidjeti!” vikne Bonkers, „Bilo je odlično! Odlično! Umjesto Waltera, na papučicu od gasa smo stavili stijenu te kamion pustili niz liticu. Skočio sam kroz prozor taman na vrijeme.”
„Kako je eksplodiralo!” doda Walter, „I zapalilo se.” Priča se usavršavala i nadopunjavala čitavu večer kroz prepričavanja uz zdjele „Iznenađenja od žireva”.
Pancho proguta prve dvije zdjele, no pri trećoj zdjeli shvati da mu jelo ne prija samo zbog gladi. Iznenađenje u složencu od žireva bijahu jabuke.
\chapter{5}
Zora je stigla prije nego što su je saboteri očekivali, a grupa nije htjela otezati s odlaskom prema Špiljskom kampu. Najbolje je da budu što dalje kada korporacija shvati da su joj svi strojevi uništeni.
Složenac od žireva je imao tako dobar miris jabuke u sebi da je Pancho morao upitati Maca, današnjeg šefa kuhinje, gdje ih je pronašao. „Zečevi su ih našli,” i pošto su mu šape bile zauzete, Mac pokretom glave pokaže na dva prilično otrcana zeca koji su razgovarali sa šojkama.
Svinje su imale nezasluženu reputaciju životinja s neurednom higijenom. Ovo je bilo netočno za svinje općenito, a pogotovo za Pancha koji se ponosio time što je bio dobro njegovan. S druge strane, zečevi se obično smatraju mekanim i čistim životinjama, no prosječan se zec ne uklapa u taj kalup.
„Hvala vam što ste jučer pronašli jabuke. Dale su poseban okus našoj pobjedničkoj večeri.” Pancho je htio ugodno započeti razgovor s obzirom da s Blackstoneom i Hamiltonom još nije imao priliku razgovarati. Na njegovo vlastito iznenađenje, Blackstone, čije je lijevo uho bilo potrgano i visjelo na pola, odgovori mu s gotovo šekspirijanskom rječitošću.
„Bili smo vrlo zaneseni tim našim otkrićem. Kuhinja koju nam omogućavaju naši radišni i dobronamjerni drugari nažalost nema nikakvog okusa. Svaki je dodatak dobrodošao skromnom složencu, no bojim se da će proći još dosta vremena da iznova okusimo zlatnu smjesu.” Blackstone tužno odmahne glavom. Mlitavo mu uho udari o nos. Hamilton nastavi: „Međutim, moramo priznati ono što se priznati mora. Jabuke je našlo božansko stvorenje u obliku mladog muškog laneta s nesretnim imenom Bambi.”
„Bambi mu sigurno nije pravo ime.” reče Pancho pun sažaljenja.
„Mislim da jest,” uzdahne Hamilton, „pre, preslatko.”
Kada su svi počeli odlaziti, Pancho zgrabi svoju malu kutiju, koja je sada bila prazna, i stavi je u svjetlucavo plavu vrećicu za kupovinu ukrašenu slikom karanfila i riječima „Dan bijelih cvjetova.” Pancho nije znao njihovo značenje, no izazivale su u njemu ugodan osjećaj.
Mnogo je suvenira iz borbe bilo na putu prema Špiljskom kampu. Gotovo je svatko nosio poneki ključ ili odvijač. Bonkers je našao i ponosno nosio kapu na kojoj je velikim slovima pisalo MAČKA. Walter je započeo modu nošenja ključeva. Bonkers je imao onaj od teretnog kamiona oko vrata, a Pancho je nosio ključ od kamioneta. Walter je imao „Kutiju za alat” te je još uvijek skupljao uredski pribor. No u vrećici za kupovinu skrivala su se još dva ključa. Pancho je jedan htio dati Judi, a zbog drugog nije htio pokrenuti svađu.
Bonkers je na prsima imao prekrižene lance od pile, kao što vojnici nose metke. Matice i brtve s rastavljenog bagera bile su jelenima prilično lijepe ogrlice, a neke su ih ptice upotrebljavale kao ukrase za članke. Lasice su imale gotovo novi pokrivač za krevet s cvjetnim uzorkom zahvaljujući Crvenom koji ga je uzeo iz kamiona. Put kući činio se dužim i strmijim nego jučer. Pancho se zaista nadao da su papiri i dokumenti u plastičnoj vrećici koju je vukao za sobom po podu važni.
Nakon večere Pancho uspije uhvatiti Judi nasamo i da joj brončani ključ s privjeskom „Grabilica”. Bila je zadivljena: „Zaista si zdrobio grabilicu? To su tako razorni strojevi! Oni služe da, kad se posijeku velika stabla, zgrabe manja stabla i posijeku ih vrlo brzo, kao da kose travu. Na taj način ljudi uzmu svo drveće i ne ostave ništa da raste na čistini. No, čujem da su veoma skupi. Korporacije će biti vrlo ljute kad čuju što smo napravili!”
Nasmiješi se i stavi ključ oko vrata vežući čvor straga. „Pancho, hvala. Što još imaš u vrećici?”
Pancho joj pokaže dokumente. Ni sam ih nije još imao priliku pogledati. Judi nije znala dobro čitati, no iz te mase brzo zgrabi veliku topografsku kartu. „Znam gdje je ovo,” reče, „I pogledaj, tu, i tu.” Na karti su bila označena mjesta za daljnu sječu. „Pa mi smo ovo zaista trebali!”
Pancho počne prebirati po dokumentima: datumi i zabilješke građevinskih inspektora, dozvole za sječu, ugovori i poslovna pisma. Pancho ih je znao pročitati, no ne i uhvatiti sveukupno značenje jer je premalo toga znao o šumama i sječi.
„Trebamo ovo pokazati našim stručnjacima,” reče Judi.
„Tko su oni?” upita Pancho u čudu.
„Pa Blackstone i Hamilton,” odgovori Judi tonom kao da se podrazumijevalo da to mora znati, „oni su veoma obrazovani: imaju diplomu Harevarda” Nasmiješi se.
Pancho klimne. „Ne mogu vjerovati da sam tjednima izbjegavao razgovor s njima, a ispostavilo se da su postigli toliko mnogo u životu i da su jako zanimljivi. Nikad ne bi po njima rekao.”
„Nikad ne možeš znati,” reče Judi, „Ponekad nekoga jako zavoliš, a na kraju se ispostavi da je špijun.”
„Kad govorimo već o tome, gdje je Sabo?”, našali se Pancho.
„Očekujem je sutra pošto je akcija završila danas.” Judi je također primijetila njezine sklonosti. „Sabo je u redu,” doda, „Zapamti da ne smiješ prebrzo zaključivati.”
Slijedećeg jutra poslije doručka (palačinki od žireva) Pancho dovuče stručnjacima svoju vrećicu s dokumentima. Izvadio je ključ i mali paket jer je htio zečevima predati sve dokumente i više se ne brinuti za planove o sječi drveća, ma koji oni bili.
Blackstone i Hamilton ga ugledaju kako dolazi i kažu: „Pancho, hoćeš li nam više pokazati što imaš u toj svojoj vrećici?” Pancho otvori vrećicu i pokaže im hrpu mapa i dokumenata. Stručnjaci se odmah dadu na posao. Sretan što se riješio posla oko papira, Pancho nađe lijepo mjesto za prileći.
Dok se zasluženo odmarao na travi, omete ga strka oko špilje. Uspravi se da vidi što se zbiva te ugleda Sabo kako juri kroz kamp kao da joj gori rep. Sabo primijeti Panchovu glavu koja je virila iz one visoke trave i razrogačenih očiju pojuri u njegovom pravcu. Bila je toliko zadihana da nije mogla govoriti. Pancho skoči na noge prestrašen što vidi Sabo u ovakvom stanju. Možda su i nju jurili psi sa farme. Donese joj zdjelu s vodom i ona se napije te uhvati dah i počne pričati. „Stanje na farmi je jako, jako loše,” profrflja, „Svinje su preuzele kontrolu i sve su ostale životinje njihovi zatvorenici. Svinje ubijaju svaku životinju koja se ne složi s njima.”
„Moram se vratiti,” reče Pancho, odjednom osjetivši želju da se vrati svojem prijašnjem životu na farmi.
„Ne!”, vikne Sabo, „Ne smiješ se nikada vratiti. Napričali su mnogo laži o tebi. Za sve loše što se dogodi okrivljuju tebe, a svatko tko stane u tvoju obranu biva ubijen. Ni ti ni ja se više nikada ne možemo tamo vratiti.” Sabo se onesvijesti, pretvorivši se u gomilu sjajne dlake na zelenoj djetelini. Pancho je uspravi i više ništa ne upita. No, ona se ubrzo oporavi i prokomentira: „Eto što se događa kad postoje vođe. Prije ili kasnije, čak i ako započnu s dobrim namjerama, sve završi u krvi.”
Sabo se nije uspjela oporaviti u potpunosti. Vukla se unaokolo po kampu i stalno odbijala hranu. Sve su se životinje zabrinule jer je nikad prije nisu vidjeli ovakvu. Znala je ležati pokraj Judi, no ni s njom nije htjela razgovarati.
Pancho je znao da je Sabo još u šoku i nije znao kako bi joj mogao pomoći. Bonkers je na sebe preuzeo odgovornost da razveseli Sabo.
Pošto su često zajedno smišljali kojekakve psine u kampu, Bonkers ju je smatrao srodnom dušom. Isprobao je sve stare šale, grimase, imitiranja drugih životinja, ali nju ništa nije uspjelo nasmijati.
Jednog se dana Bonkers umirio. Više se nije trudio oko toga da je nasmije. U šapi je donio kapu koju je bio uzeo s bagera. Stavio je narančastu kapu pokraj crne mačke i pokazao joj slova koja mu je Pancho pročitao. „M
A
Č
.K
.A, mačka. Vidiš Sabo, to je za tebe.” Sabo posegne za njegovom šapom i dotakne obod kape. Pogleda prvo Bonkersa, zatim Pancha te brizne u plač. Šmrcala je i šmrcala. Bonkers i Pancho su bili veoma tužni, a Judi je počne maziti, pustivši je da se isplače.
„U redu je Sabo, samo to izbaci iz sebe,” reče i klimne svinji i majmunu koji su samo nijemo stajali. Nakon toga se Sabo zaista sabrala. Počela je i jesti i pričati, no to više nije bila ona ista mačka od prije. Vidjela je nešto strašno što nikada neće moći zaboraviti. Jednom je ili dvaput pokušala nositi kapu, čisto da razveseli Bonkersa, ali joj je zaista bila prevelika. Zatakla ju je o zid u špilji i rekla Bonkersu kako tamo visi da bi mogla zauvijek podsjećati životinje na veličanstvenu pobjedu. Time je započela tradiciju: Iz svake bi akcije grupa životinja donijela nešto što bi objesila o zid.
Otkad se vratila, Sabo se nije puno udaljavala od kampa. Nije lutala okolo kao nekoć prije. Pancho je smatrao kako je to vrlo štetno jer jednostavno nije bilo u Sabinoj prirodi. Možda bi Sabo i išla s njim u šetnju kad bi je pozvao. Možda bi mogli ići u potragu za jabukama (ovo mu se posljednjih dana stalno vrtjelo po glavi). Pancho se sjeti da su zečevi rekli da je jabuke pronašlo lane Bambi. Kako bi mogao zaboraviti to ime? Počeo se raspitivati za Bambi i nije prošlo mnogo prije nego što su mu jeleni pokazali na lane. Kad mu Pancho priđe, Bambi se ponašao kao da očekuje kaznu. Bio je malo više od laneta koje je tek nedavno izgubilo mrljice.
„Bambi, ja sam Pancho.”
„Znam,” reče prigušenim glasom.
„Bambi, zečevi Blackstone i Hamilton su mi rekli da si im ti pokazao gdje su jabuke.”
„Ne mislim da je krađa ako ih pronađem na podu,” odgovori.
Pancho pažljivije izabere riječi. „Mi uzimamo žireve i s poda i sa stabla i to nije krađa. Zašto bi to bila krađa?” Pancho je znao odgovor prije nego što ga je dobio.
„Zbog ograde.”
„Pa možda je ograda to što je krivo, možda je sama ograda krađa.”
Bambi zbunjeno ušuti.
„Ako možeš odvesti mene i Sabo do tamo, mi ćemo izvidjeti situaciju i odlučiti što je krađa, a što su gladne životinje koje se bore za šumu.”
„Ja se slažem s tim,” odgovori, „ali moja majka mi neće dopustiti da pređem ogradu. Ona kaže da me mogu ustrijeliti.”
„Ima pravo”, reče Pancho, „Hoćemo li ići?”
Pokupe Sabo i krenu niz puteljak kojeg bi samo jelen mogao izabrati. Hodali su prilično brzo te nakon malo vremena stanu predahnuti pokraj potoka, izgleda pored istog onog kraj kojeg su se životinje zaustavile neku noć, samo malo više nizvodno. „Bambi, htio sam te pitati da li ti je Bambi uistinu pravo ime?” Pancho požali što je to pitao kad vidje da se on zacrvenio.
„Da i mrzim ga!” odgovori.
„Pa i Pancho je promijenio svoje, zar ne Pancho?”, doda Sabo. Izgleda da se mačka vratila svom uobičajenom zadir-kivanju.
„Ti si promijenio ime?” upita Bambi, „Kako si se prije zvao?”
Sada je bio Panchov red da se zacrveni. Bijelo mu lice postane crveno poput cikle. „Imao sam grozno, glupo i nedostojanstveno ime” reče Pancho, „To jednostavno nisam bio ja.”
„Reci mu”, navali Sabo, „Hajde.”
„Obećavaš da nećeš nikom reći?”
Bambi klimne i svinja se došulja te mu šapne ime. Ako ste ikada čuli kako se jeleni smiju, znate da je njihov smijeh zarazan. Ubrzo se svo troje od smijeha našlo na podu.
„Jasno mi je zašto si ga promijenio”, hihotao se Bambi, „Pancho je sasvim dobro, pravo ime za tebe.”
„Pa koje bi ime tebi dobro pristajalo?” upita Sabo, „Što misliš o Herkulu?”
„Ne, ne, ne,” reče Bambi, „Nešto normalno, nešto jednostavno. Tom, Bill, Ivan.”
„Ivan?” reče Pancho, „Jelen Ivan? Čekaj malo,” reče i izvuče iz svoje male kutije ključ od bagera. Srebrni je ključ imao mali reljef vrhu u obliku zastave koja se vijori te natpis koji je glasio: „Ivan Jelen”. „Evo Ivane Jelene. Ovo mora da je tvoje.”
Jelen nikad nije bio tako uzbuđen. U posljednje su vrijeme ključevi bili najtraženija roba u kampu i sada je i on imao jedan, i to vlastiti. „Joj, hvala, ovo je odlično.” Popne se više nego onaj jelen na reljefu. „Sada sam siguran sam da je Ivan pravo ime za mene.”
„I ja sam znao zašto sam čuvao taj ključ,” promisli Pancho. „Idemo prema jabukama?” upita.
„Samo ovuda,” vikne Ivan. Svinja i mačka su morale trčati kako ne bi zaostajale za jelenom. „Samo pratite potok.”
\chapter{6}
Svjež zrak, nov teren i dobro društvo su izgleda prijali staroj Sabi. Mačka je skakutala duž obale zamahujući šapom tu i tamo kad bi naletjelo koje vretence, vrtjela je repom i činila se puna života. Pancho je hodao i prskao po plićaku. Ovo je bila neka vrsta prijateljskog izlaska za koji na farmi nikada nije imao vremena. Zrak je bio miran i topao, a sunčeva se svjetlost poigravala sa sjenama lišća. Boje su bile svjetlije i imale jači miris nego inače. Pancho zatvori oči i udahne, i evo, pomiješan s vlagom mahovine, miris obližnjih jabuka! Jelen Ivan je i dalje hodao sprijeda. Mladenačka poletnost i duge noge nosile su ga do kraja šume odakle se mogla vidjeti ograda, te se tamo zaustavi poput nekog kipa i pričeka prijatelje. Mačka i svinja provire između drveća, no zbog visine nisu mogli vidjeti ogradu.
„Ivane, gdje si ?” Pancho pretraži grmlje. „Gdje je taj jelen?”
„Bu!” Ivan glasno šapne svinji u uho. Ivan je stajao tako mirno da su oni gledali kroz njega. Sabo skoči u obližnje grmlje. Živci su joj još bili tanki. Lako ju se moglo prestrašiti.
„Daj, prestrašena maco”, stade se jelen ulagivati, „To sam samo ja.”
Sabo ispuže van trudeći se izgledati ravnodušno, ali joj dlake na vratu nisu baš stajale uz kožu. „Vidiš,” reče jelen, „Evo ograde.” Manje su se životinje trebale došuljati malo bliže kako bi vidjele jako dugu ogradu, koju je na nekim mjestima trebalo popraviti. Ograda se pružala dokle god im je sezao pogled. Potok je nestao ispod drvene ograde i vijugavo nastavljao svoj put preko ogromnog voćnjaka. Gdje god bi pogledale, životinje su mogle vidjeti samo stabla s voćkama i orasima: bilo je jabuka, breskvi, trešanja, oraha, badema
zatim nekih vrsta kalifornijskog oraha i mnogo drugih vrsta kojima Pancho nije znao nazive. Za razliku od ograde, ovim stablima nije ništa nedostajalo; činila su se dobro nahranjena i veoma plodna. Nekoliko grana jabuka prelazilo je ogradu na ovu divlju stranu.
Tamo je Ivan išao pobrati voće. „No”, pažljivo objasni, „samo ako padnu na pod.”
„Tvoja je majka podigla vrlo moralno dijete,” pohvali ga Pancho, „ali zašto bi bilo drugačije ako su na podu ili na grani? Prije ili kasnije sve će završiti na podu. Vjerojatno će sutra još tucet njih pasti na zemlju, a mi nećemo biti tu da ih pokupimo. Ako ih uberemo danas, samo uzimamo sutrašnje jabuke i štitimo ih od ozljeda koje zadobiju padom.”
Pancho raširi tkaninu po zemlji i počne na nju stavljati jabuke. Sabo se uspne na drvo i zatrese grane. Jabuke su padale brže nego što ih je Pancho mogao hvatati.
„Pa, mislim da si bio u pravu. Te bi jabuke ubrzo same pale. No mislim da ne bi trebali prijeći ogradu,” reče Ivan dok mu je pomagao pokupiti jabuke.
„Naravno, u pravu si, a tu ionako imamo dosta jabuka. Međutim, ako želimo kruške ili trešnje ili orahe”, svinja ih je gotovo mogla okusiti dok ih je nabrajala, „nemamo drugog izbora doli je prijeći.”
Brzo sakupiše jabuke. Kad je tkanina bila puna, Pancho je sveže kao što skitnice vežu svoje zavežljaje te je sakrije u grmlje. Zatim troje prijatelja pojede koliko su god mogli više crvenih, sočnih jabuka, bacajući jezgre na zemlju koju su ubrzo preplavili mravi.
Gledajući niz dugu ogradu, Pancho pomisli na glas. „Što mislite koliko je velika ova farma?”
„Ogromna, divovska!”, reče Ivan, „Potok teče preko cijele farme. Pratio sam ogradu sve do druge strane gdje potok ponovo izlazi. Daleko je.” Tad iznenada doda: „Nikad nisam probao krušku.”
Svi adolescenti imaju želju da prijeđu granicu roditeljske kontrole i Ivan nije bio iznimka među njima. No Pancho nije htio ljutitu košutu za vratom. „Nema ničeg tako lijepog na svijetu poput savršeno zrele kruške. Ostani tu i donijet ću ti je.”
Mačka i svinja se provuku kroz ogradu i počnu polako hodati kroz šumu voća. Stabla su bila složena u zasebne sektore i trebalo je proći mnogo jabuka i breskvi da bi se došlo do krušaka. Nisu vidjeli ni jednu voćku na zemlji. Izaberu prikladno drvo za penjanje te se Sabo popne.
„Mogli bi i za nas uzeti po jednu krušku,” reče Pancho dok je Sabo gnječila teške žute ukrase prebrzo tresući granu. Pancho počne puzati po zemlji i skupljati kruške koje bi se otkotrljale sa strane, kad mu se ispred njuške na kotrljajućoj krušci stvori narančasta dlakava šapa. Refleksno odskoči unatrag i ugleda ponosnog zlatnog ptičara kako mu se smijao. Kad je vidio strah u mačjim očima i svinju koja se tresla naslonjena o kruškino drvo, pas sjedne u ponizan položaj obično namijenjen za donošenje novina gospodaru. „Ne bojte se, neću vam ništa. Treba li vam što?”
Panchov se strah pretvori u krivnju; Sabo se spusti s drveta, nadajući se da je neće vidjeti. Bilo bi teško u ovom trenutku izreći laž u koju bi pas povjerovao. Pancho nije znao što reći te je i dalje samo držao kruške i nevino se smiješio.
„Oh”, reče pas, „kruške su ove godine vrlo ukusne. Znate, na svijetu nema ničeg boljeg od savršene kruške.”
Pancho je taman htio reći kako je neobično čudno što je on isto to rekao nekoliko trenutaka ranije, kad shvati da je pas najvjerojatnije prečuo njihov razgovor. „Jako mi je žao što sam uzeo ove kruške, molim vas uzmite ih natrag,” Pancho ih ponudi psu na položaju.
„Oh, gluposti, insistiram da ih uzmete. Vaš mali prijatelj nikad nije kušao krušku. Ja sam Goldie i vi ste gosti na našoj farmi. Poslužite se svime što vam treba.”
Riječ „treba” je na neki način zasmetala Panchu. Implicirala je potrebu, koja se u ovom slučaju kad je on bio krcat jabukama, ne bi baš mogla primijeniti na kruške. „Puno vam hvala, moj prijatelju. Ivan će biti oduševljen kad kuša svoju prvu krušku. Ja sam Pancho, a ovo
„ Potražio je mačku, koja je virila iza debla. Domahujući joj doda „
je Sabo.”
Počnu se polako kretati u pravcu ograde. Mladi je jelen stao u svojoj pozi kipa kad ugleda da s njima dolazi i pas. Goldie je tako pažljivo nosila krušku među zubima da nije oštetila kožu voćke. Položi je na zemlju i njuškom je gurne ispod ograde prema Ivanu. Jelen otkotrlja voćku u travu da je osuši prije nego je kuša. Bila je to ljubav na prvi pogled. Žvakao ju je i sisao joj srž i sve drugo.
„Evo tu vam ima još mnogo,” reče Goldie, pokazujući rukom Panchu da spusti na zemlju one koje je držao za sebe.
„Nevjerojatne, strašne, najbolje stvari koje sam ikad jeo!” Ivan je bio u godinama kad vam se čini da hrane nikad nema dosta.
„Za jelena su veoma zdrave,” reče Goldie.
Pancho se sad malo ohrabrio s obzirom da je bio na sigurnoj strani ograde. „Zar vašem gazdi ne smeta to što vi dajete voće divljim životinjama?”
Goldie se nasmije i pogleda svinju, mačku i lane. „Ne izgledate mi tako divlji”, reče i tužno objesi glavu, „Mi nemamo gazdu.”
„Zaista”, upita Pancho, „na farmi nema ljudi?”
„Ne, ne više. Imali smo ljude ranije, no prvi je umro i zatim drugi. Duga priča.” Promijenila je temu. „Želite vidjeti farmu? Provest ću vas kroz nju.”
Pancho pogleda Sabo koja slegne ramenima. Tad oboje pogledaju Ivana. „Ivan je dobar sin,” reče Pancho, „a njegova majka ne bi voljela da on preskače ograde i da ga nastrijele.”
„I mislim da ne bi,” reče Goldie Ivanu. „Željela bih da slušaš svoju majku. I ja sam nekoć bila majka. No, na ovoj farmi nema oružja. Na prvoj farmi, kao i na većini ostalih, ima oružja, ali na ovoj ste savršeno sigurni. Ipak, sami morate prosuditi što je za vas u redu.”
Ivan pomisli na majčina pravila i na životinje koje kažu da u Špiljskom kampu nema ni pravila ni gazde. „Ja sam samostalan jelen. Ja nemam nikakva pravila i nikakve gazde. Danas sam promijenio ime. Ako kažete da nema oružja
idemo!” kaže Ivan i skoči preko ograde, među odrasle.
Ostali su ga slijedili, Goldie i Pancho hodajući bok uz bok, a Sabo vukući se po putu. Nije bila naviknuta na skitanje s čudnim psima i, iako se ovaj činio veoma sladak, bolje paziti ranije nego kasnije žaliti.
Ivan je međutim pobjegao naprijed prilično daleko i nije bio baš previše zainteresiran za službeni obilazak. Po njegovom se uzbuđenju dalo zaključiti da je jako dugo priželjkivao da preskoči tu ogradu. Hodali su preko velikih površina punih voćki svih vrsta i zatim kroz polje tako mladih stabala da nisu mogla uroditi plodom. „Ove smo posadili prije dva mjeseca,” reče Goldie, „Jako dobro napreduju.”
„Tko ih je posadio,” Pancho upita, „Psi?”
„Ne,” nasmiješi se Goldie. Činilo se kao da se uvijek smije. „Uglavnom konji i koze. Njima se voće jako sviđa. No svi pomažemo.”
Kad su životinje izašle iz voćnjaka od pogleda im zastane dah. Livada ispred njih bijaše prostrana s tu i tamo ponekim brežuljkom. Zelena je trava blještala od cvijetova kamilice i maslačaka, a potok se vijugao kroz sve njih, isprekidan mjestimice nekom stijenom ili vrbom. Zdravi jaganjci skakali su od radosti, mašući Goldie i posjetiteljima, koji su izronili iz sjene voćnjaka na žarko poslijepodnevno sunce. Panchove se oči napune suzama. Ovo je bila farma njegovih snova, ovo je ono što je on htio da njegova stara farma postane. Čak je i Sabo bila dirnuta. I ona je rođena na farmi.
„Koja predivna livada!” zaprede sva očarana te počne po livadi loviti leptire. Ivan počne skakati okolo zajedno s ostalim mladima. Za nekoliko se minuta činilo kao da se oduvijek poznaju. Njega je više zanimao novi svijet koji je otkrio nego nostalgija.
Pancho se okrene prema Goldie i zamoli je da mu kaže kako je uspjela, kako na ovoj farmi sve funkcionira tako savršeno.
„Duga priča,” reče ponovo.
„Zaista je želim čuti,” molio je Pancho. Tako oni sjednu pod vrbu uz potok među maslačke od kojih je nekoliko njih ubrzo završilo u vodi, te Goldie započne priču. Pancho je sjedio sav ukočen s bezbroj ideja koje su mu se vrtjele po glavi.
„Nismo mi napravili farmu; ona je postojala još prije nego što se itko od nas rodio. Naše ljudsko biće Margaret se rodila tu, baš kao i njena majka. Kad sam ja došla na svijet, Margaret je već bila u kasnim godinama. Supruga su joj pokopali ispod hrasta i ona nije imala nikog drugog za razgovor osim nas. Tad se razboljela i ostala prikovana za krevet. Njezini se kućni poslovi nisu obavljali, a mi smo svi ovisili o njoj.” Goldie pogleda u potočić koji je žuborio i potpuno uroni u sjećanja. „Tad jednog dana netko reče, a ja ti ne smijem reći tko, ali netko reče Napravimo sve sami i to se činilo tako ispravno i u redu. Radili smo to kako bi pomogli Margaret, naravno, no isto i da pomognemo sami sebi, jer bi u suprotnom slučaju svi pomrli od gladi.” Pogleda Pancha i nasmiješi se onim svojim pasjim smiješkom. „Iskreno govoreći, bilo je jednostavno i zabavno. Otkrili smo da znamo voditi farmu, poznavali smo svakodnevne rutine te ih čak i usavršili. S vremenom smo neke stvari počeli i mijenjati.”
Goldie stane da bolje promotri majku prepelicu i njezinu djecu koja su trčala livadom. U očima joj se vidjelo da bi htjela i ići za njima, no ne pomakne se s mjesta. Pancho je bio sav u priči i htio ju je vratiti na temu: „Koje promjene?”
„Pa,” ponovo obrati pozornost priči, „Posebno jedno poboljšanje: Margaret je uvijek držala zatvoren vrt iza kuhinje kako mi životinje ne bi ulazile unutra, no dosta bi vremena trošila na borbu s bubama i puževima koji su htjeli dominirati nad povrćem. No, nakon što se razboljela, patke su predložile da pojedu sve puževe, koji su im predstavljali posebnu poslasticu, ali da dok to rade ipak paze da ne gaze na male biljke. Ispalo je odlično za sve nas, a sada su uglavnom patke zadužene za površinu vrta.”
Sabo je završila s hvatanjem skakavaca i odlučila pridrijemati. Sklupča se blizu njih kako bi mogla čuti priču.
„Kad je Margaret umrla, već smo bili veoma uspješni u vođenju farme. Shvatili smo da što više razmišljamo o stvarima, da ih bolje radimo. S toliko različitih životinja s toliko različitih sposobnosti jedva da i moramo raditi!”
Pancho je prekine. „Kako se to dogodilo? Čini se sasvim suprotno nego na našoj farmi.”
Pas zastane i razmisli. „Možda je stvar u čaroliji zemlje. Neki smatraju da je činjenica što je Margaret ovdje pokopana pomogla da zemlja i dalje bude plodna, no ja mislim da je stvar u sestrinskoj ljubavi koju osjećamo jedan prema drugom.”
Pancho nije vjerovao u čarolije, iako je ovo bilo vrlo iznimno mjesto, jako veliko i nepokvareno. „Sestrinska ljubav?” upita, nesiguran u odnos ovog pojma prema ekonomiji.
„Znaš, brinuti se jedan za drugog,” Goldie jednostavno odgovori.
„A vaš gazda?”, upita Pancho, „Kakav je on?”
„Gazda?” Goldie razmisli na trenutak, „Mislim da je Margaret bila neka vrsta gazde, no ona je umrla,” slegne ramenima, „Gazda je nešto o čemu nismo nikad razmišljali.”
Pancho podigne obrve, „Ali tu je sve tako organizirano
tko je to napravio?”
„Nikad nije bilo problema. Valjda svi sami sebe organiziramo.” Goldie se umorila od silnog objašnjavanja. Pancho je imao još brdo pitanja kad ona povikne „Gle tko dolazi! Carlos i Juanita. Oni će te vrlo zainteresirati. U svojoj su zemlji bili borci za slobodu.” Pancho pogleda na čudne životinje koje su im se približavale preko livade. Izgledale su kao dlakave koze, ali ne baš iste.
„Što su one?”
„Zovu se ljame. One me uče španjolski.” Goldie počne mahati repom, „Hola, amigos, buenos tardes.”
„Buenos tardes, Goldie,” reče ljama boje karamele.
„Ovo je Pancho, a ovo Sabo,” reče pas i pokaže na mačku, koja je na spomen svog imena otvorila oči, „a tamo dolje na livadi je Ivan, mladi jelen.”
„Ja sam Juanita, a ovo je Carlos. Dakle, vi ste ti čuvari šume o kojima sam mnogo čula.”
Pancho ostade zbunjen jer o ovom nije još pričao s Goldie. „Vi znate za nas?” Pancho baci pogled prema Sabi koja slegne ramenima.
„Vaše ptice zadužene za medije su nam nedavno nagovijestile oluju. Je li i majmun došao s vama? Nadali smo se da ćemo ga upoznati.” Tako dakle, Bonkers je imao status zvijezde.
„Ne, nije danas došao. Možda neki drugi put, ako želite, možete vi nas posjetiti u Špiljskom kampu.”
Pancho je samo htio biti ljubazan, no ljame su bile spremne krenuti. „To će biti jako zabavno!” Od Juanitinog mekanog naglaska Pancho pomisli na daleke zemlje.
„Carlos, možeš li otići po stvari?” Carlos klimne svojom čupavom glavom, okrene se prema onom što je vjerojatno bila staja i počne trčati prema tamo. „Pratili smo vaše poduhvate i podržavamo vas u vašoj stvari. Goldie, možeš li\dots{}”
„Zaliti pšenicu umjesto tebe?” Goldie završi Juanitinu rečenicu, „Naravno, zašto ne?”
Carlos dotrči noseći dva ispletena zavežljaja žarkih boja. „Ne možemo doći u posjetu praznih ruku. Pancho, što misliš da bi trebali odnijeti? Voće i orahe?”
„Savršeno”, nasmiješi se svinja, odjednom vidjevši da sunce već zalazi, „Mislim da bi uskoro trebali krenuti. No, nismo vidjeli ostatak farme.”
„Tad imate izgovor da dođete još jednom.” Goldie i ljame napune zavežljaje najboljim voćem.
Pancho tiho šapne, „Ostavite malo mjesta. Van ograde nas čekaju još neke jabuke.”
„Stavit ćemo ih na vrh”, odgovori Juanita, „Carlos je toliko jak da neće ni primijetiti da mu je na leđima još jedna vrećica.”
Carlos se posrami, iako mu je komentar godio. Ipak ne reče ništa. Pancho zazviždi Ivanu Jelenu i signalizira mu da je vrijeme da krenu. Ako niste znali da svinje mogu zviždati
mogu, i to vrlo glasno, neke od njih. Ivanu se nije dalo ići, ali promijeni mišljenje kad ugleda ljame i voće. Sa sjajnim ključem oko vrata, odvede družinu natrag u Špiljski kamp.
\chapter{7}
Vrativši se s poklonima, životinje su ih dočekale poput heroja. Slasno su voće poslužili zajedno s kolačićima od žireva, a vjeverice spreme dragocjene orahe za drugi obrok. Ivan objasni svima svoje novo ime te prijateljima pokaže ključ. Majka ga nije ni pitala, niti su joj rekli išta o preskakanju ograde. Carlos i Juanita zauzmu središnja mjesta i počnu s Bonkersom pričati o staroj domovini. Pancho nije baš vjerovao da je majmun ikad bio na nekom takvom egzotičnom mjestu, no Bonkers je svoju stranu priče dobro držao. Čak se i Carlos toliko uživio u raz-govor da im je ispričao sve o uništavanju prašuma.
Riff Raff pomisli da bi svi trebali otići tamo i zaštititi prašume, ali mu Juanita objasni kako je to veoma daleko. Svejedno bi se ona i Carlos jednog dana htjeli tamo vratiti.
Životinje u kampu su doživjele ljame kao svjetske putnike. Pancha je zadivilo njihovo znanje o svijetu i o mogućnostima. Sve do nedavno, Pancho nije bio nigdje doli na farmi gdje se rodio. Sada je lutao šumom, čak i posjetio drugu farmu. Osjećao se slobodno i pustolovno. Kad je čuo Juanitu i Carlosa kako pričaju o stranim zemljama s čudnim vrstama životinja i s najvećom rijekom na svijetu, osjeti kako se svemir povećao, a svinja smanjila. U njemu su se borili osjećaji: svijet tako velik, s toliko avantura i problema i Pancho, svinja, tako malen, nedjelotvoran i bez iskustva.
Judi primijeti da se udaljio od ostalih pa dođe sjesti pokraj njega. „Ljame su odlične,” reče ona, „Uvijek je dobro da družina dobije neku novu energiju. I čini se da je Sabo mnogo bolje otkad je malo izašla. Pancho, jesi dobro?”
Sjedio je zureći u travu. „Osjećam se tako bespomoćan i odjednom tako izgubljen”, reče, „Vidim da na svijetu toliko toga treba napraviti i vjerujem da ima toga još što ja ne vidim. Osjećam da ne mogu sve napraviti i da ne znam gdje bih uopće započeo!”
Judi je bila pomalo iznenađena. „Naravno da ne možeš sve napraviti, kao da si ti jedina životinja na svijetu. Moram primijetiti da si prilično egoističan.” Pogleda ga u njušku. „I što misliš pod tim da ne znaš gdje bi počeo? Već si počeo, radiš nešto važno ovdje, a i tvoja je stara farma bila neka vrsta važnog koraka. Samo i dalje idi korak po korak, to je sve, i daj da i ostali idu u korak s tobom.”
Zatim promijeni temu. „Možda bi ljame htjele ići u sutrašnju akciju u šumi? Hoćemo ih pitati?”
Sutrašnja je akcija bila novost za svinju: „Koja akcija? Gdje idemo?”
„Ondje gdje smo bili posljednji put! Izgleda da su donijeli novu opremu. Blackstone i Hamilton kažu da postavljaju sve da sječu provedu u cijelosti.”
„Kako zečevi znaju za plan?” Pancho je mrzio osjećaj da nije u toku.
„Papiri koje si im dao u plavoj torbi,” objasni mu Judi, „Kažu da je sve unutra pisalo.”
„Oh,” Pancho se osjeti mnogo više upletenim, „zar ne bi trebali imati sastanak ako sutra idemo?”
„Već smo ga imali. Ti i Sabo niste bili tu tako da mislim da si opet u Osiguranju, a Sabo u Medijima.”
„Što!? Ne želim biti u Osiguranju. Želim biti u Sabotaži!”
Pancho se počne ponašati kao nedorasla svinja, lupajući nogom i zanovijetajući, „Hej, svi žele biti u Sabotaži, a tebe tu nije bilo. Uostalom, Osiguranje je važno, pogotovo kad u istom tjednu napadnemo isto mjesto.”
„Imaš pravo Judi. Dat ću drugima priliku, a i bit ću vrlo blizu akciji.” Pancho odluči pomoći najviše što može, te ode porazgo-varati s ostalima iz Osiguranja kad Bonkers doskoči.
„Pogodi što, ljame sutra idu s nama. Bit će u sabotaži tako da će nam pokazati neke nove tehnike!” Bonkers se smijao i Judi mu odgovori smiješkom.
„Odlično. Dobrodošli među nas!” povikne Judi u pravcu Juanite i Carlosa. Panchove se oči nakose na ionako smušenom licu. Poželi da te ljame nikad nisu došle u Špiljski kamp, no teško da se mogao žaliti s obzirom da ih je on doveo.
Pripreme za sutrašnje jutro bile su gotovo iste kao i prije neki dan, s dvije razlike: ovog je puta bilo puno više alata i s njima su bile dvije snažne ljame koje su sve to mogle nositi na leđima. Veličanstvena sposobnost njihovih novih prijatelja da nose teške i nespretne stvari niz stjenovite i uske puteljke bio je neočekivani dobitak. Na leđima su im pričvrstili i lonac za orahe, a tijekom puta i nekoliko ih je vjeverica zajahalo. Čak su i Tex i Mex odlučili da ovaj put idu s njima, jer nisu htjeli ostati sami i bez sigurne hrane. Putovali su brzo, a kad su se umorili, stanu u improviziranom kampu da razrade strategiju.
Ptice koje su čitav dan nadlijetale čistinu stalno su nosile svježe vijesti. Tijekom dana, tamo je stiglo mnoštvo ljudi, ali sada ih većine nije bilo. Ostala su samo dva čuvara. Korporacija je kupila hrpu novih strojeva, no ne i novu prikolicu, barem ne zasad. Čuvari su digli mali šator i počeli sa spremanjem večere na logorskoj vatrici.
„Ako im vatra bude gorjela i tijekom noći, moći će nas vidjeti,” reče Carlos zadivljenoj družini, „a vjerojatno hoće, jer ako imaju dva čuvara, to znači da će odrađivati svatko svoju smjenu.”
„A da ih samo zastrašimo?” upita Crveni, na što i veliki medvjed klimne glavom u znak potvrde.
„Sigurno imaju oružje”, podsjeti Pancho medvjede, „Moramo paziti na oružje.”
Odjednom gavran Quoth sleti dramatičnim spustom. Bio je bez daha, ili je možda radi efekta samo radio stanku. Kad je dobio potpuno pozornost, reče: „Imaju psa!”
„Koju vrstu psa?” upita Juanita. „Nije čiuvava!” našali se gavran, „Veliki. Velik i zao, eto kakav je!”
Životinje na trenutak promisle, a zatim tri vjeverice kuharice istupe naprijed.
„Što pas voli jesti?” upita srebrna vjeverica.
„Vjeverice!” zakrešti gavran, „i zečeve i svinje i jelene i ptice. Ne želimo ga za večerom!”
Svi se nasmijaše vjevericama i njihovim nevinim umovima. „No, kad bi mogli naći nešto što on voli jesti,” reče glavni vjeveričji kuhar Mac, „mogli bi ga omamiti. Ustvari, mogli bi ih sve omamiti.” Rekavši to, vjeverice se vrate svom tihom poslu pripremanja večere.
Životinje stanu začuđene prijedlogom. S istom mišlju u glavi, svi su promatrali vjeverice kako pripremaju večeru. Sve dosad, nisu nikad sumnjali u njihovu hranu. Nitko nije ni pomislio da bi ih one mogle drogirati.
Mac osjeti poglede na sebi i reče: „Dajte se opustite, to je bila samo ideja,” a zatim, pomalo obrambeno doda, „Nikom od vas nikad nije pozlilo od naše hrane.” Životinje se samo nasmijaše na tu krivu primjedbu. „Mislim, nitko se nije nikada razbolio ili nešto slično.” Mac je izgledao uvrijeđen pa Crveni stade u njegovu obranu.
„Mac, ti i sve kuharice ste odlični i mi vas zaista cijenimo, zar ne?” Okrene se družini koja u znak odobravanja počne zviždati i pljeskati.
„A tvoj prijedlog
pa nismo o njemu nikada razmišljali, no mogao bi upaliti.”
Vragolan i Bandit potvrdno klimnu. Ustvari, što su više o tome razmišljali, sve im se više sviđao.
„Mac, što si točno imao na pameti?” upita Crveni.
„Nisam siguran, ali šuma je puna biljaka koje mogu napraviti svašta: uspavati te, od nekih možeš halucinirati, od nekih čak i umrijeti.” Dok je tako govorila, vjeverica mekog glasa počne pucati žireve. Životinje klimnu u znak shvaćanja. Svi su pozna-vali opasne biljke i od ranih nogu naučili da ih ne diraju.
Vjeverica nastavi: „Kao što znate, ja i Flora skupljamo biljke i siguran sam da možemo spraviti nešto za spavanje.” Pogleda na okruglu, dlakavu Floru. „Sunčanica taman cvjeta,” doda, „To će nam pomoći da je lakše nađemo.”
„Tako, ako možete nekako urediti da je i ljudi i pas pojedu, prespavat će čitavu akciju.” Mac se nasmiješi ponosan na svoju ideju.
„Bit će vrlo opasno, no mogli bi im nekako u hranu ubaciti sredstvo za spavanje,” reče Vragolan, trljajući šapu i ujedno se smiješeći Riff Raffu.
„Amigos,” progovori Carlos, „Ako ćemo riskirati naše živote, i pošto nemamo oružja, trebali bi otrovati čuvare, a ne ih uspa-vati na jednu noć.”
„Si, oni su naši neprijatelji,” doda Juanita, „ako su živi, trebat ćemo se s njima boriti i sutra.”
„Oni neće oklijevati da nas upucaju svojim puškama,” složi se Pancho s ljamama, „no što s psom? Kako možemo znati da nam je i on neprijatelj? Možda je samo njihov rob.”
„Neki su psi vrlo ljubazni,” doda Sabo, no tad se upita zašto ona uopće brani jednog psa.
„U redu, drogirajmo psa, no ubijmo ljude!” poviče Bandit.
Judi istupi naprijed. „Ovakvo nasilje će nam se vratiti milo za drago. Uostalom, možda su čuvari robovi korporacije?”
„Misliš, možda bi mogli popričati s njima i uvjeriti ih da prijeđu na našu stranu?”, Pancho progunđa, „Smiješno! Ljudi su zli.”
„Slažem se u potpunosti,” reče Juanita, „njima je sebičnost u krvi. Kad bi barem bilo drugačije.”
„Svejedno,” Judi reče i dalje držeći svoju stranu, „ne trebamo se spustiti na njihovu razinu. Po čemu smo onda drugačiji od njih? Životinje mogu bolje od toga!”
Judino razborito razmišljanje ovaj put prevlada. Životinje odluče kako je najbolje da sve uspavaju. Flora i Mac otiđu pronaći biljku u cvatu čiji će korijen upotrijebiti kao sredstvo za spavanje. Nisu imali mnogo vremena, ali nađu jedan korijen, sasvim dovoljan da omami ljude. Psu će morati dati halucinogenu gljivu. Uostalom, pas nije imao pušku.
Pancho sjedne na panj prevrćući misli po glavi. Nikad prije nije razmišljao o trovanju nekoga. Smrt u žaru borbe bila je jedna stvar, ali ova unaprijed smišljena stvar bila je pomalo podla. Bilo mu je veoma drago što su odustali od hladnokrvnog ubijanja. Međutim, i dalje je smatrao da ljudski život ne vrijedi koliko i životinjski. Otkad su se pojavili, ljudi nisu ništa doli nevolja za sve životinje. „I ljudi ne razmišljaju uopće o masovnim ubojstvima životinja na farmama”, Pancho opravda svoje misli, „Zašto bi mi marili za dvoje ljudi koji stoje na putu obrani šume?” Ipak, nije htio gledati kako neko biće pati, pa makar to bilo i ljudsko. Ovako su se na neki način mogli osjećati nadmoćnijima u svojim akcijama.
Bandit i Bitanga se dobrovoljno jave za opasnu misiju. Bitanga će, kao najbrži trkač, trčati po čistini tako da ga pas počne naganjati, a za to će vrijeme Bandit usuti sredstvo za spavanje u posudu nad vatrom. Kad se pas približi Bitangi, on će ispustiti halucinogenu gljivu na pod koju će pas valjda pojesti. Tad će pričekati da droge počnu djelovati.
Mac spremi poseban sendvič od žireva u koji sakrije gljivu. Doda još soli pošto psi obožavaju zasoljenu hranu. Zatim u jedan list zamota sredstvo za spavanje.„Samo uspite to u posudu zajedno s listom,” objasni Banditu.
Većina životinja odluči ići i gledati, no Judi i Sabo ostanu s kojotima u sada prozvanom Potočnom kampu.
Planovi nikad nisu savršeni kao što se čine. Čim su se saboteri popeli na vrh brda i pogledali na čistinu, uvidješe probleme. Nije se još ni smračilo, a čuvari su već jeli svoju večeru, dok psa nije bilo nigdje za vidjeti.
„Moramo požuriti i nadati se da će uzeti još jednu porciju hrane. Idemo! Požurite!” požuri ih Carlos.
Bitanga ga pogleda; „Ali ne znam gdje je pas.”
„Bez brige, on će pronaći tebe. Imaš sendvič?”
Riff Raff se potrudio ohrabriti ostale. „Bandit, jesi li spreman?” Rakuni potvrdno klimnuše, osjećajući kako im srce užurbano lupa. Bitanga duboko udahne i potrči na čistinu. Trčao je cik-cak oko čitave opreme i trčeći prošao pokraj ljudi, no psa nigdje.
Ljudi su ga vidjeli kako trči okolo na što jedan reče drugom: „Što je tom rakunu? Zaista se čudno ponaša. Možda je bijesan, što misliš?” Naravno, životinje nisu mogle čuti što su ljudi govorili, ali su vidjeli kako jedan od njih uzima pušku iz šatora. Bitanga je i dalje trčao naprijed-natrag tražeći psa.
Zvuk pucnjave napokon probudi uspavanog dobermana koji je bio privezan za novu grabilicu. Prvi metak promaši Bitangu, ali ga zato drugi pogodi. Rakun od siline metka poleti u zrak i padne blizu grma.
Bez imalo razmišljanja, Riff Raff potrči tamo, zgrabi sendvič od žireva iz Bitangine stisnute šape i potrči za psom. Izmičući mecima, zabije hranu psu u lice i vrati se natrag na drugu stranu čistine koja mu je nudila sigurnost. „Naopako smo ovo napravili”, promisli sav bijesan dok je ponovo istrčao na čistinu odvratiti metke od Bandita koji je nosio sredstvo za spavanje. Odvraćanje pažnje uspije. Oba su čovjeka sada imali puške i oboje su uhodili Riff Raffa. Nisu ni primijetiti Bandita koji je pokušavao dići poklopac s lonca. Riff Raff primi metak u stražnju nogu te se sakrije u grmlje. Zatim istrči Vragolan. Sada je bio njegov red za odvraćanje pažnje.
Pancho stavi šapu na glavu: „O ne, ako ne pripazimo, ubrzo neće više biti nijednog rakuna.” Pogleda uokolo za psom, koji je istodobno i promatrao potjeru i lajao između svakog ugriza sendviča. Bandit spusti list sa sredstvom u lonac te pobjegne na drugu stranu, no Vragolan nije znao da je njegov drugar na sigurnom pa je i dalje trčao naprijed-nazad kao umjetna patka u streljani. „Grmlje, Vragolan, grmlje,” dovikivao je Pancho ispod glasa.
Odjednom se kiša kamenja obruši na čuvare, na što su se čuvari okrenuli i počeli pucati u tom smjeru. Crveni pruži svoju dugu šapu i zgrabi Vragolana. Pancho pogleda u smjeru odakle je došlo kamenje i ugleda ljame s ostalim životinjama.
„Bolje im je da su gladni poslije toliko vježbe,” reče Vragolan gledajući ljude, sa srcem još u grlu. I izgleda da su bili gladni. Čuvari nisu primijetili da na loncu više nije bilo poklopca. Nisu ni vidjeli list u njemu; bili su prezauzeti pričom o ludim raku-nima.
„Mislim da ne znaju razlikovati jednog rakuna od drugog,” pomisli Bandit koji je bio dovoljno blizu da im načuje razgovor. Čuvari su se mogli zakleti da su nekoliko puta pogodili rakuna. Na drugoj strani čistine, životinje se okupe oko Vragolanovog tijela. Crveni ga podigne jednom rukom, a ranjeni Riff Raff drugom te ga odnesu preko brda do Potočnog kampa. Kad se noć počela spuštati, životinje stanu promatrati čekajući da droga učini svoje.
U Potočnom su kampu očekivali tragediju nakon što su začuli pucnjavu. Bilo je previše pucnjave da bi se svi meci zaobišli. Kad Crveni unese rakune, Sabo se uznemiri. Ponovo padne u depresiju, popne se na drvo i ostatak noći provede skrivena gore.
„Plan nije išao baš onako kako smo očekivali,” tužno reče Crveni. Ostalo prepusti Judi i vjevericama. Nakon što su zavili Riff Raffa i položili Vragolanovo tijelo na posljednji počinak, pričekaju da sve završi.
Riff Raff im reče: „Mislim da se osim sabotaže ne može više ništa loše dogoditi,” i utone u san. No vjeverice su znale da je Riff Raff teško ozlijeđen i da još nije bio izvan životne opasnosti. Noć je tek počela i mnogo je toga moglo poći po zlu.
Doberman se počeo ponašati veoma smiješno, lovio je svoj rep i kotrljao se na leđima, a zatim lajao u iznenadnim navratima na ništa. Ljudi su jedva držali otvorene oči. Jedan odustane i legne pokraj vatre da zadrijema. Drugi se uspravi na noge i nasloni o drvo držeći pušku u rukama. Pokuša ostati budan, ali je sedativ ipak pobijedio. Glava mu se spusti na prsa te počne disati polagano i pravilno.
Bez ikakvog razloga pas počne kopati veliku rupu. Sunce zađe i nebo se iz narančastog pretvori u crno. Pancho je i dalje stajao na povoljnom položaju i promatrao. Vidi velikog otrcanog medvjeda kako gurka čovjeka ne bi li se uvjerio da ovaj doista spava.
Postalo je toliko mračno da se ništa nije moglo vidjeti, barem svinja nije mogla. „Evo zašto ja nisam dobar za Osiguranje,” pomisli. Tad njegov osjetljivi nos uhvati nešto. „Ljudi,” šapne Ivanu jelenu, „Mirišem ih.”
Ivan tiho dođe do Crvenog. „Ljudi! Pancho ih je nanjušio,” šapne.
Crveni pogleda uokolo, no ne uspije ništa vidjeti pa šapne natrag: „Vjerojatno ona dvojica dolje.” Ivan prenese poruku svinji, koja je sumnjala da je to.
„Možda,” pomisli, „no miris mi se čini tako blizu.” Međutim, ništa nije vidio, a ubrzo i miris oslabi.
Dolje su životinje iz saboterske grupe marljivo radile s novim alatom i pritom bile prilično bučne, vjerojatno zbog mraka. Mjesečine te noći nije bilo. Kada bi se neki stroj oborio na zemlju, čulo bi se previše lupetanja. Bonkers je svoje ključeve isprobavao na svim strojevima. Pancho mu je rekao da neće upaliti, jer da novi strojevi imaju nove ključeve, no majmun je htio voziti. Popne se na sjedalo novog teretnog kamiona te se mnogo razljuti kad mu stari ključ ne pomogne. Zatim se počne igrati s dugmadi i ručkama. Nakon što je neku ručku potegnuo posebno jako, dvije zrake svjetlosti izroniše iz prednje strane kamiona i obasjaju čistinu. Svjetlo zahvati Bitangu, Juanitu i Crvenog s jedne strane i troje ljudi s druge strane. Svi se ukipe.
Bitanga se prvi snađe i pobjegne u mrak. Juanita i Crveni primijete nešto drugo. Crveni je svoj ključ držao visoko, no i ljudi su ih isto imali. Juanita se nije bojala većine ljudi pa ih upita: „Tko ste vi?”
„Mi smo ekolozi. Došli smo tu da onesposobimo mašineriju za sječu.” Mladi bradati čovjek govorio je smireno, kao da se ne boji nikog. Ili se možda tako ponašao kako bi se osigurao od velikog medvjeda, koji se nalazio samo koji metar dalje.
„Mi smo prvi došli,” reče Crveni, „Mi ćemo to napraviti.”
„Jeste li vi to učinili i prije neku večer? Dobro ste to obavili.” Ovo je izustio neki viši glas, vjerojatno ženski.
Bonkers iskoči iz kabine na svjetlo: „Ja sam bacio teretni kamion niz brdo,” pohvali se. Ubrzo se i ostale životinje skupe na svjetlu. Ljudi odstupe malo natrag kad shvate koliko ih ima.
U Panchovoj je glavi bio kaos. Gledajući iz daljine, razmišljao je zašto životinje pričaju sa ljudima. Ili ih napadnite ili bježite!
„Koliko ima vas ljudi?” upita Crveni.
„Samo nas petero koliko nas je tu,” reče žena, na što još dva muškarca iskorače iz mraka, „Ima nas više, no večeras nisu tu.”
Juanita shvati da će onesposobljavanje biti vrlo težak posao: „Jeste li vi ljudi imali neki plan kako uništiti strojeve?”, upita ona, na što je Crveni prostrijeli pogledom.
„Pa jesmo, htjeli smo ih dići u zrak,” odgovori bradati čovjek pokazujući na dinamit u svom džepu.
„Da! Da! Da!” vikne Bonkers.
„Ne! Ne! Ne!” pomisli Pancho.
„Zar to neće započeti požar?” Pitanje je došlo od Ivana Jelena.
„Vjerojatno ne ako prvo ispraznimo spremnike s gorivom,” odgovori čovjek.
„U redu, učinimo to!”, oglasi se Bonkers.
„U redu,” reče svaka životinja zasebno, izražavajući svoje mišljenje.
Pancho se više nije mogao suzdržavati. „Ne!” vikne sa svog mjesta, „Prestanite razgovarati s tim ljudima! Oni su neprijatelji! To je nekakav trik ili nešto takvo. Ozlijedit će životinje.”
Životinje poslušaju i počnu s povlačenjem.
Tad Juanita vikne Panchu: „Mislim da je u redu. Večeras smo na istoj strani.”
„Istina je!” vikne čovjek, „Obećajem vam da nijedna životinja neće biti ozlijeđena.”
Pancho je bio nadglasan i bijesan. Izgleda da su svi htjeli da se strojevi dignu u zrak, bez obzira što će to učini njihovoj sigurnosti ili principima.
Korporacija je sad imala više strojeva nego prije nekoliko dana, što je značilo da će trebati dosta eksplozija. Doberman počne zavijati na mjesec kojeg nije bilo pa ga Crveni odluči odvezati i povesti u Potočni kamp, gdje će ga ponovo svezati dok ponovo ne dođe k sebi. Na nesreću, Crveni je vezao psa o drvo na kojem se skrivala Sabo, što je još više doprinijelo njenoj tjeskobi.
Tijekom eksplozija, Pancho ostade na svom mjestu. Sve su životinje bile upozorene da ostanu što dalje zbog bojazni da bi se dijelovi strojeva mogli razletjeti na sve strane. Prvih je nekoliko eksplozija bilo zabavno jer su bile prilično slabašne. Svi su se trudili biti pažljivi pa Pancho gotovo prestane biti toliko suzdržan. Strojevi su bili uništeni u potpunosti. Sve je bilo gotovo vrlo brzo i vrlo jednostavno (nekima je ovo pred-stavljalo posebnu zabavu).
Da bi raznijeli veliki kamion trebali su još dosta dinamita. Čovjek s bradom isprazni spremnik s gorivom i tempira eksploziju. Svi se ekolozi udaljiše, no ne dovoljno. Nitko nije znao da je kamion imao i dodatni spremnik.
Ogromna je eksplozija odbacila metalne dijelove mnogo dalje nego što su očekivali. Hauba velikog kamiona padne na bradatog čovjeka što ga ubije. Mnoge su životinje bile ozlijeđene, a jednu je, Ivana Jelena, ubio komadić motora.
Vatra proguta hrpu koja je nekoć bila kamion te se počne širiti po zemlji, slijedeći tragove benzina. Svi su se hitno trebali skloniti na sigurno. Otrcani medvjed pokupi koliko god je mogao ozlijeđenih životinja. Crveni ponese mlohavo tijelo jelena te se svi upute preko brda. Vatra je došla i do šatora u kojem je bio drogirani čovjek. Zahvatila je i njegov improvizirani krevet, ali je on i dalje spavao. Drugog su čuvara ubili leteći projektili.
Ljudi su se borili sa svojim mrtvim prijateljem kada se pojavi Carlos i ponudi da ga nosi na leđima. Namjeste tijelo kao što mu inače namještaju pakete. Carlos odvede ljude do Potočnog kampa. Ovog je puta Pancho mrzio to što je bio u pravu.
\chapter{8}
Tu su večer imali pobjedničku zabavu. Potočni je kamp bio ispunjen šapatima, čestitkama i suzama. Pancho je posvuda i svakom protestirao zbog ljudske prisutnosti u njihovom kampu. No, ljudi nisu još bili u stanju za odlazak. Jedan je bio mrtav, dvoje ranjeno, a ostalo dvoje paralizirani od straha. Saznanje o drogiranju dvojice stražara i o njihovoj smrti bilo je više nego što su mogli podnijeti.
„Za vas nitko ne zna,” reče žena životinjama, „Za sve što vi napravite, krive nas. Kad otkriju tijela tih čuvara prozvat će nas ubojicama i nitko nam neće vjerovati.”
„Možemo vam pomoći da se sakrijete,” reče Judi tužnim glasom.
Pancho joj zgrabi ruku i stisne: „Ne prihvaćaj ljude u Špiljski kamp!”
„Ima mnogo mjesta za skrivanje. Pancho, prestani me stiskati. Ohladi!” Judi je bila umorna, baš kao i svi ostali. „Ovi su se ljudi borili zajedno s nama i zajedno s nama umirali. Zbog nas su izloženi riziku. Ne smijemo biti puni predrasuda samo zato jer su ljudi.”
„Ako se s njima družimo, postat ćemo poput njih.”
„Kako znaš da oni neće postati poput nas?” odgovori mu Judi, „Zar misliš da su naša uvjerenja tako slaba da ćemo se zaraziti ljudskim ponašanjem, kao što lako zaradimo prehladu?”
Pancho pogleda oko sebe te mu pozli kad vidi da ljudi i životinje zajedno kuju planove. Međutim, ostane i posluša, baš kao što netko s morbidnom zadivljenošću gleda katastrofu. Šuplje je drvo bilo odabrano kao centar za obavješćivanje tako da bi grupe mogle po potrebi komunicirati. U jednoj od obli-žnjih špilja privremeno sakriju ljude; smrti se neće tako brzo zaboraviti. Ptice će i dalje obavještavati životinje o situaciji, vjeverice će pomagati s hranom.
Pancho dođe do travnate čistine gdje su medvjedi počeli kopati grob te im počne pomagati. Svinje su dobri kopači, bolji nego medvjedi. Fizička mu je aktivnost pomagala otjerati crne misli. Počne romantično razmišljati o sjećanjima na farmu, kao da je i on sam sudjelovao u sađenju i žetvi, a ne ih samo nadgle-dao. Mogao se zamisliti kako kopa polja za sađenje, ali ne i kako kopa grob za ljudsko biće. „Ja sam svinja s farme,” pomisli, „ne divlji vepar. Ne vidim uspješan kraj ove borbe. I sad su se s nama udružili i ljudi.”
Otpuhne prašinu sa stopala i zajedno s medvjedima stade gledati gotov grob. Pancho pomisli kako su ljudi imali čudan običaj da zakopaju svoje voljene ispod zemlje. Životinje su svoje mrtve ostavljali vani kako bi nahranili ostale, kao dio životnog lanca, kao posljednji velikodušni čin. „No, ne mogu se sakriti od crva,” promisli Pancho, „S druge strane, to je tako sebično, tako ljudski
„
Ljudi polože tijelo u rupu koju su životinje iskopale. Vragolana i Ivana Jelena polože u blizini na travnati dio zemlje pokraj potoka. Svi se okupe da vide i da plaču. Održano je nekoliko govora, no svi su bili slabi i nespontani. Pancho skine ključ sa svog vrata kojeg stavi na Ivanovo tijelo. Bonkers dade odvijač Vragolanu, a ljudi stave čovjeku u ruku jednu fotografiju. Pokriju grob prvo prašinom, a zatim travom i lišćem. Nisu ostavili nikakvo obilježje; tragači nikada neće otkriti grob. Svi zapjevaju držeći se za ruke, no još je bilo prerano da bi itko od njih bio potpuno svjestan zbilje. Još uvijek nitko od njih nije osjećao što se zaista dogodilo.
Logorska je vatra te noći bila toliko slaba da je jedva gorjela. Nikom se nije previše pjevalo, no Tex i Mex okupe životinje i ljude da poslušaju priču.
Sabo je slušala s drveta na kojem je visjela, u nemogućnosti da siđe dolje zbog psa, koji je bio vezan pri dnu. Pancho je sjedio sam, iza medvjeda, tako da nije imao pogled na ljude. Na nesreću, velika mu dlakava leđa zaklanjahu pogled i na pripovjedače. Zatvori oči i stade slušati, nadajući se da će u priči kojota biti nešto od čega bi se mogao osjećati bolje. No nije bilo.
Mex započne svojim tihim, usamljeničkim glasom:
„Život je pun opasnosti i teških izbora,” objasni kojot, „Sve mlade životinje koje se nađu u divljini odmah nauče: ne jedi tu gljivu, bježi od lovaca, ako ti noga zapne u zamku
„
„Odgrizi je,” recitirale su životinje jednoglasno.
„I moraš je odgristi ili se suočiti s mnogo gorom sudbinom: to su životne činjenice. Svijet je ponekad okrutan, događaji se mogu činiti nepravednim, a sva bića moraju umrijeti,” reče kojot i štapom malo razgali vatru. „Neke se stvari ne mogu promije-niti, no neke mogu. Život je dosta težak. Moramo zajedno raditi kako bi promijenili stvari koje možemo mijenjati, da učinimo ovaj svijet ugodnijim, poštenijim i boljim mjestom. Svatko u ovom kampu poznaje životne činjenice i svatko od nas sanja o boljoj budućnosti.”
Životinje polako klimnu. Mex ih je doista rastužio, a čitava je večer već otprije bila puna tuge.
„Nadam se da ovo što govoriš ima neku poantu,” promrmlja Crveni, „Mislio sam da ćeš nam ispričati priču.”
„Imat ćete priču,” reče Mex u obrani, „i ja uvijek imam poantu.” Zamahne užarenim krajem štapa po zraku. „Svi mi, čak i ovi ljudi, shvaćamo zašto se korporacije moraju zaustaviti. Imamo obvezu zaustaviti zlo kada ga vidimo ili smo jednako krivi kao i korporacija. Naš je motiv danas bio čist. Namjera je bila dobra. Međutim, sudbina je odigrala svoje. Svršeci nisu predvidljivi. No zar smo pogriješili jer smo pokušali? Neki od nas će reći da, no ja vam kažem da se uvijek moramo truditi da napravimo ispravnu stvar.” Kojot pogleda slušatelje koji su sada zurili u pod. Bilo je vrijeme da promijeni temu.
Tex preuzme. „Ljudi uvijek razmišljaju, oni vole ideje. Neke ideje počnu kao velike i završe kao male: Svijet je ravna površina i ako plovite dovoljno dugo past ćete preko ruba. Neke ideje počnu kao male i završe kao velike. Ideja da se napravi korporacija bila je ove druge vrste. Počela je kao mala i od tad nije prestala rasti. Ideja je započela s pokvarenom namjerom. Kako da iz posla izvučemo što veću dobit, a da pritom izbjegnemo gubitke? Već je to bilo pohlepno pitanje.Kako da radimo zločine i da zakonski izbjegnemo bilo kakvu odgovornost? predstavljalo je zagonetku grupi ljudi. Pošto su urotnici imali male mozgove, trebala im je čitava grupa koja je bjesomučno razmišljala sve dok nisu razradili vražji plan. Napravit ćemo maske od papira i izrezati na njima otvore za oči. Kad budemo nosili maske, to nećemo biti mi, već nešto sasvim drugo. Bit ćemo korporacija. Kad skinemo maske svi zajedno, svatko će od nas ponovo biti onaj svoj. Sve što radimo pod maskama bit će kao da je to napravila korporacija, a kad skinemo maske neće nas moći kriviti. Ideja jest da prema potrebi stavljamo i skidamo maske. Sada možda mislite da ova ideja ne bi nikada upalila. Da bi i životinje i ljudi odmah prozreli kroz maske i uvidjeli prijevaru. No kao u Carevom novom ruhu, nitko ne reče ništa. Zli ljudi stave svoje maske. Sada smo korporacija, rekoše, Hajdemo zgrtati novac! Korporacija odluči da brodovima donese zlato s druge strane oceana. Bio je to opasan i riskantan posao, no potencijalni je profit bio ogroman. Korporacije, trgovci pod maskama, posude novac za kupnju pet brodova koje potom pošalju preko mora po zlato. Četiri se broda vrate puna zlata. Korporacija skupi zlato i podijeli ga među zamaskiranim učesnicima. Tada zli ljudi skinu maske i vreće pune zlata odnesu svojim domovima. Peti se brod izgubio putem, napadnut olujom ili gusarima.
Ljudi ponovo stave maske da vrate novac onima koji su im ga posudili za kupnju brodova. Dugujete nam novac za pet brodova, a platili ste nam samo četiri, žalili su se ljudi koji su posudili svoj novac.
Korporacijske maske odgovore, Peti se brod izgubio zajedno s blagom i nemamo vam čime platiti.
No, što je sa svim onim blagom s ostala četiri broda? Bilo je tamo mnogo više novaca nego što ste nam vi dužni za peti brod. Tako su govorili oni koji su prvotno posudili novac.
Nemamo novaca, korporacija je bankrotirala, rekoše zamaskirani muškarci skidajući svoje maske nakon što su papir poderali u komadiće. Mi smo samo pojedinci, ne korporacija. Korporacija je mrtva i nema novaca, tako da nema više ničeg što možete dobiti. Zli ljudi odu kući svojim hrpama zlata. Ljudi koji su novac posudili nisu imali izbora. Korporacija je posudila novac, a sada je ona bankrotirala. Samo zato što su bivši vlasnici bili veoma bogati ne znači da su korporacije imale ikakvog novca.”
„To nije pošteno”, reče Crveni, „zar ne?”
„Ne, nije pošteno, ali je u skladu sa zakonom,” nastavi kojot. „Što mislite što se nakon toga dogodilo? Možete misliti da će se ljudi koji su posudili i izgubili novac žaliti da je ovo bilo nepošteno. Da će zahtijevati da se ideja korporacija zaustavi.” Životinje klimnu potvrdno, no Tex odmahne glavom. „Ono što se dogodilo bilo je upravo suprotno. Ljudi koji su izgubili novac se okupe i sami stave papirnate maske. Bili su to snalažljivi ljudi koji su vidjeli da u nošenju korporacijskih maski leži golem novac. Ubrzo su svi bogataši imali svoje maske. Ove maske nisu služile da se sakrije pravi identitet osobe iza nje, za što obično maske služe. Bilo je to samo lažno predstavljanje i svi se slože da se zajedno pretvaraju — kada čovjek nosi masku ne odgovara više za svoje dugove ili zločine.
Rijetko kada se vidi ljude kako surađuju, pogotovo oni bogati, no tad su se svi složili da u maskama leži ključ njihovih snova. U početku su životinje i siromašni ljudi obraćali malo pažnje na igru maski. Zašto bi marili? Nisu imali novaca za posuđivanje, niti zlata kojeg bi mogli prevesti preko oceana, niti kapitala da ga sakriju. Ne, oni su bili samo mornari na brodovima koji su tonuli, rudari zatečeni u obrušenim rovovima, radnici na farmi poprskani otrovom dok su želi korporacijske plodove. No, kada bi se događale katastrofe i kad bi radnici umirali ili bili ozlijeđeni, vlasnici korporacija skidali bi svoje maske i nestajali.”
„Ovo me stvarno ljuti,” reče Bonkers, skočivši na noge, „Kako mogu biti tako okrutni?”
„Želiš li znati što je još gore od toga?”, zavijao je Mex, „Zarade korporacija su privatizirane, a to znači da je svaki zamaskirani čovjek može odnijeti kući, s tim da su gubici društveni. To znači da jadne životinje plaćaju da zaštite velike korporacije od novčanih gubitaka. Siromašni plaćaju privilegiju da budu obmanuti, opljačkani i zloupotrebljeni.”
Bonkers je bio bijesan: „Što oni misle kakve smo mi naivčine? Zašto su im životinje dopustile da se izvuku s tim?”
„Životinje i siromašni ljudi su bili zbunjeni i nisu znali kako postupati prema sve većim korporacijama. U jednu su ruku korporacije osiguravale posao i bijedne plaće o kojima je ovisio opstanak radnika. U drugu ruku, čim bi se pojavila koja nevolja, i to često zbog nemara korporacije, nestajali bi među hrpom neupotrebljivih papira. Korporacije su rasle sve više, gutajući jedna drugu, stvarajući nove i moćnije saveze, preuzimajući tržište. Hrpe papirnatih maski prekrile su stolove najbogatijih. Vlada, sudovi, vojska, svi su se poklonili iz straha. Trebamo nove porezne olakšice, više slobodne zemlje! Razbijte nam udruge, dajte nam da posiječemo to drveće bez novčane naknade! molili su ljudi pod maskama. I svijet je slušao. Sve što su zaželjele, korporacije su i dobile.” Tex zastane da uzme dah. Mahne Mexu da nastavi s pričom.
„Kada nešto u prirodi počne rasti, ono zna kad treba stati. Vjeverica neće nikada biti velika kao medvjed. Tratinčica neće nikada narasti toliko velika kao i drvo mamutovca. Čak ni divovski mamutovac ne raste zauvijek. Zna kada treba stati. Kada nešto u prirodi preraste svoju mjeru i kada ne može stati s rastom, to nazivamo rakom. A svi znamo što se događa kada imamo rak. Ako ga se ne riješite, umirete. Korporacija je jedna vrsta raka koja je izmakla kontroli i koja svakim danom raste sve više. Što više čekamo da je zaustavimo, manje su nam šanse da preživimo” Mex pogleda životinje i ljude koji su ga gledali širom otvorenih očiju. „Ako imate rak koji vam raste na stopalu i ako se on počne penjati uz vašu nogu
znam da je grozno, i bolno i zastrašujuće, no što moramo uraditi da ga zaustavimo?”
„Odgristi je,” odgovore.
\textbf{* * *}
Aktivnost ponovo počne prije nego li je zora u potpunosti poništila svjetlost zvijezda. Kamp se brzo pospremio. Ljudi su bili negdje skriveni, Pancha nije bilo briga gdje. Osjećao se kao da je tijekom noći došao kirurg i izvadio mu srce.
Sabo se polako spusti niz drvo i pridruži Panchu: „Želim se vratiti na farmu.”
„Na staru farmu? Ne možemo,” reče Pancho monotonim glasom.
„Ne, na drugu farmu, onu s jabukama. Pođi sa mnom,” molila ga je.
„U redu, idemo,” složi se bez oduševljenja. Možda je to bila najpametnija ideja, iako baš nije bio siguran. Barem je bilo nešto.
Doberman se probudio potpuno zbunjen. Nije mogao vjero-vati da su mu njegove mogućnosti izbora objašnjavali zečevi otmjena glasa. Izabere da nastavi svojim putem u miru. Činilo se da nije imao nikakva politička stajališta i da je samo slijedio naredbe. Odvežu ga te mu daju neki doručak, koji je sumnjičavo onjušio prije nego što ga je pojeo. Izgledao je kao da se žuri da što prije ode, govoreći kako treba provjeriti kolika je šteta i zatim nestati.
„Ne jedi grašak u loncu,” upozore ga zečevi dok je teturao natrag. Pancho i Sabo se pridruže grupi životinja i sjednu pojesti kašu od žireva. Pancho započne opušteno: „Sabo i ja idemo u malo razgledavanje nekih od obližnjih farmi.”
Nikoga nije mogao prevariti. Juanita reče: „O bože, hoćete li
„
Pancho nastavi, „\dots{}zaliti pšenicu?”
„Naravno, nema problema,” odgovori, „Dakle, vi se ne vraćate?”
„Ne još,” reče ona, „Ali reci hola svima i ispričaj im našu avanturu.”
Judi odvede Pancha sa strane: „Znam da si uznemiren, oprosti što sinoć nisam bila razgovorljiva. Ne odlazi ljut.”
„Nisam ljut, zaista,” reče i zagrli je, „Ponekad se samo osjećam da ako se još malo prignem da ću se raspasti.”
Judi se nasmije: „Nećeš se raspasti, ali bi mogao početi plesati!”
On se nasmiješi. Zvučalo je mnogo jednostavnije nego što je bilo. „Sabo želi otići, a i meni će to dobro doći.”
Judi klimne te mu uputi dug pogled: „Neprijatelj mog nepri-jatelja je moj prijatelj,” reče.
Pancho je blijedo pogleda.
„Nije zagonetka,” našali se, „Mislim da je to jedini način da pobijedimo.” Pancho odškrine jedna od vratiju u svojoj glavi i Judi stavi šapu u taj prolaz. „Pogledaj,” objasni mu ona, „tko je neprijatelj šume.”
„Ljudi,” odgovori Pancho.
„Ne baš,” reče Judi, „Ne bih rekla da su se sinoć ljudi s nama borili ili čak da su je oni posjekli. Stvarni neprijatelj šume jest korporacija koja iz uništavanja izvlači dobit. Zapravo, vrlo malo ljudi. To nam većinu ostalih ljudi pretvara u potencijalne prijatelje.”
„Čuvari,” upita Pancho, „jesu li oni bili potencijalni prija-telji?”
„Pretpostavljam da su imali potencijal, no trebalo bi se dosta namučiti da nam se pridruže,” prizna Judi, „Samo postavljam teoriju, nešto o čemu možemo razmišljati.”
„Neprijatelj mog neprijatelja je moj prijatelj,” izrecitira Pancho, „Razmislit ću o tome.”
„Idemo,” zanovijetala je Sabo, „Bok Judi, vidimo se.”
„Ostanite u kontaktu,” odgovori mašući, dok su se svinja i mačka udaljavale niz potok.
\chapter{9}
Voda je žuborila prelazeći preko stijena u obliku kreveta stvarajući niske tonove. Vedar je dan nadahnuo ptice da vježbaju glasnice, a pridružili su se i razni insekti. Mačka je kao i uvijek hodala tiho, bez riječi, pognute glave i repa kojeg je beživotno vukla po podu. Pancho je hodao nesvjestan jutarnjeg koncerta. Glava mu je bila preteška te mu je zujanje energične mušice i njezino zalijetanje u vodu bilo poput zvuka zubarske bušilice.
Hodali su uz potok potpuno izgubljeni u mislima. Nisu ništa govorili, jer nije ni bilo ništa za reći.
Pancho baci letimičan pogled na Sabo. Pomisli kako je na putu ka novoj depresiji. Možda će joj se ovaj put i on pridružiti. Ali Pancho je bio previše ljut da bi bio depresivan. Ljut na nasilje koje je izgleda bilo dio sveukupne promjene. Ljut zato što su ljudi postali dio čuvara šume i ljut na život zato što nije išao onako kako je on planirao.
Slijedili su obalu jedno pola sata, obraćajući malo pozornosti na okolinu, kad stignu na mjesto gdje se potok račvao. Mačka prestane hodati i stade zuriti kao zombi u dva toka vode. Zapuše lagani povjetarac. Činilo se kao da voda teče u suprotnom smjeru. Bilo je teško za reći koji je od ova dva toka vode bio glavni. Pancho se nije sjećao da su prošli put naišli na ikakvo račvanje, no tada su slijedili Ivana, jadnog Ivana Jelena.
Svinja prekine tišinu: „Vjerojatno oba završavaju na istom mjestu,” reče Sabi, „Ovuda?” Pokaže blatnjavom nogom na desnu stranu. Mačka slegne ramenima i stane slijediti Pancha, kojem se odjednom jako pričalo: „Siguran sam da ćemo uskoro biti tamo. Ne mogu dočekati da kušam one jabuke. Uspjet ćemo vidjeti i ostatak farme koja je sigurno predivna.”
Dok su tako hodali Pancho je na glas sanjario o farmi pa se i Sabo počela razvedravati. Još uvijek nije ništa govorila, no rep joj se više nije vukao po podu, a i tu i tamo bi zamahnula prema nekom leptiru koji bi joj se usudio prići, tako da je Pancho primijetio da joj je malo bolje. Okolina je još uvijek bila nepoznata, ali je Pancho i nije mogao dobro upamtiti s obzirom da je na onoj farmi bio samo jednom. Još su neko vrijeme slijedili potok kad se vjetar naglo promijeni. Osjetljivi su nosevi svinje i mačke bili upozoreni na pažnju. „Psi,” proz-bore uglas, no prije nego što su mogli još jednom provjeriti miris, vjetar se ponovo okrene i sve što su sada mogli namirisati bila je obična djetelina.
„To nije mogla biti Goldie,” reče Pancho, „Miris je prejak.”
„Budi oprezan,” upozori ga Sabo.
Pancho klimne u znak potvrde, no pošto je miris nestao, nastave dalje s hodom.
Potok je ulazio u gusto grmlje što je zahtijevalo puzanje. „Popni mi se na leđa,” reče Pancho, „Bit će nam bolje ako budemo hodali kroz potok.”
Tako je sa Sabom na leđima, koja se malo prečvrsto držala za njega svojim pandžama, Pancho gazio kroz vodu i šikaru. Svinjske se nožice ne snalaze baš najbolje na klizavim stijena-ma, ali uskoro su stigli do boljeg terena. Čim je to bilo moguće, Sabo skoči s Panchovih leđa opet na sigurno tlo, ostavivši mu ružičaste ogrebotine na njegovoj bijeloj svinjskoj koži. Pancho zaključi u sebi da za Sabu više nema jahanja na svinjskim leđima pa se potom otkotrlja u vodu da ublaži bol.
„Što je ovo?” upita glasno i ne tražeći odgovor od nikog pošto ga je i sam znao. Izvuče iz vode mokru kartonsku kutiju na kojoj je pisalo „9-milimetarska municija”.
„Netko se ozbiljno dao u lov!”
„A pogledaj ovo!” pokaže Sabo ukočenom šapom na nešto okruglo u travi, „Ručna granata. Gdje smo to mi?”
Polako počnu puzati prema naprijed. Potok je naglo zaokre-tao nadesno preko malog brdašca. Kad se uspnu na vrh, vjetar se opet okrenuo. Nosevi i oči počnu zajedno raditi: čopor pasa. U dnu brda, iza velike čelične ograde, potok se ulijevao u veliko polje puno njemačkih ovčara. Ogradama su bili odvojeni u manje odjeljke; svaka je grupa pasa marširala u svojoj formaciji. S vrha brda sve se to činilo kao ples. Svinja i mačka su se osjećale dovoljno sigurno da mogu neprimjetno gledati.
„Što rade?” upita Sabo.
„Manevre,” odgovor im stigne s leđa.
Svinja i mačka skoče i ugledaju veliku divlju puricu i njezine mlade nekoliko koraka iza nje kako se provlače kroz travu.
„Vau, nismo vas primijetili,” Pancho reče pokušavajući smiriti svoje nemirno srce.
„Znam,” reče purica, „Zato tu uvijek i dolazim nahraniti svoju djecu jer se svi koncentriraju na pse, pa ne primijete ništa drugo što se oko njih događa.”
„Siguran sam da je tako,” reče Pancho ponovo gledajući čopor, „Zašto vježbaju? Zar planiraju napad ili nešto slično?”
„Vjerojatno da,” reče purica tjerajući svoje mlade uz brdo, „Mislim da im je planiranje najdraži posao. No, imaju oružje, tako da pretpostavljam da bi vjerojatno mogli nekog napasti.”
Pancho i Sabo su u strahu promatrali dresuru. Psi, sa oružjem! To je noćna mora svake mačke, a i za svinje nije baš neki sretan san.
„U posljednje su vrijeme posebno uznemireni,” nastavi ptica, „Vlasnik čopora je počeo uzgajati i pudlice. To znači manje mjesta za ovčare, a oni vole mnogo mjesta. Pogledajte tamo i vidjet ćete pudlice.”
Pogledaju te vide nekoliko malih kovrčavih životinja kako promatraju dril ovčara. Pudlice su bile odvojene od ostalih pasa snažnom mrežastom ogradom, no još su bile veoma zastrašene.
„Ove pudlice i ne izgledaju baš kao psi,” reče Sabo, „Više sliče ovcama.”
„Ali to jesu psi, baš kao i ovčari,” reče purica kljucajući sjemenke među visokom travom. „Ti psi ne znaju tko su im prijatelji, ili tko bi im mogli biti prijatelji,” zastane da prebroji mlade, „Ili tko su im pravi neprijatelji. I ne znaju baš ništa o slobodi.”
„Kako ti znaš toliko toga o ovim psima?” Pancho je uvijek bio oprezan sa strancima koji su previše toga znali.
„Ljeti tu živim i držim načuljene uši i otvorene oči.” Raširi perje na krilima kao da će time otresti Panchovu uvredu. „Psi pričaju o slobodi i pravima. No ono što oni smatraju slobodom jest da budu jedini psi u svom zatvoru. Umjesto da se pridruže pudlicama u zajedničkoj borbi protiv pravog neprijatelja.”
„Vlasnika čopora?” Pancho je slijedio puričinu crtu razmiš-ljanja.
„Naravno, za početak, ali tko je vlasnik vlasnika?”
„Korporacije?” Pancho ponudi odgovor.
Purica se nasmije: „Tako je lakše boriti se s pudlicama.”
Marš naglo prestane, te su psi sada stajali u potpunoj pozornosti onako kako to mogu samo njemački ovčari. U svakoj je skupini jedan pas lajao, a drugi su slušali. I Pancho je slušao, ali nije uspio razumjeti ono što su govorili. Odjednom su svi psi počeli lajati zajedno sve glasnije i glasnije. Sabo je morala prekriti uši, a mlade su se purice sklonile pod svoju majku. Pancho i dalje nije razumio.
„O čemu pjevanju?” Pancho vikne tako glasno da su ga svi mogli čuti.
„Životu, slobodi i slijeđenju sreće,” odgovori mu purica glasnim kreštanjem.
„Životu, slobodi, sreći? Pa i ja u to vjerujem,” Pancho od zbunjenosti protrese glavom.
„Naravno, svi vjeruju, barem svatko za sebe. Važno je da vjeruješ u to za sva bića, to je već neki napredak,” reče purica.
Pancho reče sam sebi: „Purice su mnogo pametnije nego što sam mislio.” Promatrao je kako se mekane smeđe i zlatne purice gnijezde oko trbuha svoje majke.
„Da bar nemaju to oružje,” reče Sabo, „to bi trebalo zabraniti.”
„To je dio slobode i ponekad im možda može zatrebati da je obrane. Samo bih htjela da ga upere u pravom smjeru.” I rekavši to, purica se okrene i potjera svoju mladu obitelj niz brdo.
„Čekaj, molim te, čekaj,” povikne Pancho, „Nismo se upoznali. Ja sam Pancho, a ovo je Sabo.” Sada je pseće pjevanje utihnulo i razgovor se opet mogao vratiti u normalu. „Mi smo malo skrenuli s puta. Možeš li nam pokazati put do farme s jabukama? Slijedili smo rijeku, ali nas je ono račvanje zbunilo.”
Purica se stane hihotati. „Vjetar vas je zbunio? Uvijek mijenja smjer — zbuni svakoga. Kad puše uzvodno, čini se kao da rijeka teče u suprotnom smjeru.”
Polako protrese glavom. Mlohava crvena koža ispod kljuna lelujala je djelujući vrlo hipnotizirajuće.
„No, ako dobro pogledate rijeku, ispod površine možete vidjet brzac. On je prejak da bi ga vjetar mogao promijeniti.” Purica istegne glavu kao da želi uhvatiti svinju i mačku. „Farma jabuka? Mislim da ciljate na stari Krug H. Rijeka teče ravno kroz to mjesto. Mislim, mogli bi se vratiti i slijediti lijevi tijek potoka, ali će vam biti mnogo lakše ako pratite liniju ograde u kojoj su psi. Krug H se nalazi tik do čopora pasa.” Majka napravi još nekoliko koraka niz brdo slijedeći svoje mlade. Tad baci pogled unatrag i reče: „Zovem se Emma. Još ćemo se viđati. I ne brinite se puno zbog pasa, oni vam nisu stvarni neprijatelji.”
Pancho i Sabo promatraše Emmu i njezine mlade kako nestaju u šikari pa se potom okrenu prema ogradi s psima. Usprkos umirujućem savjetu purice da se ne boje pasa, svinja i mačka izaberu teži, ali emocionalno ugodniji put nekoliko stotina metara udaljen od ove metalne barijere.
„Nema smisla da nas vide ili namirišu ako baš ne moraju,” reče Pancho s čim se Sabo složi. Držeći ogradu na oku, hodali su kroz visoku travu koja je za ovo vrijeme godine bila podosta suha i lomljiva. „Baš je čudno to što je ovakva pustošna zemlja u blizini onako plodne zemlje,” pomisli Pancho, a trbuh mu zakruli samo na pomisao o voćkama na obližnjoj farmi. „Nadam se da smo blizu,” promrmlja sam za sebe kad se počnu penjati uz brdo.
Tad primijete da ograda za pse završava na vrhu brda. Nacere se jedan drugom i ubrzaju korak te se ubrzo nađu na samom vrhu odakle im se pružao pogled na zelenu livadu, na voćnjak i na ribnjak. Bila je tamo i rijeka, koja je tekla baš onuda kuda je trebala! Dok se spuštao niz brdo nastojeći držati korak sa svojom brzom prijateljicom, Pancho obrati pažnju na zavara-vajuću narav vjetra — uvijek provjeri brzac — te se provuče ispod drvene grede ograde i pojuri za Sabom prema jabukama na podu.
\chapter{10}
Opuštajući se u hladu stabala jabuka mljackajući voće, Sabino se crno krzno sjajilo na onom suncu kao plavičasta lopta. Pancho je udisao smirenost doma i sigurnosti.
„Ali ti nisi doma,” podsjeti sam sebe, „ti si tu samo posjetitelj.” Međutim, smiješak mu se nije skidao s njuške dok je promatrao zelenilo tražeći među njim znakove koji bi mu ukazali na Goldie. Kutom oka vidi kako je nešto skočilo iza stabla kruške te stisne svoje svinjske oči ne bi li na ovom šarenom suncu uspio vidjeti što je to bilo, no od toga nije bilo ništa. Bilo mu je previše ugodno da bi se digao i počeo istraživati. „Nakon što se malo odmorimo, otići ćemo do ribnjaka,” promrmlja, „vidjeti kog tamo ima
„ i zatvori oči.
Mačke su poznate po svojoj sposobnosti drijemanja, a i svinje su isto tu negdje. Pancho nije bio samo osobiti spavač, nego i osobiti hrkač. Voćke na granama iznad njegove glave tresle su se od prodornih zvukova svinje koja spava od čega je i cijeli voćnjak odzvanjao najavljujući čitavoj farmi da imaju posjetitelje. Pancho i Sabo prespavaše većinu poslijepodneva. Sabo se u snu ritala nogama jer je usnula kako naganja miša (naravno samo iz zabave) kroz polje kamilice. A Pancho je sanjao da ga jabukama hrani okrugla ružičasta svinja koju je prije nekoliko godina upoznao na nekom natjecanju. Taman je bio kod omiljenog dijela (omiljenog sna) u kojem je čitavoj skupini zadivljenih ženki objašnjavao izvanredan plan kojeg je osmislio, kad ga probudi snažni zvižduk.
„Probudi se!” Sabo ga ogrebe kako bi naglasila svoju reče-nicu te Pancho skoči na noge i ugleda gomilu životinja oko njih. Pancho pomno prijeđe pogledom preko svih lica ne bi li ugledao Goldie, no zlatnog ptičara nije bilo tu.
Na čelu gomile su stajali namrgođeni crni ovan i isto tako namrgođena stara bijela koza. Pancho se iskesi i istegne nogu u znak pozdrava: „Bok, ja sam Pancho, a ovo je moja prijateljica Sabo.” Mačka se nevino nasmiješi, ako je to uopće moguće, te napravi jedan korak prema natrag.
„Mi smo Goldini prijatelji,” Pancho pogleda u crnog ovna da vidi je li to u redu, „i Juanitini i Carlosovi,” doda te pun nade pogleda kozu.
Koza iskorači prema Panchu i zableji: „Pa gdje su onda Juanita i Carlos? Danima ih nismo vidjeli? Što ste im napravili?” Zurila je ravno u Pancha. Po prvi put Pancho nije znao što bi rekao. „Ne želi reći, a?” okrene se koza prema gomili i najavi „Policijski agenti!” Neke od životinja zinu prema crnom ovnu, krenu prema naprijed i počnu gledati Sabo: „Što ćemo sad?”
Mačka pronađe svoj jezik: „Mi smo čuvari šume iz Špiljskog kampa. Carlos i Juanita su tamo.”
Velika se crna vunena lopta okrene prema slušateljstvu: „Špijuni iz Špiljskog kampa,” reče.
„Ne, nismo,” Pancho uzvrati, „I nismo policijski agenti. Mi smo prijatelji i Goldie nas je pozvala.”
„Vrlo zgodno,” povikne koza, „Goldie trenutno nije tu.”
Preko livade galopom dotrči svijetlo-smeđa krava ispred koje je trčala mahnita patka. „Za Božju milost!” vikala je glasno još prije nego što je došla do njih. Koza i ovan se vrate među gomilu. Kad se krava približila voćnjaku uspori u normalan hod i snimi čitavu situaciju. Svi su stajali u tišini. „Bob, što se događa?”, upita crnog ovna.
Bob nije gledao u nju, nego i dalje u Pancha s onim okrivlju-jućim pogledom: „Oni su špijuni iz Špiljskog kampa.”
„Ili policijski agenti,” poklopi koza.
Krava se okrene i pažljivo pogleda Pancha i Sabu. „Jeste li vi špijuni ili agenti?” upita ozbiljnim glasom.
„Ne” poviknu u isti glas svinja i mačka.
Krava se okrene prema gomili životinja i reče: „Kažu da nisu ni špijuni ni agenti.”
Životinje odu, no koza i Bob crni ovan se ostanu svađati: „Naravno da će reći da nisu špijuni!” Koza i ovan zakolutaju očima jedan drugom.
Pancho iznova pojasni: „Mi smo Goldini i Carlosovi i Juanitini prijatelji.”
„Gdje su Juanita i Carlos?” Koza skoči naprijed prema Panchu.
„Bore se u šumi kako bi sačuvali Špiljski kamp,” Pancho svoj odgovor usmjeri prema kravi koja se na to okrene prema kozi i reče: „Znaš da su otišli u Špiljski kamp. Što je s tobom, ti stara kozo?”
Koza kroz zube promrmlja „simpatizer” te se okrene i ode.
„Goldie će se brzo vratiti,” reče krava svim zainteresiranim životinjama. „Ako su oni njezini prijatelji, moramo se prema njima ponašati pristojno sve dok se ona ne vrati.” Pogleda ovna: „Bob, ti imaš prilično čudne prijatelje, ali ne optužuj njih za stvari koje ne znaš.” Bob progunđa i kaže nešto otprilike kako je veoma čudno da mačka i svinja putuju zajedno, pa se zatim okrene u suprotnom smjeru od koze.
„Ovo se dvoje nikad oko ničega ne slože, osim kad odlučuju o tome tko je špijun.” Krava se nasmije i pogleda ovna i kozu koji su išli svatko u svom smjeru. „Ovo je jedna od većih radosti u životu.” I zahihoće se tako slatko kao da je iz te svađe otelila dvoje mladih. Pancho se osjećao kao da su on i Sabo jedva preživjeli linčovanje.
„Oni su zapravo bezazleni, nitko ih ne sluša kad tako pričaju. Dođite, vrijeme je za jelo! Jeste li gladni?”
Mirno mukanje i njezin blagi pogled umiri nervoznu mačku, pa Pancho odgovori za oboje: „Uvijek!” i krenu preko livade prema staji.
Iako je krava hodala prilično sporo, mačka i svinja su se morali kretati duplo brže nego obično kako bi držali njezin tempo. Pancho primijeti sa stražnjeg povoljnog položaja žig na njezinom boku: Krug H.
„Oprosti,” započne Pancho.
Krava Rosy se okrene i nasmiješi: „Ja sam Rosy. Oprostite, zaboravila sam na bonton.”
„Drago nam je, mi smo Pancho i Sabo,” reče svinja, „Rosy, nisam mogao ne primijetiti taj barbarski žig. Sigurno nemate žigove na farmi?”
„Oh, ne više,” reče pogledavši žigosanu oznaku, „Gotovo sam i zaboravila na to. Kad sam bila mlađa, mislila sam ga promijeniti u cvijet ili nešto drugo, no sada ne znam, to mi je prošlost.” Krava ponovo počne hodati, no zbog manjih životinja uspori korak: „Čuli smo što se dogodilo u sinoćnjoj akciji.”
Pancho i Sabo izmijene poglede u čudu.
„Ptice,” nastavi Rosy, „jedva čekaju da ispričaju sve što znaju.” Objesi glavu i reče: „Svima nam je žao zbog gubitaka.”
„Hvala,” reče Pancho.
„Nije bilo vrijedno toga,” reče Sabo, pomislivši na to prvi put nakon nekoliko sati.
„Nemoj to nikada reći,” reče Rosy, „To je važna stvar. Zapravo, vrijedno je svega. I mislim da vaši poginuli prijatelji to znaju.”
Pancho se iznenadi na tako vojnički odgovor, od tako stare krave. Odgovori: „Zašto se ti ne pridružiš čuvarima šume ako se osjećaš tako snažnom?”
„Pa, ja sam stara farmerska životinja, vjerojatno beskorisna u divljini, više bih štetila nego koristila,” prozbori, „Uostalom, ja sam neka vrsta zaštite na farmi.”
Pogledavši mirnu livadu uronjenu u ružičasti zalazak sunca Pancho shvati zašto je to rekla: „No, zar farma treba zaštitu? Zar joj nešto prijeti?”
„Mislim da prijeti, opasnost dolazi,” reče, „No, ne večeras. Evo nas u staji baš na vrijeme za jelo.”
Staja je nekoć davno bila crvene boje, ali se tijekom vremena ogulila i sada je bila sivkasta. Kroz širom otvorena ogromna vrata Pancho ugleda razne vrste životinja koje su se komešale i pjevale spremajući večeru. Na podu je bilo sijeno, dok su bale služile kao stolovi. U posudama i košarama bilo je svih vrsta hrane, sortiranih u stilu kakvog šanka tako da se moglo svime poslužiti. Panchu i Sabi zastane dah od samog pogleda na tu raskoš.
Nakon hranjenja žirevima, ovo je izgledalo spremno za
„gladne životinje koje su imale težak dan!” Nakon što Pancho dovrši misao oprezno uđu u dvoranu na gozbu.
Sa zabatnih su greda visjeli fenjeri koji su dobro osvjetljavali stolove s hranom. Životinje se poredaju u liniju i večeru započnu salatom. Pancho na sebi osjeti da ga nekoliko pari očiju gleda te upita Rosy: „Što misliš kad bi se Goldie mogla vratiti?”
„Ubrzo, ona je tu u susjednoj mljekari. Neće propustiti jelo. Hajde, napunite tanjure,” ohrabri ih krava. I oni su upravo to i učinili. Ne baš tanjure nego velike listove kupusa pune žita, povrća, voća pa čak i meda. Čišćenje nakon jela će biti vrlo jednostavno — pojest će tanjure.
Rosy klekne na slamu i tamo počne jesti. Pancho sjedne odmah do nje na balu sijena sa Sabom u podnožju. Pancho, kao i obično, prvi završi, te stade zapitkivati: „Što je to mljekara?”
Rosy odgovori između zalogaja: „Nedjeljom imaju službe u kojoj Goldie i neke druge životinje uživaju.”
„Mislio sam da bi i ti išla s obzirom da se radi o mljekari, jer tamo uvijek ima drugih krava.” Pancho nije mogao zamisliti da bi krave mogle pričati o nečem što bi nekom psu moglo biti zanimljivo.
„Mislim da jednostavno nisam tip za druženje,” reče Rosy, „Posluži se još, nema nikoga u redu za hranu.”
Baš kada se Pancho spremao uzeti još, Goldie uđe u staju sretno se smiješeći. Pozdravi nekoliko životinja na putu prema šanku te skoro naleti na Pancha koji je uzimao još žita.
„Pancho! Kako lijepo od tebe što si nas ponovo posjetio.” Činilo se da je Goldie bila snena i daleko duhom.
„I meni je drago što si se ti vratila,” reče Pancho nesiguran da li se vratila u potpunosti.
„Današnje je poslijepodne bilo takva inspiracija,” uzdahne Goldie, „Sveta je Krava satima pričala, nakon čega smo satima sjedili u tišini i razmišljali o tome. Još ne mogu razmišljati, no radim na tome,” reče ponosno, „Stvarno bi trebali doći sljedeću nedjelju i čuti je dok govori, tako je smirena.”
„Pa, možda,” Pancho nije mislio da je to nešto po njegovom ukusu, te promijeni temu: „Jesi li čula za prošlu noć i akciju u šumi?”
Goldie klimne te Pancho nastavi: „Carlos i Juanita su dobro, ne brini, no događaj je vrlo uznemirio
Sabo
„ reče šapćući mačkino ime i usmjeri svoju glavu u njezinom smjeru, „Pa smo se pitali da li bi možda mogli ostati tu, barem na kratko.”
„Daj se pomakni, zadržavaš liniju!”
Pancho se okrene i ugleda dva mlada njemačka ovčara kako se laktovima probijaju do hrane. Pancho i Goldie napune listove i odu natrag do Rosy i Sabo, koje su pričale o vrtlarstvu.
„Mislim da su oni psi iz čopora. Pogledaj im krzno.” Pancho je mislio na čudno odrezane uši, kakve je primijetio i kod onih pasa od prije.
„Da,” reče Rosy, „oni su naši susjedi i pozvani su na jelo. Uvijek nešto donesu.” Pancho se sjeti neukusne metalne zdjele (koja je nekoć bila posuda za nošenje ugljena) na kraju šanka.
„Krave iz mljekare su također pozvane, no one nedjeljom poste.”
„Ti psi imaju oružje,” reče Pancho alarmantno, „Kako su uspjeli izaći iz te ograde?”
„Imaju tunel za bježanje,” reče Goldie, „Psi imaju također mnogo govornika. Možda će te više zanimati.”
Pancho pogleda Rosy: „Mislim da nisam baš za druženje”
Goldie slegne ramenima: „Nikad ne škodi poslušati, nekad nešto možeš i naučiti.” Rekavši to, podigne šapu i da znak dvojici ovčara da im se pridruže. Dok su mladi psi hodali prema njima Pancho osjeti slabost u želucu. Sabo se polako pomakne do bačve iza Rosy i provjeri putove za bijeg.
Psi sjednu i počnu jesti. „Pancho, ovo su Hans i Kurt.” Psi klimnuše na spomen njihova imena, i dalje žvačući. Goldie se usudi ići još dalje. „Pancho ima neka pitanja u vezi čopora. Možete li mu na njih odgovoriti?”
„Naravno, što želiš znati?” Odgovor je bio direktan, iako neprijazan.
„Pa, čuo sam da ste nesretni u tom čoporu,” mislio je kako je ovo bio taktičan početak.
Kurt nastavi umjesto njega: „I želiš znati zašto bi bilo koji pas htio biti nesretan zaključan, u tolikoj gužvari, s premalo hrane i s okrutnim vlasnicima?” Psi se počnu smijati na svoje interne šale.
„Pa, zašto ne odete?” upita Pancho.
„To je naš čopor. Tamo smo rođeni. Te pudlice nisu tamo rođene,” Kurtu počne pjena izlaziti na usta.
Hans se nadoveže: „Prije nekoliko godina svi su željeli ovčare. Radili smo kao čuvari i kao policijski psi, čak smo bili i kućni ljubimci. Zahtjevi su bili veliki, a uzgajatelji puni posla. No, električni su nas alarmi doslovno izbacili s tržišta čuvara dok se tržište kućnih ljubimca uglavnom prebacilo na
mačke.” Oči mu slete na Sabu, na što se njoj dlake naježe. „Vlasnici čopora su tvrdili da propadaju. Rekli su kako sve treba rekonstruirati,” posljednje je riječi izgovarao kao da su mu usta bila puna čavala, „Tako smo se mi morali stisnuti kako bi napravili mjesta nekim pomodnim pudlicama. Ali, zamisli, ni one se ne prodaju!! Hans zastane da proguta ostatak tanjura te upita: „Što je za desert?”
„Pite, mislim,” reče Rosy.
„Odlično,” psi pogledaju liniju koja se već stvarala za desert pitajući se jesu li odgovorili na dovoljno pitanja.
„Što se dogodi ako vlasnik bankrotira i posao propadne?” upita Pancho.
„Ne znamo i ne zanima nas!” odbrusi Hans.
„Ali stvarno,” reče Pancho, „Mislim, što ako se to dogodi?”
Nekoliko trenutaka zavlada tišina. Čak se i Goldie nagnula malo bliže, kad je Pancho nastavio: „Kome vlasnici duguju novac? Jer njima će pripasti čopor.”
„Bankarima,” reče Kurt.
„Korporaciji,” reče Rosy.
„Kako korporacija izgleda?” upita Hans koji se nije sjećao da je ikada vidio korporaciju.
„Teško je to reći,” reče Rosy, gledajući Pancha tražeći potporu.
„Vrlo su lukavi i uvijek mijenjaju oblike, tako da je veoma teško reći s kim imaš posla,” improvizira svinja.
„Pa, kako se onda možeš boriti protiv njih?” upita Kurt, „Znate da mi imamo oružje!”
Pancho se ugrize za donju usnu i protrese glavom: „Ne znam.” Pogleda Goldie i Rosy koji također protresu glavom.
„Borit ćemo se protiv korporacija, bez obzira kako velike bile, zar ne Kurt?” reče Hans i uputi se prema stolu s desertom. Kurt je svoj apetit izgubio.
Sabo započne razgovor sa zecom po imenu Pahuljica te mu stade pričati o avanturama čuvara šume. Ubrzo se oko nje okupi čitava skupina životinja koje su htjele slušati o hrabrosti i tragediji. Dok je pričala dio o Ivanu Jelenu i kako je on umro, većina je slušača bila sigurna da ga je vidjela kad ih je on posjetio na farmi. Sabo se osjećala bolje dok je o tome govorila.
Poslije večere životinje počiste hranu, a koze i mlađe životinje poslože bale sijena, mičući sve iz sredine staje. Na jednom je kraju staje bila pozornica. Pancho se nasmije kad se nekoliko životinja s instrumentima domaće izrade popne na nju. „Zar ćemo imati glazbu?” upita.
„Naravno, i pjevanje i plesanje,” odgovori Rosy na njegovo zadovoljstvo. Već dugo nije čuo pravu glazbu, ako ne računa bubnjeve i kojote u Špiljskom kampu. Na bini su, naravno, bili sudoper i lavabo. Osim toga bilo je i vrčeva za puhanje, zvona za udaranje, mnogo raznih pomagala koja su služila kao udaraljke, od bačava do vjedara, i nekoliko flauta napravljenih od trske. Pancha najviše zadive pametno iskorištene tikve: naravno, najviše ih se treslo, no neke su bile izdubljene, osušene i sa žicom, tako da su veoma sličile gitarama. Kad bi se svirale kao gusle (ako bi zatvorili oči i pretvarali se) zvučale su kao violine!
Bend se gomilao i gomilao dok gotovo sve životinje nisu bile na pozornici. Nakon malo premještanja i gurkanja, bili su spremni.
„Uvijek počnu s istom pjesmom,” nagne se Rosy prema Panchu da mu objasni, „Tako uštede na svađi. Uvijek se svađaju oko druge pjesme.” Nasmije se. Orkestar počne svirati struganjem i cviljenjem:
<em>Stara Margaret imaše farmu
E I E I O<\Slash{}em>
Bila je to duga verzija s tim da je svaka životinja imala svoj stih. Oni koji nisu imali instrument su ili plesali ili se bacali na pod. I, baš kao što je Rosy predvidjela, nakon posljednjeg \emph{EIEIO}, započnu prepirke oko druge pjesme.„Stara siva kobila” pobijedi „Puricu u slami”.
„Ovo je zaista zabavno,” reče Pancho okrenuvši se prema Goldie. Odjednom ostane kao očaran. Tamo na „podiju” plesala je najsavršenija, ružičasta, okrugla svinja koju je ikada vidio. Imala je lančić od tratinčica i najslađu njuškicu na svijetu. Ispostavilo se i najvlažniju. Bila je to ljubav na prvi pogled. Pancho posegne za svojim repom da ga još malo zakovrča i tad s najšarmantnijim smiješkom sklizne preko do nje.
„Bok, kako si?”, nakloni se Pancho malčice, „Mogu zamoliti za ovaj ples?” Svinja pogleda oko sebe i reče: „Zašto ne?”
Pancho se osjećao to veče kao da svinje mogu letjeti. Bend je svirao „To je samo mladenačka ljubav” kad joj on uzme nožicu i dovede je na plesni podij.
„Mene zovu Pancho,” reče.
„Suzy,” bio je njen odgovor.
Pancho u mislima prevrti ime. „Suzy”, kakvo prekrasno ime za prekrasno stvorenje. Dok su se njihali uz glazbu gledao je ravno u njene male oči. Grickao joj je uši kada bi glazba usporila osjećajući toplinu njenog tijela. Ovo je bila sigurno najčarobnija večer u njegovom životu. Kad je bend napravio stanku, izađu van iz staje malo na zrak.
„Suzy,” Pancho je bio gotovo nijem, „Nikad se nisam ovako osjećao.” Srce mu se samo otkrivalo od njezine ljepote, „Volim te, želim zauvijek biti s tobom.”
Suzy ga je blijedo gledala.
„Znam da je sve vrlo iznenada,” objasni Pancho, „no kad znaš da je nešto to
„
Suzy spusti glavu i nogom udari o prašinu na podu.
„Jesam li te uzrujao? Oprosti Suzy, ali molim te reci mi da i ti osjećaš isto.” Pancho je sada bio na koljenima i držao njezinu nožicu među svojim debelim nogama.
Suzy izvuče svoju nogu iz njegovom zagrljaja. „Oprosti Pancho, ti si vrlo drag, ali..” slegne ramenima i lančić od tratinčica joj sklizne s vrata, „Mene ne zanimaju muške svinje.”
Pancha probode u trbuhu kao da ga je netko udario nogom. „Kako to misliš Suzy?”
„Ne hodam sa muškarcima. Volim žene.” Okrene se kao da će otići te preko ramena tratinčica doda: „Ništa osobno” i nestane u noći.
Pancho ostane stajati u mraku. Uvijek je on bio taj koji je kontrolirao svoje osjećaje, ali večeras su oni kontrolirali njega, i još nisu bili gotovi. Srce ga je boljelo, glava lupala, noge otežale, a oči se napune suzama. „Svijet je kaos, moj život nema smisla i totalno sam zbunjen!” Pancho povikne prema Mjesecu. Sjedne na zemlju i stavi glavu među noge. Pripremi se da se dobro isplače, osjećajući kako mu baš to treba, kad se bez ikakva razloga počne smijati. Počelo je kao hihotanje da bi završilo grohotom. Ubrzo se našao kako se valja po prašnjavoj zemlji, držeći se za trbuh od smijeha. Sve o čemu je razmišljao natjera ga na još više smijeha. Psi s oružjem, to je tek sad bilo smiješno. Korporacije koje su uništavale šumu izazivale su mu histeričan smijeh. No posebno glupa svinja koja je sebe ozbiljno shvatila, misleći da može promijeniti svijet. Smijeh je dopirao do ostalih gotovo kao i njegovo hrkanje, te ubrzo Sabo, Goldie, Rosy i par ostalih životinja (uključujući Boba, crnog ovna) dođu vidjeti što je to tako smiješno.
Goldie se primakne bliže kotrljajućoj svinji i stavi šapu na njegov trbuh: „Pancho, jesi li u redu?”
„Što je tako smiješno?” upita Sabo.
„Ja,” zarokče Pancho kroz smijeh, „Ja sam nevjerojatno smiješan, a i ti si.” Rekavši to, sjedne uz ogradu i počne hihotati sam sa sobom.
„On je lud,” zaključi Bob.
„Nije!” Sabo glasno obrani svog drugara, „Jesi li Pancho?” doda ne tako sigurna.
„O da, definitivno sam lud!” reče svinja te se počne tako jako smijati da mu niz lice sklizne par suza. Okrene se prema Goldie koja se neko vrijeme suzdržavala, ali više nije mogla izdržati. Smijeh je obično zarazan, posebno onaj svinjski. Ubrzo se zaraze i Sabo i Rosy. Ne zadugo i djeca se počnu cerekati jedan drugom da bi se na kraju čitava staja pretvorila u zonu besplatnog smijeha za sve.
Bobu nije bilo zabavno: „Netko je nešto ubacio u punč, vjerojatno travu ludaru,” promrmlja za sebe i zabilježi nešto u svoju malu knjižicu koju je uvijek nosio sa sobom. No svi ostali izađu iz staje, zajedno s instrumentima, kako bi se zabavili.
Pancho se umori od smijanja i gotovo zaspe u dvorištu pa ga Goldie odvede u gostinjsku pregradu u staji. Tamo se ispruži i zaspi zajedno sa sklupčanom Sabom, sve do jutra.
\chapter{11}
Kad je svinja otvorila oči, jutro je već skoro bilo prošlo. Zbog umjetnog zraka u staji prespavao je poziv na doručak. Probudio se tek kad je čuo mazgu kako grabi slamu u štali. Ustane, protegne se i zarokče jutarnjim zijevom.
Jethro, starija sivkasta mazga, provuče glavu kroz otvor na drvenoj letvi: „O, ti si tu. Nisam znao da ikog tu ima,” reče, uglavnom za sebe, i nastavi s grabljenjem.
„Mislim da sam se prenaspavao,” reče Pancho posramljeno trljajući oči.
„Izgleda da ti je sinoć bila posebna večer, ili se bar samo tako činilo,” Jethro se nagne prema slami i zahihoće: „Čemu si se uostalom onako jako smijao?”
Svinja se pokuša prisjetiti prošle večeri. „Mislim da se ponekad treba ili smijati ili plakati,” reče naposljetku, „Sinoć sam se smijao. Ali, znaš da se danas osjećam odlično. Mnogo lakše!” Panchu je bilo drago što je to bila istina. Nekoliko puta udahne duboko. „Da, moram prestati pričati tako ozbiljno.” Nasmiješi se mazgi koja je stala nagnuta prema slami.
„Pa to je dobro.” Jethro otegne rečenicu i stane i dalje gledajući u Pancha. Napokon nastavi: „Ako ti ne smeta, htjela bih počistiti staju.”
„Naravno, oprosti.” Pancho se makne s puta kad je mazga počela skupljati slamu s mjesta koje je upravo napustio. „Je li to tvoj posao?” upita Pancho dok je gledao kako radi.
„Pretpostavljam da jest,” reče mazga kupeći i zadnju slamčicu iz kuta, „Volim čistiti, pa to i radim.” Skupi sijeno na veliku hrpu u sredini prostorije, „I to mi dobro ide.” Nasmije se pogledavši prazan pod u pregradi i prijeđe u drugu.
Odjednom se Pancho sjeti kako je obećao da će zaliti pšenicu. „Mislim da idem van na svjetlo. Drago mi je što smo se upoznali.”
Mazga klimne i dalje skupljajući: „Također”.
Pancho gurne velika drvena vrata i stavi šapu preko očiju da ga svjetlost ne zaslijepi. Nebo je bilo boje suncokreta i oblaci su imali oblik
Pudlica? Pitao se gdje su svi nestali. Nije još otišao u formalni obilazak te se sam uputi u razgledavanje.
Na desno od staje bile su manje građevine: kokošinjci, zečje kućice, kućica za koze, svinjci i neke druge ručno izrađene nastambe koje Pancho nije mogao prepoznati. „Ono izgleda kao Goldina kuća.” Stade gledati u tipično pasju kućicu, napravljenu od drva i s lukom na vratima. S prednje strane, kao i sa strane, cvijetovi se penjahu prema krovu. Tad pobliže pogleda druge domove. Svaka je bila napravljena, obojena i uređena da što bolje služi onima koji su ih nastanjivali. Pancha privuče svinjac i primijeti kako je pažljivo bio dekoriran — prolazi su bili izrezbareni i obojani. Blatnjava je kada bila ogromna i izgledala je jako udobno, smještena uz jedan rub svinjca i obrubljena okruglim sivim kamenjem. Na drugoj su strani bile bale sijena i lavanda slatkog mirisa razbacana po pometenom podu.
Zureći u prazan svinjac sjetio se Suzy: „Ovdje smo mogli biti tako sretni,” uzdahne, „no, na žalost, nije nam bilo suđeno!” Pancho je hodao uokolo po staji prema maloj trošnoj građevini. Kad se približi, začuje zveketanje stroja. Prozori su bili prekri-veni, a vrata dobro zatvorena, ali je Pancho mogao namirisati tko je unutra.
„Mirišem vunu, kladim se da je to Bob, crni ovan.” Pancho je stajao tako par minuta ne znajući da li da pokuca. Baš je bio odlučio otići, ne želeći si pokvariti dan neugodnostima, kad do njega dotrči koza glasno blejeći: „Sad sam vas uhvatila! Šuljaš se oko naše nastambe! Znala sam da si špijun!”
Vrata se počnu otključavati iznutra i napokon se otvore. „Čangrizalo, što se događa?” upita ovan, „Još nije tvoj red.”
„Uhvatila sam ga kako špijunira i jest moj red.” Činilo se da nisu znali oko čega bi se svađali.
„Ovo je samo jedan od tvojih trikova Čangrizavice. Pa neću na njega pasti!” Bob počne zatvarati vrata, no koza prije toga podmetne nogu u vrata.
„Moj je red. Podne je. I on je njuškao okolo. Tko zna što je vidio!”
Pozornost se ponovo usmjeri na svinju. I ovan i koza ga pogledaju škiljavim očima. „Što si vidio?” upita Bob prijeteći.
„Ništa!” Pancho nije mogao vjerovati što čuje. „Vrata su bila zaključana i rolete spuštene. Samo sam čuo\dots{}” Da bar to nije rekao!
„Što si čuo?” Koza se nagne prema svinji s prijetećim govo-rom tijela, no miris mu je zapravo predstavljao pravu prijetnju.
Pancho ustupi natrag: „Ne znam. Stroj. Možda pumpu.”
„Ha!” Čangrizalo i Bob izmijene značajan pogled. „Ti misliš da si čuo pumpu! Pa nisi baš neki špijun, zar ne? To uopće nije pumpa, već štamparski stroj.”
Bob se ljutito okrene prema Čangrizalu: „Zašto si mu rekla da imamo štamparski stroj? Mislio je da je to pumpa. Vratio bi se natrag u kamp i rekao im da imamo pumpu i onda bi imali krivu informaciju, ali sada zna. Moramo ga ubiti.”
„Ti ga ubij,” reče koza, „Na meni je red, pusti me unutra.” Gurala je vrata, no crna se vunena lopta nije baš dala lako pomaknuti.
„Još nije vrijeme. Došla si pet minuta ranije i to smo potrošili na svinju. Stoga uzimam još pet minuta.”
Pancho iskoristi njihovu zauzetost prepiranjem da pobjegne. Otrči na drugi kraj staje preko hrastovog luga sve do puta koji je vodio do dva kamena stupa. Pancho provjeri da li ga je netko slijedio, pa kad se uvjeri da je na sigurnom, nasloni se na vrata od kovana željeza da uhvati dah. Pogledavši u zrak ugleda natpis urezan u metalu poviše vrata: Krug H.
„Mora da su ovo ulazna vrata,” primijeti. Izgledala su prilično neodržavana za razliku od ostalih dijelova koje je dosad posjetio. Oko vrata rastao je korov, pokazujući jasno da ih nitko nije otvorio već neko vrijeme. Lokot i lanac držali su zavezane metalne prečke na vratima. Pancho je uspio vidjeti natpis na kamenom stupu. Stisnuo je trbuh ispod vrata da pogleda malo bolje. Pisalo je:
AUKCIJA ZA FARMU
ZEMLJA, OPREMA, STOKA
SUBOTA, 10. LIPNJA, U 8 SATI
SVE SE MORA PRODATI
Pancho triput pročita. Nije znao kada je 10. lipnja jer u šumi nije imao potrebu za datumima, no činilo mu se da je to vrlo skoro. „Pitam se znaju li životinje za ovo. Znam da neke znaju čitati.” Panchova se lakša, osjećajnija strana sada počne topiti. Ponovo se uvuče na unutarnju stranu farme i počne tražiti ostale. Svinja se polako vukla po putu te prođe pokraj stare žute farmerske kuće za koju zaključi da je vjerojatno bila Margaretina. Nastavi preko stražnjeg dvorišta pa pokraj dobro očuvanog vrta sve dok ispred sebe nije vidio farmu.
Dosta je životinja baš tad imalo svoju popodnevnu pauzu i grickalo vinovu lozu. Pancho je propustio doručak i sad osjeti kako ga trbuh vuče prema komadima kukuruza, no glava mu je i dalje tražila poznata lica. I tad ugleda Rosy s njenom novom prijateljicom Sabom kako sjede pokraj krumpira.
„Pancho! Pa bilo je i vrijeme! Jel se danas osjećaš bolje?” upita ga Rosy prijateljskim tonom.
„Pa i da i ne,” odgovori Pancho, „Mislim, osjećao sam se super, ali\dots{}” i sjedne tik do krave i mačke, „Znate li za aukciju?”
Krava zbunjeno pogleda. Pancho nastavi: „Na prednjem stupu postoji oglas. Farma i sve na njoj, uključujući životinje, će biti prodana na aukciji 10. lipnja. Koji je danas datum?”
„Ne znam. Jučer je bila nedjelja, danas je ponedjeljak.” Sabo reče, „Mislim da je to ovaj tjedan.” Brojala je na šapi: „To je onda ovu subotu.”
„Mislim da treba sazvati sastanak,” reče Rosy jako ozbiljno.
„Da!” Pancho osjeti da mu se povisio krvni tlak, „Nemamo ni minute za gubljenje.”
Rosy snažno zatrese glavom i zvono se oglasi. Životinje stanu s radom i igrom te se umire da čuju najavu. „Sastanak na ribnjaku, odmah sad.” Rosyn je glas bio prodorniji nego što je Pancho očekivao. Čak su i Čangrizalo i Bob došli, naravno svađajući se putem.
Ugledaju Pancha koji se smijao i mahao im stojeći pokraj Rosy. Ona ih upozori: „Ne sada!” i oni poslušaju. Goldie dođe kasnije nego ostali jer se morala pobrinuti za piliće i čuvati ih dok se to pahuljasto jato nije spustilo niz brdo, posebno pazeći da putem ne izgubi nijednog. Na putu do ribnjaka Pancho zgrabi klas žita i mumljajući ga sjedne čekajući da počne sastanak.
Rosy upita: „Čiji je red da vodi sastanak?” Ovo izazove malu pometnju sve dok se na sredinu podija nije dogegala debela guska.
„Ja ću paziti na vrijeme,” poviče smeđe janje koje je baš pobijedilo na igri en-ten-tinija.
Pancho pogleda Rosy: „Ovo bi trebalo biti ozbiljno.”
Rosy zazvoni zvonom i guska lupi štapom o stijenu.
„U redu, počnimo s pjesmom!” Guska ispusti svoj krik, očito ponosna što je glavna. Životinje podignu šape i uzvrate kriko-vima i parolama.
Pancho zakoluta očima i moljakavo pogleda Rosy, koja slegne ramenima i reče: „Jedna pjesma, zar to može škoditi?” Pridruži se ostalima u morbidnom zboru: „Bila jednom jedna stara žena koja proguta mušicu.” Ta je pjesma bila hit otkad je postojalo pravilo da se moraju nabrojiti sve prisutne vrste životinja. Bez glazbene pratnje pjesma je bila malo bezlična, oštra i bez ritma, no kada je došla do posljednje strofe „Bila jednom jedna žena koja proguta konja i potom umre” čitava livada zaori od grohota. Panchu je ovo bila vrlo neprikladna pjesma s obzirom na sve.
Dok su životinje predlagale slijedeću pjesmu, Rosy nešto prišapne guski koja podigne obrvu pogledavši Pancha i udari štapom: „Čini se da nam svinja ima nešto za reći,” najavi nesve-čanim tonom na što gomilom zavlada gunđanje.
Na pozornici Pancha uhvati trema. No izusti: „Tu sam samo posjetitelj i ne poznajem vas baš dobro, ali danas sam išao malo uokolo i razgledavao farmu\dots{}”
„Špijunirao!” povikne Čangrizalo odnekud straga.
„Ne, samo sam razgledavao.”
Guska je morala jako udariti štapom o stijenu kako bi ušutkala životinjski šapat. „Svinja ima riječ”, reče guska i pruži mu štap, „I štap za vođenje sastanka.”
Sva je pozornost odmah bila usmjerena prema zbunjenom Panchu koju iznova počne: „Na kamenom stupu postoji oglas prema kojem će se ubrzo na ovoj farmi održati aukcija. Oglas kaže da će se prodati zemlja, oprema i stoka, a to znači vi, i to u subotu 10. lipnja u 8 sati ujutro.”
Nastupi tišina. Nisi mogao čuti ni disanje. I voda u ribnjaku bijaše potpuno mirna. „Mislimo da je 10. lipnja ovu subotu.” Duboko uzdahne i shvati da je to bilo sve što je imao za reći. Zatim preda štap natrag guski.
Jadna guska nije znala kako nastaviti sastanak te ostane stajati držeći štap. Vijest ubije životinje.
„Vrijeme!” reče janje, uživajući u tome što može biti od pomoći, i to doista jest vratilo gusku iz razmišljanja. „Da, bitno je vrijeme,” reče, nesigurna što to točno znači. Ipak, zvučalo je službeno. Tad se u zrak digne kopito.
„Da, Bob.”
„Želim da mi svinja pokaže oglas,” reče Bob polako i ozbiljno.
„Svi ga želimo vidjeti,” Čangrizalo nije htjelo biti izostav-ljeno.
Sve su životinje htjele vidjeti za sebe i Pancho ih povede do ulaznih vrata.
„Istina je da nikad ne idemo tamo,” reče guska, „Možda to tamo stoji već duže vrijeme.”
Rosy klimne s ozbiljnim izrazom lica. Nisu se sve životinje uspjele progurati ispod vrata, a one koje su mogle ne uspiju sve pročitati. Međutim, vide dovoljno da shvate kako je ono bila istina.
Naposljetku, Goldie progovori: „Ne znam što nam je činiti, no možda o ovome možemo razmišljati nakon što obavimo svatko svoj zadatak, te se poslije večere sastanemo u staji.”
Izgleda da se drugima svidjela ova ideja te se odmah vrate na posao. Pancho pomisli kako rade upornije nego inače, možda zbog straha. Nakon što je zalio pšenicu kao što je i bio obećao, i pomogao pokupiti kruške, što je uvijek volio raditi, odšeta do staje. Na putu ga presretnu Čangrizalo i Bob. „O baš super, što sad?!” pomisli Pancho.
Koza se približi: „Bolje za tebe da nisi špijun,” upozori ga.
Bob je prekine: „Svi znamo za tebe i za onu tvoju farmu. Tvoji te vlastiti drugari optužuju za izdaju. Otjerali su te!” Napravi pauzu te nastavi: „No, znam da lažu o mnogo toga i ne sviđa nam se što se tamo događa,” zastane opet, što Čangrizalo iskoristi: „Izgleda da tamo jest oglas, no zašto bi ga tamo stavili? Ti si ga prvi vidio? Zar ti to nije sumnjivo? Promatramo te!” I snažno zatrese svojom bradicom.
„U redu, pazite na mene,” reče Pancho frustrirano, „Ja nisam špijun. Samo ne želim da zbog ljudi izgubite ovu predivnu farmu!” I rekavši to ode u staju, ostavljajući ovna i kozu da pričaju ispod glasa.
Mazga Jethro je uređivala buket grahorica u nekom starom ćupu. Pancho primijeti kako je ova staja mirisala ljepše nego bilo koja u koju je ikad ušao. „Zaista paziš na ovo mjesto,” da kompliment mazgi, kojoj je izgleda ovaj komentar veoma godio.
„Pomaže što većina životinja spava vani kada je lijepo vrijeme. No, za kišnog je razdoblja druga priča.” Jethro se na sekundu nasmiješi te se opet uozbilji: „Dakle, Pancho, što ćemo mi s tom aukcijom?”
Pancho sjedne na balu sijena. Osjećao se starim i umornim i bez ideja. Jethro mu doda malo vrućeg čaja u starom limenom vrčiću. „To ti je kamilica. Smiruje živce.”
„Hvala, to mi i treba,” Pancho uze jedan gutljaj. Mazga skine neku paučinu s greda, a zatim sjedne do svinje.
„Ti imaš nešto iskustva vezano uz ovu
„ mazga je tražila pravi izraz, „\dots{}situaciju. Kako je tvoja farma to riješila?”
Pancho je udisao paru iz čaja i uzdahnuo: „Borili smo se,” reče svinja.
„I pobijedili ste,” podsjeti ga Jethro.
„Da, pobijedili smo i izgubili također,” sjeti se svinja pobune, „Velika je to odluka. Dosta mi je nasilja, ali ponekad\dots{}” ostavio je to postrani.
Mazga si uspe čaja i dolije još u Panchovu polupraznu šalicu. „Možda postoji drugi način,” reče optimistično.
„Nadajmo se”.
Dok su tako sjedili u tišini i pijuckali čaj, Pancho je gladio mazgu po ramenu. Kad su završili, Pancho joj pomogne urediti staju za večerašnji važan sastanak. Mazga je ponovo posložila bale u krug, a Pancho je pronašao neka stara vrata i malo papira za umatanje mesa, koji će dobro poslužiti pri planiranju. Našao je i žutu olovku koju je trebalo malo zašiljiti i jednu kemijsku bez čepa. Iako ovo nije bila njegova farma, a situacija prilično ozbiljna, Pancho je čitavo vrijeme radeći pjevušio neku melodiju. Zaista je volio planirati sastanke.
„Pancho, jesi li gladan?” upita ga Jethro kad su bili gotovi.
„Naravno,” Pancho pogleda uokolo, „Gdje je večera?”
„Pa, ne jedemo svi uvijek zajedno! Različite životinje vole različitu hranu,” pokaže mazga na svoj trbuh, „Ja najviše volim zob, a ti si dobrodošao ako mi se želiš pridružiti, iako bi možda više volio otići u vrt i uzeti ono što voliš.”
„Mislim da ću to učiniti,” odgovori Pancho i krene prema vani. Volio je zob, ali je svježi kukuruz kojeg je probao za ručkom stvarno obožavao, a možda je čak htio i malo jabuka za desert. Sunce je već zalazilo iza brda. Pancho je išao ravno prema kukuruzu, koji je za ovo doba lipnja bio prilično velik, te izabrao najveće klasje koje je mogao naći.
„Bok, Pancho,” glas ga probode poput bodeža.
„Bok, Suzy,” zamucnu, i padne preko kukuruza koji je ispu-stio. Kad se nagnuo da pokupi klasje koje mu je palo na zemlju, Suzy mu ponudi svoju košaru.
„Oprosti ako sam ti sinoć davala lažne signale.”
„U redu je, nema veze.”
„Prijatelji?” ispruži svoju desnu šapu.
„Naravno, prijatelji,” Pancho ispruži svoju i dodirne njenu, ali očima izbjegne njen pogled.
„Hoćeš li doći na večeru? Ja kuham.”
Suzy je zaista znala put ka svinjskom srcu.
„Naravno, zašto ne.” Pancho je dugo žudio za društvom svinja. Zajedno su sakupili povrće za kuhanje te malo voća za poslije.
„Koliko je svinja na ovoj farmi?”
„Tri,” odgovori Suzy, „Sve žene.”
„Nema muškaraca?”
„Samo ti,” zadirkivala ga je.
Pancho oprezno nastavi: „Zašto samo žene?”
„Pa, moj je tata bio jedini muškarac, a on je lani umro,” reče tužno.
„Žao mi je,” reče Pancho i na putu ka svinjcu shvati da je pitao dovoljno pitanja.
„Mama, ovo je Pancho. Pozvala sam ga da jede s nama.”
„Dobrodošao u naš svinjac.” Velika se pjegava svinja nasmi-ješi Panchu, „Nadala sam se da ćeš svratiti.” Požuri ga je do blatnjave kupke i Pancho, u skladu sa starim svinjskim bonto-nom, sklizne unutra.
„Aa, ovo je predivno. Odavno se nisam dobro uvaljao.” Osjećao je kako mu mekano blato njeguje tijelo. „Zar mi se nećete pridružiti?”, upita svinju.
„Ja sam upravo izašla,” reče Suzyina majka.
„A ja spremam večeru. Slobodno se raskomoti”, reče Suzy dok je gulila kukuruz. Stara je svinja sjedila sa strane i proma-trala Pancha kako uživa u kupki.
Pancho pristojno započne razgovor: „Suzy mi je rekla za vašeg supruga. Vrlo mi je žao, gospođo.”
„Molim te, zovi me Marta,” nasmije se zbog formalnosti, „Da, George nam jako nedostaje. Znaš li da se on mnogo divio tvojoj farmi, ustvari oboje smo se divili, barem u početku.” Pogled joj odluta dok se tako prisjećala. „Kad smo bili mladi, pričali smo o odlasku tamo, da vam se pridružimo, prije nego što su nastupili problemi.” Ponovo pogleda svog blatnjavog gosta. „Vi ste zaista nanijeli ljagu na svinjsko ime.”
Pancho odjednom osjeti potrebu da se brani. Činilo se tako nepravednim da ga osuđuje netko izvana. Lice mu se zacrvenilo, ali je držao jezik za zubima sve dok se nije ohladio i smirio. Marta je mogla jasno vidjeti da je ljut. „Znam da ste imali dobre namjere, ali to je ono što moć čini,” slegne ramenima, „Treba kriviti i druge životinje. Predali su vam odgovornost, a vi ste je uzeli.”
Pancho utone u blato dok mu njuška nije sama izronila. U hladnom je mraku prebirao po mislima. „Svi misle da je zabavno donositi odluke i nositi se s problemima. Čitavo sam se vrijeme brinuo za dobro farme. Nemam obitelj, a ni svoj život.” Zaronio je još dublje. „Nisam ga barem imao dok nisam pobjegao i napokon dobio priliku da pomislim na sebe. Vjerojatno je to bio najsretniji dan u mom životu.”
U blatu se Pancho napokon oprostio od svoje stare farme. Marta je namjestila stol za četvero. Pancho pogleda uokolo tražeći druge svinje. „Sally opet kasni,” reče Suzy vrteći svojom lijepom glavom, „Ona je učiteljica u školi i ponekad ostane jako dugo da pomogne učenicima pri čitanju.”
Pancho pažljivo formulira svoje pitanje: „Je li Sally
tvoja prijateljica?”
Suzy prijeđe preko njegove aluzije i reče: „Ne, ona je moja sestra.”
„Blizanke,” reče Marta ponosno.
„O, stvarno,” Pancho nije znao što bi rekao i pošto su dis-krecija i oprez bili uvijek njegov način, promijeni temu: „Ovo izgleda predivno Suzy, no zar ne bismo trebali čekati
„
„Tu sam, tu sam, oprostite što ste me čekali.” Sally nahrupi unutra, poljubi Martu, zagrli Suzy i Panchu pruži nogu. „Drago mi je.”
Imala je istu slatku njušku kao i Suzy. Stvarno je mislio ono što je slijedeće rekao: „Ja sam Pancho. Drago mi je da sam te upoznao.”
Pancho je jedva mogao jesti, sa Suzy na jednoj i Sally na drugoj strani. Svinje ne pričaju puno tijekom jela, jer uzimaju hranu za ozbiljno i uvijek brzo završe tako da im poslije ostane mnogo vremena za razgovor.
„Ukusno jelo!”
„Da, Suzy, vrlo dobro.”
Suzy se nasmiješi dok je dodavala jabuke, a Sally potom počisti stol. Marta sjedne do Pancha i nježno reče: „Nadam se da moji komentari glede tvoje stare farme nisu probudili neka loša sjećanja. Ona nas je dugo zanimala. Mnogo smo naučili iz primjera vaše farme.”
Pancha je zanimalo ovo potonje: „Što ste naučili?”
„Pa, o moći, kao što sam ranije rekla. Da ona na neki način zahtijeva pristanak dvije strane: nitko ti ne može oduzeti moć ukoliko mu je ti ne daš.”
Marta zastane da razmisli i Pancho uskoči: „Pa kako možeš zaustaviti nekog da svoju moć preda nekom drugom,” pitao se na glas, „I kako zaustaviti nekog da je uzme?”
Marta se nasmijala ovom pitanju. „Ako je ti ne zaustaviš, oni će.” Napravi stanku da se sjeti nekog primjera. „Da li bi ti slušao moje naredbe samo kad bih ja to željela?”
„Ne,” odgovori Pancho brzo.
„A da li bi očekivao da ja slušam tvoje naredbe? Bi li to čak i htio?”
„Nema šanse,” reče Pancho osvježen od nedavne kupke.
„Zašto ne?” Marta je željela dobiti odgovor.
„Zato što sam to naučio.”
„Točno! Naučio si i ono što si naučio se može podučiti. Shvatila sam to odgajajući svoju djecu.” Pokaže na dva slatka stvorenja koja su se hihotala u kuhinji.
„Što ste ih točno naučili?” Pancho nije još uvijek bio siguran što je to on točno naučio.
„Radost samopouzdanja,” reče, „No, nisam ih ja to naučila, one su mene naučile.”
„Dakle, to je prirodno?” Pancho je bio skeptičan glede novog načina gledanja na stvari.
„Da, svi smo mi rođeni sa sposobnošću i naginjanjima prema samopouzdanju i odgovornosti. Šteta što toliko nas zaboravi na te stvari još odmalena.”
„Dakle, naučeni smo na predaju moći!” Pancho se mučio oko ovoga.
„Ne kažem da to radimo namjerno,” objasni Marta, „Ali netko čeka da je dobije.”
„Mama, da li ti to dosađuješ Panchu sa svojim teorijama?” Sally i Suzy mu priskoče u pomoć, ali Pancho odgovori kako je tema vrlo zanimljiva.
„Ali ne smijemo zakasniti na sastanak.” Sally je bila u pravu. Sunce je zašlo za horizont i mogli su vidjeti ostale kako idu prema staji.
Pancho pođe za svinjama. Za razliku od ostalih koji su zauzeli mjesta u krugu, on ostane u pozadini da potraži Sabo. Ona je već pričala s nekim zečevima, no kad joj on mahne, Sabo dođe do njega. I Pancho i Sabo nisu htjeli ništa govoriti na sastanku osim ako ih se ne pita, s obzirom da su oni ipak samo posjetitelji.
Kad su se sva sjedala napunila (prema Sabinoj računici, tamo je bilo gotovo stotinu životinja) sastanak počne. Guska nastavi svoju dužnost vođenja sastanka. Ovog je puta imala novi štap kojim je sada lupkala po onoj tabli koju je Pancho pronašao ranije tog dana. Ovaj se put nije raspravljalo o pjesmama.
Guska započne jednostavno: „Svi znamo za situaciju u kojoj se nalazimo. Želi li netko pričati?”
Gledajući uokolo po staji, Pancho se bojao da nitko neće. Napokon Jethro počne: „Kako ja to vidim, imamo dva izbora: dopustiti im da prodaju nas i farmu ili se boriti.” Zatim sjedne.
Životinje počnu međusobno šaputati, no šapat se ubrzo pretvori u viku. Debela crvena kokoš na bali sijena reče: „Jesmo li se onda dogovorili da nećemo dati farmu bez borbe?”
Guska reče: „Da vidimo koliko vas podržava ovu inicijativu,” i sve životinje dignu šapu, papak ili krilo. „Prošlo!” poviče guska.
Digne olovku i napiše na papiru: „Nećemo predati farmu bez borbe”
Pancho se nagne i šapne Sabi u uho: „Ovo je najbrži sastanak na kojem sam ikada bio. Zar ne bi trebali barem malo raspravljati o ovom?”
„Sada,” reče gospođa guska, „kako ćemo se boriti?”
Goldie ustane i reče: „Mislim da ne smijemo pribjeći nasilju bilo koje vrste.”
„Slažem se,” reče Rosy.
„To vam neće upaliti.” Bila je to Bobova izjava. Pancho je mislio kako će ovo potaknuti dugu raspravu.
Sally ustane i licem se okrene prema gomili: „Bob, možda si u pravu, no veoma je važno da prije nego što pribjegnemo nasilju isprobamo sve mirne načine.”
Glave u gomili počnu potvrdno klimati, a Bob slegne ramenima. „U redu, no i dalje mislim da to neće upaliti,” reče.
Pancho se iznenadio kako je Bob lako popustio pred grupom, pomislivši u sebi „Možda je previše puta izgubio. No barem se zauzeo za svoj stav.”
Mačka i svinja osjete iza sebe prodoran miris te se okrenu i vidješe Hansa i Kurta. „Samo smo došli vidjeti o čemu je sastanak,” šapne Kurt Panchu, „Čuli smo da je važno.”
Pancho klimne. Guska zatraži „odobrenje da se prvo upotrijebe nenasilna sredstva” i iznova prijedlog bi jednoglasno prihvaćen, na što ona zapiše \#2 na papir.
Ostatak je sastanka prošao u ugodnoj atmosferi bez imalo prepirki. Životinje su odlučile blokirati ulazna vrata i ne dopustiti više nikom ulazak. Osim toga, svojim će susjedima reći za svoju situaciju nadajući se da će im doći u pomoć. Formi-ralo se nekoliko odbora, od kojih je Pancho odabrao raznosače letaka, što se Bobu i Čangrizalu nije svidjelo jer su imali podosta teškoća jedan s drugim, a kamoli još sad i s Panchom. Ali svi su uglavnom bili zadovoljni, štoviše uzbuđeni.
Dva prekrasna janjeta dođu u sredinu kruga. Napišu nove stihove za omiljenu životinjsku pjesmu:
<em>Sve životinje dijeliše farmu
EIEIO!<\Slash{}em>
To postade veliki hit; svi je zajedno otpjevaše triput još na sastanku. Nakon toga više nisu ni upotrebljavali stare riječi, jer su se ove nove svima više sviđale.
Kurt i Hans ostanu razočarani. „Nasilja će biti, naravno,” reče Kurt, „ali će životinje biti žrtve. Sve po starom.”
Pancho i Sabo sjednu u kut i stanu razmjenjivati misli. Neiskustvo je bio jedini razlog zašto je sastanak prošao tako glatko i u dobrom raspoloženju i zašto su životinje bile tako sretne i optimistične. No, ubrzo će steći nešto iskustva. Svinja i mačka stisnu jedan drugom šapu, odnosno papak. Pancho pogleda Sabo i ona reče: „Zaista se nadam da će ovo uspjeti.”
\chapter{12}
Baš prije nego je sunce izašlo, Pancho začu pijetlovo kukurikanje. „Danas neću propustiti doručak!” reče sam sebi. Istegne se i pogleda uokolo ne bi li vidio gdje je Sabo, ali nje nije bilo na vidiku . „Možda bih trebao opet početi spavati na otvorenom, kao u Špiljskom kampu.”
Pancho probije put između bala sijena prema ružičastom svjetlu koje je prodiralo kroz pukotine na daskama stajskih vrata. Previše spavanja izgledalo mu je kao lijenost, dakle kao karakterna slabost, ponekad je preoštro kritizirao druge, a sam se osjećao krivim. Lagano gurne vrata i otvori ih. Vani je već bio dan. Fotografi ovaj dio dana nazivaju magičnim satom, jer su sjene duge, a sunce kao da nosi svoje ružičaste naočale.
Rosa na livadi smoči Panchu noge dok je hodao u potrazi za ostalima. „Gdje su svi?” mrzio je kad bi ga izostavili iz nečeg. „Što bi mogli raditi u zoru?” Dođe do koraljne ograde i provuče se kroz slomljenu prečku. „Na ovoj se farmi održava sve osim ograda,” primijeti sam za sebe. Na njegovoj je staroj farmi to bila prva stvar o kojoj su vodili računa. „Da su me oni psi lovili samo dan kasnije, ograda bi bila popravljena.” Volio je razmiš-ljati ovako povezano. „Danas ne bi bio tu.”
Pancho okrene ovu misao u glavi još jednom i nasmije se ironiji — na njemu je bio red da zakrpi ogradu, a da je to učinio ranije više ga ne bi bilo. Tad dođe do vrha humka i pogleda livadu koja mu se pružala kao na dlanu. „Što se zaboga dolje događa?” Svinja u čudu počeše uho.
Na prvi se pogled činilo kao da netko naganja stado ovaca. Prvo su bježali na jednu stranu, da bi zatim stali. Odjednom, kao da su jedno biće, počeli bi trčati u drugom smjeru. Čudno je bilo to što ih nitko nije jurio. Još je bilo čudnije ono što je primijetio: u stadu nije bilo samo ovaca, nego i krava i koza, svinja i mazgi, kokoši i, zapravo — svi sa farme. Pancho ugleda Goldie skoro u centru gomile. „Pa, to je već nešto,” prodrma glavom, „ovce naganjaju psa.”
Ptičar uhvati Panchov pogled i zamahne mu repom kao da kaže „dobro jutro”, a svinja mu odmahne. Pancho zatim sjedne na travnatu kosinu i stade promatrati igru stajanja i kretanja, okreta i preokreta životinja koje su trčale dok je on sjedio kao da iz sjedala gleda baletnu predstavu.
Koreografija je bila impresivna. Plesali su oko jezera energično i savršeno graciozno. Stanka, zatim nagli okret nalijevo, otkriju malu crnu figuru kako bezuspješno hvata korak s osta-lima. „Sabo,” Pancho zažmiri na tren i izgubi je u onoj masi koja je svaki put bila sve gušća i gušća.
Manji i manji, krug bi se stiskao svaki put kad bi trčanje postalo hodanje, još više kad bi samo stajali. Životinje su se smijale i pljeskale kad bi se gomila raspršila.
Pancho primijeti još jedno lice koje nije očekivao, Emmu, divlju puricu. Zajedno s Goldie, popne se na vrh brda, ostajući bez daha. Pancho im pođe u susret da ih pozdravi.
„Dobro jutro!” Pancho se stražnjim nogama posklizne o mokru travu i dramatično završi na zemlji ispred psa i purice.
„Izgleda zabavno, možda bi i mi trebali to probati?” nasmije se purica. Goldie se naceri onako kako samo to ona zna, i bez da su si namignule, obje padnu na mokru travu i zatim se, umirući od smijeha, otkotrljaju niz brdo.
Pancho je oprezno hodao niz klizavu padinu. Nije bio siguran da li mu se rugaju ili ne. Što se dogodilo sa svima? Zar su zaboravili važan problem o kojem se sinoć raspravljalo? Sjedne na suhu stijenu blizu jezera. Polagano hodajući, Emma i Goldie mu se pridruže. Većina ostalih je otišla, vjerojatno na doručak. Purici se pridruže njeni mladi, koji su kljucali oko jezera dok su stariji razgovarali.
„O čemu je tamo bila riječ?” reče Pancho pokazujući nogom na livadu.
„Jutarnja vježba,” reče Goldie, tresući sa sebe rosu. „Evo ih!” Pas i purica pogledaše prema gore, a zatim i Pancho. Žućkaste zrake sunca osvijetle nešto što je izgledalo kao divlji oblak, prebrz i prečvrst da bi bila samo para. Roj preleti iznad njih, te zaokrene u širokom luku. Pancho je, naravno, vidio jata ptica. Njihova je preciznost bila oduvijek svojevrsna inspi-racija za njega s vojničkog stajališta, no ovakvo jato nije nikad prije vidio. Iznad glava, u aerodinamičnim akrobacijama od čega bi svakom zastao dah, kretali su se kao jedno tijelo vrteći se, padajući, obrušavajući se, lebdeći i klizeći.
„Zašto?” bilo je sve što je svinja uspjela izgovoriti.
„Zašto ne?” uzdahne Emma, „Da sam barem i ja mlada pa da im se mogu pridružiti.”
„Hajde, idi gore,” pogurne je Goldie, „ja ću čuvati djecu.”
„Zašto ne?”
Purica se nasmije i zaleti se šireći krila. Trebalo joj je nekoliko krugova po zraku da ih uhvati, no Pancho uspije jasno vidjeti trenutak kad se Emma pridružila formaciji, baš kao kad klizač zgrabi ruku svog partnera u zraku. Jednu je minutu letjela zasebno da bi se potom potpuno stopila s jatom. Pancho se očima punih čuđenja okrene prema Goldie: „Vidio sam i ranije ptice kako lete, no zašto je ovo mnogo ljepše?”
„Mislim da je stvar u raznolikosti,” reče pas, „Jesi li ikada vidio Božićno drvce?”
Zbunjeni Pancho odmahne glavom.
„Mi psi smo češće od vas svinja pozvani u ljudske domove,” prizna ona, „Najbolja i najljepša Božićna drvca uvijek imaju najšarenije kuglice i najviše vrsta svih mogućih ostalih ukrasa, za koje ne bi nikad pomislio da bi zajedno izgledali lijepo, no nekako na Božićnom drvcu izgledaju božanstveno. Jednom smo posjetili nekog tko je imao bijelo drvce sa crvenim kuglicama,” slegne Goldie ramenima, „Govoreći kao pas, uvijek su mi se sviđale crvene kuglice, ali jednostavno nisu bile zanimljive.”
Pancho je napola slušao jer se sav bio udubio u ptice. „Mogao bih ih gledati cijeli dan. Da bar mogu letjeti.” Vidio je kad se jato razdvojilo na dva dijela koja su zatim kružila u suprotnim smjerovima. „Kako znaju kako to napraviti? I kad to napraviti? Tko ide kuda?”
„To je instinkt jata, tj. njihov mentalni sklop,” reče Goldie.
„Mentalni sklop”, ponovi Pancho s prezirom. Svinje nisu imale zajednički mentalni sklop. Takva vrsta aktivnosti bila je za životinje niže vrste. Pancho je o sebi uvijek razmišljao kao o pojedincu, čak kao o vođi. Sada bi se vjerojatno složio s tim da uloga vođe možda i nije najzahvalnija stvar na svijetu, no barem je mogao misliti za sebe, stati na svoje četiri noge, biti sam svoja svinja. Tu kontrolu ne bi nikada prepustio nekom drugom.
No, začudo, uzimanje kontrole od drugih mu nije smetalo. „Zato što se meni može vjerovati,” pomisli, „Drugi
pa, tko zna kamo mogu krenuti, i hoće li se uvući putem u
neku opasnu situaciju.” Pancho prestane gledati ptice i nogom počne kotrljati oblutak u blatu. Skupljenih očiju pogleda Goldie. „Zar je to sve što ste jutros radili na livadi? Pokušavali postati jato?”
Posebno je naglasio posljednju riječ šutirajući oblutak u jezero gdje je potonuo u blato ispod površine, radeći pravilne krugove koji su se širili sve do rubova. Goldie je gledala krugove sve dok nisu potpuno nestali. Tad ustima pokupi veliki kamen i baci ga u sredinu jezera. Od njegovog pada voda snažno prsne i napravi val od kojeg se čitavo jezero uznemiri. Životinje promatraše u tišini sve dok površina nije opet bila savršeno mirna.
Goldie izabere mali oblutak i odnese ga na daleki rub jezera. Pusti ga da padne iz njezinih usta na što se na vodi opet naprave mali krugovi koji su se polagano širili do rubova. Pas se okrene i nasmiješi Panchu. „Ovo je ono što mi pokušavamo biti”, reče.
Pancho se naceri: „Obluci?”
„Ne,” reče Goldie, „Jezero!” Glavom lagano gurne svinju u vodu. Pancho se nasmije kad pas skoči za njim.
Plivali su po jezeru, a ptice su im se obrušavale iznad glava. Na obali jezera mlade su purice cvrčale i pokušavale otići za dadiljom u vodu.
„Znaju li purice plivati?” upita Goldie.
„Pa, patke znaju,” reče Pancho, „Možemo im pomoći ako im voda pređe preko glave.” Tako pas i svinja pomognu malim puricama da uđu u plićak na rubu jezera.
Kao i svim mladima i njima se svidjelo prskati jedan drugoga. Hihotali su tako glasno da su uspjeli probuditi patke koje su drijemale u obližnjem visokom šašu. One doplivaju do njih kako bi im se pridružile u zafrkanciji, a Pancho i Goldie izađu van kako bi ih nadzirali s obale. Igra se pretvorila u neku vrstu lovice prskanjem vode.
„Pretpostavljam da purice znaju plivati,” reče Pancho okre-nuvši se prema psu. „No, i dalje ne shvaćam. Ti želiš postati jezero?” „Ne znam kako bih to objasnila,” uzdahne Goldie, „Zašto jednostavno ne bi sutra ujutro i pokušao?”
„Nema šanse. Prestrašno je.” Pancho zadrhti, „Naježim se od same pomisli na to.”
„Strašno,” pas raširi svoje smeđe oči i zakoluta ih ne vjerujući onom što je upravo čuo.„Zabavno je. Zato to i radimo. Neka vrsta igre i zabave. Ostalo je sve samo zanimljiva popratna pojava.”
Pačići i purići odu malo dublje u vodu gdje su ih trstike zaklanjale od pogleda, no Goldie se kao pravi čuvar premjestila na mjesto s boljim pregledom — pogleda prema nebu da provjeri gdje su ptice, ali ih ne uspije vidjeti. „Emma, daj.” reče pas, „Danas imam mnogo posla.”
Pancho se sjeti da mora polijepiti plakate, ali se pritom sjeti i svog želuca. „A danas još nismo ni doručkovali!”
„Ja ne doručkujem,” reče pas, „Jedem samo jedan obrok dnevno, no ti daj.”
„Samo malo nečega,” reče Pancho, „Donijet ću i nešto kukuruza za purice,” te krene prema brdovitom dijelu livade kako bi skratio put do polja kukuruza. Vratio se vrlo brzo s nekoliko klasja slatkog kukuruza. Goldie je još uvijek glumila čuvara. Patke su se igrale na sredini jezera. Pancho primijeti da patke puno bolje plivaju od purica. „Vjerojatno zbog mrežastih stopala,” pomisli ljušteći kukuruz i mašući zlatnim klasjem iznad glave pozivajući mlade na doručak.
Oni brzo istrče iz vode, potamane sav kukuruz u roku od par minuta te se vrate natrag u jezero. No, mame Emme još nije bilo na vidiku.
Pancho sjedne pokraj Goldie koja je sad već bila prilično uznemirena. „Obično se ne bih brinula,” reče, „Ali sam u odboru za barikade i mislim da će im trebati moja pomoć.”
„Idi,” pogurne je Pancho, „Ja mogu paziti na djecu, a i siguran sam da će se Emma brzo vratiti.” Pancho je znao da ne nedostaje nikome u svom odboru. Ipak je žarko želio poviriti u tiskane novine. „Vidim da nisi nikada bio roditelj,” reče pas, „Emma je meni povjerila djecu i ja moram ostati s njima bez obzira koliko dugo trebalo. Ona računa na mene.”
„Naravno,” klimne Pancho. Nekoliko minuta u tišini promatraše plivanje, nakon čega Goldie reče: „Juanita i Carlos
Trebali bi im javiti za aukciju. Mislim da bi htjeli biti tu. A i trebamo ih.”
Pancho se složi. „Možda bi ih ptice mogle naći u Špiljskom kampu.”
„Tako bi bilo najbrže”, odgovori Goldie i stade zuriti u nebo. „Pa bilo je i vrijeme.”
Spuštajući se prema njima u spiralnoj formaciji koja je sličila na vadičep, ptice se prizemlje na drugom kraju jezera. Sve osim Emme, koja se obrušila tik do zlatnog ptičara.
„Oprosti,” nasmiješi se purica ljubazno, „No, bilo je tako zabavno.”
„U redu je, ali sada bih zaista trebala krenuti,” Goldie otrči uz brdo u pravcu staje. „Bok, vidimo se uskoro,” zalaje preko ramena i nestane iza živice.
„Izgledalo je prekrasno,” Pancho reče Emmi, koja je hvatala dah, „Nisam znao da purice mogu letjeti.”
Emma prestane dahtati, te se okrene i pogleda ga u oči. „Što si rekao?” upita svinju.
„Nisam znao, mislim, uvijek su mi govorili da purice ne znaju letjeti,” Pancho se osjećao kao da mu tlo klizi pod nogama.
„Uvijek su ti govorili? Tko to?” Emma mu se kljunom gotovo zarine u njušku. Pancho se polako i oprezno ispravi: „Pa, svi kažu da ne znate letjeti.”
„Svi? Možda svi ponavljaju te klevete, no jedino nekolicina njih može profitirati širenjem takve kontrole uma.”
Pancho stade uzmicati. Emmino je perje bilo zaista nakostriješeno. „Što je ovo?” Raširi krila i zategne ih tako da pokaže svako pero.
„Krila,” Pancho proguta knedlu.
„A čemu služe krila?”
„Za letenje. Da, naravno.” Pancho je tražio prave riječi, „Mislim da su zapravo htjeli reći da purice ne mogu dugo letjeti, već samo nekoliko metara.”
„To je smiješno,” Emma se napuhala toliko da je sada bila dvaput veća nego inače. „To je isto kao kad kažu da svinje po mraku ništa ne vide, kad i sam znaš da svinje po noći vide itekako dobro. Samo ne žele dati svinjama ideju da pobjegnu po noći, jer su zapravo farmeri ti koji ne vide ništa kad se smrači. No, ovi farmeri,” malo se smirila i glas joj je sad odisao više gnušanjem nego ljutnjom, „ovi farmeri izmišljaju laži i svima govore da purani ne znaju letjeti, pa mlade purice to čuju i izgube samopouzdanje.” Nanovo se okrene prema Panchu: „Možeš li zamisliti koliko ti samo treba vjere da uopće pokušaš poletjeti? Treba ti nevjerojatna hrabrost i snaga i samopo-uzdanje da skočiš s drveta, vjerujući samo u svoja krila i u zrak.”
Pancho klimne potvrdno. Nije mogao shvatiti to skakanje s drveta i očekivanje da će poletjeti.
„No, farmeri, prvo kažu pilićima Vi ne možete letjeti. Bolje vam je da ostanete u kokošinjcu i malo po malo oni počnu u to vjerovati. Tad to isto kažu i puricama koje također povjeruju u farmerske laži i počnu se bojati. Nikad nisu letjele i zato svojoj djeci govore da uopće i ne pokušavaju poletjeti, no purice to rade stalno. Moja djeca neće nikada čuti laži tih farmera. Izrast će u jake purice pune samopouzdanja i radit će ono što žele.” Nakon što je završila s lekcijom, zapuše i pogleda uokolo.
„Usput, gdje su djeca?”
„Plivaju,” reče Pancho.
„Plivaju? U vodi?” Emma potrči do ruba jezera mičući one trstike koje su joj zaklanjale pogled.
„Da, u jezeru s patkama.” Pancho se požuri dolje kako bi se pridružio zabrinutoj majci. „Nadam se da je u redu što smo ih pustili. Nisam znao znaju li purice plivati, no vidim da im ide dosta dobro.”
Emma je gledala svoju djecu kako se utrkuju s pačićima. Mahnu majci na obali te im Emma nekako s oklijevanjem odmahne. Purica i svinja stajaše promatrajući djecu kako se igraju na toplom lipanjskom jutru. Pancho primijeti kako Emma stražnjim perjem za letenje briše navlažene oči. „Emma, što nije u redu?” upita Pancho. „Ništa,” reče ona, „Nikad nisam znala da purice mogu plivati.” Nasmiješi se ponosnim majčin-skim osmijehom.
„Pogledaj, sve su ostale ptice otišle.” Pancho pogledom pretraži livadu. „Mislio sam nekoga zamoliti da odleti do Špiljskog kampa da kaže Juaniti i Carlosu za aukciju.”
„Idem ja,” ponudi se Emma, „Nisam vidjela Judi otkad su se djeca rodila, a Mac i Crveni
stvarno mi nedostaju.”
Pancho pomisli kako su za jedan tajni kamp svi znali previše o njemu. Osim, nadajmo se, ljudi.
„Možeš paziti na djecu, zar ne?” Emma se počne zagrijavati za let.
„Ja!?” Pancho promrmlja, „Ja bih trebao nešto raditi. Napra-viti plakate i letke. I zaliti kukuruz.”
„Najviše dva sata.” Emma dade djeci znak da dođu na obalu.
„Vratit ću se do ručka.” Sad se mama purica obrati svojim trima mokrim lopticama: „Želim da ostanete s Panchom dok se ne vratim. Radite što kaže i budite blizu njega, bez obzira na sve.”
Zadnju je rečenicu uputila najvećoj među njima, ako ijednu možete nazvati velikom. Pancho je već ranije zamijetio da je ta purica bila sklonija avanturama od drugih.
„Pripazi na Orvillea. Wilber i Amelia su dosta dobri. Budi dobar. Vratit ću se brzo.” Na to Emma počne hvatati zalet. S minimalnim mahanjem podigne noge i ubrzo nestane iza vrhova drveća. Svinja posluša što joj je rečeno. Male su ga purice pažljivo promatrale. Pancho pomisli u sebi: „Ako želiš da te poštuju, ne smiješ im nikada pokazati strah. Moraš se ponašati kao da si glavni i kao da imaš plan.” No, već je bilo prekasno. Djeca su znala da pred sobom imaju novopečenu dadilju i samo međusobno izmijene poglede. „U redu,” reče Pancho prijaznim glasom, „Idemo zaliti kukuruz.”
Okrene se da ih povede do vrta, ali već nakon nekoliko koraka začuje pljuštanje vode i graktanje purica. Djeca su se vratila u jezero.
\textbf{* * *}
U staji su pripreme za subotu već bile u tijeku. Goldie, Jethro, Rosy i nekoliko ostalih većih životinja počnu graditi barikade i izvidnice. Pošto su im pojmovi barikada i izvidnica bili pomalo nejasni, tako su i građevine dobile više na estetskoj, umjetničkoj kvaliteti. Građevinari su se ponašali kao arhitekti, svađajući se oko toga da li će stepenice ili prozor staviti tu ili tamo.
Prilično suprotno od onog u kućici za tisak: tamo je bio pravi biznis. Tisak je imao mnogo vrsta štamparskih stilova, no malo slova iste vrste ili veličine. Izgleda da to nije smetalo ovnu i kozi pri svađi oko teksta na letku, jer su uvijek odabirali najmanja slova, tako da bi mogli složiti što duže i složenije rečenice. Na stranu su odložili velika slova svih fontova, koja će poslužiti za naslovnicu, o kojoj će odlučiti tek na kraju.
Neke životinje odšetaju do susjedne mljekare gdje ih je Sveta Krava podučavala nenasilju.
Pilići, pačići, janjad i sva ostala mladež prema Suzynim i Sallynim uputama sakupe svu hranu, te je skupe na jednu hrpu. Od toga napravili školski projekt. Sally je mislila kako će im to dobro poslužiti kao edukativno iskustvo. Sabo i njezini prijatelji sakupe lance i komade užadi.
U međuvremenu je Pancho sjedio i promatrao male purice kako plivaju u jezeru. Besposlenoj se svinji činilo da vrijeme nikako ne prolazi pa je stao obilaziti jezero i proučavati floru i faunu, uvijek krajičkom oka pazeći na svoju dužnost.
Perunike su taman počele cvjetati izgledajući kao ružičaste i bijele zastave na zelenim kolcima. Gomila se raznih biljaka borila za svoje mjesto među stijenama. Pancho je razdvojio nekoliko trstika uz rub vode kako bi mogao bolje promotriti ljubičasto-plavi lopoč da bi se ubrzo našao pred ljutitim očima divljeg patka. Tata patak je sjedio na hrpi jaja i iz svog skrovitog gnijezda promatrao male pačiće.
„Oprostite,” reče Pancho, zatečen jednako kao i patak, „Pitao sam se tko pazi na ove pačiće.” Nije mu baš uvijek dobro išao neobavezan razgovor. „Ja vodim brigu o ovim puričicama.”
„Purićima,” reče patak.
„Oprostite, što ste rekli?” Pancho nije uspio zaključiti iz ljutitog tona tog patka da li je to bila uvreda ili ne.
„Purići,” žuti je kljun sročio riječ što je jasnije mogao, „Nisu to puričice, već purići.”
„Zaista?” Pancho se pokuša sjetiti tog termina, „Nisam nikada prije čuo da ih zovu purići.”
„Pa to je ono što oni jesu i tako ih se treba zvati,” bio je nepopustljiv patak.
„U redu, purići!” Pancho slegne ramenima. Dvije su životinje sjedile u tišini samo nekoliko minuta, ali su se one činile kao vječnost.
„Iskreno, ne bi trebale ni plivati.” Patku kao da je pozlilo.
„A zašto ne?” Čitav je ton razgovora iznenadio Pancha, koji se počeo osjećati zaštitnički prema
purićima.
„Emma misli da je to u redu.”
„Emma je luda. Zar Emma misli da može letjeti?”
„Emma zna letjeti.” Panchovo se lice počne crveniti.
„Pa ne zna letjeti. Purice ne znaju plivati i purići ne znaju plivati.” Patak je svoje rekao.
Pancho nije mogao vjerovati onom što je čuo. „Ali gledaj,” pokaže na puriće koji su se prskali vodom na sredini jezera, „Oni plivaju.” Divlji patak zatvori oči. „No, ne bi smjeli.” Protrese glavom izražavajući nešto između tjeskobe i straha.
Pancho nije znao kako da protumači ovu potonju izjavu, ili oklijevanje, pa nastave još nekoliko minuta sjediti u napetoj tišini.
„Šššš,” izusti divlji patak prskajući Pancha po licu da to naglasi. „Nisam proizveo niti jedan zvuk,” prošapne svinja brišući njušku blatnjavom šapom. „Pa i nemoj, samo slušaj.” Oboje zatvore oči kako bi se bolje koncentrirali. I da, osim zvukova dječje igre moglo se čuti mrmljanje i prigušeno hihotanje: stranci u blizini vode.
Patak zagrakće dvaput na što pačići prekinu igru te počnu plivati prema tati. Purići ih instinktivno stanu slijediti. Ubrzo su se svi naganjali.
„Idi provjeri tko je to,” zapovijedi patak.
„Ja?” Pancho se ukoči.
„Ja sam malo zaposlen,” zagrakće patak sarkastično i pokaže na jaja i pačiće.
„Vi purići ostanite tu,” reče Pancho. Sve se mlade ptice okupe oko gnijezda osjećajući opasnost.
Pancho duboko uzdahne i krene prema otvorenom provjeriti čiji su to bili glasovi. Trudio se što tiše hodati kroz blato i stijene, ne toliko da iznenadi strance, nego zato što je mogao jasno zamisliti divljeg patka kako osluškuje svaki njegov pogrešni korak. Što je duže hodao u smjeru glasova, sve je jasnije mogao čuti razgovor stranaca. Pancho zastane i istegne glavu. Zar su razgovarali o glazbi? Ako uhodiš bespomoćne pačiće, ovo nije bila stvar o kojoj bi raspravljao. Međutim, opreza nikad dovo-ljno. Svinja nastavi pretraživati područje. Skrenuo je iza zavoja i ostao iza ogromne gromade stijene te se popeo na prste i virio.
Tamo su sjedili i jeli ukradene jabuke, nimalo ne mareći za jezero ili plivače.
„Štakori!” Pancho promrmlja malo preglasno. Četiri se šarene glave okrenu prema njemu. Pancho se nakesi shvativši što je učinio te izađe iz skrovišta iza stijene. Sva četiri stranca ustanu i pojure prema svinji. Pancho stade uzmicati sve dok ne vidje da su oni ispružili šape.
„Bok, bok. Lijepo vam je ovdje.” Vidjelo se da je govornik nekoć bio bijeli štakor, no izgleda da je upao u nekakvu plavu boju koja se lagano primila za bijelo krzno. Samo su mu oči bile originalne ružičaste boje.
„Kako ste?” reče Pancho oprezno pružajući šapu plavom štakoru. Pokušao se nasmiješiti, ali mu je pogled zastao na ukrasu na štakorovom prozirnom uhu, tako da je smiješak ispao neka vrsta grimase.
Štakor kucne o ukras i reče: „Dixion, to mi je ime.”
Pancho primijeti neko ime otiskano na metanom ukrasu za uho. Plava šapa zamahne u smjeru crnog štakora s bijelim mrljama, s ponekim obrijanim dijelom. „Ovo je Nick.”
Pancho se okrene na stranu i pročita napis na ukrasu: „Za Nikolu.”
„Da, to sam ja.” odgovori mrljasti glodavac. Nick je bio mnogo mlađi nego što bi se dalo zaključiti iz njegova zapuštena izgleda.
„Ja sam Ben.” Zelenoglavi štakor pruži šapu svinji, koja nije odgovorila jer je pokušavala pročitati ono što je pisalo na njegovom uhu. „Stavljaju ih naopako,” reče Ben slegnuvši ramenima te se okrene kako bi Pancho mogao vidjeti.
„Benzin?” Koja čudna imena, pomisli Pancho.
Iza svih ostalih stajala je mala ružičasta mišica. Pancho je primijetio da joj je, osim repa koje je bilo u duginim bojama, čitavo krzno bilo ružičasto. Činilo se kao da joj nije baš bilo stalo da se predstavi, pa se Pancho odšetao do nje i pročitao natpis na ukrasu.
„Saharin!” ustanovi, „Vrlo slatko ime.”
Pancho je mislio kako je ovo bila pametna rečenica, no ružičasta je mišica očito već previše puta čula tu šalu. Zurila je u svinju pogledom koji je odavao nešto između odvratnosti i dosade.
Pancho se okrenuo prema drugima.
„Ja sam Pancho i ovo baš i nije moja farma, ja sam tu samo posjetitelj.”
„Oh,” reče Dixion. Pancho osjeti pad na prijateljskoj razini.
„Pa
mi smo grupa Slobodni radikali, možda si čuo za nas?”
„Mislim da nisam,” reče svinja. Osjeti još manje prijateljske naklonosti.
„Dosta smo poznati u gradu,” reče Saharin s visokim tonom i kreštavim glasom.
„Nadam se da im ona nije pjevačica,” pomisli Pancho sam za sebe.
„Trenutno smo na turneji,” objasni Ben, „Ima li na farmi staja?” Pancho klimne. „Možda možemo jednom ili dvaput zasvirati?”
Pancho pogleda štakore. Znao je da ekscentrični divlji patak neće dopustiti da svoja jaja i pačiće izloži ovoj opasnoj pojavi. A i sjeti se svog obećanja Emmi.
„Staja je tamo preko,” pokaže neodređeno u glavnom smjeru, „Danas su svi zauzeti.” Pribrao se. Možda su ovi gradski štakori zapravo špijuni ili policijski detektivi. Sada je razmišljao poput stare koze ili ovna. Možda im ne bi smio dopustiti da bez pratnje njuškaju oko staje, a i kako bi to izgledalo kad bi on bio taj koji ih je poslao, a kad bi se ispostavilo da su oni zaista špijuni?
Tad mu je sinula ideja.
„Jesu li to vaši instrumenti?” upita ih gledajući čudne svežnje koji su ležali sa strane.
„Naravno da jesu!” Nick s osmijehom odgovori.
„Pitao sam se,” reče Pancho slatkim nevinim glasom, „da li bi mogli odsvirati jednu stvar za mene? Obožavam dobru glazbu!”
Štakore nije trebalo dvaput pitati. Sa zadovoljnim izrazom na licima, počnu se pripremati. Dixion i Ben su imali svatko svoju gitaru. (Pancho nije bio siguran, ali mu se činilo da je Ben držao bas), Nick je svirao saksofon, a Saharin je bila za bubnjevima. Iako su bubnjevi bili mišje veličine, njoj je trebalo dosta vremena da ih složi. Gitaristi su bili toliko željni svirke da su se za par minuta već uštimavali.
„Gdje se možemo ukopčati?” upitaju zbunjenog Pancha. Svinja pogleda uokolo po livadi i slegne ramenima. „Nemamo struju,” reče.
„Što?” Štakori ostanu šokirani. „Svi imaju struju.”
Dixion potapša Bena po ramenu istovremeno pogledom pretražujući livadu i voćnjak u potrazi za utičnicom. „Tamo!” Plavi štakor okrene sve ostale glave prema visokom mjestu koje Pancho nikada ranije nije zamijetio. Na vrhu su bile žice. Ben i Dixion potrče do drvenog stupa, noseći na ramenima duge snopove električnih žica poput nekakvih planinara. Ben se poput pravog štakora uspne na stup, izvuče žice te ih baci dolje Dixionu. Za par minuta svirka je već počela.
Baš kao što se Pancho nadao, zvukovi električnih gitara, saksa i bubnjeva odjekivali su čitavom farmom i vjerojatno čitavom okolinom. Ubrzo su stanovnici farme prestali sa svojim zadacima i krenuli u smjeru zvukova. Čak su i pačići i purići malo isplivali da vide što se događa.
Dixion preuzme mikrofon.
„Dobrodošli svi,” započne s estradnim žargonom, kao da su životinje bile gosti, a on njihov domaćin. „Mi smo Slobodni radikali.”, reče uz Saharininu pratnju bubnjeva. Životinje su stajale u tišini. „Mi smo laboratorijski štakori koji su pobjegli u gradsku kanalizaciju. Prva stvar koju bi vam htjeli odsvirati jest pjesma o našem bijegu. Zove se Uhvaćen u zamku poput miša.”
Ovo su bile posljednje razgovjetne riječi koje je Pancho čuo. Pojačalo je bilo odvrnuto na 11, bubnjevi su lupali, a saksofon kukao poput medvjeda u zamci. Pjevači su vrištali (ispalo je da su svi članovi benda pjevali prije ili kasnije), ali ih se nikako nije moglo razumjeti.
Pancho ovo nije mogao nazvati glazbom, no publika je, kako je vidio, bila puna onih koji su se smijali, klimali glavom i tapkali nogama.
Sabo dođe do Pancha te mu postavi tako očito pitanje: „Što se događa?”
„Putujući bend,” vikne joj u uho na što primijeti da se i on sam počeo pomalo njihati u ritmu glazbe.
Purići uoče Pancha gore, gotovo posve naprijed. Odlučili su da bi u ovoj prigodi trebali biti pored svoje dadilje. Napuste jezero te se provuku između kravljih i kozjih nogu i dođu do, odnosno ispred, Pancha.
Što je bend duže svirao (a prva je pjesma trajala malo duže) mladi su se sve više gurali prema naprijed. Starije su se životinje susretljivo odmicale unatrag. Pancho se odmakne da napravi mjesta za neku djecu koja su se bacala njemu ispred lica. U isto je vrijeme pokušavao držati mlade purice na oku. One su pak pred pjevačima širili svoje perje na repu.
Pancho leđima naleti na Sally, punašnu ružičastu učiteljicu. Sally je radila poprilično isto što i Pancho, pazila na svoje učenike i istodobno se odmicala prema natrag da sačuva bubnjiće.
„Zar nije odlično?” povikne, „Baš smo ovo trebali!”
Pancho se nasmiješi i klimne, iako nije imao blage veze o čemu je ona pričala. Sally počne plesati, a Pancho ju je samo nepomično gledao. Bila je potpuno ista kao i njezina sestra Suzy, možda čak i slađa jer je bila malo punašnija. Nije htio ispasti nepažljiva budala koja ne želi plesati, a i jedan mu ples nije nikako mogao škoditi. Ponudi joj nogu te je odvede do otvorenog mjesta na livadi. Od tamo su jednako dobro mogli vidjeti gomilu, a imali su puno više mjesta za ples. Plesali su prilično razigrano, no ipak na prijateljski način, udarajući se stražnjicama i trljajući se o njuške.
Obje su se svinje smijale kad je glazba odjednom stala. Gomila žestoko zaplješće i stade ispuštati životinjske krikove. Štakori se vidno zadovoljni naklone pa se ponovo predstave svojim novim obožavateljima. Panchove oči pretraže livadu u potrazi za njegovom dužnošću, kad ugleda nešto što nije očekivao. Iz kuta u kojem su bili, svinje su mogle vidjeti daleko u voćnjak i još daleko iza, sve do stabala bresaka.
Pancho prepozna Hansa, ovčara iz susjednog čopora. Vjerojatno je došao provjeriti tko to svira, pomisli Pancho, no uz koga se ono priljubio i koga to on mazi? Izgledalo je kao ovca, no Pancho baš i nije u to mogao vjerovati. „Sally, tko je ono s Hansom?”
Pancho pokaže u smjeru breskvi, no Sally nije niti ni pogle-dala. „Vjerojatno Monika,” reče i okrene se prema Panchu. „Zar si šokiran što vidiš ovčara i pudlicu zaljubljene?”
„Recimo da sam iznenađen što vidim bilo kojeg ovčara s bilo kojom pudlicom, u ljubavi ili prijateljstvu,” reče Pancho, „Mislio sam da Hans i njegovi mrze pudlice.”
„Već se godinama skrivaju tamo kako bi zajedno provodili vrijeme. Jadna Monika, ni njena se obitelj ne slaže što je s Hansom,” uzdahne Sally, „Svi rade probleme tamo gdje ih nema, a zapostavljaju veliki nered koji im se događa ispred očiju.”
Štakori ponovo pojačaju, tako više nije bilo moguće pričati. Nije se moglo raditi ništa drugo osim plesati. Pancho i Sally su se mogli koncentrirati jedno na drugo znajući da djeca nisu u nikakvoj opasnosti. Nakon što su otplesali još tri pjesme, koje su zvučale gotovo identično kao i ona prva, sjednu na travu i stanu gledati.
Svi su životinjski pogledi bili usmjereni prema bendu. Pogledavši tamo dolje gdje su bili Hans i Monika, Pancho primijeti da su čak i njih dvoje počeli plesati. Ali, čekaj, tko su bile one životinje pokraj električnog stupa? Pancho skupi oči da bolje vidi. Bob crni ovan i Čangrizalo stara koza stajali su leđima okrenuti bendu i zurili u električne žice.
\chapter{13}
Emmin dolazak u Špiljski kamp izazvao je poprilično uzbuđenje. Let nije bio dug, no od jutarnjeg je akrobatskog letenja osjećala umor. Nakon što je sletjela trebalo joj je dosta vremena da počne normalno disati.
Nakon posljednje diverzije, čuvari šume su se odlučili pritajiti. Doručak je postao ležerna aktivnost. Emma je stigla baš kada su jeli posljednje palačinke od žireva.
„Gle, pa to je Emma!” zavrišti srebrna vjeverica nakon što se Emma obrušila u krug gdje se doručkovalo.
„Emma, što je?”
„Gdje su ti djeca?”
„Je li sve u redu?”
Emma je puhala i dahtala istodobno dižući krila u znak da prestanu s pitanjima, ali oni nisu mogli čekati.
„Zar sijeku drveće?”
„Jesu li ljudi doznali za nas?”
„Gori li?”
„Carlos i Juanita,” zine Emma.
Ljama nije bilo u krugu oko Emme, no mladi je zečić otrčao do obronka gdje su šetale. Emma sjedne na panj. Jedna od vjeverica joj donese malo vode da se napije. Kad su ljame galopom dotrčale, purica je već skupila svoja krila i počela normalno govoriti.
„Nije tako hitno,” pokušala je objasniti životinjama, „ali je ozbiljno.”
„Aaaa.” Društvo je slušalo.
„Radi se o našoj farmi,” reče ljamama, koje klimnu tražeći da nastavi, „Ove će se subote održati aukcija i sve će biti prodano, što podrazumijeva i životinje.”
„Ne!” Bučno u zboru uzviknu u znak nevjerice.
„Životinje jednostavno mogu doći tu,” reče jelen, „Ne trebaju biti prodane.”
„To je vrlo ljubazno,” reče Juanita, „no, to je naša zemlja i mi ćemo se boriti za nju.”
„Da!” uskoči Carlos, „Moramo se boriti! Baš njih briga za životinje. Uvijek ih mogu rasploditi. Zemlja je ono po što dolaze, a mi im nećemo dopustiti da je uzmu.”
„Baš kao što se vi borite za vašu šumu, mi se moramo boriti za našu farmu.” Dok je tako govorila Juaniti se oči napune suzama.
Životinje utihnu na nekoliko minuta, kad Vragolan progo-vori. „U redu, idemo. Vi ste nama pomogli da zaštitimo šumu, sad ćemo mi vama pomoći da zaštitite farmu!” Sve životinje toliko glasno kliknu iz sveg srca u znak odobravanja da čitava šuma odjekne. Judi je na ljaminim licima primijetila tjeskobu.
„Prije nego svi odemo na farmu, možda bi bilo najpametnije da Juanita i Carlos odu kući i da nam jave kad im budemo potrebni.” U redovima životinja zavlada nezadovoljstvo. „Na taj način ostajemo element iznenađenja,” doda.
„Oooo,” razumješe životinje.
„Tako će biti najbolje,” složi se Juanita. Znala je da se ponekima ne bi svidjelo da među njih dođu divlje životinje, iako i s najboljim namjerama. „Mnogo nam znači to što znamo da ste nam u slučaju nužde spremni pomoći!”
„Mnogo,” doda Carlos.
Emma pročisti grlo. „A što ćemo sa zečevima?” potiho reče ljamama, glavom pokazujući u smjeru Hamiltona i Blackstonea.
Juanita i Carlos izmjene poglede. Blackstone i Hamilton im baš i nisu bili najomiljeniji drugari, no Emma je bila u pravu: bili su pametne i trenutno možda najkorisnije životinje. Osim toga, životinje na farmi se ne boje zečeva, čak ni onih najdivljih.
„Da, bilo bi dobro da oni dođu,” reče Carlos.
Carlos na leđima osjeti majmunovu težinu i pandže. Bonkers mu je postao najbolji prijatelj. Njega neće ostaviti sa strane u ovoj avanturi. Popne se na Carlosov vrat i šapne mu u uho: „Ako idu one malenkosti od zečeva, idem i ja!” I Carlos potvrdno klimne.
Ljame se bace na posao jer su se morale spremiti za povratak kući. Natovare se zavežljajima, nakrcaju zečeve i majmuna, i za sat vremena krenu na put.
Emma ostane još na čašici razgovora. Purice su poznate po sakupljanju tračeva, a Judi je mnogo toga imala za ispričati. Uz nadopunjavanja sa strane vjeverica i rakuna, Judi je ispričala Emmi sve o posljednjoj akciji u šumi i o zaboravljenim ljudskim prijateljima. Emmi samo što oči nisu iskočile.
„Ljudi, moram priznati da nisam nikada mislila da ću vas vidjeti kako branite ljude,” reče u čudu.
„Nisu svi isti,” objasni Judi, „Baš kao što nisu isti ni svi medvjedi ni sve purice.”
Emma malo razmisli o tome. „Ako nisu svi zli, kako možeš znati tko je od njih neprijatelj?”
„Teško je reći,” Judi zazvuči obeshrabreno, „Nadam se da nismo napravili gadnu pogrešku što smo drogirali one čuvare, jer možda i nisu bili loši, možda bi nam se bili pridružili da smo prvo popričali s njima.”
Emma odmahne glavom, što ponovi i nekolicina rakuna. „Ne bih rekla Judi,” reče purica, „Ljudi s oružjem, ljudi koji očito čuvaju mašineriju
Bez uvrede, trebalo bi mnogo priče da ih se nagovori da se pridruže odrpanim životinjama.”
Judi uzdahne: „Onda bih mnogo pričala.”
Emma je uvijek voljela biti otvorena prema novim mogućnostima. „Ljudi, hm,” mozgala je, „Nikad ni s jednim čovjekom nisam pričala, uvijek sam ih zaobilazila.”
„Ja isto. Pametna odluka,” složi se Vragolan.
„Ovi su bili prvi s kojima sam pričala,” reče Judi, „No, vjerojatno ne i posljednji. Naravno da su drugačiji od nas, ali\dots{}” pogledaju jedan drugoga, „Svi smo mi poprilično različiti.”
Istina, pomisli Emma, godinama je živjela isključivo sa puricama. Tako je odrasla, no sada su joj prijatelji bile sve životinje koje su razmišljale slično kao ona. Zašto onda ne i ljudi?
„Mislim da ću otići vidjeti te ljudske čuvare šuma,” kvocne, „možda čak i popričati s njima.”
„Gavran Quoth ti može dati upute za let,” reče joj Judi, „Nikad ne znaš, možda će nam oni pomoći riješiti problem oko farme.”
„Oh, mislim da ne želimo da se ljudi umiješaju,” Emma zagrli Judi na odlasku, „Nadam se da ćemo se uskoro vidjeti,” reče purica i odšeta do starog Quotha da nabavi plan leta.
„Koliko dugo ćemo mi još pomagati tim glupim ljudima?” upita Vragolan na glas. „Govorimo o potencijalnim špijunima.”
Judi ne odgovori, pa on nastavi. „Prvo su ubili Bitangu i malu srnu.”
„To je bila nesreća,” uskoči vjeverica Mac.
„To oni žele da mi mislimo,” reče Vragolan tajnovito, „Možda je to dobro izrađen plan. Prvo dobiju naše povjerenje
„
„Vragolan!” prekine ga oštro Judi, „To nimalo ne zvuči poput tebe. Odakle ti sve te zamisli?”
„Pa, Blackstone i Hamilton su rekli\dots{}” oči mu počnu tražiti pomoć, no nje nije bilo.
Judi uskoči. „Ti si bio tamo, ja ne. Blackstone i Hamilton isto nisu bili tamo, barem ne na samom poprištu događaja. Reci mi sam, je li to bila nesreća?”
„Da,” zajeca, „Grozna, grozna nesreća.”
Emma je mahala čuvarima šume kružeći iznad njihovih glava te joj oni uzvrate pozdrav. Čak je i Vragolan podigao svoje vlažno lice da je pogleda na odlasku. Iz zraka sve izgleda drugačije, a Emma se uvijek divila lijepom pogledu iz velike udaljenosti. Što je više letjela, to je Špiljski kamp bio sve manji i slika je postajala sve veća. Ispod sebe je mogla vidjeti šumu kao na dlanu; drveće je izgledalo poput mahovine na stijenama. Ovako se mogao uočiti i užas sječe. Sa zemlje, istina je što govore, ponekad od silnoga drveća ne vidiš šumu.
S neba na sjeveru mogla je vidjeti silovane obronke, smeđe i mrtve, koji su pripadali korporacijama. Ispod njih ležala je betonska masa grada. Purici je ovaj pogled bio odvratan, pa zatvori oči i skrene nadesno. Kad ponovo otvori oči, ugleda na rubu grada ranč konja. Iz daljine je izgledao zelen i ugodan te se spusti niže da malo bolje pogleda.
Trava je bila poput baršuna, a uredne bijele ograde presi-jecale su imanje uzduž i poprijeko, dijeleći ga u male odjeljke.
Emma proleti pokraj bijelo-zelene kuće vlasnika, na kojoj su svi kapci bili zatvoreni. Letjela je pored uređenih vrtova i dolje pokraj staja, tih dugih građevina s crvenim krovovima i bijelim vratima na svakom pedlju. Nad svakim je vratima visjela po jedna konjska glava.
Zatim okruži oko staja ne bi li ugledala znakove opasnosti. Pošto ih nije bilo, ležerno se spustila u prolaz između staja privlačeći pažnju svakoga konja kojeg je vidjela. Konji se isti čas stanu komešati, od silnog uzbuđenja toptajući i njišteći.
„Mora da im je dosadno kad se ovako lako uzbude.” Ptica se u sebi nasmijala dok je po drugi put kružila okolo, ovog puta najbrže što je mogla, tek toliko da ih uzbudi. Publika je poludjela, lupala o vrata, rzala i mahala svojim grivama kako bi im ulari počeli zveckati.
Emma sleti na kupolu jednog od krovova, previsoko da bi je konji mogli vidjeti. Slušala je sve dok se staja nije ponovo posve umirila. Tad ugleda zašto. Čovjek s bičem u ruci kretao se u smjeru staje.
Maleni je čovjek šepao, i iako ga je bilo koji od tih konja mogao lako pogaziti, svi se šćućure u tišini. Emma je ostala skrivena dok je čovjek tražio razlog zbog kojeg su se konji uznemirili. Par puta zapucketa svojim bičem i kaže par riječi koje Emma nije razumjela, no njihovo se značenje dalo zaključiti iz samog tona. Sve se smirilo, nijedan konj više nije proizvodio nijedan zvuk. Činilo se kao da su prestali i disati.
Čovjek progovori malo ljubaznije: „Corvette, što je bilo?” Emma se prišulja niže niz krov kako bi mogla gledati te vidi čovjeka kako gladi Corvettin smeđi nos. Ubrzo su se svi nosevi htjeli maziti te je čovjek hodao duž pregrada nekima dajući pažnju, nekima šećer, a pri kraju čak mrkvu ili dvije. Tad se zaputi prema staji.
Emma je primijetila da čovjek nije pogladio sve konje. Jedan čak nije ni pomolio glavu u nadi da će ga pogladiti. No, sada kada je čovjek otišao, konj pomoli glavu iz svoje pregrade i pogleda pravo prema Emmi koja je sjedila na krovu.
„Što ti pokušavaš?” upita je, keseći se i pokazujući joj velike bijele zube, „Uvaliti nas u nevolje?” Smijao se ludim konjskim smijehom na što se Emma povuče iz odvoda za kišu.
„Ti si taj koji nas uvijek uvali u nevolju,” prekine ga Corvette, „Ponašaj se pristojno.”
„Ne želimo da se vrati, zar ne?” reče ogroman palomin, mašući svojom bijelom grivom, „Prestani se smijati.”
No, konj nije stao. Sad kad se razgovor pokrenuo, Emma se ohrabri i sklizne s krova. Došeta do pregrade u kojoj je bio konj koji se još uvijek smijao. „Možda će sa mnom pričati,” pomisli te reče na glas: „Prestani s tim smijanjem ili ću ja nastaviti letjeti.” Emma pogleda blistavog crnog konja i čudnu riječ koja je stajala nad vratima te pregrade. „Edsel”, zakrešti, „Što to znači?” Nadala se da će ovim uspjeti zapodjenuti razgovor.
Crni se konj prestane smijati i odgovori bez većeg interesa. „To je auto koji svojim vlasnicima zadaje mnogo muka,” reče jednostavno, „To je usput i moje ime.”
Emma pogleda duž reda konjskih glava i iznad svake ugleda po jednu riječ za koje nije znala značenje. „Mercedes, Rolls, Beamer, Volvo, Porsche,” čitala je sporo i glasno.
„Imena auta”, reče Edsel, „Zar nije prepametno?” podrugljivo se nasmije. „Znaš, ljudi obično aute nazivaju po konjima. Piuto, Colt, Mustang
„ Emma odmahne glavom. „Ne znam ništa o autima,” prozbori.
„Sad on nastupa,” zanjišti Corvette i povuče glavu u svoju pregradu.
„Molim te, samo nemoj da počne,” zamoli Mercedes koji je žalio što je njegova pregrada pored Edselove.
„Govorim purici, ne vama,” reče dok mu oči počnu treptati kao da nagovještavaju nevolju. „Ako vas ne zanima, nemojte slušati.”
Emma je znala da se ovaj izbor nije odnosio na nju. Bacila se na balu sijena, nadajući se da će lekcija biti kratka.
„Kada su izumili automobile, oni su trebali biti spas za konje.” Sve se glave povuku u sjenu. „Konji više nisu trebali raditi teške poslove za čovjeka, služiti kao prijevozno sredstvo ili orati njive. Konji diljem svijeta vidjeli su pred sobom novo razdoblje odmora i slobode za svoju ždrebad. No, nije tako ispalo. Konji su postali zastarjela roba koju nitko više nije trebao. Jedini način na koji možemo preživjeti jest da posta-nemo visoko obrazovani i specijalizirani, da bi tek tada nekoli-cina nas postala tražena. Ako si najbrži i najljepši ili možeš najviše skočiti, tada možeš živjeti zaključan u ovim malim ćelijama trudeći se iz petnih žila da svom vlasniku doneseš dobit.” Edsel zastane uronjen u misli.
„Za što si se ti specijalizirao?” upita Emma. Čitav koncept ovoga bio je podosta čudan za jednu divlju puricu.
„Dresuru.” Primijetivši da ga je ptica blijedo pogledala, konj objasni: „Slijeđenje uputa i činjenje svega što mi se kaže bez oklijevanja.” Iz susjednih se pregrada začuje hihotanje. Bilo je očito da su ga slušali. „Smiju se jer sam se ja, ovaj, slomio. Jedan dan više jednostavno nisam mogao podnijeti da još jednom poslušam glupu, besmislenu zapovijed pa sam usred velikog događaja stao. Jahačica me pokušavala natjerati na posluh. Udarala me i bičevala pa sam je ja zbacio s leđa.” Edsel je ovaj posljednji dio rekao s ponosom, pogledavši puricu ravno u oči.
„Baš dobro!” povikne Emma, „Jesi li ti onda nju udarao i bičevao?” Sve životinje zinu u čudu te pomole glave da pogle-daju tu groznu pticu. Čak je i Edsel izgledao šokirano. „Naravno da nisam. Ona je dobro, čak nije ni ozlijeđena.” Ovo se također činilo kao nešto na što je bio ponosan.
„Ali, ti se ne ponašaš kao da ti je žao, u tome je problem,” grdila ga je Corvette preko puta, „Oprostit će ti i dati ti još jednu šansu, ali ne, ti čak ne želiš ni poljubiti konjušara i dati da te pogladi.”
„A znaš što se događa s pastusima koji se ne ponašaju lijepo
„ reče Mercedes podrugljivo na što okrene glavu prema smeđoj glavi iza vrata s oznakom Fiat.
„Još jedan auto koji zadaje muke?” pomisli Emma.
„Bolje im je da me ne pokušavaju uškopiti,” izjavi Edsel, „Ili će netko biti isprebijan!”
„I tad će te uspavati,” podsjeti ga Corvette, „Bum, jedan metak u čelo.” Emma nije mogla shvatiti. „Zašto ne odeš? Zašto ste svi vi ovdje, a pogotovo ti Edsel?”
Crni konj uzdahne. „Ali gdje bih mogao poći, što bih mogao raditi? Dresura je sve što znam.”
„Mislim da je vrijeme da nešto naučite.” Emma skoči s bale sijena i prošeta duž zacementiranog puta između redova u staji. Pogleda konje i primijeti kako su im kaputi čisti i blistavi. Neki su nosili otmjene pokrivače te imali grivu u pletenicama ukra-šene mašnom. Svi su bili dobro nahranjeni i istimareni. U malenim je pregradama sijeno bilo svježe.
„Neće vam biti lako tamo vani,” upozori ih, „Nikad nećete biti toliko sigurni niti će vam biti tako ugodno, ali bit ćete slobodni. Vjerojatno nećete svaki dan jesti otmjenu zob, no što zapravo imate izgubiti?”
Edsel spusti pogled prema podu. Pokušao se zamisliti kako odustaje od svega za što se teško mučio. Prisjetio se pljeskanja i nagrada, kocki šećera i pohvale vlasnika. Bilo je razdoblja koja su mu se činila bitnima. Kad bi se pokajao i počeo lijepo ponašati, sve bi to opet mogao imati.
Sve se oči upere u Edsela koji je upravo stavljao na vagu svoju budućnost. Koliko se itko od njih mogao sjetiti, nijedan konj nikada nije otišao od tamo svojom voljom.
Tišinu razmišljanja uništi prodoran glas. „Daj Edsel, idemo!” Svi se okrenu u smjeru malenog ponija koji nije bio zaključan u pregradi. Čupava mu je dlaka bila smeđe-bijele boje, a jedno mu je oko neprestano prekrivala griva koja je neumorno padala sa strane.
„O Jeep, ne budi smiješan. Ti ne možeš nigdje ići.” Corvettin se ton glasa snizi.
„Mogu ići kamo god hoću,” reče Jeep, „a može i Edsel.”
„Ti si premlad,” reče mu Mercedes majčinskim tonom.
„Da, ja sam dovoljno mlad da se još sjećam otoka Chinoco-league,” reče Jeep okrenuvši se prema Edselu. „Stvarno to mislim, idemo!”
Crni pastuh pogleda ponija. Zatim pogleda ostale konje zaključane u pregradama. Na kraju spusti pogled na Emmu. „Zašto ne,” reče sa smiješkom.
Jeep od uzbuđenja zabaci stražnje noge. Već je toliko dugo planirao bijeg. „Trebali bi pričekati noć za bijeg tako da se tijekom dana možemo skrivati i spavati u šumi, a noću putovati. Ti si snažan i pametan, a ja znam koje su biljke jestive. Bit ćemo dobar tim.”
„Slijedite tok rijeke,” reče Emma.
„Tiho,” Corvette ih pokuša umiriti, „Opet dolazi.”
Emma ugleda šepavog čovjeka koji se gegao prema njima, noseći u rukama uzdu od konopa.
„Ja brišem odavde,” reče, a Edselu zamahujući krilima doda „Zapamti: niz rijeku!” Purica se podigne iznad staja kružeći gore dovoljno dugo da vidi kako je čovjek onu uzdu stavio oko Jeepovog vrata, te ga odveo prema glavnoj kući.
\chapter{14}
U ovakvim je prilikama Emma bila sretna što ima krila. „Slobodna poput ptice,” reče sama sebi dok se ispod nje ranč konja sve više i više smanjivao, napokon opet postavši minijaturan.
Hvatajući struju, igrala se sa živahnim proljetnim zrakom istodobno se boreći sa svojom savješću. „Znam da bih se trebala vratiti natrag na farmu, no\dots{}” purica je udisala miris lutanja. „Tako rijetko imam priliku istraživati, a i uvjerena sam da su djeca sigurna s Panchom.”
Emma se prisjeti ovojutarnje lekcije iz plivanja što je nasmiješi. „Tko zna što će još naučiti dok se ne vratim.”
S tom si mišlju dopusti markiranje.
Površina ispod nje pretvorila se u smeđe krovove protkane asfaltnim ulicama i činilo se kao da tome nema kraja. Zelenih je površina bilo izuzetno malo, a o stablima da i ne govorimo. „Neka vrsta sječe?” pomisli purica trudeći se letjeti što brže da prijeđe taj opustošen prizor.
Kretala se prema smaragdno-zelenoj oazi koja se nalazila baš pravo ispred nje. Kad je stigla tamo, izgledalo joj je kao neki park sa cvijećem u cvatu, zelenim čistinama i cvrkutom ptica. „Naravno,” klimne Emma, „Ovo je mjesto gdje bi ptice živjele. Prepametne smo da bi živjele zarobljene u smeđe-sivom beživotnom okružju.” Nakon što par puta okruži područje, spusti se na čistinu pokraj betonskog kupališta za ptice s fontanom u sredini. Emma pogleda naokolo po njegovanom posjedu i ostane impresionirana.
„Ovo je ptičji raj,” povikne sama za sebe hodajući po malenom mostu nad ribnjakom. Ispred nje, u liniji sa šetalištem, u sjenicama drveća stajao je red prečki. Na svakoj je stajala po jedna prekrasna ptica. Emma nikada ranije nije vidjela ptice tako sjajnih boja. Nekoliko je trenutaka oklijevala promatrajući prigušene boje na vlastitom perju.
„Koja glupost,” pomisli trgnuvši se iz sanjarenja, „Pticama nije bitno kako izgledam. Bitno je ono u meni.”
No, dok se približavala najbližoj prečki, ipak se trudila raširiti rep, kako bi ostavila dobar dojam.
„Bok,” obrati se Emma velikoj plavoj papigi. Papiga je sjedila savršeno mirno kao da nitko nije ništa rekao.
„Ja sam Emma,” pokuša purica nanovo, „Lijepo vam je ovdje.”
Plava je papiga i dalje zurila u istu točku, no slučajno udari o posudu sa sjemenkama suncokreta te nekoliko njih padne na zemlju pred Emmu.
Purica zbunjeno prvo pogleda sjemenje pa zatim opet plavu papigu poviše sebe. „Možda misli da prosim,” pomisli Emma, „i ne želi da se osramotim pričom o mom nesretnom stanju.”
Ipak, znala je da za nekog tko gladuje izgleda predebelo.
„Hvala, ali nisam gladna.” Emma pokuša što pristojnije odgovoriti na njenu gestu. „Kući me čeka ručak”, veselo doda pokušavajući susresti pogled ptice na prečki. Papiga sklopi oči i zavrti se na metalnoj šipci pokazavši purici perje na svom repu.
Emma shvati znak te krene dalje. No, ostale su joj ptice okretale leđa i prije nego bi došla do njih.
„Što je sa svima vama?” upita purica glasno, „Zar se bojite pričati? Zar vam prijete?” Emma je zurila u red šarenih repova, no nijedan se ne pomakne.
„Ne shvaćaš.” Bio je to glas stajskog palčića koji je kljucao bačeno sjemenje ispod metalnog koluta na kojem je sjedila crvena ara žutih krila. Palčićevo je perje bilo sivkasto, baš kao i svima njegove vrste, no tu se moglo naći i poneko šareno pero, koje je nekoć pripadalo nekoj od papiga, a koje je on našao i zabio ih među svoje. Emmi je palčić izgledao glupo, ali začepi kljun da posluša što joj je on počeo objašnjavati: „Razlog zbog kojeg one ne žele pričati s nama jest zato što su one egzotične.” Siva je ptica ovu posljednju riječ intonirala kao da se radi o nečem velikom.
„Što znači egzotično?” upita Emma.
„Znači da su veoma skupe,” namigne palčić purici, „Ova zelena tamo stoji čitavo bogatstvo, a ona plava s kojom si pokušala pričati još više. No, crvena
„ palčić snizi ton i pokretom ruke joj da znak da se nagne. „Velika crvena, ta je najskuplja!”
„Zašto?” upita purica istežući glavu da promotri sve papige, „Zašto je crvena najskuplja?”
„Zato što je najegzotičnija.” Palčić je izgleda mislio da se to podrazumijeva, no Emmi i dalje ništa nije bilo jasno.
„Dakle, zato ti nosiš šareno perje tih ptica.” upita purica, „Da budeš egzotičan?”
„Nikad neću moći biti uistinu egzotičan,” prizna palčić tužno, „Znaš li ti koliko ja vrijedim? Ništa!”
Nastavi sa skupljanjem otpalog perja.
Emma ga je promatrala koju minutu, pa opet reče: „Mislim da si u krivu. Ti si savršen palčić, a palčići su vrlo važne ptice. Imate lijep glas i mogu se kladiti da možete letjeti brže čak i od one Velike Crvene tamo.”
„Ona uopće ne može letjeti. Nijedna od njih ne može. Donesu im sve što im treba. Koji život.”
„Zaista koji život!” progunđa Emma, „Bez obzira koliko da sam skupa, ne bih se nikada odrekla svojih krila.”
Palčić je suosjećajno pogleda: „Ti vjerojatno vrijediš koliko i ja. Ništa. Osim možda na Dan zahvalnosti.”
„Iskreno, ja sam sebi i svojoj djeci važna,” Emma reče te se stane drsko šepiriti. „Te su ptice možda egzotične, ali meni izgledaju kao zatvorenici.”
„Imaš pravo!” reče hrapavi glas iza njih. Emma se okrene i ugleda papigu u krletci koja je bila odvojena od ostalih.
„Ti pričaš s nama! To mora značiti da ti nisi egzotična.” Emma se dogega do krletke.
„Ne, ne, vrlo sam egzotična,” reče sa smiješkom.
Ova je papiga većinom bila bijelo-narančaste boje, no vrat joj je bio gol, bez ikakvog perja. Tužne su joj oči imale u sebi dozu nestašluka. Emma uzvrati osmijeh.
„Zašto si u krletci?” Emma ih je mrzila. „Što ti se dogodilo s perjem?”
„Iščupala sam ga,” nasmijala se zatočena ptica, „Tako ne vrijedim mnogo. K tome još i grizem. Zato sam u krletci.”
Emma širom otvori oči. „Da te pustim?” Purica počne petljati oko zasuna.
„Ne, nisam spremna,” reče zatvorenica, „Kad mi perje na krilima naraste, pobjeći ću i odletjeti kući.”
Purica pogleda jadnu očerupanu pticu. „Nadam se da će ispasti baš kako si rekla.”
„Ponekad se za slobodu trebaš žrtvovati,” reče ptica tužno, čupajući još par pera s vrata koji je izgledao bolno. Palčić brzo pokupi svježe iščupano perje koje doda u mješavinu na svom trbuhu.
„Zar ti to perje ne otpadne kad letiš?” upita Emma palčića koji se dosta trudio oko toga da mu novo narančasto perje ostane tamo gdje ih je stavio.
„Da, ali više ne letim,” odgovori palčić, „Nitko od dobro nahranjenih ptica ne leti. Zapravo, ni najbolje nahranjene purice ne lete. Mislio sam da bi ti to trebala znati.”
Emma je to znala, a znala je i zašto.
„Te purice koje nazivaš dobro nahranjenima uzgajaju zbog njihovog mesa!” progunđa i zatim se, u naletu spoznaje, okrene prema zatočenoj ptici. „Zar i papige uzgajaju zbog mesa?” zabrinuto upita.
„Ne baš,” odgovori zatočenica, „Ne jedu nas, no svejedno se tu radi o mesu.”
Emma nije razumjela papigin neodređeni odgovor i taman kad ju je krenula upitati što je pod tim mislila, otvore se vrata na kraju puteljka. Čovjek se stade komešati u njihovom smjeru. Palčić zgrabi puricu za nogu i povuče je u grmlje. Sakriju se iza grmlja podrezanog u obliku zeca. Emma je virila između dva uha.
Ugleda ženu u mekanoj šarenoj tkanini. Iz kose su joj vijorile mašne, dok su joj oči i usne bile premazane nekakvom bojom. Žena je nosila zdjelu s voćem koje je dijelila zahvalnim papigama.
„Bok, bok, bok,” reče ista plava papiga koja je ranije ignorirala Emmu.
„Bok, Atena,” gugutala je žena milujući je.
Atena uzme iz zdjele nekoliko zrna grožđa.
„Zgodna damo,” poviče zelena ptica, „Zgodna damo!” Činilo se da ženi ovo godi.
„Zgodna Venero,” pogladi zelenu papigu i da joj breskvu.
„Afrodita želi naranču,” zakrešti Velika Crvena ptica.
Žena dolebdi do njene prečke. „Što kaže Afrodita?” upita je žena kao da govori nekom djetetu.
„Hoćeš li me poljubiti?” bockala ju je žena držeći naranču van papiginog domašaja. Crvena se papiga nagne i poljubi ženu u obraz svojim kljunom, a zatim brzo zgrabi naranču.
Žena se nagne da popriča sa bijelo-narančastom zatočenom papigom. Nagne se još malo i stavi lice vrlo blizu rešetki.
„Kako je danas mala Diana?” upita milim dječjim glasićem, „Želi li Diana jednu šljivu?”
Očerupana se papiga povuče u drugi kraj svoje ćelije. Žena je držala šljivu u ruci i pokazivala je ptici. „Dođi, Diana, vidi lijepe šljive.”
Ptica je i dalje ignorirala i šljivu i ženino moljakanje.
Tad žena otvori vrata Dianine krletke i pokuša je podragati. Papiga ženu snažno ugrize za prst, otkinuvši joj mekano bijelo meso.
Žena skoči i stane vikati, dok joj je haljina poprimala drugu boju, onu crvene krvi. Udari krletku, te kroz plač počne trčati kroz staklena vrata.
Krletka je i dalje stajala na svom mjestu, ali vrata su sada bila otvorena. Zatočena papiga slegne ramenima i zakorači van.
„Ne mogu se boriti sa sudbinom,” nakesi se Emmi koja ispuže iza grmlja u obliku zeca.
„Zar namjeravaš pobjeći?” upita je purica istodobno promatrajući kako ova isprobava svoja krila.
„Pokušat ću,” odgovori Diana, „Vjerojatno neću daleko stići, ali odavde mogu otići.”
Emma joj mahne gledajući kako papiga jedva prelijeće vanjsku živicu. „To je ono što ja zovem egzotičnom pticom”, reče palčiću. No, palčić nije slušao. Uvukao se u praznu krletku i zatvorio vrata.
Emma odmahne glavom i polako odšeta preko mosta nad ribnjakom do čistine gdje je mogla uzletjeti. Propusti vjetar u svoja nepodrezana krila i podigne se na nebo. Pogled na vrtove s te visine ju je natjerao da se zapita kako tako divno mjesto može biti zamka i zatvor. „No, većina je tih zatvorenika tu dobrovoljno,” pomisli, „Slobodu su mijenjali ili za lagodnost ili za sigurnost ili pak ljepotu.” Nekoliko se puta zarotira u zraku sretna što posjeduje krila te se zatim uputi na zapad. Lebdeći iznad dugih i niskih skladišta, gradilišta i tvornica, Emma skoro i ne primijeti elektranu i tvornicu papira. Napokon joj nešto privuče pažnju: velika zbirka krletki s raznim vrstama zatvorenika. U masivnim je i čvrstim ćelijama bilo i okrutnih i krotkih životinja. One divlje su bile iza metalnih rešetaka i žičanih ograda. Već je ranija bila čula za ovo mjesto, zoološki vrt, no izgledao je mnogo strašnije nego što je to zamišljala.
Emma se okrene i krene prema istoku. Mogla je čuti lupanje vlastitog srca. Jedan se dio nje želio vratiti natrag i vidjeti, dok se drugi htio pretvarati da zoološki vrt ne postoji. „Neću sletjeti,” odluči, „Samo ću na brzinu pogledati i zatim krenuti dalje svojim putem.” Purica se ponovo okrene prema zoološkom vrtu. Letjela je iznad slonova, žirafa i nilskih konja — puricama su to bile životinje o kojima su slušale samo legende. Vidjela je noge u lancima koji su ih držali na mjestu i visoke zidove preko kojih nisu mogli pobjeći. U kući s majmunima, Bonkersovi su prijatelji i rođaci virili kroz rešetke sanjajući o slobodi. Tigrovi su razočarano hodali naprijed-natrag, a čak je i veličanstveni orao bio zatočen u malom prostoru gdje nije mogao ni raširiti svoja krila. Emmi je bilo dosta. Tijekom ovako predivnog dana nije htjela gledati još patnje. Poleti i krene istočno, slijedeći jato morskih galebova. „Sigurno idu na predivno mjesto,” pomisli, „Ne u zatvor ili zoološki vrt.”
Galebovi je povedu preko malog brda. Na drugoj strani, skrivenoj od pogleda, galebovi slete u rupu punu smeća iskopa-noj u zemlji. Emma zadrži dah da ne udiše smrad raspadajućeg smeća dok je promatrala galebove kako se prepiru i bore oko komadića hrane koje su pronašli među otpacima. Purica oprezno sjedne na naslon neke stare fotelje. Potanko je proučavala smetlište. Bila je to hrpa odbačene ljudske civilizacije, a pored materijalnih otpadaka (starih strojeva, guma, jedno-kratnih pelena i ostalog), Emma ugleda i živa stvorenja koje je društvo odbacilo.
Štakori su bili posvuda. Skupljali su što god su mogli prije nego što bi otpatke zgrabili šugavi psi upalih očiju, toliko mršavi da su im se vidjela sva rebra. Galebovi su vodili glasne bitke protiv ostalih strvinara oko zlatnog rudnika otpada. Purica skoči kad na njeno iznenađenje iz razderanog jastuka njezine fotelje ispuže divlja mačka i njezinih šest gladnih mačića. Mama mačka pokaže svoje zube i šapu punu kandži uperi prema velikoj purici koja je stajala iznad njezine obitelji.
„Nisam vas mislila prestrašiti!” objasni preplašena Emma, „Neću vam nauditi!”
Mačka pogleda poviše nje i izgleda da joj se ono što je vidjela nije svidjelo. „Odlazi odavde!”, zasikće, što Emma posluša i makne se na izbijenu nogu nekog okrenutog stolića. Oči su joj pratile mačju obitelj kako prazne jastuk fotelje da bi se nakon toga raspršili po smeću. Mama mačka se smjesti na sigurnoj udaljenosti zalijepivši svoje oči za puricu zbog čega se Emma osjećala neugodno.
„Dakle, ti živiš tu?” upita velika ptica koju ova mršava narančasta mačka nije uspjela zastrašiti. Dapače, zainteresirala ju je.
„Jel ti to smeta?” drsko se okomi mačka.
„Da, tebi ne?” nastavi Emma.
„Ne,” odgovori mačka, „Tu sam se rodila i čitav život živim tu.”
„Sviđa ti se tu?” zastane purica, „Izgleda baš kao savršeno mjesto za otići iz njega.”
„A kamo bi otišli?” mačka zabaci šape u zrak, „Za nas ne postoji mjesto. Ovdje barem možemo jesti ostatke i spavati u staroj fotelji.”
Oprezna se majka počela malo opuštati u puričinoj blizini. Stade kopati smeće ispred nosa te ubrzo pronađe polovično pojeden hot-dog kojeg je gladno žvakala. Emma ju je bez riječi promatrala kako jede. Jedan od mačića doskoči do majke, koja mu preda ostatak svog hot-doga.
„Ovo nije dobro mjesto za mačiće,” prizna Emmi, „Brinem za njihovu sigurnost i budućnost. No, što mogu?”
„Ne znam,” prizna Emma. Gledajući ženku mačića, upita: „Što bi htjela biti kad odrasteš?”
Mačić zaprede: „Biti ću majka, baš kao i ti.” Okrene se i poliže svoju majku.
„Da draga, možeš biti majka. I što još?” potakne je starija mačka. Ovo pitanje zbuni mačića. „Ne znam. Što i ti, mama.”
Majka mačka pogleda Emmu i sva u strahu reče: „Zaista bi se trebali maknuti odavde, no kako? I gdje?” Tražila je odgovor negdje na puričinom licu.
Emma slegne ramenima. „Ja i moja djeca putujemo uokolo. Radimo malo ovo, malo ono. Dobar je to život za jednu puricu, no ne znam je li i za mačku.” Odmahne glavom.
Dvije majke sjednu i stanu razmišljati. „Teško je napustiti jedini dom za kojeg si ikada znao,” požali se mačka, „Meni je moja majka pričala kako je njezina majka živjela u gradu, no to je bilo vrlo davno, kada su ljudi marili za mačke. Bila su to bolje vremena.”
„Možda možeš ovdje popraviti stvari,” reče purica u nadi, ali posumnja u to pogledavši hrpe smeća oko sebe, „Ili možda jednom kad odeš otkriješ da to i nije tako teško.”
„Ponekad mi se čini da mi ništa od ovog tu ne bi nedostajalo,” ustvrdi mačka, „no da li bi mogli uspjeti u divljini, tamo vani sami?”
„Mnogi uspiju, a mnogi i ne,” reče Emma filozofski, „Što mislite o farmi? Na jednoj farmi imam prijatelje i možda bi mogli otići tamo. Međutim, sada nije baš najbolje vrijeme za to. Imaju velike probleme s jednom korporacijom.”
„Eto ideje! Na farmi uvijek ima posla za mačke, barem sam tako čula.” Na tu joj se pomisao načule uši.
„To je odlično mjesto, samo sa životinjama, nema ljudi. Samo se nadam da će je uspjeti i dalje držati podalje od bankara.” Emma pojasni, „Ako odeš u šumu i slijediš rijeku nizvodno, ne možeš je promašiti.”
„Dobra ideja. Možda ćemo otići jednog dana.” Mačka se vrati natrag kopanju po hrpama. „Sada ipak ne možemo otići. Imam puno posla, a za takav put treba dosta planiranja.” Slegne ramenima. „Putovati sa šestero mačića!”
Emma klimne. Možda farma i nije bila odgovor za sve životinje. Međutim, bilo joj je žao mačića koji odrastaju gotovo bez ikakve nade.
„Tako, a sad trebam krenuti dalje.” Purica napusti mačku.
„Vidimo se kasnije,” zamijauče mačka preko ramena, nastavljajući svoju potragu za hranom. „Sumnjam,” pomisli Emma, odgurnuvši se o nogu stola i žestoko klepećući krilima da poleti. Gore na nebu se za mjesto trebala boriti s galebovima koji su se vrtjeli u viru sve dok se ponovo nije našla iznad šume.
„Bolje da idem provjeriti te ljude, pa da se vratim djeci,” pomisli Emma zureći dolje prema drveću, tražeći nešto što bi joj poslužilo kao orijentir.
\chapter{15}
„Da vidimo, Quoth je rekao lijevo od mrtvog stabla, južno od stijene koja izgleda kao prepelica,” Emma je lijeno kružila nad jednim te istim pedljem šume, pokušavajući dati smisao gavranovim uputama. Stade gledati obližnju stijenu trudeći se u njoj vidjeti prepelicu. „Ne, nije ta, ta definitivno nije dio fazanove obitelji. Više kornjačine, mislim.” Tad ispred sebe ugleda dva mrtva drveta.
Uzdahne i počne letjeti prema sivim deblima čije su ćelave glave virile kroz zelenilo. Polako sleti na neku slomljenu granu da provjeri hoće li izdržati težinu ne više tako mršave purice, pa s pomalo razočaranja glasno reče: „Lijevo? Kako da znam što je lijevo?”
„Teško je, vrlo nedokučivo,” reče glas unutar drveta.
„Oprostite?” Emma pogleda uokolo i ugleda pospanu sovu čija je glava sada virila iz rupe na deblu.
„Znaš, to je ono da su sve stvari povezane,” zijevne sova, „Kao kad misliš da znaš što je lijevo, pa se okreneš i onda ti je to desno!”
„Izgubljena sam,” reče Emma, pokušavajući opet svesti razgovor na realne stvari.
„Čujem te,” reče sova, „U potpunosti se osjećam kao ti.”
Emma uzdahne i nanovo proba: „Znaš li gdje mogu pronaći stijenu koja izgleda kao prepelica?”
Sova se pribere i otvori svoje velike okrugle oči u kojima su se zjenice širile: „Čekaj, čekaj, nemoj mi reći. Mogu pretpostaviti
stijena nalik na prepelicu?”
Potpuno okrene glavu, što Emmu zapanji, te brzo odgovori: „Za doći na drugu stranu. Ne, ne, nije ta.”
„Nije zagonetka” Emma pokuša još jednom. „Tražim ljude koji se skrivaju u pećini. Jesi li ih možda vidjela?”
„Zašto? Jesam da,” reče sova ponosno. „Stražarim da ih zaštitim od opasnosti. Pokazat ću ti gdje su.”
„Ti si stražar?” upita Emma iznenađeno, „Zašto je tebi stalo do njih?”
„Ali, ovi su ljudi skroz u redu.” Sova stade šepiriti perje, spremna za polijetanje. „Zaista su mi pomogli i najmanje što mogu učiniti za njih jest da im budem stražar. Idemo.”
Emma je slijedila sovu dolje kroz drveće sve do podnožja brda. Nekoliko grmova koji su se činili kao da baš ne pripadaju tamo skrivali su ulaz u malu pećinu. Ptice otkotrljaju grmlje sa strane i zavire unutra. Bio je to medvjeđi brlog, kojeg je on koristio za svoj zimski san. Iako je bilo proljeće, njegov je miris ostao, a dodatno se pomiješao s toliko snažnim smradom ljudi koji su hitno trebali kupanje, da je Emma morala izvući glavu odatle da udahne malo svježeg zraka.
„Nisu tu,” reče sova sliježući ramenima.
„Očito nisu.” Emma se spremala vratiti natrag na farmu, no spomene „Znaš, kao jedan stražar, dio tvog posla jest da znaš gdje su ljudi.”
„Zar je?” Sova je tek napola slušala.
„I zaista, mislim da me nisi ni trebala dovesti sve do tu. Mogla sam biti korporacijski špijun ili tako nešto,” Emma je objašnjavala ptici koja se sad čistila i pogledala je sva tjeskobna.
„Jesi li ti špijun?” Oči joj se nanovo raširiše.
„Ne, nisam,” nasmiješi se Emma.
„Onda je sve u redu,” reče sova.
„Ali gledaj, da sam ja špijun, ne bih ti rekla istinu jer bih htjela da me dovedeš do ovog mjesta,” objasni joj polako.
Sova u čudu sjedne. „Dakle, ti si možda špijun?”
Emma pogleda malu nakupinu smeđeg i bijelog perja. Nije ni čudo da je ovo stvorenje na rubu izumiranja. „Nisam špijun,” reče odrješito.
„Ali to bi mi rekla i da jesi,” promrmlja sova. Emma zakoluta očima.
Upravo su u tom trenutku doskakutali ljudi, smijući se i zadirkujući, no ipak pazeći da ne budu preglasni. Približe se pećini i ugledavši odgurnuto grmlje stanu u tišini. Sova izađe iz pećine i ljudi odahnu.
„Horace, što radiš tu?” jedan od ljudi upita sovu.
„Pa, doveo sam ovu ovdje puricu da vas vidi, no budite oprezni, možda je špijun!”
„Nisam špijun,” ponovi Emma probijajući se iza grmlja. „Ja sam Emma,” reče. Ostane otvorenog kljuna kad ugleda ljude potpuno gole.
„Ako je ona možda špijun, zašto si je doveo tu?” Upita čovjek sovu dok je purica polako kružila oko ljudi, bezobrazno zureći u njihova gola tijela. Drugi muškarci i žena počnu stavljati svoju mokru odjeću na nisko granje. Emma primijeti da se ispod svakog od njih stvarala lokvica vode koja se slijevala s njihove kose i tijela.
Sova počne zamuckivati smišljajući odgovor: „Nisam znao da je špijun sve dok nismo došli tu. Tad mi je to rekla.”
„Nisam!” Emma se okrene čovjeku da pojasni. On se nagne prema njoj tako da joj je voda s njegove crvene brade i duge kovrčave kose smočila noge. Emma podigne glavu i dobro ga pogleda. „Izgleda kao Goldie nakon kupanja,” pomisli. No, previše je bila zaprepaštena njegovom golotinjom da je zaboravila što je htjela reći. „Oprosti što zurim,” reče, „ali nikada prije nisam vidjela čovjeka bez odjeće.” Zatim pogleda četvero otrcanih stvorenja s kojih je curila voda kako mašu glavama ne bi li tako osušili kosu, baš kao što to rade i životinje. „Bolje izgledate ovako,” prozbori, „Nisam došla kao špijun, već samo da porazgovaramo.”
„Emma, zar ne?” Čovjek joj se nasmiješi, „Ja sam Redwood, ovo su River i Rocky, a ono tamo je Rainbow. Ono posljednje stvorenje bila je žena, koja joj je sad mahala iza grmlja gdje je slagala mokre čarape.
Čudna imena, pomisli Emma, konji koji se zovu po autima, ljudi koji se zovu po prirodi. „Baš sam bila u Špiljskom kampu i Judi mi je predložila da vas posjetim,” počne Emma nespretno.
Redwood sjedne na stijenu spreman za razgovor. Drugi su se rasporedili na krpice sunca da se osuše, istodobno slušajući.
„Vrlo smo osjetljivi kad se radi o špijunima jer vjerujemo da u Špiljskom kampu postoji barem jedan ili dva špijuna.” Prešao je na vrlo ozbiljnu temu, prekinuvši tako bezbrižan razgovor.
Emma je bila skeptična prema ovom. Kako bi oni mogli znati što se događa u Špiljskom kampu? I zašto bi vjerovala ljudima, a ne životinjama? Ipak, probudio joj je znatiželju i nije se mogla oduprijeti pitanju: „Tko?” Čak se i Horace približio da čuje odgovor.
Rainbow upadne: „Nismo sigurni. Zašto zvučiš kao da imamo dokaz ili nešto slično?” prigovori Redwoodu.
„Ali želimo upozoriti nekog kome možemo vjerovati u Špiljskom kampu,” podsjeti ju, „da bude na oprezu.”
„U Špiljskom se kampu može svima vjerovati,” Emma reče kao u obrani, „no, životinje dolaze i odlaze
„ zastane dok je tako pričala na glas, te rečenicu završi u sebi, „zaista ih ne poznajem sve.”
„Nije to nitko tko je tamo dugo kao Judi ili Crveni ili Mac,” nastavi Redwood, „No, prije otprilike godinu dana su do nas počele dolaziti informacije.” Pogleda Emmu, koja potišteno objesi glavu.
„Želimo nekome javiti o tome, jer nam životinje iz Špiljskog kampa pomažu i na istoj smo strani,” reče Rocky.
„Ali tko?” Emma podigne glavu i počne se gegati, „Tko je špijun?”
„Tko god da je, zna vrlo dobro pisati i čitati,” reče Redwood, „A Judi i ostali imaju u njega dosta povjerenja.”
„Ali, mi ne poznajemo Špiljski kamp,” nadopuni ga Rainbow, „Tako da ne znamo imena.”
„Za koga oni špijuniraju?” upita Horace nevino.
Emma i ljudi odgovore u isti glas: „Korporaciju.”
„Ah, da,” klimne sova, „Korporacija.”
Emma sjedne kako bi razmislila o svemu ovom, prebirući u glavi sve životinje koje su znale čitati i pisati.
„O čemu si došla razgovarati?” Rocky upita tihu pticu.
„O ničem posebno, samo nikad ranije nisam pričala s ljudima, i nikad nisam ni jednog čovjeka vidjela bez odjeće.” Emma se nasmiješi. „Ovako izgledate više kao obične životinje,” reče, trljajući krilom nogu. „Neko krzno ili perje ili nešto takvo bi vam dobro došlo,” našali se.
„Posebno zimi,” Rainbow se pretvarala kao da drhti. „Da bar imam pernati pokrivač kao ti.”
Emma zatvori oči i reče sama sebi: „Sigurna sam da je to bila bezbrižna primjedba, no ne bih se čudila da kući ima takav barbarski primjer.”
„Jesi li ti čuvar šume?” upita River.
„Volim za sebe misliti da jesam,” Emma reče, „Divlja sam, znate, i živim tu, tako da dosta dobro znam sve što se događa.” Zastane te se okrene Riveru: „Što ćete vi tu?”
„Divljina je važna za sve na planeti, bez obzira da li živiš u njoj ili ne, jesi li divlji ili ne.” Mladi je muškarac govorio kao da se brani. Znao je da nije bio divlji onoliko koliko je to bila purica.
„Istina, istina, to je pravi odgovor,” gugutala je, šećući se oko muškarca kao kirurg koji pregledava svog pacijenta. „No, što je s poslom? Mislila sam da ste svi vi ljudi opterećeni tim poslovima, a korporacije, eto, nude poslove!”
„Korporacije ne mare toliko za poslove koliko za novac, profit i moć,” reče River ljutito.
„Priznaj River da ti je manje stalo do posla nego korporaciji!” reče Rocky sa smiješkom.
„Istina, posao u kojem sam rob plaći nije moja ideja života, ali nije mi teško raditi za nešto do čega mi je stalo, kao što su to šume i oceani i sloboda od ugnjetavanja.”
„Ugnjetavanja?” zakrešti Emma. „Što vi ljudi znate o ugnjetavanju?”
„Znam da se vas životinje više muči, no muče se i ljudi,” zakuka River, „Većinu nas barem. Samo nekolicina ljudi posje-duje novac i moć. Ostatak nas može birati između onoga što oni kažu, ili gladovanja, ili odlaska u zatvor.”
„I ljude drže u zoološkom vrtu?” upita Emma.
„Zatvor je kao zoološki vrt,” reče joj River, „i prema ljudima se tamo ponašaju kao prema životinjama. Skoro jednako. Zato smo došli živjeti u šumu gdje možemo slobodno disati. Međutim, šuma će vrlo brzo nestati, i više neće biti mjesta gdje ćemo moći umaći korporaciji.”
„Sada smo slobodni,” doda Redwood, „no, ako nas korporacija dohvati, optužit će nas za ubojstvo onih stražara, a to znači da će nas osuditi na smrt.”
Svi ušute.
Emma promisli prije nego progovori. Možda se ovim mladim ljudima zaista moglo vjerovati. Možda bi im oni mogli čak i pomoći. „Nešto se počelo događati,” započne Emma, „životinje na farmi i u šumi su nemirne.”
„Stvarno? Zar će biti pobune? Mislim, više nego samo da sačuvate šumu?” Rainbow raširi svoje smeđe oči toliko da je Emma u njima mogla jasno vidjeti svoj odraz.
„Nadam se. Mislim da hoće,” no Emma nije htjela reći previše toga. „Obavještavat ću vas o svemu ako budem mogla.”
„Nadam se da neće biti nasilja,” šapne Rainbow.
„Ja isto,” Emma snizi ton, „iako se korporacija neće jedno jutro probuditi i shvatiti da je bila nepoštena i sebična te se samo okrenuti i umrijeti. Mnogo im je toga na kocki i ako moraju, ubit će, samo da zadrže kontrolu.”
„U pravu si, korporacija je nasilna u svojoj srži i ne pokazuje nikakvo žaljenje,” požali se River. „Zašto mi uvijek moramo poštovati zakon i hodati uokolo na vrhovima prstiju kako ih ne bi uznemirili?”
„Zato jer oni imaju oružje!” reče Emma. „To jest, većina ih ima.”
„Tko ima moć, uvijek je u pravu,” River zavrti glavom pokazujući gađenje.
„Kako ide ona stara poslovica?” pitao se Redwood na glas. „Diskrecija je ponekad bolja strana junaštva.”
„Što bi to trebalo značiti?” upita River, „Da sam ja prerevan?”
„Ne, ali bi bilo predivno kad bi mogli pronaći barem najmanje nasilan put do slobode, zar ne?” Redwood napokon dobije potvrdan odgovor svog prijatelja koji mu klimne.
Emma također klimne potvrdno. „Možemo pokušati biti nenasilni, možemo planirati najbolje kako znamo, no moramo ostati realni. Pogledajte što se dogodilo pri posljednjoj akciji u šumi. Važno je da postavimo najvažnije ciljeve, no banke i vlada i korporacije će se protiv njih boriti do smrti
„ govorila je sve sporije.
Svi spuste pogled prema zemlji, zadubljeni svatko u svoje misli. Purica razbije tišinu. „Dakle, to su vaša stopala?” Smijala se. „Stvarno izgledaju čudno!” Došeta do Rivera i stavi svoju pandžu do njegovog stopala, te odmahne glavom. „Čudno,” reče, „te kandže nisu baš dobre, zar ne?”
Ljudi se nasmiju i priznaju da ne, nokti na nožnim prstima nisu bile od svakodnevne koristi kao što bi se netko mogao nadati.
„Znaš, neki ljudi možda misle da su vaša stopala smiješna,” reče Rainbow sa smiješkom dok je gledala reptilsku kožicu na Emminoj nozi.
„Vjerujem da ih ima,” prizna ptica. Tad primijeti položaj sunca na nebu. „Zaista sam izgubila pojam o vremenu,” uzvikne, „Čekaju me. Bilo je vrlo zanimljivo upoznati vas ljude. Pokušat ću vas obavještavati o situaciji.”
„Bilo nam je drago,” reče Redwood, kao i obično govoreći u ime svih. „Razmisli o onom sa špijunom.”
„Oh, da!” Sjeti se Emma, „Špijunski posao\dots{}”
Purica odšeta preko i protrese zaspalu sovu. „Zbogom!” reče pospanom Horaceu. „Koji stražar!”
Još jednom zaklepeće svojim umornim krilima i podigne se na nebo.
\chapter{16}
Kad su ljame dotrčale u galopu, Slobodni radikali su dovršavali svoj set. Farma je sad svoju pažnju od štakora prebacila na Carlosa i Juanitu, no ponajviše na samog Bonkersa, koji je zbog svoje sposobnosti upravljanja vozilima postao prilično slavan. Blackstone i Hamilton nisu bili posebice zanimljivi, te je Pancho mogao lakše doći do njih i pozdraviti ih.
„Brz način putovanja!” reče Pancho pruživši šapu odvjetnicima Špiljskog kampa. „Zašto ste se odlučili vratiti?”
Hamilton se držao za trbuh, a Blackstone zadihano ležao u travi. Zečevi se međusobno pogledaju pa odmahnu svojim prljavim glavama. „Mislim da je to bila Emmina ideja,” reče Hamilton. „Put je bio užasan!”
„A gdje je Emma?” Svinja odjednom shvati da je zbog čuvanja djece propustila većinu akcije.
„Zadnji put sam je vidio kod Oraha kako jede palačinke od žireva,” uzdahne Blackstone i zatvori oči.
Pancho okupi puriće i krene prema Sally. Ona je već bila sa svojom djecom s kojima je sada trčala po vrtu. Pancho je zamoli da mu pričuva mlade purice, ali ona nije željela prihvatiti takvu odgovornost.
„Možemo li onda ići s vama?” Pancho u nadi zapita. „Tko zna kad će se Emma vratiti.”
Sally smiješkom potvrdno odgovori, te dvije svinje stanu zajedno s djecom skupljati hranu iz vrta i stavljati ih na sigurno spremajući se za eventualnu opasnost.
Bonkers nađe Sabo i čvrsto je zagrli, od čega je ona počela presti. Sabo zatim predstavi majmuna ostalim životinjama i nakon što ga je pozorno promatrala skrivena iza ružičastog štakorskog bubnjarskog seta, krenu u istraživanje farme. Razgledavanje nepoznatog mjesta s Bonkersom je uvijek zabavno. On je sve gledao na neki svoj poseban način. Štakori su se spremali za nastavak svoje turneje.
Ljame su zajedno s Goldie i Rosy krenule prema staji da prokomentiraju odluke koje su sinoć donijeli i da popričaju o tome kako im one mogu najbolje pomoći u trenutnoj krizi.
Ubrzo su se sve životinje vratile svojim zadaćama, ostavlja-jući zečeve da se na livadi odmaraju od napornog puta. No kad ostanu sami, Blackstone i Hamilton naglo ožive, te počnu istraživati električne instrumente. Barem se tako činilo Bobu, koji se s električnog stupa polagano spuštao prema svojem skrovištu.
Crni ovan zastane i, skriven iza grma kupina, promotri što to zečevi rade. Nakon nekoliko ukopčavanja i iskopčavanja, zečevi su krenuli prema staji, a Bob oprezno otiđe do električnih gitara da vidi što su to oni učinili. Vječno sumnjičav, ne toliko zbog same opreme električnog benda, crni ovan pronjuška oko mikrofona i pojačala. Sve su ove crne kutije izgledale identično, no slijedeći kabel, vidi da je samo mali kovčežić bio uključen u struju. Svi znaju da se bombe uvijek nalaze unutar kovčega tako da ga se Bob nije usuđivao otvoriti. No, jest pročitao natpis na njemu. „Motorolina pokretna stanica”, prozbori, ali ne uspije odgonetnuti što to znači. „Gdje je ta stara koza kad je trebaš?”
Bob sjedne tik do kovčega da malo razmisli o svemu, kad Emma stade kružiti iznad livade tražeći Pancha i mlade. Vidjevši samo crnog ovna, sleti do njega i upita nije li negdje vidio njezinu djecu.
„Ne vodim računa o potomcima drugih životinja,” odbrusi Bob.
„Pitam se zašto te nitko nikad ne pita da im pričuvaš djecu!” odgovori Emma istodobno se krećući oko seta instrumenata. „Kakve su ovo stvari?”
„Odlazi odavde,” crni ovan reče tonom od koje Emma poskoči, „Mislim da je to bomba!”
„Ne budi smiješan. Uvijek si tako paranoičan,” reče purica, no ipak zakorači unatrag. „Izgleda poput nekakvih glazbenih instrumenata,” reče podignuvši glavu, „zar ne? Te još neke kutije i košare.” Zamahne krilom prema setu bubnjeva.
Bob duboko udahne, te polako ispusti dah. Zatim, svojim joj najmilijim glasom počne pričati o bendu štakora i onom što su zečevi radili.
„Znam što misliš Emma, da sam uvijek sumnjičav glede pridošlica, no oni su se zaista čudno ponašali.” Ovan se činio tako iskren da mu je Emma skoro rekla ono što je zapravo mislila, ono što su joj ljudi rekli za špijune u Špiljskom kampu. No, još jednom promisli. Bob bi odmah zaključio da su jadni Blackstone i Hamilton špijuni te bi ovi, vjerojatno nevini, bili optuženi.
Emma se dogega i pogleda kovčeg. „Isključimo ga,” reče, „i pogledajmo što je unutra.”
Bob potvrdno i važno klimne, dođe do kovčega i izvuče iz njega kabel. Pokušaju ga otvoriti, ali je brava bila zaključana. Purica i ovan stanu razmišljati o tome što će učiniti s kovčegom kad on počne zvoniti. Je li to bio alarm? Ili možda upozorenje o bombi? Purica odskoči unatrag, a Bob u trenutku hrabrosti zgrabi kovčeg i baci ga usred jezerca. Kovčeg potone radeći oko sebe velike koncentrične krugove koji su se odbijali o rubove. Purica i ovan pokriju uši i pričekaju, no nije bilo nikakve eksplozije. Bob zgrabi uže te ga otrgne od stupa.
„Struja je zlo,” reče, „Oduvijek sam to znao.” Zatim odmaršira u štampariju.
Emma stane tražiti svoju obitelj. Išla je prema vrtu, jer je mislila da će najvjerojatnije tamo pronaći svinju. Zečevi doskoče do nje takvom silinom da su je umalo zgazili. Potrče prema instrumentima i počnu nešto tražiti oko kabela. Emma vidje da su našli strgano uže bezuspješno tražeći kovčeg. Hamilton je držao nešto crno veličine krumpira, samo kvadratnog oblika. Pogleda u nešto, odmahne glavom i baci to u jezero prije nego što se zajedno s Blackstoneom vrati natrag u staju.
Emma odluči riskirati. „Nešto nije u redu?” reče slatkim glasom, „Možda ja mogu pomoći.”
Zečevi zastanu i počnu zamuckivati. „Zašto, ne, Emma, sve je u redu. Pancho je s tvojom djecom u vrtu,” reče Hamilton.
„Lijepa farma,” doda Blackstone te njih dvojica odskakuću.
„To je bilo vrlo sumnjivo,” promisli majka dok je trčala prema vrtu. „Za sada ću držati kljun začepljen i oči otvorene,” zakune se. Raširenih krila dotrči do svoje djece, kojima nije bilo ni upola tako drago što je vide kao što je to bilo Panchu.
Zagrlivši Sally, Pancho krene prema štampariji i svom odboru za plakate. Kad se približio maloj nastambi, začuje prigušene glasove ovna i koze zadubljene u dubok i tajnovit razgovor. Pancho zastane da posluša koji trenutak, no iz straha da ga ne optuže za špijunažu, digne šapu i stade snažno lupati o vrata svojim svinjskim zglobovima.
Nakon par sekundi vrata se malo otvore i koza proviri svoju bradicu.
„Što hoćeš?” zableji prema Panchu.
„Ja sam u vašem odboru. Došao sam pomoći,” objasni svinja bradici. Vrata se zalupe i Pancho je jasno mogao čuti svađu unutra. Napokon se vrata ponovo otvore, ovaj put dovoljno široko da bi Pancho uspio ući.
„Odlučili smo da nam je ovako lakše držati te na oku, uđi,” bila je njegova dobrodošlica.
Pancho je neko vrijeme privikavao oči s danjeg svjetla na prigušeno svjetlo lampe u štampariji. Prozori su bili oblijepljeni nečim što je izvana izgledalo kao papir, no Pancho je sad vidio da su to zapravo bili stari politički plakati. Prostorija je bila prepuna prašine. Štamparija je bila prastara. Zgužvani papiri i pisma su bili razbacani posvuda. Ipak, Panchu se svidio miris tinte. Bio je nestrpljiv da počne.
„Evo,” Bob mu pod njušku gurne vlažan letak. „To je to, trebamo još samo naslov.”
Pancho pogleda komad propagandnog lista kojeg mu je ovan dao. Vrh papira je bio prazan, a ostatak je papira podijeljen na tri dijela i ispunjen najmanjim mogućim slovima, s više vrsta fontova, u kojem je bila opisana čitava farma, njezina povijest, sadašnja situacija, osobna filozofija stare koze i Bobova uvjerenja (koja su bila slična, no to se u letku nije vidjelo jer su tamo naglašavali svoje različitosti). Pancho je sebe smatrao intelektualcem, ali ipak nije bio siguran što pojedine riječi znače. Nakon trećeg paragrafa, potpuno se izgubio.
Ipak, letak je zaista izgledao impresivno. Kad bi još samo smislili pravi naslov, možda bi mogao i upaliti.
Imali su nekoliko ideja: Anarhosindikalizam sada, Sva moć mašti, Natrag u pleistocen, Potkopajmo korporacijsku urotu, i Branimo prava životinja.
Svađali su se oko svakog. Kad bi koza bila za jedan naslov, ovan bi bio protiv. Panchu je bilo jasno da nikakvog kompromisa neće biti, no barem su se kretali u smjeru da spoje nekoliko njih u jedan: Srušimo korporacijsku paradigmu kroz maštovit anarhosindikalizam.
Sally ih prekine pokucavši na vrata.
„Nadam se da još niste dovršili letak,” zaskvikne, „jer štakori imaju odličnu ideju: besplatan koncert i ples za sutra. Životinje će doći odsvuda pa im možemo reći sve o dražbi i zamoliti ih za pomoć. To će biti tako zabavno!” Nasmiješi se Panchu, koji je u grudima osjetio da mu je srce poletjelo. Tad ona ode.
„Zabava. Ovdje se ne radi o zabavi,” bjesnila je koza.
Naslov je nakon još nekoliko sati prepiranja glasio: „POTKOPAJMO KORPORACIJSKU UROTU KROZ BESPLATAN KONCERT I PLES,” napisan najvećim slovima različitih fontova. Zatim u sljedećem redu manjim slovima: „Srijeda navečer na farmi Krug A”. Sve dok se nisu odštampali svi leci, nitko nije primijetio tipografsku pogrešku, a tada je već bilo prekasno za bilo kakve ispravke.
Sve su životinje bile impresionirane i zadovoljne lecima.
„A zbog čega se farma uopće zove Krug H ?” upita Bob u obrani.
„Hrana,” povikne Čangrizalo, „a Krug A znači
„
„Advokat,” vikne Pancho i sve se životinje nasmijaše.
Samo je Goldie mahala glavom. „H znači Hansen,” reče, „to je bilo Margaretino prezime.”
No, nije bilo nikog tko bi s njom podijelio tu nostalgiju.
Za par minuta Bonkers uze čekić te se uspne na ulazna vrata. Lupao je po vrhu slova „H” napravljenog od kovanog željeza sve dok se okomite crte nisu približile i stvorile slovo „A”.
Životinje se okupe oko vrata kako bi gledali Bonkersa u njegovom radu. Majmun im izmami osmijeh na lica, a novi simbol ulije novu nadu u njihova srca.
Pancho došeta do ptičara koji je stajao na rubu gomile. „Novo ime je dobra stvar. To će nas zbližiti. Nov identitet,” reče svinja. Ptičar se nasmiješi i ode natrag svom poslu na barikadama.
Rosy je njezin žig staromodan pa je Sabo donijela kist i boju i malo poradila na njemu. Ubrzo se stvorio red mladih životinja koje su čekale da im Sabo oboji Krug A na njihovim stražnjicama.
Pancho je primijetio kako su štakori već podosta utjecali na mlade, koji su se obojili u široki spektar boja. Janjadi i djeci se boja primila dosta dobro. Oni s tamnijim krznom su stavili ukrase na uši, od čega se starijima dizala kosa na glavi.
Pripreme za predviđeni sukob u subotu su jenjavale, no skupljala se energija za besplatan koncert. Nova je skupina fanova uredila staju za narednu večer. Jethro je pokušao par puta nešto predložiti, no svi su se njegovi prijedlozi odbacili jer su sljedbenici imali nove ideje za uređenje. Suzy i Sally su skupile sve što je bilo potrebno za uređenje, a mazga i krmače su bile zamoljene da pričekaju vani dok štakori i njihovi novi fanovi ne dovrše što su imali u planu.
„Boju i sve ostalo samo ostavite na vratima.” cvrkutao je Orville, Emmin sin, „I ne virite unutra. Želimo sve iznenaditi novim klubom.”
Jethro odmahne glavom. „Nadam se da postoji odbor za čišćenje,” reče svinjama.
Sally se nasmije: „Oh, sigurna sam da će vas pozvati da im pomognete oko toga. Međutim, lijepo je vidjeti ih tako angaži-rane i uzbuđene.”
„Od toga se osjećam staro,” uzdahne Jethro.
„Od toga se osjećam mlado!” reče Sally.
„Jesi li sigurna da se zbog ovoga osjećaš mlado?” Suzy je bockala sestru.
„Ne znam o čemu pričaš,” smijuljila se Sally dok je odlazila mašući ostalima repom.
„Mislim da joj se sviđa Pancho,” šapne Suzy mazgi. „Nadam se da se i ona njemu sviđa.”
Jethro je obožavao kad je znao neku tajnu.
Srećom, djeca su bila zaposlena uređivanjem staje. Emma je bila potpuno zaokupljena zečevima. Nije ih htjela krivo optužiti, no zbog razgovora s ljudima bila je na oprezu. Nakon onog kovčega koji sada leži na dnu jezera, hm
„Samo ću čitavo vrijeme biti uz Blackstonea i Hamiltona. Neće moći špijunirati, ako je to ono što pokušavaju,” odluči.
Emma se držala zečeva poput ljepila. Naposljetku su se zečevi počeli živcirati i biti sumnjičavi.
„Nisam znao da te toliko zanima zakon o izumima,” Black-stone skeptično upita puricu, „Imaš li neki izum ili ideju koju želiš zaštiti?”
„Pa,” Emma zastane, „Nemam još pravi izum, no mislim u budućnosti nešto izmisliti.” Bilo joj je teško zadržavati pozor-nost zečeva, a i sve je teme već iscrpila. „Reci mi Hamilton, koji je bruto nacionalni proizvod Brazila?” Primijeti da Hamilton zuri u smjeru staje. „Nikako to ne mogu zapamtiti.”
„Emma, gdje su one male baršunaste loptice koje ti obično oduzimaju vrijeme?” nasmiješi se Hamilton purici, te pogledavši Blackstonea zakoluta očima. Tad zečevi spoje misli, kao što to može svaki urotnik, i shvate kako pobjeći. Zajedno kažu: „Emma, bilo je predivno, no moramo ići!” Skoče u suprotnim pravcima.
Purica se zbuni: što da radi? Počne trčati u jednom smjeru, zastane pa počne trčati u drugom, ne znajući kojeg zeca slijediti. Napokon sjedne. Emma je prije nekoliko sati stisnula zečeve u kut i zaista je bila iscrpljena razgovorom. Sada su sumnjali na nju, te su je počeli izbjegavati. „Čak i ako su nevini,” prizna purica sama sebi, „sigurna sam da im je zlo od mene. Trebam pomoć.” I zaklepeće krilima prema barikadama.
Goldie je radila sama, gomilajući drva i grmlje kako bi napra-vila lažnu živicu. Namjera joj je bila da sakrije životinje tako da bankari i policija ne znaju koliki je zapravo otpor.
Emmin krik razbije Goldinu koncentraciju. „Goldie, zovi Rosy i nađimo se kod štamparije.”
Pas klimne. Iz puričina je držanja mogla vidjeti da se radi o nečem važnom. Emma odleti do štamparije i stade udarati o vrata. Unutra su stara koza, crni ovan i bijela svinja Pancho skupljali letke za predvečernje bacanje iz zraka koje su trebali obaviti golubovi.
„Tko je?” Vrata se malo otvore i kozja bradica proviri vani.
„Emma je. Bob, jesi li unutra?”
Crni se ovan pojavi i, naravno, i ovo drugo dvoje, baš kada su dolazile Goldie i Rosy.
„Pogledaj moj novi žig!” reče krava, zabijajući svoju stražnjicu Emmi u lice.
„Vrlo lijepo, Rosy, no ovo je važno,” počne purica, „Danas sam pričala s nekim ljudima.” Štampari uzdahnu, no Emma nastavi. „Onima koje naši čuvari šume skrivaju.” Pancho se nagnuo da bolje čuje jer je purica od silnog pričanja promukla.
„Nisu imali nikakvu odjeću na sebi.”
„Stvarno!?”
„Kako su izgledali?” Bobove se oči skupe dok je pokušavao zamisliti kako to izgleda.
„Bolje, malo bolje. Bez mnogo dlaka ili krzna. Slično
„ Emma pogleda životinje, pa krilom pokaže na svinju, „\dots{}njemu. Na kožu mislim.”
Svi se ostali nasmiju dok se Pancho crvenio. „Mnogo hvala. Izgledam kao čovjek!” Okrenuo se da krene natrag u štampariju.
„Nisam tako mislila, vrati se Pancho,” Emma mu se stala ulagivati, te se on vrati. „Uostalom, izgledali su mnogo sličnije životinjama, znate, pa je i bilo lakše pričati s njima.” Ostali klimnu.
„No, ono što sam vam htjela reći jest ovo: ljudi su rekli da u Špiljskom kampu postoji špijun. Ili dva. Ne znaju tko je, no stvari su počele curiti prije otprilike godinu dana, a špijuni znaju i čitati i pisati.”
„Većina nas zna čitati i pisati,” reče Pancho, osjećajući kao da se treba braniti. „Barem malo.”
„No, to nije sve,” Emma pogleda Boba, koji se jedva suzdr-žavao, „Bob, reci im.”
Ovan je bio toliko zadovoljan što ima publiku koja će mu ovaj put vjerovati, da se bacio na vrlo dramatičnu prezentaciju onoga što se događalo na jezeru. Čak je imao i Emmu da to sve potvrdi.
„Cijelo sam popodne nadgledala zečeve, ali su mi pobjegli,” doda Emma.
„Mi ćemo to srediti,” reče koza, klimajući Bobu.
„Budite pristojni vas dvoje, imajte na umu da smo ih mi pozvali u goste,” reče Goldie, „Nećete biti toliko sumnjivi ako vam Pancho i Rosy pomognu u tome.”
„Kao ekipa za igranje lovice,” mukne Rosy.
„Emma, daj mi pokaži gdje je kovčeg. Moramo imati dokaz,” nakesi se Goldie, „Ne zovu me uzalud ptičar.”
Purica i pas krenu prema jezeru. Ostali krenu u potragu za zečevima.
Hamiltona i Blackstonea nije bilo teško pronaći. Sjedili su ispred staje i s nekoliko životinja razgovarali o planovima za subotu. Pancho je bio ljut, no sam sebi reče kako nitko nije kriv dok se ne dokaže suprotno. Njih su dvoje sjedili tu i radili upravo ono što im je i bilo rečeno da rade: savjetuju u vezi sa situacijom s bankama.
„Nije važno što znaju sve dok im mi ne dopustimo da to procuri,” svinja šapne Bobu.
Ovan klimajući potvrdi, iako se činilo da se baš ne slaže s tim.
„Ne znam da li je pametno da se odupirete u subotu,” savjetovao je Hamilton.
„Definitivno ne,” složio se Blackstone. Bilo bi bolje da im dopustimo da misle da su pobijedili, a zatim ih iznenaditi s pobunom.”
Životinje ovo zbuni.
„Ali, mi smo odlučili da im nećemo dopustiti da preuzmu farmu. Bit ćemo miroljubivi, no moramo pružiti otpor,” izrecitira Jethro polako.
„Imate li uopće ideju protiv koga se borite?” Hamilton nabaci svoj ulizivački ton, „Banka je ogromna, a korporacija, hm, korporacija je prevelika da bi ju se izazivalo.” Protrese glavom i nekoliko mu buha ispadne iz uha i sleti na prljavštinu ispred njega. „Zgazit će vas poput kukaca,” i rekavši to digne stražnju nogu te s takvom silinom zdrobi one buhe da su vjerojatno završile u Kini.
„Imat će oružje, a i policiju,” objasni Blackstone, „Vidite, policija je prvobitno tu da zaštiti korporaciju, nemojte to smetnuti s uma.”
„Psi sa susjedne farme imaju oružje,” jedna od gusaka reče optimistično.
„Ne bih računao na pomoć pasa,” nasmije se Hamilton, „Ne mogu ni sebe zaštititi.”
Pancho je slušao ono što su zečevi govorili. Sve što su rekli o moći banaka i korporacija bilo je istinito. Možda je bilo besmisleno da se pokušaju boriti protiv nečega tako velikog i moćnog kao što je to korporacija. Pancho je vidio promjenu na licima životinja dok su slušale zečeve. Postale su nesigurne i pune straha, no možda je sve to bila realnost.
„Možemo im prirediti iznenadni napad!” reče ratoborni pijetao koji se tuda šetao, „U zoru!”
Blackstone uzdahne, a zatim prigušenim, ali ozbiljnim glasom reče: „Slušajte, ne razumijete ništa. Kad vas korporacija napadne, morate znati da su oni sve. Policija, mediji, čak i vlada i banka. No, kad vi napadnete korporaciju, ona je nitko. Skriva se iza gomile papira i ne može je se pronaći.”
„Ako korporacija želi farmu, uzet će je,” nastavi Hamilton, „Ako za to mora pobiti sve vas, to će i učiniti, mediji će to lijepo prikazati, a vlada će pronaći način da to opravda, banke će to financirati i svi će ostali ignorirati vaše molbe za pomoć, jer, naposljetku, ne radi se o njima.”
Životinje ostanu zabezeknute. Pogledaju zečeve, zatim jedni druge, zatim u pod, no nitko ne reče ni riječi. Staja je bučala od priprema za zabavu i sretnih mladih glasova odbora za uređenje. Pancho pogleda letak koji je ležao pred njim. Odjed-nom se osjetio naivnim. Stvari su se promijenile od starih dana kada su pobune bile uspješne. Jedna se farma nije mogla sama boriti protiv velike korporacije. Čak i da u subotu pobijede, do ponedjeljka će biti poraženi.
Životinje su se počele povlačiti svojim zadaćama spuštenih glava i izgubljene u mislima. Uskoro su uz zečeve ostali samo Bob, Pancho, Rosy i Čangrizalo. Pancho progovori kako bi razbio neugodnu tišinu.
„Što je s čuvarima šume?” upita, „Oni se bore protiv korporacije.”
„Naravno, bore se, no da li pobjeđuju?” odgovori Blackstone. „Jedan korak naprijed, dva natrag.”
„Ako počnu pobjeđivati, zgazit će ih,” odgovori Hamilton, „Mislim, nas će zgaziti.”
„Mora da vam je teško boriti se za nešto za što mislite da je beznadno,” doda Rosy najslađim mogućim glasom. Bob se ugrize za jezik i pogleda prema jezeru, pitajući se što je sa dokazom.
Već je počeo padati mrak, a i muljavo je dno jezera još više otežalo potragu za crnim kovčegom. Goldie je ronila i ronila sve dok ga nije nanjušila, te posljednji put zaroni i izvuče ga van na obalu. Prije nego što su otvorile kovčeg s nekim štapom, Emma i Goldie pažljivo prekontroliraju kovčeg.
„To je telefon,” reče pas, „Nikad ranije nisam vidjela nijedan u kutiji, no to je to, sigurna sam.”
„Drago mi je što nije bomba,” reče Emma, „Je li to dokaz špijuniranja?”
Pas pretraži svoju memoriju znanja o telefonima. „Oni služe za razgovaranje s prijateljima,” sjetila se Goldie, „Svejedno, i špijuni ti mogu biti prijatelji.”
„Što je ovo ovdje napisano, ovo malim slovima?” Emma pokaže na nekoliko naljepnica pored svakog gumba. Od vode su se počeli guliti, no Goldie ih je unatoč tome uspjela pročitati, iako nije znala što znače.
„FBI, CIA, Sjed. Korp., Mama,” izgovarala je polako. „Čangrizalo bi to mogla znati. Ili Pancho.”
„Idem po njih,” uzvikne Emma i krene.
„Ponašaj se uobičajeno”, upozori je Goldie.
„Uvijek,” odgovori.
Njezino više nego negraciozno spuštanje u dvorište staje privuče pažnju svih. Zečevi počnu gunđati na pomisao da bi mogla neprestano pričati, no umjesto toga Emma polako došeta do iza zečeva i trzajima glave prvo dade signal crnom ovnu, a zatim i svinji. Još je nekoliko puta morala trznuti glavom da ostale upozori o onom što se događa. S jeftinim se isprikama upute niz brdo, prvo Bob, zatim Pancho i Emma, ostavljajući Rosy i nervoznu kozu da pripaze na zečeve.
„Vrlo čudna ptica,” isceri se Blackstone.
„Možda je popila previše,” Hamilton sarkastično primijeti te se oboje nasmiješe.
Bob i Pancho prvo pregledaju gumbe na telefonu, pa izmijene poglede.
„Pa, FBI i CIA,” počne ovan, „su vladine anti-životinjske organizacije. FBI znači Farmski Biro za Istraživanja. CIA znači Centar za Iskorjenjivanje Animalizma.”
Pancho klimne. „Špijunski centar.”
Pas i purica su izgledali vrlo uznemireno.
„Sjed. Korp. vjerojatno znači sjedište korporacije,” doda svinja, „No, Mama
što bi to moglo biti?”
Svi su neko vrijeme premišljali, nakon čega Goldie sramežljivo predloži, „Možda je to majka, što mislite?”
Sliježući ramenima, životinje se slože da bi to mogla biti nečija mama.
„U svakom slučaju, druge nam oznake sve govore,” reče Bob.
„Sve,” doda Pancho.
„Je li to dovoljan dokaz?” upita purica, „Da ih izbacimo s farme?”
„Meni je ovo prilično dovoljan dokaz!” izjavi Bob.
„No, znaju previše da bi ih pustili.”
„Mora biti suđenje,” reče Goldie, s čim se Pancho složi. „Možemo čekati do iza subote. Tad će, čak i ako ih pustimo, biti prekasno da nam upropaste plan.”
Penjući se uz brdo, životinje su nosile telefon iz kojeg je još uvijek kapala voda. Bob stavi kovčeg pred zečeve, koji su hinili nevinost.
„Nikad to nisam vidio,” reče Hamilton.
„Pozivam se na ustavno pravo da ništa ne kažem,” odlučno reče Blackstone.
Rosy oglasi svoje zvonce te se ubrzo sve životinje skupe na dvorištu. Svi su pregledavali telefon. Bob im ispriča svoju priču, zatim Emma svoju, dok su Pancho i Goldie nadopunjavali s onim što su znali.
„Ovo nije suđenje, njega ćemo imati poslije, no trebamo zaštiti naš tajni plan,” objasni Goldie životinjama.
„Tajni plan!” uzvikne Blackstone, „Čemu onda svi ovi leci? Koncert će vam biti prepun špijuna svih vrsta.”
„Amateri,” Hamilton s prijezirom reče.
„Šljam CIA-e,” povikne Carlos, negdje iz pozadine gomile. Životinje ga počnu propuštati da prođe. Nitko nikad nije čuo takvo nešto od ljame koja je uvijek bila slatkorječiva. „Kad samo pomislim da sam vas ja donio tu, na svojim leđima. U moj zemlji znamo što treba uraditi sa špijunima.”
„Ne,” Rosy mu zapriječi put, „Imat će suđenje.” Pogleda Carlosa. „Pošteno suđenje. No, do tada moramo pronaći neko mjesto gdje ćemo ih držati tako da nas više ne mogu špijunirati.”
„Imamo takvo mjesto.”
Svi se okrenu da vide tko je to zarežao odostraga. Tamo su stajali Hans i Kurt.
„Da, dajte nam da ih mi uzmemo. Pazit ćemo na njih vrlo dobro,” zalaje Hans.
„Hm, oni su profesionalni psi čuvari,” reče Suzy, „Zašto ne?”
„Ja se slažem,” reče Goldie, „U redu?” upita skup.
Klimanje i povici potvrde zamisao. Zečevi su se doimali potresenima: mislili su da će se razgovorom uspjeti izvući iz škripca. Čak i sada nisu odustajali.
„Ne možete to napraviti. Što je s našim pravima?” reče Blackstone.
„Odbijamo otići u čopor!” zaprijeti Hamilton.
„Nemate pravo izbora,” reče Bob, iznimno sretan što ima posla s pravim špijunima.
„Sretni ste što vjerujemo u pravu demokraciju, jer bi u suprotnom slučaju već bili mrtvi,” doda Čangrizalo, tresući svoju bradicu direktno njima u lice.
„Nemojte ih ozlijediti,” upozori Goldie Hansa i Kurta.
„Ne bi na to niti pomislili,” reče Kurt dok je grubo ščepao Blackstonea za uši.
„Nježno, kao s mojom rođenom bakom,” reče Hans, noseći Hamiltona u tunel. Psi gurnu zečeve u tunel i nestanu iz vida.
\textbf{- 17 -}
U srijedu ujutro dan bijaše čist i ružičast. Pancho je to jutro vidio zoru, jer je spavao vani zajedno s ostalim životinjama. Staja je bila zatvorena zbog priprema za veliki događaj. Noćno ispuštanje letaka je prošlo uspješno, a leci su na susjednim područjima uzrokovali podosta strke. Farma se rano probudila i, kao obično, većina je životinja krenula prema livadi na jutarnju tjelovježbu.
„Oh, zašto ne,” pomisli Pancho. „Mogu probati nešto novo, a i malo vježbanja bi mi dobro došlo,” mislio je dok se zajedno s ostalima gegao prema jezeru.
„Stani tu,” dozva ga Goldie, te se Pancho progura kroz stado i stane između psa i Jethra.
„Što trebam raditi” upita svinja, no prije nego dobije odgovor, ovan iza njega ga obori na pod. Životinje se zatrče udesno, ostavljajući iza sebe Pancha koji ih je pokušavao uhvatiti.
Goldie ga ponovo uvede u grupu. „Pokušaj se koncentrirati na ostale oko sebe,” reče. „Ne brini se gdje oni idu, pazi na ostale i kada će oni krenuti.”
Pancho pokuša, ovaj put s malo više uspjeha. Koncentrira se na Goldie i potrči prema naprijed zaustavivši se tamo gdje i ona. Kad je stado krenulo na drugu stranu, Pancho je ipak propustio znak, te je njegovo oklijevanje prouzrokovalo pad desetero životinja jedne preko druge. Svi se nasmiješe i podignu jedan drugoga s vlažne trave.
„Trebaš biti svjestan svakog, ne samo jedne ili dvije životinje,” reče mu Sabo dok se kretala kroz poludjelu masu u kojoj je i nestala.
„Ovo je teže nego što izgleda,” pomisli Pancho, no pokuša iznova. Svaki je put bio sve uspješniji u tome da se osjeća kao dio grupe. „Vrlo zanimljivo, toliko da se od toga osjećaš moćno, štoviše značajno.” Bio je iznenađen, jer je uvijek mislio da grupa pojedincu oduzima moć. „Zaista smo sila na koju treba računati.”
Pancho se na kraju trčanja osjećao vrlo moćno. Sjedne uz jezero da uhvati dah. Pridruži mu se vesela bijela ovca s crnim licem. „Za prvi si put bio odličan,” čestita mu bijela ovca. „Zovem se Isadora,” nasmiješi se. „Tvoje ime već znam, ali sada se zoveš Pancho, zar ne?”
Svinji padne vilica. Dobro pogleda ovcu, no morao je priznati da su njemu sve ovce izgledale poprilično isto. Pancho nije znao tko je ona.
„Sigurna sam da me se ne sjećaš. Bila sam malo veća od lampe kad sam pobjegla s naše stare farme,” nastavi Isadora, „Na svu sreću otišla sam prije nego su se stvari zaista pogoršale.”
Pancho gotovo da nije mogao vjerovati. Ovca s njegove stare farme! Ali, ona je pričala o bijegu. Zar je ostalim životinjama bilo tako grozno da su morale planirati bijeg? I zar su svinje bile tako gluhe na njihovo stanje da nisu čak ni primjećivale kad bi pobjegle? U ovom je slučaju Pancho mogao pretpostaviti da je odgovor bio „da”.
„Dakle, ti si došla tu?” Bilo je to retoričko pitanje.
„I ti si!” nasmiješi se ovca, „Uvijek sam mislila da si ti jednako loš kao i ostale svinje, sve dok nisi došao tu. Izgleda da se mijenjaš.”
To je boljelo. Pancho nije baš znao što reći na to. „Dosta sam naučio. I još uvijek učim.” Mahnuo je prema livadi koju su baš napuštali. „Vi ovce ste prirodni stručnjaci u što god bilo da smo dolje vježbali.” Pancho se nije mogao prisiliti na to da kaže „vježbanje stada.”
„Mislim na to kao na suosjećanje,” reče Isadora, „Sposobnost da osjećaš ono što drugi osjećaju. Zar nisi primijetio da se ovce međusobno osjećaju? Ozljeda jednog je ozljeda sviju.”
Pancho klimne te ovca nastavi. „Mnoge bi se svinje bojale suosjećanja, jer one to vide kao smanjivanje njihove individual-nosti, no to je zaista samo njezino proširivanje, a ne uzimanje. Poput zaljubljivanja.”
Ovca namigne Panchu. „To je ono zbog čega se razlikuješ od svih ostalih svinja na staroj farmi.” Pošto Pancho nije ništa govorio, Isadora odluči otići.
„Moram ići, kasnim na vježbe pucanja,” reče ovca.
„Vježbe pucanja?” Pancho je sada napokon progovorio, „Mislio sam da na farmi nema oružja.”
„Idem u čopor. Kurt me uči kako da upotrijebim strojnicu.” Isadora se nasmije. „Nikad ne znaš kad će ti takvo znanje zatrebati.” Zatim doda: „Vidimo se sutra ujutro.”
„Drago mi je što sam te napokon upoznao,” reče svinja, „Bit ću sutra tu.” Promatrao je ovcu dok je hodala prema čoporu. „To je jedna ovca koja je jedinka,” promisli, „no, što je s Bobom, crnim ovnom?” Pancho je to vrtio po glavi. „Kako da kažem, on sigurno ne trči u stadu.”
Pancho sjedne i promotri farmu. Štakori su do staje razvukli nove kablove. Počelo je i pripremanje hrane za zabavu. Preko u voćnjaku, blizu stabala breskvi, Hans i pudlica Monika su se valjali u travi. Pancho se nađe kako mu misli lutaju do određene školske učiteljice s mekanom vlažnom njuškom.
„Nadam se da ona još nije našla partnera za zabavu,” mislio je hodajući do svinjca. Sally se spremala da započne sat u malom oboru pokraj staje, no prije nego što počne, stane popričati s Goldie i Sabo.
„Idemo posjetiti Svetu Kravu,” reče Goldie, „Prestara je da dođe na večerašnju zabavu, no želim da zna što se događa.” Pancho klimne i Goldie ga upita: „Želiš li je možda upoznati?”
„Naravno, bilo bi mi drago,” odgovori Pancho, „Samo sam htio nešto pitati Sally.” Sabo i Goldie ostanu na mjestu gledajući kako Pancho promatra Sally. „Nasamo, ako vam ne smeta.”
„Oh, nasamo,” zasikće Sabo, te se nasmije psu dok su se malo odmicali natrag. Sabo se trudila čuti. Pancho je nešto mrmljao, a Sally se smijala i klimala glavom. Sabo je bila uvjere-na da je čula riječ „partner”. Svinja se okrene da mahne Sally prije nego se pridruži mački i psu. Izgledao je vrlo zadovoljno.
„Dogovor za izlazak Pancho?” zaprede mačka.
„Što nije u redu s tim?” svinja zapuše, „Ona je vrlo inteligentna krmača.”
„Ostavi ga na miru, to je baš slatko,” reče Goldie, upotrebljavajući riječ koju nitko nikad nije rabio da opiše njega ili njegove aktivnosti.
Pređu ogradu između mljekare i farme, pažljivo hodajući kroz livadu miniranu kravljim izmetom. U bijeloj staji na kraju livade ležala je majušna smeđe-bijela krava. Bila je tako mršava da su joj se na leđima jasno vidjele kosti, a velike smeđe oči kao da su upale u mekano lice. Nasmiješi se životinjama koje su dolazile.
„Nema Rosy?” upita ptičara. Kad je Goldie odmahnula glavom, krava uzdahne: „Rosy je moja kći, no sada me rijetko dolazi vidjeti.”
„Dobro je,” reče Goldie, „Ovo je Sabo, a ovo je Pancho, novi su na farmi.”
„Došli ste u važno vrijeme,” reče krava pozdravljajući ih.
„Baš smo o tome došli porazgovarati,” nastavi Goldie, te joj ispriča sve o problemima i špijunima.
„Što ti misliš, Majko Krava?”
Krava malo razmisli, pa odgovori nježnim mukom: „Nekad se moraš roditi, nekad moraš umrijeti, nekad moraš preživati, a nekad trčati u stampedu.”
„Stampedo!” reče Pancho iznenađen, „Može li to upaliti?”
„Stampedo je nezaustavljiv,” odgovori stara krava, „No, pravi stampedo zahtijeva potpuno sudjelovanje, potpuno posvećivanje i sve životinje koje će trčati zajedno kao jedan.”
„Ali trebat će toliko mnogo planiranja da uskladimo sve grupe,” reče Pancho.
Krava polako odmahne glavom. „Ne zahtijeva nikakvo planiranje, jer ga ono može samo uništiti. Zar požaru u šumi treba plan? Ne, samo šibica.”
„No, to sa špijunima?” upita Pancho, „Mogu biti posvuda.”
„Špijuni, špijuni, špijuni. Svi se vi previše brinete oko špijuna.” Kravu je izgleda toliko objašnjavanja prilično umorilo. „Ne znam koliko špijuna treba da zaustavi stampedo.”
„Istina,” odgovori Pancho, „Ako nemamo plan, što će im onda špijuni?”
Goldie je također razmišljala. „Majko Krava, uvijek si nas učila nenasilju. No, zar stampedo ne bi bio nasilan? Zar se životinje ne bi ozlijedile?”
„Životinje se ozlijede svaki dan, život je opasan. Životinja se može ozlijediti dok obrađuje polje, ili dok preskače ogradu ili dok se penje uz brdo. Međutim, tu nema nasilja. No, ako ne krenete u stampedo, doći će korporacija i sve vas ubiti, čak i ako budete surađivali. Stampedo nema nasilje kao svoj cilj i bit će najuspješniji ako se nijedna životinja ne ozlijedi. Stoga, može biti opasan, ali nije nasilan.”
Pancho razmisli o ovom. Njemu nije bilo toliko do toga da li je stampedo nasilan ili ne koliko do toga hoće li on uspjeti. „No, što ako krenemo u stampedo i nitko nas ne bude slijedio?” napola se šalio. „Kako možemo biti sigurni da će nam se životinje pridružiti? Znam da nas je mnogo, i ako uspijemo nagovoriti svakog da se posveti Velikom Stampedu, mogli bi pobijediti korporaciju i uspostaviti nov tip vladavine.” Pancho digne šaku u zrak da potvrdi svoju izjavu.
Sveta Krava ga pogleda istodobno preživajući. „Kakvu to vrstu vladavine misliš uspostaviti?” upita. „Oh, znaš, ljubazniju, nježniju\dots{}” Pancho pogleda Goldie i Sabo tražeći pomoć, no oboje su stajali tiho. „Ne znam, bolju vladu,” reče, „Onu u kojoj su sve životinje jednake.”
„Zar to nismo već pokušali?” podsjeti ga Sabo.
„Mislim da bi bilo pametno da preskočimo novu vladu. Dosta nam je stare vlade,” reče krava umornim mukom. „Znam da je meni bilo dosta. I da odgovorim na tvoje pitanje, ne možeš biti siguran da će nam se pridružiti, ali to i nije bitno.” Pancha su izgleda ove riječi iznenadile. „Ako se životinje ne kreću kao jedno biće, ako to ne bude spontana složna reakcija, onda to nije Veliki Stampedo.”
Pancho počne hodati uokolo po staji. Što je mogao učiniti? Nešto se mora poduzeti! On mora nešto učiniti.
Krava mu pročita misli. „Mala svinjo, ti nisi vođa. Možeš pomoći zasijati sjeme, možeš pomoći u njihovom zalijevanju, i ako si sretan možda dobiješ malo kruha. Ali ti nisi pekar.”
„O čemu ti pričaš?” Svinjin je glas bio malo prebučan. „Želim biti pekar!” Pancho se sad osjećao malo glupo, pa doda: „Možda bih mogao biti jedan od pekara?”
Krava nastavi žvakati. Pancho još malo prošeta, zatim stane i pogleda kravu oči u oči. „Zašto ti moraš odabrati pekara?” Smeđe oči ne trepnu. Pancho još malo prošeta.
Goldie se suzdržavala od smijeha. Vidjela je Svetu Kravu kako to radi i prije, ali joj je to uvijek bilo tako zabavno. Sabo zakoluta očima prema Panchu, no on je i dalje hodao. Zaustavi se još jednom ispred ostarjele krave.
„U redu,” progunđa, „tko je pekar? Ja ću mu pomoći,” uhvati se, „Ili njoj, na bilo koji način. Posvetit ću se pekaru!” Preklinjao je kravu, „Tko je to?”
„Kako da ja znam?” odgovori krava.
Pancho zabaci papke u zrak. „Onda o čemu mi pričamo?”
„Nemam pojma,” reče krava i stade još malo preživati. Pancho stisne oči i odšeta još jedan krug. Prevrtao je razgovor u glavi. „Rekla si da ja nisam pekar?” zahtijevao je.
„Zar jesi?” upita ga krava, „Što bi ti ispekao?”
Pancho ostane bez riječi. Više mu nije bilo jasno o čemu su pričali. „Kruh?” Mislio je da je čuo da se to spomenulo.
„Koju vrstu?” upita krava.
„Ne znam, zavisi o vrsti žita,” pažljivo odgovori. Zatim, misleći da mu je odgovor prilično tanak, doda: „Cijelu pšenicu! Ispekao bih kruh od cijele pšenice.” Nasmije se slavodobitno.
„A što ako bi žito bila raž?”
„Onda vjerojatno raženi kruh.” Počeo se osjećati nesigurno.
„Sada pretpostavimo da ono sjemenje nije uopće bilo žito i da su možda narasle tikve?”
„Pita!” Pancho nije bio siguran da li je ispravno odgovorio.
„A možda sjemenje nije bilo posijano i ništa nije izraslo,” postavi se krava ozbiljno, „Što bi tad ispekao?”
„Ništa?” zastane Pancho u čudu, „Zar ne?”
„Naravno,” reče krava, „Ne bi bilo ničeg za ispeći i stoga ne bi bilo potrebe za pekarom.” Zatim opet sjedne i ušuti. Pancho također. Opet je u mozgu prevrtao ovo s pekarom.
„Dakle, to što ti želiš reći jest da je još prerano za pekara, no možda kasnije ipak to mogu biti ja?”
Sabo upadne: „Zašto je toliko važno tko je pekar?” upita Pancha. „Zašto se toliko brineš tko će biti pekar?”
„Rekla je kao da je to bitno,” Pancho počne cviljeti pokazu-jući na kravu, „I implicirala je da ja nisam dovoljno dobar da budem pekar,” namrgodi se.
„Ne, nije,” reče mačka. „Sve sam čula i ti si to sam pretpostavio. Sve što je Sveta Krava mislila jest da trebaš posijati neko sjeme, vidjeti hoće li išta narasti i ne pokušavati ispeći kruh prije nego li uopće posiješ sjeme.” Mačka se zatim okrene prema kravi. „Zar ne?”
Stara smeđa glava klimne.
„I, također, nemoj se truditi kontrolirati sve i svakoga. Neko sjeme i ne treba pekara.”
I rekavši to Sveta im Krava okrene leđa, signalizirajući time kraj sastanka.
Svinja i pas krenu, a Sabo dotrči do umorne stare krave i šapne joj u uho: „Mogu li te opet doći posjetiti?”
„Bilo bi mi drago,” reče krava sa smiješkom.
Farma je čitav dan bila prepuna različitih aktivnosti. Bonkers je uspio isposlovati da odsvira par stvari sa Slobodnim radikalima. Uporno je i s puno buke pokušavao uklopiti komad metala u čelični bubanj. Ostali su napravili veliku vatru, održavajući je neprestano drvima i grmljem. Nekoliko im se pasa pridružilo u tome zbog osobnog zadovoljstva. Toranj vatre gotovo da je dosegnuo visinu staje.
„Odakle im sve te stvari?” pitao se Pancho na glas.
Goldie je polako kružila oko hrpe, sumnjičavo je pregledavajući, da bi zatim s iznenadnim režanjem trkom pobjegla. Pancho je stade slijediti do prednje barikade gdje je Goldie stajala gledajući uništenu barikadu.
„Ne mogu vjerovati da su je uništili,” žalila se.
„Pretpostavljam da je bila tako dobro prerušena da nisu ni skužili da je to barikada,” Pancho je pokuša nekako umiriti. „Možemo je sutra sagraditi iznova.”
„Od čega?” Goldie odšeta do pasje kućice i tamo legne.
„Možda nećemo ni trebati barikadu,” pomisli Pancho, „Ne ako budemo dobro izveli stampedo.”
Sabu je Sveta Krava tako dojmila da je potražila Rosy, koja je u voćnjaku brala jabuke.
„Upoznala sam ti majku, Svetu Kravu,” reče mačka u strahopoštovanju.
Rosy ne reče ništa te nastavi sa sakupljanjem, stavljajući žute, zelene i crvene jabuke zajedno u jednu veliku košaru izrađenu od šiblja.
„Pitala je za tebe,” nastavi Sabo, „Trebala bi je poći posjetiti.”
„Dobro je, zar ne?” upita Rosy, „Nije bolesna i ne umire?”
„Ne, mislim da ne,” mačka razmisli, „ali je stara.”
„Je li još puna onog naoko pobožnog smeća?” krava prezirno puhne i zazvoni zvonce, „Zaista ne mogu podnijeti njezino držanje kao da je svetica. Poludim od toga.”
Sabu ovo iznenadi. „Meni se čini veoma mudrom, sviđa mi se.”
„Onda je ti posjećuj,” reče Rosy pokupivši jabuke i krenuvši prema stolovima za piknik koji su stajali pokraj staje.
„Idem i ja,” povikne Sabo za njom. Uspne se na zlatno ukusno drvo da malo razmisli. Nikad nije vidjela Rosy tako naživciranu.
Nakon nekog vremena Goldie krene u šetnju voćnjakom, provjeravajući ima li kakvog otpalog granja koje bi moglo poslužiti u obnovi barikade. Na nesreću, nije bilo ničega, pošto je ona sve to još jučer pokupila. Sabo skoči sa stabla jabuke i počne trčati za njom.
„Ne razumijem zašto se Rosy toliko ljuti na svoju majku,” reče mačka, „Zaista su jako slične.”
„Vjerojatno je to razlog,” reče pas, „Kao Bob i Čangrizalo, koji se uvijek svađaju i cijepe svaku dlaku, bar se to meni tako čini.”
„Ali zašto je Rosy tu umjesto u mljekari?”
„Rosy je bježala još otkad je bila mlada, preskakala ogradu i dolazila tu preko. Život u mljekari je poput vojske, pun pravila, uvijek je svaki dio dana određen za neku radnju. Sveta Krava je svaki put trebala dolaziti po Rosy kad bi ova pobjegla,” smijuljila se Goldie. „Neke životinje ne možeš istrenirati, ustvari čitava nam je farma prepuna nekomformista, u slučaju ako nisi primijetila. Na dan kad su ljudi žigosali životinje u Krugu H, Rosy je doskočila u red. Vjerojatno ni sama nije znala koliko će je to boljeti. No, zbog žiga je majka više nije mogla odvlačiti natrag u mljekaru. Mačke i psi su sretni jer ne nosimo nikakve oznake ili žigove. Dovoljno nam je loše što moramo nositi ogrlicu.”
Sabo klimne. Nijedna ogrlica nije preživjela na njoj duže od sat vremena.
„No, Majka Krava je u svoje vrijeme bila buntovnica,” doda Goldie, „Pričala nam je o velikim protestima za prava životinja, o pobjedama i tragedijama. Bila je jako mlada kad je mislila da se svijet može promijeniti. I sama sam se nekad tako osjećala, ali poput stare krave, počela sam se usmjeravati prema onome što je u meni da bih pokušala shvatiti značenje ovog svijeta u kojem živimo.” Glas joj je bio tako nježan.
„Dakle, Rosy želi da joj majka ponovo bude ona stara buntovnica?” upita Sabo.
„Ne znam što Rosy želi, nije ni ona više tako mlada,” odgo-vori Goldie, „Na svijetu postoje različite mogućnosti, čak i za jednog pojedinca. Moj Bože, počela sam zvučati poput Svete Krave.”
Sabo se složi.
Hans i Kurt počnu gurati teško deblo do lomače. „Hej, svinjo, daj nam nogu!” poviknu.
Pancho uskoči među njih i prednjim nogama stade gurati veliki komad bora. Guranje je i dalje bilo preteško, te nakon par minuta odluče da od debla naprave lijepu klupicu baš tamo gdje su stali.
„Oni zečevi tamo lude,” reče Hans, „Stvarno se trude da ih pustimo.”
„Vjerujem,” reče Pancho.
„Stalno nam govore da će netko napasti čopor i da oni ne žele biti tamo kad se to dogodi,” podsmjehne se Kurt, „Kako oni mogu znati bilo što o čoporu?”
„Samo nas žele zastrašiti, to je trik, zar ne?” upita Kurt.
„Vjerojatno imaš pravo,” reče Pancho uvjeravajuće, „No, ipak, oni su špijuni. Tko zna koje informacije imaju. Zašto bi netko napao čopor?”
„Zečevi kažu da zato što imamo oružje i vlada ne želi da nitko osim njih posjeduje naoružanje,” reče Kurt, „A to je sigurno istina.”
„Imamo pravo na posjedovanje oružja, ali vlada kaže da nam ono ne treba.” Hansu počne pjena izlaziti na usta. „Ako nas napadnu da nam ga oduzmu, zar to ne dokazuje da ga ipak trebamo?”
Pancho ostane zatečen. Nije mu se sviđala ideja pasa s oružjem, no bio je u pravu.
„Nemam pojma hoće li ili ne čopor biti napadnut, ali znam da su zečevi lažljivci i neće nam biti nikako bolje ako ih pusti-mo,” reče svinja. Psi zamišljeno klimnu.
„Mogu se kladiti da su se one ružičaste pudlice žalile vladi na nas ovčare,” zareži Kurt, „Oh, da, vlada je uvijek spremna zaštititi te strane francuske pudlice. Što je s pravima starosjedi-laca njemačke krvi?”
Emma ih je slušala sa svog sjedala na ogradi. Razgovor je postao previše živahan da bi ona i dalje mogla šutjeti.
„Onog dana kad vlada bude poslušala pudlice, ja ću poslušati vladu,” zagrakće purica svima oko vatre, „Nema šanse da će vlada napasti bilo koga zato što su im tako rekle pudlice ili ovčari ili svinje ili purice. Ako vlada napada, onda to čini iz jednog jedinog razloga i zbog zaštite jedne stvari.”
Svi ostanu šutke gledati kao da su u razredu. Pancho osjeti potrebu da podigne šapu prije nego što će ponizno predložiti: „Korporacije?”
„Naravno, korporacije. Oni posjeduju i vladu i medije i sve čega se dočepaju,” Emma napuše prsa. „I kad već govorimo o doseljenicima, mi purice smo domoroci, a ne vi psi koji ste došli i oduzeli drugima posao.”
„Vidiš, rekao sam ti da se ne radi o pudlicama,” reče Hans Kurtu.
„Obožavatelju pudlica!” Kurt odgovori i ode mrmljajući, „Korporacija, urota, ubojice pod vladinom čizmom
„
„Slušaj,” Emma stavi ruku Hansu na rame, „Ne možemo se stalno boriti jedni protiv drugih. Moramo se držati zajedno i boriti se protiv pravog neprijatelja.”
„Podijeli i vladaj, to je njihov plan,” složi se Pancho, „Umjesto da uvijek gledamo u čemu se razlikujemo, moramo gledati u čemu smo slični.”
„Ali, mi jesmo različiti,” reče Hans razdraženo.
„Naravno da jesmo, ali problem nije u tome,” reče mu Emma, „To je naša najveća prednost.”
„Monika kaže da se njezin djed borio s Francuzima u podzemlju,” ispriča Hans, „Ona kaže da su pudlice hrabri borci. Upotrijebit ćemo kojeg god psa budemo mogli u borbi protiv korporacije.” Tad se Hans okrene i krene prema čoporu. „Idem do zečeva. Imamo mi svoje načine da progovore,” reče i ode.
Kad sunce zađe, postave hranu na stolove za piknik i na obližnji privremeni šank. Mladi su kružili oko hrane nadajući se uranjenoj milostinji, a Pancho im se mislio pridružiti. Međutim, primijetio je svoja blatnjava stopala. „Možda kratak skok u jezero prije nego što se nađem sa Sally,” odluči te krene prema livadi.
Još je nekoliko njih imalo istu ideju, te je svinja uskoro plivala zajedno s kozama, kravama, ovcama, guskama, psima, patkama i jednim majmunom. Samo je Sabo ostala na obali, jer joj je draže bilo da se samo poliže. Goldie i Pancho izađu iz vode tamo blizu stijene na kojoj je stajala Sabo, iako ih ona izgleda nije primijetila, smrzavajući se i gledajući negdje u daljinu.
„Što je ono?” Pancho pokuša vidjeti na blijedom svjetlu.
„Tko su oni?” upita Sabo. Hodajući niz tijek rijeke prema jezeru, približavali su im se najveći i najcrnji konj kojeg je ikada prije vidjela i pokraj njega malen skakutavi poni s grivom u očima.
„Vjerojatno su došli na koncert,” povikne Goldie te im otrča ususret.
Konji ostanu na mjestu da pričekaju psa koji je jurio prema njima, još uvijek vlažan od vode.
„Dobrodošli u Krug A. Osjećajte se kao kod kuće,” Goldie se nasmiješi kako je najprijaznije mogla, „Koncert je gore u staji. Došli ste prvi, no hrana je već gotova.”
Veliki konj zadrži svoj stav i pogledom snimi livadu, te na kraju zaustavi oči na zlatnom ptičaru.
„Otišli smo s ranča konja blizu grada. Kako nam je purica rekla, samo smo slijedili rijeku,” objasni psu.
„To je vjerojatno bila Emma,” nakesi se Goldie, „Ona je gore u staji.”
„Vidiš Edsel da je sve u redu,” reče poni, mičući grivu da bolje promotri psa, „Rekao si da je hrana gotova?”
Goldie potvrdno klimne i šapom im pokaže u smjeru staje. Poni ode skakućući, a Edsel ga stade slijediti statičnim hodom. Goldie bi bila otišla s njima, no primijeti još nekoliko posjetitelja koji su baš preskakali ogradu voćnjaka. I Pancho i Sabo ih ugledaju, te im odu u susret da ih pozdrave. Bili su to Judi i Vragolan, zajedno sa svim vjevericama. Iza njih dolazili su Crveni i svi medvjedi i rakuni, jeleni i sve životinje iz Špiljskog kampa. Svinja i mačka se obraduju svojim čuvarima šume, upoznaju ih s Goldie, te ih provedu po farmi.
Stanovnici Kruga A su se pripremali za divlje novajlije, no očito ne dovoljno, jer je njihov dolazak izazvao veliko uzbuđenje. Djeca su jedan drugoga izazivali da dotaknu medvjeda, a kokoši su se trudile da rakunima nikad ne ponestane hrane na tanjurima tako da kad budu gotovi i ne pomisle više na još jedan griz.
I krave iz mljekare su sad bile tu, a kroz tunel su pristizali psi, i to ne samo ovčari, već i pudlice.
Pancho se našao sa Sally. Napunili su tanjure i sjeli pored Judi, koju je Sally oduvijek željela upoznati.
„Učim svoje učenike o čuvarima šume,” reče Sally medvjedu, „Vi ste im heroj.”
Judi se nasmiješi. „Nadam se da će nam jednog dana doći i pomoći nam, jer nam je potrebna sva moguća pomoć.”
Pancho je promatrao čudnu skupinu mačaka koje su upravo stigle na zabavu. Nosile su tamne naočale i pušile cigarete, a neke su imale obojane šape sjajnim bojama. Sally se nagne te mu šapne: „Umjetnici.”
„Stvarno?” Pancho je bio iznenađen.
„Pa, možda ne baš,” nasmije se Judi, „ali one to misle. Ili su možda pjesnikinje.”
Mačke su pažljivo odabirale razne poslastice, kušale ih i pravile se kao da su otrovne. Zatim bi uzele drugu. Panchu su se činile veoma mršave i nesretne.
„Gdje žive?” upita Pancho svoju djevojku.
„Većina se njih rodila u predgrađu,” odgovori Sally, „No, završe na tavanima ili podrumima.” To je negdje pročitala.
„Oh,” Pancho nije razumio, „Ali one ne rade za korporaciju, jel da?”
„Pokušavaju ne raditi to, ali ponekad završe kao dio propagandne mašinerije,” doda Judi, „No, ove mačke ne. Očito je da još umiru od gladi.”
Glasna glazba počne privlačiti prave zaljubljenike glazbe u staju. Mačke umjetnice su bile među prvima koji su ušli u novouređeni noćni klub. Pancho je bio siguran da im se sviđa, jer su odmah skinule naočale i nabacile smiješak na lice.
Štakori i njihovi pomoćnici su zaista dobro preuredili staju. Struja im je omogućila da na splavima imaju svjetla u boji i da pozornicu osvijetle zrakama svjetla. Sijeno je bilo pometeno i drveni je pod sada bio savršen za plesanje. Stolovi i stolice (kutije i gajbe) su bili posloženi u stilu kabarea. Glazbenici su donijeli svoju kuglu s ogledalcima koja su stvarala tanke svjetleće točkice u mraku i davale još magičniji izgled staroj staji. Jedan ručno obojani oglas najavljivao je bend, „Slobodne radikale”, a drugi cilj, „Krug A zauvijek”.
Pancho i Sally sjednu za stol sa strane, malo više prema pozadini, jer su se sjetili razglasa. Štakori uključe instrumente, a Bonkers se pridruži Saharini tamo iza sa svojim novim čeličnim bubnjem. Mlade se životinje počnu komešati oko kabela i mikrofona, dok se staja punila gostima do trenutka kada više nije bilo nimalo mjesta.
Dixion uzme mikrofon. Na onom mu je svjetlu plavo krzno zaista blještalo. „Dobrodošli u Krug A.” Uslijedila je velika buka pomiješanih uzvika uzbuđenja i nestrpljenja. „Mi smo Slobodni radikali, a uz nas je večeras i jedan majmun.” Bonkers mahne publici iz pozadine svojim čekićem. „Željeli bismo početi s omiljenom pjesmom na farmi,” i rekavši to bend počne sa sviranjem neslušljive i gotovo neprepoznatljive izvedbe „Sve životinje imaše farmu, EIEIO!”
Panchu je zvučala jako slično kao i sljedeća stvar i ona iza nje, no nitko nije mario, jer su na podiju stare staje svi plesali zajedno sa svojim susjedima i prijateljima. Na podiju je nastala takva gužva da su se životinje jedva mogle micati, a u staji je postalo užasno vruće. Sally i Pancho su odlučili izaći van malo na zrak, ali su ubrzo shvatili da to baš i nije toliko pametna ideja. U stvari, većina većih životinja i onih s teškim krznom preselila je zabavu van.
„Ovdje se isto dobro čuje bend,” reče Judi, dajući znak svinjama da joj se pridruže, „A i bliže smo hrani.”
Neke su životinje plesale u vrtu, a neke su se samo tu okupile da bi pričale. Kurt i još jedan ovčar pokušaju zapaliti lomaču. Palili su šibicu za šibicom, ali, svejedno, vatra se nije uhvatila.
Pancho reče: „Zar nije čudno da je tamo ogromna hrpa vrlo zapaljivog drva i netko je pokušava zapaliti, a ipak nema vatre.”
Judi klimne. „A jedna jedina šibica nehajno odbačena u šumu ponekad pokrene pravi pakao.”
Psi su sada točili benzin na hrpu. Odmaknu se, upale šibicu i stanu gledati kako će eksplodirati u vatru.
„Pa, eto i to je jedan od načina,” reče Pancho dok su zauzimali mjesta oko lomače.
Emma i konji, Edsel i Jeep, dođu do plamena. Emma se nagne preko prema Judi i, lakomo jedući hranu, upita: „Što ti misliš o onim zečevima?”
Judi je izgledala iznenađeno.
„Zaboravio sam vam reći,” reče Pancho.
„Dopusti meni!” zagrakće purica. Nastavi s pričanjem priče o spletkama i špijunima. Vjeverice su naravno bile radoznale, te se približe, a isto učine i konji i svi ostali koji to još nisu čuli.
No, Panchove su misli lutale, baš kao i oči, sve dok nije primijetio neke od slušača na kraju lomače. Na treperavom je svjetlu bilo teško raspoznati tko su oni ili pak što su oni. Svinja ustane i polako došeta na drugu stranu sasvim neprimjetno, čitavo vrijeme fiksiranog pogleda na strance. Odjednom ga netko odostraga zgrabi i stavi kopito na usta. Tako blizu nosa, Pancho nije mogao pogriješiti tko je to bio: stara koza Čangri-zalo i s njom Bob, crni ovan.
„Šššš\dots{}” rekoše u isti glas te koza pusti svinju i pokaže u smjeru stranaca koje je sada svjetlo vatre dobro osvjetljavalo.
„Ljudi!” Pancho se umalo uguši kad mu samoodređeni čuvari udare kopitima opet po njušci. Kad su se svi smirili Pancho šapne: „Ima nas mnogo više od njih.”
„Idi po medvjeda,” reče Čangrizalo.
Pancho se došulja preko, do mjesta gdje se Crveni izvalio da malo odrijema nakon silnog pića i plesa. Šapat u uho ponovo razbudi medvjeda koji odmah posta živahan. Svinja ga dovede do koze i ovna. Svi zajedno, s medvjedom naprijed, dođu do ljudi.
„Hej,” zareži Crveni nerazgovijetnim, ali strašnim glasom. Ljudi skoče, te se licem okrenu prema medvjedu. Strah u njihovim očima se međutim brzo otopi.
„Oh, Crveni, ti si,” reče bradati muškarac.
„U redu je,” okrene se Crveni snagama sigurnosti, „To su oni ljudi iz šume, sjećaš se Pancho?”
Pancho se sjeti. „Što rade tu?” ljutito upita.
Ljudi podignu letke da svojim ispitivačima pokažu razlog.
„Besplatan koncert,” reče Rocky, „Dođite svi,” pročita s papira.
Dotad su se Judi, Emma i dosta ostalih životinja okupili oko njih. Judi je stajala pored Pancha. Mogla je osjetiti kako se trese od ljutnje. „Neprijatelj mog neprijatelja\dots{}” šapne te Pancho uzdahne.
Tad Emma progovori. „Imam ideju! Zašto se ne skinete?”
„Molim?” reče Rainbow crveneći se na svjetlu vatre, „Jedva vas poznajemo.”
„Uostalom, hladno je,” doda Redwood.
„Pa, stanite pored vatre, ili još bolje, idite u staju, tamo je zaista vruće,” reče purica.
„Ok, mislim da sam shvatio,” reče River počevši skidati košulju sa sebe, „Kao neka vrsta solidarnosti.”
„Recimo samo da odjeća čini svojevrstan nepotreban zid među nama,” odgovori purica.
Ljudi slegnu ramenima, skinu odjeću i ostanu goli pored lomače. Pancho, Bob, Čangrizalo i sve radoznale i oprezne životinje bace dobar pogled na njih.
„Bolje izgledaju, zar ne?” upita Emma.
„Ne bih baš to tako rekao, no stvarno izgledaju kao prave životinje,” reče Bob.
„Jako ružne životinje,” doda Čangrizalo.
„Ja ne izgledam tako,” odbrusi Pancho Emmi sjetivši se njezine ranije primjedbe.
„Moja greška. Mogu li sada ući unutra i zaplesati?”
Mrmljanje koze zadužene za sigurnost uzelo se kao da. Za razliku od ostalih koji su ušli u „Klub Kruga A”, Redwood ostane vani čuti ostatak priče o zečevima.
Jeep je bio mlad i spreman za zabavu. Ušuljao se unutra zabaciti noge na plesnom podiju. Sally uze Pancha za nogu, te ga dovuče do rotirajuće kugle-ogledala. Tik do njih Sabo je plesala s vrlo zgodnim mačkom prošaranim narančastim pruga-ma i kratkog odrezanog repa. Pancho se prema mački osjećao malo zaštitnički te odluči pripaziti na ovog umjetničkog tipa. No, ubrzo se ponovo izgubio u sitnim Sallynim očima. Glazba i nije bila najromantičnija, no atmosfera u staji je bila takva. Monika i Hans su stalno visjeli u kutu, jedan drugom u zagrljaju zamaskiranom tako da se činilo kao da plešu. Suzy i njezina djevojka iz zoološkog vrta su se neprestano ljubakale. I stari i mladi parovi su se smijali i mazili, a onda magija nestane. Glazba je stala.
„Bend će uzeti malu stanku,” najavio je plavi štakor, „no nemojte otići, netko s farme vam želi nešto reći.”
Životinje stanu pogledavati uokolo tražeći govornika. Prvo je mikrofon uzela Goldie, koja ga je potom dala Rosy. Krava ga preda Jethru koji ga opet njoj vrati. Rosy s oklijevanjem izađe na binu. Zahvali mnoštvu na dolasku i pohvali bend.
„Mi u Krugu A smo suočeni s korporacijom koja nas želi preuzeti,” nastavi, „Znam da mnogi od vas imate slične probleme tamo gdje živite i radite.” Na to uslijedi opće odobra-vanje. „Preuzimanje znači da ćemo izgubiti kontrolu nad farmom i samim tim nad svojim životima.” Rosyina šutnja nakon ove rečenice još više naglasi njenu važnost. Jethro uspije primijetiti da je ona proplakala, te se stoga on popne na pozornicu i uze mikrofon iz ruke krave, koja je još jecala.
„Životnije Kruga A odlučile su da neće predati farmu,” nastavi mazga umjesto Rosy, „Borit ćemo se protiv preuzimanja kako je to god moguće, a nadamo se da ćemo to postići bez nasilja.” Jethro zastane kad shvati da je staja puna životinja, a da je on na pozornici. Obuze ga strah te preda mikrofon zlatnom ptičaru.
Goldie skoči na platformu i dovrši govor. „Molimo vas za pomoć u našoj borbi protiv korporacijske grabežljivosti i nudimo vam podršku u ovoj zajedničkoj borbi.” Sve su glave klimale i započele međusobne razgovore. Kroz otvorena vrata staje, Goldie ugleda štakore koji su doslovno gutali besplatnu hranu, pa otvori diskusiju.
„Da li bi netko tko nije s farme želio nešto reći?” Naravno, psi prvi stignu.
„Naš je čopor napala vlada,” najavi osijedi ovčar. „Prvo je postojala urota da nam se oduzme posao i da nas, pse čuvare, zamijene novima sustavima alarma. Oni od nas koji su bili kućni psi počinju gubiti poslove zbog uvoznih vrsta.” Baci pogled na grupicu lepršavih pudlica u blizini pozornice. „Skupili smo oružje i naoružali se. Namjeravamo se boriti protiv vlada i njezinog korporacijskog gazde do posljednjeg psa.” Njemački se ovčar lijepo okrene i siđe s pozornice.
Monika je svoj jezik zadržavala dosta dugo. Skoči na binu i stane braniti pudlice. „Suočimo se sa stvarnošću, za pse više nema posla. Ponekad žele nas pudlice, jer smo manje i jeftinije za hranjenje,” nježni joj naglasak sakrije ljutnju. „Kažu da nas je lakše izdresirati i da se ne linjamo. No, svjesne smo da će nas zamijeniti nekim strojem čim to budu mogli.” Pogleda Hansa pored sebe. „Korporacija nas želi posvađati tako da se međusobno zamrzimo i pobijemo. To nam oduzima previše vremena tako da se ne možemo boriti protiv njih.”
Hans istupi naprijed: „Ako se udružimo bit ćemo dvaput jači. Trebamo se koncentrirati na pravog neprijatelja.” Hans pogleda starog ovčara, koji objesi glavu na stranu i stane razmišljati.
Edsel dođe naprijed. Sjajni mu se kaput svjetlucao na svjetlu rotirajuće kugle. „I ranč konja ima slične probleme. Nas su konje prilično zamijenili automobili. Nas se nekoliko natječe za specijalizirane poslove, no većina je istjerana na pašu.” Svi u prostoriji s razumijevanjem klimnuše, te konj nastavi: „Korpo-racija nam pokušava sportom isprati mozak, tako da počnemo vjerovati kako su trke konja i skakanje i sve ostale igre zaista važne na neki način. Konji na ranču se više brinu oko toga tko će pobijediti na Kentucky derbiju, nego tko će postati predsje-dnik države.”
Vjeverica Mac iz Špiljskog kampa preuzme mikrofon. Sićušna je životinja trebala sjesti na mikrofon da bi ju se vidjelo. „Uostalom, zaista nije bitno tko će postati predsjednik, jer su svi oni isti. Baš kao i kod nas u kampu kad ponudimo izbor za večeru: lagano kuhano jelo od žireva ili pak kaša od žireva. Sve je to isto.”
Vragolan se nagne prema Judi te joj šapne: „I mislio sam,” te izvuče medvjedu osmijeh na lice.
Mac zaključi: „Svi se osjećaju dobro kad misle da imaju izbor, no izbori su u principu korporacija koja nas poslužuje istim lješnjacima koje zove drugačijim imenima.”
Judi preuzme pozornicu od Maca. „Šuma je već desetljećima pod opsadom korporacije. Gubitak divljina utječe na sve životinje na svijetu, a ipak ih tako malo ulaže energiju u njezino očuvanje. Ponestaje nam vremena. Ovo nam svima mora biti najveći prioritet ili ovi drugi problemi neće uopće biti bitni.” Rekavši to Judi preda mikrofon Riveru.
Mladi je muškarac stajao ispred skeptičnih životinja. Nije se baš pripremio za govor. „Dakle, moji prijatelji ljudi i ja se slažemo s onim što je rekla Judi,” bubne bez razmišljanja, „U stvari, svatko je rekao nešto bitno. Želim da znate da postoji mnogo ljudi koji dijele vaša razmišljanja. Naravno, ima i onih koji ih ne dijele.” Pogleda uokolo tražeći pomoć, te mu Rainbow doskoči u spas.
„Željela bih znati,” upita ona, „što možemo napraviti?”
Pancho se sada bio spreman pojaviti. Dođe na podij. Probije put kroz mnoštvo i dohvati mikrofon. No, nije bio jedini koji se želio izraziti. S lijeva dođe koza, a s desna crni ovan. Iznena-đena Rainbow skoči unatrag baš na vrijeme da izbjegne centar sukoba. Mikrofon poleti u zrak i padne u ruke brzo razmišljajuće Emme. Purica doleti na pozornicu i nastavi s raspravom kao da se ništa nije dogodilo, što uvelike razočara Boba, Čangrizala i Pancha.
„Prvo što moramo napraviti jest odložiti na stranu naše razlike, i kao pojedinci i kao grupe. Kokoši nemaju iste ciljeve kao rakuni, to je činjenica. No, svi mi ovdje imamo jednu stvar koja nam je zajednička: veliku moćnu korporaciju, bankarstvo, medije, vladu, vojsku i ekološke katastrofe koje utječu na sve nas i koje nas sprečavaju da postignemo ono što želimo kao pojedinci.”
Emma napravi pauzu da odahne, na što hrpa šapa i kopita posegne za mikrofonom. „Ne,” zagrakće purica, mašući mikro-fonom po zraku, „Ovo je jedini štap za razgovor i ja ga još uvijek imam.” Tad upita civiliziranijim tonom: „Možemo li se svi složiti u jednoj stvari: da je korporacija naš neprijatelj?”
Mnoštvo počne divljati. „Uzimam to kao da,” reče, „Gotova sam!” I s tim Emma baci mikrofon među životinje koje su ga se trudile ugrabiti. Pancho je bio toliko zadovoljan što je završio baš kod njega.
„Samo sam htio spomenuti jednu zamisao koju sam danas čuo od Svete Krave.” Među publikom se pokaza znak pošto-vanja, te Pancho nastavi: „Svi smo se složili oko problema, no kao što je muškarac rekao, što možemo napraviti? Predlažem da razmislimo o stampedu.”
„Ta luda krava,” Rosy se nije trudila da dođe do mikrofona. „Zašto nije predložila potres ili tornado?” zafrkće krava, „Ne možeš tek tako dobiti stampedo kao što si dobio zabavu.”
Svi se nasmiju. Pancho preda mikrofon štakorima koji su se baš bili vratili, na razočaranje Čangrizala i Boba, te svirka ponovo počne.
Panchu se i nije plesalo te se stoga makne sa strane zajedno sa Sally. Lipanjski je mjesec bio pun reflektirajući se u jezeru i vodenim koritima. Mlade su se životnije lovile oko lomače dok su stariji nastavili s ozbiljnom raspravom. Činilo se da drugi nisu sasvim odbacili ideju o stampedu kao sredstvu promjene. Mali je Jeep pričao o divljim ponijima, koji su se zaletjeli na Chincoteague, a jelen se sjetio grupnog bježanja od lovaca. Krave iz mljekare se slože da se ideji mora dati neka pozornost, ako je došla od Svete Krave.
Pancho i Sally su tu večer pričali o raznim stvarima. Nijedno od njih nije nikada ranije iskusio stampedo tako da su se držali bližih im tema šećući se i gledajući kako vatra gori.
Bob je bio razočaran jer se nije dočepao mikrofona, no nađe malu grupicu pasa koje je izgleda zanimalo njegovo predavanje o povijesti pokreta za prava životinja. Koza Čangrizalo se povremeno ubacivala u razgovor dodajući činjenice o revoluciji u Cataloniji. Nije bilo jasno da li ih psi slušaju ili pak spavaju. U bilo kojem slučaju, bili su tihi.
Sabo se šetala uokolo s novim prijateljem i čak je probala pušiti cigaretu, no nakon što je uvukla samo jedan dim, nije mogla prestati kašljati. Vidjela je Rosy kako se iskrada iz dvorišta i preskače ogradu tamo na putu za mljekaru.
„Možda bih trebala ići za njom,” pomisli, ali odluči ipak ostati s mačorom.
Tex i Mex su u svom podnožju imali čitavu skupinu mladih. Nesposobni da se glazbeno nadmeću sa svojim starim gitarama, kojoti su to i više nego nadomjestili pričajući priče. Nakon što im je lomača ugrijala žuljevite šape, Mex pomogne Texu u pričanju priče:
„Večeras ćete čuti divlju i vunenu priču. Postoji mnogo, mnogo priča o Vunenima, jer svi Vuneni vole pričati priče. Uz to vole i pjevati i plesati noću. No, bave se i ozbiljnim organiza-cijama s puno vike i sabotiranja.”
„Ostanimo poslušati ovo,” reče Sally, „Obožavam priče o Vunenima.” Pancho se složi, te sjednu dolje da poslušaju.
„Vuneni postoje već jako, jako dugo. Neki od vas sigurno misle da su svi Vuneni ovce, no to nije istina. U početku su bili većinom ovce i koze, no ubrzo su im se pridružile svakojake vrste životinja, čak i par kojota izmučenih dugim putovanjem.” Tex i Mex namignu jedan drugome. „Neki pričaju loše stvari o Vunenima, ali nemojte u to vjerovati. Borili su se u teškim bitkama, u teškim vremenima i na ovim komadićima ponosa koje danas imamo, možemo dijelom zahvaliti i njima.”
Tex se nakesi mladim slušačima koji su bili tako željni priče. „U ta su se vremena korporacije počele naglo razvijati. Ugrabili su sve male farme i od njih napravili ogromne korporacijske. Iskopali su rupe u planinama u potrazi za ugljenom i zlatom. Drveće su posjekli što su najbrže mogli. Pomislili biste da su se utrkivali u tome. Zvuči poznato? No, u svakom slučaju, životinje su izvukle deblji kraj. Ukrali su im zemlju, a zatim su morali raditi za korporaciju, i to prekovremeno i za mizernu plaću.
Tako su na poljima, rudnicima i područjima za sječu drva Vuneni organizirali otpor, a njihovo je članstvo raslo sve dok se korporacija nije prilično zabrinula. Vuneni su čitavo vrijeme pričali o Velikom Stampedu, radeći za dan kad će se on dogoditi.” Kojot uzdahne. Činilo se kao da se izgubio u razmišljanjima.
Mex ga gurne laktom, te Tex nastavi s pričom:
„Jedna vrlo velika industrija u to vrijeme radila je tkaninu od vune. Trikovima su privlačili životinje iz cijelog svijeta i odvodili ih u velike gradove, gdje su ih iskorištavali kao robove u proizvodnji tkanine. Životinje su bile svih vrsta i svih nacionalnosti, tako da su mnoge govorile različitim jezicima. Ovo je unijelo još više zbunjenosti u posao, a najviše im je otežalo zajedničku borbu za zaštitu i pravdu.
Dnevne porcije zobi bile su veoma male pa bi životinje uvijek ostale gladne. Korporacija je međutim shvatila da može dosta uštedjeti ako ih bude još manje hranila. Životinje koje su umirale od gladi počele su padati u očaj. No, što su mogle napraviti? Ako se neka od životinja pobunila, ne bi uopće dobila zob te bi zaista umrla od gladi. Napokon su neke životinje rekle Pozovimo Vunene!
Neki od Vunenih su došli i pomogli im u rješavanju prvog većeg problema. Osnovali su odbor životinja koje su radile u proizvodnji tkanina predstavljajući sve vrste i sve jezike. Životinje su počele međusobno razgovarati. Što možemo učiniti, kako možemo pobijediti? Da pokušamo s Velikim Stampedom? Previše smo umorni i slabi zbog gladovanja, nije vrijeme za to! Ali moramo štrajkati, to nam je jedina šansa.
Životinje su napravile hrabar i precizan plan pri čemu su im pomogli i Vuneni. Vuneni su imali dosta prijatelja na nižim položajima, a na takve se moglo računati. Životinje radnici su zatim objavili štrajk. Odbijali su raditi u tvornici tkanina.
Korporacija im se nasmijala. Imamo mnogo novca i možemo ih pričekati da se predomisle. Ubrzo će gladovati pa će raditi za još manje zobi nego što im sada dajemo. No, korporacija je podcijenila odluku životinja i pamet Vunenih prijatelja. Vuneni su im krijumčarili hranu, a mlade su odveli na prijateljske farme gdje su ih dobro čuvali i hranili. I tako se štrajk održao.
Korporacija je shvatila da sve što treba jest pronaći Vunene i riješiti ih se da bi štrajk završio. No, to je bilo nemoguće, jer su im se sada pridružile sve životinje i sve su postale Vunene. Korporacija ih se mogla svih riješiti, no onda više ne bi imala nikoga tko bi im radio u tvornicama tkanina.
Korporacija je počela gubiti novac, a to nije mogla podnijeti. Morali su se dogovoriti sa životinjama, koje su sada sve bile Vunene, te se slože da im se porcija zobi udvostruči. Bila je to predivna pobjeda za Vunene i za sve životinje posvuda.”
Tex malo stane da se napije iz zdjele ispred sebe. Pancho ustane i upita: „No, zar nije bilo Velikog Stampeda?”
„Ne, ne, nije bilo vrijeme za tako nešto,” reče Tex, „Ne mogu shvatiti zašto nikada nije vrijeme za bilo što.”
„Pa, što se dogodilo s Vunenima?” Izgleda da je priča više zainteresirala Pancha nego mlađu publiku.
„Pa, ovo je samo jedna od tisuću priča o Vunenima, kao što sam ranije rekao i uglavnom su sve istinite. Dakle, možete vidjeti kako su se vlada i korporacija jako zanimale za uklanjanje Vunenih. Osnovali su Farmski Biro za Istraživanja da bi opravdali lov na Vunene i njihovo ubijanje.”
„Što!” uzvikne Pancho, „FBI je osnovan samo da bi se mogli ubijati Vuneni?”
„To sam rekao, nisam li?” reče Tex, „Ulovili su svaku životinju za koju su sumnjali da je uvučena u aktivnosti Vunenih, ubili je ili je tako zastrašili da se prestala žaliti. No, FBI se nije domogao svih Vunenih. Oni još uvijek postoje.”
„No, moramo biti veoma oprezni što radimo i kako to radimo,” reče Mex, „Ne brinite se, Vuneni će sudjelovati u Velikom Stampedu, kad za njega dođe vrijeme.”
Bend je i dalje svirao. Bonkers je odsvirao par solaža na čeličnom bubnju uz pratnju ljama sa šuškalicama. Shvatio je da mu se sviranje sviđa podjednako kao i vožnja kamiona. Štakori su već dvaput prešli svoj repertoar tako da je sada na redu bio slobodni stil. Sve se više životinja skupljalo vani oko lomače. Kako je bilo dosta kasno, mnoge zaspu.
Psi i krave iz mljekare odu kući pošto su stanovali u blizini, a sve ostale životinje ostanu prespavati na Krugu A. Nenaviknuti na hladnoću, ljudi se sklupčaju vrlo blizu vatre, a pošto su se jako tresli, Goldie ih u sitne sate pokrije njihovim jaknama. „Vrlo, vrlo krhko i jadno napravljeni, čudim se kako opstaju,” pomisli. Neki od čuvara šume ostanu spavati u staji da isprobaju nešto novo, a mačke umjetnici popnu se na stabla u voćnjaku tek kada se razdanilo.
Bila je to predivna noć, a jutro koje ih probudi donese očaj.
\chapter{18}
Pospanim životinjama nije trebalo više od par sekundi da se saberu nakon što su shvatili da se na farmi zapucalo iz pušaka. Iz smjera čopora mogli su se čuti jauci i lajanje pasa koji su uzvraćali vatru.
Goldie je bila prva koja je uspjela doći do tunela kroz koji je Monika što je brže mogla gurala štenad prema Krugu A. Sićušne čupave pudlice i štenci njemačkih ovčara još obješenih ušiju upadnu na livadu. Sally požuri do njih da ih brzo skloni na sigurno.
Pancho je za to vrijeme promatrao borbu kroz ogradu pričvršćenu lancima. Posvuda uokolo u prljavštini ležali su ovčari.
„Zečevi su govorili istinu,” pomisli svinja, „Znali su unaprijed za raciju. A i ovčari su bili u pravu. Korporacija se boji životinja s oružjem.”
Psi su bili na gubicima, no kad god je netko od ovčara pao, jedna od pudlica bi uzela njegovo oružje i pridružila se borbi.
„Razbijte ogradu,” cvilio je Edsel, „Dajte im prolaz za bježanje.” Konj udari i metalni dio napukne. Bonkers dođe s komadićima limenke, te se ubrzo velik dio ograde sruši. Čopor je sada bio izravno povezan s farmom. No, psi su ostali na svom području, nadjačani vojnim automatskim oružjem. Željeli su umrijeti u borbi.
Užasnuti su im gledatelji vikali da pobjegnu. Goldie i Crveni počnu vući ranjenike na farmu gdje su se Suzy, Jethro i ostali na farmi mogli pobrinuti za njih. Mnogi su se na farmi sakrili od straha ili su pak stajali kao zakopani, ne znajući što im je činiti.
Pancho pomogne Sally da okupi svu štenad u svinjcu, gdje ih je Marta uvaljala u blato „da ih preruši u praščiće,” kako je s nadom izjavila.
Sabo nije mogla podnijeti pucanje. Mačke umjetnici se popnu na stabla u voćnjaku, a Sabo otrči u mljekaru što je brže mogla. Nije stala trčati sve dok nije došla do jasla Svete Krave. Tamo zateče vrlo uzrujanu Rosy pored svoje majke. Mačka je jedva hvatala dah, a krave su htjele doznati što se vani dogodilo.
Sabo prijavi: „Vlada masakrira pse.” Rekavši to, primijeti da je stara krava izgledala poprilično loše. „Jeste li u redu, Majko Krava?”
„Jesam, draga moja, dobro sam. Idem tamo gdje ima mnogo nedirnutih pašnjaka.” Sveta se Krava nasmije. Sabo je mogla vidjeti suze u Rosynim očima. Stara Krava nastavi tako slabašnim glasom da su joj se Rosy i Sabo morale skroz približiti. „Veliki Stampedo,” šapne, „sve životinje zajedno trče i brinu se jedna za drugu kao da se brinu za sebe.” Uzdahne. „Predivan je to san i vjerujem da će se i ostvariti kada za to dođe vrijeme.”
Sabine su oči bile širom otvorene. „Kad će doći to vrijeme?” Molila je za odgovor.
„Kada sijeno razbije devina leđa,” šapne stara krava.
„Što to znači?” upita Sabo Rosy, koja ne znajući odmahne glavom.
„Majko Krava,” reče crna mačka, trljajući njušku, „Molim Vas, ne ostavljate nas. Trebamo Vas!”
„Mala maco, sjedni tu blizu. Imam za tebe jednu priču,” odgovori joj stara krava. Sabo položi glavu blizu požutjelih zubi i posluša.
„Bila jednom jedna mačka koja je htjela znati kako opstati u svijetu. Ode u šumu da od najstarijeg i najmudrijeg drveta zatraži pomoć. Molim te, mudro drvo, pokaži mi moj put, zamoli ga mačka, no drvo je šutjelo. Mačka sjedne na korijenje drveta čekajući odgovor. Nakon dugo vremena, ispod nekog grmlja primijeti osakaćenu lisicu. Pitam se kako ta lisica preživljava, osakaćena i nesposobna za lov?, pomisli mačka.
Odjednom na čistinu, baš tamo blizu lisičjeg grmlja, doskoči tigar. U ustima je držao zeca kojeg je pojeo ispred njih. No, ne pojede ga čitavog. Veliki komad mesa ostavi točno pored grmlja. Tigar ode natrag u šumu, a osakaćena lisica ispuže van i pojede meso.”
Sabo klimne. „Shvaćam,” reče.
„Shvaćaš li?” reče krava i lagano zakašlje. „Priča nije gotova.”
„Mačka pogleda drvo poviše nje i reče, Hvala ti, sada vidim svoj put. Ako sjedim tu i čekam kao ova lisica, moje će se potrebe zadovoljiti. Sve je u vjerovanju.
I tako je mačka sjedila pored drveta i čekala dan za danom. Svaki je dan dolazio tigar i osakaćenoj lisici nosio hranu, ali mačka nije ništa dobivala. Postajala je jako gladna. Naposljetku reče, Oh, mudro drvo, ne razumijem. Sjedila sam tu i čekala, baš kao i lisica, no nijedan tigar nije došao da me nahrani.
Drvo zašuška svojim lišćem i spusti jednu granu te šapne mački. Mala maco, ti nisi osakaćena lisica, ti si tigar.”
Stara je krava jedva završila posljednju rečenicu. Malo zakašlje, te joj Sabo pogladi nos.
„Hvala Vam, mislim da shvaćam,” reče mačka nježno.
Sabo je smatrala da treba ostaviti Rosy nasamo s majkom u njezinim posljednjim trenucima. Krave u mljekari stajaše tiho poput kipova, gledajući ravno ispred sebe. Znale su da Majka umire i to im se činilo važnije čak i od pomora u čoporu. Stotine se smeđih očiju okrene prema Sabo, nakon što je ova napustila jasle. Mačka tužno protrese glavom, te se na vrhovima prstiju vrati nazad na farmu. Pucanje je prestalo i u ovo je grozno vrijeme trebala biti uz prijatelje.
Puškaranje u čoporu je možda čak prebrzo završilo. Poraženi su psi bili ili mrtvi ili ranjeni, te su vojnici počeli češljati tuda da se uvjere kako je uništenje potpuno. Na Krugu A sve su se životinje sakrile u staju, a s njima i četvero ljudi. Iako veoma uplašeni, pokušali su ostati tihi. Jethro izvana zatvori vrata staje, a zatim legne ispred njih da svojim tijelom zapriječi put.
Emma je letjela iznad čopora i brojala mrtve pse, istodobno držeći neprijatelje na oku. Gledala je ne bi li ugledala nešto što bi joj ukazalo na zečeve, ali ne uspije ništa vidjeti. „Možda su izdajnici pobjegli,” razmišljala je purica, „ili su ih vladine ubojice oslobodile.” Promatrajući tako polje smrti, ugleda mnoga poznata lica, među njima i Kurta, a pored njega malu sivu pudlicu, Monikinog oca.
Jedan od vojnika krene prema razbijenoj ogradi, te gotovo dođe do livade u posjedu Kruga A. Goldie se zadržala tamo baš za ovakav slučaj. Dobro se slagala s ljudima i nitko se nikad nije loše odnosio prema njoj. Zlatni je ptičar vjerovao da će prijateljski pristup izazvati ono dobro u vojniku. Možda mu je mogla odvući pažnju i pomoći mu da se sjeti kako zapravo voli pse. Barem je mogla pokušati. Bilo je to jedino čega se uspjela sjetiti da zaustavi nasilje.
Emma je s gađenjem gledala kako Goldie maše repom i polako šeće prema vojniku. On joj se obrati grubim tonom, nastavljajući svoj put prema staji na Krugu A. Emmi se nije sviđalo što je svoju pasju prijateljicu morala gledati kako se ponižava na ovakav način, no Goldie se sada duplo potrudila. Pas se počne trljati o vojnika svojim bakrenim leđima, te mu čak pokuša polizati ruku. „Ako ga natjeram da me pogladi, sigurna sam da bih ga mogla pridobiti,” pomisli. No, vojnik je i dalje polako koračao prema staji, ignorirajući molbe ptičara.
Sabo ugleda mazgu koja je blokirala ulaz u staju i vojnika koji joj se približavao iz smjera livade, sav u zelenoj kamuflaži i naoružan puškom. Goldie je trčala oko njega, dajući sve od sebe da ga spriječi da ide dalje. Baš tada mačka ugleda Emmu kako im leti iznad glava, te slijeće na krov staje. Shvativši kako je to dobro mjesto, Sabo se popne gore na krov da se pridruži Emmi u ovoj ptičjoj perspektivi.
Unutra u staji, životinje su planirale obranu za trenutak kada se vrata staje otvore. Medvjedi na čelu, ostali okupljeni oko njih. Bili su spremni. Najmlađi i oni ranjeni ostanu u pozadini. Hans je ležao s ranjenim psima, dok je on sam bio jedva ogreban. Goldie ga je odvukla iz čopora „slučajno”, kako je sama rekla, no Crveni je rekao sasvim suprotno. Monika je pored tolike tragedije bila vrlo zahvalna na ovom čudu.
Ljudski čuvari šume razderu svoju odjeću u krpe da zaviju ranjene životinje. Sada su bili obvezani na golotinju. Mačke umjetnici ostanu na kraju mnoštva, nesigurne u što su se to uvukle.
Štakori su, s druge strane, bili skroz ažurni i željni borbe. Judi ih je stalno trebala podsjećati da za sada budu mirni.
Pancho, Bob i Čangrizalo zauzeli su položaje odmah iza medvjeda. Položaje časti, ne ludosti. Ipak, svo troje požali što nisu ostali vani. Iščekivanje ih je ubijalo. Bonkers nađe lijepu rupu za virenje prijavljujući sve što se dešava Carlosu, koji bi to prokomentirao sa svojom partnericom Juanitom, prije nego bi ona to tiho proslijedila dalje. „Jedan od njih dolazi. Ima pušku. Goldie ga usporava, no ne može ga zaustaviti.”
S krova, mačka i purica promatraše dramu koja se odvijala ispod njih. Razočarana Sabo promrmlja nešto za sebe.
„Što si rekla?” upita Emma.
„Moramo imati devu,” reče mačka, „Je li ljama neka vrsta deve?”
„Mislim da ne,” razmisli purica koju minutu, „Možda. Ali što će ti deva?”
„Da započnemo stampedo.” Što se vojnik više približavao staji, mačka je sve više bjesnila. „Sveta je Krava rekla da sijenom moramo razbiti devina leđa ili nećemo moći imati stampedo, a mi ga trebamo.” Mačka potpuno razrogači oči.
„Ta je krava luda!” odgovori purica.
Vojniku dosade ptičareve budalaštine. Podigne kamen s poda, te ga baci prema psu. Goldie se pravila kao da se igra „baci i donesi”, te dotrča natrag do muškarca noseći kamen u zubima, no on se nije htio igrati. Ionako je bilo prekasno. Stajao je samo nekoliko centimetara od staje.
Jethro pogleda vojnika u oči i dalje ležeći pred vratima. Oboje su znali da se mazga neće dobrovoljno pomaknuti. Muškarac podigne pušku i držeći je uperenu u Jethra, poviče „Miči se!”, no mazga je ostala ležati.
Goldie je hodala naprijed — natrag. Emma i Sabo skoro padnu s krova pokušavajući vidjeti što se događa. Unutar staje nitko se nije usuđivao disati.
Tad u tišini, začuju malen klik otponca na puški. Taj mali klik upali svjećicu u Goldijevoj glavi. Ptičar skoči na vojnika i ugrize ga za nogu.
Muškarac zavrišti, okrene se prema psu i zapuca. Jačina metka odbaci Goldie na drugu stranu dvorišta, te ona završi u vodenom koritu. Potpuno zaokupljen svojom ranjenom nogom, vojnik se nije niti potrudio pogledati u pravcu psa.
Sabo ugleda crvenu boju. Nije razmišljala, nije se mogla bojati. Razrogači oči, nakostriješi dlaku, a leđa savije u luk. Izgledala je strašno, kao da je Noć vještica na vratima. Skoči s krova i zarije svoje kandže i zube u leđa sagnutog muškarca. Poput minijaturnog tigra, grizla mu je i derala lice i oči. Vojnik ispusti pušku kako bi mu obje ruke bile slobodne. Zgrabi Sabo, te je baci što je jače mogao u smjeru Goldie, no mačka se dočeka na noge.
Jethro ustane. Osjećao je kako u njemu raste nešto nepoznato i kako mu prožima cijelo tijelo. Pogleda Goldino mlohavo i krvavo tijelo, te pun mržnje krene prema strancu. Jedan dobar udarac je bio dovoljan: vojnikov pad na zemlju proizvede veliku tutnjavu.
U tom trenutku, farmu obuze kukanje i mukanje iz susjedne mljekare. Sveta je Krava umrla. Pošto se mazga digla, ništa više nije držalo vrata staje, te se ona otvore. Životinje ostanu zaprepaštene scenom ispred njih. Emma i Sabo su plakale pored Goldinog tijela, kojeg su izvukle iz vodenog korita. Vojnik je ležao u rijeci krvi koja se u malim potočićima slijevala nizvodno.
Jezovito mukanje iz mljekare inspiriralo je životinje Kruga A da zavijaju, zagrakću ili zableje vlastiti rekvijem. Jethro je i dalje stajao na nogama snažno drhteći, istovremeno gledajući livadu iza sebe, nesposoban da shvati što se upravo dogodilo i što je on to učinio. Sve što je mogao osjetiti, sve što je znao jest da treba trčati. S eksplozijom energije zatrči prema livadi.
Mljekara odmah shvati. I oni su tamo drhtali. Obično mirne krave sruše ogradu, te se sliju na livadu i okruže Jethra koji je trčao.
Ovan osjeti kako ga nešto vuče, te gotovo pogazi medvjede koji su već počeli trčati niz brdo. Sve ostale životinje, kao i ljudi, nahrupe na livadu i pridruže se trci.
Rosy je stajala pored Goldinog tijela. Otupjela je od silne boli tijekom dana, Sabo joj šapne i pokaže na životinje u trku.
„Da, počelo je,” Rosy duboko udahne, „Pa, idemo.”
Mačka i krava se pridruže ostalima. Trčali su svi osim najteže ranjenih. Oko jezera i kroz voćnjak, po livadi, životinje otrče dosta krugova. I umjesto da se umore, dobivale su sve više energije. Svaka je životinja imala svoj razlog za trčanje, ali su svi imali isti cilj. Rakuni su trčali za šumu, a ovčari za čopor, no to nije bilo bitno. Trčali su za slobodu. Ptice se skupe na komadu neba iznad livade i stanu pratiti put galopirajućih životinja kao njihova vlastita sjena. Emma je letjela u centru svojih purića. Iako su još bili mladi, ovo nisu mogli propustiti. Uvijek će se sjećati da su bili dio Velikog Stampeda.
Nakon par krugova, trkači primijete promjenu. Bila je jedva primjetljiva, ali važna. Duboka, štoviše. Neke su životinje počele plakati u trku, neke su počele graktati, a neke pak smijati se. Rakuni su i dalje trčali za šumu, no i za čopor pasa. Krave iz mljekare trčaše za svoju Majku, no i za ranč konja. Pancho je trčao za Goldie i za farmu, no također i za ljude, a to stvarno nije znao kako objasniti. Sada su bili jedna cjelina, jedna ogromna životinja usmjerena prema pravdi za sve.
Silom otvore ulazna vrata Kruga A i zauzmu čitavu cestu, životinje galopirajući dolje na zemlji, a ptice radeći nebeski svod iznad njih. Pancho je trčao pored Sally i Rosy. Sabo se između nogu velikih životinja poput strelice progura do Judi, koja je trčala usprkos tome što je bila ranjena, baš kao i ostali. Ovo je bilo previše važno.
Mala grupica vojnika sakrije se iza kamiona dok je stampedo prolazio kroz vrata čopora. Nije ih se moglo prevariti. Svaka životinja zna, a ljudi u tome nisu iznimka, da kad se stampedo pokrene, moraš se ili priključiti ili maknuti s puta. Pokušaj ga zaustaviti i zgazit će te. Nakon što životinje prođoše poput oluje i prašina se slegne, zapovjednik podigne slušalicu da prenese upozorenje: „Životinje su poludjele i kreću se u stampedu prema gradu. Ostanite kod kuće kako bi izbjegli opasnost. Traži se pomoć Nacionalne garde.” Zapovjednik nije primijetio četvero golih ljudi u stadu, ili ako jest, smatrao ih je životinjama.
Promatrači uz cestu su ih pozdravljali kliktanjem, ignorira-jući upozorenje vojske. Neki su samo mahali, no dosta se njih priključi stampedu.
„Trčite s nama da zgazimo korporaciju!” Nekima se to činilo uzbudljivo, te su trčali zbog avanture, dok su im se drugi pridružili nemajući što za izgubiti.
Kad je stampedo prolazio pored ranča konja, Edsel počne razbijati pregrade. Galopirao je kroz staje udarajući o vrata. „Dođite s nama, osim svojih uzdi nemate što izgubiti!”, te konji izađu na ulicu i stanu se propinjati niz ulice, zajedno s ostalim borcima za slobodu.
U zoološkom vrtu, zatočene životinje pobijede svoje čuvare, te pomognu jedna drugoj u bijegu kako bi se pridružili stampedu.
Pobunjenici su bujali kao gruda snijega koja se kotrlja niz brdo. Kroz svako mjesto kroz koje su prošli nailazili su na sve više životinja koje su mrzile korporaciju zbog onoga što je učinila od njihovih života i zemlje, a koje su imale hrabrosti i ljubavi riskirati sve kako bi je zaustavile.
S toliko mnogo tijela stampedo se malo usporio, te Pancho uspije uhvatiti dah. Pogleda oko sebe nepoznato okruženje: zgrade od kojih se ne vidi nebo, bez trave ili drveća. „Kako bi nam se netko mogao ne pridružiti”, pomisli, „Tu se ne može živjeti.”
Sada su štakori preuzeli vodstvo pošto su znali put do sjedišta korporacije. Kad su se našle u uskim uličicama, životinje su više marširale nego trčale. Njihova se parada rastegla na nekoliko blokova zgrada. Dixion je vodio stampedo niz neku sporednu ulicu koja je završavala visokom, visokom zgradom u obliku piramide. Stigli su do sjedišta korporacije.
Zbog konja, jelena i medvjeda ispred sebe Pancho nije ništa mogao vidjeti. Ubrzo su ptice donijele vijesti. Nacionalna je garda blokirala ulicu zbog obrane korporacije.
Bilo koja životinja mogla je shvatiti da su se našli u zamci. Vojska se bez sumnje postavila i na kraju kolone. Povlačenje nije bila jedna od opcija.
S oružjem ispred sebe, stampedo se naglo zaustavio. Mnoštvom zavlada šaptanje. Jedino su ptice mogle zaista dobro promotriti situaciju. Emma poleti naprijed. Nije mogla vjerovati onom što je vidjela. Iza ogromnih staklenih vrata te velike, velike zgrade izlazile su one otrcane malenkosti od špijuna odjeveni u mornarsko plava vunena odjela s prugastim kravatama.
Blackstone je nosio crni kovčeg, a Hamilton zgrabi mikrofon da se obrati mnoštvu. Iako većina životinja nije mogla vidjeti govornika, njegov se glas nije mogao zamijeniti s nekim drugim.
„Prijatelji,” počne mršavi zec, „Pokušao sam vas upozoriti da ovo neće uspjeti i pogledajte sada što se dogodilo. Došli ste čak do tu da bi zurili u cijev pušaka.” Protrese glavom i proizvede slabi zvuk kao kuckanje sata. „Srećom po vas, nije napravljena nikakva veća šteta. Posjed korporacije je ostao nedirnut, te je korporacija spremna zaboraviti ovaj ispad i većini vas dopustiti da odete u miru. Međutim, kaznit ćemo one koji su počeli ovaj stampedo, a to su životinje iz Kruga A, tj. H.”
Od galame gomile sljedeća se rečenica gotovo i nije čula, no Pancho zaključi kako će sad nastupiti Blackstone. „Korporacija je također voljna priznati da u vašim žalbama ima ponešto istine. Hamilton i ja smo bili nekoliko sati s odborom, pokušavajući uvjeriti u to predsjedatelja i ostale. I ono do čega smo došli jest sporazum i to vrlo velikodušan od strane korporacije.” Otvori kovčežić jednim potezom i izvadi debelu fasciklu koja je izgledala prilično službeno. „Korporacija je voljna sastaviti odbor životinja koji bi iznosio svoje prijedloge. Želimo raspravljati i surađivati s vama kao s dobrim članovima društva.”
Svi oni koji su slušali glasnogovorničku poruku zečeva znali su da su to sve laži. Ne samo životinje i ljudi kojima je ova ponuda bila namijenjena, nego i vojnici, predsjednici korporacije, a posebno sami zečevi. Bila je to stara igra i svi su je igrali već predugo.
„Ne možemo se predati,” reče Pancho onima oko sebe, „iako se nalazimo u teškom položaju.”
„Došla sam tu uništiti korporaciju i to namjeravam spro-vesti,” reče Rosy odlučno i stade se probijati kroz gužvu.
„Ali puške!” zaviče Pancho, „Ubit će te.”
„Mislim da hoće,” uzdahne Rosy, te stade na čelo stampeda.
Popne se stepenicama do mjesta gdje su stajali zečevi. Vojnici su je nišanili dok se penjala. Rosy se nagne prema mikrofonu: „Ne govorim u ime svih, samo za sebe. Ne prihvaćam ni ovu ni bilo koju ponudu zle korporacije. Došla sam tu da je uništim, ne da je reformiram.”
Krava pogleda vojnike: „Idem unutra, a vi, ako me želite zaustaviti, morate me ubiti.” Rosy počne polako i ponosno hodati prema staklenim vratima.
„Priprema, pozor, paljba!” Zapovijed je bila izrečena. No, vojnici su oklijevali. Nitko nije htio prvi zapucati, tako da nitko i nije zapucao.
„Ponavljam! Vojnici, priprema, pozor, paljba!” Ovaj su put puške odgovorile, no vojnici su pucali u zrak, tako da su se ptice morale povući.
Zapovjednik se počeo crvenjeti od bijesa. Mogao je i sam upucati ludu kravu, ali je morao uspostaviti kontrolu nad svojim jedinicama. Koji im je vrag?
„Rosy, brže hodaj!” Pancho povikne, „Prođi kroz vrata!”
„Dajem vam svima još jednu šansu prije nego cijeli odred dam na vojni sud. Upucajte kravu teroristkinju! Priprema, pozor, paljba!”
Puške odzvone. Vjerojatno se svaki vojnik nadao da će izgledati poput nesreće. No, meci koji nisu otišli u zrak završe u zapovjednikovom tijelu. Srušio se poput krvave otrcane lutke.
Rosy prestane hodati. Provjeri obje strane ne bi li se uvjerila da nije pogođena, a zatim pogleda iznenađene vojnike.
„Upucajte kravu!” zaviče Hamilton čuvarima. No, oni su bili previše šokirani da bi ga mogli čuti.
Napokon jedan od njih prošapće par riječi zdravog razuma: „Brzo se maknimo odavde.” Bace puške, te se rasprše u mnoštvu.
Rosy uvuče jezik i vikne „Hajde!” dok je probijala staklena vrata.
Gurajući zečeve u odijelima na stranu, životinje se u stam-pedu popnu uz stepenice i uđu u predvorje korporacijskog lažova. Slijedeći miris starog, prljavog novca, životinje poput oluje dođu gore do vijećnice. Edsel zamoli za privilegiju da razvali debela vrata od čvrstog drva. Dopusti Jeepu i nekolicini njih da mu pomognu, kao što stariji dozvoljavaju djeci da neke stvari otvore prvi. Tada sa dva snažna udarca stražnjim nogama rastavi vrata na predivna, stara drva za potpaljivanje. U najdaljem kutu blizu šanka, a iza stola od mahagonija šćućurio se proćelavi, trbušasti ostarjeli čovjek u odijelu, plačući od straha.
Životinje nisu mogle vjerovati svojim očima. Stajale su tako oči u oči sa svojom kaznom, predsjednikom korporacije. Sally pomisli na film koji je gledala gdje je mršavi sićušan terijer povlačio zavjesu, a grozni čarobnjak izgledao baš kao ovaj čovjek — malen i bespomoćan u usporedbi s mislima, srcima i hrabrošću revolucije životinja.
„Jesi li siguran da si ti predsjednik korporacije?” upita ga Judi, došetavši preko do čovjeka da ga ponjuši.
Uzmičući prema staklenom prozoru, čovjekov je glas drhtao dok je izgovarao „Bojim se da jesam.” Čak i činjenica da te ponjuši mali medvjed kao što je to Judi sasvim je strašno iskustvo za nekog tko se toliko izolirao od prirode. „Ja sam i izvršni direktor.”
„Ovo ne može biti on. Ovaj jad od čovjeka nije nikako mogao napraviti onoliko štete: uništiti okoliš, razbiti naše sindikate, prebaciti naše poslove na drugu stranu mora, zatvoriti naše farme i zamijeniti nas sa strojevima. On se jedva suzdržava da ne padne u nesvijest,” kaže Rosy s gađenjem.
„Vjerojatno je imao pomoć!” povikne Bob gurajući se unutra u salu.
„Naravno da jest,” reče Čangrizalo. Ovo se dvoje nagnu sasvim blizu predsjednika korporacije i primijene svoje tajno oružje: aromaterapiju. „Imenuj svoje suučesnike,” zahtijevala je koza. „Tko je još bio umiješan?” zableji Bob.
„Svi su umiješani! Naravno da nisam sam djelovao,” vikao je čovjek, želeći sačuvati vlastitu kožu, „Što je s bankama?”
Emma zamahne krilima, te stvori put do čovjeka. „Vi posje-dujete banke. Banke su vi.”
„Dobro, a što je s vladom? I na njima je sigurno dio krivnje,” cmizdrio je čovjek.
„Prestani, prestani se izvlačiti od odgovornosti!” zaprijeti purica, „Vi posjedujete vladu. Vi plaćate izbore i kampanje, posjedujete novine koji odlučuju o izborima, imenujete suce i unajmljujete policiju. Možda se neće sve popraviti ako vas se riješimo, no rekla bih da bi to bio vrlo dobar početak.”
„Zar ste upucali zapovjednika?” upita predsjednik, osjećajući da je došao kraj, „Hoćete li i mene ubiti?”
„Generala su ubili vojnici. Pretpostavljam da im je dosadilo da im se stalno naređuje,” reče Rosy, „I nama je. Imat ćete pošteno suđenje. Bojim se da nećete imati kolege iz vašeg staleža u poroti, jer nema nikoga vašeg staleža. Mislim da će vam porota morati biti vaše žrtve.”
Odvuku predsjednika ispred zgrade.
Zečeve odvjetnike nađoše iza stroja za sađenje gdje su se skrivali u strahu od odmazde životinja.
Predsjednik korporacije mahne odvjetnicima pokazujući im da će se sam braniti, na što svi odahnu. Pošto je mikrofon još uvijek bio na mjestu, sve su životinje mogle pratiti čitav slučaj čak i onda kad su im zaklanjali pogled.
Porota se odabirala po principu en-ten-tini. Marta, Sallyina majka odabrana je za predsjednicu porote. Ostalih je jedanaest predstavljao prilično dobar presjek svih životinja: Corvette, konj boje lješnjaka, Mac iz „Oraha za sve”, Crveni iz Špiljskog kampa, Daisy, jedna od krava iz mljekare i ujedno Rosyina tetka, Monika iz čopora, Jethro mazga, Sabo zajedno s još jednom mačkom po imenu Dali, Nikotin, umrljani štakor, čovjek River te Horace, sova na mrlje, njegov čuvar u pravom značenju te riječi.
Bilo je to brzo suđenje. Emma je odigrala ulogu suca. Bob i Čangrizalo su preklinjali da oni budu ti koji će postavljati pitanja kriminalcu i koji će nabrojati njegove zločine. Izvršni direktor nije zanijekao ništa osim definicije samog zločina.
„Nisam uradio ništa protuzakonito,” rekao je, „Sve je bilo u skladu sa zakonom.”
Životinje se najviše zbune oko pitanja motiva. Zašto bi ijedno stvorenje ili ijedan čovjek bio tako zao?
„Novac, učinio sam to zbog novca i moći,” izjavio je, „a to je također savršeno legalno.”
„Dakle, zbog novca i moći ste uništili šumu, bacili bespomoćne životinje iz njihovih domova, otpustili ih, osujetili demokratski proces, potakli rat, obavljali grozne eksperimente na životinjama koje nisu ničeg bile svjesne
„ Koza Čangrizalo govorila je hodajući naprijed-natrag ispred malog muškarca, nabrajajući zločine koje je korporacija učinila.
„Sve je legalno!” provali izvršni direktor.
„Legalno jer ste vi donijeli zakone!” upadne Bob, „Ali to ne znači da je to što ste napravili bilo ispravno!”
Ovan prijeđe na konkretnu stvar. Kad se rulja ponovi umiri, Bob reče „Životinje su iznijele svoj slučaj.”
„Imate li nešto za dodati?” Emma upita predsjednika korporacije i njezinog izvršnog direktora.
„Ponavljam da je sve što je korporacija napravila legalno. Podsjećam porotu da mora podržati zakon!” Ćelava se glava počela znojiti.
„Oh, gluposti,” reče Marta, gledajući ga u oči, „Nas ne zanima zakon, već pravda!”
Sudnicom pod vedrim nebom zavlada burno odobravanje. Porota se na nekoliko trenutaka došaptavala, pa donese jedno-glasnu odluku. Iznenađenja nije bilo.
„Mi, porota vaših žrtava, proglašavamo vas krivim po svim točkama optužnice,” Marta sroči jasnim glasom. „Predlažemo slijedeću kaznu: pošto su novac i moć bili vaši motivi za zločine, od sada nećete moći uživati ni u jednom od navedenog. Nećemo vas zatvoriti u zatvor jer bi nam tamo bili samo na teret. No, zato ćete ostatak svog života provesti u nastojanju da očistite nered koji ste napravili.”
„Možete početi sa sadnjom drveća u šumi koju ste uništili,” poviče Crveni i sve se životinje glasno slože.
Emma preuzme mikrofon. „Došli smo uništiti korporaciju. Kao i njezine zle polusestre, banku i vladu. Došli smo i osloboditi njezinog zatočenika, tisak.” Purica pogleda bujno more životinjskih lica. „Ima li netko neki prijedlog?”
Životinje su u tišini razmišljale. To je tako dugo vremena bio tako veliki problem da se jednostavno rješenje činilo neprikladnim. Iz prednjeg dijela gomile janje digne svoj papak. Emma se zadovoljno nasmije, te joj mahne krilom u znak da dođe do mikrofona.
„Možemo li jednostavno reći: od sada bez nasilnika?” Visokotonsko blejanje malog janjeta nasmije gomilu. Janje pocr-veni i požuri natrag do majke.
„Znate, to je pravi način.” Bila je to zečja malenkost Blackstone, koji se penjao iza mikrofona. On i njegov kompanjon Hamilton skinuše poslovna odjela kako bi se svidjeli životinjama.
„Samo ukinite sve hijerarhije i sve prisile,” Hamilton uskoči, „bez interesa, novca ili šefova.”
Emma ponovo zgrabi mikrofon. „Što kažete da budemo bez odvjetnika i špijuna!?”
Pancho je također imao nešto za reći, te se približi i reče: „Nema zakona, nema odvjetnika. Nema hijerarhije, nema nasilnika. Janje je u pravu.”
„Mogli bi vam sve to zapisati,” Hamilton se javi dobrovoljno, „Tako da sve bude legalno.”
„Ne, hvala,” reče Emma, ponovo grabeći mikrofon. „Nema više legalno-ilegalno. Što kažete na pošteno i nepošteno, pravo i krivo? To je nešto što svi možemo razumjeti. Ne treba nam to napismeno.”
Zečevi zabace šape u očaju. Znali su da će ubrzo saditi drveće zajedno s bivšim izvršnim direktorom.
Marta progovori iz porotničke lože: „Prije nego odemo, glasujmo šapama hoćemo li korporaciju, vladu i banke ukinuti, a sve životinje vratiti u njihovo prirodno stanje slobode? Svi koji su za?”
Svi osim jednog dignu ruke.
„Svi koji su protiv?”
Izvršni direktor i zečevi odvjetnici dignu šape.
Ako se pitate kako je ovo bilo moguće
odvjetnici su, naravno, dvaput glasovali.
\chapter{19}
„Tata, možemo li otići do čopora i igrati se s psićima?” Molio je okrugli bijeli praščić. Prije nego da svoj pristanak, Pancho prvo pogleda toplo lipanjsko sunce da dozna koliko je sati. „Pitaj prvo mamu i nemoj dugo ostati. Ne zaboravi što je danas!” Nasmije se svom mladunčetu. „Dolaze teta Judi i teta Sabo.”
„I štakori!” zacviknu tri praščića dok su se koprcali prema svinjcu. „Mama, možemo li malo otići do psića? Vratit ćemo se na zabavu. Hans i Monika ionako dovode psiće. Možemo li onda?”
Sally je bila zauzeta pripremanjem voćne salate za zdjelu sreće. „U redu, ali dođite na vrijeme da se okupate prije zabave.” Poljubi tri njuškice i vrati se natrag svojim jabukama.
Staja je izgleda prekrasno. Ove je godine odbor za uređenje nadmašio sam sebe, a stolova za hranu je sada bilo šest.
„Čini se da svake godine dodajemo po jedan stol za hranu,” Jethro se zadovoljno nasmiješi.
„Na to nemam prigovora!” Pancho odgovori pomažući mazgi da postavi šank.
„Bit će ovo najveća lomača dosad!” Vikao je Hans svinji dok je pomagao sivoj pudlici složiti suho granje što više u visinu, „Pa, napokon! Evo benda.”
Ovčar reče istinu. Uz brdo, tamo iz smjera livade, vukući ogromne količine opreme, dolazili su Slobodni radikali i njihovi prijatelji, mačke umjetnice. „Pogledajte sve te teške instrumente!” Pancho se našali: „Pretpostavljam da je to jedan od tereta slave.”
Dixion zagrli svinju. „Štakor stvarno zna da je došao kad ima mačku za suputnika.”
„Sabo!” Pancho potrči zagrliti dragu mu prijateljicu, koja odloži gitaru da oslobodi ruke. „Kakav je život u zajednici?”
„Uglavnom odlično. Koristimo se zgradom piramidom za umjetničke studije. Moraš to doći vidjeti,” zaprede, „Kako obiteljski život?”
„Uglavnom odlično,” odgovori svinja, „Gdje je tvoj prijatelj mačor?”
„Dolazi. Pomaže nositi mikrofon.”
Sabo šapom pokaže kad se iza brda pojavi najveći mikrofon kojeg je Pancho u životu vidio ili zamišljao. Trebale su četiri mačke da ga konopcem vuku po podu. Svinja odmahne glavom ne vjerujući. Sve što je bilo vezano uz ovo slavlje postajalo je sve veće i bolje. Pomisli kako bi se ovo Goldie zaista svidjelo.
Emma i Judi dođu zajedno, noseći divlje jagode iz šume. Vjeverice, koje su došle u posjet zajedno s nekim kravama iz mljekare, kao i neka druga stvorenja, morali su obići novu školu izgrađenu pored čopora pasa. Imali su pravo biti na to ponosni. Bila je to prva škola za životinje.
„Gdje su oni ljudi? Kasne po običaju,” žalila se purica.
„Ali oni i žive najdalje od svih,” podsjeti je Judi. „Stalno ih mislim posjetiti da vidim što rade,” uzdahne medvjed.
„Otišla sam do njih prije par mjeseci,” reče Emma, „Koje čudno mjesto, ali njima se izgleda sviđa. Previše zatvoreno za mene. No, ako odlučite poslovati s ljamama, morate živjeti tamo gdje je hladno. To pogoduje boljoj vuni, kaže Juanita.”
„Biti zatvoren unutra mjesecima zbog snijega s tim majmunom — to bi od svakog stvorilo Bonkersa!” našali se Pancho.
Bob se dogega preko i da Judi novine. „Pažljivo, tinta je još mokra,” upozori dok je još jedan primjerak davao purici. Naslovnica je glasila: Krug A, slobodni tisak, urednici: Pancho, Bob i Čangrizalo.
Judi je baš namjeravala reći kako izgledaju profesionalno napravljene kad bend udari početne akorde tako glasno da nitko više nije mogao pričati.
Sve što su mogli bilo je plesati.
\textbf{KRAJ}
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\begin{center}
Anarhistička biblioteka
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Anti-Copyright
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\includegraphics[width=0.25\textwidth]{logo-yu}
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Jane Doe
Anarhistička farma
\bigskip
http:\Slash{}\Slash{}www.stocitas.org
Naslov originala: Anarchist Farm, prvo izdanje objavljeno 1996. godine u SAD-u. Prijevod 2002. objavio Što čitaš?, www.stocitas.org Prevela: Barbara Slade
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\textbf{anarhisticka-biblioteka.net}
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%Title: Measuring $F_L(x,Q^2)/F_2(x,Q^2)$ from Azimuthal Asymmetries in Deep Inelastic Scattering
%Author: T.Gehrmann (Karlsruhe, TTP)
%Published: <EM> Phys. Lett. </EM> <B> B480 </B> (2000) 77-79.
%hep-ph/0003156
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\begin{document}
\begin{titlepage}
\vspace*{-1cm}
\begin{flushright}
TTP00--03\\
March 2000 \\
\end{flushright}
\vskip 3.5cm
\begin{center}
{\Large\bf Measuring $F_L(x,Q^2)/F_2(x,Q^2)$ from Azimuthal\\[0.2cm]
Asymmetries
in Deep Inelastic Scattering}
\vskip 1.cm
{\large T.~Gehrmann}
\vskip .7cm
{\it Institut f\"ur Theoretische Teilchenphysik,
Universit\"at Karlsruhe, D-76128 Karlsruhe, Germany}
\end{center}
\vskip 2.6cm
\begin{abstract}
We demonstrate that the angular
distribution of hadrons produced in semi-inclusive
deep inelastic final states is related to the
inclusive longitudinal structure function. This relation could provide
a new method of accessing $F_L(x,Q^2)$ in deep inelastic scattering
measurements.
\end{abstract}
\vfill
\end{titlepage}
\newpage
The internal structure of the proton as probed in deep inelastic
lepton-proton scattering can be parameterised in terms of two structure
functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$:
\begin{equation}
\frac{\d \sigma}{\d x \d Q^2} = \frac{2\pi \alpha^2}{xQ^4}
\left [ \left ( 1+(1-y)^2 \right) F_2(x,Q^2) - y^2 F_L(x,Q^2)\right]\; .
\label{eq:incl}
\end{equation}
$x$ and $Q^2$ are the usual deep inelastic scattering variables related
to the momentum of the outgoing electron, and $y=Q^2/(xs)$, with $s$
being the lepton-proton centre-of-mass energy squared.
While measurements of $F_2(x,Q^2)$ have been made with high precision
over a large kinematical range
(see e.g.~\cite{disrev} for a review), experimental determinations on
$F_L(x,Q^2)$ are still limited. Given that $F_L(x,Q^2)$, apart from
encoding information on the internal structure of the proton, plays an
important role in QED radiative corrections to processes in
lepton-proton scattering, a precise determination of this structure
function over a wide kinematical range would be very desirable.
The experimental measurement of $F_L(x,Q^2)$ in inclusive deep
inelastic scattering is far from trivial, since the inclusive
cross section (\ref{eq:incl})
is dominated by the structure function $F_2(x,Q^2)$, with
$F_L(x,Q^2)$ entering as a correction only. The contributions from
$F_2(x,Q^2)$ and $F_L(x,Q^2)$ to the deep inelastic cross section
can be disentangled only from their
kinematical factors; a measurement of $F_L(x,Q^2)$ requires
therefore the comparison of data at fixed $(x,Q^2)$ taken at different
centre-of-mass energies. Such measurements have so far been carried
out only at fixed target energies. A determination of $F_L(x,Q^2)$ at
HERA energies has up to now
been made only in an indirect manner~\cite{flh1} by
assuming the contribution to the deep inelastic cross section from
$F_2(x,Q^2)$ to be known from a next-to-leading order QCD fit.
In this note, we investigate an alternative possibility to determine
$F_L(x,Q^2)$. We argue that the azimuthal distribution of hadrons in
semi-inclusive deep inelastic scattering can be related to the
longitudinal structure function by integrating out the final state
hadron momentum in a appropriate way to recover inclusive expressions.
The cross section for semi-inclusive hadron production
reads~\cite{def,men,hag}:
\begin{equation}
\frac{\d \sigma}{\d x\d Q^2 \d z \d \phi} = \frac{\alpha^2 \pi}{2Q^4 z}
\,\left( A + B \cos \phi + C \cos 2\phi \right) \; .
\label{eq:diff}
\end{equation}
$z$ is the longitudinal
momentum transfer from virtual photon to the final state hadron, and
$\phi$ is the angle between the outgoing lepton direction and outgoing
hadron direction measured in the
plane transverse to the virtual photon direction.
The coefficients $A$--$C$ can be computed in the parton model, they
correspond to convolutions of parton distributions $D_{a/N}$
in the target, hard subprocess coefficient functions
$f^{b/a}$, and partonic
fragmentation functions into the final state hadron $D_{h/b}$.
While $A$ is of ${\cal O}(1)$ in perturbation
theory, $B$ and $C$ are of ${\cal
O}(\alpha_s)$. For neutral
current deep inelastic scattering at
HERA energies, one finds~\cite{ahmed} that the
coefficients of the angular
dependent terms can be expected to
amount up to 10\% of the constant term, which is
confirmed by a recent measurement~\cite{zeus} by the ZEUS collaboration.
Momentum conservation in partonic fragmentation implies
that the second moment of the fragmentation functions summed over all
hadrons has to be unity for any parton $b$:
\begin{equation}
\sum_h \int_0^1 \d z\; z\; D_{h/b} (z,Q^2) = 1 \;.
\end{equation}
This relation is preserved under perturbative evolution.
Using this relation, it is possible to relate the second moment of any
semi-inclusive observable to the corresponding inclusive observable.
The use of this relation in deriving sum rules for semi-inclusive
observables in deep inelastic scattering has first been suggested
in~\cite{men}.
Integrating over the angle $\phi$ and
taking the second moment in $z$ of (\ref{eq:diff}), one recovers the
inclusive cross section~(\ref{eq:incl}):
\begin{equation}
\sum_h \int_0^1 \d z \int_0^{2\pi} \d \phi \; z \;
\frac{\d \sigma}{\d x\d Q^2 \d z \d \phi} =
\frac{2\pi \alpha^2}{xQ^4} \left[
\left ( 1+(1-y)^2 \right) F_2(x,Q^2) - y^2 F_L(x,Q^2)\right]\; .
\end{equation}
The coefficient of $\cos 2\phi$ can be expressed by a semi-inclusive
structure function~\cite{hag}:
\begin{equation}
C=(1-y) F_6(x,Q^2,z)\;,
\end{equation}
with
\begin{equation}
F_6(x,Q^2,z) = \frac{z}{\pi}\sum_{a,b} \int_x^1\frac{\d\xi}{\xi}
\int_z^1\frac{\d \eta}{\eta}\,
D_{h/b}(\eta,Q^2)\, D_{a/N} (\xi,Q^2)\, 4 e_{b/a}^2\, \frac{\alpha_s}{2\pi}
\, f_6^{b/a} \left(\frac{x}{\xi},\frac{z}{\eta}\right) \;,
\end{equation}
where
\begin{eqnarray}
f_6^{q/q}(\hat{x},\hat{z})= f_6^{g/q}(\hat{x},1-\hat{z})
& =& 2 C_F \hat{x} \hat{z}\; , \nonumber \\
f_6^{q/g}(\hat{x},\hat{z}) = 4T_F \hat{x}(1-\hat{x})\;.
\end{eqnarray}
In the above $q$ is representing a quark or antiquark.
Taking the second moment of $f_6^{b/a}(\hat{x},\hat{z})$ with respect to
$\hat{z}$ and summing over the
final state parton, one recovers the
longitudinal coefficient functions:
\begin{eqnarray}
\sum_{b=q,g} \int_0^1 \d \hat z \; \hat{z} f_6^{b/q} (\hat{x},\hat{z})
= C_F \hat x &=& \frac{1}{2}\, C^{(1)}_{L,q}(\hat x) \nonumber \\
\sum_{b=q,\bar q} \int_0^1 \d \hat z \; \hat{z} f_6^{b/g} (\hat{x},\hat{z})
= 4T_F \hat{x}(1-\hat{x}) &=& \frac{1}{2}\, C^{(1)}_{L,g}(\hat x) \;.
\end{eqnarray}
Consequently, one finds that the ratio of the second moment of the
coefficients of the $\cos 2\phi$ term and the constant term in
(\ref{eq:diff}) yields:
\begin{eqnarray}
A_{\cos 2\phi}^{(2)}(x,Q^2) &\equiv&
\frac{\displaystyle \sum_h \int_0^1 \d z \int_0^{2\pi}\d \phi
\; z \; \cos 2\phi \; \frac{\d \sigma}{\d x \d Q^2 \d z \d \phi}}
{\displaystyle \sum_h \int_0^1 \d z \int_0^{2\pi}\d \phi \;
z \; \frac{\d \sigma}{\d x \d Q^2 \d z \d \phi}}\label{eq:master} \\
& =&
\frac{1}{2}\, \frac{(1-y)F_L(x,Q^2)}{\left(1+(1-y)^2\right)F_2(x,Q^2)-y^2
F_L(x,Q^2)}\;.
\end{eqnarray}
The ratio of the deep inelastic structure functions can therefore be
expressed as
\begin{equation}
\frac{F_L(x,Q^2)}{F_2(x,Q^2)} = 2 \frac{1+(1-y)^2}{1-y
+ 2y^2 A_{\cos 2\phi}^{(2)}(x,Q^2) } A_{\cos 2\phi}^{(2)}(x,Q^2)
\end{equation}
It should be noted that the sum over all hadrons $h$ in the above
equations also includes
neutral hadrons, whose momentum direction is difficult to track
experimentally. Restricting the summation to charged hadrons only would
introduce subprocess-dependent correction factors, relating to the
different probabilities of quarks and gluons to fragment into charged
hadrons, thus altering the relative magnitude of quark and gluon
contributions in the above asymmetry. Furthermore, the summation
includes only hadrons that participated in the hard scattering process,
i.e.\ it excludes the proton remnant. Hadrons from the proton remnant
will however emerge with low $z$, their contribution in the second
moment can therefore be expected to be small.
In summary, we have demonstrated that the longitudinal structure
function $F_L(x,Q^2)$ is related to the second moment of the
angular $\cos 2\phi$ distribution of hadrons produced in
semi-inclusive deep inelastic scattering. The asymmetry defined in
(\ref{eq:master}) provides a possibility of measuring the structure
function ratio $F_L(x,Q^2)/F_2(x,Q^2)$ in a deep inelastic scattering
experiment at fixed collision energy.
\section*{Acknowledgement}
The author would like to thank Jim Crittenden and
Nick Brook for pointing his attention to
the issue discussed in this note and for numerous valuable discussions.
\begin{thebibliography}{99}
\bibitem{disrev}
T.~Gehrmann, R.G.~Roberts and M.R.~Whalley, J.\ Phys.\ {\bf G25}
Suppl. (1999) A1.
\bibitem{fl}
L.~Whitlow et al., Phys.\ Lett.\ {\bf B250} (1990) 193;\\
E140 Collaboration: S.~Dasu et al., Phys.\ Rev.\ {\bf D49} (1994)
5641;\\
NMC Collaboration: M.\ Arneodo et al., Nucl.\ Phys.\ {\bf B487} (1997)
3;\\
E143 Collaboration: K.\ Abe et al., Phys.\ Lett.\ {\bf B452} (1999) 194.
\bibitem{flh1}
H1 Collaboration: C.\ Adloff et al., Phys.\ Lett.\ {\bf B393} (1997) 452.
\bibitem{def}
H.~Georgi and H.D.~Politzer, Phys.~Rev.~Lett.~{\bf 40} (1978) 3.
\bibitem{men}
G.~K\"opp, R.~Maciejko and P.M.~Zerwas, Nucl.~Phys.~{\bf B144} (1978) 123;\\
A.~Mendez, Nucl. Phys. {\bf B145} (1978) 199.
\bibitem{hag}
K.~Hagiwara, K.~Hikasa and N.~Kai, Phys.~Rev. {\bf D27} (1983) 84.
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M.~Ahmed and T.~Gehrmann, Phys.~Lett.~{\bf B465} (1999) 297.
\bibitem{zeus}
ZEUS Collaboration: J.\ Breitweg et al., preprint
DESY-00-040 (hep-ex/0003017).
\end{thebibliography}
\end{document}
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\begin{document}
\lecture{3 --- February 20, 2007}{Spring 2007}
{Prof.\ Erik Demaine}{Hui Tang}
\section{Overview}
In the last lecture we discussed Binary Search Trees and the many
bounds which achieve $o(\lg n)$ per operation for natural classes of
access sequences. This motivates us to search for a BST which is
optimal (or close to optimal) on \emph{any} sequence of
operations.
In this lecture we discuss lower bounds which hold for any Binary
Search Tree (the Wilber bounds). Based on such a bound, we develop the
Tango tree, which is an $O(\lg\lg n)$-competitive BST structure. The
Tango upper bound and the Wilber lower bounds represent the tighest
bounds on the offline optimal BST known to date.
\section{Wilber Bounds}
The two Wilber bounds are functions of the access sequence, and they
are lower bounds for all BST structures. They imply, for instance,
that there exists a \emph{fixed} sequence of accesses which takes
$\Omega(\lg n)$ per operations for \emph{any} BST.
\subsection{Wilber's 2nd Lower Bound}
Let $\langle x_{1},x_{2},...,x_{m} \rangle$ be the access sequence.
For each access $x_{j}$ compute the following Wilber number. We look
at where $x_{j}$ fits among $x_{i},x_{i+1},...,x_{j-1}$ for all $i = j-1, j-2...$
that is, counting backwards from $j-1$ until the previous access to the key
$x_{j}$. Now, we say that $a_{i} < x_{j} < b_{i}$, where $a_{i}$ and
$b_{i}$ are the tightest bounds on $x_{j}$ discovered so far. Each
time $i$ is decremented, either $a_{i}$ increases or $b_{i}$ decreases
(more tightly fitting $x_{j}$), or nothing happens (the access is
uninteresting for $x_j$). The Wilber number is the number of
alternations between $a_{i}$ increasing and $b_{i}$ decreasing.
\begin{center}
\scalebox{.5}{\includegraphics{wilber2.eps}}
\end{center}
Wilber's 2nd lower bound \cite{wilber} states that the sum of the
Wilber numbers of all $x_{j}$'s is a lower bound on the total cost of
the access sequence, for any BST. It should be noted that this only
holds in an amortized sense (for the total cost): the actual cost to
access some $x_j$ may be lower than its Wilber number on some BSTs.
We ommit the proof; it is similar to the proof of Wilber's 1st lower
bound, which is given below.
An interesting open problem is whether Wilber's second lower bound is
tight.
We now proceed to an interesting consequence of Wilber's 2nd lower
bound: key-independent optimality. Consider a situation in which the
keys are just unique identifiers, and, even though they are
comparable, the order relation is not particularly
meaningful. In that case, we "might as well" randomly permute the keys. In other words, we are interested in
$E_\pi[OPT(\pi(x_{1}),\pi(x_{2}),...,\pi(x_{m})]$, where the expectation is
taken over a random permutation $\pi$ of the set of keys.
Key-independent optimality is defined as usual with respect to the
optimal offline BST.
\begin{theorem}[key independent optimality \cite{iacono}]
A BST has the key-independent optimality property iff it has the
working-set property.
\end{theorem}
In particular, splay trees are key-independently optimal.
\begin{proof} (sketch)
We must show that:
$$ E_\pi[\text{dynamic OPT}(\pi(x_{1}),\pi(x_{2}),...,\pi(x_{m})] = \text{Working-Set Bound } \Theta\left(\sum_{i=1}^m \lg t_i (x_i)\right)$$
The $O(\cdot)$ direction is easy: the working-set bound does not
depend on the ordering, so it applies for any permutation. We must now
show that a random permutation makes the problem as hard as the
working-set problem:
\begin{itemize}
\item $wilber2(x_j)$ only considers the working-set of $x_j$
\item define $W = \{\text{elements accessed since last access to } x_j\}$
\item permutation $\pi$ changes $W$
\item $x_{j}$ falls ``roughly'' in the middle with constant probability
\item $E[\textrm{\# times } a_i \textrm{ increases}] = \Theta(\lg \left|W\right|)$
\item $E[\textrm{\# times } b_i \textrm{ decreases}] = \Theta(\lg
\left|W\right|)$
\item {\bf Claim:} We expect a constant fraction of the increases in $a_i$ and the
decreases in $b_i$ to interleave $\Rightarrow E[wilber2(x_j)] =
\Theta\left(\lg\left|W\right|\right)$
\end{itemize}
\end{proof}
\subsection{Wilber's 1st Lower Bound}
Fix an arbitrary static lower bound tree $P$ with no relation to the
actual BST $T$, but over the same keys. In the application that we
consider, $P$ is a perfect binary tree. For each node $y$ in $P$, we
label each access $x_{i}$ $L$ if key $x_i$ is in $y$'s left subtree in
$P$, $R$ if key $x_i$ is in $y$'s right subtree in $P$, or leave it
blank if otherwise. For each $y$, we count the number of interleaves
(the number of alterations) between accesses to the left and right
subtrees: $interleave(y) = \text{\# of alternations } L
\leftrightarrow R$.
Wilber's 1st lower bound \cite{wilber} states that the total number of
interleaves is a lower bound for all BST data structures
serving the access sequence $x$. It is important to note that the
lower bound tree $P$ must remain static.
\begin{proof}(sketch)
We define the transition point of $y$ in $P$ to be the highest node
$z$ in the BST $T$ such that the root-to-$z$ path in $T$ includes a
node from the left and right subtrees of $y$ in $P$. Observe that the
transition point is well defined, and does not change until we touch
$z$. In addition, the transition point is unique for every node $y$.
\begin{center}
\scalebox{.75}{\includegraphics{transpt.eps}}
\end{center}
We must touch the transition point of $y$ in the next access to a key
labeled $L$ or $R$, that is, within the next 2 $interleave(y)$'s. This
implies that the price we pay for accessing the sequence $x$ is
greater than or equal to half the number of interleaves, that is, $pay
\geq \frac{interleave(x)}{2}$.
\end{proof}
\section{Tango Trees}
Tango trees \cite{tango} are an $O(\lg\lg n)$-competitive BST. They
represent an important step forward from the previous competitive
ratio of $O(\lg n)$, which is achieved by standard balanced trees.
The running time of Tango trees is $O(\lg\lg n)$ higher than Wilber's
first bound, so we also obtain a bound on how close Wilber is to
$OPT$. It is easy to see that if the lower bound tree is fixed without
knowing the sequence (as any online algorithm must do), Wilber's first
bound can be $\Omega(\lg\lg n)$ away from $OPT$, so one cannot achieve
a better bound using this technique.
To achieve this improved performance, we divide a BST up into smaller
auxiliary trees, which are balanced trees of size $O(\lg n$). If we
must operate on $k$ auxiliary trees, we can achieve $O(k\lg\lg n)$
time. We will achieve $k = 1 + $ the increase in the Wilber bound
given by the current access, from which the competitiveness follows.
Let us again take a perfect binary tree $P$ and select a node $y$ in
$P$. We define the preferred child of $y$ to be the root of the
subtree with the most recent access (i.e. the preferred child is the
left one iff the last access under $y$ was to the left subtree). If
$y$ has no children or its children have not been accessed, it has no
preferred child. An interleave is equivalent to changing the
preferred child of a node, which means that the Wilber bound is the
number of changes to preferred children.
\begin{center}
\scalebox{.75}{\includegraphics{prefchild.eps}}
\end{center}
Now we define a preferred path as a chain of preferred child
pointers. We store each preferred path from $P$ in a balanced
auxiliary tree that is conceptually separate from $T$, such that the
leaves link to the roots of the auxiliary trees of ``children''
paths.
\begin{center}
\scalebox{.75}{\includegraphics{auxtrees.eps}}
\end{center}
Because the height of $P$ is $\lg n$, each auxiliary tree will store
$\le\lg n$ nodes. A search on an auxiliary tree will therefore take
$O(\lg\lg n)$ time, so the search cost for $k$ auxiliary trees $= O(k
\lg\lg n)$.
A preferred path is not stored by depth (that would be impossible in
the BST model), but in the sorted order of the keys.
\subsection{Searching Tango trees}
To search this data structure for node $x$, we start at the root node
of the topmost auxiliary tree (which contains the root of $P$). We
then traverse the tree looking for $x$. It is likely that we will
jump between several auxiliary trees -- say we visit $k$ trees. We
search each auxiliary tree in $O(\lg\lg n)$ time, meaning our entire
search takes place in $O(k\lg\lg n)$ time. This assumes that we can
update our data structure as fast as we can search, because we will be
forced to change $k-1$ preferred children (except for startup costs if
a node has no preferred children).
\subsection{Balancing Auxiliary Trees}
The auxiliary trees must be updated whenever preferred paths
change. When a preferred path changes, we must cut the path from a
certain point down, and insert another preferred path there.
\begin{center}
\scalebox{.75}{\includegraphics{cutjoin.eps}}
\end{center}
We note that cutting and joining resemble the $split$ and
$concatenate$ operations in balanced BST's. However, because auxiliary
trees are ordered by key rather than depth, the operations are
slightly more complex than the typical $split$ and $concatenate$.
\begin{center}
\scalebox{1}{\includegraphics{splitcat.eps}}
\end{center}
Luckily, we note that a $depth > d$ corresponds to an interval of
keys. Thus, cutting from a point down becomes equivalent to cutting a
segment in the sorted order of the keys. In this way, we can change
preferred paths by cutting a subtree out of an auxiliary tree using
two split operations and adding a subtree using a concatenate
operation. To perform these cut and join operations, we label the
roots of the path subtrees with a special color and pretend it's not
there. This means we only need to worry about doing the $split$ and
$concatenate$ on a subtree of height $\lg n$ rather than trying to
figure out what to do with all the auxiliary subtrees hanging off the
path subtree we are interested in. We know that balanced BSTs can
support $split$ and $concatenate$ in $O(\lg size)$ time, meaning they
all operate in $O(\lg\lg n)$ time. Thus, we remain $O(\lg\lg
n)$-competitive.
%\bibliography{scribe}
\bibliographystyle{alpha}
\begin{thebibliography}{DHIP04}
\bibitem[DHIP04]{tango}
Erik~D. Demaine, Dion Harmon, John Iacono, and Mihai Patrascu.
\newblock Dynamic optimality --- almost.
\newblock In {\em FOCS '04: Proceedings of the 45th Annual IEEE Symposium on
Foundations of Computer Science (FOCS'04)}, pages 484--490. IEEE Computer
Society, 2004.
\bibitem[Iac02]{iacono}
John Iacono.
\newblock Key independent optimality.
\newblock In {\em ISAAC '02: Proceedings of the 13th International Symposium on
Algorithms and Computation}, pages 25--31. Springer-Verlag, 2002.
\bibitem[Wil89]{wilber}
R.~Wilber.
\newblock Lower bounds for accessing binary search trees with rotations.
\newblock {\em SIAM J. Comput.}, 18(1):56--67, 1989.
\end{thebibliography}
\end{document}
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\title{The Occult Assault on Institutions}
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\author{Hakim Bey}
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The levels of Immediatist organization:
\begin{enumerate}[1.]
\item\relax
The gathering. Could be anything from a party to a riot. Can be planned or unplanned but depends on spontaneity to “really happen”. Examples: anarchist gathering, neo-pagan celebration, Rave, brief urban riot or spontaneous demo. Of course the best gatherings become TAZ’s such as some of the Be-Ins of the 60’s, the early Rainbow tribe gatherings, or the Stonewall Riot.
\item\relax
The horizontal potlatch. A one-time meeting of a group of friends to exchange gifts. A planned orgy might fall into this category, the gift being sexual pleasure – or a banquet, the gift being food.
\item\relax
The Bee. Like a quilting bee, the Immediatist Bee consists of a group of friends meeting regularly to collaborate on a specific project. The Bee might serve as an organizing committee for a gathering or potlatch, or as a creative collaborative, an affinity group for direct action, etc. The Bee is like a Passional Series in Fourier’s system, a group united by a shared passion which can only be realized by a group.
\item\relax
When the Bee acquires a more-or-less permanent membership and a purpose larger than just a single project – an on-going project, let’s say – it can either become a “club” or Gesellschaft organized non-hierarchically for open activity, or else a “Tong” organized non-hierarchically but clandestinely for secret activity. The Tong is of more immediate interest to us now for tactical reasons, and also because the club operates in danger of “institutionalization” and hence (in Ivan Illich’s phrase), “paradoxical counter-productivity”. (That is, as the institution approaches rigidity and monopoly it begins to have the opposite effect from its original purpose. Societies founded for “freedom” become authoritarian, etc.) The traditional Tong is also subject to this trajectory, but the Immediatist Tong is built, so to speak, to auto-destruct when no longer capable of serving its purpose.
\item\relax
The TAZ can arise out of any or all of the above forms singly, in sequence, or in complex patterning. Altho I’ve said the TAZ can last as briefly as one night or as long as a couple of years, this is only a rough rule, and probably most examples fall in between. A TAZ is more than any of the first four forms, however, in that while it lasts it fills the horizon of attention of all its participants; it becomes (however briefly) a whole society.
\item\relax
Finally, in the uprising, the TAZ breaks its own borders and flows (or wants to flow) out into the “whole world”, the entire immediate time\Slash{}space available. While the uprising lasts, and has not been terminated by defeat or by changing into “Revolution” (which aspires to permanence), the Insurrection keeps the consciousness of most of its adherents spontaneously tuned in to that elusive other mode of intensity, clarity, attention, individual and group realization, and (to be blunt) that happiness so characteristic of great social upheavals such as the Commune, or 1968. From the existential point of view (and here we invoke Stirner, Nietzsche, and Camus), this happiness is actually the purpose of the uprising.
\end{enumerate}
The goals of the Immediatist organization are:
\begin{enumerate}[1.]
\item\relax
Conviviality: the coming together in physical closeness of the group for the synergistic enhancement of its membership’s pleasures.
\item\relax
Creation: the collaborative production, direct and unmediated, of necessary beauty, outside all structures of hypermediation, alienation, commodification.\footnote{I’m not using the term hypermedia here in the sense assigned to it by our comrades at Xexoxial Endarchy, who call hypermedia simply the appropriation of all creative media to single effect (i.e., the next stage beyond “mixed Media”) \dots{} I’m using “hypermediation” to mean representation exacerbated to the point of an immiserating alienation, as in the image of the commodity.} We’ve long since grown weary of quibbling over terms, and if you don’t know what we mean by “necessary beauty” you may as well stop reading here. “Art” is only a possible sub-category of this mystery and not necessarily the most vital.
\item\relax
Destruction: We’d go farther than Bakunin, and say that there is no creation without destruction. The very notion of bringing some new beauty into being implies that an old ugliness has been swept away or blown up. Beauty defines itself in part (but precisely) by destroying the ugliness which is not itself. In our version of the Sorelian myth of social violence, we suggest that no Immediatist act is completely authentic and effective without both creation and destruction: the whole Immediatist dialectic is implied in any immediatist “direct action”, both the creation-in-destruction and the destruction-in-creation. Hence “poetic terrorism”, for example; and hence the real goal or telos of all our organizational forms is:
\item\relax
the construction of values. The Maslovian “peak experience” is value-formative on the individual level; the existential factuality of the Bee, Tong, TAZ or uprising permits a “revaluation of values” to flow from its collective intensity. Another way of putting it: – the transformation of everyday life.
\end{enumerate}
The link between the organization and the goal is the tactic. In simple terms, what does the Immediatist organization do? Our “strategy” is to optimize conditions for the emergence of the TAZ (or even the Insurrection) – but what specific actions might be carried out to construct this strategy? Without tactics, the Immediatist organization might as well disperse at once. “Direct action” should further the “cause” but also must itself hold all the potential for the flowering of the cause within itself. In fact, each act must be in potentia both aimed at the goal and identical with the goal. We cannot use tactics which are limited to mediation; each action must immediately realize the goal, at least in some respect, lest we find ourselves working for abstractions and even simulations of our purpose. And yet the many different tactics and actions should also add up to more than the sum of their parts, and should give birth to the TAZ or the Uprising. Just as ordinary organizations cannot provide the structures we need, so ordinary tactics cannot satisfy our demand for both immediate and insurrectionary “situations”.
Conviviality is both a tactic and a goal. Noble in itself, it may serve as both form and content for such organizational modes as the gathering, the potlatch, the banquet. But conviviality by itself lacks the transformative energy that generally arises only out of a complex of actions which includes what we’ve called “destruction” as well as “creation”. The ideal Immediatist organization aims at this more complex goal, and gains conviviality as a necessary structure along with it. In other words, gathering together in a group to plan a potential TAZ for an even larger group is already an Immediatist act involving conviviality – like the kingdom of heaven, is “added unto” all sincere striving for more exalted break-throughs. It would seem that the quintessential immediatist act or tactic however will involve simultaneous creation and destruction rather than just conviviality – hence the Bee and Tong are “higher” organizational forms than the gathering and potlatch.
In the Bee the emphasis is on creation – the quilt, so to speak – the collaborative art project, the group’s act of generosity toward itself and toward reality rather than toward an “audience” of mediated consumers. Of course the Bee can also consider and undertake destructive or “criminal” actions. But when it does so it has perhaps already taken the first step toward becoming a secret society or Immediatist Tong. Hence I think that the Tong is the most complex (or “highest”) form of immediatist organization which can be pre-determined to a significant degree. The TAZ and the uprising depend finally on many factors for the “organization” process to achieve without “luck”. As I’ve said, we can maximize possibilities for the TAZ or the insurrection but we cannot really “organize” them or make them happen. The Tong however can be clearly defined and organized and can carry out complex actions, both material and symbolic, both creative and destructive. The Tong cannot guarantee the TAZ, much less the insurrection, but it can surely gratify many or most immediate desires of lesser complexity – and after all it might succeed in precipitating the grant event of the TAZ, the Commune, the “restoration of the Ming” as Great Festival of Consciousness, the objective correlative of all desire.
Keeping all this in mind let us try to imagine – and then criticize – possible tactics for the Immediatist group, and ideally for the well-organized semi-permanent Tong or virtually clandestine action group or affinity web, capable of attempting fully-evolved complex direct actions in an articulated strategy. Each such action must simultaneously damage or destroy some real and or imaginal time\Slash{}space of “the enemy”, even as it simultaneously creates for its perpetrators the strong chance of peak experience or “adventure”: each tactic thus in a sense moves to appropriate and detourner the enemy’s space, and eventually to occupy and transform it. Each tactic or action is already potentially the whole “Path” of autonomy in itself, just as each invocation of the Real already contains the entirety of the spiritual path (according to the “gnosis” of Ismailism and heterodox sufism).
But wait! First: – who is “The Enemy”? It’s all very well to mutter about conspiracies of the Establishment or the networks of psychic control. We’re talking about real-time direct actions which must be carried out “against” identifiable nodes of real-time power. Discussion of abstract enemies such as “the state” will get us nowhere. I am not oppressed (or alienated) directly by any concrete entity called the state, but by specific groups such as teachers, police, bosses, etc. A “Revolution”: may aim at overthrowing a “state”. But the Insurrection and all its Immediatist action-groups will have to discover some target which is not an idea, a piece of paper, a “spook” that enchains us with our own bad dreams about power and impotence. We’ll play at the war of images, yes. But images arise from or flow through specific nexuses. The spectacle has a structure, and the structure has joints, crossings, patterns, levels. The Spectacle even has an address – sometimes – maybe. It’s not real in the same way the TAZ is real. But it’s real enough for an assault.
Because the Immediatist texts have largely been addressed to “artists” as well as “non-authoritarians” and because Immediatism is not a political movement but a game, even an aesthetic game, it would seem inescapably obvious that we should look for the enemy in the media, especially in those media we find to be directly oppressive. For example for the student the oppressive and alienating medium is “education”, and the nexus (the pressure point) must therefore be the school. For the artist the direct source of alienation would seem to be the complex we usually call the Media, which has usurped the time and the space of art as we wish to practice it – which has redefined all creative communicativeness as an exchange of commodities or of alienating images – which has poisoned “discourse”. In the past the alienating medium was the church and the insurrection was expressed in the language of heretical spirituality vs. organized religion. Now the Media plays the role of the Church in the circulation of images. As the Church once concocted a false scarcity of sanctity or salvation, so the Media constructs a false scarcity of values, or “meaning”. As the Church once tried to impose its monopoly on the spirit, the Media wants to re-make language itself as pure mind, divorced from the body. The media denies meaning to corporeality, to everyday life, just as the Church once defined the body as evil and everyday life as sin. The Media defines itself, or its discourse, as the real universe. We mere consumers live in a skull-world of illusion, with TVs as eyes-sockets through which we peer at the world of the living, the “rich \& famous”, the real . Just so did religion define the world as illusion and heaven only as real – real, but so far away. If insurrection once spoke to the Church as heresy, so it must speak now to the Media. Once, the revolting peasants burned churches. But what exactly are the churches of the Media?
It’s easy to feel nostalgia for such a once-magnificent enemy as the Roman Catholic Church. I’ve even tried to convince myself that today’s washed-out sex-hating charade is still worth conspiring against. Infiltrate the church; fill up the tractate shelf with beautiful porno flyers labelled “This is the Face of God”; hide dada\Slash{}voodoo objects under the pews and behind the altar; send occult manifestos to the Bishop and clergy; leak satanic scares to the idiot press; leave evidence incriminating the Illuminati. An even more satisfying target might be the Mormons, who are completely enthralled by hypermediated CommTech and yet intensely sensitive to “black magic”.\footnote{Mormonism was founded by rogue Freemason occultists, and Mormon leaders remain extremely susceptible to hints of a buried past coming back to haunt them. The Roman Catholic Church might treat a “magical assault” with a millennial shrug of Italiante sophistication – but Mormons would go for their guns.} Televangelism offers an especially tempting mix of media and bad religion. But when it comes to real power, the churches feel quite empty. The god has abandoned them. The god has his own talk-show now, his own corporate sponsors, his own network. The real target is the Media.
The “magical assault” however still holds promise as a tactic against this new church and “new inquisition” – precisely because the Media, like the church, does its work thru “magic”, the manipulation of images. In fact our biggest problem in assaulting the Media will be to invent a tactic which cannot be recuperated by Babylon and turned to its own power-advantage. A breathless “live-news” report that CBS had been attacked by radical sorcerers would simply become part of the “spectacle of dissidence”, the sub-manichean drama of the discourse of simulation. The best tactical defense against this co-optation will be the subtle complexity and aesthetic depth of our symbolism, which must contain fractal dimensions untranslatable into the flat image-language of the tube. Even if “they” try to appropriate our imagery, in other words, it will carry an unexpected “viral” subtext which will infect all attempts at recuperation with a nauseating malaise of uncertainty – a “poetic terror”.\footnote{It’s important not to get caught, as this neutralizes any power we might have gained or sought to express, and even turns our own power against us. A good Immediatist action should be relatively impeccable, to coin an oxymoron. Getting expelled from High-school might spoil the effect. Immediatism wants to be a martial art, not a road to martyrdom.}
One simple idea would be to blow up a TV transmission tower and then take credit for the action in the name of the American Poetry Society (who ought to be blowing up TV towers); but such a purely destructive act lacks the creative aspect of the truly immediatist tactic. Each act of destruction should ideally also be an act of creation. Suppose we could blank TV transmission in one neighborhood and at the same time sage a miraculous festival, liberating and transforming the local mall into a one-night TAZ – then our action would combine destruction and creation in a truly Immediatist “direct action” of beauty and terror – Bakuninesque, situationistic, real dada at last. The media might try to distort it and appropriate its power for itself, but even so it could never erase the experience of the liberated neighborhood and its people – and chances are the Media would after all remain silent, since the whole event would seem too complex for it to digest and shit out as “news”.
Such an immensely complicated action would lie beyond the capabilities of all but the richest and most fully-developed Immediatist Tong. But the principle can be applied at lower levels of complexity. For example, imagine that a group of students wish to protest the stupefying effect of the education-medium by disrupting or shutting down school for some time. Easily done, as many bold high school saboteurs have discovered. Carried out as a purely negative action, however, the gesture can be interpreted by authority as “delinquency” and thus its energy can be recuperated to the benefit of Control. The saboteurs should make a point of simultaneously providing valuable information, beauty, a sense of adventure. At the very least anonymous leaflets about anarchism, homeschooling, media critique or something of the sort can be “left at the scene” or distributed to other students, faculty, even press. At best, an alternative to school itself should be suggested, through conviviality, festival, liberated learning, shared creativity.
Obviously the TAZ usually leaves not a wrack behind. Building isn’t its top priority. And yet all lived space is architecture – built space, made space – and the TAZ by definition has presence in real time and space. The nomad encampment should perhaps serve as the primordial prototype. Tents, trailers, RV’s, houseboats. The old travelling tent circus or carnival might offer a model for TAZ architecture. In an urban setting the squat becomes the commonest possible space for our purposes, but in America at any rate the law of property makes the squat almost be definition a poor space. The TAZ wants rich space, not so much rich in articulation (as in the space of control, the official building of capital, religion, state) but rich in expression. The temporary playful spaces proposed by situationist and urbanist radicals in the 60’s had some potential but finally proved too expensive and too planned. The ur-TAZ architecture is that of the Paris Commune. The micro-neighborhood is closed off by barricades. The identical houses of the poor are then connected by driving passageways thru all connecting walls on the ground floor. These passageways remind us of Fourier’s arcades, by which the Planasterians would circulate thru their communal palace, from private to public space and back again. The Commune city-block became a fortified TAZ with public military space on ground level (and roofs) and private space on upper stories, with the enclosed streets as festival-space. This plan influences the architecture of “P.M.”‘s bolo’bolo where the commune-block becomes a more permanent urban utopian commune. As for the TAZ, it is effected by a kind of closure, but one paradoxically shot through with openings. It escapes the asphyxiating enclosure of Capital, and the tragic ugliness of industrial space. Its architecture is smooth, not striated – hence the tent not the prison, the passageway not the portal, the barricade, not Haussman’s boulevards.
Getting back to the project of a “magical assault” on the Media, or media-hex:: – it too should combine in one gesture (more or less) both the creative and destructive elements of the effective Immediatist artwork or work of poetic terrorism. In this way it will (we hope) prove too complex for the usual recuperation-process. For example, it would be futile to bombard the Media-target with images of horror, bloodshed, serial murder, alien sex abuse, S\&M splatter and the like, since the Media itself is the chief purveyor of all such imagery. Guignol demi-satanism fits right into the spectrum of horror-as-control where most broadcasting occurs. You can’t compete with the “News” for images of disgust, repulsion, atavistic panic, or gore. The Media (if we can personify it for a moment) might at first be surprised that anyone would bother to mirror this crap back at the Media – but it would have no occult effect.\footnote{The trouble with most “transgressive” art is that it transgresses none of the Consensus values – it merely exaggerates them, or at best exacerbates them. Aesthetic obsession with “Death” makes a perfect commodity (image-without-substance), since the delivery of the meaning of the image would actually put an end to the consumer. To buy death is to buy either failure or fascism – a brink upon which Bataille himself teetered with sickening lack of balance. I say this despite admiration for Bataille.}
Let us imagine (another “thought-experiment!”) that an Immediatist cabal of some size and seriousness has somehow gotten hold of the addresses (including fax, phone, E-mail, or whatever) of the executive and creative staff of a TV show we might feel represented a nadir of alienation and psychic poison (say “NYPD Blue”). In “The Malay Black Djinn Curse” I suggested sending packages of dada\Slash{}voodoo objects to such people, along with warnings that their place of work had been cursed. At that time I was reluctant to recommend curses against individuals. I would now however recommend even worse. Moreover, for these media moghuls I might well favor the kind of creepy Moslem\Slash{}heretic jungle reptile imagery I outlined in the “Black Djinn” operation – since the Media show such fear of “Moslem” terror and such bigotry against Moslems – but I would now make the whole scenario and imagery far more complex. The TV exec’s and writers should be sent objects as exquisite and disturbing as surrealist “boxes”, containing beautiful but “illegal” images of sexual pleasure\footnote{This will prevent the images from ever appearing on TV or in news photos. It will also, coincidentally, make a statement about the relation between “beauty” and “obscenity”, and between “art” and “censorship”. etc., etc.}, and intricate spiritual symbolism, evocative images of autonomy and pleasure in self-realization, all very subtle, convoluted, mysterious; these objects must be made with real artistic fervor and the highest inspiration, but each one meant only for one person – the victim of the hex.
The recipients may well be disturbed by these anonymous “gifts” but will probably neither destroy them nor even discuss them at once. No harm to our scheme if they do. But these objects may well look too fine, too “expensive” to destroy – and too “dirty” to show to anyone else. Next day, the victims each receive a letter explaining that their receipt of the objects effected the delivery of a curse. The hex will cause them to come to know their true desires, symbolized by the magical objects. They will also now begin to realize they are acting as enemies of the human race by commodifying desire and working as the agents of soul-Control. The magic art-objects will weave into their dreams and desires, making their jobs now seem not only poisonously boring but also morally destructive. Their desires so magically awakened will ruin them for work in the Media – unless they turn to subversion and sabotage. At best they can quit. This might save their sanity at the expense of their meaningless “careers”. If they remain in Media they will waste away with unsatisfied desire, shame, and guilt. Or else become rebels, and learn to fight against the Eye of Babylon from within the idol’s belly. Meanwhile their “show” has been picked for total black magic assault by a group of Shiite terrorist sorcerers, or the Libyan Voodoo Hit squad, or something of the sort. Of course it would be nice to have an inside agent to plant “clues” and to spy out information, but some variation on this scheme can be carried out without active infiltration of the institution. The initial assault might perhaps be followed up with mailings of anti-Media propaganda, and even Immediatist tracts. If possible, of course, some bad luck could be produced for the victims or for their institution. Pranks, you know. But again, this is not necessary, and may even get in the way of our pure experiment in mind-fuck and image-manipulation. Let the bastards produce their own bad luck out of their inner sadness at being such evil assholes, out of their atavistic superstition (without which they wouldn’t be such media-wizards), out of their fear of otherness, out of their repressed sexuality. You can be sure they will – or at least, that they’ll remember the “curse” every time something bad happens to them.
The general principle can be applied to media other than television. A computer company for example might be cursed thru its computers by a talented hacker, altho one would have to avoid SciFi scenarios such as William Gibson’s haunted cyberspace – too baroque. Advertising companies run on pure magic, film-makers, PR firms, art galleries, lawyers, even politicians.\footnote{Generally not worth attacking as “politicians”, since they are after all mere “paper tigers” – but perhaps worth attacking as paper tigers.} Any oppressor who works through the image is susceptible to the power of the image.
It should be stressed that we are not describing the Revolution here, or revolutionary political action, or even the Uprising. This is merely a new kind of neo-hermetic agit-prop, a proposal for a new kind of “political art”, a project for a Tong of rebel artists, an experiment in the game of Immediatism. Others will struggle against oppression in their own fields of expertise, work, discourse, life. As artists we choose to struggle within “art”, within the world of the Media, against the alienation which oppresses us most directly. We choose to battle where we live, rather than theorize about oppression elsewhere. I’ve tried to suggest a strategy and imagine certain tactics which would further it. No other claims are made and no further details should be divulged. The rest is for the Tong.
I’ll admit that my own taste might run toward an even more violent approach to Media than proposed here in this text. People talk about “taking over” TV stations, but not one of them has succeeded. It might make more sense to shoot TV sets in electronic shop windows, ludicrous as it seems, than to dream of taking over the studios. But I draw the line at suggesting attentats against News fascists, or even killing Geraldo’s dog, for several reasons which still seem sufficient to me. For one, I have taken to heart Nietzsche’s remarks on the inferiority and futility of revengism as a political doctrine. Mere reaction is never a sufficient response – much less a noble path. Moreover, it wouldn’t work. It would be seen as an “attack on free speech”. The project proposed here includes within its structure the possibility of actually changing something – even if it’s only a few “minds”. In other words it has a constructive aspect integrally bound up with a destructive aspect, so that the two cannot be separated. Our dada\Slash{}voodoo object is both an attack and a seduction in one, and both motives will be thoroughly explained in the accompanying flyers or letters. After all, there’s the chance we might convert someone. Of course, we may easily fail here too. All our efforts could end up in the trash, forgotten by minds too well armored even to feel a moment’s unease. This is, after all, merely a thought experiment, or an experiment in thought. If you like you could even call it merely a form of aesthetic criticism directed at the perpetrators rather than the consumers of bad art. The time for real violence is not yet, if only because the production of violence remains the monopoly of the Institutions. There’s no point in sticking one’s head up and waving a gun if one is facing a star war death beam satellite.\footnote{All praise to the activists who destroyed such a satellite in California with axes. Unfortunately they were caught, and punished by having their salaries seized to pay off the cost of destruction. Not good.} Our task is to enlarge the cracks in the pseudo monolith of social discourse, gradually uncovering bits of empty spectacle, labeling subtle forms of mind-control, charting escape routes, chipping away at crystallizations of image suffocation, banging on pots and pans to wake a few citizens from media trance, using the intimate media\footnote{The intimate media by definition don’t reach the mass unconscious like TV, movies, newspapers. They can still “speak” to the individual. FM radio, cable public access video, small press, CDs and cassette tapes, software and other CommTech can be used as intimate media. Here the Xexoxial Endarchy’s idea of “hypermedia” as a tool for insurrection finds its true role. There exist two contending factions within non-authoritarian theory at present: – the anti-tech primitivists (Fifth Estate, Anarchy: A Journal of Desire Armed, John Zerzan) and the pro-Tech futurologists (including both left-wing anarcho-syndicalists and right-wing anarcho-libertarians). I find all the arguments vastly informative and inspiring. In TAZ and elsewhere I’ve attempted to reconcile both positions in my own thinking. I would now suggest that the question proposed by these arguments cannot be answered except in the process-of-becoming of an active praxis (or politique) of desire. Let us imagine that “the Revolution” has taken place. We’re free to decide our level of technology, in a spectrum ranging from pre-Ice-Age primitive to post-industrial SciFi. Will the neo-paleolithics force the futurists to give up their tech? Will the space cadets force the Zerzanites to buy VR rigs? Piously, one hopes not. The question will rather be: how much do we desire the hunting\Slash{}gathering life? or the CyberEvolutionary life? Do we desire computers enough to forge the silicon chips ourselves? Because after the Revolution no one will accept alienated work. On this, all non-authoritarian tendencies agree. You want a forest full of game? You are responsible for its fecundity and wildness. You want a spaceship? You are responsible for its manufacture, from mining the ore to black smithing the nose cone. By all means form a commune or net-work. By all means demand that my level of tech doesn’t interfere with yours. Other than these few ground-rules for avoiding civil war, non-authoritarian society can depend on nothing but desire to shape its techne’. As Fourier would put it, the level of economic complexity of utopian society will be in harmony with the totality of all Passions. I can’t predict what exactly might emerge. All I can imagine is what I’m capable of desiring to the point of willing its realization. \protect\endgraf Personally (as a matter of taste) I envision something very like bolo’bolo: – infinite variety with in the basic revolutionary context of positive freedom. By definition there could be no such thing as a NASA-bolo or a Wall Street-bolo, because NASA and Wall Street depend on alienation to exist. I would expect something like low-tech or “appropriate” tech (envisioned by 60’s theorists such as Illich) to become the Utopian average, with extreme wings occupying a restored Wild(er)ness on the one hand, and the Moon on the other \dots{} In any case, it’s all science fiction. In my writing I try to envision tactics which can be used now by any non-authoritarian tendency. Both the “Tong” and the assault on Media should appeal to both the primitivists and the techies. And I discuss the use of both magic and computers because both exist in the world I inhabit, and both will be used in the liberating struggle. Not only the future but even the present holds too much possibility, too many resources, a superabundant-redundant excess of potentials, to be limited by ideology. A theory of technology is too constraining. Immediatism offers instead an aesthetics of technology, and prefers praxis to theory.} to orchestrate our assaults on Big Media and its Big Lies, learning again how to breathe together, how to live in our bodies, how to resist the image-heroin of “information”. Actually what I’ve called “direct action” here might better be known as indirect action, symbolic, viral, occult and subtle rather than actual, wounding, militant, and open. If we and our natural allies enjoy even a little success, however, the superstructure may eventually lose so much coherence and assurance that its power will start to slip as well. The day may come (who would’ve thought that one morning in 1989 Communism would evaporate?), the day may come when even too-late Capitalism begins to melt down – after all it’s only outlasted Marxism and fascism because it’s even more stupid – one day the very fabric of the consensus may start to unravel, along with the economy and the environment. One day the colossus may tremble and teeter, like an old statue of Stalin in some provincial town square. And on that day perhaps a TV station will be blown up and will stay blown up. Until then: – one, ten, a thousand occult assaults on the institutions.
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Hakim Bey
The Occult Assault on Institutions
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Retrieved on 17\textsuperscript{th} May 2021 from \href{https://hermetic.com/bey/occultassault}{hermetic.com}
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\chapter{Getting Started}
\label{chap:started}
\section{Hello Proof}
The graphical interface allows to browse into a file or a set of
files, and check the validity of goals with external provers, in a
friendly way. This section presents the basic use of this GUI. Please
refer to Section~\ref{sec:ideref} for a more complete description.
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\title{Закат эры машин détourned}
\date{2009}
\author{Ахмед Хомейни}
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Много ли еще осталось тех, кто не знает, какое направление принимает всемирная система и в особенности современное общество? Глобальное потепление, функция индустриальной цивилизации, уничтожит биосферу до того, как закончится это столетие. Живые виды на планете вымирают быстрорастущими темпами, мертвые зоны в океанах увеличиваются, интоксикация почвы и воздуха повышается, тропические леса уничтожены, все остальное постигла та же участь.
Малолетние дети сидят на антидепрессантах, в то время как количество психических расстройств среди молодежи за последние 20 лет выросло более чем в два раза. Коэффициент подростковых самоубийств с 1970-х годов увеличился в три раза. Недавние исследования показали, что треть студентов уходит в запой как минимум раз в месяц. Специалисты сделали вывод, что употребление алкоголя несовершеннолетними в США достигло эпидемических пропорций. Между тем почти каждый американец нуждается в ежедневном употреблении определенных наркотиков. С другой стороны, отмечается всплеск убийств на рабочих местах, в школах и дома. Одним из последних патологических явлений является убийство родителями своих детей. Внешние проявления шокирующего и ужасающего феномена обусловливаются распадом общества. Мы живем в пространстве пустоты, горя, стресса, скуки и беспокойства, где наша «человеческая природа» настолько деградирует, насколько что-либо исчезает из естественного мира.
Объем знаний удваивается каждые пять лет, но в этом все более технофицирующемся и одномерном мире закостенелая реальность пока что не вызывает сомнений. Цивилизация сама по себе доказала свой провал, и человечество завершается самоликвидацией в полной капитуляции перед властью. В гармонии с властью окончательно потерпел поражение циничный постмодерновый дух времени.
Символическая культура атрофировала наши чувства, уничтожила непосредственный опыт и привела нас, как предсказывал Фрейд, к состоянию «постоянного внутреннего несчастья». Мы унижены и доведены до такого предела, что вынуждены задаться вопросом, почему человеческая деятельность стала столь враждебной человечеству, не говоря уже о других формах жизни на этой планете. В недавно вышедших книгах с громкими названиями «Все сейчас связано», «Жизнь в первой глобальной цивилизации и что случится», «Как новый информационный мир изменит наши жизни» выражено смирение перед стандартной, лишенной надежды ситуацией. Подобные работы являют творческое истощение и моральную неспособность поколения, в котором массированная дегуманизация и неистовое разрушение природы соперничают друг с другом за осуществление своих взаимосвязанных проектов.
Овеществленное существование прогрессивно сводит на нет любой вопрос, кто бы его ни задал. Как еще подсчитать поразительно приспособленческую природу постмодернизма, аллергичного к любым сомнениям относительно базы царства техно-капиталистической злобы? Но сомнения все еще появляются и быстро принимают форму глубинной движущей силы обновленного социального движения. В то время как витальные структуры различных жизненных миров ухудшаются на всех уровнях, лучшие умы должны искать решение проблемы. Вместо этого большинство оказалось неспособным определить пути анализа парализующей дихотомии «цивилизация — природа» и прийти к необходимым умозаключениям. Некоторые исследователи все же обозначили круг вопросов. Хоркхеймер пришел к выводу, что доминация природы и людей, а также причины, способствующие этому, кроются в «глубочайших пластах цивилизации». Батай констатировал, что «сущностное движение в каждом человеке отвергает Мать-Землю, давшую ему рождение, открывает путь к ее подчинению».
По прошествии 30 лет мы наблюдаем возрождение интереса к проблеме. Люди обладают информацией и, подталкиваемые возрастающим кризисом во всех сферах, исследуют процесс, стремясь адекватно понять ситуацию, более глубоко, чем в 1960-х. Новое движение является «анархичным» и нуждается в ином определении. Даже после нескольких дней боев против ВТО на улицах Сиэттла в 1999 г. направленность антиглобализации стала устойчивой и более явной. «Анархизм является основной перспективой внутри движения», — заявила Барбара Эпштейн осенью 2001 года. Эстер Каплан в феврале 2002 г. заметила, что «после Сиэттла все больше и больше активистов под скромные фанфары приходят к точной самоидентификации как анархистов и анархо-мыслящие коллективы увеличиваются, анархическая периферия быстро становится центром движения». Дэвид Грэбер определил это более кратко: «Анархия является центром движения, его душой, источником всего наиболее нового и обнадеживающего». Генри Киссинджер ссылается на антиглобалистские протесты 1999 и 2000-го как на «ранние предупредительные сигналы потенциального политического значения в развитых странах и Третьем Мире, как саму угрозу мировой системе». В отчете ЦРУ «Глобальные тренды 2015», который был обнародован весной 2000 г., предсказано, что наибольшей помехой глобализации в новом тысячелетии может явиться возможное объединение движений протеста развитых стран и борьба местных жителей за сохранение их целостности против вторжений капитала и технологий.
Я думаю, совершенно ясно, что оно становится чем-то другим, чем часть левого движения. До настоящего времени каждое современное антикапиталистическое движение в сущности одобряло экспансию средств производства и продолжающееся развитие технологий. Сейчас же наблюдается явный отказ от этого производительного направления. Эта анархо-примитивистская (или просто примитивистская) тенденция понимает, что учет суровых реалий наших дней нуждается в глубоком исследовании когда-то принятых как должное институций. Несмотря на постмодернистский запрет на изучение происхождения этих институций, в решении вопроса «Что является главной причиной нынешней крайности существования?» — новый подход находит то же разделение труда и приручение. Технология, предполагающая систему интенсивного разделения труда или специализации, обвиняется как двигатель всегда интенсивной технификации жизненного пространства. Цивилизация добивается успеха, когда разделение труда достигает той стадии, при которой начинается приручение и сейчас представляется чрезвычайно проблематичной. Тогда как приручение животных и растительности однажды было принято как данность, сейчас эта логика вынесена в фокус. Чтобы увидеть значение генной инженерии и человеческого клонирования, необходимо усвоить их как подразумеваемые в базовом устройстве для доминации над природой, что является преступлением. Думается, понятно, что такой критический подход больше ставит вопросы, развивающие анархическое мышление, и не предполагает какие-либо определенные ответы.
Одной из точек прикосновения или вдохновения примитивистской анархии за прошедшие десятилетия является парадигма сдвига в области антропологии и археологии в отношении человеческой общественной жизни в течение «предыстории». Цивилизация появилась только около 9000 лет назад. Это время отдалено тысячами поколений людей, которых удовлетворяло то, что может быть названо государством природной анархии. Основная линия в антропологической литературе, включая учебники, описывает жизнь вне цивилизации как обильное, праздное время; с обычаями коллективного владения продуктами питания, относительной автономией или равенством полов и отсутствием организованных преступлений. Люди использовали огонь для приготовления пищи около 2 миллионов лет назад и свободно перемещались в открытом море как минимум 800 000 лет назад. Они имели мозг, подобный мозгу современного человека, и наслаждались наиболее успешной, недеструктивной адаптацией к природному миру.
Если раньше вопрос в учебнике звучал: «Почему люди так долго учились приручать животных и вести аграрное хозяйство?», то теперь спрашивается, зачем вообще они это сделали.
По мере того как негативные и даже предельно допустимые результаты технологии и цивилизации все более осознавались, поворот к луддизму, антицивилизационной политике придает огромный смысл всей эпохе. Не будет открытием то, что это влияние было зафиксировано в различных обстоятельствах, включая протесты против «Большой восьмерки» в Генуе в июле 2001 года. В них принимали участие 300 000 человек, результат — 50 млн. дол. убытков. Министр внутренних дел Италии возложил всю ответственность на анархистский «черный блок», и в данном случае это примитивистская точка зрения.
Сколько времени нужно, чтобы определить, что необходимо для спасения биосферы и человечества? Старые подходы слишком дискредитированы, чтобы использовать их в этом мире, который стал массированной сеткой производства и отчуждения. Зеленые, или примитивистские, анархисты предпочитают перспективу радикальной децентрализации, общество лицом-к-лицу, базирующееся на том, что может дать природа, а не на попытках достичь окончательной доминации над ней. Мы выступаем против господствующего направления развития технологии и капитала по ряду очевидных причин.
Поражение левых увековечено в отношениях индивидума и природы, в то время как дистанция между левыми и новым анарходвижением остается огромной. Например, выступления Пьера Бурдо и Ричарда Рорти за обновление связей между интеллектуалами и союзами, будто эта химера сможет что-либо изменить на базовом уровне, бессмысленны. Юрген Хабермас в «Между фактами и нормой» апологетичен из-за тех вещей, каковыми они и являются, но слеп в отношении реальной колонизации современной жизни, и даже менее критичен, нежели в своих ранних работах. Хардт и Негри говорят о выборе, который желательно сделать сразу: «Мы были бы анархистами, если бы у нас не было права говорить с точки зрения материализма, учрежденного в сетях производственной кооперации, другими словами, с позиции человечества, которое построено на производительности\dots{} Нет, мы не анархисты, мы коммунисты». Наоборот, к дополнительному объяснению результата приходит Иисус Сепульведа, говоря, что «анархия и местные движения борются против цивилизационного порядка и его практики стандартизации». Не все анархисты присоединяются к возрастающим подозрениям относительно технологии и цивилизации. Ноам Хомски и Мюррэй Букчин, например, настаивают на традиционном использовании прогрессивного развития. Марксистское сердце анархо-синдикализма является типичным образцом такой приверженности и постепенно исчезает со своими левыми родственниками.
Маркс прекрасно знал о влиянии производственного процесса и его деструктивной причине — разделении труда, но тем не менее верил (или хотел верить), что технологическое развитие сможет разрушить капитализм. Но «все это крепко» и не «растворяется в воздухе», а, скорее, останется тем, чем было всегда. Это также верно как для цивилизации, так и для капитализма.
Цивилизация, обладающая той формой, которую дает технология, неотделима от остальных социальных законов — мирового ландшафта капитала — и олицетворяет и выражает свои глубочайшие ценности. «Мы имеем только целиком технологические условия», — приходит к выводу Хайдеггер, и эта формулировка сама по себе достаточна, чтобы развеять миф о «нейтральности» технологии.
С момента возникновения, в результате разделения труда и до сегодняшнего дня технология являлась допущением, подавленным как объект внимания. С момента, когда обобщенная технизация характеризует мир и является наиболее существенным аспектом современной жизни, завеса поднялась. Надвигающаяся колонизация технологией повседневной жизни и систематическое изменение физического окружения не может более игнорироваться или утаиваться. Рождаются тысячи вопросов.
Здоровье — первый вопрос. Так, мы являемся свидетелями возрождения и увеличения болезней, которые способны противостоять индустриальной медицине, претендующей на их искоренение. Антидепрессанты маскируют определенные симптомы возрастающей степени тоски, депрессии, беспокойства и разочарования, в то время как мы позволяем остаться в тени богатству, разнообразию и непосредственности, которые технология выхолащивает из наших жизней.
Что же является культурным духом, который представляет собой притупленный критицизм и сопротивление и в результате легитимизирует нелигитимное? Не что иное, как постмодернизм, который в итоге может достичь периода упадка, своего морального и интеллектуального банкротства. Сила Бенхабиб предлагает яркую версию постмодерна в трех тезисах: «Смерть человека понимается как смерть автономного, самомыслящего субъекта, способного к принципиальному действию; смерть истории понимается как потеря эпистемологического интереса к истории враждующих групп в процессе конструкции их прошлых повествований; смерть метафизики понимается как невозможность критиковать легитимные институции, практики и традиции иначе, как через имманентную аппеляцию к самолегитимизации «небольших повествований». Маршал Берман определяет постмодернизм как «философию отчаянного маскарада, радикальный интеллектуальный шик.., контрапункт цивилизационного коллажа, происходящего внутри нас».
Постмодернисты защищают разнообразие, различие, гетерогенность, привередливо рассматривая реальность как флюид и неопределенность. Актуальная параллель к этому — движение товаров с инструкциями, лежащих на полках и бессмысленно циркулирующих в глобализированном и унылом фаст-фуд потреблении.
Постмодерн настаивает на поверхностности и старается дискредитировать любые представления об аутентичности. Скрытые смыслы не допускаются, любыми универсалиями пренебрегают в пользу предполагаемой специфики. С другой стороны, значение универсальной гомогенизированной технологии принято без всяких сомнений.
Начало поражения движения в 1960-х и растущее замешательство на протяжении последующих десятилетий упадка и реакции, постмодернизм — вот название той прострации, в результате которой появляются ужасающие факты. Донна Харэвэй счастлива принять настоящее как мир техноприроды и технокультуры и определяет постмодерн как капитуляцию. Технологии, по-видимому, всегда были, «выхода из этой культуры нет», «природное» — это не более чем распространенная натурализация культуры. В итоге, нет «природы», чтобы ее защищать, «мы все киборги». Этот станс явно извлекает выгоду из войны против природы, более определенно из войны против женщин, местных обычаев, уцелевших видов и против любой несмодулированной жизни.
Для Харэвэй технологический протез «становится фундаментальной категорией для понимания наших наиболее интимных сторон». Так как мы слиты с машиной, «технонаука становится бесспорной наукой для нас». Не удивительно, что она бранит тех, кто сопротивляется генной инженерии, и напоминает, что мир слишком «грязен и неопределен» для простейших вердиктов в отношении технонауки. Дэниэл Вайт пишет, подражая Харэвэй: «Мы все становимся киборгами. Какими созданиями мы хотим быть? Хотим ли мы быть вообще живыми созданиями? Могут ли машины быть лучше? Какими машинами мы можем стать?»
Мишель Фуко был, несомненно, ключевой фигурой постмодерна, чье влияние не стало освободительным. Он кончил, потеряв свой путь в сфере власти, сделав вывод, что власть везде и нигде. Этот аргумент облегчил самомнение постмодерна о том, что противостояние угнетению является прошедшим. Точнее, Фуко определил, что сопротивляться технологии бесполезно и что человеческие отношения безвыходно технологичны. Период постмодерна, согласно Полю Вирилио, — это «эра внезапной индустриализации конца, тотальная глобализация опустошения, выпущенная на волю прогрессом». Мы должны уйти от прошлого постмодернистского компромисса и уничтожить прогресс.
Цивилизация — это учреждение, которое принуждает остальных. Как писал Фрейд, «существуют трудности, прикрепленные к природе цивилизации, которые не приведут к реформам». «Трудности» начинаются с происхождения цивилизации как вынужденный отказ от Эроса и инстинктивной свободы; «трудности», которые, как он предсказывал, вызовут состояние всеобщего невроза.
Фрейд также ссылался на чувство вины, рожденное цивилизацией и остающееся в большей степени в подсознании или проявляющееся как вид беспокойства и неудовлетворения. Важность обиды, которая присуща цивилизации, объясняет это огромное количество вины, особенно с тех пор, как введение в силу обиды, усмиряющей инстинктивную свободу, обязательно сохраняет насилие и деструктивность, что является фактором цивилизации.
Шпенглер, Тэйнтер и многие другие сходятся во мнении, что коллапс присущ цивилизации. Мы можем приблизить его гораздо быстрее, чем это осознаем, с более разительными результатами. Неужели вместе с быстрой деградацией физического мира мы не видим распада символической системы западной цивилизации?
Есть много способов фиксации вероятности уничтожения того, что всегда более явно, чем прямое правление технологии и капитала. Вебер, например, идентифицировал искажение, или маргинализацию, этических чувств как наиболее выразительное следствие современного процесса развития.
Список преступлений виртуально бесконечен. Является ли проблемой вопрос, когда цивилизации наступит конец, будет ли она допущена к рециклированию еще одного варианта первоначального преступления? Новое движение отвечает негативно. Примитивисты черпают силу из понимания того, что не имеет значения, насколько убогой стала наша жизнь за последние 10 000 лет. Для тех, кто жил около 2 миллионов лет назад на планете, человеческая жизнь явствовала здоровой и аутентичной. Мы движемся антиавторитарным путем в направлении примитивного натурализма и против тоталитаризма, который при таких условиях определенно исчезнет. Как говорил Дарио Фо, «лучшее сегодня — этот фантастический бриз, солнце и молодежь, которая организовывается по всему миру». Другой итальянский голос дополнил этот восхитительный сентимент:
\begin{quote}
«И, подойдя к сути проблемы, что же представляет собой глобализация, о которой так много говорят? Может быть, это процесс рыночной экспансии в направлении развивающихся стран, чтобы эксплуатировать их ресурсы в пользу богатых? Возможно, стандартизация культуры и диффузия доминирующей модели? Но тогда почему бы не использовать термин «цивилизация», который, конечно, звучит менее угрожающе, но является более подходящим, и без необходимости неологизма. Здесь нет сомнений, что медиа, и не просто медиа, заинтересованы смешать все в смутный антиглобалистский суп. Так что нам необходимо внести ясность в эти понятия, произвести глубокую критику и в результате действовать» (Terra Salunggio, июль 2000).
\end{quote}
Это борьба за все или ничто. Анархия — лишь имя для тех, кто принимает перспективы освобождения и цельности и пытается смело осмыслить, насколько далеко нам нужно зайти для того, чтобы этого достичь. Мы, люди, один раз были правы, если антропологам доверять сейчас, мы найдем выход, если сможем правильно им воспользоваться. Вполне возможно, что это наша последняя возможность как вида.
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Библиотека Анархизма
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Антикопирайт
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Ахмед Хомейни
Закат эры машин détourned
2009
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Сохранено 8 мая 2012 года из \href{http://primitiv.anho.org/?q=node/17}{primitiv.anho.org}
Перевод с английского: Леонид Савин Переводчик указал автором Джона Зерзана, в действительности же данный текст — перевод реценции на зерзановский сборник «Twilight of the Machines» за авторством некоего Achmed Hibaab Azzizi Homeini. Оригинал: \href{http://72.52.202.216/\%7Efenderse/Twilight.htm}{72.52.202.216}
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\textbf{ru.theanarchistlibrary.org}
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\iteman{ZMATH 2013d.00453}
\itemau{Richardson, Kerri; Reynolds, Anne; Schwartz, Catherine S.}
\itemti{Exploring quadrilaterals through flexible approaches.}
\itemso{Math. Teach. (Reston) 106, No. 4, 288-294 (2012).}
\itemab
From the text: The quadrilaterals problem is a particularly rich task, applicable to in-service teachers as well as to the students they teach. The ways in which students engage in this task, the strategies they use, and the mathematics that results align well with this focus issue on flexible mathematical thinking. The authors offer their observations of various groups of in-service teachers as they investigate this problem and then extend these insights by showing how middle-grades students approached the same task. The purpose of sharing these experiences is to expose the rich potential of the task and to highlight the flexible nature of students' thinking about the task.
\itemrv{~}
\itemcc{G30 D50}
\itemut{thinking skills; cognitive processes; mathematics skills; mathematical concepts; geometric concepts; measurement techniques; 3-D shapes; problem solving; problem posing; representation; quadrilaterals}
\itemli{doi:10.5951/mathteacher.106.4.0288 http://www.nctm.org/publications/article.aspx?id=34686}
\end
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\input texinfo @c -*- texinfo -*-
@settitle FFmpeg Documentation
@titlepage
@sp 7
@center @titlefont{FFmpeg Documentation}
@sp 3
@end titlepage
@chapter Introduction
FFmpeg is a very fast video and audio converter. It can also grab from
a live audio/video source.
The command line interface is designed to be intuitive, in the sense
that ffmpeg tries to figure out all the parameters, when
possible. You have usually to give only the target bitrate you want.
FFmpeg can also convert from any sample rate to any other, and resize
video on the fly with a high quality polyphase filter.
@chapter Quick Start
@c man begin EXAMPLES
@section Video and Audio grabbing
FFmpeg can use a video4linux compatible video source and any Open Sound
System audio source:
@example
ffmpeg /tmp/out.mpg
@end example
Note that you must activate the right video source and channel before
launching ffmpeg. You can use any TV viewer such as xawtv
(@url{http://bytesex.org/xawtv/}) by Gerd Knorr which I find very
good. You must also set correctly the audio recording levels with a
standard mixer.
@section Video and Audio file format conversion
* ffmpeg can use any supported file format and protocol as input:
Examples:
* You can input from YUV files:
@example
ffmpeg -i /tmp/test%d.Y /tmp/out.mpg
@end example
It will use the files:
@example
/tmp/test0.Y, /tmp/test0.U, /tmp/test0.V,
/tmp/test1.Y, /tmp/test1.U, /tmp/test1.V, etc...
@end example
The Y files use twice the resolution of the U and V files. They are
raw files, without header. They can be generated by all decent video
decoders. You must specify the size of the image with the @option{-s} option
if ffmpeg cannot guess it.
* You can input from a RAW YUV420P file:
@example
ffmpeg -i /tmp/test.yuv /tmp/out.avi
@end example
The RAW YUV420P is a file containing RAW YUV planar, for each frame first
come the Y plane followed by U and V planes, which are half vertical and
horizontal resolution.
* You can output to a RAW YUV420P file:
@example
ffmpeg -i mydivx.avi -o hugefile.yuv
@end example
* You can set several input files and output files:
@example
ffmpeg -i /tmp/a.wav -s 640x480 -i /tmp/a.yuv /tmp/a.mpg
@end example
Convert the audio file a.wav and the raw yuv video file a.yuv
to mpeg file a.mpg
* You can also do audio and video conversions at the same time:
@example
ffmpeg -i /tmp/a.wav -ar 22050 /tmp/a.mp2
@end example
Convert the sample rate of a.wav to 22050 Hz and encode it to MPEG audio.
* You can encode to several formats at the same time and define a
mapping from input stream to output streams:
@example
ffmpeg -i /tmp/a.wav -ab 64 /tmp/a.mp2 -ab 128 /tmp/b.mp2 -map 0:0 -map 0:0
@end example
Convert a.wav to a.mp2 at 64 kbits and b.mp2 at 128 kbits. '-map
file:index' specify which input stream is used for each output
stream, in the order of the definition of output streams.
* You can transcode decrypted VOBs
@example
ffmpeg -i snatch_1.vob -f avi -vcodec mpeg4 -b 800 -g 300 -bf 2 -acodec mp3 -ab 128 snatch.avi
@end example
This is a typical DVD ripper example, input from a VOB file, output
to an AVI file with MPEG-4 video and MP3 audio, note that in this
command we use B frames so the MPEG-4 stream is DivX5 compatible, GOP
size is 300 that means an INTRA frame every 10 seconds for 29.97 fps
input video. Also the audio stream is MP3 encoded so you need LAME
support which is enabled using @code{--enable-mp3lame} when
configuring. The mapping is particularly useful for DVD transcoding
to get the desired audio language.
NOTE: to see the supported input formats, use @code{ffmpeg -formats}.
@c man end
@chapter Invocation
@section Syntax
The generic syntax is:
@example
@c man begin SYNOPSIS
ffmpeg [[options][@option{-i} @var{input_file}]]... @{[options] @var{output_file}@}...
@c man end
@end example
@c man begin DESCRIPTION
If no input file is given, audio/video grabbing is done.
As a general rule, options are applied to the next specified
file. For example, if you give the @option{-b 64} option, it sets the video
bitrate of the next file. Format option may be needed for raw input
files.
By default, ffmpeg tries to convert as losslessly as possible: it
uses the same audio and video parameter for the outputs as the one
specified for the inputs.
@c man end
@c man begin OPTIONS
@section Main options
@table @option
@item -L
show license
@item -h
show help
@item -formats
show available formats, codecs, protocols, ...
@item -f fmt
force format
@item -i filename
input file name
@item -y
overwrite output files
@item -t duration
set the recording time in seconds. @code{hh:mm:ss[.xxx]} syntax is also
supported.
@item -title string
set the title
@item -author string
set the author
@item -copyright string
set the copyright
@item -comment string
set the comment
@item -target type
specify target file type ("vcd", "svcd" or "dvd"). All the format
options (bitrate, codecs, buffer sizes) are automatically set by this
option. You can just type:
@example
ffmpeg -i myfile.avi -target vcd /tmp/vcd.mpg
@end example
@item -hq
activate high quality settings
@end table
@section Video Options
@table @option
@item -b bitrate
set the video bitrate in kbit/s (default = 200 kb/s)
@item -r fps
set frame rate (default = 25)
@item -s size
set frame size. The format is @samp{WxH} (default 160x128). The
following abbreviations are recognized:
@table @samp
@item sqcif
128x96
@item qcif
176x144
@item cif
352x288
@item 4cif
704x576
@end table
@item -aspect aspect
set aspect ratio (4:3, 16:9 or 1.3333, 1.7777)
@item -croptop size
set top crop band size (in pixels)
@item -cropbottom size
set bottom crop band size (in pixels)
@item -cropleft size
set left crop band size (in pixels)
@item -cropright size
set right crop band size (in pixels)
@item -vn
disable video recording
@item -bt tolerance
set video bitrate tolerance (in kbit/s)
@item -maxrate bitrate
set max video bitrate tolerance (in kbit/s)
@item -minrate bitrate
set min video bitrate tolerance (in kbit/s)
@item -bufsize size
set ratecontrol buffere size (in kbit)
@item -vcodec codec
force video codec to @var{codec}. Use the @code{copy} special value to
tell that the raw codec data must be copied as is.
@item -sameq
use same video quality as source (implies VBR)
@item -pass n
select the pass number (1 or 2). It is useful to do two pass
encoding. The statistics of the video are recorded in the first pass and
the video at the exact requested bit rate is generated in the second
pass.
@item -passlogfile file
select two pass log file name to @var{file}.
@end table
@section Advanced Video Options
@table @option
@item -g gop_size
set the group of picture size
@item -intra
use only intra frames
@item -qscale q
use fixed video quantiser scale (VBR)
@item -qmin q
min video quantiser scale (VBR)
@item -qmax q
max video quantiser scale (VBR)
@item -qdiff q
max difference between the quantiser scale (VBR)
@item -qblur blur
video quantiser scale blur (VBR)
@item -qcomp compression
video quantiser scale compression (VBR)
@item -rc_init_cplx complexity
initial complexity for 1-pass encoding
@item -b_qfactor factor
qp factor between p and b frames
@item -i_qfactor factor
qp factor between p and i frames
@item -b_qoffset offset
qp offset between p and b frames
@item -i_qoffset offset
qp offset between p and i frames
@item -rc_eq equation
set rate control equation (@pxref{FFmpeg formula
evaluator}). Default is @code{tex^qComp}.
@item -rc_override override
rate control override for specific intervals
@item -me method
set motion estimation method to @var{method}. Available methods are
(from lower to best quality):
@table @samp
@item zero
Try just the (0, 0) vector.
@item phods
@item log
@item x1
@item epzs
(default method)
@item full
exhaustive search (slow and marginally better than epzs)
@end table
@item -dct_algo algo
set dct algorithm to @var{algo}. Available values are:
@table @samp
@item 0
FF_DCT_AUTO (default)
@item 1
FF_DCT_FASTINT
@item 2
FF_DCT_INT
@item 3
FF_DCT_MMX
@item 4
FF_DCT_MLIB
@item 5
FF_DCT_ALTIVEC
@end table
@item -idct_algo algo
set idct algorithm to @var{algo}. Available values are:
@table @samp
@item 0
FF_IDCT_AUTO (default)
@item 1
FF_IDCT_INT
@item 2
FF_IDCT_SIMPLE
@item 3
FF_IDCT_SIMPLEMMX
@item 4
FF_IDCT_LIBMPEG2MMX
@item 5
FF_IDCT_PS2
@item 6
FF_IDCT_MLIB
@item 7
FF_IDCT_ARM
@item 8
FF_IDCT_ALTIVEC
@item 9
FF_IDCT_SH4
@item 10
FF_IDCT_SIMPLEARM
@end table
@item -er n
set error resilience to @var{n}.
@table @samp
@item 1
FF_ER_CAREFULL (default)
@item 2
FF_ER_COMPLIANT
@item 3
FF_ER_AGGRESSIVE
@item 4
FF_ER_VERY_AGGRESSIVE
@end table
@item -ec bit_mask
set error concealment to @var{bit_mask}. @var{bit_mask} is a bit mask of
the following values:
@table @samp
@item 1
FF_EC_GUESS_MVS (default=enabled)
@item 2
FF_EC_DEBLOCK (default=enabled)
@end table
@item -bf frames
use 'frames' B frames (supported for MPEG-1, MPEG-2 and MPEG-4)
@item -mbd mode
macroblock decision
@table @samp
@item 0
FF_MB_DECISION_SIMPLE: use mb_cmp (cannot change it yet in ffmpeg)
@item 1
FF_MB_DECISION_BITS: chooses the one which needs the fewest bits
@item 2
FF_MB_DECISION_RD: rate distoration
@end table
@item -4mv
use four motion vector by macroblock (only MPEG-4)
@item -part
use data partitioning (only MPEG-4)
@item -bug param
workaround not auto detected encoder bugs
@item -strict strictness
how strictly to follow the standarts
@item -aic
enable Advanced intra coding (h263+)
@item -umv
enable Unlimited Motion Vector (h263+)
@item -deinterlace
deinterlace pictures
@item -interlace
force interlacing support in encoder (only MPEG-2 and MPEG-4). Use this option
if your input file is interlaced and if you want to keep the interlaced
format for minimum losses. The alternative is to deinterlace the input
stream with @option{-deinterlace}, but deinterlacing introduces more
losses.
@item -psnr
calculate PSNR of compressed frames
@item -vstats
dump video coding statistics to @file{vstats_HHMMSS.log}.
@item -vhook module
insert video processing @var{module}. @var{module} contains the module
name and its parameters separated by spaces.
@end table
@section Audio Options
@table @option
@item -ab bitrate
set audio bitrate (in kbit/s)
@item -ar freq
set the audio sampling freq (default = 44100 Hz)
@item -ab bitrate
set the audio bitrate in kbit/s (default = 64)
@item -ac channels
set the number of audio channels (default = 1)
@item -an
disable audio recording
@item -acodec codec
force audio codec to @var{codec}. Use the @code{copy} special value to
tell that the raw codec data must be copied as is.
@end table
@section Audio/Video grab options
@table @option
@item -vd device
set video grab device (e.g. @file{/dev/video0})
@item -vc channel
set video grab channel (DV1394 only)
@item -tvstd standard
set television standard (NTSC, PAL (SECAM))
@item -dv1394
set DV1394 grab
@item -ad device
set audio device (e.g. @file{/dev/dsp})
@end table
@section Advanced options
@table @option
@item -map file:stream
set input stream mapping
@item -debug
print specific debug info
@item -benchmark
add timings for benchmarking
@item -hex
dump each input packet
@item -bitexact
only use bit exact algorithms (for codec testing)
@item -ps size
set packet size in bits
@item -re
read input at native frame rate. Mainly used to simulate a grab device.
@item -loop
loop over the input stream. Currently it works only for image
streams. This option is used for ffserver automatic testing.
@end table
@node FFmpeg formula evaluator
@section FFmpeg formula evaluator
When evaluating a rate control string, FFmpeg uses an internal formula
evaluator.
The following binary operators are available: @code{+}, @code{-},
@code{*}, @code{/}, @code{^}.
The following unary operators are available: @code{+}, @code{-},
@code{(...)}.
The following functions are available:
@table @var
@item sinh(x)
@item cosh(x)
@item tanh(x)
@item sin(x)
@item cos(x)
@item tan(x)
@item exp(x)
@item log(x)
@item squish(x)
@item gauss(x)
@item abs(x)
@item max(x, y)
@item min(x, y)
@item gt(x, y)
@item lt(x, y)
@item eq(x, y)
@item bits2qp(bits)
@item qp2bits(qp)
@end table
The following constants are available:
@table @var
@item PI
@item E
@item iTex
@item pTex
@item tex
@item mv
@item fCode
@item iCount
@item mcVar
@item var
@item isI
@item isP
@item isB
@item avgQP
@item qComp
@item avgIITex
@item avgPITex
@item avgPPTex
@item avgBPTex
@item avgTex
@end table
@c man end
@ignore
@setfilename ffmpeg
@settitle FFmpeg video converter
@c man begin SEEALSO
ffserver(1), ffplay(1) and the html documentation of @file{ffmpeg}.
@c man end
@c man begin AUTHOR
Fabrice Bellard
@c man end
@end ignore
@section Protocols
The filename can be @file{-} to read from the standard input or to write
to the standard output.
ffmpeg handles also many protocols specified with the URL syntax.
Use 'ffmpeg -formats' to have a list of the supported protocols.
The protocol @code{http:} is currently used only to communicate with
ffserver (see the ffserver documentation). When ffmpeg will be a
video player it will also be used for streaming :-)
@chapter Tips
@itemize
@item For streaming at very low bit rate application, use a low frame rate
and a small gop size. This is especially true for real video where
the Linux player does not seem to be very fast, so it can miss
frames. An example is:
@example
ffmpeg -g 3 -r 3 -t 10 -b 50 -s qcif -f rv10 /tmp/b.rm
@end example
@item The parameter 'q' which is displayed while encoding is the current
quantizer. The value of 1 indicates that a very good quality could
be achieved. The value of 31 indicates the worst quality. If q=31
too often, it means that the encoder cannot compress enough to meet
your bit rate. You must either increase the bit rate, decrease the
frame rate or decrease the frame size.
@item If your computer is not fast enough, you can speed up the
compression at the expense of the compression ratio. You can use
'-me zero' to speed up motion estimation, and '-intra' to disable
completely motion estimation (you have only I frames, which means it
is about as good as JPEG compression).
@item To have very low bitrates in audio, reduce the sampling frequency
(down to 22050 kHz for mpeg audio, 22050 or 11025 for ac3).
@item To have a constant quality (but a variable bitrate), use the option
'-qscale n' when 'n' is between 1 (excellent quality) and 31 (worst
quality).
@item When converting video files, you can use the '-sameq' option which
uses in the encoder the same quality factor than in the decoder. It
allows to be almost lossless in encoding.
@end itemize
@chapter Supported File Formats and Codecs
You can use the @code{-formats} option to have an exhaustive list.
@section File Formats
FFmpeg supports the following file formats through the @code{libavformat}
library:
@multitable @columnfractions .4 .1 .1
@item Supported File Format @tab Encoding @tab Decoding @tab Comments
@item MPEG audio @tab X @tab X
@item MPEG1 systems @tab X @tab X
@tab muxed audio and video
@item MPEG2 PS @tab X @tab X
@tab also known as @code{VOB} file
@item MPEG2 TS @tab @tab X
@tab also known as DVB Transport Stream
@item ASF@tab X @tab X
@item AVI@tab X @tab X
@item WAV@tab X @tab X
@item Macromedia Flash@tab X @tab X
@tab Only embedded audio is decoded
@item FLV @tab X @tab X
@tab Macromedia Flash video files
@item Real Audio and Video @tab X @tab X
@item Raw AC3 @tab X @tab X
@item Raw MJPEG @tab X @tab X
@item Raw MPEG video @tab X @tab X
@item Raw PCM8/16 bits, mulaw/Alaw@tab X @tab X
@item Raw CRI ADX audio @tab X @tab X
@item SUN AU format @tab X @tab X
@item NUT @tab X @tab X @tab NUT Open Container Format
@item Quicktime @tab X @tab X
@item MPEG4 @tab X @tab X
@tab MPEG4 is a variant of Quicktime
@item Raw MPEG4 video @tab X @tab X
@item DV @tab X @tab X
@item 4xm @tab @tab X
@tab 4X Technologies format, used in some games
@item Playstation STR @tab @tab X
@item Id RoQ @tab @tab X
@tab used in Quake III, Jedi Knight 2, other computer games
@item Interplay MVE @tab @tab X
@tab format used in various Interplay computer games
@item WC3 Movie @tab @tab X
@tab multimedia format used in Origin's Wing Commander III computer game
@item Sega FILM/CPK @tab @tab X
@tab used in many Sega Saturn console games
@item Westwood Studios VQA/AUD @tab @tab X
@tab Multimedia formats used in Westwood Studios games
@item Id Cinematic (.cin) @tab @tab X
@tab Used in Quake II
@item FLIC format @tab @tab X
@tab .fli/.flc files
@item Sierra VMD @tab @tab X
@tab used in Sierra CD-ROM games
@end multitable
@code{X} means that the encoding (resp. decoding) is supported.
@section Image Formats
FFmpeg can read and write images for each frame of a video sequence. The
following image formats are supported:
@multitable @columnfractions .4 .1 .1
@item Supported Image Format @tab Encoding @tab Decoding @tab Comments
@item PGM, PPM @tab X @tab X
@item PAM @tab X @tab X @tab PAM is a PNM extension with alpha support
@item PGMYUV @tab X @tab X @tab PGM with U and V components in YUV 4:2:0
@item JPEG @tab X @tab X @tab Progressive JPEG is not supported
@item .Y.U.V @tab X @tab X @tab One raw file per component
@item Animated GIF @tab X @tab X @tab Only uncompressed GIFs are generated
@item PNG @tab X @tab X @tab 2 bit and 4 bit/pixel not supported yet
@end multitable
@code{X} means that the encoding (resp. decoding) is supported.
@section Video Codecs
@multitable @columnfractions .4 .1 .1 .7
@item Supported Codec @tab Encoding @tab Decoding @tab Comments
@item MPEG1 video @tab X @tab X
@item MPEG2 video @tab X @tab X
@item MPEG4 @tab X @tab X @tab Also known as DIVX4/5
@item MSMPEG4 V1 @tab X @tab X
@item MSMPEG4 V2 @tab X @tab X
@item MSMPEG4 V3 @tab X @tab X @tab Also known as DIVX3
@item WMV7 @tab X @tab X
@item WMV8 @tab X @tab X @tab Not completely working
@item H263(+) @tab X @tab X @tab Also known as Real Video 1.0
@item MJPEG @tab X @tab X
@item Lossless MJPEG @tab X @tab X
@item Apple MJPEG-B @tab @tab X
@item Sunplus MJPEG @tab @tab X @tab fourcc: SP5X
@item DV @tab X @tab X
@item Huff YUV @tab X @tab X
@item FFmpeg Video 1 @tab X @tab X @tab Lossless codec (fourcc: FFV1)
@item Asus v1 @tab X @tab X @tab fourcc: ASV1
@item Asus v2 @tab X @tab X @tab fourcc: ASV2
@item Creative YUV @tab @tab X @tab fourcc: CYUV
@item H.264 @tab @tab X
@item Sorenson Video 1 @tab @tab X @tab fourcc: SVQ1
@item Sorenson Video 3 @tab @tab X @tab fourcc: SVQ3
@item On2 VP3 @tab @tab X @tab still experimental
@item Theora @tab @tab X @tab still experimental
@item Intel Indeo 3 @tab @tab X @tab only works on i386 right now
@item FLV @tab X @tab X @tab Flash H263 variant
@item ATI VCR1 @tab @tab X @tab fourcc: VCR1
@item ATI VCR2 @tab @tab X @tab fourcc: VCR2
@item Cirrus Logic AccuPak @tab @tab X @tab fourcc: CLJR
@item 4X Video @tab @tab X @tab used in certain computer games
@item Sony Playstation MDEC @tab @tab X
@item Id RoQ @tab @tab X @tab used in Quake III, Jedi Knight 2, other computer games
@item Xan/WC3 @tab @tab X @tab used in Wing Commander III .MVE files
@item Interplay Video @tab @tab X @tab used in Interplay .MVE files
@item Apple Animation @tab @tab X @tab fourcc: 'rle '
@item Apple Graphics @tab @tab X @tab fourcc: 'smc '
@item Apple Video @tab @tab X @tab fourcc: rpza
@item Cinepak @tab @tab X
@item Microsoft RLE @tab @tab X
@item Microsoft Video-1 @tab @tab X
@item Westwood VQA @tab @tab X
@item Id Cinematic Video @tab @tab X @tab used in Quake II
@item Planar RGB @tab @tab X @tab fourcc: 8BPS
@item FLIC video @tab @tab X
@item Duck TrueMotion v1 @tab @tab X @tab fourcc: DUCK
@item VMD Video @tab @tab X @tab used in Sierra VMD files
@item MSZH @tab @tab X @tab Part of LCL
@item ZLIB @tab X @tab X @tab Part of LCL, encoder experimental
@end multitable
@code{X} means that the encoding (resp. decoding) is supported.
Check at @url{http://www.mplayerhq.hu/~michael/codec-features.html} to
get a precise comparison of FFmpeg MPEG4 codec compared to the other
solutions.
@section Audio Codecs
@multitable @columnfractions .4 .1 .1 .1 .7
@item Supported Codec @tab Encoding @tab Decoding @tab Comments
@item MPEG audio layer 2 @tab IX @tab IX
@item MPEG audio layer 1/3 @tab IX @tab IX
@tab MP3 encoding is supported through the external library LAME
@item AC3 @tab IX @tab X
@tab liba52 is used internally for decoding
@item Vorbis @tab X @tab X
@tab supported through the external library libvorbis
@item WMA V1/V2 @tab @tab X
@item Microsoft ADPCM @tab @tab X
@item MS IMA ADPCM @tab X @tab X
@item QT IMA ADPCM @tab @tab X
@item 4X IMA ADPCM @tab @tab X
@item G.726 ADPCM @tab X @tab X
@item Duck DK3 IMA ADPCM @tab @tab X
@tab used in some Sega Saturn console games
@item Duck DK4 IMA ADPCM @tab @tab X
@tab used in some Sega Saturn console games
@item Westwood Studios IMA ADPCM @tab @tab X
@tab used in Westwood Studios games like Command and Conquer
@item SMJPEG IMA ADPCM @tab @tab X
@tab used in certain Loki game ports
@item CD-ROM XA ADPCM @tab @tab X
@item CRI ADX ADPCM @tab X @tab X
@tab used in Sega Dreamcast games
@item Electronic Arts ADPCM @tab @tab X
@tab used in various EA titles
@item RA144 @tab @tab X
@tab Real 14400 bit/s codec
@item RA288 @tab @tab X
@tab Real 28800 bit/s codec
@item AMR-NB @tab X @tab X
@tab supported through an external library
@item AMR-WB @tab X @tab X
@tab supported through an external library
@item DV audio @tab @tab X
@item Id RoQ DPCM @tab @tab X
@tab used in Quake III, Jedi Knight 2, other computer games
@item Interplay MVE DPCM @tab @tab X
@tab used in various Interplay computer games
@item Xan DPCM @tab @tab X
@tab used in Origin's Wing Commander IV AVI files
@item Apple MACE 3 @tab @tab X
@item Apple MACE 6 @tab @tab X
@end multitable
@code{X} means that the encoding (resp. decoding) is supported.
@code{I} means that an integer only version is available too (ensures highest
performances on systems without hardware floating point support).
@chapter Platform Specific information
@section Linux
ffmpeg should be compiled with at least GCC 2.95.3. GCC 3.2 is the
preferred compiler now for ffmpeg. All future optimizations will depend on
features only found in GCC 3.2.
@section BSD
@section Windows
@subsection Native Windows compilation
@itemize
@item Install the current versions of MSYS and MinGW from
@url{http://www.mingw.org/}. You can find detailed installation
instructions in the download section and the FAQ.
@item If you want to test the FFmpeg Simple Media Player, also download
the MinGW development library of SDL 1.2.x
(@file{SDL-devel-1.2.x-mingw32.tar.gz}) from
@url{http://www.libsdl.org}. Unpack it in a temporary place, and
unpack the archive @file{i386-mingw32msvc.tar.gz} in the MinGW tool
directory. Edit the @file{sdl-config} script so that it gives the
correct SDL directory when invoked.
@item Extract the current version of FFmpeg (the latest release version or the current CVS snapshot whichever is recommended).
@item Start the MSYS shell (file @file{msys.bat}).
@item Change to the FFMPEG directory and follow
the instructions of how to compile ffmpeg (file
@file{INSTALL}). Usually, launching @file{./configure} and @file{make}
suffices. If you have problems using SDL, verify that
@file{sdl-config} can be launched from the MSYS command line.
@item You can install FFmpeg in @file{Program Files/FFmpeg} by typing @file{make install}. Don't forget to copy @file{SDL.dll} at the place you launch
@file{ffplay}.
@end itemize
Notes:
@itemize
@item The target @file{make wininstaller} can be used to create a
Nullsoft based Windows installer for FFmpeg and FFplay. @file{SDL.dll}
must be copied in the ffmpeg directory in order to build the
installer.
@item By using @code{./configure --enable-shared} when configuring ffmpeg,
you can build @file{avcodec.dll} and @file{avformat.dll}. With
@code{make install} you install the FFmpeg DLLs and the associated
headers in @file{Program Files/FFmpeg}.
@item Visual C++ compatibility: if you used @code{./configure --enable-shared}
when configuring FFmpeg, then FFmpeg tries to use the Microsoft Visual
C++ @code{lib} tool to build @code{avcodec.lib} and
@code{avformat.lib}. With these libraries, you can link your Visual C++
code directly with the FFmpeg DLLs.
@end itemize
@subsection Cross compilation for Windows with Linux
You must use the MinGW cross compilation tools available at
@url{http://www.mingw.org/}.
Then configure ffmpeg with the following options:
@example
./configure --enable-mingw32 --cross-prefix=i386-mingw32msvc-
@end example
(you can change the cross-prefix according to the prefix choosen for the
MinGW tools).
Then you can easily test ffmpeg with wine
(@url{http://www.winehq.com/}).
@section MacOS X
@section BeOS
The configure script should guess the configuration itself.
Networking support is currently not finished.
errno issues fixed by Andrew Bachmann.
Old stuff:
François Revol - revol at free dot fr - April 2002
The configure script should guess the configuration itself,
however I still didn't tested building on net_server version of BeOS.
ffserver is broken (needs poll() implementation).
There is still issues with errno codes, which are negative in BeOs, and
that ffmpeg negates when returning. This ends up turning errors into
valid results, then crashes.
(To be fixed)
@chapter Developers Guide
@section API
@itemize
@item libavcodec is the library containing the codecs (both encoding and
decoding). See @file{libavcodec/apiexample.c} to see how to use it.
@item libavformat is the library containing the file formats handling (mux and
demux code for several formats). See @file{ffplay.c} to use it in a
player. See @file{output_example.c} to use it to generate audio or video
streams.
@end itemize
@section Integrating libavcodec or libavformat in your program
You can integrate all the source code of the libraries to link them
statically to avoid any version problem. All you need is to provide a
'config.mak' and a 'config.h' in the parent directory. See the defines
generated by ./configure to understand what is needed.
You can use libavcodec or libavformat in your commercial program, but
@emph{any patch you make must be published}. The best way to proceed is
to send your patches to the ffmpeg mailing list.
@section Coding Rules
ffmpeg is programmed in ANSI C language. GCC extensions are
tolerated. Indent size is 4. The TAB character should not be used.
The presentation is the one specified by 'indent -i4 -kr'.
Main priority in ffmpeg is simplicity and small code size (=less
bugs).
Comments: for functions visible from other modules, use the JavaDoc
format (see examples in @file{libav/utils.c}) so that a documentation
can be generated automatically.
@section Submitting patches
When you submit your patch, try to send a unified diff (diff '-up'
option). I cannot read other diffs :-)
Run the regression tests before submitting a patch so that you can
verify that there are no big problems.
Patches should be posted as base64 encoded attachments (or any other
encoding which ensures that the patch wont be trashed during
transmission) to the ffmpeg-devel mailinglist, see
@url{http://lists.sourceforge.net/lists/listinfo/ffmpeg-devel}
It also helps quite a bit if you tell us what the patch does (for example
'replaces lrint by lrintf') , and why (for example '*bsd isnt c99 compliant
and has no lrint()')
@section Regression tests
Before submitting a patch (or committing with CVS), you should at least
test that you did not break anything.
The regression test build a synthetic video stream and a synthetic
audio stream. Then these are encoded then decoded with all codecs or
formats. The CRC (or MD5) of each generated file is recorded in a
result file. Then a 'diff' is launched with the reference results and
the result file.
The regression test then goes on to test the ffserver code with a
limited set of streams. It is important that this step runs correctly
as well.
Run 'make test' to test all the codecs.
Run 'make fulltest' to test all the codecs, formats and ffserver.
[Of course, some patches may change the regression tests results. In
this case, the regression tests reference results shall be modified
accordingly].
@bye
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\title{Postmodern Anarchism in the Novels of Ursula K. Le Guin}
\date{2007}
\author{Lewis Call}
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It is easy enough to locate anarchist themes in the science fiction of Ursula K. Le Guin. Her frequent critiques of state power, coupled with her rejection of capitalism and her obvious fascination with alternative systems of political economy, are sufficient to place her within the anarchist tradition. She has, from time to time, explicitly embraced that tradition. Le Guin is, among other things, a popularizer of anarchist ideas. The political philosophy of anarchism is largely an intellectual artifact of the nineteenth century, articulated in England by William Godwin, in France by Pierre-Joseph Proudhon, and in Russia by Peter Kropotkin and Mikhail Bakunin. Yet this vibrant intellectual tradition remains largely invisible to ordinary people in the early twenty-first century. By describing anarchist ideas in a way that is simultaneously faithful to the anarchist tradition and accessible to contemporary audiences, Le Guin performs a very valuable service. She rescues anarchism from the cultural ghetto to which it has been consigned. She introduces the anarchist vision to an audience of science fiction readers who might never pick up a volume of Kropotkin. She moves anarchism (ever so slightly) into the mainstream of intellectual discourse.
Yet Le Guin, like many whose anarchist views developed in the late 1960s and early 1970s, also seems to recognize that this is not enough. Like classical Marxism, modern anarchism developed within the specific political, economic and intellectual environment of the nineteenth century. In that context, it made perfect sense for anarchists to focus their critical powers upon the twin sources of oppressive power in the age of the Industrial Revolution: capital and the state. By the late twentieth century, however, this traditional anarchism had become dangerously outdated. During the 1960s in particular, political activists throughout the western world added critiques of ethnic power and gender power to the list of anarchist concerns. In the intellectual world, Michel Foucault identified and criticized the disciplinary power that emerges in schools, hospitals, military barracks, psychiatric clinics and families, while Jean Baudrillard articulated a radical symbolic critique of the semiotic system that dominates the contemporary world. Meanwhile, Guy Debord and others argued that citizens of the late twentieth century lived in a world dominated by the spectacular mass media, a world in which consumerism has found its way into every aspect of people’s lives, a world in which the traditional forms of political action (and perhaps even the political subjects who might perform such action) have become dangerously fragmented. In such a world, the anarchist critique cannot afford to remain trapped within the modern, industrial mode of thinking. Anarchism must become more flexible, more fluid, more adaptable. In a word, it must become postmodern. Along with Todd May and Saul Newman, I have tried to describe the approximate contours of such a postmodern anarchism (see May, \emph{Political Philosophy of Poststructuralist Anarchism}; Newman, \emph{From Bakunin to Lacan}; and Call, \emph{Postmodern Anarchism}).
An analysis of Le Guin’s science fiction will be helpful to this project. Yes, Le Guin dreams of utopian worlds and moons, free of the inequalities of capitalism and the injustices of state power (just as Kropotkin did before her). More importantly, however, Le Guin develops new forms of anarchist thinking, forms that are urgently needed in the United States and other post-industrial societies. The crucial foundation for this new postmodern anarchism is to be found in three remarkable novels that Le Guin wrote in a five-year period between 1969 and 1974. This period — which marks the culmination of both the radical social movements of the 1960s and the poststructuralist and postmodernist movements in the intellectual world — represents a vitally important historical moment in the anarchist tradition. This is the moment when anarchism took its “postmodern turn.” And Le Guin was instrumental in bringing about this remarkable transformation in anarchist thinking. In \emph{The Left Hand of Darkness} (1969), Le Guin subverted the traditional binary concept of gender identity, to promote an \emph{anarchy of gender}. In \emph{The Lathe of Heaven} (1971), she told the story of a psychiatric patient whose dreams literally redesigned the world, thus creating the possibility of an \emph{ontological anarchy}. And in her 1974 masterpiece \emph{The Dispossessed}, Le Guin made two major contributions to the philosophy of postmodern anarchism. She created a fictional anarchist language called Pravic, which underscores the importance of linguistics for any contemporary anarchist project. And she developed an equally radical concept of time, creating the possibility of a \emph{chronosophic anarchy}. The existence of an explicitly anarchist society on the moon of Anarres has led many critics of \emph{The Dispossessed} to focus only on the traditional anarchist themes of this novel. Yet the truly radical legacy of this novel (and of Le Guin’s other major works from the late 1960s and early 1970s) is that these works transgress the boundaries of conventional anarchist thinking to create new forms of anarchism that are entirely relevant to life in the postmodern condition. Le Guin updates the conventional anarchist project and positions anarchism to move into the third millennium.
\section{The Debate: Critical Awareness of Le Guin’s Anarchism}
Le Guin’s masterpiece \emph{The Dispossessed} drew a tremendous amount of critical attention after it appeared in 1974, but the critical reception of Le Guin’s work remained remarkably orthodox during the late 1970s and 1980s. Critics of this period did acknowledge that Le Guin’s work was strongly influenced by anarchism, but they persisted in reading that anarchism in purely modern terms. Thus David L. Porter argued that by the mid-1970s Le Guin had “moved to a much richer social critique and explicit anarchist commitment” (Mullen and Suvin 273), while John P. Brennan and Michael C. Downs read \emph{The Dispossessed} “as a penetrating critique of all utopian experience, even that of anarchism” (117). At this time criticism generally failed to recognize the postmodern aspects of Le Guin’s writing. A notable exception was Fredric Jameson, apostle of the postmodern. In 1975, Jameson noted in passing that the General Theory of Time described in \emph{The Dispossessed} employs a “vocabulary of a subversive reason, which has therefore had first to pass through the false, nonreasonable and by themselves non-cognitive expressions of parareason” (Mullen and Suvin 266). Jameson was one of the first to recognize the truly transgressive nature of Le Guin’s fiction, namely its ability to call into question the forms of scientific, technical and instrumental reason that have come to dominate the modern West. But criticism was slow to adopt Jameson’s position. As late as 1986, Tom Moylan was arguing that the utopia of \emph{The Dispossessed} was locked into a series of binary oppositions, and that the text thus “expresses the continued closure of the current social formation” (114). Remarkably, Moylan found Le Guin’s work to be insufficiently postmodern.
It was only in the 1990s that some feminist critics began to embrace the postmodern reading of Le Guin. In 1993, Marleen Barr argued that “reading Le Guin\dots{} sometimes involves encountering an alliance between humanism and antihumanism,” which resembles Christopher Butler’s version of the Lacanian position (155). Here Barr has identified the \emph{anarchy of the subject} that is such a crucial part of the postmodern anarchist project. Subjectivity, for the postmodern anarchist, cannot be understood solely in the coherent, rational terms of the Enlightenment. Instead, subjectivity must be viewed as perpetually provisional, deeply contextual, and powerfully psychological. This is certainly the type of subjectivity found in Le Guin’s work, particularly \emph{The Lathe of Heaven}. This type of subjectivity recognizes that the subject of Enlightenment discourse is implicitly statist, and acknowledges that a meaningful anarchist politics will require a radical reconceptualization of that subject.
The recently published collection of essays on \emph{The New Utopian Politics of Ursula K. Le Guin}’s \emph{The Dispossessed} features three essays that deal specifically with Le Guin’s anarchist politics. Dan Sabia correctly notes that the inspiration for Le Guin’s Anarres is the “anarchist communism” of Peter Kropotkin (Davis and Stillman 112–113), with its emphasis on mutual aid (114) and decentralization (120). However, Sabia also argues that “not even anarchist communism can reconcile completely the ideals of individualism and community” (125). For Sabia, then, Le Guin remains trapped within the basic dilemma that has haunted political theory at least since Rousseau: the problem of reconciling the specific needs of the individual with the broader social needs of the community. This is, however, a specifically modern political problem, which can be resolved through the attainment of a postmodern perspective. In the same volume, Mark Tunick interprets Le Guin’s project as Hegelian (129). Tunick thus joins a long line of critics who have identified the form of Le Guin’s thinking as dialectical (see, for example, Donald F. Theall’s argument in Mullen and Suvin 286–294; see also Widmer 44ff). I find the dialectical interpretation of Le Guin difficult to sustain, and the specifically Hegelian form of that interpretation even more so. Certainly any attempt to describe Le Guin’s thinking as Hegelian must address the disturbingly statist nature of Hegel’s political philosophy; more urgently, the attempt to describe Le Guin as a dialectical thinker must find a way to account for the sustained assault on binary thinking that is such a fundamental feature of her work. Finally, Winter Elliot approaches \emph{The Dispossessed} from the perspective of individualist anarchism. For Elliot, an authentic anarchism must always be an interior personal anarchism (such as that of Shevek, the novel’s protagonist). By advocating individualist anarchism in this way, Elliot is certainly going against what we might describe (with appropriate irony) as the “mainstream” anarchist tradition — i.e. the tradition that emphasizes the importance of community and collective social action. Yet by emphasizing the autonomy of the unique individual, Elliot shows that she has this much in common with mainstream anarchism: she remains trapped within the modern.
This, then, is the current state of scholarship on the subject of Le Guin’s political philosophy. With a few notable exceptions, critics tend to read Le Guin’s narratives in dialectical and\Slash{}or utopian terms. They understand her anarchism primarily as a conventional challenge to state power and capitalism. In short, these readings of Le Guin remain relentlessly modern. It is particularly striking that these modernist readings of Le Guin’s anarchism remain so prevalent today, some 35 years after Le Guin initiated a major postmodern move in her science fiction. Clearly, the modern does not give up without a fight. Yet it is imperative for today’s critics to move beyond their fascination with modernism, particularly if they wish to understand the depth and significance of Le Guin’s anarchism. That anarchism cannot simply be understood as an updated version of Kropotkin’s utopian dreams. Rather, Le Guin’s postmodern anarchism is a sustained challenge to conventional modes of radical thinking. This is an anarchism that rejects teleologies, explodes traditional concepts of subjectivity in general (and concepts of gender identity in particular), proposes radical new cosmologies, and embraces the anarchistic possibilities inherent in the creation of new languages. It is, in short, an anarchism for the twenty-first century, and it is time for criticism to recognize this.
\section{The Novels: Le Guin’s Postmodern Anarchism}
In both structure and content, Le Guin’s 1969 novel \emph{The Left Hand of Darkness} is a postmodern masterpiece. The novel is relentlessly experimental and fragmented. It has no narrative center. It alternates between two radically different points of view: that of a Gethenian called Estraven, and that of Genly Ai, a diplomat who is visiting the planet Gethen as a representative of the interstellar Ekumen. While such fluctuations in viewpoint might produce some interesting cognitive effects in the audience, one could argue that their radical potential is limited. A novel that depended upon the binary alternation between two points of view could easily fall victim to the kind of back and forth, either\Slash{}or thinking that characterizes the modern mentality in general and its dialectical form in particular. And so Le Guin must go further. The novel’s two main viewpoints are supplemented with a host of other narrative forms. Some chapters are extracted from fictional bureaucratic reports that circulate among the officials of Genly Ai’s Ekumen. Others are drawn from the myths, legends and poems of Gethen. The cognitive effect of this radical narrative strategy is disorienting, destabilizing \dots{} and also remarkably satisfying. The discourse of \emph{Left Hand} can never become totalizing or totalitarian, for such a fate would require far more unity and stability than the text actually possesses. Le Guin’s novel refuses the comforts of binary thinking and closed, orderly narrative. \emph{Left Hand} is thus a self-deconstructing text that cannot arrive at any ultimate teleological destination.
This narrative form is entirely appropriate, given the topics Le Guin addresses in this remarkable work. We learn a good deal about the political structure of the Ekumen, the star-spanning polity that is such a prominent feature of Le Guin’s Hainish Cycle. No one familiar with Le Guin’s basic political perspective will be surprised to find that the internal politics of the Ekumen are essentially anarchistic. Indeed, James Bittner has argued persuasively that Le Guin’s Ekumen represents an anarchist alternative to the imperialist “Galactic Empires” so common in late twentieth-century science fiction (110). Genly Ai observes that “the Ekumen is not essentially a government at all. It is an attempt to reunify the mystical with the political, and as such is of course mostly a failure; but its failure has done more good for humanity so far than the successes of its predecessors” (Le Guin, \emph{Left Hand} 136–137). So the Ekumen is anarchist, and not merely in the traditional sense, for the Ekumen introduces a spiritual component into its anarchism. The dimensions of this spirituality are approximately Taoist; \emph{Left Hand} thus foreshadows the strong Taoist element of later works such as \emph{The Lathe of Heaven}. Intriguingly, the premodern anarchism of the Taoist tradition thus serves as a starting point for Le Guin’s postmodern anarchism.
The novel’s major contribution to postmodern anarchism is to be found in its philosophy of gender. The inhabitants of Gethen are human, but they do not have the binary gender system that characterizes most human societies. Gethenians spend most of their lives in an androgynous state, neither male nor female. However, they periodically enter into an active reproductive state known as \emph{kemmer}. While in kemmer, a Gethenian body will acquire either male or female characteristics. On Gethen, gender identity is therefore provisional, temporary and arbitrary. In many ways, then, Gethenian gender corresponds to the postmodern gender theories developed by anti-essentialists such as Judith Butler and Donna Haraway. For Gethenians as for postmodern feminists, gender is no absolute category, but rather something that must be viewed as flexible and fluid.
Le Guin uses the character of Genly Ai to describe what the Gethenian gender system might look like to an outside observer. Because he is a permanently male human from another planet, Ai can never be a part of Gethen’s unique system of perpetually changing gender identities. Yet he clearly appreciates the significance of this system. Ai speaks admiringly of the ways in which gender operates on Gethen: “There is less coding, channeling, and repressing of sex there than in any bisexual society I know of. Abstinence is entirely voluntary; indulgence is entirely acceptable. Sexual fear and sexual frustration are both extremely rare” (177). Remarkably, Ai is able to set aside the prejudices of his “bisexual society” (at least to a certain extent) and recognize the great benefits that Gethenian androgyny has to offer. A Freudian would be well pleased; indeed, Ai’s description of a world without repression reminds us of the “erotic utopia” proposed by the radical Freudian Herbert Marcuse in \emph{Eros and Civilization} (see Marcuse, especially chapter ten).
Nor is the lack of repression the only remarkable feature of Gethenian society. Ong Tot Oppong, a member of the first Ekumenical landing party to visit Gethen, was careful to note that on Gethen “There is no unconsenting sex, no rape. As with most animals other than man, coitus can be performed only by mutual invitation and consent; otherwise it is not possible” (94). The sexual practices of the Gethenians, then, could be described as both feminist and anarchist. The concept of consent is, after all, a crucial theoretical aspect of both traditions. Feminists use consent to draw clear ethical boundaries around sexual practices. Anarchists use consent more broadly, to distinguish ethical political actions from unethical ones. Clearly, the concept of consent holds vast significance for the people of Gethen; they are, in effect, practicing anarcho-feminists.
They also appear to be anarcho-pacifists. Oppong goes on to note that Gethenians “have never yet had what one could call a war. They kill one another readily by ones and twos; seldom by tens or twenties; never by hundreds or thousands. Why?” (96) Perhaps the peculiarities of Gethenian gender identity make warfare unnecessary, or even impossible. Again, the Freudian reading is tempting here. One can read warfare as a destructive sublimation of the basic instinctive impulses. Historically, warfare in our world has been primarily a masculine enterprise, carried out by armies of men who often operate under conditions of ongoing sexual repression. Gethenians, on the other hand, lack the repression that may be a necessary psychological precursor to war. And although any Gethenian may become provisionally masculine, that gender identity will not endure long enough to permit major military action. Because principles and practices of masculinity cannot dominate Gethenian culture as they have dominated our own, there is much more room on Gethen for the articulation of an alternative feminine principle. In an important commentary on \emph{Left Hand} entitled “Is Gender Necessary? Redux” (1987) Le Guin identifies this feminine principle as fundamentally anarchistic. “The ‘female principle’ has historically been anarchic; that is, anarchy has historically been identified as female. The domain allotted to women — ’the family,’ for example — is the area of order without coercion” (\emph{Dancing at the Edge of the World} 11–12). This is what the Gethenians have attained: a well articulated, orderly society, which they have organized without recourse to military coercion.
These few examples illustrate the basic fact of Gethenian culture, which is that it represents a profound challenge to the type of binary thinking that has so thoroughly dominated the modern West. Ong Tot Oppong notes that “the whole tendency to dualism that pervades human thinking may be found to be lessened, or changed, on Winter [Gethen]” (94). The Gethenians, then, are Le Guin’s answer to the Cartesian philosophy and its descendents. Like \emph{Left Hand} itself, the Gethenians are self-deconstructing. They occupy no fixed subject position. The very structure of their identity is anarchistic in the postmodern sense. And this identity clearly represents a major threat to the fixed gender concepts that characterize our patriarchal culture. To make her critique of realworld gender categories as explicit as possible, Le Guin introduces us to the Gethenian concept of perversion. Genly Ai speaks: “Excessive prolongation of the kemmer period, with permanent hormonal imbalance toward the male or the female, causes what they call perversion; it is not rare; three or four percent of adults may be physiological perverts or abnormals — normals, by our standard. They are not excluded from society, but they are tolerated with some disdain, as homosexuals are in many bisexual societies. The Karhidish slang for them is \emph{halfdeads}. They are sterile” (64). Passages like this produce what Darko Suvin might call a radical effect of cognitive estrangement (Suvin 8). The function of such passages is to confront the reader with a system of values and standards that is radically Other. On Gethen, permanently male or female individuals receive treatment quite similar to that which real-world gays, lesbians, transsexuals and kinksters must endure. This radical inversion of values calls into question those cultural discourses that privilege hetero-normative and “vanilla” forms of sexual behavior. The Gethenians suffer from heterophobia, a profound fear and distrust of fixed, binary gender distinctions. This heterophobia is certainly no more irrational than real world homophobia. And it performs a vital function for Le Guin’s real-world audience, by undermining certainty and challenging the very concept of the normal. By inverting real-world gender codes, the Gethenians also subvert those codes, thus initiating a remarkable anarchy of gender.
Some critics of \emph{Left Hand} have argued that there are serious limitations to Le Guin’s androgynous society. According to Patricia Frazer Lamb and Diana L. Veith, for example, the Gethenian Estraven is formally androgynous, but within the narrative of \emph{Left Hand}, he is typically described in masculine terms (226). For her part, Le Guin has admitted that “the Gethenians seem like men, instead of menwomen” (\emph{Dancing at the Edge of the World} 14). She attributes this to her use of masculine pronouns to refer to Gethenians (15), and she acknowledges that “the Gethenian protagonist, Estraven [was cast] almost exclusively in roles that we are culturally conditioned to perceive as ‘male’” (15). But perhaps Le Guin is too quick to endorse these criticisms of her work. If Le Guin chose to use masculine pronouns when speaking of the Gethenians, that is simply because the language in which she was writing (American English) offered her no clear alternatives. And if Le Guin’s audience perceives the activities of Prime Minister Estraven as “male,” that says more about the audience than it does about Estraven. The concept of gender articulated in \emph{Left Hand} was as radical as Le Guin could make it in 1969. What some critics have described as limits to Le Guin’s philosophy of androgyny are really limits of the largely patriarchal, heteronormative culture of the United States in the late twentieth century. Le Guin’s work attempts to challenge and transcend those limitations. To be sure, she could not hope to overcome the entire history of binary gender thinking in a single novel. Nonetheless, The \emph{Left Hand of Darkness} remains a major contribution to postmodern feminism, and to the anarchist theory with which that thinking is closely allied.
Le Guin’s next major contribution to postmodern anarchism was \emph{The Lathe of Heaven}, which appeared in 1971. Here Le Guin’s Taoism, already evident in \emph{Left Hand}, was given full expression. \emph{Lathe} describes an encounter between the Western scientific ideology that holds that knowledge and reason can be used to shape the world for the good of humanity, and a very different Taoist perspective, which holds that the attempt to shape the world through human willpower is futile and potentially destructive, both to the world and to those humans who would mold it. The connection between Taoism and anarchism is well established, and has been noted by writers working in both traditions.\footnote{See, for example, Watts 43, Marshall 53–60 and Rapp. In 1998, Le Guin published her own English language version of Lao Tzu’s classic Taoist text, \emph{Tao Te Ching}.} Yet few commentators have recognized the powerful connections between the delightful premodern philosophy of Taoism and late twentieth-century critical theory. By insisting that human rationality can never succeed in its quest to dominate, Taoism provides a powerful critique of the form of reason that was of such great concern, for example, to the Frankfurt School. Marcuse called it the logic of domination (111); it is the controlling rationality that governs the West. In place of this, Le Guin offers us the spontaneous joys of world creation. \emph{Lathe} teaches us that if we would truly make the world a better place, we must abandon all pretense towards rational control. We must renounce all distinctions between ourselves and the rest of the world. Only when we know ourselves to be inseparable from the world can we dream the dreams that will change it.
The novel’s protagonist is George Orr, a man whose dreams literally redesign the world. Orr’s “effective” dreams — dreams that radically revise reality — represent an intriguing new anarchist possibility. Because these dreams change everything, they do much more than simply alter a political or economic system. They alter the structure of the universe, thus creating what I call \emph{ontological anarchy}. When it is challenged on the terrain of politics or economics, hierarchical thinking retreats to the level of ontology: here, at least, there must always be fixed structures, law and order. Yet Orr’s dreams challenge the final recourse of statist thinking. His dreams mean that nothing is permanent and everything is provisional. From a perspective of power, such a position is intolerable. And so the hierarchical system must try to recapture Orr’s dreams, to harness them and put them to use for its own purposes. It does so in the person of Dr. Haber, Orr’s psychiatrist. Haber is the model scientist: orderly, disciplined, rational and progressive, in a purely technocratic way. He is confident that if Orr dreams under his direction, then all the world’s ills can simply be wished away. But Orr recognizes how hopeless Haber’s quest is. “You’re handling something outside reason. You’re trying to reach progressive, humanitarian goals with a tool that isn’t suited to the job. Who has humanitarian dreams?” (86) Here Orr rightly raises the specter of the id. If dreams give us access to the deep structure of the world itself — the thesis is Freudian, or even Lacanian — then that implies that this structure can never be susceptible to reason, for the dream world is one where logic has no place. Naturally, Haber attempts to refute the Freudian argument. “Your unconscious mind is not a sink of horror and depravity. That’s a Victorian notion, and a terrifically destructive one\dots{}Don’t be afraid of your unconscious mind! It’s not a black pit of nightmares” (88). Haber is right to be afraid of Freud, for Freud was one of the few psychiatrists to see that the Western attempt to dominate the earth through science might carry a heavy price.\footnote{See, for example, Freud’s argument in Chapter III of \emph{Civilization and Its Discontents}.} Of course, Haber is a different sort of analyst, one who is unshakably convinced that science has the power to cure the world. He cannot understand the Taoist George Orr. An irritated Haber confronts Orr: “You’re of a peculiarly passive outlook for a man brought up in the Judaeo-ChristianRationalist West. A sort of natural Buddhist. Have you ever studied the Eastern mysticisms, George?” Orr replies: “No. I don’t know anything about them. I do know that it’s wrong to force the pattern of things. It won’t do. It’s been our mistake for a hundred years” (82–83). If anything, Orr is guilty of understatement. The attempt to force the pattern of things — to coerce the world into a rigorously rational framework — has been characteristic of Western thought at least since Descartes, and possibly since Plato. Against this, Orr invokes the Taoist principle of wu wei or “actionless action.” He refuses to force the world down a path charted by human reason. In this way he acts as a good Taoist, and also as a good postmodern anarchist.
Orr consistently refuses the comforting but restrictive binary logic that characterizes the modern Western mode of thought. Naturally, Haber finds this incredibly frustrating. “Where there’s an opposed pair, a polarity, you’re in the middle; where there’s a scale, you’re at the balance point. You cancel out so thoroughly that, in a sense, nothing is left” (134). Haber says this as if it’s a bad thing, and of course from his perspective, it is. Orr is the living embodiment of deconstruction. He can have no teleology. He can never arrive at a final position. The text constantly emphasizes that he is in the middle. “There was a singular poise, almost a monumentality, in the stance of his slight figure: he was completely still, still at the center of something” (68). Because Orr is the node through which all reality must flow, he himself cannot succumb to any fixed discourse, any ultimate interpretation. His ontological anarchy is thus postmodern in its orientation. It is supremely ironic, then, that Orr, who renounces the rationalist attempt to control the world, is actually the only person in the novel who does have power over that world. Orr attains this special status precisely because he has come to understand himself as an integral, organic part of the universe, rather than an autonomous Cartesian subject at war with his environment. Orr can change the world only because he is the world. In this sense, what he does is no different from the actions of any other human, animal, vegetable or mineral. “Everything dreams. The play of form, of being, is the dreaming of substance. Rocks have their dreams, and the earth changes” (161).
This is the radical message of \emph{Lathe}. The modern model of revolutionary change presupposes the existence and efficacy of rational, independent political actors. But \emph{Lathe} argues that we must not look to progressive technocrats or revolutionary vanguards of the working class for change. Instead, we must become the change we wish to see in the world, as Gandhi suggested. \emph{Lathe} creates the possibility of an anarchism that will be highly spiritual, deeply personal and yet also intimately engaged with the world. Le Guin made this point explicitly in her 1973 essay “Dreams Must Explain Themselves”:
\begin{quote}
The Taoist world is orderly, not chaotic, but its order is not one imposed by man or by a personal or humane deity. The true laws — ethical and aesthetic, as surely as scientific — are not imposed from above by any authority, but exist in things that are to be found — discovered. (\emph{The Language of the Night} 49)
\end{quote}
Both anarchism and Taoism propose a model of social and ontological order that is consensual and ethical, one in which “laws” are not created by political elites, but rather derived through direct interaction between the individual and the world. Because this anarchism contains the crucial precept that the Western project of dominating the earth through scientific or technical reason is ethically and epistemologically bankrupt, it may also be described as postmodern.
The strongest and most direct statement of Le Guin’s anarchist vision appears in her 1974 novel \emph{The Dispossessed}. This novel describes a statist society located on the world known as Urras, and an anarchist society that is to be found on that world’s moon, Anarres. Certainly Le Guin’s Anarres has much to offer modern anarchists. Apart from her gender, the founder of Anarres, Odo, is largely indistinguishable from the nineteenth-century Russian anarchist Peter Kropotkin. The Odonians “have no law but the single principle of mutual aid between individuals” (\emph{Dispossesed}, 300). \emph{Mutual Aid} was the title of one of Kropotkin’s most influential works, and this concept was a fundamental element of his anarchist philosophy. Le Guin even goes to the trouble of recreating the intellectual debates out of which Kropotkin’s views on mutual aid developed, especially debates about evolution (see Kropotkin, \emph{Evolution and Environment}, 117ff). The Urrasti favor the type of reductionist Darwinism that always drew Kropotkin’s critical wrath. For them, “The law of existence is struggle — competition — elimination of the weak — a ruthless war for survival” (Le Guin, \emph{The Dispossessed} 143). Shevek, the Anarresti protagonist of Le Guin’s novel, takes a very different view: “the strongest, in the existence of any social species, are those who are most social. In human terms, most ethical” (220). This is strikingly similar to the subversive reading of Darwinism that Kropotkin provides in his \emph{Ethics}. Here Kropotkin argues that “Darwin explained the origin of the sense of moral duty in man by the preponderance in man of the feeling of social sympathy over personal egoism” (282). Much to the delight of modern anarchists, then, \emph{The Dispossessed} provides a clear, concise and accessible account of the major theoretical features of classical anarchism.
Yet the novel also recognizes the limits of modern anarchism. When Shevek visits Urras, he is surprised to find that its rulers do not censor him. “He talked pure anarchism, and they did not stop him. But did they need to stop him? It seemed that he talked to the same people every time: well dressed, well fed, well mannered, smiling” (144). Perhaps it is not enough to explain anarchist ideals in rational terms — especially when one’s audience has been so conditioned by the dominant material and cultural system that they are essentially incapable of internalizing those ideas. Indeed, the problem of internalization is a significant one in \emph{The Dispossessed}, and not just for the Urrasti. Shevek has a rather disturbing conversation with the Urrasti woman Vea at a party:
\begin{quote}
“I know that you’ve got a — a Queen Teaea inside you, right inside that hairy head of yours. And she orders you around just like the old tyrant did her serfs. She says, ‘Do this!’ and you do, and ‘Don’t!’ and you don’t.”
“That is where she belongs,” he said, smiling. “Inside my head.” “No. Better to have her in a palace. Then you could rebel against her” (219).
\end{quote}
Remarkably (given the fact that she is the product of a statist society), Vea has made a postmodern anarchist argument, one that parallels those of Michel Foucault and Herbert Marcuse. This argument holds that power is to be found not only in the political and economic structures of the external world, but also internally, in the psychological structure of the individual. Shevek comes to recognize the importance of this point toward the end of the novel: “The Odonian society was conceived as a permanent revolution, and revolution begins in the thinking mind” (333). An authentic, vital anarchism, then, cannot be content simply to reproduce the logic and the critiques of its founders. “Kids learn to parrot Odo’s words as if they were \emph{laws} — the ultimate blasphemy!” declares the Anarresti subversive Bedap (168).
If \emph{The Dispossessed} is to make a major contribution to the theory and practice of anarchism, then, it must offer more than a popularized version of nineteenth-century radical philosophy. And indeed it does. For one thing, Le Guin’s novel offers a remarkable form of \emph{linguistic anarchy}. Building upon the postmodern insight that language is equivalent to power, Le Guin imagines what a truly anarchistic language might look like. The result is Pravic, the language of Anarres. Pravic is a fundamentally egalitarian language, and this is true at the deepest level of structure and grammar. Pravic avoids the possessive pronouns, even (especially?) in those cases where an English speaker might be particularly committed to the possessive form (as with family relationships). “The singular forms of the possessive pronouns in Pravic were used mostly for emphasis; idiom avoided them. Little children might say ‘my mother,’ but very soon they learned to say ‘the mother’” (58). Similarly, Pravic has no way to speak about property. When Anarresti wish to speak of the “propertied class,” the must use the Iotic language of Urras to do so, for Pravic has no equivalent term (42). This means that ideas regarding the accumulation of private wealth or class divisions based upon such accumulation are quite literally unthinkable in Pravic. The implications are profound. The Anarresti cannot be capitalist, because they lack the vocabulary of capitalism.
Pravic problematizes the easy distinctions that English speakers make between “work” and “play” — and rightly so, from an anarchist viewpoint. The idea that “work” is something exploitative and alienating, done from strict necessity and redeemed only by leisure time, is fundamental to the capitalist mode of social organization. Pravic, on the other hand, uses the same word for “work” and “play” (92). A separate word, the eminently descriptive \emph{kleggich}, is used to describe drudgery (\emph{Ibid.}). Again, one is reminded of Eros and Civilization (see Marcuse 214ff). Andrew Reynolds is thus quite right to suggest that the Odonians have tried “to rehabilitate work in Marcusian fashion” (Davis and Stillman 87). The argument is clear: on Anarres, meaningful, authentic, creative work is indistinguishable from play. Such work may be done for its own sake, and need not (must not!) be inscribed within the alienating framework of a market economy.
Pravic clearly has much to recommend it. The Terran ambassador Keng speaks admiringly of the tongue: “I don’t know your language. I am told that it’s a most interesting one, the only rationally invented language that has become the tongue of a great people” (339). Yet here is Pravic’s fatal flaw. Though it is light years beyond American English in terms of its social consciousness, its ethics, its sense of equality and justice, Pravic is still limited by the horizons of human rationality. Pravic was invented by an Odonian called Farigv, and “Farigv didn’t provide any swear words when he invented the language, or if he did his computers didn’t understand the necessity” (234). Here one is reminded of Dr. Haber, who proceeded from the best humanist intentions, but was doomed to failure by his rejection of the irrational. Language cannot be purely rational, for the humans who speak it certainly are not. Language must be able to express not only logical concepts but also emotions, even those that might be seen as undesirable from the perspective of social engineering. When Shevek needs to swear, he must switch to Iotic: “‘Hell!’ he said aloud. Pravic was not a good swearing language. It is hard to swear when sex is not dirty and blasphemy does not exist” (258). Ironically, the success of Odonianism sets the stage for its failures. Pravic is a fair language and a just one. It encourages egalitarian thinking and actively works against the establishment of hierarchy. Yet it remains dry and sterile. This brings us back to the message of postmodern anarchism: the world cannot be saved through the articulation of a rational revolutionary philosophy, even if that philosophy does contain admirable elements.
Fortunately, \emph{The Dispossessed} does contain one element that is truly revolutionary in the postmodern sense, and that is Shevek’s General Temporal Theory. Shevek is a theoretical physicist; his term for his field of study is \emph{chronosophy}. This gives us an important clue as to the nature and significance of his theories. What Shevek is working on is a \emph{philosophy of time}. Le Guin’s text makes it quite clear that this philosophy has radical political implications. The Urrasti physicist Oiie observes that “The politician and the physicist both deal with things as they are, with real forces, the basic laws of the world” (203). Naturally, Shevek rejects Oiie’s statist formulation. And yet Shevek does accept Oiie’s basic insight: that there is a politics of physics, and a physics of politics. Of course, for an anarchist like Shevek, politics and ethics are virtually coterminous. Thus Shevek acknowledges that “chronosophy does involve ethics. Because our sense of time involves our ability to separate cause and effect, means and end” (225). Thus, Shevek’s attempt to articulate a General Temporal Theory is also, fundamentally, an attempt to create a viable and vibrant ethical theory.
Shevek’s objective is to bring together two apparently contradictory fields of physics, known as Sequency and Simultaneity. Sequency deals with the linear concept of time, which has dominated the perception of history in the West. Simultaneity acknowledges and endorses the nonlinear, including in particular those philosophies that see time as cyclical or recursive. Shevek describes the two concepts of time: “So then time has two aspects. There is the arrow, the running river, without which there is no change, no progress, or direction, or creation. And there is the circle or the cycle, without which there is chaos, meaningless succession of instants, a world without clocks or seasons or promises” (223). Shevek’s invocation of promises is interesting, for it recalls Nietzsche’s definition of the human being as an animal with the right to make promises (\emph{Genealogy of Morals}, second essay, section 2). Shevek even makes the Nietzschean element of his thinking explicit: “And so, when the mystic makes the reconnection of his reason and his unconscious, he sees all becoming as one being, and understands the eternal return” (Le Guin, \emph{The Dispossessed} 222). In this remarkable passage, Shevek acknowledges that the project he is pursuing in the physical sciences is parallel to the project Nietzsche undertook in philosophy. In \emph{Thus Spoke Zarathustra}, Nietzsche famously described his world-shaking vision of eternal return: “everything goes, everything comes back; eternally rolls the wheel of being. Everything dies, everything blossoms again; eternally runs the year of being” (217). In \emph{Zarathustra}, Nietzsche dreamed of a being who could not only accept the terrifying thought of eternal recurrence but could actively embrace it, cherish it, celebrate it. He called this being Overman.
To a remarkable extent, Le Guin’s Shevek completes the project outlined in \emph{Zarathustra}. Shevek embraces the principle of eternal return embodied in the theory of Simultaneity. Remarkably, he is also able to continue thinking of time in linear or Sequential terms as well. He can do this only because, as Heidegger has argued, “the overman is the expressly willed negation of the previous essence of man. Within metaphysics man is experienced as the rational animal” (III 217). Shevek is a scientist, but he is not a rationalist. A purely rational science could not produce his temporal theory. To achieve this theory, Shevek must give up a great deal. He must abandon a restrictive rationalism, and with it the humanism that dominated the intellectual history of the West until Nietzsche (Heidegger’s “previous essence of man”). In short, to achieve his goals in physics, Shevek must take a postmodern turn. Thus Andrew Reynolds is right to argue (albeit in a somewhat different context) that “\emph{The Dispossessed} is equally the product of anarchism and Nietzschean postmodernism” (Davis and Stillman 88). As an Odonian, Shevek has already internalized the basic principles of modern anarchism. When he moves beyond rationalism and humanism to grasp a radically new concept of time, he takes his anarchism a step further. Ellen Rigsby is quite correct to note that by embracing the cyclical concept of time, Shevek challenges the entire mainstream intellectual tradition of Europe; thus “Shevek’s thoughts move into an explicitly anarchist form” (Davis and Stillman 173). More precisely, by accepting Simultaneity as well as Sequency, Shevek becomes a postmodern anarchist.
I must therefore challenge the extensive body of literature that characterizes Shevek’s reconciliation of Sequency and Simultaneity as an example of Le Guin’s “dialectical thinking” (see, for example, Bittner 121). Most recently, Tony Burns has argued that Shevek “like his creator is a thoroughgoing ‘dialectical’ thinker” (Davis and Stillman 199) whose attitude towards time “demonstrates a tendency for him to think in terms of those ‘binary oppositions,’ such as that between the notion of ‘Being’ and the notion of ‘Becoming,’ which have been central to the Western philosophical tradition from the time of the ancient Greeks, and which are rejected by Nietzsche, postmodernism, and the ‘academic left’” (201). Burns attempts to relate Shevek’s theory to the Hegelian philosophical method, to show that \emph{The Dispossessed} is a “modern” rather than a “postmodern” work, and that Shevek’s views on science “fall firmly within the classical anarchist tradition” (203). There are serious problems with this approach. First and foremost, there is no dialectical reconciliation of Sequency and Simultaneity in \emph{The Dispossessed}. Shevek develops the ability to think both thoughts together, but not in a synthetic way. The two thoughts remain separate and distinct. Rather than a synthetic reconciliation of thesis and antithesis, Shevek’s theory represents the perpetual embrace of two theories that are and remain contradictory. Shevek’s experience of time is thus an experience of permanent cognitive dissonance. He is prepared to experience time as both linear and cyclical at every moment of his life, and he must never allow this experience to solidify into a stagnant synthesis.
Shevek’s views on time must remain tentative, provisional, unresolved — in short, postmodern. He must abandon the false certainties of reason. His rewards for doing so are substantial. The major practical benefit of Shevek’s theory is that it will permit the creation of the ansible, a device that will allow instantaneous interstellar communication. Thus Shevek’s theory creates the opportunity for an infinite proliferation of discourse without resolution: a truly postmodern possibility. Indeed, this is more than a mere possibility. For the universe that Shevek made is the universe of Genly Ai’s Ekumen: a community of worlds linked together in radically egalitarian, non-hierarchical fashion by the ansible. Thus the conclusion of \emph{The Dispossessed} points back to \emph{The Left Hand of Darkness}. This is a beautiful statement of time’s circle, and a powerful structural assertion of the anarchistic possibilities that emerge when we embrace the contradictory aspects of sequential and simultaneous time.
Ursula Le Guin’s writing shows a remarkable knowledge of — and a deep respect for — the classical anarchist tradition. It is hardly surprising, then, that her critics should focus mainly on the ways in which her work builds upon that tradition. Yet criticism must do more than this, for Le Guin certainly does. Le Guin’s novels of the late 1960s and early 1970s offer anarchist possibilities that extend well beyond the horizons of the modern. In these novels, Le Guin experiments with androgyny, subverts rational ontologies, articulates anarchist languages, and proposes a radical philosophy of time. The themes of postmodern anarchism are clearly present in her work. So far these themes have remained largely hidden, but it is time to bring them to the surface. Modern anarchists need not fear this critical project, for the postmodern elements of Le Guin’s anarchism do not oppose that philosophy’s modern elements. Rather, the modern and postmodern aspects of Le Guin’s anarchism are part of a permanent, ongoing, open-ended dialogue about the possibilities of anarchist thinking in the contemporary era. Such a dialogue can only enrich anarchist theory.
\begin{quote}
\emph{California Polytechnic State University, San Luis Obispo}
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\section{Works Cited}
Barr, Marleen S. \emph{Lost in Space: Probing Feminist Science Fiction and Beyond.} Chapel Hill: The University of North Carolina Press, 1993.
Bittner, James. \emph{Approaches to the Fiction of Ursula K. Le Guin.} Ann Arbor, MI: UMI Research Press, 1984.
Brennan, John P. and Michael C. Downs. “Anarchism and Utopian Tradition in \emph{The Dispossessed}.” Ursula K. Le Guin. Ed. Joseph D. Olander and Martin Harry Greenberg. New York: Taplinger, 1979. 116–152.
Call, Lewis. \emph{Postmodern Anarchism}. Lanham, MD: Lexington Books, 2002.
Davis, Laurence and Peter Stillman, eds. The New Utopian Politics of Ursula K. Le Guin’s \emph{The Dispossessed}. Lanham, MD: Lexington Books, 2005.
Freud, Sigmund. \emph{Civilization and Its Discontents.} Standard Edition. Trans. and Ed. James Strachey. New York: W. W. Norton and Company, 1989.
Heidegger, Martin. \emph{Nietzsche}. Ed. David Ferrell Krell. San Francisco: HarperSanFrancisco, 1991.
Kropotkin, Peter. \emph{Ethics: Origin and Development}. Montréal: Black Rose Books, 1992.
—. \emph{Evolution and Environment}. Ed. George Woodcock. Montréal: Black Rose Books, 1995.
—. \emph{Mutual Aid: A Factor of Evolution}. Montréal: Black Rose Books, 1989.
Lamb, Patricia Frazer and Diana L. Veith. “Again, \emph{The Left Hand of Darkness}: Androgyny or Homophobia?” \emph{Erotic Universe: Sexuality and Fantasy Literature}. Ed. Donald Palumbo. New York: Greenwood Press, 1986.
221–231. Le Guin, Ursula K. \emph{Dancing at the Edge of the World}. New York: Grove Press, 1989.
—. \emph{Lao Tzu: Tao Te Ching. A Book About the Way and the Power of the Way}. Boston: Shambhala, 1998.
—. \emph{The Dispossessed}. New York: HarperPrism, 1994.
—. \emph{The Language of the Night}. Ed. Susan Wood. New York: G. P. Putnam’s Sons, 1979.
—. \emph{The Lathe of Heaven}. New York: Avon Books, 1973.
—. \emph{The Left Hand of Darkness}. New York: Ace Books, 1987.
Marcuse, Herbert. \emph{Eros and Civilization}. Boston: Beacon Press, 1974.
Marshall, Peter. \emph{Demanding the Impossible: A History of Anarchism}. London: FontanaPress, 1993.
May, Todd. \emph{The Political Philosophy of Poststructuralist Anarchism}. University Park, PA: Pennsylvania State University Press, 1994.
Moylan, Tom. \emph{Demand the Impossible: Science Fiction and the Utopian Imagination}. New York: Methuen, 1986.
Mullen, R. D. and Darko Suvin. \emph{Science-Fiction Studies: Selected Articles on Science Fiction 1973–1975}. Boston: Gregg Press, 1976.
Newman, Saul. \emph{From Bakunin to Lacan: Anti-Authoritarianism and the Dislocation of Power}. Lanham, MD: Lexington Books, 2001.
Nietzsche, Friedrich. \emph{On the Genealogy of Morals and Ecce Homo}. Ed. Walter Kaufmann. New York: Vintage Books, 1969.
—. \emph{Thus Spoke Zarathustra}. Trans. Walter Kaufmann. New York: Penguin Books, 1988.
Rapp, John A. “Daoism and Anarchism Reconsidered.” \emph{Anarchist Studies} 6.2 (October 1998): 123–151.
Suvin, Darko. \emph{Metamorphoses of Science Fiction}. New Haven, CT: Yale University Press, 1979.
Watts, Alan. \emph{Tao: The Watercourse Way}. New York: Penguin Books, 1986.
Widmer, Kingsley. \emph{Counterings: Utopian Dialectics in Contemporary Contexts}. Ann Arbor, MI: UMI Research Press, 1988.
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The Anarchist Library
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Lewis Call
Postmodern Anarchism in the Novels of Ursula K. Le Guin
2007
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Retrieved on November 2, 2010 from \href{http://www.scribd.com/doc/36303088/Call-L-2007-Postmodern-Anarchism-in-the-Novels-of-Ursula-K-Le-Guin-Substance-113-36-87-105}{www.scribd.com}
From “SubStance” \#113, Vol. 36, no. 2, 2007
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\DeclareDocumentCommand \adhochangulfont { o m }
{ \__xtxko_pass_args:nnn \__xtxko_adhochangulfont:nn {#1} {#2} }
\cs_new:Nn \__xtxko_adhochangulfont:nn
{
\__xtxko_hangul_assign_font_opts:n {#1}
\newfontfamily \XK@adhoc@hangul@font [\l_xtxko_rem_tl] {#2}
\tl_put_right:NV \XK@adhoc@hangul@font \l_xtxko_font_opts_tl
\tl_set:Nn \XKhangulfont
{
\XK@storeltnfont
\tl_set_eq:NN \XKcurrentfont \c_one
\XK@adhoc@hangul@font
\XK@storecjkfont
}
\ignorespaces
}
\cs_set_eq:NN \hangulfontspec \adhochangulfont
\DeclareDocumentCommand \adhochanjafont { o m }
{ \__xtxko_pass_args:nnn \__xtxko_adhochanjafont:nn {#1} {#2} }
\cs_new:Nn \__xtxko_adhochanjafont:nn
{
\__xtxko_hanja_assign_font_opts:n {#1}
\newfontfamily \XK@adhoc@hanja@font [\l_xtxko_rem_tl] {#2}
\tl_put_right:NV \XK@adhoc@hanja@font \l_xtxko_font_opts_tl
\tl_set:Nn \XKhanjafont
{
\XK@storeltnfont
\tl_set_eq:NN \XKcurrentfont \c_two
\XK@adhoc@hanja@font
\XK@storecjkfont
}
\ignorespaces
}
\cs_set_eq:NN \hanjafontspec \adhochanjafont
%% new{hangul,hanja}font{family,face}
\DeclareDocumentCommand \newhangulfontfamily { m o m }
{ \__xtxko_pass_args:nnn { \__xtxko_newhangulfontfamily:Nnn #1 } {#2} {#3} }
\cs_new:Nn \__xtxko_newhangulfontfamily:Nnn
{
\__xtxko_hangul_assign_font_opts:n {#2}
\exp_args:Nc \newfontfamily { XK@newfont@family \token_to_str:N #1 }
[\l_xtxko_rem_tl] {#3}
\tl_put_right:cV { XK@newfont@family \token_to_str:N #1 }
\l_xtxko_font_opts_tl
\DeclareRobustCommand #1
{
\tl_set:Nn \XKhangulfont
{
\XK@storeltnfont
\tl_set_eq:NN \XKcurrentfont \c_one
\use:c { XK@newfont@family \token_to_str:N #1 }
\XK@storecjkfont
}
}
}
\DeclareDocumentCommand \newhanjafontfamily { m o m }
{ \__xtxko_pass_args:nnn { \__xtxko_newhanjafontfamily:Nnn #1 } {#2} {#3} }
\cs_new:Nn \__xtxko_newhanjafontfamily:Nnn
{
\__xtxko_hanja_assign_font_opts:n {#2}
\exp_args:Nc \newfontfamily { XK@newfont@family \token_to_str:N #1 }
[\l_xtxko_rem_tl] {#3}
\tl_put_right:cV { XK@newfont@family \token_to_str:N #1 }
\l_xtxko_font_opts_tl
\DeclareRobustCommand #1
{
\tl_set:Nn \XKhanjafont
{
\XK@storeltnfont
\tl_set_eq:NN \XKcurrentfont \c_two
\use:c { XK@newfont@family \token_to_str:N #1 }
\XK@storecjkfont
}
}
}
\DeclareDocumentCommand \newhangulfontface { m o m }
{ \__xtxko_pass_args:nnn { \__xtxko_newhangulfontface:Nnn #1 } {#2} {#3} }
\cs_new:Nn \__xtxko_newhangulfontface:Nnn
{
\__xtxko_hangul_assign_font_opts:n {#2}
\exp_args:Nc \newfontface { XK@newfont@family \token_to_str:N #1 }
[\l_xtxko_rem_tl] {#3}
\tl_put_right:cV { XK@newfont@family \token_to_str:N #1 }
\l_xtxko_font_opts_tl
\DeclareRobustCommand #1
{
\tl_set:Nn \XKhangulfont
{
\XK@storeltnfont
\tl_set_eq:NN \XKcurrentfont \c_one
\use:c { XK@newfont@family \token_to_str:N #1 }
\XK@storecjkfont
}
}
}
\DeclareDocumentCommand \newhanjafontface { m o m }
{ \__xtxko_pass_args:nnn { \__xtxko_newhanjafontface:Nnn #1 } {#2} {#3} }
\cs_new:Nn \__xtxko_newhanjafontface:Nnn
{
\__xtxko_hanja_assign_font_opts:n {#2}
\exp_args:Nc \newfontface { XK@newfont@family \token_to_str:N #1 }
[\l_xtxko_rem_tl] {#3}
\tl_put_right:cV { XK@newfont@family \token_to_str:N #1 }
\l_xtxko_font_opts_tl
\DeclareRobustCommand #1
{
\tl_set:Nn \XKhanjafont
{
\XK@storeltnfont
\tl_set_eq:NN \XKcurrentfont \c_two
\use:c { XK@newfont@family \token_to_str:N #1 }
\XK@storecjkfont
}
}
}
%% add{hangul,hanja}fontfeature[s]
\DeclareDocumentCommand \addhangulfontfeature { m }
{
\group_begin:
\XKhangulfont
\tl_clear:N \l_xtxko_font_opts_tl
\keys_set_known:nxN { xtxko-font } {#1} \l_xtxko_rem_tl
\addfontfeature {\l_xtxko_rem_tl}
\use:x
{
\group_end:
\exp_not:N \tl_set:Nn \exp_not:N \XKhangulfont
{
\exp_not:V \XKhangulfont
\exp_not:N \fontfamily { \f@family } \exp_not:N \selectfont
\exp_not:V \l_xtxko_font_opts_tl
\exp_not:N \XK@storecjkfont
}
}
\ignorespaces
}
\cs_set_eq:NN \addhangulfontfeatures \addhangulfontfeature
\DeclareDocumentCommand \addhanjafontfeature { m }
{
\group_begin:
\XKhanjafont
\tl_clear:N \l_xtxko_font_opts_tl
\keys_set_known:nxN { xtxko-font } {#1} \l_xtxko_rem_tl
\addfontfeature {\l_xtxko_rem_tl}
\use:x
{
\group_end:
\exp_not:N \tl_set:Nn \exp_not:N \XKhanjafont
{
\exp_not:V \XKhanjafont
\exp_not:N \fontfamily { \f@family } \exp_not:N \selectfont
\exp_not:V \l_xtxko_font_opts_tl
\exp_not:N \XK@storecjkfont
}
}
\ignorespaces
}
\cs_set_eq:NN \addhanjafontfeatures \addhanjafontfeature
%% default font features
\defaultfontfeatures
[
\kormainfont, \korsansfont, \hnjmainfont, \hnjsansfont,
]
{Ligatures=TeX}
\DeclareDocumentCommand \defaulthangulfontfeatures { t+ o m } % o is ignored
{
\IfBooleanTF {#1}
{
\tl_set_eq:NN \l_xtxko_font_opts_tl \l_xtxko_hangul_font_opts_init_tl
}
{
\tl_set_eq:NN \l_xtxko_font_opts_tl \l_xtxko_font_opts_init_tl
}
\keys_set_known:nxN { xtxko-font } {#3} \l_xtxko_rem_tl % rem_tl ignored
\tl_set_eq:NN \l_xtxko_hangul_font_opts_init_tl \l_xtxko_font_opts_tl
}
\DeclareDocumentCommand \defaulthanjafontfeatures { t+ o m } % o is ignored
{
\IfBooleanTF {#1}
{
\tl_set_eq:NN \l_xtxko_font_opts_tl \l_xtxko_hanja_font_opts_init_tl
}
{
\tl_set_eq:NN \l_xtxko_font_opts_tl \l_xtxko_font_opts_init_tl
}
\keys_set_known:nxN { xtxko-font } {#3} \l_xtxko_rem_tl % rem_tl ignored
\tl_set_eq:NN \l_xtxko_hanja_font_opts_init_tl \l_xtxko_font_opts_tl
}
%% math hangul font
\DeclareDocumentCommand \setmathhangulfont { o m }
{ \__xtxko_pass_args:nnn \__xtxko_setmathhangulfont:nn {#1} {#2} }
\cs_new:Nn \__xtxko_setmathhangulfont:nn
{
\fontspec_set_family:Nnn \xetexko@math@hangul@family {#1} {#2}
}
%%%%%%%%%%%%%%%%%%%%
%% xetexkofontregime
\keys_define:nn { xtxko-char }
{
alphs .code:n = \use:c { #1alphs } ,
nums .code:n = \use:c { #1nums } ,
parens .code:n = \use:c { #1parens } ,
quotes .code:n = \use:c { #1quotes } ,
puncts .code:n = \use:c { #1puncts } ,
colons .code:n = \use:c { #1colons } ,
hyphens .code:n = \use:c { #1hyphens } ,
cjksymbols .code:n = \use:c { #1cjksymbols } ,
}
\DeclareDocumentCommand \xetexkofontregime { o m }
{ \__xtxko_pass_args:nnn \__xtxko_xetexkofontregime:nn {#1} {#2} }
\cs_new:Nn \__xtxko_xetexkofontregime:nn
{
\use:c { #2marks }
\keys_set:nn { xtxko-char } { #1 }
}
\ExplSyntaxOff
%%%%%%%%%%%%%%%%%%%%%%%%%%
% font switching for latex
\def\XKstoreprevfont{%
\ifx\f@family\XKcjkprevfont\let\f@family\XKltnprevfont\fi
}
\def\XK@storeltnfont{%
\ifx\f@family\XKcjkprevfont\else\let\XKltnprevfont\f@family\fi
}
\def\XK@storecjkfont{%
\let\XKcjkprevfont\f@family
\edef\XKplaincjkprevfont{\the\font}%
}
\edef\XKlatinfont{\unexpanded\expandafter{\XKstoreprevfont
\chardef\XKcurrentfont\z@
\edef\XK@plain@curr@font{\the\font}%
\ifx\XK@plain@curr@font\XKplaincjkprevfont
\selectfont
\fi
}}
\def\XK@rm@korean@font{%
\ifx\XKhangulfont\relax\else
\def\XKhangulfont{%
\XK@storeltnfont
\chardef\XKcurrentfont\@ne\kormainfont
\XK@storecjkfont
}%
\fi
\ifx\XKhanjafont\relax\else
\def\XKhanjafont {%
\XK@storeltnfont
\chardef\XKcurrentfont\tw@\hnjmainfont
\XK@storecjkfont
}%
\fi
}
\def\XK@sf@korean@font{%
\ifx\XKhangulfont\relax\else
\def\XKhangulfont{%
\XK@storeltnfont
\chardef\XKcurrentfont\@ne\korsansfont
\XK@storecjkfont
}%
\fi
\ifx\XKhanjafont\relax\else
\def\XKhanjafont {%
\XK@storeltnfont
\chardef\XKcurrentfont\tw@\hnjsansfont
\XK@storecjkfont
}%
\fi
}
\def\XK@tt@korean@font{%
\ifx\XKhangulfont\relax\else
\def\XKhangulfont{%
\XK@storeltnfont
\chardef\XKcurrentfont\@ne\kormonofont
\XK@storecjkfont
}%
\fi
\ifx\XKhanjafont\relax\else
\def\XKhanjafont {%
\XK@storeltnfont
\chardef\XKcurrentfont\tw@\hnjmonofont
\XK@storecjkfont
}%
\fi
}
\edef\rmfamily{\unexpanded\expandafter{\rmfamily\XK@rm@korean@font}}
\edef\sffamily{\unexpanded\expandafter{\sffamily\XK@sf@korean@font}}
\edef\ttfamily{\unexpanded\expandafter{\ttfamily
\XK@tt@korean@font\disablehangulspacing
}}
\edef\verbatim@font{\unexpanded\expandafter{\verbatim@font
\disablehangulspacingandlinebreak
\let\XKstoreprevfont\XKlatinfont
}}
% for default font loading
\def\XKiffontisaccessible#1#2#3{%
\begingroup
\suppressfontnotfounderror\@ne
\font\x="#1" at 10pt
\expandafter
\endgroup
\ifx\x\nullfont #3\else #2\fi
}
\def\XKiffonthasunichar#1#2#3#4{%
\begingroup #1\expandafter\endgroup
\iffontchar\font"#2\relax #3\else #4\fi
}
\AtBeginDocument{%
%%%%%%%%%%%%%%%%%%%%%%%%%%
% default main hangul: nanummyeongjo, batang if absent
\ifdefined\kormainfont\else
\XKiffonthasunichar{\fontfamily\rmdefault\selectfont}{AC00}
{\let\kormainfont\relax}
{\XKiffontisaccessible{NanumMyeongjoExtraBold}
{\setmainhangulfont{NanumMyeongjo}[Renderer=OpenType,BoldFont=*ExtraBold]}
{\XKiffontisaccessible{NanumMyeongjo}
{\setmainhangulfont{NanumMyeongjo}[Renderer=OpenType]}
{\XKiffontisaccessible{Batang}
{\setmainhangulfont{Batang}[AutoFakeBold]}
{\let\kormainfont\relax}%
}%
}%
}%
\fi
% default main hanja: nanumgothic, batang if absent
\ifdefined\hnjmainfont\else
\XKiffonthasunichar{\kormainfont}{4E00}
{\let\hnjmainfont\kormainfont}
{\XKiffontisaccessible{NanumGothic}
{\setmainhanjafont{NanumGothic}[Renderer=OpenType]}
{\XKiffontisaccessible{Batang}
{\setmainhanjafont{Batang}[AutoFakeBold]}
{\let\hnjmainfont\kormainfont}%
}%
}%
\fi
% default sans hangul: nanumgothic, dotum if absent
\ifdefined\korsansfont\else
\XKiffonthasunichar{\fontfamily\sfdefault\selectfont}{AC00}
{\let\korsansfont\relax}
{\XKiffontisaccessible{NanumGothic}
{\setsanshangulfont{NanumGothic}[Renderer=OpenType]}
{\XKiffontisaccessible{Dotum}
{\setsanshangulfont{Dotum}[AutoFakeBold]}
{\let\korsansfont\relax}%
}%
}%
\fi
% default sans hanja: nanumgothic, dotum if absent
\ifdefined\hnjsansfont\else
\XKiffonthasunichar{\korsansfont}{4E00}
{\let\hnjsansfont\korsansfont}
{\XKiffontisaccessible{NanumGothic}
{\setsanshanjafont{NanumGothic}[Renderer=OpenType]}
{\XKiffontisaccessible{Dotum}
{\setsanshanjafont{Dotum}[AutoFakeBold]}
{\let\hnjsansfont\korsansfont}%
}%
}%
\fi
\ifdefined\kormonofont\else \let\kormonofont\korsansfont \fi
\ifdefined\hnjmonofont\else \let\hnjmonofont\kormonofont \fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% reset hangul font and normalfont
\expandafter\ifx\familydefault\rmdefault
\XK@rm@korean@font
\protected\edef\normalfont{\unexpanded\expandafter{\normalfont
\XK@rm@korean@font}}
\else \expandafter\ifx\familydefault\sfdefault
\XK@sf@korean@font
\protected\edef\normalfont{\unexpanded\expandafter{\normalfont
\XK@sf@korean@font}}
\else
\XK@tt@korean@font
\protected\edef\normalfont{\unexpanded\expandafter{\normalfont
\XK@tt@korean@font}}
\fi\fi
\let\reset@font\normalfont
%%%%%%%%%%%%%%%%%%%%%
% hangul in math mode
\begingroup
\ifx\xetexko@math@hangul@family\undefined
\edef\@tempb{\sfdefault}\edef\@tempc{\ttdefault}%
\ifx\f@family\@tempb \korsansfont \else
\ifx\f@family\@tempc \kormonofont \else
\kormainfont \fi\fi
\xdef\xetexko@math@hangul@family{\f@family}\fi
\endgroup
\DeclareSymbolFont{mathhangul}\zf@enc\xetexko@math@hangul@family
\mddefault\updefault
\ifcsname \zf@enc/\xetexko@math@hangul@family/\bfdefault/\updefault\endcsname
\SetSymbolFont{mathhangul}{bold}\zf@enc\xetexko@math@hangul@family
\bfdefault\updefault
\fi
\setmathhangulblock{AC00}{D7A3}
}
%%%%%%%%%%%%%%%%%%%%%%%
% under [hangul] option
\if@hangul
\linespread{1.3888}
\footnotesep=1.3888\footnotesep
\skip\footins=1.3888\skip\footins plus6pt minus3pt
% frenchspacing is default
\frenchspacing
\fi
\endinput
|
http://ctan.sharelatex.com/tex-archive/usergrps/dante/dtk/dtklogos.sty
|
sharelatex.com
|
CC-MAIN-2014-15
|
text/x-tex
| null |
crawl-data/CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00625-ip-10-147-4-33.ec2.internal.warc.gz
| 86,703,001
| 2,745
|
%%
%% This is file `dtklogos.sty',
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% $Id: dtklogos.sty 36 2012-05-02 19:43:14Z herbert $
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Purpose:
%% LaTeX Class and Styles for ``Die TeXnische Komoedie''.
%%
%% Copyright (C) 1995-1996 Gerd Neugebauer
%% Copyright (C) 1997-2011 DANTE, Deutschsprachige
%% Anwendervereinigung TeX e.V.
%%
%% This file may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%% The latest version of this license is in
%% http://www.latex-project.org/lppl.txt
%% and version 1.3c or later is part of all distributions of LaTeX
%% version 2005/12/01 or later.
%%
%% This package is still under development and may be replaced with
%% a new version which provides enhanced functionality.
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\fileversion{2.15}
\def\filedate{2012/05/02}
\let\docversion=\fileversion
\let\docdate=\filedate
\ProvidesPackage{dtklogos}[\filedate\space\fileversion\space (hv)]
%
\RequirePackage{graphicx}
\RequirePackage{metalogo}
\RequirePackage{ifpdf}
\providecommand\AmS{{\normalfont\(\cal A\)\kern-.1667em\lower.5ex\hbox{\(\cal M\)}\kern-.125em{\(\cal S\)}}}
\providecommand\AMS{\AmS}
\providecommand\AmSLaTeX{\AmS-\LaTeX}
\providecommand\AMSLaTeX{\AmSLaTeX}
\providecommand\AmSTeX{\normalfont%
$\cal A$\kern-.1667em\lower.5ex\hbox{$\cal M$}%
\kern-.125em$\cal S$-\TeX}
\providecommand\AMSTEX{\AmSTeX}
\providecommand\AMSTeX{\AmSTeX}
\DeclareRobustCommand{\BibTeX}{B\kern-.05em%
\hbox{$\m@th$% %% force math size calculations
\csname S@\f@size\endcsname
\fontsize\sf@size\z@
\math@fontsfalse\selectfont
I\kern-.025emB}%
\kern-.08em%
\-\TeX}
\providecommand\BIBTeX{\BibTeX}
\providecommand\BIBTEX{\BibTeX}
\providecommand\LAMSTeX{%
L\raise.42ex\hbox{\kern-.3em\the\scriptfont2 A}%
\kern-.2em\lower.376ex\hbox{\the\textfont2 M}%
\kern-.125em {\the\textfont2 S}-\TeX}
\providecommand\LamSTeX{\LAMSTeX}
\providecommand\LAmSTeX{\LAMSTeX}
\providecommand\La{L\kern-.36em\raise.3ex\hbox{\sc a}}
\providecommand\LaTeX{%
L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em\TeX}
\providecommand\LATEX{\LaTeX}
\DeclareRobustCommand{\LaTeXTeX}{(\kern-.15emL\kern-.36em%
{\sbox\z@ T%
\vbox to\ht0{\hbox{$\m@th$%
\csname S@\f@size\endcsname
\fontsize\sf@size\z@
\math@fontsfalse\selectfont
A}%
\vss}%
}\kern-.2em)%
\kern-.15em%
\TeX}
\providecommand\TeXLive{\TeX{}Live}
\DeclareFontFamily{U}{logo}{}
\DeclareFontShape{U}{logo}{m}{n}{
<8> <9> gen * logo
<10> <10.95> <12> <14.4> <17.28> <20.74> <24.88> logo10
}{}
\DeclareFontShape{U}{logo}{m}{it}{
<8> <9> gen * logosl
<10> <10.95> <12> <14.4> <17.28> <20.74> <24.88> logosl10
}{}
\DeclareFontShape{U}{logo}{m}{sl}{
<-> ssub * logo/m/it
}{}
\DeclareFontShape{U}{logo}{sbc}{n}{
<8> <9> sub * logo/m/n
<10> <10.95> <12> <14.4> <17.28> <20.74> <24.88> logobf10
}{}
\DeclareFontShape{U}{logo}{b}{n}{
<8> <9> sub * logo/m/n
<10> <10.95> <12> <14.4> <17.28> <20.74> <24.88> logod10
}{}
\DeclareFontShape{U}{logo}{bx}{n}{
<-> ssub * logo/b/n
}{}
\DeclareRobustCommand\logofamily{%
\not@math@alphabet\logofamily\relax
\fontencoding{U}\fontfamily{logo}\selectfont}
\DeclareTextFontCommand{\textlogo}{\logofamily}
\newcommand\MF{\mbox{\textlogo{META}}\-\mbox{\textlogo{FONT}}\@}
\newcommand\MFun{\mbox{\textlogo{META}}\-\textsc{Fun}\@}
\newcommand\MP{\mbox{\textlogo{META}}\-\mbox{\textlogo{POST}}\@}
\providecommand\METAFONT{\MF}
\providecommand\METAFUN{\MFun}
\providecommand\METAPOST{\MP}
\def\LuaTeX{Lua\kern-0.15em\TeX}
\let\luatex\LuaTeX
\providecommand\LuaLaTeX{Lua\LaTeX}
\providecommand\SLITEX{%
S\kern-.065em L\kern-.18em\raise.32ex\hbox{i}%
\kern-.03em\TeX}
\providecommand\SLiTeX{\SLITEX}
\providecommand\SliTeX{\SLITEX}
\providecommand\SLITeX{\SLITEX}
\providecommand\NTS{\mbox{\mathsurround=0pt
\(\cal N\mkern -4mu\lower .5ex\hbox{$\cal T$}\mkern -2mu S\)}}
\providecommand\MakeIndex{\textit{Make\-Index}}
\providecommand\emTeX{{em\TeX}}
\providecommand\PubliCTeX{PubliC\TeX}
\providecommand\TeXXeT{%
\TeX--X\kern-.125em\lower.5ex\hbox{E}\kern-.1667emT}
\providecommand\TeXeT{%
\TeX-X\kern-.125em\lower.5ex\hbox{E}\kern-.1667emT}
\providecommand\WinEdt{\mbox{\textsf{WinEdt}}}%
\providecommand\WinEdtKK{\mbox{\textsf{WinEdt2k}}}%
\providecommand{\LyX}{L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@}
\providecommand*{\exTeX}{%
\textrm{% das Logo grunds^^e4tzlich serifenbehaftet
\ensuremath{\textstyle\varepsilon_{\kern-0.15em\mathcal{X}}}%
\kern-.15em\TeX
}%
}
\providecommand\eV{e.V\kern-.18em\@ifnextchar.{}{.}}
\providecommand\dante{DANTE \eV}
\providecommand\Dante{DANTE,
Deutschsprachige Anwendervereinigung \TeX~\eV}
\providecommand\DTK{Die \TeX\-ni\-sche Ko\-m{\"o}\-die}
\providecommand\LaTeXe{%
\LaTeX{}\kern.05em2$_{\textstyle\varepsilon}$}
\providecommand\PS{Post\-Script}
\providecommand\PiC{P\kern-.12em\lower.5ex\hbox{I}\kern-.075emC}
\providecommand\PiCTeX{\PiC\kern-.11em\TeX}
\providecommand\TUG{\TeX{} Users Group}
\providecommand\TUGboat{\textsl{TUGboat}}
\let\TUB\TUGboat
\providecommand\TTN{\textsl{\TeX{} and TUG NEWS}}
\providecommand\NFSS{\textsf{NFSS}}
\providecommand\NTS{\leavevmode
\hbox{$\cal N\kern-0.35em\lower0.5ex\hbox{$\cal T$}\kern-0.2emS$}}
\providecommand\eTeX{{\leavevmode\hbox{$\varepsilon$}-\TeX}}%$
\providecommand*{\ExTeX}{% RN 2005-01-15
\textrm{% das Logo grunds^^e4tzlich serifenbehaftet
\ensuremath{\textstyle\varepsilon_{\kern-0.15em\mathcal{X}}}%
\kern-.15em\TeX
}%
}
\IfFileExists{ot1dante.fd}% RN 2005-01-15
{%
\providecommand*\DANTE[1][]{%
\begingroup
\usefont{OT1}{dante}{m}{n}\selectfont DANTE%
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% Program MNU -- The Documentation written in plain \TeX
% ======================================================
% January 1993 Petr Ol¨ k
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% begin of text
\null\vskip 30pt
\centerline{\titl Program MNU}
\bigskip
\centerline{\titl A configurable menu for starting applications under DOS}
\bigskip
\centerline{\bigit Petr Ol\v s\'ak}
\bigskip
\centerline{Prague, January 1993}
\bigskip\hrule\medskip
\sect 1. A brief description
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The program MNU allows, together with its control batch (".bat"),
repeated starting of various application programs. It has been developed
for the \TeX\ packages, nonetheless, it can be utilized elsewhere.
The batch "demotex.bat" starts an exhibition of possibilities of the
program MNU itself. The second batch "demotex.bat" shows a more complicated
example of configuration of emTeX used in \CS\TeX package. This example
exhibits possibilities of MNU program itself on the one hand, and of its
suggested configuration "cfg.mnu" suitable for the emTeX packages with DOS
on the other hand. These examples are documented in chapter 5.
The documentation is intended for the users, who wish to change the
existing configuration of the system, where the program is applied, or who
wish to develop a new one. Therefore some deeper knowledge of DOS is
assumed, esp. some advanced skills in batch (".bat") programming.
The program keeps up appearances of an integrated environment for starting
of various processes. This environment is fully configurable, including
window colours and shapes, names and ways of application of individual menu
items, context help, etc. The process is controlled by the batch. In a
definite moment, the batch starts the MNU program with a single parameter --
the configuration file name (e.g. "cfg.mnu"). The program MNU reads
a full description of menu structure from this file and displays menu items on
the screen. Now the user can choose the particular item comfortably. When
the item is chosen, the program MNU terminates and the control batch
evaluates the error code corresponding to the respective item. In the
batch, the chosen item number is determined using a set of "if errorlevel"
commands, and the batch branches to separate application processes. When
the application ends, the batch calls the MNU program again, and the user
can choose a new item, and so on.
The batch can also communicate with the MNU program by means of DOS
``environment variables'', and of input and/or output files. The program can
display and edit the content of these variables (if this is given in the
configuration file). Moreover, there exists a special environment variable
called ``MNU'' influencing the start of the program -- the item specified
in this variable is offered as active when the program starts. Seeing that,
the user does not need to choose tediously the next item, provided his
activity proceeds in the ``normal'' sequence. For example, after the
\TeX\ program run it is possible for the batch to examine (using the "if
errorlevel" command) whether the translation ended without errors. If so,
then the variable ``MNU'' can be set in such a way that the item "View" is
active in the next call of the menu. In the menu environment, the user can
do nothing but "Enter" pressing.
The advantage of this ``batch'' philosophy is that the MNU program does not
occupy the memory during the application run. Furthermore, concerning the
system configuration, there are practically no limitations on variability
in setting the behaviour of particular processes. The only limitations are
due to the DOS itself. Only a batch allows to express all configuration
possibilities of separate application programs.
\medskip
The list of files contained in the MNU program package is given in the
following table:
\begtab{25em}
& "readme.txt" \: Basic information about the program &\cr
& "mnu.doc" \: Detailed documentation of the program &\cr
& "examples.doc" \: Description of some tricks used in the batches &\cr
& "mnu.tex" \: Contents of three previous files in plain \TeX\ --
this text &\cr
& "mnu.exe" \: The MNU program itself &\cr
& "demo.bat", "demo.mnu" \: A simple example of program MNU possibilities &\cr
& "demotex.bat", "cfg.mnu", \: &\cr
& "sorry.mnu", "*.bat" \: A more complicated example of em\TeX
configuration &\cr
& "totext.exe", "totext.c" \: Switches the screen to the text mode
$80 \times 25$ &\cr
& "dupcent.exe", "dupcent.c" \: Duplicates {\tt\char37} (utility program)
&\cr
& "kalk.exe", "kalk.hlp" \: The calculator -- an illustration of an
application program
\endtab
\medskip
The software contained in the files listed above is in the public domain.
The author transfers it to the \CSTUG\ association (Czechoslovak
\TeX Users Group) and expects that they will care about its popularization
and further distribution. It is not allowed to utilize these programs
and/or their modifications for commercial purposes. That means, it is not
allowed to sell this software (with the exception of a diskette copying
fee), nor to include it in systems designed merely for commercial purposes.
Since of the first public distribution of this product (Euro-\TeX\ 92)
some unimportant improvements were made. This changes keep full
compatibility with the old configuration files and offers some new
possibilities (see the end of the documentation).
The author will not more change or improve this software, esp.\ its basic
conception. However, he welcomes all suggestions leading to elimination of
errors, which can, unfortunately, appear in any software.
The source code of the MNU program (written in C language) is not public.
\medskip
\noindent\halign{\bf #\hfil &\quad #\hfil\cr
address: & Petr Ol\v s\'ak \cr
& Department of Mathematics \cr
& Faculty of Electrical Engineering \cr
& Czech Technical University \cr
& $\underline{\strut \hbox{166 27 PRAGUE}}$ \cr
& Czech republic \cr
& \cr
email: & {\tt\char60}"[email protected]>" \cr}
\sect 2. Description of the program
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsect 2.1 Start of the program
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The MNU program operates in the $80 \times 25$ text screen mode. If
the screen is switched to another mode, the program can display incorrectly.
In that case, it is recommended first to call the program "totext.exe",
which redefines the screen mode.
In the text mode, the MNU program does not depend on the way, how
nonstandard ASCII characters (national specialities) are represented. All
displayed texts are being read from the configuration file, which is to be
prepared in agreement with the implemented coding. The correct display of
national characters is not a part of the program, so that other technical
means are to be used.
The program is to be called with at least one parameter---the name of the
configuration file (incl. the path if necessary). The other parameters are
optional. These are the names of input and/or output files, and the program
can use them following the commands from the configuration file.
If the program is started without any parameter, it displays an error
message, and terminates returning the error code 255. The same occurs if the
configuration file cannot be opened for reading.
A rule: Whenever the program terminates because of any error, an error
message is displayed and the error code 255 is returned.
\subsect 2.2 Data in the configuration file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The following data are read from the configuration file:
\begitems
* Item texts
* Highlighted letters in item texts
* Item numbers---each item is assigned a number (a positive integer)
* Program action after choosing each item
* Item sequence in each window
* Structure of mutual calling of items
* Type of items (editable or non-editable)
* Explanatory texts in the windows
* Window sizes and their allocation on the screen
* All necessary colour attributes
* Help texts and their relation to individual items
* Sizes, allocations and colours of help windows
* Way of communication with the outer environment (input/output files,
environment variables)
* The hot keys definition
\enditems
There is a lot of other information in the configuration file. For more
details see para 3.
\subsect 2.3 Starting item
%%%%%%%%%%%%%%%%%%%%%%%%%%%
When started, the MNU program presents the item, the number of which
corresponds with the content of the environment variable ``MNU''.
An example of calling the MNU program:
\begtt
set MNU=17
mnu config.mnu
\endtt
In this case, the item with number 17 is presented when the MNU program is
started. (We suppose that such an item is defined in the file
"config.mnu".)
If the starting item belongs to a partial sub-menu involved in the
mutual linkage of windows and items, all ``parent'' windows are opened
automatically before the window with the particular item is opened.
If the environment variable ``MNU'' does not exist or if its content is not
of the type integer, it is considered as having the value zero.
If there is no item defined with the number equal to the content of the MNU
variable in the configuration file, the program displays an error message
and is terminated.
\subsect 2.4 Selection of the item from the keyboard
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Within a window, the user switches the active item by arrows. Pull down
menus are the exception -- left/right arrows cause a jump to the
neighbouring window there (this is to be defined precisely in the configuration
file).
The key "Esc" returns the selection process to the ``parent'' window. If
there is no such window (the active window is the ``root'' of the
structure), then the program finds the item corresponding to the number 0.
In the case such an item is not defined the program is terminated and the
control is returned to DOS with the code 0. If the item exists, the program
opens the corresponding window and offers this item as active. This
procedure allows to configure the window with the last question of the type
``Do you really want to finish?'', when the item with number 0 can contain
the text ``Yes''.
\medskip
There are three possibilities of the "Enter" key reactions:
\begitems
* The next window with items opens. More precisely: the specified item in
the next ``child window'' is offered as active.
* The program terminates its operation, closes all open windows, and
returns the error code equal to the number of the selected item. If the
item number is greater than 254, the programs returns the code 255.
* The program calls the process defined by a single DOS line (so-called
line process calling). In this case, the program resides in the computer
memory, calls the process required, and at the end of this process offers
the next specified item as active.
\enditems
The way of the "Enter" key reaction is defined in the configuration file.
A special type is the so-called ``editable'' item. It allows to do a line
editing right in the place of the item. The result of this editing is
stored in a special buffer for later utilization in the ``line process
calling'' or for including into output files. This way, it is possible to
change the content of DOS environment variables, arrange parameters for a
line process, etc.
The built-in item editor works in the ``insert'' mode only. The keys "Del",
"Backspace" and right/left arrows work as usual. If the first pressed key
is an arrow key, the offered text is edited. Otherwise, the original text
disappears and a new text can be entered. The "Esc" key returns to the
original text, the "Enter" key keeps new text in the buffer and starts the
``item actions'' defined in the configuration file. If the editation process
does not begin the up/down keys can be used to select the required editable
item else up/down keys does not work because it is not specified whether
to confirm ("Enter") or to cancel ("Esc") of the edited text.
The "F1" key calls the help corresponding to the active item. The help
windows are configured in the configuration file, and they can contain,
in any place, further items (highlighted notions), which allow jumping to other
help windows. Thus, a structured help can be defined. The "Esc" key quits
the help. In the case that the help window does not contain any item, the
"Enter" key has the same meaning as the "Esc" key.
If there is a ``highlighted letter'' defined in the item, the item can be
selected by simple touching the key with this letter. The program reaction
is the same as when arrows and the "Enter" key are used.
In the case of any inconsistency in the configuration file (e.g. the number of
the consequential item cannot be found) the error message occurs and the
program terminates.
\subsect 2.5 Selection of the item by the mouse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
If the mouse driver is installed, the mouse cursor appears on the screen.
Pressing the left mouse button causes the selection of the item under the
cursor (the same function as "Enter"). Pressing the same button outside the
window acts similarly as "Esc", i.e. the last opened window is closed. The
right button calls and cancels the help. The middle button has no function.
The program was tested with the ``Genius mouse'' only. It is possible that
other mice could disobey (e.g. the Mickey mouse).
\sect 3. Format of the configuration file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Inspect the content of the file "demo.mnu" or "cfg.mnu". It can serve as an
illustrative example. The following text may be difficult to understand
without parallel keeping the content of that file in view.
\subsect 3.1 The basic structure
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The whole configuration file divides into sections, where attributes and
make-ups of individual windows are defined. Such a section begins with the
character "^" in the first column of the first line. We call this line a
``window-defining line''. The window-defining line is followed
(optionally) by the definition "~param", which is local for the
particular window. The text to be displayed in the window follows. In this
text, individual items, incl. corresponding program actions after a selection
of any of them, are given. The end of the section is in the place of a new
window-defining line, or (not very often) of a global definition
"~param".
Prior to the first window-defining line, there may be arbitrary text
(comment lines), and, next to it, global definitions "~param", "~start",
"~final", "~hotkeys", "~sound", and "~copy". These definitions are written
on separate lines introduced with the character~"~".
Accordingly, the structure of the configuration file is as follows:
\begtt
comment lines (optional)
~global definitions (optional)
^the first window-defining line
~param -- parameters for the first window
text of the window incl. description of items and actions
~param -- global parameters (optional)
other comments (optional)
^the second window define line
... etc.
\endtt
The text of the window may exceed number of lines of the window. The
exceeding lines (in the bottom) are ignored. It is possible to use them for
further comments.
It is not recommended to utilize this place for larger comments. The program
searches data from the configuration file sequentially (line by line), so
that extensive comments could result in a slow-down of the program execution.
It is sensible to locate definitions of more frequent windows at the
beginning. For instance, it is advisable to put helps at the end of the
file.
\subsect 3.2 Active characters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Active are those characters that mark off the structure of the
configuration file. The other characters are usually to be displayed in a
window, or they serve as a comment.
Most of the characters are active only under some conditions. For instance,
the character "~" is active only if in the first column. In another place
it is interpreted as any other text character.
The following table gives the list of the active characters:
\begtab{16em}
& Character && Condition && Meaning & \title
& "^" && in the first column && window-defining line &\cr
& "~" && in the first column && global or local definition &\cr
& "|" && anywhere in the text of the window && marks off the beginning
and/or the end of the item &\cr
& "#" && immediate following the~character~"|" opening an item
&& this item is editable &\cr
& "^" && immediate following the~character~"|" opening an item
&& this item is ``auto-run item'' &\cr
& "!" && immediate following the~character~"|" opening an item
&& marks the highlighted text &\cr
& "^" && inside an item && marks the highlighted letter &\cr
& "{" && immediate following the~character~"|" closing an item
&& the action after the item selection is
defined and close in braces &\cr
& "[%" && in any place && introduces the requirement for a text
substitution
\endtab
This table implies several restrictions on the window texts:
\begitems
* No ``common'' line can begin with the characters "~" or "^" .
* The character "|" cannot be included in the window text. If necessary,
the~character~\vrule\ with the extended ASCII code 179 can be used.
* Inside an item it is impossible to type the character "^" .
* In the whole configuration file you cannot use the pair "[%" -- this
starts an requirement for a text substitution anywhere.
* The text of a non-editable item cannot begin with the characters "!" or
"#"~.
\enditems
The active characters were chosen so as to minimize the restrictions.
\subsect 3.3 Requirements for text substitutions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Anywhere in the text of the configuration file, the following construction
can appear:
\medskip
\indent "[%<NAME>%<LENGTH>]", where the parameter <LENGTH> is optional.
\medskip
This construction is substituted by the content of the environment variable
<NAME>. The length of the corresponding string counts <LENGTH>. It means that
the superfluous characters (to the right) are omitted, if the content is
longer, or the string is completed with blank characters, if the content is
shorter. If the parameter <LENGTH> is not given, the length of the
corresponding string is set equal to the length of the content of the
environment variable.
\medskip
There is another possibility of a text substitution---to substitute a text
from another file. That construction is of the form
"[%<N>% <X>, <Y>, <LENGTH>]". The text from the ``<N>-th file'' is
substituted for this construction. The <N>-th file is that given as the
<N>-th parameter in the command line of the MNU program call.
Further, <Y> is the line number, and <X> the column number of the position
in the file, where the text is to be read from, and <LENGTH> is the length of
the resulting string. The text is being read only from the indicated line,
and is, if necessary, completed with blank characters to the right. If <LENGTH> =
is 0, then the length of the resulting string is equal to the length of the
<Y>-th line in the file (or of its part if $<X> > 1$).
The parameter <LENGTH> is the only optional one; if it is not present, the
program reads the file from the position <X>, <Y> to the end of file (more
than only one line can be read).
{\bf Examples.} We suppose the program to be called in the following
situation:
\begtt
set ENVIN=babble
mnu config.mnu myfile.txt
\endtt
and that the file "myfile.txt" contains the following two lines:
\begtt
experimental text
in two lines containing [%ENVIN%]
\endtt
In the following table the reader can find various examples:
\begtab{20em}
& construction && result & \title
& "[%ENVIN%3] " && "bab" &\cr
& "[%ENVIN%] " && "babble" &\cr
& "[%2% 1, 1, 5] " && "exper" &\cr
& "[%2% 10, 1, 9]" && "tal text " &\cr
& "[%2% 1, 1] " && "experimental text "\hfil\break
"in two lines containing babble" &\cr
& "[%2% 14, 2, 0]" && "containing babble"
\endtab
If the environment variable does not exist, the result of the construction
is blank. The program does not report any error at that moment. For
example, "[%%80]" means 80 spaces.
Similarly, if the file cannot be opened for reading, the result of the
construction is blank.
For security reasons, the program does not allow any construction including a
call of the file with the numbers 0 or 1 (the configuration file calls itself).
The input files can contain the next requirements for text substitution.
A never-ending recursive call of files is treated (for security) in such a
way, that during the eighth attempt to open a new file the program displays
an error (stack overflow), or an attempt to open a file for reading fails
(number of open files is limited in DOS).
If the text substitution construction calls a file containing
other defining lines in its text, then such a construction is to be
situated at the beginning of a line. The program reads only first
characters on each line when scanning the definitions, and does not waste
time with substitutions required in the middle of lines. Such substitutions
are accomplished only when the program needs to read the whole line or the
text of the window.
\medskip
If the global definition "~copy" precedes the first defining line, then all
lines of the configuration file following this line are copied at the
screen. The definition "~copy" does not contain parameters, so that its
format is simply "~copy".
When copying (by "~copy"), text substitutions are performed in agreement
with the above rules. The MNU program finishes its activity when copying
has been accomplished. That means that the definition "~copy" switches the
program into a special mode, when no commands or definitions of the
configuration file are performed, and no items or windows are treated. Only
the character pair "[%" is active there.
Such copying is reasonable particularly when the output is directed not to
the screen, but into a file. This can be reached by an easy command:
\begtt
mnu input next input > output
\endtt
\noindent A utilization of this program mode is possible for making
installation batches and environment handling.
{\catcode`\~=12
\subsect 3.4 Definition "~param"
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
}
The definition begins with the character "~", and its format is as follows:
\begtt
~param {<NUMBERS>} "<HEAD>" ; <COMMENT>
\endtt
The parameters \dd<HEAD>\dd\ and "; <COMMENT>" are optional.
\bull <NUMBERS> -- are integers separated by spaces or
commas. These numbers are arranged in the order
\begtt
{<XMIN>, <YMIN>, <WIDTH>, <HEIGHT>, <FRAME>, <GROUND>, <ITEM>, <LETTER>, <A-ITEM>, <A-LETTER>}
\endtt
\noindent and their meaning is as follows:
{\narrower\parindent=0pt
<XMIN>, <YMIN> -- x and y coordinates of the upper left corner of the
window (incl. the frame if exists)
<WIDTH>, <HEIGHT> -- window width and height (incl. the frame)
<FRAME> -- 0 : no frame, 1 : a simple frame, 2 : a double frame
<GROUND> -- basic text color attribute for the window (0~to~255)
<ITEM> -- text color attribute of inactive items for the window
<LETTER> -- highlighted letter color attribute for inactive items
<A-ITEM>, <A-LETTER> -- similar as <ITEM>, <LETTER>, but for active items
}
\medskip
If less than 10 parameters are given, the other parameters to the right
keep their global or implicit values. If more than 10 numbers are given,
the superfluous numbers (to the right) are ignored.
The wildcard "*" used instead of a parameter leaves the parameter unchanged
with the global or implicit value.
\bull <HEAD> -- text (heading) to overwrite the middle of the window frame
top line. When not present, the frame is not interrupted.
\bull <COMMENT> -- the text separated by a semicolon is ignored.
\medskip
A global definition "~param" is valid for all windows until another global
definition "~param" appears. More exactly, the next global definition
"~param" overwrites some (or all) parameters of window defined here.
On the other hand, a local definition "~param" influences parameters (all
or some of them) only for the particular window.
If neither global nor local definition determine the parameters, they keep
their values predetermined as follows:
\begtt
~param {10, 5, 62, 17, 1, 31, 30, 30, 14, 14}
\endtt
i.e. a blue window approximately in the middle of the screen with a simple
frame and yellow items.
\subsect 3.5 Window-defining line
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
is of the form
\medskip\noindent
" ^(<HELP>) <ITEMS> [<PARENT>] "{\tt\char60}"<L-R>> \ ; <COMMENT>"
\medskip
The types of parameters are identified by the shape of the brackets. The order
of the parameters cannot be changed.
All parameters (incl. brackets), with the only exception of the parameter
<ITEMS>, are optional; the shortest window definition is of the form:
"^ <ITEMS>".
\bull "("<HELP>")" -- if this parameter is present, a window for help is defined.
Be aware: The left parenthesis should immediately follow the character
"^" . <HELP> is a list of item numbers (separated by commas or spaces),
showing where you can call the help window from. For instance, the active
item is 17, and the user hits "F1". Then the program opens such a window,
which has the number 17 given (among others) in parentheses. If no such
window is defined, the program does not report any error, but merely
gives an acoustic signal (see the definition of "~beep" in para 3.8).
If the parameter <HELP> is present, the parameter <ITEMS> is also optional.
\bull <ITEMS> -- a list of item numbers (non-negative integers),
corresponding to the item definitions in the window text. The items follow
in the same order.
If there is less numbers than items in the window text, the superfluous
items have a number given by the last number in the list ``<ITEMS>''.
This implies that more items with the same number can appear without
problems. The search algorithm searches only first item with given number.
If the list ``<ITEMS>'' is empty then the items are without
number (it is possible only in help window).
If there is more numbers than items, the superfluous numbers are ignored.
If the jump to an item with such an ignored number is requested, the window
opens, but no item is active there. The key "Enter" gets the same function
as the key "Esc", and the arrows work only to the right or to the left (and
only under the assumption that the parameter <L-R> is defined).
\bull "["<PARENT>"]" -- is a number defining the ``parent'' item for the
window. If the parameter <PARENT> is given, the program checks, whether the
window with the parent item is open, prior to opening of the particular
window. If the parent window is not open, the program opens it at first.
Thus a tree structure for the menu is given.
\bull {\tt\char60}<L-R>">" -- Two numbers of items, where the program jumps
in the case that the left, resp. the right arrow is pressed. The active
window is closed before the jump. If the parameter <L-R> is not present,
the right/up arrows (as well as the left/down arrows) have the same
meaning.
The parameter <L-R> allows to configure the ``pull-down'' menu, where the
left and the right arrows ``switch sub-menus''.
\bull "\" -- the presence of this character defines the so-called
``automatic closing window''. If the parameter is present then the
window is closed automatic when its ``child window'' is being closed.
Poetic expressed, the parent, having given life to a child, cannot live
longer than his child.
\subsect 3.6 Window and item texts
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The text following the window-defining line is copied line by line into the
window, starting immediately with the first line of the window (except the
local definition "~param"). If the line is longer than the inner width of
the corresponding window (have the frame in mind!), the rest of the line is
ignored.
If there are more lines than the inner height of the window, the
superfluous lines are ignored.
If there are less lines, the window has blank lines in the bottom. Such a
situation can appear also in the case that the program comes across the end
of the configuration file, or across a line beginning with the character
"~" or "^" . Such lines can terminate the copying of the text into the
window.
Copying of item texts to the window is not standard. The copying starts
when the character "|", introducing the item text, is first found. This
character is not copied. If the character "#" resp. "^" resp.~"!" follows
immediately, the item is editable or co called ``auto-run item'' or
highlighted text is to be set respectively (see para 3.9). Otherwise, the
text which follows is copied. If the character "^" appears inside an item,
this character is ignored, and the preceding (attention! not the following)
character is marked as the highlighted letter. Retyping of the item ends,
when the closing character "|" is found; this character is not copied.
The item text can be followed by the character "{" (immediately after the
closing character "|"). Inside the braces, the action in case of the item
selection is given. This definition (incl. braces) is not copied.
If the carriage return character appears inside the item text, the program
displays an error massage and terminates.
\subsect 3.7 Definition of the action after the item selection
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The action, which is to be performed after the selection of the item, can be
defined in braces after the closing character "|" of the item.
This definitions is composed of some commands separated by commas or
spaces. There can be no command at all (then the braces can be omitted).
The list of possible commands is given in the following table:
\begtab{26em}
& command syntax && meaning & \title
& "$"<CODE> && program terminates with given error-code number &\cr
& <NUMBER> && a ``goto'' command -- jump to the item with number
<NUMBER>. If the new item is in a not yet open window, the window is opened
(incl.~the substructure, if necessary). &\cr
& "\" && The character "\" closes an active window. &\cr
& "*" && Closing of all windows on the screen. &\cr
& \dd<TEXT>\dd">"<N>
&& If $<N> = 0$, <TEXT> is called as a DOS line. \hfil\break
If $<N> = 1$, an error is reported.\hfil\break
If $<N> > 1$, <TEXT> is added as the last line into the <N>-th file.
\hfil\break
If <N> is the name of an environment variable, <TEXT> is stored in
it. &\cr
& "!><N>" or {\tt\char37><N>} && <N> is to be $\null > 1$: reset of the
<N>-th file for writing. The contents of this file (if any) is erased.
\endtab
{\bf Remarks.}
\bull The ``goto'' command is to be the last one in the action definition. The
commands are executed in the order from the left to the right, and the ``goto''
command passes the control to the next item, so that the commands given
after it are never executed.
\bull If there is no ``goto'' command (there is no item to take on the control),
the program closes all windows and terminates with the code equal to the
current item number.
\bull The command "\" is equivalent to pressing the "Esc" key. If the
active window is different from the latest opened window, some difficulties
can appear. Such a situation appears if the programmer of the configuration
file does not observe the tree menu structure, and without closing the
windows in question, he jumps somewhere to the middle of the tree
parent-child structure of windows. Then closing of a window gives automatic
cause for closing all windows opened later.
\bull The commands "*" a "\" need not be separated from the others by a
space nor by a comma. Thus, the following notations are equivalent and
cause closing the window and jump to the item number 17:
\nobreak\medskip\noindent
" {\, 17} " or " {\ 17} " or " {\17}"
\bull Before calling a DOS line by the command \dd<TEXT>\dd">0" (the ``line
process calling''), it is senseful to use the command "*". The started
process could scroll down the screen, and thus also all open windows would
be scrolled together. The program MNU would then display objects chaotic on
the screen. A correct example of calling a DOS line follows:
\begtt
{*"dir a:">0, 17}
\endtt
This construction first closes all windows, then executes "dir a:", and
finally opens again all windows up to the item 17.
\bull The command \dd<TEXT>\dd"><N>" ($<N> > 1$) only adds a new line to
the already existing text in the file. If you wish to overwrite the old
contents of the file, use the command "!><N>" at first.
\bull The storing of new value in environment variable is local only during
the MNU program run. If you can set global value of environment variable
then you must open the auxiliary batch file and first you must store
the text "set NAME=value" to this file. After terminating the MNU program
the calling this auxiliary batch implies the setting "value" to the
"NAME" globally.
\bull Commands "!><N>" and {\tt\char37><N>} both reset the <N>-th file. The
difference is in the way of storing the {\tt\char37} character to the file.
The second command invokes the special mode of writing to the file---all
occurrences of characters {\tt\char37} is duplicated. This is useful for
auxiliary batches mentioned above because DOS requires the per cent sign
to be duplicated while batch processing.
\bull Once a file is used as an output one, it cannot be used for an input
any more. A requirement for an input such as "[%<N>%...]" will return a
blank string in such case.
\bull Strings \dd<TEXT>\dd\ can contain the special character "#". The
latest edited text is substituted for this character. This way the results
of editing of items can be passed to the output. See also para 3.9.
{\catcode`\~=12
\subsect 3.8 Global definitions "~hotkeys", "~start", "~final", "~beep", "~mouse"
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
}
The definition "~hotkeys" is of the form
\medskip
" ~hotkeys F<n>{<REACTION>}, ... "
\medskip
\noindent
where <N> is number of function key (in interval 1 to 10) and <REACTION> is
a list of commands to be executed if associate function key is pressed.
The list of commands has the same syntax and semantic as in action after
the item selection, mentioned above in para 3.7. You can define at the most
10 ``hot keys'' using the single "~hotkeys" definition line (separated by
space or comma). If you define the "F1" key by "~hotkeys" definition you
cannot use the help feasibility of the program MNU but for example, you can
call a special and better help program by the ``line process calling''.
\medskip
The definitions "~start" and "~final" can contain in braces the same
commands as possible in the item starting action definitions.
\bull
The definition "~start" introduces a list of commands, that are executed
when the program starts. It is senseful to use e.g. commands
"!><N>" for the output file reset.
If there is a ``goto'' command in the definition "~start", the program jumps to
the given item regardless the contents of the environment variable "MNU".
If there is no ``goto'' command there, the program jumps in agreement with the
contents of the environment variable "MNU".
\bull
The definition "~final" introduces a list of commands, that are executed
when the program terminates without any error, after closing all windows.
That's why some commands are senseless there. The ``goto'' command, as well
as the commands "*", "\", are ignored.
When the commands from the definition "~final" are executed, the symbol
"#" represents the number of the selected item (hexadecimal number as
text). This information can be saved in an output file.
\bull
The definition "~beep" is of the form:
\begtt
~beep {<FREQUENCY>, <DURATION>}
\endtt
\noindent
where <FREQUENCY> defines the frequency of the sound, and <DURATION>
is its duration in~milliseconds. A sound defined this way beeps always when
the user hits a key, which the program is not able to interpret. If the
definition is omitted or if at least one parameter is equal to zero, we get
no sound (which is often better).
\bull In the case that the definition "~mouse" is present with the syntax:
\begtt
~mouse {<REG-CX>, <REG-DX>}
\endtt
\noindent
then the mouse cursor is re-coloured in agreement with your wish by calling
the system service\m
"int 33h"\m with the registers state:\m "AX=10", "BX=1", "CX=<REG-CX>",
"DX=<REG-DX>".\m If this definition is not present, the mouse cursor is red
with white ink in any place (the cursor color is not changed with
changing background colors). This implicit value corresponds to the
definition \m
"~mouse {255, 20224}".
\medskip
The five preceding global definitions have to be stated prior to the first
window-defining line. Otherwise they are ignored.
\subsect 3.9 Editable item, auto-run item and highlighted text in the window
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
An editable item is of the form:
\begtt
|#<TEXT>|{<ACTION>}
\endtt
where
\bull <TEXT> -- is the text offered for editing.
\bull <ACTION> -- is a list of commands to be performed, when the editing
is terminating by the key "Enter" (see para 3.7). Strings of the type
\dd<text>\dd, defined in these commands, can contain the character "#",
for which the result of editing is substituted. For example,
\dd"copy # c:"\dd">0"
means, that the result of editing should be a file name, which is to be
copied to the disk "c:".
\medskip
\vbox{
{\bf Example.} The construction
\begtt
|#[%FILE%8]|{"set FILE=#">2, \17}
\endtt
creates an item, offering the contents of the environment variable "FILE"
(of the length of 8 characters) as the initial text for editing. The text\m
"set FILE="\m followed by the result of editing is then saved in the file
number 2. Finally, the window is closed and the program jumps to the item
number 17.}
Remark. When the item is editable, the closing character "|" is to be
followed by the character "{"; thus if there is no action defined, it is
necessary to write: "{}". This difference from non-editable items is
meaningful: the closing sign of the text to be edited is the pair "|{", so
that there can appear the character "|" in the offered text. This increases
the ability of the program to be ``foolproof''. The offered text is
usually variable -- the result of the last editing. The user would cause
the program collapse only if he entered the pair "|{" or "[%". Taking into
account that the user can input from the keyboard about 100 characters, the
probability of the program collapse due to user's mistake is roughly
2/10000.
\medskip
{\bf The auto-run item} is in the form
\begtt
|^<TEXT>|{<REACTION>}
\endtt
\noindent
where <TEXT> is the text of the item and <REACTION> is definition of
reaction to be immediately processed. More exactly: the <REACTION> is
processed in case that the item is highlighted. No "Enter" pressing is
required. This situation can be occurs in three cases: first, the program
activates this item as first offered item, second, the item is highlighted by
``goto'' command, third, the item is highlighted using arrow keys.
This possibility can be useful for configuring of complicated structures of
windows.
\medskip
{\bf A highlighted text} in the window can be defined in the form:
\begtt
|!<TEXT>|{}
\endtt
The text is displayed in the window colored as an inactive item. In fact,
it is a common text, no item. To be used if we need a two-color text in
the window.
Notice that also here the closing pair "|{" is necessary; it has the same
reason as in the case of an editable item. It is supposed that the
highlighted text can be variable, for example the value of environment
variable.
\sect 4. Error messages and program restrictions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The MNU program performs a syntax check when reading the configuration
file. About 40 errors can appear there; the program displays an error
message. It is not necessary to list all the error messages here; e.g.~if
the message reads\m "'}' expected"\m, we should easy recognize the error.
Moreover, the program displays the line number in the configuration file,
where the error has appeared, and the error line is displayed on the screen
in such a way, that in the place of the error the line is broken, and the rest
of the line continues one line below.
If the error occurs in another operation than reading the configuration
file, the error line with its number are not displayed.
\medskip
Let us discuss only those error messages, that are connected with some
program restrictions.
\bull
"! out of memory"\m
The error occurs if, opening more larger windows one over the other, the
data memory of 64 kB is overflowed. This memory is sufficient for about 7
simultaneously open windows of a full-screen size, which should be
satisfactory, because it is senseless to open full-screen windows one over
the other.
Adding the length of the program and the memory preassumed for its data
structures, we get 88 kB of the memory, i.e.~the space occupied by the
program in the operation memory. One should be aware of it if calling
one-line DOS processes when the program resides in the memory.
\bull
"! maximal number of open windows is out"\m
The maximum number of simultaneously opened windows is 25.
\bull
"! the head is too long"\m
The maximum length of the window heading is 35 characters.
\bull
"! max 25 items in one window is allowed"\m
The maximum number of items in a window is exceeded. Because there are no
more lines on the screen and the items should not be arranged in a matrix
(the program would misinterpret the arrow key control), this limitation is
not important.
\bull
"! the file number in interval 2..9 expected"\m
The number of input/output files is limited to 8 (not counting the
configuration file).
\bull
"! stack of input files overflow"\m
The maximum number of hierarchically open files (i.e.~files, where for a
construction is substituted another file with a construction, substituted
by a further file, etc.) is limited to 8.
\bull
"! the SIZE parameter is too long"\m
The parameter <LENGTH> in the substitution construction is so long that
the maximum length of the input line, i.e.~255 characters, is exceeded.
\sect 5. Examples
%%%%%%%%%%%%%%%%%
In the demo batches you can find some methods and tricks used with the MNU
program. There are two examples.
\subsect 5.1 The first simple example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The first example shows a basic MNU program principles. This example
describes not really application, but the basic principles of program MNU
is clearly shown.
The files used in the example are listed in the following table:
\begtab{20em}
& "demo.bat " \: The control batch &\cr
& "demo.mnu " \: The configuration file &\cr
& "envir.bat" \: The auxiliary batch (it will be created)
\endtab
\noindent{\bf Remarks}
\bull The batch "demo.bat" controls the main loop of application processes.
After terminating the MNU program the batch branches next executing by set
of commands
\begtt
if errorlevel ... goto ...
\endtt
\noindent
One should have in mind that these "if errorlevel" commands must have a
decreasing order of constants ("if errorlevel" does mean ``if errorcode is
greater or equal to'').
\bull Instead of the really application calls there are the "echo" commands
in the control batch "demo.bat" only. You can remove this word ("echo") and
write the really applications.
\bull If the user changes the file name (value of the "FILE" environment
variable), the program MNU writes the line
\begtt
set FILE=<newname>
\endtt
\noindent
into the file "envir.bat" (see file "demo.mnu", line 26). After terminating
of the MNU program the control batch "demo.bat" calls this auxiliary batch
(see line 44 in "demo.bat"). This is a way to set new value to environment
variable globally.
\bull The MNU variable is set to the probably next used item number after
each applications. So that the user can press only the "Enter" key repeatedly
to make the loop "Edit"---"Compile"---"Execute".
\bull After the ``executing of compiler'' the line with test of error code
of compiler is included (see line 29 in "demo.bat"). If the compiler does
not end successfully, the batch sets the value 10 (instead 30) to MNU
variable and this setting influences the next state of MNU program (the
Edit item offers instead the Execute item). This command is commented out
("rem") because the really compiler run does not preceded.
\bull If user press the "Esc" key, the MNU program searches the item with
number zero and the "Quit" item offers.
\subsect 5.2 The second more complicated example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
This is the example of em\TeX\ configuration using the MNU program.
The files listed below are really used in \CS\TeX\ package. In this package
distributed by \CS TUG (Czechoslovak \TeX\ Users Group), the em\TeX\
programs and MNU configuration are included. The MNU configuration is
separated from the \CS\TeX\ package and included as the example here.
\begtab{24em}
& "demotex.bat " \: This batch starts the example &\cr
& "texset.bat " \: Initialization batch &\cr
& "texbat.bat " \: The main loop &\cr
& "texrun.bat", \: &\cr
& "others.bat", \: &\cr
& "prints,bat", \: &\cr
& "metafont.bat" \: The applications batches (called from "texbat.bat") &\cr
& "cfg.mnu " \: The configuration file for menu &\cr
& "sorry.mnu " \: The configuration file for ``sorry-messages'' &\cr
& "texcfg.bat " \: User's configuration &\cr
& "mfbat.bat " \: The auxiliary batch (it can be changed) &\cr
& "gfbat.bat", \: &\cr
& "dos.bat", \: &\cr
& "envir.bat " \: The auxiliary batches (they will be created) &\cr
& "dupcent.exe " \: Duplicates the "%" character (utility program) &\cr
& "totext.exe " \: Sets the screen to text mode (utility program) &\cr
& "kalk.exe " \: Calculator -- a simple application program &\cr
& "kalk.hlp " \: help texts for "kalk.exe" &\cr
& "dupcent.c", \: &\cr
& "totext.c " \: The source codes for utility programs
\endtab
Unfortunately, this example cannot show the applications in really action,
because application programs are other matter and they are not included in
this small MNU package. If you are interested in this problem, you can take
the whole \CS\TeX\ package from public international network archives.
Note that the installation program of this package is based on MNU program
too.
You can run the staring batch "demotex.bat" and try the menu. The helps
are translated from Czech language to English (more exactly to my poor
English and bad English). So, the sense of individual items can be read
from this helps.
The files listed here can be used in various configuration of \TeX\
systems, but some modifications are needed. If you intend to use these
files as a motivation when designing the \TeX\ configuration for your
computer, you will have to modify some parts as your needs can be.
In any case, the files listed here can serve as a source of inspiration. At
least you can find the key to a better understanding the philosophy
of the communication between the control batch and the MNU program there.
The remarks to individual tricks and most important parts of files used in
this example follow here.
\subsect Remarks to "demotex.bat"
\bull There is only one line here---the call of the batch "texset.bat" via
the command "command". The environment variable "COMSPEC" will be expanded
to command "command" including path. The command "command" enlarges the
system environment. Many environment variables will be used.
\bull The "texset.bat" has four parameters. First: the format file name
("csPLAIN" in the example in "demotex.bat"), second: the item text for
\TeX\ executing ("PlainT^eX" in the example), third: the working and main
filename ("%1" in the example) and fourth: the working filename if
different ("%2" in the example).
\bull The ``starting batch'' "demotex.bat" has others names in original
\CS\TeX\ package. For example "plain.bat", "latex.bat" etc. This batches
are placed in directory where the system "PATH" points. So that the user
can call the \TeX\ system from his own current directory by the command
(for instance)
\begtt
latex <filename>
\endtt
\noindent
All working files (".tex", ".dvi", ".log", etc.) will be created in the
current directory.
\subsect Remarks to "texset.bat"
\bull There are "set" commands here to set the environment of em\TeX\
variables and others. Some variables are used only in batches. The field
signed as ``system dependent variables'' includes variables dependent on
disk structure. Note that the first settings are nonstandard in demo-version
of "texset.bat" because only demonstration without special path handling is
done. The really settings can look as following:
\begtt
set TEXDIR=c:\emtex <the main directory with programs>
set TEXDIRCFG=c:\emtex\cfg <the directory with configuration files>
set RAM=e:\temp <ram disk with directory for temporary files>
set EDIT=c:\editors\ne <the main editor>
set SHELL=c:\nc\nc <the file manager>
\endtt
\bull After environment settings the "texset.bat" calls the "texcfg.bat" if
present (see line 57). So that the user can change the default setting in
his own ``configuration batch'' "texcfg.bat" if this file is placed in
current directory.
\bull Some batches and configuration files ("texbat.bat", "cfg.mnu",
"texrun.bat", "mfbat.bat") are copied into RAM disk to increase the speed
(see lines 50--53 in "texset.bat"). This process is skipped in demo version
because the environment variable RAM does not point to RAM disk. (see line
50: ".. goto start").
\bull The "texset.bat" calls the "texbat.bat"---the main loop of
applications (see line 61).
\subsect Remarks to main loop "texbat.bat"
\bull The MNU is called here (compare with "demo.bat" from previous
example). Then the process branches to individual applications or
application batches.
\bull The auxiliary batch "envir.bat" is called after each MNU run to
restore the global environment setting (see line 5).
\bull If the typical file of application is not found the process go to
"sorry" label (line 139) and calls the MNU program with "sorry.mnu"
configuration file to display a message about no-installed program (see
line 80 for instance). This handling is included to control batches because
no all applications may be installed---the installation program of \CS\TeX\
offers many variabilities that no all programs can be installed.
\bull The "texbat.bat" calls directly only some applications, others are
called via application batches. You can compare this batches to
``procedures'' in programming languages.
\subsect Remarks to application batches "texrun.bat", "others.bat",
"prints.bat" and "metafont.bat"
\bull The error code from MNU is still stored and the process branches to
individual applications again.
\bull The ``sorry handling'' is similar as in the "texbat.bat".
\bull The individual application will not work in demo version because they
are not installed.
\bull Some tricks are used here. These tricks are related to em\TeX\
configuration itself and they are not in our first interest while we
are studying the MNU philosophy.
\subsect Remarks to "cfg.mnu" configuration file
By means of questions and answers, we are going to look into some
constructions in the file "cfg.mnu" installed. We focus on those
parts of the file which need not be quite comprehensible even after reading
the documentation through.
\quest Where to look for the item 100 defined in the line " ^ 100 \" (see
line 10).
\answ This item does not exist. It is the case when there are less items
(zero in this place) in the window than set in the definition line of the
window. The window opens if the item is called, but there is no item
active. The window is called as a parent window by the window with the
basic menu (see line 16). Pressing the key "Esc" at the moment when only
the basic menu is offered does not cause a jump to the non-existing item
100, because the window is defined as automatically closeable (the
character "\").
\quest Why is the result of choosing (e.g.~"amstex") in\m "Formats menu"\m
stored not only in the environment variable, but also in the file 2 in the
form\m \dd"set FMT=amstex"\dd">2" (see line 122).
\answ The command\m \dd"csAMSTEX"\dd">FMT"\m has a local character within
the MNU program, and because the next command (i.e.~"*") means closing all
windows and a jump onto the item 61, also the contents of the window with
the non-existing item 100 is restored; it bears information about the
chosen format. On the other hand, the command\m
\dd"set FMT=amstex"\dd">2"\m enables to forward the information about the
chosen format to the control batch via the file 2, i.e.~the file
"envir.bat".
\quest How to make sense of definitions of items in the "Diskette menu"
(lines 172--179).
\answ The environment variable "AR" means the direction of copying (from
or onto the disk), and the variable "D" is the letter of the chosen diskette
drive (either A or B). The batch works with both variables, and therefore
the values as stored in the file "envir.bat" in the form of a command
"set". Moreover, the value "D" is stored also locally, because it is used
when opening the window with the item 105 (there is a variable text reading
"Insert diskette to drive [%D%]" ).
\quest In the window with ``final question'', the numbers in the window definition do
not match with the number of items. Unlike the window 100, there are less
numbers then items (lines 186--189).
\answ The program jumps to the item 0 (i.e.~"Yes") when closing all
windows, that is if "Esc" was pressed in the main menu. The item "No" does
not need to have a number, because the program does not leave it, but the
window with the item 3 is opened.
\quest How to arrange the final question, where "No" is implicitly
offered.
\answ In the window definition, we write e.g.: " ^ 1, 0 "; and in the
control batch, we use the commands "if errorlevel" to ensure that the batch
terminates in the case of "errocode=1".
\quest Why is the item "DOS" solved intricated using the file 3 (i.e. the
auxiliary file "dos.bat", see line 203). Is it not sufficient to call a line process by a
definition: "{*"\dd"#"\dd">0} "?
\answ Yes, it will do. But there is a little defect here. The user would
like to find the last edited value under the item "DOS". We cannot
guarantee it other way than to store this value in a file. The MNU program
should terminate and restart several times before the user wishes to use
the item "DOS" again.
\quest Why are items with the same number in "Print menu" ? (See
line 49.)
\answ Why not? If user chose the item, the error code of program
terminating is set to the number of chosen item and this does not make any
conflict. The batch "print.bat" branches next process by the environment
setting and not only by the error code.
\quest There is an error in the definition of the editable variable in
"METAFONT parameters"!
The line 210
\begtt
METAFONT |#[%4% 31, 1, 66]|{!>4, "[%4% 1, 1, 30]#">4}
\endtt
\hangindent\parindent
means that the program first reads 66 characters of the text from the file 4
("mfbat.bat") and opens the window with editable item.
After editing, the file 4 is reset by the command "!>4". Thus, the
following construction "[%4% 1, 1, 30]" returns a blank string from the
resetted file instead of first 30 characters of the old contents of file
as intended by the programmer of this definition.
\answ Congratulations. If you have succeeded to discover this discrepancy
by yourself, it is evident that you are an attentive reader of the
documentation. The moment, when the substitution in the constructions
"[%...]" is performed, is not stressed there. The substitution is done
during opening the window, and all the text related to the opened window is
kept in the memory in the substituted form. The commands defining the item
reaction are performed only when the item has been chosen by the key
"Enter". These commands are not read from the file, but from the memory,
where the substitutions have been done. Therefore it works properly.
\sect 6. History
%%%%%%%%%%%%%%%%
\noindent
Euro-\TeX-92: The first public version.
\begitems
* User can select between editable items by up/down arrows. (2.4)
* The mouse cursor takes the same place as the highlighted item, when the
program starts.
* Hot-keys definitions F1 to F10. (3.8)
* Explicit error code, when program terminates (the "$" command, 3.7).
* All items has a number now. If there are more items then length of the
list of item numbers, the last number of the list is used. (3.5)
* Special mode for writing files---duplicating per cent sign. (3.7)
* Auto-run items. (3.9)
\enditems
\noindent
The last change: January 1993.
\bye
|
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| 52,975,655
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\[\mathop{\mathrm{g}\/}\nolimits\!\left(ze^{{\pm\pi i}}\right)=\mp\pi ie^{{\mp iz%
}}+\mathop{\mathrm{g}\/}\nolimits\!\left(z\right).\]
|
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| 14,567,810
| 725
|
\bib{1998/haible}
\yr 1998
\mr 2000i:11197
\by Bruno Haible
\by Thomas Papanikolaou
\paper Fast multiprecision evaluation of series of rational numbers
\inbook \cite{1998/buhler}
\pages 338--350
\seeolder \cite{1997/haible}
\url http://cr.yp.to/\allowbreak bib/\allowbreak entries.html#\allowbreak 1998/\allowbreak haible
\endref
|
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|
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| 384,602,134
| 2,700
|
\hypertarget{c__logger_8cpp}{
\section{c\_\-logger.cpp}
\label{c__logger_8cpp}\index{c\_\-logger.cpp@{c\_\-logger.cpp}}
}
\begin{DoxyCode}
00001 \textcolor{comment}{/***************************************************************************}
00002 \textcolor{comment}{ c\_logger.cpp - description}
00003 \textcolor{comment}{ -------------------}
00004 \textcolor{comment}{ begin : Thu May 10 2007}
00005 \textcolor{comment}{ copyright : (C) 2004-2010 Marian VooDooMan Meravy}
00006 \textcolor{comment}{ email : ghostvoodooman -a.T= users (dot) sourceforge.net}
00007 \textcolor{comment}{ ***************************************************************************/}
00008
00009 \textcolor{comment}{/***************************************************************************}
00010 \textcolor{comment}{}
00011 \textcolor{comment}{VooDoo cIRCle - an IRC (ro)bot}
00012 \textcolor{comment}{Copyright (C) 2004-2010 Marian VooDooMan Meravy}
00013 \textcolor{comment}{ (ghostvoodooman -a.T= users (dot) sourceforge.net)}
00014 \textcolor{comment}{}
00015 \textcolor{comment}{This program is free software; you can redistribute it and/or}
00016 \textcolor{comment}{modify it under the terms of the GNU General Public License}
00017 \textcolor{comment}{as published by the Free Software Foundation; either version 2}
00018 \textcolor{comment}{of the License, or (at your option) any later version.}
00019 \textcolor{comment}{}
00020 \textcolor{comment}{This program is distributed in the hope that it will be useful,}
00021 \textcolor{comment}{but WITHOUT ANY WARRANTY; without even the implied warranty of}
00022 \textcolor{comment}{MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the}
00023 \textcolor{comment}{GNU General Public License for more details.}
00024 \textcolor{comment}{}
00025 \textcolor{comment}{You should have received a copy of the GNU General Public License}
00026 \textcolor{comment}{along with this program; if not, write to the Free Software}
00027 \textcolor{comment}{Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.}
00028 \textcolor{comment}{}
00029 \textcolor{comment}{****************************************************************************/}
00030 \textcolor{comment}{}
00031 \textcolor{comment}{/*!}
00032 \textcolor{comment}{ \(\backslash\)file}
00033 \textcolor{comment}{ \(\backslash\)brief Class 'c\_logger'}
00034 \textcolor{comment}{*/}
00035
00036 \textcolor{preprocessor}{#if defined(HAVE\_CONFIG\_H)}
00037 \textcolor{preprocessor}{}\textcolor{preprocessor}{# include <config.h>}
00038 \textcolor{preprocessor}{#endif}
00039 \textcolor{preprocessor}{}
00040 \textcolor{preprocessor}{#include "../utils/memleak.h"}
00041 \textcolor{preprocessor}{#include "../utils/my\_assert.h"}
00042 \textcolor{preprocessor}{#include "../utils.h"}
00043 \textcolor{preprocessor}{#include "../params.h"}
00044
00045 \textcolor{preprocessor}{#include "\hyperlink{c__logger_8h}{c_logger.h}"}
00046 \textcolor{preprocessor}{#include "../compat.h"}
00047 \textcolor{preprocessor}{#include "../utils/precomp.h"}
00048
00049 \textcolor{preprocessor}{#if defined(\_MSC\_VER) || defined(\_\_BORLANDC\_\_)}
00050 \textcolor{preprocessor}{}\textcolor{preprocessor}{# pragma hdrstop}
00051 \textcolor{preprocessor}{}\textcolor{preprocessor}{#endif}
00052 \textcolor{preprocessor}{}
\hypertarget{c__logger_8cpp_source_l00053}{}\hyperlink{classc__logger_aa8093d045d6964e9f9794c669b07ae21_aa8093d045d6964e9f9794c669b07ae21}{00053} \hyperlink{classc__logger_a72de5c25de5247364654ca7d30aaeefb_a72de5c25de5247364654ca7d30aaeefb}{c_logger::c_logger}(\textcolor{keyword}{const} \textcolor{keywordtype}{string}& dir\_global\_logs, \textcolor{keyword}{const} \textcolor{keywordtype}{string}& dir\_module\_logs,
\textcolor{keyword}{const} \textcolor{keywordtype}{string}& custom\_log\_name, \textcolor{keywordtype}{int} default\_scope, \hyperlink{classc__conf}{c_conf}* global\_conf, \hyperlink{classc__conf}{c_conf}* mo
dule\_conf)
00054 : dir\_global\_logs\_(dir\_global\_logs), dir\_module\_logs\_(dir\_module\_logs), custo
m\_name(custom\_log\_name), default\_scope\_(default\_scope), glob\_conf(global\_conf), m
od\_conf(module\_conf),
00055 was\_rotation(false)
00056 \{
00057 \textcolor{keywordflow}{if}(\hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}.length() && \hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}[\hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}.length()-1]
!=FILE\_SLASH\_CH)
00058 \hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}+=\hyperlink{compat_8h_ab14dfc779b4bb7887f3e1f5ba6898d13_ab14dfc779b4bb7887f3e1f5ba6898d13}{FILE_SLASH};
00059 \textcolor{keywordflow}{if}(\hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}.length() && \hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}[\hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}.length()-1]
!=FILE\_SLASH\_CH)
00060 \hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}+=\hyperlink{compat_8h_ab14dfc779b4bb7887f3e1f5ba6898d13_ab14dfc779b4bb7887f3e1f5ba6898d13}{FILE_SLASH};
00061 \}
00062
\hypertarget{c__logger_8cpp_source_l00063}{}\hyperlink{classc__logger_a6ab6372405f1612df81cf40a5eab5418_a6ab6372405f1612df81cf40a5eab5418}{00063} \hyperlink{classc__logger_a72de5c25de5247364654ca7d30aaeefb_a72de5c25de5247364654ca7d30aaeefb}{c_logger::c_logger}(\textcolor{keyword}{const} \hyperlink{classc__logger}{c_logger}& orig)
00064 \{
00065 \hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}=orig.\hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_};
00066 \hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}=orig.\hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_};
00067 \hyperlink{classc__logger_ae1dc4cdf6ff0381706caf9df6551aa6a_ae1dc4cdf6ff0381706caf9df6551aa6a}{custom_name}=orig.\hyperlink{classc__logger_ae1dc4cdf6ff0381706caf9df6551aa6a_ae1dc4cdf6ff0381706caf9df6551aa6a}{custom_name};
00068 \hyperlink{classc__logger_af3defffa9171ef809901ae6d658838a9_af3defffa9171ef809901ae6d658838a9}{default_scope_}=orig.\hyperlink{classc__logger_af3defffa9171ef809901ae6d658838a9_af3defffa9171ef809901ae6d658838a9}{default_scope_};
00069
00070 \textcolor{comment}{// do NOT copy-construct these 2 classes! just copy the pointers!}
00071 \hyperlink{classc__logger_abdc10e827c4cb4b906a4f59e5ec7e815_abdc10e827c4cb4b906a4f59e5ec7e815}{glob_conf}=orig.\hyperlink{classc__logger_abdc10e827c4cb4b906a4f59e5ec7e815_abdc10e827c4cb4b906a4f59e5ec7e815}{glob_conf};
00072 \hyperlink{classc__logger_a440f0fc6b7433a7949f165e564add05b_a440f0fc6b7433a7949f165e564add05b}{mod_conf}=orig.\hyperlink{classc__logger_a440f0fc6b7433a7949f165e564add05b_a440f0fc6b7433a7949f165e564add05b}{mod_conf};
00073
00074 \hyperlink{classc__logger_a4c2ee4d34730a61200c55be69cc93521_a4c2ee4d34730a61200c55be69cc93521}{was_rotation}=orig.\hyperlink{classc__logger_a4c2ee4d34730a61200c55be69cc93521_a4c2ee4d34730a61200c55be69cc93521}{was_rotation};
00075 \}
00076
\hypertarget{c__logger_8cpp_source_l00077}{}\hyperlink{classc__logger_a3c27e3a6cbd4ac4c34c1f2c2e7d34941_a3c27e3a6cbd4ac4c34c1f2c2e7d34941}{00077} \textcolor{keywordtype}{void} \hyperlink{classc__logger_a3c27e3a6cbd4ac4c34c1f2c2e7d34941_a3c27e3a6cbd4ac4c34c1f2c2e7d34941}{c_logger::init}(\textcolor{keyword}{const} \textcolor{keywordtype}{string}& dir\_global\_logs, \textcolor{keyword}{const} \textcolor{keywordtype}{string}& dir\_module\_logs,
\textcolor{keyword}{const} \textcolor{keywordtype}{string}& custom\_log\_name, \textcolor{keywordtype}{int} default\_scope, \hyperlink{classc__conf}{c_conf}* global\_conf, \hyperlink{classc__conf}{c_conf}* m
odule\_conf)
00078 \{
00079 \hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}=dir\_global\_logs;
00080 \hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}=dir\_module\_logs;
00081 \hyperlink{classc__logger_ae1dc4cdf6ff0381706caf9df6551aa6a_ae1dc4cdf6ff0381706caf9df6551aa6a}{custom_name}=custom\_log\_name;
00082
00083 \textcolor{keywordflow}{if}(\hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}.length() && \hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}[\hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}.length()-1]
!=FILE\_SLASH\_CH)
00084 \hyperlink{classc__logger_af49856e960f61a55b0fc2fa906c9d7e9_af49856e960f61a55b0fc2fa906c9d7e9}{dir_global_logs_}+=\hyperlink{compat_8h_ab14dfc779b4bb7887f3e1f5ba6898d13_ab14dfc779b4bb7887f3e1f5ba6898d13}{FILE_SLASH};
00085 \textcolor{keywordflow}{if}(\hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}.length() && \hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}[\hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}.length()-1]
!=FILE\_SLASH\_CH)
00086 \hyperlink{classc__logger_a747c895df9941f40f84e5db939ad72bd_a747c895df9941f40f84e5db939ad72bd}{dir_module_logs_}+=\hyperlink{compat_8h_ab14dfc779b4bb7887f3e1f5ba6898d13_ab14dfc779b4bb7887f3e1f5ba6898d13}{FILE_SLASH};
00087
00088 \hyperlink{classc__logger_af3defffa9171ef809901ae6d658838a9_af3defffa9171ef809901ae6d658838a9}{default_scope_}=default\_scope;
00089
00090 \hyperlink{classc__logger_abdc10e827c4cb4b906a4f59e5ec7e815_abdc10e827c4cb4b906a4f59e5ec7e815}{glob_conf}=global\_conf;
00091 \hyperlink{classc__logger_a440f0fc6b7433a7949f165e564add05b_a440f0fc6b7433a7949f165e564add05b}{mod_conf}=module\_conf;
00092 \}
00093
\end{DoxyCode}
|
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|
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| 200,210,644
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\documentclass[10pt,a4paper]{article}
% Packages
\usepackage{fancyhdr} % For header and footer
\usepackage{multicol} % Allows multicols in tables
\usepackage{tabularx} % Intelligent column widths
\usepackage{tabulary} % Used in header and footer
\usepackage{hhline} % Border under tables
\usepackage{graphicx} % For images
\usepackage{xcolor} % For hex colours
%\usepackage[utf8x]{inputenc} % For unicode character support
\usepackage[T1]{fontenc} % Without this we get weird character replacements
\usepackage{colortbl} % For coloured tables
\usepackage{setspace} % For line height
\usepackage{lastpage} % Needed for total page number
\usepackage{seqsplit} % Splits long words.
%\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem} % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath} % Symbols
\usepackage{MnSymbol} % Symbols
\usepackage{wasysym} % Symbols
%\usepackage[english,german,french,spanish,italian]{babel} % Languages
% Document Info
\author{romangrankin}
\pdfinfo{
/Title (ukr-eng-medical-phone-conversations-1.pdf)
/Creator (Cheatography)
/Author (romangrankin)
/Subject (Ukr - Eng Medical phone conversations 1 Cheat Sheet)
}
% Lengths and widths
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\addtolength{\textheight}{-1cm}
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\renewcommand{\arraystretch}{1.3}
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% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
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% Font and Colours
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\color{TextColor}
% Header and Footer
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\fancyhead{} % Set header to blank
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
\SetRowColor{DarkBackground}
\vspace{-7pt}
{\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
\hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
}
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
\vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Ukr - Eng Medical phone conversations 1 Cheat Sheet}}}} \\
\normalsize{by \textcolor{DarkBackground}{romangrankin} via \textcolor{DarkBackground}{\uline{cheatography.com/123196/cs/23130/}}}
\end{tabulary}
\end{multicols}}
\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
\SetRowColor{FootBackground}
\mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\
\vspace{-2pt}romangrankin \\
\uline{cheatography.com/romangrankin} \\
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
\SetRowColor{FootBackground}
\mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\
\vspace{-2pt}Published 8th June, 2020.\\
Updated 15th June, 2020.\\
Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
\SetRowColor{FootBackground}
\mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\
\SetRowColor{white}
\vspace{-5pt}
%\includegraphics[width=48px,height=48px]{dave.jpeg}
Measure your website readability!\\
www.readability-score.com
\end{tabulary}
\end{multicols}}
\begin{document}
\raggedright
\raggedcolumns
% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.
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\begin{tabularx}{5.377cm}{x{1.69218 cm} x{3.28482 cm} }
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♀ female & жіночий \tn
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% Row 1
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♂ male & чоловічий \tn
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– hypen & дефіс \tn
% Row Count 15 (+ 1)
% Row 9
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‰ permille & проміле \tn
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% Row Count 18 (+ 2)
% Row 11
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' apostrophe & апостроф \tn
% Row Count 19 (+ 1)
% Row 12
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@ at-sign & собачка \tn
% Row Count 20 (+ 1)
% Row 13
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\# pound, hash & решітка \tn
% Row Count 21 (+ 1)
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— dash & тире \tn
% Row Count 22 (+ 1)
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⌘ looped square & квадрат з петельками \tn
% Row Count 24 (+ 2)
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/ (forward) slash & скісна риска \tn
% Row Count 26 (+ 2)
% Row 17
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\textbackslash{} backslash & обернена скісна риска \tn
% Row Count 28 (+ 2)
% Row 18
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␣ space & пробіл \tn
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pancreas & підшлункова залоза \tn
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small intestine & тонка кишка \tn
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Gnawing & гризуща \tn
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bloated & роздутий \tn
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shiver & тремтіння \tn
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oxygen & кисень \tn
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pass out & \seqsplit{непритомніти} \tn
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yawn & позіхати \tn
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pill & таблетки \tn
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\par\addvspace{1.3em}
% That's all folks
\end{multicols*}
\end{document}
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https://ctan.math.washington.edu/tex-archive/info/examples/lb2/A-1-9.ltx
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washington.edu
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%%
%% Der LaTeX-Begleiter, zweite Auflage (September 2005)
%%
%% Beispiel A-1-9 von Seite 883.
%%
%% Copyright (C) 2005 Frank Mittelbach, Michel Goossens,
%% Johannes Braams, David Carlisle, and Chris Rowley
%%
%% Uebersetzung: Copyright (C) 2005 Claudia Krysztofiak,
%% Rebecca Stiels und Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
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http://www.ipm.ac.ir/papers/pdf/abs7394.tex
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\documentclass[12pt]{article}
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In this paper, by using the theory of Gorenstein dimension, we
study the uniform annihilation theorem for local cohomology
modules over a (not necessary finite dimensional) Noetherian
Gorenstein ring.
\end{document}
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https://melusine.eu.org/syracuse/B/BaseCollege/Sixieme/axesym/notion/exo50.tex?enregistrement=ok
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eu.org
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%@metapost:6axesymexo50.mp
%@Auteur:Véronique Glaçon\par
Complète le dessin suivant afin que la droite $(d)$ soit un axe de
symétrie.
\[\includegraphics{6axesymexo50.1}\]
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http://ftp.uni-hannover.de/tex-archive/info/tex-primer_vms-specific/e.tex
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uni-hannover.de
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% Save file as: E.TEX Source: [email protected]
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https://www.tug.org/PSTricks/Examples/Gallery/exa106.tex
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https://mirror.anarhija.net/bibliotecaanarchica.org/mirror/s/sc/scritto-contro-marx.tex
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anarhija.net
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\title{Scritto contro Marx}
\date{1872}
\author{Michail Bakunin}
\subtitle{}
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\chapter{Nota introduttiva}
Bakunin tira fuori le sue armi migliori, finalmente, per attaccare Marx e il gruppo di potere che si era insediato nell’Internazionale. In queste pagine è finito il tempo delle illusioni e delle collaborazioni, le critiche sono chiare e dirette.
Una volta aveva detto che bisognava separare le grandi capacità analitiche di Marx, la sua preparazione filosofica ed economica, la quale poteva essere utilizzata anche dagli anarchici (invero in questo campo endemicamente carenti) e per il resto lo si poteva mettere tra parentesi. Adesso affronta le trame intestine, le calunnie, le chiacchiere di corridoio, i soppesamenti dietro le quinte, le correnti di potere, le meschinerie personali, e tutto quel bagaglio che in una parola si potrebbe definire come “politica”. Semplicemente politica, l’arte di far fare agli altri quello che questi non vogliono fare. E così scopriamo che Marx, prima ancora di essere filosofo ed economista (la grandezza in questi campi è faccenda opinabile), è un politico, un piccolo uomo, un Talleyrand in sedicesimo, rinchiuso nella cucina di casa sua a rimestare le sue carte sul suo sudicio tavolo, sognando di governare il mondo.
Ecco, che l’ombra delle mie antiche, fruttuose, letture del marchese Pareto, feroce reazionario, venga qua beneficata di un doveroso ricordo. Marx era proprio questo, e i suoi seguaci moderni e, insisto nel precisare, modernissimi (si fa per dire), lo sono altrettanto.
Che il coraggio di Bakunin, finalmente da lui preso a due mani, ci serva da utile strumento per saperci comportare di fronte a tanti fracassoni odierni che del loro antico predecessore non hanno in mano che la bieca ottusità politica.
Andiamo avanti.
\bigskip
Trieste, 26 aprile 2014
\begin{flushright}
Alfredo M. Bonanno
\end{flushright}
\clearpage
\begin{quote}
“L’uomo non è a tutte le ore ugualmente morale, questo si sa, se si giudica la sua moralità dalla capacità di sacrificio di sé e di risoluzioni grandi e altruistiche, cosa che, se costante e abituale, costituisce la santità, egli è sommamente morale nell’affetto, la più intensa emozione gli arreca motivi affatto nuovi, dei quali, se calmo e distaccato come al solito, egli forse nemmeno si crederebbe capace. Come accade ciò? Probabilmente per la vicinanza di tutto quanto è grande ed eccitante, se l’uomo è portato a una tensione eccezionale, può decidersi sia per una terribile vendetta sia per una rottura terribile del suo bisogno di vendetta. Sotto l’effetto di una potente emozione, egli vuole in ogni caso il grande, il violento, l’immenso, e se per caso nota che il sacrificio di sé lo soddisfa altrettanto, o ancora più, del sacrificio dell’altro, egli sceglie quello. In effetti, dunque, gli preme soltanto scaricare la sua emozione, allora, per alleviare la sua tensione, egli può bene afferrare le lance dei suoi nemici e affondarsele in petto. Che nel rinnegare se stessi, e non soltanto nel vendicarsi, ci sia qualcosa di grande, poté essere instillato nell’umanità solo da una lunga consuetudine, una divinità che sacrifica se stessa fu il simbolo più evidente ed efficace di questo tipo di grandezza. Come vittoria sul nemico più difficile a vincersi, come subitaneo dominio di un affetto, tale appare questo rinnegamento, e, in tale senso, esso è considerato anche il culmine della moralità”.
\begin{flushright}
Friedrich Nietzsche
\end{flushright}
\end{quote}
\chapter{Scritto contro Marx}
\dots{} [per] uno sfruttamento e necessariamente anche per una comprensione solidale attraverso tutte le frontiere di tutti i paesi, e malgrado tutte le differenze politiche attualmente esistenti tra molti Stati.
Essendo solidale lo sfruttamento borghese, deve esserlo altrettanto la lotta contro di esso; e l’organizzazione di questa solidarietà militante tra i lavoratori del mondo intero, è il fine unico dell’Internazionale. Questo fine, così semplice e così ben espresso dai nostri statuti generali originari [Per “statuti generali e primitivi” Bakunin intende gli statuti adottati al primo Congresso dell’A.I.T., Ginevra 1866], i soli legittimi ed i soli obbligatori per tutti i membri, sezioni e federazioni dell’Internazionale, ha riunito sotto l’insegna di questa Associazione, nello spazio di otto anni appena, ben più di un milione di aderenti, e ne ha fatto una reale potenza; una potenza della quale i monarchi più potenti della terra si vedono oggi costretti a tenere conto.
Ma ogni potenza attira gli ambiziosi, e i sigg. Marx e compagni che, forse, non si sono mai resi conto della natura e delle cause di questa potenza così giovane e insieme così prodigiosa dell’Internazionale, si sono immaginati che avrebbero potuto servirsene da trampolino o come uno strumento per la realizzazione delle loro pretese politiche. Il sig. Marx, che è stato uno dei fondatori principali dell’Internazionale, – ecco un attestato di gloria che nessuno gli contesterà – e che, per otto anni di seguito, ha costituito quasi da solo tutto il Consiglio generale, avrebbe dovuto comprendere tuttavia, meglio di chiunque, due cose che saltano agli occhi, e che solo l’accecamento inerente all’ambizione vanitosa ha potuto fargli disconoscere:
1° Che l’Internazionale non ha potuto svilupparsi ed estendersi in una maniera così meravigliosa perché ha eliminato dal suo programma \emph{ufficiale ed obbligatorio} tutte le questioni politiche e filosofiche; e 2° che essa non ha potuto farlo perché, fondata principalmente sulla libertà delle sezioni e delle federazioni, era stata privata di tutti i vantaggi di un governo centralizzatore, capace di dirigere, cioè, d’impedire e di paralizzare, il suo sviluppo; non essendo stato, fino al 1870, precisamente nel periodo del più grande sviluppo dell’Associazione il Consiglio generale che una specie di re d’Yvetot, che ragiona sempre a cose fatte, e lasciandosi, non per mancanza di pretese ambiziose, ma per impotenza e perché nessuno lo avrebbe ascoltato, trascinare a rimorchio del movimento spontaneo dei lavoratori del Belgio, della Francia, della Svizzera, della Spagna e dell’Italia.
In quanto alla questione politica, tutti sanno che, se essa è stata eliminata dal programma dell’Internazionale, non è certo per colpa del sig. Marx. Come ci si doveva attendere da parte dell’autore del famoso programma dei comunisti tedeschi, pubblicato nel 1848 da lui e dal suo amico, confidente e complice, il sig. Engels, non ha affatto mancato di porre questa questione al primo posto nel proclama inaugurale pubblicato nel 1864 dal Consiglio generale provvisorio di Londra, proclama di cui Marx è stato l’unico autore. In questo proclama o circolare indirizzata ai lavoratori di tutti i paesi, il capo dei comunisti autoritari della Germania non si è affatto fatto scrupolo di dichiarare che \emph{la conquista del potere politico} era il primo dovere dei lavoratori; ha svelato anche la sua natura \emph{pangermanista}, aggiungendo che attualmente lo scopo politico principale dell’Associazione Internazionale dei Lavoratori doveva essere quello di combattere l’Impero di tutte le Russie, scopo senza dubbio molto legittimo e molto nobile, il quale, come amico del popolo russo, sottoscrivo di tutto cuore, persuaso come sono che questo popolo non cesserà d’essere uno schiavo miserabile finché questo Impero esisterà, – ma che, per prima cosa, non potrebbe divenire, senza snaturarne completamente il carattere e l’oggetto, quello dell’Associazione Internazionale dei Lavoratori; e che, in secondo luogo, per essere posto in un modo veramente giusto, serio ed utile per la causa dei Lavoratori, dovrebbe essere determinato in un altro modo. Se il sig. Marx avesse dichiarato guerra a tutti gli Stati, o almeno agli Stati monarchici, dispotici, militari come la Prussia, come l’Austria, come la Francia imperiale o anche repubblicana attuale, e se avesse detto che occorreva mettere al primo posto fra questi lo Stato modello, l’Impero di tutte le Russie, almeno non lo si sarebbe potuto accusare di pangermanesimo. Ma facendo astrazione del dispotismo tedesco, un dispotismo molto insolente, molto brutale, molto ingordo, ed eccessivamente minaccioso per la libertà dei popoli vicini, come tutti possono vederlo oggi, e sforzandosi di rivolgere l’indignazione dei lavoratori di tutti i paesi contro il dispotismo russo, escludendo tutti gli altri, pretendendo pure che esso era la sola causa di quello che non ha mai cessato di regnare in Germania, da quando vi è una Germania; rigettando infine tutte le onte e tutti i crimini politici di questo paese dalla scienza e dall’obbedienza proverbiali sulle ispirazioni della diplomazia russa, il sig. Marx si è manifestato prima come un cattivo e poco veridico storico, e poi non come un rivoluzionario socialista internazionale, ma come un ardente patriota della grande patria bismarckiana.
È risaputo che il primo Congresso dell’Internazionale, tenutosi a Ginevra nel 1866, ha fatto giustizia di tutte queste velleità politiche e patriottiche di colui che si pone oggi da dittatore della nostra grande Associazione. Non ne è restato nulla nel programma né negli statuti votati da questo Congresso e che costituiscono ormai la base dell’Internazionale. Datevi la pena di rileggere i magnifici considerando che si trovano in testa dei nostri statuti generali, non vi troverete che queste parole in cui sia fatta menzione della questione politica:
“Considerando:
“Che l’emancipazione dei lavoratori deve essere l’opera dei lavoratori stessi; che gli sforzi dei lavoratori per conquistare la loro emancipazione non devono tendere a costituire nuovi privilegi, ma a stabilire per tutti gli stessi diritti e gli stessi doveri;
“Che l’asservimento del lavoratore al capitale è l’origine di ogni servitù \emph{politica}, morale e materiale;
“Che, per questa ragione, \emph{l’emancipazione economica dei lavoratori è il grande fine al quale deve essere subordinato ogni movimento politico}”, ecc.
Ecco la frase decisiva di tutto il programma dell’Internazionale. Essa ha tagliato il cavo, per servirmi della memorabile espressione di Sieyès, ha spezzato i legami che tenevano incatenato il proletariato alla politica borghese. Riconoscendo la verità che essa esprime e convincendosene ogni giorno di più, il proletariato ha risolutamente girato le spalle alla borghesia, ed ogni passo che farà in avanti allargherà di più l’abisso che ormai li separa.
L’Alleanza, sezione dell’Internazionale a Ginevra, aveva tradotto e commentato questo paragrafo dei considerando in questi termini:
“L’Alleanza respinge \emph{ogni azione politica che avrà come scopo immediato e diretto il trionfo dei lavoratori contro il capitale}”; in conseguenza di ciò, essa si pone per scopo l’abolizione dello Stato, di tutti gli Stati, e l’organizzazione de “l’associazione universale di tutte le associazioni locali mediante la libertà”.
Di contro, il Partito della democrazia socialista degli operai tedeschi, fondato nello stesso anno (1869), sotto gli auspici dei sig. Marx, dai sigg. Liebknecht e Bebel, annunciava nel suo programma che \emph{la conquista del potere politico era la condizione preliminare dell’emancipazione economica del proletariato}, e che, di conseguenza, l’obiettivo immediato di questo partito doveva essere l’organizzazione di una larga agitazione legale per la conquista del suffragio universale e di tutti gli altri diritti politici; il suo scopo finale è la costituzione di un grande Stato pangermanico e sedicente popolare.
Tra queste due tendenze, lo si vede, esiste la stessa differenza, lo stesso abisso, che [esiste] tra il proletariato e la borghesia. C’è forse da stupirsene dopo ciò che esse si siano misurate nell’Internazionale come degli avversari irriconciliabili, e che esse continuino a combattersi, sotto tutte le forme e in tutte le occasioni possibili, ancora oggi? L’Alleanza, prendendo sul serio il programma dell’Internazionale, aveva respinto con sdegno ogni patteggiamento con la politica borghese, per quanto radicale si dica e per quanto da socialista essa si trucchi, raccomandando al proletariato come la sola via dell’emancipazione reale, come la sola politica per lui veramente salutare, la politica esclusivamente negativa della distruzione delle istituzioni politiche, del potere politico, del governo in generale, dello Stato, e, come necessaria conseguenza, l’organizzazione internazionale delle forze sparse del proletariato in una potenza rivoluzionaria diretta contro tutte le potenze costituite della borghesia.
I democratici socialisti della Germania raccomandano, interamente al contrario, ai lavoratori che hanno la disgrazia di ascoltarli, di adottare, come scopo immediato della loro associazione, l’agitazione legale per la conquista preliminare dei diritti politici; essi subordinano, con ciò, il movimento per l’emancipazione economica al movimento innanzitutto esclusivamente politico, e, tramite questo ostensibile rovesciamento di tutto il programma dell’Internazionale, hanno colmato in un sol colpo l’abisso che essa aveva aperto tra il proletariato e la borghesia. Essi hanno fatto più di questo, hanno attaccato il proletariato a rimorchio della borghesia. Perché è evidente che tutto questo movimento politico esaltato dai socialisti della Germania, poiché deve precorrere la rivoluzione economica, non potrà essere diretto che da dei borghesi, o, ciò che sarà ancora peggio, \emph{da degli operai trasformati per la loro ambizione, o per la loro vanità in borghesi}; e passando, in realtà, e come tutti i suoi predecessori, sopra la testa del proletariato, questo movimento non potrà evitare di condannare nuovamente quest’ultimo a non essere che uno strumento cieco e infallibilmente sacrificato nella lotta dei diversi partiti borghesi fra loro per la conquista del potere politico, cioè della potenza e del diritto di dominare sulle masse e di sfruttarle. A chiunque potrebbe dubitarne, noi non dovremmo che mostrare ciò che succede oggi in Germania, dove gli organi della democrazia socialista cantano inni di allegria vedendo un Congresso di professori d’economia politica borghese raccomandare al proletariato della Germania l’alta e paterna protezione degli Stati, e nelle parti della Svizzera in cui prevale il programma marxiano, a Ginevra, a Zurigo e a Basilea, dove l’Internazionale è decaduta al punto di non essere altro che una specie di urna elettorale a profitto dei borghesi radicali. Questi fatti incontestabili mi sembrano più eloquenti di ogni parola.
Essi sono reali, e sono logici nel senso che sono un effetto naturale del trionfo della propaganda marxiana. Ed è per questo che noi combattiamo le teorie marxiane ad oltranza, convinti che se esse avessero trionfato in tutta l’Internazionale, non avrebbero mancato di ucciderne almeno lo spirito ovunque, come hanno già fatto in grandissima parte in quei paesi che ho appena citato.
Noi abbiamo senza dubbio deplorato molto e continuiamo a deplorare profondamente oggi l’immenso scompiglio e demoralizzazione che queste idee pangermaniche hanno gettato nello sviluppo così bello, così meraviglioso e così naturalmente trionfante dell’Internazionale. Ma nessuno di noi ha mai pensato d’interdire a Marx, né ai suoi troppo fanatici discepoli, di propagarle in seno della nostra grande Associazione. Avremmo creduto di venir meno al suo principio fondamentale, che è quello della \emph{libertà più assoluta della propaganda sia politica che filosofica}.
L’Internazionale non ammette censure, né \emph{verità ufficiali} in nome delle quali si potrebbe esercitare questa censura; essa non le ammette, perché mai fino ad ora si era posta né come Chiesa, né come Stato, ed è precisamente perché non l’ha fatto che ha potuto sbalordire il mondo per l’incredibile rapidità della sua estensione e del suo sviluppo.
Ecco ciò che il Congresso di Ginevra, ispirato meglio che il sig. Marx, aveva capito. Eliminando dal suo programma tutti i princìpi politici e filosofici, non come oggetti di discussione e di studio, ma in quanto \emph{princìpi obbligatori}, ha fondato la potenza della nostra Associazione.
È vero che nel secondo Congresso dell’Internazionale, tenutosi nel 1867 a Losanna, degli amici sventurati, non degli avversari, non rendendosi ancora ben conto della vera natura della potenza di questa Associazione, avevano provato a rimettere sul tappeto la questione politica. Ma molto fortunatamente essi non giunsero che a questa dichiarazione platonica, che \emph{la questione politica era inseparabile dalla questione} \emph{economica} – una dichiarazione che ognuno di noi può sottoscrivere, perché è evidente che la politica, cioè l’istituzione ed i mutui rapporti degli Stati, non ha altro scopo che di assicurare alle classi governanti lo sfruttamento legale del proletariato, da cui risulta che dal momento che il proletariato vuole emanciparsi, è costretto a prendere in considerazione la politica, per combatterla e per rovesciarla. Non è così che l’intendono i nostri avversari; ciò che hanno voluto e ciò che vogliono, è la politica positiva, la politica dello Stato. Ma non avendo trovato il terreno favorevole a Losanna, essi vi si erano saggiamente astenuti.
La stessa saggezza li aveva ispirati un anno più tardi al Congresso di Bruxelles. D’altronde il Belgio, comunalista, anti-autoritario e anticentralista per tutta la sua storia, non offriva loro nessuna probabilità di successo e, ancora una volta, si sono saggiamente astenuti.
Tre anni di sconfitta! Fin troppo per l’ambizione impaziente del sig. Marx. Così ordinò al suo esercito un attacco diretto, che in effetti fu eseguito al Congresso di Basilea (1869). Le probabilità gli sembravano favorevoli. Il Partito della democrazia socialista aveva avuto il tempo di organizzarsi in Germania sotto la direzione dei sigg. Liebknecht e Bebel, e aveva esteso le sue ramificazioni nella Svizzera tedesca, a Zurigo, a Basilea, e anche fino nella Sezione tedesca di Ginevra. Era per la prima volta che dei delegati della Germania si presentavano in un numero molto grande in un Congresso dell’Internazionale. Il piano di battaglia, approvato dal sig. Marx, il generale in capo dell’esercito, era stato combinato fra il sig. Liebknecht, capo del corpo tedesco, e i sigg. [Karl] Bürkli e [Herman] Greulich, comandanti del corpo svizzero; i sigg. Amand Goegg, Philippe Becker e [M.] Rittinghausen – l’inventore della votazione diretta delle leggi e delle costituzioni da parte del popolo, il plebiscitario tedesco –, si disposero da parte loro come degli ausiliari volontari. (La Lega borghese della Pace e della Libertà, rappresentata da quel brillante campione della democrazia borghese, e il comunismo autoritario del sig. Marx si erano dati la mano e si erano fraternamente abbracciati sul terreno politico, come del resto bisognava attendersi). In più ebbero dalla loro parte alcuni tedeschi del Consiglio generale, infeudati alla politica del sig. Marx, e alcuni inglesi dello stesso Consiglio che ignoravano completamente la questione, ma che votarono con i marxiani come conseguenza di una cattiva abitudine di cui sembrano essersi completamente disfatti oggi.
Così organizzati, i marxiani impegnarono la grande battaglia e la persero. La questione della \emph{legislazione diretta da parte del popolo}, posta dal sig. Bürkli, difesa con molto calore e molta insolenza contro di noi dal sig. Liebknecht, con molta reticenza diplomatica dal sig. Philippe Becker, che non ama mai pronunciarsi chiaramente prima di sapere da quale lato sta la vittoria, e con un’enfasi eroica dal sig. Amand Goegg, fu affossata e eliminata di fatto dal programma del Congresso. Fu una sconfitta memorabile per il sig. Marx, una sconfitta che non ci perdonerà mai.
La sua collera fu molto grande, e se ne conoscono tutte le conseguenze oggi. Fu dopo il settembre del 1869 che il Consiglio generele – o piuttosto il sig. Marx, quos ego di quel povero Consiglio –, uscendo dal suo torpore obbligato e così salutare per l’Internazionale, intraprese una politica militante. Si sa come essa si manifestò all’inizio. Fu un torrente d’ingiurie ignobili e di odiose calunnie versate contro tutti coloro che avevano osato combatterlo, e diffuse tramite i giornali in Germania, e negli altri paesi con delle lettere intime, con delle circolari confidenziali e con ogni sorta di agenti guadagnati in un modo o nell’altro alla causa del sig. Marx. Venne poi la Conferenza di Londra (1871), che, preparata da molto tempo dal sig. Marx, votò tutto ciò che egli volle: e la questione politica, la conquista del potere da parte del proletariato come parte integrante del programma obbligatorio dell’Internazionale, e la dittatura del Consiglio generale, cioè quella del sig. Marx in persona, e di conseguenza la trasformazione dell’Internazionale in un immenso e mostruoso Stato, di cui egli divenne il capo.
Essendo stata contestata la legittimità di questa Conferenza, il sig. Marx, prestigiatore politico molto abile, che era senza dubbio ansioso di dimostrare al mondo che, in mancanza di fucili e di cannoni, si potevano governare le masse con la menzogna, con la calunnia, con l’intrigo, organizzò il \emph{suo} Congresso dell’Aia. Sono trascorsi appena due mesi da questo Congresso, e in tutta l’Europa – tranne la Germania di cui gli operai sono sistematicamente accecati dai loro capi, e dai loro giornali, di cui i redattori sono interessati alla menzogna – in tutte le Federazioni libere, belga, olandese, inglese, americana, francese, spagnola, italiana senza dimenticare la nostra eccellente Federazione del Giura, non vi è che un grido d’indignazione e di disprezzo contro questa cinica commedia a cui si è osato affibbiare il nome di un Congresso dell’Internazionale. Grazie ad una maggioranza fittizia, composta quasi esclusivamente da membri del Consiglio generale, da Tedeschi disciplinati alla prussiana, e da blanquisti francesi ridicolmente giocati dal sig. Marx, qui tutto è stato travestito, falsificato, brutalizzato e violato: giustizia, buonsenso, onestà. Vi si è immolato senza vergogna, senza pietà, l’onore dell’Internazionale, si è messo in gioco la sua stessa esistenza, al fine di meglio assicurare senza dubbio la potenza dittatoriale del sig. Marx. Non era soltanto un crimine, era una demenza. E il sig. Marx, che egli stesso si considera il padre dell’Internazionale e che è stato incontestabilmente uno dei suoi principali fondatori, ha lasciato fare tutto ciò! Ecco dove conducono la vanità personale, l’adorazione di se stessi e, soprattutto, l’ambizione politica. Per tutti questi fatti e questi atti deplorevoli di cui egli è stato la grande fonte e l’unico autore, il sig. Marx ha almeno reso un grande servizio all’Internazionale, dimostrando ad essa in una maniera interamente drammatica, del tutto viva, che se qualche cosa può ucciderla, è l’introduzione della politica nel suo programma.
L’Associazione Internazionale dei Lavoratori, ho detto, ha potuto prendere un’estensione immensa solo perché ha eliminato dal suo programma obbligatorio tutte le questioni politiche e filosofiche. La cosa è talmente chiara che si è veramente stupiti di doverla ancora dimostrare.
Io non credo di avere bisogno di dimostrare che affinché l’Internazionale sia e resti una potenza, essa deve essere capace di trascinare nel suo seno e di abbracciare e di organizzare l’immensa maggioranza del proletariato di tutti i paesi dell’Europa e dell’America. Ma qual è il programma politico filosofico che potrebbe illudersi di riunire sotto la sua insegna dei milioni? Solo un programma eccessivamente generale, cioè indeterminato e vago, può farlo, perché ogni determinazione in teoria corrisponde fatalmente ad una esclusione, ad una eliminazione nella pratica.
Non ci può più essere, per esempio, oggi della filosofia seria che non prenda come punto di partenza, non positivo ma negativo (storicamente diventato necessario, come negazione delle assurdità teologiche e metafisiche), l’ateismo. Ma si crede forse che se si fosse scritto questa semplice parola, “\emph{l’ateismo}”, sulla bandiera dell’Internazionale, questa associazione avrebbe potuto riunire nel suo seno non meno di qualche centinaio di migliaia di aderenti? E ciò, come tutti sanno, non perché il popolo sia realmente religioso, ma perché crede di esserlo finché una buona rivoluzione sociale non gli avrà dato i mezzi di realizzare tutte le sue aspirazioni qui in basso. È certo che, se l’Internazionale avesse messo l’ateismo, come un principio obbligatorio, nel suo programma, essa avrebbe escluso dal suo seno il fiore del proletariato – e con questa parola io non intendo, come fanno i marxiani, lo strato superiore, il più civile e il più agiato del mondo operaio, quello strato di operai quasi borghesi di cui vogliono precisamente servirsi per costituire la loro \emph{quarta classe governativa}, e che è veramente capace di formarne una, se non vi si mette ordine nell’interesse della grande massa del proletariato, perché, col suo benessere relativo e quasi-borghese, essa si è, per disgrazia, troppo profondamente imbevuta di tutti i pregiudizi politici e sociali e delle grette aspirazioni e pretese dei borghesi. Si può dire che questo strato è il meno socialista, il più individualista in tutto il proletariato.
Per \emph{fiore del proletariato}, intendo soprattutto quella grande massa, quei milioni di non civilizzati, di diseredati, di miserabili e di analfabeti che il sig. Engels e il sig. Marx pretendono di sottomettere al regime paterno di un \emph{governo molto forte} (sono gli stessi termini di cui il sig. Engels si è servito in una lettera molto istruttiva che ha indirizzato al nostro amico Cafiero), senza dubbio per la loro stessa salvezza, siccome tutti i governi sono stati costituiti, si sa, soltanto nell’interesse proprio delle masse. Per fiore del proletariato, intendo precisamente quella carne da eterno governo, quella grande canaglia popolare (i sigg. Marx ed Engels la chiamano ordinariamente con questa parola insieme pittoresca e sprezzante, Lumpen-Proletariat, il “proletariato straccione”, i pezzenti) che, essendo quasi vergine da ogni civiltà borghese, porta nel suo seno, nelle sue passioni, nei suoi istinti, nelle sue aspirazioni, in tutte le necessità e nelle miserie della sua posizione collettiva, tutti i germi del socialismo dell’avvenire, e che sola oggi è abbastanza potente per inaugurare e per fare trionfare la rivoluzione sociale.
Ebbene, in quasi tutti i paesi, questa canaglia, in quanto massa, avrebbe rifiutato di aderire all’Internazionale se si fosse scritto sulla sua bandiera, come parola ufficiale, questa parola ateismo. E ciò sarebbe un grande danno, perché, se essa voltasse la schiena all’Internazionale, sarebbe finita tutta la potenza della nostra grande Associazione.
La stessa cosa vale assolutamente per tutti i princìpi politici. Primo, non ve ne è più uno solo – e i sigg. Marx ed Engels avranno un bel darsi da fare, essi non cambieranno questo fatto divenuto oggi lampante in tutti i paesi –, non esiste più alcun principio politico, dico, che sia capace di smuovere le masse. Essi falliranno, dopo un’esperienza di qualche anno, anche in Germania. Ciò che le masse vogliono ovunque, è la loro emancipazione economica immediata, perché è là che realmente è per esse tutta la questione della libertà, dell’umanità, della vita o della morte. Se vi è ancora un ideale che le masse oggi sono capaci di adorare con passione, è quello dell’uguaglianza economica. E le masse hanno mille volte ragione, perché finché l’\emph{uguaglianza economica} non avrà affatto sostituito il regime attuale, tutto il resto, tutto ciò che costituisce il valore e la dignità dell’esistenza umana, la libertà, la scienza, l’amore, l’azione intelligente e la solidarietà fraterna, resterà per esse allo stato di orribile menzogna.
La passione istintiva delle masse per l’uguaglianza economica è così grande che, se esse avessero potuto sperare di riceverla dalle mani del dispotismo, si sarebbero indubbiamente e senza molta riflessione, come hanno fatto spesso, consegnate al dispotismo. Fortunatamente, l’esperienza storica è servita a qualche cosa anche alle masse. Oggi esse incominciano a comprendere ovunque che nessun dispotismo ha, né può avere, né la volontà né il potere di darla a loro. Il programma dell’Internazionale è, molto fortunatamente, esplicito sotto questo aspetto: \emph{L’emancipazione dei lavoratori non può essere opera che dei lavoratori stessi}.
Non è forse sorprendente che il sig. Marx abbia creduto di potere innestare su questa dichiarazione, pertanto così precisa, così chiara, e che ha probabilmente redatta lui stesso, il suo \emph{socialismo scientifico}, cioè l’organizzazione e il governo della nuova società da parte dei socialisti sapienti – il peggiore di tutti i governi dispotici!
Grazie a questa cara, grande canaglia popolare che si opporrà da sola, spinta da un istinto così invincibile quanto giusto, a tutte le velleità governative della piccola minoranza operaia già disciplinata e classificata come si deve per divenire il fautore di un nuovo dispotismo, il \emph{socialismo sapiente} del sig. Marx resterà sempre allo stato di sogno marxiano. Questa nuova esperienza, forse più triste di tutte le esperienze passate, sarà risparmiata alla società, perché il proletariato in generale e in tutti i paesi oggi è animato da una diffidenza profonda verso ciò che è politico e verso tutti i politici del mondo, qualsiasi sia il loro colore, avendolo tutti ugualmente ingannato, oppresso, sfruttato, i repubblicani più rossi così come i monarchici più assoluti.
Con simili stati d’animo realmente esistenti nelle masse, come sperare di poterle attirare con un qualsiasi programma politico? E supponiamo, il qual caso è oggi in effetti, che esse si lascino trascinare nell’Internazionale da un’altra esca, come sperare che il proletariato di tutti i paesi, trovandosi in condizioni così diverse di temperamento, di cultura, e di sviluppo economico, potrà attaccarsi al giogo di un programma politico uniforme? Non si potrebbe concepirlo, sembra, senza demenza. Ebbene, il sig. Marx non si è soltanto trastullato a concepirlo, l’ha voluto mettere in pratica. Stracciando con un colpo di mano dispotico il patto dell’Internazionale, egli ha voluto, pretende ancora oggi, imporre, un programma politico uniforme, il \emph{suo proprio programma}, a tutte le Federazioni dell’Internazionale, cioè al proletariato di tutti i paesi!
Ne è risultato un grandissimo dissidio nell’Internazionale. Non bisogna farsi illusioni, la grande unità dell’Internazionale è stata messa in questione, e ciò, lo ripeto ancora, grazie unicamente al partito marxiano, che, mediante il Congresso dell’Aia, ha tentato d’imporre il pensiero, la volontà, la politica del suo capo a tutta l’Internazionale. È evidente che se le risoluzioni del Congresso dell’Aia dovessero essere considerate come l’ultima parola, o anche soltanto come una parola seria, non falsificata, dell’Internazionale, la nostra grande e bella Associazione non avrebbe più che una sola cosa da fare, cioè dissolversi. Perché bisogna essere veramente insensati per concepire che i lavoratori dell’Inghilterra, dell’Olanda, del Belgio, della Francia, del Giura, dell’Italia, della Spagna, dell’America, senza parlare già dei lavoratori slavi, vorranno sottomettersi alla disciplina marxiana.
E pertanto, se si crede, con i politici di ogni specie dell’Internazionale, con i giacobini rivoluzionari, con i blanquisti, con i democratici repubblicani, senza dimenticare i democratici socialisti o marxiani, che la questione politica deve fare parte integrante del programma dell’Internazionale, bisognerà confessare che il sig. Marx ha ragione. Non potendo l’Internazionale costituire una potenza che essendo una, bisognerà assolutamente che il suo programma politico sia uno, lo stesso per tutti, perché altrimenti vi sarebbero tante internazionali quanti programmi differenti vi saranno. Ma siccome è evidentemente impossibile che i lavoratori di tanti paesi diversi si uniscano liberamente e spontaneamente sotto uno stesso programma politico, essendo oggi l’Internazionale lo strumento necessario per l’emancipazione del proletariato, e non potendo questa Internazionale salvaguardare la sua unità che alla condizione di non riconoscere che un solo programma politico, bisognerà imporlo loro. Per non avere l’aria d’imporlo loro dispoticamente, attraverso un decreto del Consiglio generale o marxiano, che, dimostrando in una maniera tutta nuova quanta verità vi sia nel sistema rappresentativo e nel suffragio universale, in nome della libera volontà di tutti, decreterà la schiavitù di tutti. Ecco ciò che ha fatto in realtà il Congresso dell’Aia.
Fu per l’Internazionale la battaglia e la capitolazione di Sedan, l’invasione trionfante del pangermanesimo non bismarckiano, ma marxiano, che imponeva il programma politico dei comunisti autoritari o democratici socialisti della Germania, e la dittatura del loro capo al proletariato di tutti gli altri paesi dell’America e dell’Europa. Per nascondere meglio il suo gioco e per indorare un po’ la pillola, questo memorabile Congresso ha mandato in America un simulacro del Consiglio generale, eletto e scelto dal sig. Marx stesso, e che, obbedendo sempre alla sua direzione occulta, assumerà tutte le apparenze, le noie e le responsabilità del potere, lasciandone al sig. Marx, protetto dalla sua ombra, l’esercizio reale.
Ebbene, dichiaro che per quanto disgustoso possa apparire questo gioco a degli amici delicati e timorati, era assolutamente necessario dal momento che si era ammesso che la questione politica doveva essere determinata nel programma dell’Internazionale. Poiché l’unità dell’azione politica è riconosciuta necessaria, non potendo sperare di vederla uscire liberamente dall’intesa spontanea delle federazioni e sezioni dei diversi paesi, si è dovuto imporla loro. In questa sola maniera si è potuto creare quella unità politica tanto desiderata e predicata, ma nello stesso tempo si è creato la schiavitù.
Riassumo la questione: introducendo la questione politica nel programma obbligatorio dell’Internazionale, si è posta la nostra Associazione in un terribile dilemma, di cui ecco i due termini:
\emph{O l’unità con la schiavitù}.
\emph{O la libertà con la divisione e la dissoluzione}.
Come uscirne? Molto semplicemente ritornando ai nostri primitivi statuti generali, che fanno astrazione della questione propriamente politica, lasciando il suo sviluppo alla libertà delle federazioni e delle sezioni. Ma allora ogni federazione, ogni sezione seguirà la direzione politica che vorrà? – Senza dubbio. – Ma allora l’Internazionale si trasformerà in una torre di Babele? – Al contrario, soltanto allora essa costituirà la sua reale unità, economica prima, e necessariamente politica poi; allora creerà, senza dubbio non in un sol colpo, la grande politica dell’Internazionale, emanata non da una testa isolata, ambiziosa, molto sapiente e tuttavia incapace di abbracciare i mille bisogni del proletariato, per quanto imbottita di cervello sia, ma dall’azione assolutamente libera, spontanea e simultanea dei lavoratori di tutti i paesi.
La base di questa grande unità, che vanamente si cercherebbe nelle idee filosofiche e politiche del giorno, si trova completamente data attraverso la solidarietà delle sofferenze, degli interessi, dei bisogni e delle reali aspirazioni del proletariato del mondo intero. Questa solidarietà non è affatto da creare, essa esiste di fatto; costituisce la vita propria, l’esperienza quotidiana del mondo operaio, e tutto ciò che resta da fare è di fargliela conoscere e di aiutarlo ad organizzarla coscientemente. È \emph{la solidarietà delle rivendicazioni economiche}. Averlo compreso, questo è, secondo me, l’unico, ma, nello stesso tempo, il grandissimo merito dei primi fondatori della nostra Associazione, tra i quali, mi piace ricordarlo sempre, il sig. Marx ha avuto un ruolo così utilmente preponderante, eccetto alcune velleità tutte politiche e tedesche che il Congresso di Ginevra ha eliminato saggiamente dal programma che egli aveva presentato.
Ho sempre evitato di chiamare il sig. Marx e i suoi numerosi collaboratori i “fondatori“ dell’Internazionale; non perché, ispirato da un qualsiasi sentimento meschino, voglia diminuire il loro merito, al quale al contrario amo molto rendere giustizia, ma perché realmente sono convinto che l’Internazionale non è affatto stata opera loro, ma bensì quella del proletariato stesso. Essi ne furono in qualche modo gli ostetrici, ma non gli autori. Il grande autore, incosciente come lo sono ordinariamente gli autori di cose molto grandi, fu il proletariato, rappresentato da qualche centinaia di anonimi operai, francesi, inglesi, belgi, svizzeri e tedeschi. Fu il loro vivo e profondo istinto di lavoratori provati dall’oppressione e dalla sofferenza inerente alla loro posizione che ha fatto trovare loro il vero principio e il vero scopo dell’Internazionale: la solidarietà dei bisogni come base già esistente, e \emph{l’organizzazione internazionale della lotta economica del lavoro contro il capitale} come vero oggetto di questa Associazione. Dandogli esclusivamente questa base e questo scopo, essi stabilirono in un sol colpo tutta la potenza dell’Internazionale.
Essi ne aprirono ampiamente le porte a tutti i milioni di oppressi e di sfruttati dell’attuale società, astrazione fatta delle loro credenze, del loro grado di cultura, della loro nazionalità. Perché per concepire il desiderio e per avere il diritto di entrare nell’Internazionale, conformemente ai suoi statuti primitivi, non occorsero e non occorrono ancora oggi che le seguenti condizioni:
1° Essere un lavoratore serio, cioè provare realmente le sofferenze alle quali il proletariato si trova assoggettato ai nostri giorni, o almeno, se si è nati in una qualsiasi classe privilegiata, volere francamente, senza reticenze e senza ambiziosi secondi fini, la piena emancipazione del mondo operaio;
2° Comprendere che questa emancipazione non può essere un fatto individuale né locale, né il fatto eccezionale di un qualsiasi mestiere isolato; ma che essa non può realizzarsi che a condizione di abbracciare in un’azione solidale i lavoratori di tutti i mestieri industriali, commerciali ed agricoli, il proletariato di tutti i comuni, di tutte le province, di tutti i paesi, di tutti i continenti, e di formare di conseguenza una potente reale organizzazione della solidarietà internazionale di tutti i lavoratori sfruttati di tutto il mondo contro lo sfruttamento sistematico e legale di tutti i capitalisti e di tutti i proprietari del mondo;
3° Comprendere che le classi possidenti, che sfruttano e governano, non faranno mai volontariamente, per generosità o per giustizia, alcuna concessione, per quanto urgente sembri e per quanto lieve sia, al proletariato; perché è contro natura, e precisamente contro la loro natura particolare, in modo tale che non si ha mai avuto l’esempio nella storia che una classe dominante abbia fatto di buon grado tali sacrifici; non avendo mai acconsentito nessun privilegiato a farne nemmeno di molto piccoli che quando, invaso e minacciato nella sua stessa esistenza dalla potenza ascendente del proletariato, si è visto costretto a farne di molto più importanti. Perciò, di conseguenza, il proletariato non deve attendere nulla né dall’intelligenza, né dall’equità dei borghesi, e ancora meno dalla loro politica, fosse anche quella dei radicali borghesi e dei borghesi cosiddetti socialisti, e, infine, nemmeno dai rappresentanti borghesi della scienza, e che \emph{l’emancipazione dei lavoratori non può essere esclusivamente che l’opera dei lavoratori stessi}, come si è detto all’inizio dei nostri considerando. Ciò che significa che i lavoratori non potranno realizzare questa emancipazione e conquistare i loro diritti umani che a viva forza, \emph{attraverso la guerra organizzata dei lavoratori di tutto il mondo contro i capitalisti e i proprietari sfruttatori del mondo intero};
4° Comprendere che per meglio vincere in questa guerra internazionale, i lavoratori di tutti i paesi devono organizzare internazionalmente la loro potenza solidale, e che questo è il vero, l’unico scopo dell’Associazione Internazionale dei Lavoratori;
5° Comprendere che, dato che questa organizzazione non ha altro scopo che l’emancipazione dei lavoratori \emph{per essi stessi}, essa non può essere costituita che direttamente ed immediatamente da essi stessi, per la loro azione spontanea, cioè dal basso in alto tramite la via francamente popolare della libera federazione, al di fuori di tutte le combinazioni politiche degli Stati, e non dall’alto in basso, alla maniera di tutti i governi più o meno centralizzatori, aristocratici e borghesi;
6° Comprendere che, dato che il proletario, il lavoratore manuale, l’uomo da fatica, è il rappresentante storico della primitiva e, nello stesso tempo, dell’ultima schiavitù sulla terra, la sua emancipazione è l’emancipazione di tutti, il suo trionfo è il trionfo finale dell’umanità; e che, di conseguenza, l’organizzazione della potenza del proletariato di tutti i paesi per mezzo dell’Internazionale e la guerra che essa solleva contro tutte le classi sfruttatrici e dominanti non possono avere per scopo la costituzione di un nuovo privilegio, di un nuovo monopolio, di una classe, di una nuova dominazione, o di un nuovo Stato, ma la fondazione della libertà, dell’uguaglianza e della fraternità di tutti gli esseri umani, sulle rovine di tutti i privilegi, di tutte le classi, di tutti gli sfruttamenti, di tutte le dominazioni, in una parola di tutti gli Stati;
7° Si deve comprendere infine che, poiché lo scopo unico dell’Internazionale è la conquista di tutti i diritti umani per i lavoratori, per mezzo dell’organizzazione della loro solidarietà militante attraverso le differenze di tutti i mestieri e le frontiere politiche e nazionali di tutti i paesi, \emph{la legge suprema e per così dire unica} che ognuno s’impone entrando in questa salutare e straordinaria Associazione, è di sottomettersi e di sottomettere d’ora in poi tutti i suoi atti, volontariamente, appassionatamente, con piena conoscenza di causa e nel suo interesse proprio come altrettanto in quello dei suoi fratelli di tutti i paesi, a tutte le condizioni, conseguenze ed esigenze di questa solidarietà.
Ecco i veri princìpi dell’Internazionale. Essi sono così ampi, così umani, e nello stesso tempo così semplici, che bisogna essere un borghese ben interessato alla conservazione del monopolio, o molto abbrutiti dai pregiudizi borghesi, per non comprenderne affatto e per non riconoscerne la perfetta giustezza. Per falsificarli, c’è voluto un democratico socialista della scuola del sig. Marx. Ma non vi è nessun vero e serio proletario, per quanto poco colto o per quanto intontito sia da questa massa di pregiudizi, sia religiosi che politici, che vengono fatti piovere sistematicamente sulla sua povera testa, fin dalla sua più tenera infanzia, al quale, con un poco di pazienza e di buona volontà, non si possa far comprendere tutto ciò in una conversazione di alcune ore. Perché già egli porta tutto ciò nel suo istinto e in tutte le sue aspirazioni sviluppati ogni giorno di più dalle sue esperienze, dai suoi dolori quotidiani. Spiegandogli questi princìpi, e deducendogli tutte le applicazioni pratiche, non si farà che dare una forma, un nome, a ciò che egli sente. Ecco ciò che attirerà invincibilmente la massa del proletariato nell’Internazionale, se l’Internazionale, nel momento in cui si organizza e si sviluppa sempre più, resterà fedele alla semplicità del suo programma e della sua istituzione primitiva.
Non si può commettere più grande errore che quello di domandare sia a una cosa, sia ad un’istituzione, sia ad un uomo, più di quanto non possano dare. Esigendo di più da essi, li si demoralizza, li si ostacola, li si falsa, li si uccide. L’Internazionale, in poco tempo, ha prodotto grandi risultati. Ha organizzato, e organizzerà ogni giorno in un modo anche più straordinario, il proletariato per la lotta economica. Questa è forse una ragione per sperare che ci si possa servire di essa come di uno strumento per la lotta politica?
Il sig. Marx, per averlo sperato, ha corso il rischio di assassinare l’Internazionale con il suo criminale tentativo dell’Aia. È la storia della gallina dalle uova d’oro. All’appello per la lotta economica, masse di lavoratori dei diversi paesi sono accorse per schierarsi sotto la bandiera dell’Internazionale, e il sig. Marx si era immaginato che le masse vi sarebbero rimaste, che dico? che sarebbero accorse in quantità ancora più straordinaria, quand’egli, nuovo Mosè, avrebbe iscritto le sentenze del suo decalogo politico sulla nostra bandiera, nel programma ufficiale e obbligatorio dell’Internazionale.
Ecco dove è stato il suo errore. Le masse, senza differenza nel grado di cultura, di credenze religiose, di paesi e di lingue, avevano compreso il linguaggio dell’Internazionale, quando essa aveva parlato della loro miseria, della loro sofferenza e della loro schiavitù sotto il giogo del capitale e della proprietà sfruttatrice; esse l’hanno compreso quando essa ha loro dimostrato la necessità di unire i loro sforzi in una grande lotta solidale e comune. Ma ecco che si viene a parlar loro di un programma politico molto sapiente, soprattutto molte autoritario, e che, in nome della loro propria salvezza, viene ad imporre loro, in questa stessa Internazionale che doveva organizzare la loro emancipazione attraverso i loro sforzi, un governo dittatoriale, senza dubbio provvisorio, ma, nell’attesa, del tutto arbitrario, e diretto da una testa straordinariamente piena di cervello.
A quale grado di demenza bisogna che sia stato spinto sia per l’ambizione, sia per la vanità, sia per entrambe assieme, per avere potuto concepire la speranza che si potessero trattenere le masse operaie dei diversi paesi dell’Europa e dell’America, sotto la bandiera dell’Internazionale, a queste condizioni!
Ma il successo più trionfante non ha dato ragione al sig. Marx, e al Congresso dell’Aia non hanno forse votato tutto ciò che aveva comandato?
Nessuno meglio del sig. Marx sa quanto poco le risoluzioni votate da quel disgraziato Congresso dell’Aia esprimano il pensiero e le aspirazioni reali delle Federazioni di tutti i paesi. La composizione e la falsificazione di quel Congresso gli sono costate troppa pena perché possa farsi la minima illusione sul suo vero significato e valore. E, d’altronde, se anche avesse potuto per un istante farsi questa illusione, ciò che accade oggi è adatto per dissiparla completamente. Eccettuato il Partito della democrazia socialista della Germania, le Federazioni di tutti i paesi, gli Americani, gli Inglesi, gli Olandesi, i Belgi, i Francesi, gli Svizzeri del Giura, gli Spagnoli e gli Italiani protestano contro tutte le risoluzioni di quel nefasto e vergognoso Congresso, o piuttosto contro quell’ignobile intrigo.
Ma lasciamo da parte la questione morale, e non consideriamo che la parte principale della questione. Un programma politico non ha valore che quando, uscendo dalle vaghe generalità, determina in modo preciso le istituzioni, che propone di mettere al posto di quelle che vuole rovesciare o riformare. Tale è, in effetti, il programma del sig. Marx. È una impalcatura completa di istituzioni economiche e politiche fortemente centralizzate e molto autoritarie, sanzionate senza dubbio, come tutte le istituzioni dispotiche nella società moderna, dal suffragio universale, ma tuttavia sottomesse ad un governo \emph{molto forte}, per servirmi delle espressioni proprie del sig. Engels, l’alter ego del sig. Marx, il confidente del legislatore.
Ma perché è precisamente proprio questo programma che si pretende introdurre \emph{ufficialmente}, obbligatoriamente, negli statuti dell’Internazionale? Perché non quello dei blanquisti? Perché non il nostro? Sarebbe forse perché l’avrebbe inventato il sig. Marx? Non è una ragione. O perché gli operai della Germania sembrano accettarlo? Ma il programma anarchico è accettato, escluso pochissime eccezioni, da tutte le Federazioni latine; gli Slavi non ne accetteranno mai altri. Perché dunque il programma autoritario dei Tedeschi dovrebbe dominare nell’Internazionale, che solo la libertà ha creato e che non potrà mai prosperare che nella libertà e per la libertà? Sarebbe forse perché gli eserciti tedeschi non sono riusciti a conquistare la Francia? Ma anche questa non sarebbe [una ragione]; sarebbe piuttosto, al contrario, una ragione per diffidare molto di un programma che ci viene oggi dalla Germania!
(I Tedeschi hanno una maniera di valutare gli uomini, i fatti e le cose completamente singolare. Lo trovo, per esempio, nel n. 81 (del 9 ottobre 1872) del “Volksstaat”, l’organo ufficiale e principale del Partito degli operai democratici socialisti della Germania, un organo che viene pubblicato a Lipsia non sotto la redazione, ma sotto l’ispirazione immediata e diretta del sig. Marx stesso, il seguente trafiletto: “Una notizia. L’interdizione dell’Internazionale in Francia è soppressa! – È possibile! – Non lo credete? E tuttavia è così. L’Internazionale, che era stata espulsa attraverso la porta delle associazioni (\emph{die durch das Vereinsthor hinausgehetzt war}), è di nuovo rientrata trionfante nella Capitale della Francia attraverso il negozio di un libraio. \emph{Il Capitale} di Karl Marx tradotto in francese è in vendita presso Lachâtre a Parigi. In questo momento stesso abbiamo qui davanti la prima serie magnificamente stampata di questa opera con il ritratto e l’autografo dell’autore\dots{}”. Non è incredibile! Non è forse tutto tedesco! Vi domando se, in un qualunque altro paese, si oserebbe stampare una cosa simile in un giornale che si dice democratico, socialista, organo dell’Internazionale, e che pretende di rappresentare, che rappresenta, ohimè! in effetti una organizzazione molto numerosa di operai. Come! l’apparizione del libro, del ritratto e dell’autografo del sig. Karl Marx, in una libreria di Parigi, equivale al ritorno trionfante dell’Internazionale in Francia! È buffonesco, è ignobile, ed è la più grossolana ingiuria che si sia gettata sull’Internazionale! Dunque, un solo uomo, che questo sia Marx o un altro, ha tanto peso quanto tutta l’Internazionale! Per osare dire simili cose agli operai della Germania, che fanno di questo giornale la loro lettura quotidiana, non occorre forse disprezzarli molto e crederli piegati a tutte le discipline e a tutte le umiliazioni? L’idolatria delle persone e il culto dell’autorità sono entrati molto profondamente nei costumi dei Tedeschi; ma non mi sarei mai immaginato che fossero depravati al punto che un giornale popolare, letto da almeno una o due decine di migliaia di operai, osasse impunemente stampare simili cose. Il “Volksstaat” l’ha fatto senza dubbio molto ingenuamente, e nessuno in Germania se ne è risentito).
Ed è il programma politico applaudito da una democrazia socialista simile che il Congresso dell’Aia ha preteso imporre alle Federazioni libere di tutti i paesi!
È evidente che, a meno di voler tiranneggiare le Federazioni di molti paesi, imponendo loro sia con la violenza, sia con l’intrigo, sia con entrambi insieme, il programma politico di un solo paese; o anche, ciò che è molto più probabile, a meno di dissolvere l’Internazionale, dividendola in molti tronconi, di cui ciascuno seguirebbe il suo proprio programma politico – per salvare la sua integrità e per assicurare la sua prosperità, non vi è che un solo mezzo: \emph{è di mantenere l’originaria eliminazione della questione politica dal programma ufficiale e obbligatorio dell’Associazione Internazionale dei Lavoratori, organizzata non per la lotta politica, ma unicamente per la lotta economica, e rifiutandosi assolutamente per lo stesso motivo di servire da strumento politico tra le mani di chicchessia}. A tal punto che tutte le volte che si vorrà impiegarla come una potenza politica positiva in una lotta positivamente politica dei differenti partiti di Stato, essa si demoralizzerà immediatamente, si sminuirà, si limiterà e si dissolverà in una maniera ostensibile, e finirà col distruggersi del tutto nelle mani di colui che follemente s’immaginerà tenere quella potenza.
Ma allora sarebbe dunque vietato occuparsi di questioni politiche e filosofiche nell’Internazionale? L’Internazionale, facendo astrazione da tutto lo sviluppo che si fa nel mondo del pensiero, come altrettanto degli avvenimenti che accompagnano o che seguono la lotta politica, sia esterna che interna, degli Stati, non si occuperebbe più che della questione economica? Essa farebbe della statistica comparata, studierebbe le leggi della produzione e della distribuzione delle ricchezze, si occuperebbe esclusivamente del regolamento dei salari, formerebbe delle casse di resistenza, organizzerebbe degli scioperi locali, nazionali, internazionali, costituirebbe localmente, nazionalmente e internazionalmente i corpi di mestiere, e formerebbe delle società cooperative di credito mutuale, di consumo e di produzione, nei momenti e nelle località e paesi dove simili creazioni sarebbero possibili?
Ma una tale astrazione è assolutamente impossibile. Questa preoccupazione esclusiva degli interessi soltanto economici, sarebbe per il proletariato la morte. Senza dubbio la difesa e l’organizzazione di questi interessi – questione di vita o di morte per lui – devono costituire la base di tutta la sua azione attuale. Ma gli è impossibile arrestarsi lì senza rinunciare all’umanità, e senza privarsi anche della forza intellettuale e morale necessaria alla conquista dei suoi diritti economici. Senza dubbio nello stato miserabile nel quale si vede ora ridotto, il primo problema che gli si presenta, è quello del pane quotidiano, del pane della famiglia; ma, più di tutte le classi privilegiate oggi, è un essere umano, in tutta la pienezza di questa parola, e come tale ha sete di dignità, di giustizia, di uguaglianza, di libertà, di umanità e di scienza, e intende conquistare tutto ciò contemporaneamente al pieno godimento del prodotto integrale del suo proprio lavoro. Dunque, se le questioni politiche e filosofiche non fossero state nemmeno poste nell’Internazionale, il proletariato stesso le avrebbe poste infallibilmente.
Ma allora come risolvere questa apparente contraddizione: da un lato, le questioni filosofiche e politiche devono essere escluse dal programma dell’Internazionale, e dall’altro esse devono necessariamente esservi discusse?
Questo problema si risolve da solo attraverso la libertà. Nessuna teoria filosofica o politica deve entrare, come fondamento essenziale, ufficiale, e come condizione obbligatoria, nel programma dell’Internazionale, perché, come noi abbiamo appena visto, ogni teoria imposta diverrebbe, per tutte le Federazioni di cui l’Associazione si compone oggi, sia una causa di schiavitù, sia la causa di una divisione e di una dissoluzione non meno disastrosa. Ma non ne consegue che tutte le questioni politiche e filosofiche non possano e non debbano essere liberamente discusse nell’Internazionale. Al contrario, è l’esistenza di una teoria ufficiale che ucciderebbe, rendendola assolutamente inutile, la discussione viva, cioè lo sviluppo del pensiero proprio nel mondo operaio. Dal momento che vi sarebbe una \emph{verità ufficiale}, scientificamente scoperta dal lavoro isolato di quella grande testa eccezionalmente – e perché anche non provvidenzialmente? – provvista di cervello, una verità annunciata ed imposta a tutto il mondo dall’alto del Sinai marxiano, perché discuterla? Non resta altro che impararne a memoria tutti gli articoli del nuovo Decalogo.
Al contrario, se nessuno ha né può avere la pretesa di dare la verità, la si cerca. Chi la cerca? Tutti, e soprattutto il proletariato che ne ha sete e bisogno più di tutti gli altri.
Molti non vorranno credere a questa ricerca spontanea della verità politica e filosofica da parte del proletariato stesso. Io ora tenterò di dimostrare come questa ricerca si effettui nel seno stesso dell’Internazionale.
I lavoratori, ho detto, non entrano nell’Internazionale e non vi si organizzano da prima che con un fine eminentemente pratico, quello della rivendicazione solidale della pienezza dei loro diritti economici contro lo sfruttamento oppressivo della borghesia di tutti i paesi. Notate che, per questo solo fatto – incosciente, se volete, da prima – il proletariato si pone già, sotto un doppio aspetto, in una situazione molto decisivamente, ma anche molto negativamente, politica. Distrugge, da un lato, le frontiere politiche e tutta la politica internazionale degli Stati, in quanto fondata sulle simpatie, sulla cooperazione volontaria e sul fanatismo patriottico nelle masse asservite; e, dall’altro, accresce l’abisso fra la borghesia e il proletariato, e pone quest’ultimo al di fuori dell’azione e del gioco politico di tutti i partiti dello Stato; ma, mettendolo al di fuori di ogni politica borghese, lo indirizza necessariamente contro di essa.
Dunque ecco una posizione politica ben determinata, nella quale il proletariato si trova posto, prima inconsciamente come io ho appena detto, per il solo fatto della sua adesione all’Internazionale. È vero che è una posizione politica assolutamente \emph{negativa}, e la grande colpa, per non dire il tradimento e il crimine dei democratici socialisti che trascinano il proletariato della Germania nelle vie del programma marxiano, è di aver voluto trasformare questa inclinazione negativa in una cooperazione positiva alla politica dei borghesi.
L’Internazionale, mettendo così il proletariato al di fuori della politica degli Stati e del mondo borghese, costituisce un mondo nuovo, il mondo del proletariato solidale di tutti i paesi. Questo mondo è quello dell’avvenire; è, da un lato, l’erede legittimo ma, nello stesso tempo, il demolitore e l’affossatore di tutte le civiltà storiche, privilegiate e, come tali, completamente esaurite e condannate a morire; di conseguenza il creatore obbligato di una nuova civiltà, fondata sulla rovina di tutte le autorità divine ed umane, di tutte le schiavitù e di tutte le ineguaglianze. Questa è la missione e, di conseguenza, questo è il vero programma dell’Internazionale, non ufficiale, – tutti gli dèi del paradiso pagani e cristiani ce ne guardino! – ma implicito, inerente alla sua organizzazione stessa.
Il suo programma ufficiale, io lo ripeterò mille volte, è molto semplice e, in apparenza, molto modesto: \emph{è l’organizzazione della solidarietà internazionale per la lotta economica del lavoro contro il capitale}. Da questa base, prima esclusivamente materiale, deve sorgere tutto il nuovo mondo sociale, intellettuale e morale. Perché sia realmente così, bisogna che tutti i pensieri, tutte le tendenze filosofiche e politiche dell’Internazionale, nascendo nel seno stesso del proletariato, abbiano come principale punto di partenza, se non esclusivo, quella rivendicazione economica che costituisce l’essenza stessa e lo scopo manifesto dell’Internazionale. È possibile?
Sì, e in effetti è così. Chiunque abbia seguito gli sviluppi dell’Internazionale per qualche anno ha potuto accorgersi come ciò vi si effettui lentamente, senza che appaia del tutto, ora simultaneamente, ora successivamente, e sempre per tre strade diverse, ma indissolubilmente unite: prima attraverso l’organizzazione e la federazione delle casse di resistenza e la solidarietà internazionale degli \emph{scioperi}, in secondo luogo, attraverso l’organizzazione e la federazione internazionale dei corpi di mestiere; e infine attraverso \emph{lo sviluppo spontaneo e diretto delle idee filosofiche e sociologiche nell’Internazionale}, accompagnamento inevitabile e conseguenza, per così dire, forzata, di quei due primi movimenti.
Consideriamo ora queste tre strade nella loro azione particolare, differente, ma, come ho detto, inseparabile, e cominciamo con l’organizzazione delle casse di resistenza e degli scioperi.
Le casse di resistenza hanno per unico scopo quello di costituire il fondo necessario per rendere possibili l’organizzazione e il sostentamento così costoso degli scioperi. E lo sciopero è l’inizio della guerra sociale del proletariato contro la borghesia, ancora nei limiti della legalità. Gli scioperi sono una via preziosa sotto questo doppio rapporto, che, primo, elettrizzano le masse, ritemprano la loro energia morale e risvegliano nel loro seno il sentimento dell’antagonismo profondo che esiste fra i loro interessi e quelli della borghesia, mostrando loro, sempre di più, l’abisso che ormai li separa irrevocabilmente da quella classe; e che, poi, essi contribuiscono immensamente a provocare e a costituire fra i lavoratori di tutti i mestieri, di tutte le località e di tutti i paesi, la coscienza e il fatto stesso della solidarietà: doppia azione, una negativa e l’altra completamente positiva, che tende a costituire direttamente il nuovo mondo del proletariato, opponendolo, in una maniera quasi assoluta, al mondo borghese.
È una cosa degna di nota che il radicalismo, come il socialismo borghese, si siano sempre dichiarati gli antagonisti accaniti del sistema degli scioperi e abbiano fatto, e facciano ancora oggi, quasi ovunque, degli sforzi inimmaginabili per distoglierne il proletariato. Mazzini non ha mai voluto sentir parlare degli scioperi; e se i suoi discepoli, d’altronde passabilmente demoralizzati, disorientati e disorganizzati dopo la sua morte, oggi prendono, del resto molto timidamente, la loro difesa, è perché la propaganda della rivoluzione sociale ha talmente invaso le masse italiane, e perché le rivoluzioni sociali si sono manifestate con una tale potenza nei differenti scioperi che ultimamente sono scoppiati contemporaneamente in molti punti dell’Italia, che essi hanno sentito che, se si fossero opposti più a lungo a questo movimento irresistibile e formidabile, essi si sarebbero trovati presto completamente soli. Mazzini, con tutti i radicali e i socialisti borghesi dell’Europa, aveva avuto ben ragione a condannare gli scioperi – dal suo punto di vista, s’intende. Cosa voleva? Che vogliono ancora i mazziniani, che oggi spingono lo spirito di conciliazione fino ad unirsi anche con i cosiddetti radicali del Parlamento italiano? La costruzione di un grande Stato unitario, democratico e repubblicano. Ma per costruire questo Stato, bisogna rovesciare prima quello che esiste, e perciò il braccio potente del popolo è indispensabile. Una volta che il popolo avrà reso questo grande servizio ai politici della scuola mazziniana, lo si rimanderà naturalmente nelle sue officine o nelle sue campagne, perché vi riprenda il suo lavoro così utile, sotto l’egida non più paterna, ma fraterna, benché non meno autoritaria, del nuovo governo repubblicano. Ora, al contrario, bisogna chiamarlo sulla piazza pubblica. Come sollevarlo?
Fare appello ai suoi istinti socialisti? È impossibile. Sarebbe il mezzo più sicuro per aizzare contro di sé e contro la repubblica che si sogna, tutta la classe dei capitalisti e dei proprietari, ed è esattamente con essi che si vuole vivere e che si vuole costituire il nuovo governo. Non si costituisce un governo regolare con delle masse barbare, ignoranti, anarchiche, soprattutto quando queste masse sono state sollevate nel nome delle loro rivendicazioni economiche attraverso la passione della giustizia, dell’uguaglianza e della loro reale libertà, che è incompatibile con qualsiasi governo. Dunque, bisogna evitare la questione sociale, e sforzarsi di risvegliare [presso i lavoratori] le passioni politiche e patriottiche, grazie alle quali il loro cuore potrà battere all’unisono con il cuore dei borghesi, e il loro braccio sarà disposto a rendere ai politici radicali di quella classe il prezioso servizio che domandano, quello di rovesciare il governo della monarchia.
Ma noi abbiamo [visto] che gli scioperi hanno per primo effetto quello di distruggere quell’armonia commovente e così vantaggiosa alla borghesia, ricordando al proletariato che esiste un abisso fra quella e lui stesso, e risvegliando nel suo seno delle passioni socialiste che sono assolutamente incompatibili con le passioni politiche e patriottiche. Dunque, Mazzini ha avuto mille volte ragione: bisogna condannare gli scioperi.
Si è mostrato in ciò mille volte più logico che i marxiani, capi attuali del Partito della democrazia socialista della Germania, che pongono anch’essi come scopo immediato e principale dell’agitazione legale del loro partito, la conquista del potere politico, e che, di conseguenza, come Mazzini, vogliono servirsi della potenza muscolare del popolo tedesco per conquistare quel potere, così ardentemente bramato, per offrirlo, senza dubbio, al loro capo supremo, il dittatore dell’Internazionale, il sig. Marx.
Vi sono oggi, tra il programma politico dei marxiani e quello dei mazziniani, più punti di somiglianza di quanto ci si possa immaginare, ed io non sarei per niente stupito se il sig. Marx, certamente respinto da tutti i rivoluzionari socialisti seri e sinceri dell’Italia, finisse per concludere un’alleanza offensiva e difensiva con il partito, i discepoli del suo irriconciliabile antagonista, Mazzini. Mazzini, malgrado tutto il suo idealismo, tanto profondo quanto sincero, e che gli faceva disprezzare i beni materiali per se stesso e, facendo senza dubbio una concessione necessaria alla brutalità inerente alle masse, aveva fatto loro quasi tutte le promesse economiche e sociali che oggi fa loro Marx. È anche giunto fino a parlare loro dell’uguaglianza economica e del diritto di ogni lavoratore al prodotto integrale del suo lavoro. Ma questa sola parola non contiene in effetti tutta la rivoluzione sociale?
Mazzini, per le ragioni che ho appena esposto, non voleva affatto l’antagonismo delle masse contro le classi. Ma il sig. Marx lo vuole ben sinceramente, questo antagonismo, che rende assolutamente impossibile ogni partecipazione delle masse all’azione politica dello Stato? Perché questa azione, al di fuori della borghesia, non è affatto praticabile; essa non è possibile che quando si sviluppa di concerto con un qualsiasi partito di quella classe e si lascia dirigere da dei borghesi. Il sig. Marx non può ignorare tutto ciò; e del resto ciò che succede oggi a Ginevra, a Zurigo, a Basilea, e in tutta la Germania, dovrebbe bene aprirgli gli occhi, se su questo punto li aveva chiusi, ciò che francamente non credo. Mi è impossibile crederlo, dopo aver letto il discorso che ha pronunciato ultimamente ad Amsterdam e nel quale ha detto che, in certi paesi, e forse anche in Olanda, la questione sociale poteva essere risolta pacificamente, legalmente, senza lotta, in via amichevole, ciò che non può significare altra cosa che questo: essa può risolversi con una serie di transazioni successive, pacifiche, volontarie e sagge, fra la borghesia e il proletariato. Mazzini non ha mai detto altro.
Infine Mazzini e Marx sono d’accordo ancora su questo punto capitale, che le grandi riforme sociali che devono emancipare il proletariato non possono essere realizzate che da un grande Stato democratico, repubblicano, molto potente e fortemente centralizzato e che, per la stessa salvezza del popolo, per potergli dare l’istruzione e il benessere, bisogna imporgli, per mezzo del suo stesso suffragio, un governo molto forte.
Fra Mazzini e Marx esiste tuttavia un’enorme differenza, e questa è tutta ad onore di Mazzini. Mazzini era un credente profondo, sincero, appassionato. Egli adorava il suo Dio, al quale rapportava tutto ciò che sentiva, tutto ciò che pensava, tutto ciò che faceva. In relazione alla sua stessa persona, era l’uomo più semplice, più modesto, più distaccato da se stesso. Il suo cuore traboccava d’amore per l’umanità e di benevolenza per tutti. Ma diventava spietato, furioso, quando si toccava il suo Dio.
Il sig. Marx non crede in Dio, ma crede molto in se stesso, e rapporta tutto a se stesso. Ha il cuore pieno non di amore, ma di fiele, e molto poca benevolenza naturale per gli uomini, ciò che, tuttavia, non gli impedisce di diventare altrettanto furioso e infinitamente più malvagio di Mazzini, quando si osi solamente mettere [in] questione l’onniscienza della Divinità che adora, cioè del sig. Marx stesso. Mazzini voleva imporre all’umanità il giogo di Dio, il sig. Marx pretende imporle il suo. Io non voglio né l’uno né l’altro, ma, se fossi costretto a scegliere, preferirei ancora il Dio mazziniano.
Ho creduto dover dare questa spiegazione perché i discepoli, e amici di Mazzini, non possano accusarmi di ingiuriare la memoria del loro maestro paragonandolo al sig. Marx. Io ritorno al mio soggetto.
Dunque dico che, per tutte le ragioni che ho esposto, non mi meraviglierò per nulla se sentiremo parlare presto di una riconciliazione, di un’intesa, di un’alleanza fra l’agitazione mazziniana e l’intrigo marxiano in Italia. Se questa non si realizza, sarà colpa dei mazziniani, non del sig. Marx. Sostengo che, per poco che il partito marxiano, quello della democrazia cosiddetta socialista, continui a marciare sulla strada delle rivendicazioni politiche, si vedrà costretto a condannare, presto o tardi, quella della rivendicazione economica, la strada degli scioperi, a tal punto queste due vie sono realmente incompatibili.
Noi abbiamo avuto un esempio sorprendente di questa incompatibilità nel 1870 a Ginevra, dove, un grande sciopero di operai edili era scoppiato prima della guerra, gli internazionalisti-cittadini della “ fabbrica”, dopo aver sostenuto ed anche incoraggiato questo sciopero per un po’ di tempo, per ostentazione, lo fecero cessare d’un colpo e quasi per forza, a detrimento di quei disgraziati operai, appena i capi del partito radicale borghese di Ginevra ne ebbero intimato loro l’ordine. Abbiamo egualmente visto, sei o otto mesi fa, sempre a Ginevra, un avvocato appartenente al partito radicale e contemporaneamente all’Internazionale, il sig. Amberny – quello che il sig. Marx stesso, in una lettera che gli ha spedito, ha graziosamente ringraziato di aver servito l’Internazionale di Ginevra – garantire pubblicamente, davanti ai suoi concittadini borghesi, a nome dell’Internazionale, che non vi sarebbero stati scioperi per quell’anno.
Mi si obietterà che nei paesi dove l’organizzazione degli scioperi ha raggiunto un grado di potenza sconosciuto in altri paesi, vedi in Inghilterra, gli operai, lungi dal restare indifferenti alle agitazioni politiche, al contrario vi si interessano molto, e mi si mostrerà la Lega per la conquista del suffragio universale fondata da appena sei anni e che, composta in maggior parte da lavoratori manuali, costituisce già il nucleo di una forza politica francamente popolare e talmente rispettabile che gli stessi ministri di sua Maestà la regina, si vedono già costretti a tenerne conto e a parlamentare con essa.
Tutto ciò costituisce un fatto esclusivo, ma evidente, un fatto di cui mi è impossibile negare l’importanza, per quanto contrario sia alle mie idee generali. Vi sono ben anche altri fatti che si producono in questo stesso paese e in una maniera così seria che si è costretti ad accettarli o a prenderli almeno in considerazione molto seriamente, sebbene, del resto molto più in apparenza che in realtà, essi si trovino in completa opposizione con lo sviluppo logico delle idee. Tale è, per esempio, la tendenza manifesta del proletariato inglese alla costruzione di uno Stato comunista, unico banchiere, e unico proprietario della terra che amministrerà da sovrano a nome del popolo intero, e che farà coltivare, come ce l’ha spiegato un delegato inglese al Congresso di Basilea, membro dell’ex Consiglio generale di Londra, dagli operai agricoli, sotto la direzione diretta dei suoi ingegneri.
Cerchiamo di spiegarci questa apparente contraddizione di un popolo così geloso dei suoi diritti e che attende la sua emancipazione dalla potenza dello Stato. Nel mondo non esistono che due grandi paesi in cui il popolo gode realmente della libertà e della potenza politica. Sono l’Inghilterra e gli Stati Uniti d’America. La libertà è qui più che un diritto politico. È la natura sociale di tutti, talmente generale che gli stessi stranieri più diseredati, i più miserabili, qui godono di questa libertà con altrettanta pienezza quanto i cittadini più ricchi e più influenti. Essi ne godono senza esserne in alcun modo debitori ai governi di quei paesi, e senza che questi governi abbiano la minima possibilità di restringere i loro diritti, che, sotto l’aspetto della libertà, sono uguali ai diritti di tutti. Noi sappiamo ciò che è costato, dopo l’attentato di [Felice] Orsini, a Lord Palmerston, uno dei ministri più popolari che vi siano mai stati in Inghilterra, aver tentato di sottomettere la libertà degli stranieri al dispotismo ministeriale. L’indignazione unanime del popolo inglese l’avrebbe rovesciato in un sol colpo.
Il fatto che ho ricordato dimostra anche che quella libertà del popolo inglese costituisce una vera potenza, ciò che si chiama la potenza dell’opinione, ma non soltanto dell’opinione delle classi politiche o privilegiate, ma \emph{la vera potenza dell’opinione popolare}, potenza che esiste come un fatto sociale e che agisce come una forza sempre latente e sempre pronta a risvegliarsi e a farsi sentire, al di fuori e al di sopra di tutte le forme politiche e dei diritti esplicitamente espressi e consacrati dalla Costituzione inglese. Non soltanto oggi che i diritti elettorali sono considerevolmente allargati, ma anche allora che erano esclusivamente concentrati nelle mani di una minoranza altamente privilegiata, le agitazioni delle masse, gli immensi meeting popolari che gli Inglesi sanno così ben organizzare, pesavano in modo molto considerevole sulla direzione politica e sulle risoluzioni del Parlamento inglese.
Si è voluto fare onore, con questo fatto, alla prudente perspicacia e alla grande saggezza politica dell’aristocrazia e della ricca borghesia. Io non pretendo contestare loro questa saggezza, ma penso che si debba cercare la principale ragione di questo fatto nel temperamento storico e nelle abitudini sociali del popolo inglese, che, da moltissimo tempo, si è abituato a fare rispettare la sua libertà e a esercitare questa pressione politica con la sua opinione e con le sue aspirazioni sugli atti dei rappresentanti legali del suo paese. In una parola, il popolo inglese non ha bisogno di conquistare né la sua libertà, né la sua potenza politica, le possiede già di fatto, nei suoi costumi. Ciò che gli manca ancora e ciò che non mancherà di conquistare presto, è la conformità completa delle sue istituzioni e delle sue leggi di fatto già da lungo tempo realizzata. Ciò che io dico del popolo inglese si rapporta naturalmente, ancora di più, al popolo degli Stati Uniti d’America, dove la libertà e dove l’azione politica direttamente esercitate dalle masse, hanno raggiunto il più alto grado di sviluppo conosciuto finora nella storia.
Si può dire che non esiste oggi, nel mondo, un altro popolo veramente politico come questi due popoli. Per essi, la politica è un fatto, una realtà ben conosciuta e da molto esercitata; per tutti gli altri, senza eccettuarne nemmeno il popolo francese, è un ideale; per i Tedeschi, è una dottrina. Il popolo francese ha avuto pure i suoi momenti politici, ma non furono che dei momenti, e per questa ragione stessa essi crearono altrettante rivoluzioni che raramente durarono dei mesi, e più spesso soltanto qualche giorno. Questi giorni furono dei giorni di libertà e di festa, durante i quali le masse, inebriate della loro vittoria, credevano di aver conquistato il diritto di respirare a pieni polmoni; dopo di che, con il loro stesso consenso, e servendosi del loro stesso suffragio, li si rimetteva di nuovo sotto quelle macchine pneumatiche che si chiamano governi, monarchici o repubblicani: il nome non cambiava niente, perché nessuno ignora che, gli uni come gli altri, in Francia, come in tutti gli altri paesi del continente dell’Europa, non hanno mai significato altra cosa che la piena compressione della libertà popolare, sotto il giogo di una burocrazia insieme religiosa, poliziesca, fiscale, militare e civile.
Se si considerano queste enormi differenze di temperamento, di sviluppo storico, di costumi e di abitudini sociali, si arriva a questa conclusione: che soltanto il popolo americano e il popolo inglese hanno la coscienza politica, e che tutti i popoli del continente dell’Europa non l’hanno assolutamente. Ora sorge un problema. Si può sperare di poter dare, attraverso la propaganda, questa coscienza ad un popolo che non la trova né nel suo temperamento, né nelle sue abitudini, né nella sua propria storia? Ciò che equivale a domandare: si può fare di un tedesco, di un francese, un americano o un inglese? Forse vi sarebbe un’altra domanda da porre: è ugualmente desiderabile vedersi risvegliare la coscienza politica presso le nazioni che ne sono state private fino ad ora, e ciò esattamente in un’epoca come la nostra, nella quale, presso gli stessi popoli che la possiedono, questa coscienza, giunta al suo punto culminante, e dopo aver prodotto tutti i suoi frutti, tende evidentemente a trasformarsi in coscienza anti-politica, cioè socialista rivoluzionaria?
Ma consideriamo la prima domanda. Una volta risolta quella, la seconda si risolverà da sola. Si può sperare di poter dare, per mezzo della propaganda più abilmente organizzata e più energicamente esercitata, alle masse popolari di una nazione, delle tendenze, delle aspirazioni, delle passioni, dei pensieri che non siano il prodotto della loro propria storia e che, di conseguenza, esse non portano affatto naturalmente, istintivamente nel loro seno? Mi sembra che ad una domanda posta così, ogni uomo coscienzioso, ragionevole, e che ha la minima idea della maniera in cui si sviluppa la coscienza popolare, non può dare che una risposta negativa. E in effetti, nessuna propaganda ha mai dato ad un popolo la sostanza delle sue aspirazioni e delle sue idee, essendo sempre stata, questa sostanza, il prodotto dello sviluppo spontaneo e delle condizioni reali della sua vita. Che può fare, dunque, la propaganda? Apportando un’espressione generale, più giusta, una forma felice e nuova, agli istinti propri del proletariato, essa può, qualche volta, facilitarne e precipitarne lo sviluppo, soprattutto dal punto di vista della loro trasformazione in coscienza e in volontà ponderata delle stesse masse. Essa può dare loro la coscienza di ciò che esse hanno, di ciò che esse sentono, di ciò che vogliono già istintivamente, ma mai essa potrà dare loro ciò che non hanno, né risvegliare nel loro seno delle passioni che sono loro estranee per la loro stessa storia.
Ora, per decidere questa questione, se per mezzo della propaganda si può dare la coscienza politica a un popolo che non l’ha mai avuta fino a quel momento, esaminiamo ciò che costituisce realmente \emph{nelle masse popolari}, questa coscienza. Io dico espressamente \emph{nelle masse popolari}, perché noi sappiamo molto bene che nelle classi più o meno privilegiate, questa coscienza non è altra cosa che quella del diritto conquistato, assicurato e regolato di sfruttare il lavoro delle masse e di governarle, in vista di questo sfruttamento. Ma nelle masse, che sono state eternamente asservite, governate, sfruttate, che cosa può costituire la coscienza politica? Non può essere sicuramente che una sola cosa, la santa rivolta, questa madre di ogni libertà, la tradizione della rivolta, l’arte consueta di organizzare e di far trionfare la rivolta, quelle condizioni storiche essenziali di ogni pratica reale della libertà.
Noi dunque vediamo che queste due parole, coscienza politica, fin dalla loro stessa origine, e attraverso tutto lo sviluppo della storia, hanno due sensi assolutamente diversi, opposti, secondo i due punti di vista, egualmente opposti, nei quali ci piace esaminarle. Dal punto di vista delle classi [privilegiate], significano conquista, asservimento, e \emph{organizzazione dello Stato tale e quale}, in vista dello sfruttamento delle masse asservite e conquistate. Dal punto di vista delle masse, al contrario, significano \emph{rivolta contro lo Stato}, e, nella loro ultima conseguenza, distruzione dello Stato. Due cose, come si vede, talmente diverse che sono diametralmente opposte.
Ora si può affermare con una certezza assoluta che non vi è mai stato nessun popolo sulla terra, per quanto imbastardito o per quanto maltrattato sia stato dalla natura, che non abbia sentito, almeno all’origine del suo asservimento, qualche velleità di rivolta. La rivolta è un istinto della vita; il verme stesso si rivolta contro il piede che lo schiaccia e, in generale, si può dire che l’energia vitale e la dignità comparativa di ogni animale si misura dall’intensità dell’istinto di rivolta che porta in se stesso. Nel mondo animale, come nel mondo umano, non vi è affatto facoltà o abitudine più degradante, più stupida e più vile, di quella di obbedire e di rassegnarsi. Ebbene, io sostengo che non vi è mai stato nessun popolo così degradato, sulla terra, che non si sia affatto rivoltato, almeno agli inizi della sua storia, contro il giogo dei suoi conquistatori, dei suoi asservitori, dei suoi sfruttatori, contro il giogo dello Stato.
Ma bisogna riconoscere che, dopo le lotte sanguinose del Medioevo, il giogo dello Stato è prevalso contro tutte le rivolte popolari e che, ad eccezione dell’Olanda e della Svizzera, si è consolidato trionfante in tutti i paesi del continente dell’Europa. Ha creato una civiltà nuova: quella dell’asservimento forzato delle masse e della schiavitù interessata e, di conseguenza più o meno volontaria, alle classi privilegiate. Ciò che si è chiamato, fino qui, rivoluzione – ivi compresa anche la grande Rivoluzione francese, malgrado la magnificenza dei programmi a nome dei quali era stata compiuta – non è stata in effetti niente altro che la lotta di quelle classi fra di loro, per il godimento esclusivo dei privilegi garantiti dallo Stato, la lotta per la dominazione e per lo sfruttamento delle masse.
Ma le masse? Ahimé! bisogna riconoscerlo, si sono lasciate profondamente demoralizzare, asservire, per non dire castrare, dall’azione deleteria della civilizzazione dello Stato. Schiacciate, avvilite, esse hanno contratto l’abitudine fatale ad una obbedienza e ad una rassegnazione pecoresca, e, di conseguenza, si sono trasformate in immense greggi artificialmente divise e ammassate, per la più grande comodità dei loro sfruttatori di ogni sorta.
Io so molto bene che i sociologi della scuola del sig. Marx, come il sig. Engels vivo, come [Ferdinand] Lassalle morto, ad esempio, mi obietteranno che lo Stato non fu affatto la causa di questa miseria, di questa degradazione e di questa schiavitù delle masse; che la miserabile situazione delle masse, come la potenza dispotica dello Stato furono, al contrario, una e l’altra, gli effetti di una causa più generale, i prodotti di una fase inevitabile nello sviluppo economico della società, di una fase che, dal punto di vista della storia, costituisce un vero progresso, un immenso passo verso ciò che essi chiamano, essi, la rivoluzione sociale. A tal punto che Lassalle non ha esitato a proclamare ad alta voce che la disfatta della formidabile rivolta dei contadini della Germania nel sedicesimo secolo – disfatta deplorevole, quant’altre mai, e dalla quale inizia la schiavitù dei Tedeschi – e il trionfo dello Stato dispotico e centralizzato che ne fu la conseguenza necessaria, costituirono un vero trionfo per questa rivoluzione; perché i contadini, dicono i marxiani, sono i rappresentanti naturali della reazione, mentre lo Stato militare, burocratico, moderno – prodotto ed accompagnamento obbligato della rivoluzione sociale che, a partire dalla seconda metà del sedicesimo secolo, ha iniziato la trasformazione lenta, ma sempre progressiva, dell’antica economia feudale o terriera in produzione di ricchezze, o, ciò che significa la stessa cosa, in sfruttamento del lavoro popolare, da parte del capitale – fu una condizione essenziale di quella rivoluzione.
Si concepisce che, spinto da quella stessa logica, il sig. Engels, in una lettera indirizzata nel corso di quest’anno ad uno dei nostri amici, abbia potuto dire, senza la minima ironia e, al contrario, molto seriamente, che il sig. Bismarck, come il re Vittorio Emanuele, hanno reso immensi servizi alla rivoluzione, avendo, sia l’uno che l’altro, creato la grande centralizzazione politica dei loro rispettivi paesi. Io raccomando molto lo studio e lo sviluppo di questo pensiero, tutto marxiano, ai Francesi alleati o partigiani del sig. Marx nell’Internazionale.
Materialisti e deterministi, come il sig. Marx stesso, anche noi riconosciamo la concatenazione fatale dei fatti economici e politici nella storia. Riconosciamo anche la necessità, il carattere inevitabile di tutti gli avvenimenti che accadono, ma non ci inchiniamo indifferentemente davanti ad essi, e soprattutto ci guardiamo bene dal lodarli o dall’ammirarli quando, per loro natura, si mostrano in opposizione flagrante con il fine supremo della storia, con l’ideale sostanzialmente umano che si ritrova, sotto forme più o meno manifeste, negli istinti, nelle aspirazioni popolari e sotto i simboli religiosi di tutte le epoche, perché è inerente alla razza umana, la più socievole di tutte le razze animali sulla terra.
Questo fine, questo ideale, oggi più compresi che mai, possono riassumersi con queste parole: \emph{È il trionfo dell’umanità, è la conquista e il compimento della piena libertà e del pieno sviluppo materiale, intellettuale e morale di ciascuno, tramite l’organizzazione assolutamente spontanea e libera della solidarietà economica e sociale, tanto completa quanto} \emph{possibile, fra tutti gli esseri umani viventi sulla terra}.
Ora, tutto ciò che nella storia si mostra conforme a questo fine, dal punto di vista umano – e noi non possiamo averne altri – è buono; tutto ciò che gli è contrario è cattivo. Sappiamo anche molto bene che, ciò che noi chiamiamo buono e ciò che noi chiamiamo cattivo, sono sempre, l’uno e l’altro, dei risultati naturali di cause naturali e che, di conseguenza, uno è inevitabile quanto l’altro. Ma come, in ciò che si chiama propriamente la natura, riconosciamo molte necessità che siamo molto poco disposti a benedire, ad esempio la necessità di morire arrabbiati quando si è stati morsi da un cane arrabbiato, così, in questa continuazione immediata della vita naturale che si chiama la storia, noi incontriamo molte necessità che troviamo molto più degne di maledizione che di benedizione, e che crediamo di dover stigmatizzare con tutta l’energia di cui siamo capaci, nell’interesse della nostra moralità, sia individuale che sociale, sebbene riconosciamo che, dal momento che sono compiuti, anche i fatti storici più detestabili, recano in sé quel carattere di inevitabilità che noi ritroviamo altrettanto in tutti i fenomeni della natura che in quelli della storia.
Per rendere il mio pensiero più chiaro, lo voglio illustrare con qualche esempio. Quando studio le condizioni politiche e sociali rispettive nelle quali i Romani ed i Greci si sono imbattuti al declino dell’evo antico, arrivo a questa conclusione; che la conquista e la distruzione della libertà, in paragone così altamente umana della Grecia, da parte delle barbarie militari e civiche dei Romani, è stato un fatto logico, naturale, assolutamente inevitabile. Ma ciò non mi impedisce affatto di prendere retrospettivamente e molto risolutamente la parte della Grecia contro Roma in questa lotta, e io trovo che l’umanità non ha guadagnato assolutamente nulla dal trionfo dei Romani.
Ugualmente, considero come un fatto perfettamente naturale, logico e, di conseguenza, inevitabile, che i cristiani, che erano per grazia di Dio dei cretini, abbiano annientato, col santo furore che si sa, tutte le biblioteche dei pagani, tutti i tesori dell’arte, della filosofia e della scienza antiche. Ma mi è decisamente impossibile cogliere i vantaggi che ne sono risultati per il nostro sviluppo politico e sociale. Sono anche molto disposto a pensare che, al di fuori di questo progresso fatale dei fatti economici, nel quale, se si dà retta al sig. Marx, bisogna cercare, con l’esclusione di tutte le altre considerazioni, la causa unica di tutti i fatti ineluttabili e morali che si producono nella storia, – sono molto disposto a pensare che questo atto di santa barbarie, o piuttosto questa lunga serie di atti barbari e di crimini che i primi cristiani, divinamente ispirati, commisero contro lo spirito umano, fu una delle cause principali dell’avvilimento intellettuale e morale e, di conseguenza, anche dell’asservimento politico e sociale, che riempirono questa lunga serie di secoli nefasti che si chiama Medioevo. Siatene ben certi, se i primi cristiani non avessero distrutto le biblioteche, i musei ed i templi dell’antichità, noi oggi non saremmo condannati a combattere questo mucchio di assurdità orribili, vergognose, che ostruiscono ancora i cervelli al punto di farci dubitare, qualche volta, della possibilità di un avvenire più umano.
Seguendo sempre lo stesso ordine di proteste contro fatti che si sono compiuti nella storia e di cui, di conseguenza, anch io riconosco il carattere inevitabile, io mi fermo davanti allo splendore delle repubbliche italiane e davanti al magnifico risveglio del genio umano, all’epoca del Rinascimento. Quindi io vedo avvicinarsi due geni del male, tanto antichi quanto la storia, i due boa constrictor che hanno divorato, fin qui, tutto ciò che la storia ha prodotto di umano e di bello. Si chiamano la Chiesa e lo Stato, il \emph{Papato e l’Impero}. Eterni rivali e inseparabili alleati, io li vedo riconciliarsi, abbracciarsi, e divorare e soffocare e schiacciare insieme la disgraziata e troppo bella Italia, condannarla a tre secoli di morte. Ebbene, trovo ancora tutto ciò molto naturale, logico, inevitabile, ma tuttavia abominevole, e io maledico, al tempo stesso, e il Papa e l’Imperatore.
Passiamo alla Francia. Dopo una lotta che è durata un secolo, il cattolicesimo, sostenuto dallo Stato, vi ha finalmente trionfato sul protestantesimo. Ebbene, ancora oggi, non si trovano in Francia dei politici o degli storici della scuola fatalista e che, dicendosi rivoluzionari considerano questa vittoria del cattolicesimo – vittoria sanguinosa ed inumana più che mai – come un vero trionfo per la Rivoluzione? Il cattolicesimo, pretendono, allora era lo Stato, la democrazia, mentre il protestantesimo rappresentava la rivolta dell’aristocrazia contro lo Stato e, di conseguenza, contro la democrazia. È con simili sofismi, d’altronde del tutto identici ai sofismi marxiani, che anch’essi, considerano i trionfi dello Stato come quelli della democrazia sociale, – è con queste assurdità così disgustose quanto rivoltanti che si corrompe lo spirito e il senso morale delle masse, abituandole a considerare i loro sfruttatori sanguinari, i loro nemici secolari, i loro tiranni, padroni servitori dello Stato, come degli organi, dei rappresentanti, degli eroi, dei servitori devoti della loro emancipazione. Quanto [Louis] Veuillot non è più sincero, più logico e più vero, constatando la profonda somiglianza che esiste fra la San Bartolomeo, ad esempio, e il massacro dei Comunardi da parte di quegli eccellenti cattolici di Versailles, diretti dalla Caterina dei Medici dei nostri giorni, il sig. Thiers? Ha mille volte ragione di dire che il protestantesimo allora, non come teologia calvinista, ma come protesta energica ed armata, rappresentava la rivolta, la libertà, l’umanità, la distruzione dello Stato; mentre il cattolicesimo era l’ordine pubblico, l’autorità, la legge divina, la salvezza dello Stato da parte della Chiesa e della Chiesa da parte dello Stato, la condanna della società umana ed un asservimento senza limiti e senza fine.
Riconoscendo l’inevitabilità del fatto compiuto, non esito a dire che il trionfo del cattolicesimo in Francia nel sedicesimo e diciassettesimo secolo, fu una grande disgrazia per tutta quanta l’umanità, e che la San Bartolomeo, così come la revoca dell’editto di Nantes, furono dei fatti tanto disastrosi per la stessa Francia, quanto lo è stata ultimamente la sconfitta e il massacro del popolo di Parigi. Mi è accaduto di sentire dei Francesi assai intelligenti e assai rispettabili spiegare quella sconfitta del protestantesimo in Francia, con la natura essenzialmente rivoluzionaria del popolo francese. “Il protestantesimo, dicevano, non è stato che una mezza rivoluzione; noi volevamo la rivoluzione intera, è per questo che la nazione francese non ha voluto, non ha potuto, arrestarsi alla riforma. Essa ha preferito rimanere cattolica fino al momento in cui avrebbe potuto proclamare l’ateismo; ed è a causa di ciò che ha sopportato con una rassegnazione così perfetta, così cristiana, e gli errori della San Bartolomeo e la tirannia, non meno orribile, degli esecutori della revoca dell’editto di Nantes”.
Questi stimabili patrioti sembrano non voler considerare una cosa. Cioè che un popolo che, sotto qualsiasi pretesto, sopporta la tirannia, necessariamente a lungo andare perde l’abitudine salutare di rivoltarsi, e perfino lo stesso istinto di rivolta. Perde il sentimento della libertà, e la volontà, l’abitudine di essere libero e, una volta che un popolo ha perso tutto ciò, diviene necessariamente, non soltanto per le sue condizioni esteriori, ma interiormente, nell’essenza stessa del suo essere, un popolo schiavo. È perché il protestantesimo è stato vinto in Francia che il popolo francese ha perso, o piuttosto non ha acquistato, i costumi della libertà; è perché questa tradizione e questi costumi gli mancano, che egli non ha oggi ciò che noi chiamiamo la \emph{coscienza politica}, ed è perché è privato di questa coscienza che tutte le rivoluzioni che ha fatto fin qui, non hanno nemmeno potuto dargli od assicurargli la libertà politica. Ad eccezione dei suoi grandi giorni rivoluzionari, che sono i suoi giorni di festa, il popolo francese resta, oggi come ieri, un popolo schiavo.
Passando ad un altro ordine di fatti, io giungo alla \emph{spartizione della Polonia}. Qui sono molto felice di potermi, almeno una volta, incontrare con Marx, perché anch’egli, come me, come tutti, chiama questa spartizione un \emph{grande crimine}. Soltanto, vorrei sapere come lui, essendosi dato un punto di vista fatalista e ottimista insieme, ha potuto permettersi, ha potuto motivare, una simile condanna di un grande fatto storico compiuto. Proudhon, che egli ama tanto, è stato più logico, più conseguente di lui. Volendo ad ogni costo assolvere la storia, ha scritto un opuscolo sfortunato, nel quale, dopo aver dimostrato con molta ragione che la Polonia nobiliare doveva perire, perché portava in sé i germi della dissoluzione, ha provato ad opporle l’Impero degli zar, come rappresentante della democrazia socialista trionfante. Ciò era più che un errore, non esito a dirlo, malgrado il tenero rispetto che ho per la memoria di Proudhon, era un crimine: il crimine di un sofista che, trasportato dal bisogno della polemica, non ha temuto d’insultare una nazione martire, nel momento stesso in cui, rivoltatasi per la centesima volta contro i suoi orrendi tiranni russi e tedeschi, per la centesima volta cadeva abbattuta sotto i loro colpi. (Il crimine di Proudhon non fu di avere vittoriosamente dimostrato due verità: la prima, è che l’antica repubblica e l’antica libertà polacche erano istituzioni nobiliari fondate sull’asservimento e sullo sfruttamento di tutta la popolazione rurale; e la seconda, che l’insurrezione del 1863, ispirata, come tutte le insurrezioni precedenti, dal pensiero patriottico ed ardente, esclusivamente politico, ma per nulla socialista, di ristabilire il grande Stato polacco nei suoi antichi confini, doveva essere fatalmente un’impresa fallita. Era forse crudele dire queste verità ad una nazione sfortunata, nel momento stesso in cui soccombeva sotto il ferro stesso dei suoi assassini. Ma infine erano delle verità, e come tali potevano, dovevano essere dette. Il crimine di Proudhon è consistito in questo: per opposizione ai patrioti polacchi, si è sforzato di rappresentare le truppe, i funzionari, gli sbirri dello zar come degli emancipatori socialisti dei contadini della Polonia, oppressi dai loro signori insorti. Proudhon, come la maggior parte dei suoi compatrioti, ignorava profondamente sia la Polonia che la Russia; ma in mancanza di conoscenza, il suo istinto di rivoluzionario avrebbe dovuto premunirlo contro una mostruosità che gli è valsa i ringraziamenti calorosi dei nostri patrioti panslavisti di Mosca, e ciò nel momento stesso in cui i loro compagni, i loro amici, i [Dimitrij] Miljutin, [Aleksej] Cerkasskij e molti altri procedevano alla conquista dei beni dei Polacchi insorti, non per darli ai contadini, ma per dividerli fra i funzionari e i generali russi, che fin da allora hanno fatto di tutto, come ci si doveva attendere, per fare detestare ancora di più il regime imperiale in Polonia. L’Impero russo emancipatore; ecco una assurdità rivoltante, che non fa certo onore né al giudizio né all’istinto rivoluzionario di Proudhon).
Ma per quale caso il sig. Marx si è lasciato trascinare, una volta, a fare dell’umanità a detrimento della conseguenza delle sue stesse idee? Ma la spiegazione di ciò non è affatto difficile da dare.
Il sig. Marx non è soltanto un socialista sapiente, è anche un politico molto abile e un ardente patriota. Come Bismarck, benché per vie un po’ diverse, e come molti altri suoi compatrioti, socialisti o non socialisti, vuole la costruzione di un grande Stato germanico, per la gloria del popolo tedesco e per la felicità, per la civilizzazione, volontaria o forzata, del mondo. La realizzazione di questo scopo ha incontrato tre ostacoli: 1° la rivalità fatale dei due più grandi Stati germanici, la Prussia e l’Austria; 2° la potenza gelosa della Francia; e 3° la potenza minacciosa dell’Impero di tutte le Russie, che si pone come protettore dei popoli slavi contro la civiltà tedesca.
I due primi ostacoli sono stati in parte superati con la politica, tanto abile quanto potente, di Bismarck. L’Austria, che ha avuto questo grande torto agli occhi dei patrioti chiaroveggenti della Germania, di non aver saputo germanizzare completamente i popoli slavi sottomessi al suo giogo, e di aver permesso, fin dal secondo quarto di questo secolo, al pensiero, alla lingua, alla passione, alla rivendicazione slave, di risvegliarsi nel suo seno, l’Austria è stata definitivamente vinta sotto i colpi degli eserciti vittoriosi della Prussia. Essa non si risolleverà mai, tutti lo sentono, tutti lo vedono. Invano essa cerca in se stessa dei nuovi equilibri, cercando di appoggiarsi, volta a volta, ora sui Magiari, ora sugli Slavi, ora, e di nuovo, sui suoi cari Tedeschi, che, sentendola perire, cominciano a girarle le spalle per adorare l’astro brillante che sorge a Berlino. L’Austria non ha soltanto cessato di essere un ostacolo per la Prussia, o, ciò che ora significa la stessa cosa, per la Germania; la sua esistenza separata è divenuta momentaneamente un bisogno perché, a Berlino, non ci si sente ancora abbastanza preparati né abbastanza forti per ereditare da essa, per prendere il pieno possesso di tutto ciò che possiede. Se essa fosse vinta ora, sarebbe necessario abbandonarne una buona parte all’Impero di Russia, e ciò non farebbe affatto il tornaconto del sig. Marx, né quello del sig. Bismarck.
Contrariamente a Marx, Bismarck si guarda bene dall’insultare e dal provocare lo zar. Ancora per qualche tempo avrà molto bisogno di lui e, di conseguenza, lontano dall’insultarlo, lo lusinga e si dice suo amico. Ma, in politica, l’amicizia non significa nulla, e Bismarck sa, così bene come Marx, che l’ora della grande lotta fra il pangermanesimo, rappresentato dalla Prussia o da tutta la Germania prussificata, e il panslavismo, personificato nello zar, non può mancare di scoccare. Ma prima che questa scocchi, bisogna finirla innanzitutto con la Francia.
La Francia è stata certamente vinta, crudelmente ferita, ma ancora non è affatto abbattuta. Essa non è per niente rovinata, e si trova appena indebolita. Checché se ne dica – sempre considerando tutte queste questioni dal punto di vista degli Stati, non da quello della Rivoluzione sociale, che avrà come prima conseguenza quella di spazzare via tutte le vecchie questioni, per far posto a questioni nuove e del tutto differenti. Dunque, checché se ne dica, la Francia non ha dimenticato l’ingiuria sanguinosa che ha ricevuto dalla Germania. Essa riprenderà fatalmente la sua rivincita, sia prendendo l’iniziativa di una terribile rivoluzione sociale che farà crollare insieme i due Stati della Francia e della Germania e di cui, probabilmente, la direzione non sarà affidata nelle mani di nessun dittatore, sia attraverso una lotta a morte di Stato contro Stato, attraverso un duello fra la Repubblica e l’Impero.
Bismarck lo sa molto bene, ed è per questo che ha ancora bisogno dell’alleanza dello zar e per questo dirige i suoi armamenti, ancora oggi, quasi esclusivamente contro la Francia. Ma, come ho già detto, nel suo pensiero, così come in quello di Marx, la lotta con la Russia, la guerra a morte fra l’imperatore di Germania e lo zar, che scoppi un po’ più tardi o un po’ più presto, è una cosa di cui è compresa l’inevitabilità e deciso il compimento. Soltanto Bismarck vuole prima finirla completamente con la Francia, perché, politico ancora più eccellente di Marx, si dice che se tutta la Germania concentrata nelle sue mani dovesse lottare contro la Russia e la Francia contemporaneamente, potrebbe anche soccombere. Egli teme che al gabinetto di San Pietroburgo lo si comprenda troppo presto, e che, avendolo compreso, lo zar si rivolti contro di lui allorché egli attaccherà la Francia. Dunque, più saggio sotto questo rapporto di Marx, si guarda bene dall’indisporre lo zar contro di lui, e si dà tutte le pene immaginabili per disarmare le sue gelosie ed i suoi timori. Cerca di guadagnare la sua fiducia e di assicurarsi la sua connivenza lasciandogli sperare, come ricompensa della sua neutralità e, naturalmente, ancora di più, della sua cooperazione attiva, per quanto possibile, una grande estensione di territorio a detrimento sia della Turchia, sia dell’Austria.
È evidente che Bismarck darà alla Russia quanto meno possibile. Si guarderà bene dall’aumentare in un modo troppo reale la potenza di un impero contro il quale si prepara ad entrare in conflitto più tardi. Tuttavia sarà ben costretto a lasciargli fare qualche conquista seria, ma, dato che la Germania indubbiamente ne farà, nello stesso tempo, di ancora più serie, e dato, secondo tutte le probabilità, il governo e l’amministrazione germanica, incomparabilmente più capaci e meglio diretti del governo e dell’amministrazione russi, sapranno trarre più vantaggi dalle loro conquiste che non i Russi, Bismarck si dice che, alla fine dei conti, e conservata ogni proporzione, la potenza della Germania, paragonata a quella della Russia, diverrà ancora più grande, e che, rimanendo allora la Russia il solo nemico, alla Germania sarà molto più facile vincerla e schiacciarla.
Bisogna essere ciechi per non vedere che questa è, questa deve essere, la politica di Bismarck, sia di fronte alla Francia che di fronte alla Russia. Una volta dati i rapporti attuali di questi tre grandi Stati, la Francia, la Germania e la Russia, ciò risulta con la conseguenza rigorosa di una deduzione matematica. Ed è esattamente perché Bismarck lo comprende, che è un grande uomo di Stato. La sua politica è quella del presente, quella di Marx, che si considera per lo meno come il suo successore e il suo continuatore, è quella dell’avvenire. E quando dico che Marx si considera come il continuatore di Bismarck, sono lontano dal calunniare Marx. Se non si considerasse come tale, non avrebbe permesso al confidente di tutti i suoi pensieri, Engels, di scrivere che Bismarck serve la causa della Rivoluzione sociale. La serve ora a modo suo, e Marx la servirà, più tardi, in un’altra maniera. Ecco in che senso sarà, più tardi, il continuatore, come oggi è l’ammiratore, della politica di Bismarck.
Ora, esaminiamo il carattere particolare della politica di Marx. E, prima, constatiamo i punti essenziali sui quali si separa dalla politica bismarckiana. Il punto principale, e si potrebbe dire unico, è questo: Marx è democratico, socialista autoritario, e repubblicano; Bismarck è un Junker pomeraniano, aristocratico e monarchico ad ogni costo. La differenza è dunque molto grande, molto seria e, da entrambe le parti, è ugualmente sincera. Sotto questo rapporto non vi è punto d’intesa, né di riconciliazione possibile, tra Bismarck e Marx. Anche al di là di molti pegni irrecusabili che Marx, durante tutta la sua vita, ha dato alla causa della democrazia socialista, la sua stessa posizione e la sua ambizione ne sono una garanzia certa. In una monarchia, per quanto liberale sia, o anche in una repubblica conservatrice come quella di Thiers, non vi può essere alcun posto, alcun ruolo, per Marx, a maggior ragione non c’è in un Impero prusso-germanico fondato da Bismarck, con un imperatore spauracchio, caporale e devoto per capo, e con tutti i baroni e i burocrati della Germania per guardiani. Prima di arrivare al potere, Marx dovrà spazzare via tutto ciò. Dunque, egli è forzatamente rivoluzionario.
Ecco ciò che separa Marx da Bismarck: è la forma e le condizioni del governo. Uno è aristocratico e monarchico ad ogni costo; l’altro è democratico, repubblicano ad ogni costo, e, per di più, democratico socialista e repubblicano socialista.
Vediamo ora ciò che li unisce. \emph{È il culto dello Stato a qualsiasi costo}. Non ho bisogno di provarlo per Bismarck, le sue prove sono i fatti. Egli è, dalla testa ai piedi, un uomo di Stato, e niente altro che un uomo di Stato. Ma io non credo di aver bisogno di sforzi troppo grandi per dimostrare che la stessa cosa vale per Marx. Egli ama a tal punto il governo, che ne ha voluto costituire uno anche nell’Associazione Internazionale dei Lavoratori; e adora talmente il potere che ha voluto, che pretende ancora oggi di imporci la sua dittatura. Mi sembra che ciò sia sufficiente per caratterizzare le sue inclinazioni personali. Ma il suo programma socialista e politico ne è l’espressione molto fedele. Lo scopo supremo di tutti i suoi sforzi, come ce lo rivelano gli statuti fondamentali del suo partito, in Germania, è la costruzione di un grande \emph{Stato popolare} (\emph{Volksstaat}).
Ma chi dice Stato, dice necessariamente uno Stato particolare, limitato, comprendente senza dubbio, se è molto grande, molte popolazioni e paesi differenti, ma che ne esclude ancora di più. Perché, a meno di sognare lo Stato universale, come avevano fatto Napoleone e Carlo V, o come il papato aveva sognato la Chiesa universale, Marx, malgrado tutta l’ambizione internazionale che lo divora oggi, dovrà bene, quando l’ora della realizzazione dei suoi sogni sarà scoccata per lui – se suonerà mai – accontentarsi di governare un solo Stato, e non più Stati alla volta. Di conseguenza, chi dice Stato dice uno Stato, e chi dice uno Stato afferma con ciò l’esistenza di \emph{più} Stati, e chi dice più Stati dice inevitabilmente concorrenza, invidie, guerra senza tregua e senza fine. La più semplice logica come anche tutta la storia lo attestano.
È nella natura dello Stato rompere la solidarietà umana e negare, in qualche modo, l’umanità. Lo Stato non può conservarsi come tale nella sua integrità e in tutta la sua potenza, se non quando si pone come lo scopo supremo, assoluto, almeno per i suoi stessi cittadini, o, per parlare più francamente, per i suoi propri sudditi, non potendosi imporre come tale ai sudditi degli altri Stati. Da ciò risulta inevitabilmente, una rottura con la morale umana in quanto universale, con la ragione universale, a causa della nascita della morale dello Stato e di una ragione di Stato. Il principio della morale politica o di Stato, è molto semplice. Essendo lo Stato lo scopo supremo, tutto ciò che è favorevole allo sviluppo della sua potenza è buono; tutto ciò che gli è contrario, fosse anche la cosa più umana del mondo, è cattivo. Questa morale si chiama \emph{patriottismo}. L’Internazionale, come abbiamo visto, è la negazione del patriottismo e, di conseguenza, la negazione dello Stato. Dunque, se Marx e i suoi amici del Partito della democrazia socialista tedesca, potessero riuscire ad introdurre il principio dello Stato nel nostro programma, ucciderebbero l’Internazionale.
Lo Stato, per la sua conservazione, deve necessariamente essere potente al di fuori; ma se lo è al di fuori, esso lo sarà infallibilmente all’interno. Ogni Stato, dovendo lasciarsi ispirare e dirigere da una morale particolare, conforme alle condizioni particolari della sua esistenza, da una morale che è una restrizione e, di conseguenza, una negazione, della morale umana e universale, dovrà vigilare affinché tutti i suoi sudditi, nei loro pensieri e, soprattutto, nei loro atti, non s’ispirino che a princìpi di quella morale patriottica o particolare, e che restino sordi agli insegnamenti della morale meramente o universalmente umana. Da qui risulta la necessità di una censura di Stato; una libertà troppo grande del pensiero e delle opinioni essendo, come pensa Marx, d’altronde con molta ragione, dal suo punto di vista eminentemente politico, incompatibile con quella unanimità di adesione richiesta dalla sicurezza dello Stato. Che tale sia, in realtà, il pensiero di Marx, ci è sufficientemente provato dai tentativi che ha fatto per introdurre, sotto dei pretesti plausibili, mascherata, la censura nell’Internazionale.
Ma qualunque sia la vigilanza di questa censura, quand’anche lo Stato prendesse esclusivamente nelle sue mani tutta l’educazione e tutta l’istruzione popolare, come Mazzini ha voluto, e come oggi vuole il sig. Marx, lo Stato non potrebbe mai essere sicuro che non scivolino dei pensieri proibiti e pericolosi, di contrabbando, nella coscienza delle popolazioni che governa. Il frutto difeso ha molta attrattiva per gli uomini, e il diavolo della rivolta, questo eterno nemico dello Stato, si risveglia così facilmente nei loro cuori, quando non siano sufficientemente abbrutiti, che né questa educazione, né questa istruzione, né questa stessa censura, garantiscono sufficientemente la tranquillità dello Stato. Gli serve ancora una polizia, degli agenti devoti che sorveglino e dirigano, segretamente e senza che ciò appaia, il flusso dell’opinione e delle passioni popolari. Abbiamo visto che lo stesso sig. Marx è talmente convinto di questa necessità, che ha creduto bene di dover riempire di suoi agenti segreti tutte le regioni dell’Internazionale e, soprattutto, l’Italia, la Francia e la Spagna.
Infine, per quanto perfetta sia, dal punto di vista della conservazione dello Stato, l’organizzazione dell’educazione e dell’istruzione popolare, della censura e della polizia, lo Stato non può essere sicuro della sua esistenza finché non ha, per difenderla contro i \emph{nemici dell’interno}, contro il malcontento delle popolazioni, una forza armata. Lo Stato è governo dall’alto in basso di un’immensa quantità di uomini molto diversi dal punto di vista del grado della loro cultura, della natura dei paesi o delle località in cui abitano, delle loro posizioni, delle loro occupazioni, dei loro interessi e delle loro aspirazioni, da parte di una minoranza qualsiasi; questa minoranza, fosse anche mille volte eletta dal suffragio universale e controllata nei suoi atti da delle istituzioni popolari, a meno che non sia dotata dell’onniscienza, dell’onnipresenza e dell’onnipotenza che i teologi attribuivano al loro Dio, è impossibile che essa possa conoscere, prevedere i bisogni, e soddisfare, con una uguale giustizia, gli interessi più legittimi, i più palesi di tutti. Ci saranno sempre dei malcontenti, dato che ci saranno sempre dei sacrificati.
Del resto lo Stato, come la Chiesa, per sua stessa natura, è un grande sacrificatore di uomini vivi. È un essere arbitrario, nel seno del quale tutti gli interessi positivi, viventi, sia individuali che locali, delle popolazioni, vengono a misurarsi, ad urtarsi, a distruggersi a vicenda, ad immergersi in quella astrazione che si chiama interesse comune, \emph{bene pubblico}, \emph{salute pubblica}, e dove tutte le volontà reali si annullano in quell’altra astrazione che porta il nome di \emph{volontà del popolo}. Da ciò risulta che questa sedicente volontà del popolo non è mai altra cosa che il sacrificio e la negazione di tutte le volontà reali delle popolazioni; come anche, questo sedicente bene pubblico, non è altro che il sacrificio dei loro interessi. Ma, affinché questa astrazione onnivora possa imporsi a milioni di uomini, occorre che sia rappresentata e sostenuta da un essere reale, da una qualunque forza vivente. Ebbene, questo essere, questa forza, sono sempre esistiti. Nella Chiesa, si chiama clero e, nello Stato, classe dominante o governante.
Nello Stato popolare del sig. Marx, ci dicono, non ci sarà affatto classe privilegiata. Tutti saranno uguali, non soltanto dal punto di vista giuridico e politico, ma anche dal punto di vista economico. Almeno lo si promette, benché dubiti molto che, con la piega che ha preso e nella strada che vuole seguire, possa mantenere mai la sua promessa. Non ci saranno dunque più classi, ma un governo, e, notatelo bene, un governo eccessivamente complicato, che non si accontenterà di governare e di amministrare politicamente le masse, come lo fanno oggi tutti i governi, ma che, in più, le amministrerà economicamente, concentrando nelle sue mani la produzione e la giusta ripartizione delle ricchezze, la coltivazione delle terre, la costruzione e lo sviluppo delle fabbriche, l’organizzazione e la direzione del commercio, infine, la destinazione del capitale alla produzione tramite l’unico banchiere, lo Stato. Tutto ciò esigerà una scienza immensa e molte teste traboccanti di cervello in questo governo. Sarà il regno dell’\emph{intelligenza scientifica}, il più aristocratico, il più dispotico, il più arrogante e il più sprezzante di tutti i regimi. Ci sarà una nuova classe, una nuova gerarchia di sapienti reali e fittizi, e il mondo sarà diviso in una minoranza, dominante in nome della scienza, ed un’immensa maggioranza ignorante. E allora guai alla massa degli ignoranti!
Un simile regime non mancherà di sollevare dei malcontenti molto seri in questa massa, e per contenerla, il governo illuminatore ed emancipatore di Marx, avrà bisogno di una forza armata non meno seria. Perché il governo deve essere molto forte, dice Engels, per mantenere all’ordine quei milioni di analfabeti il cui sollevamento brutale potrebbe tutto distruggere e tutto rovesciare, anche un governo diretto da delle teste traboccanti di cervello.
Vedete bene che dietro tutte le frasi e tutte le promesse democratiche e socialiste del programma di Marx, si trova, nel suo Stato, tutto ciò che costituisce la natura dispotica e brutale propria di tutti gli Stati, qualsiasi sia la forma del loro governo, e che, alla fine dei conti, lo Stato popolare, tanto raccomandato da Marx, e lo Stato aristocratico-monarchico, mantenuto con tanta abilità quanta potenza, da Bismarck, s’identificano completamente per la natura del loro scopo sia interno che esterno. All’esterno, è lo stesso spiegamento di forza militare, cioè la conquista; e, all’interno, è lo stesso impiego di quella forza armata, ultimo argomento di tutti i poteri politici minacciati, contro le masse che, stanche di credere, di sperare, di rassegnarsi e di obbedire sempre, si rivoltano.
Lasciamo ora le considerazioni generali sullo Stato, ed entriamo più dentro alla politica reale, nazionale di Marx. Come Bismarck, egli è un patriota tedesco. Egli vuole la grandezza e la potenza della Germania come Stato. Nessuno, del resto, potrà fargli una colpa di amare il suo paese e il suo popolo; e, dato che è profondamente convinto che Io Stato è la condizione sine qua non della prosperità dell’uno e dell’emancipazione dell’altro, si troverà naturale che egli desideri che la Germania si organizzi in Stato e, necessariamente, in uno Stato molto grande e molto forte, poiché gli Stati deboli e piccoli corrono sempre il rischio di vedersi inghiottire. Di conseguenza Marx, come patriota perspicace e ardente, deve volere la potenza e la grandezza della Germania come Stato.
Ma, da un altro lato, Marx è un socialista celebre, e per di più uno degli iniziatori principali dell’Internazionale. Egli non si accontenta di lavorare per la sola emancipazione del proletariato della Germania; ci tiene, e considera come suo dovere, lavorare, nello stesso tempo, per l’emancipazione del proletariato di tutti gli altri paesi; ciò che fa sì che si trovi in piena contraddizione con se stesso. Come patriota tedesco, vuole la grandezza e la potenza, cioè la dominazione della Germania; ma come socialista dell’Internazionale, deve volere l’emancipazione di tutti i popoli del mondo. Come risolvere questa contraddizione?
Non vi è che un solo mezzo, cioè di proclamare, dopo essersene persuaso lui stesso, s’intende, che la grandezza e la potenza della Germania come Stato è la condizione suprema dell’emancipazione di tutti, che il trionfo nazionale e politico della Germania, è il trionfo dell’umanità e che, tutto ciò che è contrario all’avvento di questa nuova grande potenza omnivora, è nemico dell’umanità. Una volta creata questa convinzione, non è soltanto permesso, ma è comandato dalla più santa delle cause, di servirsi dell’Internazionale, ivi comprese tutte le Federazioni degli altri paesi, come un mezzo molto potente, molto comodo e, soprattutto, molto popolare, per l’edificazione del grande Stato pangermanico. È precisamente ciò che Marx aveva tentato di fare, sia con le deliberazioni della Conferenza che aveva riunito nel settembre 1871 a Londra, come con le risoluzioni votate dai suoi amici tedeschi e francesi al Congresso dell’Aia. Se non ci è riuscito meglio non è, certamente, per mancanza di sforzi molto grandi, né di molta abilità da parte sua ma, probabilmente, perché l’idea fondamentale che lo ispira è falsa e la sua realizzazione impossibile.
Questa identificazione della causa dell’umanità con quella della grande patria germanica non è affatto un’idea assolutamente nuova. Essa è stata esplicitamente espressa, per la prima volta, se non mi sbaglio, dal grande filosofo e patriota tedesco Fichte, in una serie di letture che ha fatto a Berlino, dopo la battaglia di Jena, per così dire sotto le baionette dei soldati francesi che erano di stanza nella capitale della Prussia, e che, inebriati da tutte le loro vittorie e ignoranti, come si conviene a dei bravi generali, ufficiali e soldati della Francia, si curavano poco di ciò che poteva dire un professore tedesco.
Fichte era stato scacciato poco tempo prima dall’università di Jena, sotto il governo molto illuminato del duca di Saxe-Weimar, amico di Goethe, a causa della sua fede rivoluzionaria ed atea. Ebbene, fu a quest’uomo che Stein e Hardenberg, i due ministri nuovi del re Federico Guglielmo III di Prussia, in un momento in cui la Prussia, conquistata completamente e non respirando più che per grazia del suo vincitore, si era vista immersa in uno sconforto infinitamente più opprimente di quello in cui si è trovata la Francia tra il 1870 e il 1871 – fu a quest’uomo che il governo della Prussia, ben più felicemente ispirato di quanto non lo fosse stato quello di Thiers, fece ricorso per rimontare, per rifare l’energia morale, della gioventù prussiana e tedesca.
Cosa sorprendente e degna di restare nella memoria delle nazioni! La vera grandezza della Prussia, la sua nuova potenza datano dalla catastrofe di Jena. È vero che cause anteriori, sia prussiane che tedesche, l’avevano preparata. Tra le cause esclusivamente prussiane, bisogna mettere in primo piano la politica perseverante e tortuosa di quella casa di Brandeburgo che, per tre secoli di seguito, di padre in figlio, ha sempre perseguito un solo scopo: quello della creazione di una grande potenza tedesca, fondata in parte sulla distruzione e in parte sull’asservimento, delle popolazioni slave che erano i primitivi abitanti di tutto l’attuale regno di Prussia, e di cui una parte ha conservato ancora i loro tratti, i loro costumi e persino la loro lingua slava, malgrado tutti gli sforzi che si sono fatti per germanizzarli. Da prima vassalli della corona di Polonia, i duchi di Prussia finirono per spodestare il loro antico sovrano. Prima si resero indipendenti, poi cominciarono a staccare una a una le sue province, infine, si proclamarono re, e, per mano del loro potente successore, Federico il Grande, di concerto con la Russia e l’Austria, diedero il colpo di grazia a questa disgraziata Polonia, già loro sovrana.
A meno di dar prova di profonda ignoranza, nessuno potrà contestare che tutta la potenza politica della Prussia è stata fondata esclusivamente a detrimento, e sulla completa rovina, della Polonia. Questa potenza data la sua nascita realmente dalla spartizione di quel regno-repubblica, e dalla conquista della Slesia, provincia una volta completamente e oggi ancora in gran parte polacca. È giusto ricordare questa origine, che pesa e che peserà sempre, come una fatalità, sulla potenza prussiana, e anche sulla potenza tedesca, in quanto la potenza tedesca sarà prussiana.
Ma questa nuova potenza, creata definitivamente da Federico II, non era ancora, per così dire, che una potenza tutta esteriore, tutta artificiale, meccanica, o soltanto politica. Le mancava l’anima, la sanzione nazionale. Per la maggior parte slava nelle campagne, essa non era tedesca che nelle città, nella classe borghese, nella nobiltà, nella sua burocrazia, nei suoi professori, e nel suo clero protestante, infine, alla corte, fino al momento in cui Federico II ebbe trasformato quest’ultima in una specie di corte francese, che scimmiottava, alla maniera dei Tedeschi, cioè con una grazia un po’ pesante, lo spirito, le mode e le maniere eleganti, dei Francesi.
Per farsi un’idea giusta di ciò che era la nazionalità tedesca, rappresentata dalle classi che ho appena elencato, non soltanto in Prussia, ma in tutta la Germania, non c’è niente di meglio che leggere la \emph{Storia del diciottesimo secolo} scritta dal grande storico tedesco [Julius von] Schlosser. Non ci si può immaginare niente di più abietto, di più stupido, di più vile. Erano la povertà, l’aridità, la pesantezza pedantesca di uno spirito privato di movimento e di vita, unite ad una vigliaccheria di cuore senza limiti.
Cosa strana e ugualmente degna di non essere dimenticata dai popoli! Il protestantesimo, che, se non aveva creato, aveva almeno stimolato e accompagnato, il movimento emancipatore dei popoli in tutti gli altri paesi, in Svizzera, in Inghilterra, in Olanda, in Svezia e, più tardi, in America, anche in Francia finché non vi fu vinto, solo in Germania aveva prodotto un effetto tutto contrario. Qui esso divenne la religione del dispotismo. Non bisogna forse concluderne che i Tedeschi sono un popolo veramente predestinato alla creazione di uno Stato molto potente e molto grande, dato che l’obbedienza e la rassegnazione, queste prime virtù di un suddito e queste supreme condizioni dello Stato, si trovano così profondamente radicate nei loro cuori; al punto che la Riforma, una rivoluzione religiosa che aveva scrollato il torpore di tante altre nazioni e che aveva risvegliato nel loro seno il principio di ogni libertà, la rivolta, non aveva prodotto, in Germania, altro effetto che rinforzare il sentimento e la pratica della disciplina?
Nella prima parte di questo scritto [\emph{L’Impero knut-germanico e la rivoluzione sociale}] ho mostrato come la nazione tedesca, assorbita pietosamente nei suoi sogni, aveva passato la sua adolescenza e la sua giovinezza, tutto il lungo periodo del medio evo, nella più completa e tranquilla schiavitù. Ho constatato, in seguito, come, verso la fine del quindicesimo secolo, aveva fatto segno di risvegliarsi. All’inizio del sedicesimo secolo, essa ebbe, in effetti, qualche anno di slancio magnifico: Lutero, Ulrich von Hutten, Franz von Sickingen, Thomas Müntzer, e altri ancora, sembrarono volerla trascinare su una strada sconosciuta e ricca di pensiero, di passione e di azione, sulla via della libertà. Elettrizzate dalle loro ardenti prediche, frementi di speranze e di fede, masse di contadini, spezzando le loro antiche catene, insorsero al grido di \emph{Guerra ai castelli e pace alle capanne}! Saccheggiarono e distrussero i castelli, e impiccarono o massacrarono i signori e i preti.
“Era la reazione”, dice Lassalle e ripetono, con lui, tutti i marxiani. Era la reazione, dicono, perché la rivoluzione, che non è tale se non quando è ben civile, ben scientifica, cioè ben borghese, non può scaturire dalla barbarie delle campagne. Il contadino non può fare che della reazione, da ciò risulta che, il primo dovere della rivoluzione, è d’impedire, di reprimere a tutto spiano, qualunque movimento di contadini. Docili a questo precetto, i borghesi radicali della Germania, l’hanno in effetti represso nel 1830, come anche nel 1818, ed è, senza dubbio, a causa di ciò che godono oggi di una così grande libertà. Nel 1525, il trionfo di questa strana “rivoluzione”, tutta tedesca, su questa “reazione” contadina, fu completo. I contadini, abbandonati e traditi dai borghesi delle città, furono disfatti dai nobili e massacrati e torturati a decine di migliaia, dopo di che, tutta la Germania ritornò nella calma. Vi restò immersa per più di tre secoli, come l’Italia, con la differenza che l’Italia era stata soffocata dall’alleanza dell’imperatore e del papa, mentre la Germania era stata travolta \emph{volontariamente} sotto il peso della sua stessa rivoluzione.
Fu precisamente allora che iniziò a svilupparsi in tutto il suo strano splendore, in Germania, la crescente potenza sedicente progressista e rivoluzionaria dello Stato militare, burocratico e tranquillamente dispotico. I prìncipi sovrani rimpiazzarono il papa e si dichiararono capi delle loro Chiese nazionali, con gran soddisfazione di un clero di cui il servilismo abietto superò tutto ciò che di simile si era visto fino a quel momento anche in Germania. Essi divennero, in qualche modo, gli Dèi del loro Stato, Dèi molto grossolani, ignoranti come si conviene a dei prìncipi, stupidamente infatuati della loro volontà sovrana ed eccessivamente depravati; sotto di loro una nobiltà piattamente cortigiana, adattata a tutti i servizi, ricercatrice di fortuna, di grazie e di padroni, e non domandante niente di meglio che di vendere le sue donne e i suoi figli al primo piccolo sultano venuto. I contadini, schiacciati, decimati e abbrutiti triplicamente e dalla sconfitta, e dalla miseria, e dagli insegnamenti dei loro pastori protestanti, predicatori della schiavitù cristiana, non si agitarono più, se non per portare, curvati e tremanti, i frutti del loro lavoro al castello. La borghesia e i corpi di mestiere ripresero tranquillamente le loro occupazioni e le loro laboriose abitudini quotidiane, non guardando, per distrarsi e per consolarsi, che alla lettura della Bibbia, e pagando tutte le imposte che si chiesero senza resistenza, senza protesta, senza mormorio.
La Germania era così definitivamente divenuta, e restò per tre secoli interminabili, il paradiso dei despoti, la terra della tranquillità, della sottomissione, della rassegnazione, e della mediocrità più desolante, sì, desolante sotto tutti gli aspetti, perché anche il movimento economico, quello dell’industria e del commercio, era considerevolmente rallentato, in paragone all’energia e all’attività che aveva dispiegato, dopo la nascita della Lega Anseatica, fra il tredicesimo e il quindicesimo secolo. Dopo la Riforma, questo movimento, per così dire, si gelò, in modo che, la Germania, restò ben lontana, non soltanto dietro i paesi protestanti come l’Inghilterra e l’Olanda, ma anche dietro la Francia cattolica. Si può anche dire che non è che a partire dal primo quarto del nostro secolo che ha iniziato a partecipare al grande movimento dell’industria e del commercio mondiale.
Anche oggi, essa non occupa, evidentemente, che il quarto o anche il quinto posto, dopo l’Inghilterra, la Francia, gli Stati Uniti, e il piccolissimo, ma molto industrioso, Belgio, e, sotto l’aspetto del commercio marittimo almeno, è anche dopo l’Olanda.
Dunque, per tre secoli, anche sotto l’aspetto economico, restò quasi stagnante, così povera di spirito come di ricchezze materiali. Ne era risultata una specie di virtù relativa, o piuttosto, negativa, conosciuta sotto il nome proverbiale di onestà tedesca; la si era attribuita, a torto, non so quale forza morale, inerente, si credeva, al carattere della nazione, mentre, questa virtù, non era che il prodotto naturale di quella doppia povertà, della borsa e dello spirito. E, per convincersene, non vi è che da guardare con quale rapidità quell’onestà tedesca, tanto vantata, si evapori oggi sotto il soffio depravatore e potente della grande speculazione bancaria, delle grandi transazioni commerciali e della grande industria.
Questa onestà non era, dunque, una forza morale, ma il prodotto della mediocrità, sia materiale che intellettuale. Era l’abitudine dei poveri a vivere di poco e a non conoscere che pochissimi bisogni, a trascinare tutta la loro esistenza al di fuori delle grandi passioni, dei grandi godimenti e delle grandi tentazioni, sia del pensiero che della vita. Accontentarsi di poco, ecco in che cosa consistette questa virtù – una virtù negativa quant’altre mai – e non cercare dei compensi e delle consolazioni che nella contemplazione religiosa e nella lettura della Bibbia, che inebriava a buon mercato questi buoni borghesi protestanti con la comunione del Santo Spirito e con la comunione diretta con Dio, attraverso il Cristo. Si capisce come, un simile regime, abbia dovuto formare dei sudditi molto appropriati ai bisogni del dispotismo.
Questo fu, dunque, in questo strano paese, l’effetto della doppia rivoluzione, che segnò la transizione dal Medioevo all’età moderna; della rivoluzione economica che, sulle rovine della proprietà feudale, doveva fondare la nuova potenza del capitale e della rivoluzione religiosa, che aveva risvegliato la vita politica in tutti gli altri paesi. In Germania, questo effetto può essere riassunto con queste parole: impoverimento e torpore materiale, prostrazione intellettuale e morale.
Alcuni scrittori tedeschi, fra gli altri Schiller, hanno cercato di spiegarsi questo fatto, così doloroso per il loro patriottismo, attribuendolo esclusivamente agli immensi disastri causati in Germania dalla Guerra dei Trent’anni, di cui essa fu, nello stesso tempo, il teatro e la vittima. Ma gli altri paesi furono realmente risparmiati? L’Olanda non fu forse altrettanto devastata da Filippo II, l’Inghilterra dagli Stuart, e la Francia dalla Lega cattolica e dalla monarchia assoluta, dopo l’inizio delle guerre di religione fino al proclama dell’editto di Nantes? Ebbene, tutto ciò non ha impedito all’Olanda di fondare la sua libertà e la sua prosperità materiali; all’Inghilterra di avere i suoi Shakespeare, i suoi Milton, di rovesciare il dispotismo degli Stuart, e di mettere in scacco il dispotismo tedesco apportato dalla casa di Hannover. Anche in Francia, malgrado il trionfo del cattolicesimo, malgrado l’annientamento e l’espulsione definitivi delle popolazioni protestanti, le più industriose e più ricche del paese, malgrado, infine, la costituzione di una monarchia assoluta in modo orientale, con tutto lo sfoggio insolente del suo Re Sole che riassume nella sua persona tutto lo Stato, – in Francia, dopo Rabelais, Montaigne e Descartes fino a Voltaire e Diderot, attraverso la grande letteratura del XVII secolo e del XVIII secolo, voi trovate una corrente, non interrotta e sempre crescente, di libero pensiero, che ispira spiriti nobili, fonda a Parigi dei saloni letterari e filosofici, delle Accademie di scienze e di lettere, crea un’opinione pubblica opposta, sia al cattolicesimo, al dogma cristiano, al Padrone celeste, sia al dispotismo reale, e che, sviluppandosi prima di nascosto, diffondendosi a poco a poco, attraverso mille filiere sotterranee ed invisibili, in tutte le classi della società, finì con l’abbracciare tutta quanta la nazione, portando alla Rivoluzione e trascinando alla ghigliottina il padrone terrestre.
Ma in Germania niente, niente del tutto. Dalla morte di Lutero, fino all’apparizione dei primi scritti di Lessing, cioè per due secoli di seguito, interruzione completa del pensiero, di ogni movimento intellettuale e della vita morale; a meno che, per pietà verso tanta miseria, non si vogliano considerare come segni di sviluppo intellettuale e morale, i vagiti malaticci e sentimentali del pietismo, oppure le stravaganze teosofiche di Jacob Böhme. La stessa lingua tedesca, di cui si era così magnificamente servito Lutero, era ricaduta in disuso: era la lingua della Bibbia, dei cantici e dei trattati religiosi; la scienza disdegnava di servirsene, e non vi era propriamente della letteratura. Leibniz, uno dei più notevoli spiriti del XVII secolo, non scriveva che in francese o in latino. Nelle università, le scienze non si insegnavano che in latino.
E quali scienze! Che strani professori! La teologia ortodossa luterana vi dominava ovunque. Dopo di essa veniva il diritto, l’una e l’altro predicando il potere assoluto del sovrano e il dovere, non meno assoluto, dell’obbedienza passiva dei sudditi. Era il culto teorico dello Stato, base e condizione preliminare del culto pratico che aveva fatto della Germania ciò che era: la patria dei despoti e quella degli schiavi volontari, dei lacchè. I professori, pedanti, ridicoli, assurdi, vili ed ignobili come lacchè, in ginocchio dinnanzi ad ogni autorità, anticipatamente venduti e votati corpo e anima al servizio di tutti i poteri, che essi adulavano in versi latini e in prosa e, nello stesso tempo, arroganti, gelosi, molesti, si ingiuriavano, si calunniavano, si denunciavano a vicenda e, spingendo questa guerra incivile di pedanti, come nella commedia di Molière, fino, qualche volta, a prendersi per i capelli – questi furono i nobili istruttori ed educatori della gioventù tedesca durante questi due secoli.
A fianco delle due scienze principali, la teologia e il diritto, ve ne era una terza, che insegnava, in qualche modo, la teoria della loro applicazione alla vita pratica: era la scienza politica, la scienza dello Stato o, più precisamente, la scienza del servizio dello Stato. Essa abbracciava l’amministrazione, le finanze e la diplomazia, e doveva, come le altre due, ma in una maniera ancora più specifica, [formare] i burocrati, i fedeli senatori dello Stato. Perché bisogna osservare che, a quell’epoca, in Germania, le parole “patria”, “nazione”, erano completamente ignorate. Non vi era che lo Stato o, piuttosto, un’infinità di Stati, grandi, medi, piccoli e molto piccoli. Non ve ne era precisamente che uno solo veramente grande, era quello dell’Austria, che era alla testa di tutta la Germania come capo dell’Impero, ma che non aveva né la potenza, né la volontà di mettere un freno all’arbitrio dispotico dei sovrani medi e piccoli nei loro rispettivi Stati. Per il suddito e a maggior ragione per il funzionario la Germania non esisteva: non conosceva che lo Stato grande, medio o piccolo che serviva e che, per lui, si riassumeva nella persona del principe.
Tutta la scienza del burocrate consisteva in questo: mantenere l’ordine pubblico e l’obbedienza dei sudditi, e carpire loro tanto più denaro possibile per il tesoro del sovrano, senza rovinarli completamente e senza spingerli, per la disperazione, alla rivolta; pericolo che, d’altronde, non era eccessivamente [grande], in Germania, che, almeno allora, fu, se non oggi, il classico paese della sottomissione, della pazienza e della rassegnazione, così come dell’onestà.
Ci si può immaginare quale dovette essere lo spirito di questi onesti filistei della burocrazia tedesca, che, non riconoscendo, dopo Dio, altro oggetto di culto che questa terribile astrazione dello Stato, personificata nel principe, gli immolavano coscienziosamente, spietatamente, tutto. Nuovo Bruto, con la cuffia di cotone e la sua pipa che pendeva dalla bocca, ogni funzionario tedesco era capace di sacrificare i suoi stessi figli a ciò che egli chiamava, egli, la ragione, la giustizia, il diritto supremo dello Stato.
A fianco di questi onesti “filistei” della burocrazia, vi erano i compagni di bagordi del reggente, i furfanti patentati e titolati della diplomazia. La burocrazia, si può dire, è nata e si è sviluppata, principalmente, in Germania, vi è divenuta contemporaneamente una scienza, un’arte, un culto. Ma è l’Italia che reclama l’onore, molto equivoco, di aver dato i natali alla diplomazia. Divisa in una serie di piccole repubbliche, nel Medioevo, tutte indipendenti l’una dall’altra, e in eterna lotta le une contro le altre; minacciata da un altro lato dalle periodiche invasioni della Germania, della Francia, della Spagna, e dal permanente tradimento dei papi, è l’Italia che ha creato, sviluppato e coltivato, nel suo seno, quest’arte infernale della diplomazia, così ben descritta da Machiavelli, e che, dopo aver formato e illustrato i grandi furfanti storici, conosciuti sotto i nomi dei Medici e dei Borgia, ha finito per demoralizzare e per disorganizzare così completamente questa nobile nazione, che divenne, alla lunga, incapace di resistere alla doppia tirannia degli imperatori e dei papi.
Le stesse ragioni che l’avevano fatta nascere in Italia dovevano farla prosperare in Germania, dove ogni piccola corte formava un focolaio permanente di complotti e di intrighi, sia all’interno che all’esterno. All’interno, era il grande affare del favore del principe, che una folla di nobili valletti si disputavano con un accanimento feroce, impiegando in questa lotta tutta la villania di cui la bassezza, la perfidia, l’avidità e la vanità dei cortigiani e delle cortigiane sono capaci. Più una corte era piccola, e più questo complotto incessante, che ne costituiva, in qualche modo, l’atmosfera, si manifestava cinico, ridicolo, atroce, disgustoso. Maritare il principe, dargli un’amante, rimpiazzarla con un’altra, scacciare un favorito per nobilitarne uno nuovo, ecco i grandi affari che assorbivano l’intelligenza della gioventù nobiliare della Germania. Questa cabala interna serviva, in qualche modo, come scuola, dove si formavano gli uomini di Stato, i diplomatici. Una volta formati, si lanciavano sul teatro pubblico della diplomazia esterna, che divenne, in qualche modo, la scienza o, piuttosto, l’arte privilegiata della gente nobiliare in Germania, così come in tutti gli altri paesi.
Si sa che cosa è la diplomazia: è l’arte e la scienza della bricconeria, legittimata dal servizio dello Stato. Si è detto, con molta ragione, che se, nel suo interesse privato, qualunque sia, un individuo volesse permettersi la decima parte degli atti che i diplomatici più rinomati dell’Europa, compiono sotto i nostri occhi, lo si porterebbe davanti alla giustizia e lo si porterebbe al bagno, a meno che non sia abbastanza ricco e potente da evitare l’uno e l’altro. Machiavelli, il fondatore della scienza politica, in quanto scienza storica e positiva, l’ha dimostrato molto bene: lo Stato, ogni Stato, monarchico o repubblicano, è la medesima cosa – non esistendo lo Stato che attraverso la violenza e, non essendo esso stesso nient’altro che una violenza sistematica o continua, aperta o mascherata, ma sempre imposta alle masse da una minoranza dominante o da un governo qualsiasi – lo Stato non può mantenersi che attraverso una violenza continua e sistematica del diritto umano, della morale umana; ciò che ritorna a dire che non può esistere che attraverso il crimine. Ma una volta che lo Stato, la sua integrità, la sua grandezza, la sua potenza, e, di conseguenza, anche la sua estensione, per quanto possibile, sono poste come scopo supremo al quale ogni uomo nato nel suo seno, ogni suddito, deve sacrificare tutto il resto, è evidente che ogni crimine che si commette nell’interesse dello Stato, diviene altrettanta virtù. Così gli uomini di Stato, i diplomatici che se ne rendono colpevoli, lontano dal nascondersi, se ne fanno una gloria. Quanti crimini flagranti, per esempio, Bismarck ha commesso, direttamente, contro la Francia e, indirettamente, contro la Germania! Ebbene, tutti lo festeggiano oggi come il più grande uomo di Stato dell’Europa. E Thiers, perché non soltanto i monarchici e i conservatori dell’Europa e della Francia, ma anche gli stessi repubblicani, l’estrema sinistra, anche l’uomo dell’avvenire, Gambetta, perché tutti lo proclamano l’uomo indispensabile e il salvatore della Francia? Perché, per la salvezza dello Stato, ha fatto assassinare quarantamila difensori della Comune di Parigi, questa negazione, ormai storica, dello Stato, e perché continua a fucilarne ancora alcuni, come vittime reclamate da questo grande idolo che è lo Stato.
Si vede che, sotto tutte le forme di governo, nella monarchia così come nella repubblica dal momento che la salvezza dello Stato lo reclama, tutti gli uomini di Stato sentono, pensano e fanno, la medesima cosa. Su questo terreno tutti si danno la mano, Murav’ev e Haynau, Bismarck e Thiers, Gambetta, e fino allo stesso Marx, se mai Marx sarà chiamato a governare uno Stato.
Tuttavia, ai nostri giorni, si fa un vero progresso. Io non so più chi ha detto che l’ipocrisia era un omaggio, che il vizio rendeva alla virtù; la diplomazia moderna tende a giustificare questo proverbio. Leggendo i proclami che gli attuali uomini di Stato non mancano di lanciare, quando intraprendono qualche cosa di molto sinistro, si direbbe che essi non hanno che un solo scopo, il bene di questa povera umanità. Ma, all’epoca di cui io parlo, questa parola era quasi sconosciuta, così in Germania come altrove. Dio era allora il grande paravento – il Dio delle battaglie e dei re, o, come ha detto più tardi il grande Federico, il Dio dei grandi battaglioni. Del resto, a quell’epoca, non si aveva nemmeno bisogno di pretesto. La furfanteria dei cortigiani e dei diplomatici s’installava, con tutto il suo cinismo, tanto più onorata e festeggiata quanto più era abile e felice. Si disprezzava tanto il pubblico borghese e la canaglia popolare, che non ci si prendeva nemmeno la pena di ingannarli. I diplomatici francesi, che davano il tono a quelli di tutti gli altri paesi, erano dei cortigiani raffinati. Ci si può immaginare ciò che dovevano essere i diplomatici della Germania, che uguagliavano e, spesso, sorpassavano i loro modelli francesi in tutte le cose, meno che nello spirito.
A fianco della burocrazia e della diplomazia, vi fu ancora un’arte che prosperò molto in Germania. L’arte militare. È in Germania che nacque la mania, la passione, di giocare [al] soldato. La vera patria di questa nobile passione, è la Prussia. Si sa che presso il padre del grande Federico, essa era diventata una vera follia; non sognava che uniformi; avaro, spendeva molto denaro per comprare dei bei soldati, e, quando non poteva comprali, li rubava e li irreggimentava con la violenza. I prìncipi della Germania, che volevano fargli la loro corte, gli consegnavano i loro più bei sudditi. Non bisogna stupirsene, poiché alla stessa vigilia della Rivoluzione francese, allorché tutta l’Europa, già inondata dalla luce del libero pensiero, fremeva nell’attesa dei grandi avvenimenti che dovevano scompigliarla tutta, allorché dei despoti stessi, come Caterina II, Federico II, Giuseppe II e molti altri ancora, trascinati dalla vertigine di un liberalismo universale, credevano di dover incoraggiare questo spirito nuovo che aveva invaso tutto il mondo, due sovrani tedeschi, il duca di Brunswick e il conte di Haynau, vendevano tranquillamente una ventina di migliaia di soldati tedeschi al re dlnghilterra, senza nemmeno darsi la pena di concludere con lui un trattato di alleanza effettiva contro l’America insorta, contro la quale, questi soldati, furono impiegati, ma facendosi pagare semplicemente, con denaro contante. Fu una vendita di uomini, di soldati e di sudditi tedeschi in piena regola. Questo fatto caratterizza, da solo, il potere dei prìncipi tedeschi, la pazienza angelica dei loro sudditi, e, in particolare, lo spirito del militare tedesco a quell’epoca.
Era l’ideale del soldato macchina, dell’uomo abbrutito dalla disciplina militare al punto che ammazza e che si fa ammazzare, per qualche soldo al giorno, senza sapere nemmeno chi ammazza e perché lo ammazza. In quanto agli ufficiali tedeschi, nobili in maggior parte, erano dei veri cavalieri di ventura, che affittavano i loro servizi al sovrano che dava di più, tedesco o anche straniero, e che portavano, in tutti i paesi che onoravano con i loro servizi lucrativi, la stessa fedeltà del cane di fronte ai loro capi e ai loro prìncipi d’occasione, la stessa durezza per il soldato, e lo stesso disprezzo per il borghese e per il popolo.
Che si riuniscano, che si combinino tutti gli elementi sociali che ho appena esaminato uno a uno, e si avrà un’idea perfettamente giusta della Germania, così come era uscita dalla Riforma e dalla Guerra dei Trent’anni, fino alla seconda metà del diciottesimo secolo, cioè per più di tre secoli di seguito. E ora, la mano sul cuore, che ognuno dica se io non ho avuto mille volte ragione di affermare, contrariamente a Marx, che non è affatto la Russia, che è la Germania, che dal sedicesimo secolo fino ai nostri giorni, è stata la fonte e la scuola permanente del dispotismo di Stato in Europa. Di ciò che, negli altri paesi dell’Europa, non è stato che un fatto, la Germania ha fatto un sistema, una dottrina, una religione, un culto: il culto dello Stato, la religione del potere assoluto del sovrano e dell’obbedienza illimitata del suddito, l’umiliazione, l’annichilimento di ogni subalterno di fronte al suo capo, e il rispetto del rango come in Cina, la nobiltà della sciabola, l’onnipotenza meccanica di una burocrazia gerarchicamente pietrificata, il regno assoluto della scartoffia giuridica e ufficiale, sulla vita, infine, l’assorbimento completo della società nello Stato; al di sopra di tutto ciò, il beneplacito del principe quasi-Dio e, necessariamente, quasi-folle, con la depravazione cinica di una nobiltà contemporaneamente stupida, arrogante e servile, pronta a commettere tutti i crimini per compiacerlo; e al di sotto, la borghesia e il popolo che dava, al mondo intero, l’esempio di una pazienza, di una rassegnazione e di una subordinazione senza limiti.
Marx pensa, forse, che un popolo, per quanto dotato sia, possa restare impunemente in una simile situazione per un lungo periodo storico, senza che la schiavitù penetri fino nell’ultima ramificazione delle sue vene, divenga sua abitudine, la sua seconda natura? E se questo popolo, come si può dire con piena giustizia del popolo tedesco, nemmeno prima di questi tre secoli, ha mai conosciuto né desiderato la libertà; se, in mezzo al movimento progressivo dei popoli vicini, è rimasto un popolo stagnante, contemplativo, meditativo – lavorando molto è vero, ed è lì il suo onore, ma non rivoltandosi mai, eccetto un momento, molto breve, della sua vita, all’inizio della Riforma – che cosa ha dovuto diventare, durante questi tre secoli di immobilità e di assenza di pensiero assoluti? Un eccellente strumento per tutte le imprese del dispotismo, sia dentro che fuori; una base molto solida per la propaganda, l’irraggiamento e le invasioni, del dispotismo in tutto il mondo.
Se la Germania non è più stata conquistatrice, a partire dalla Riforma fino alla fine del diciottesimo secolo, se ha lasciato questo ruolo alla Francia di Richelieu e di Luigi XIV, non fu per mancanza di stati d’animo, ma unicamente per mancanza di potere. La Riforma aveva portato un colpo mortale all’Impero germanico, l’aveva sgretolato di fatto, se non ancora di diritto. La Germania era infinitamente divisa. La Germania cattolica, spezzata, del resto, in due parti ineguali dalla gelosia secolare dell’Austria e della Baviera, era tenuta in scacco da una folla di piccoli prìncipi protestanti, sempre pronti a coalizzarsi e, al bisogno, anche ad appoggiarsi sulla Francia cattolica contro di essa. Ciò riduceva, naturalmente, tutta la Germania in una completa impotenza.
Strana situazione quella di un popolo molto numeroso, molto robusto, conquistatore e invasore, sia per tradizione che per inclinazione – gli Slavi ne sanno qualche cosa, e gli Italiani anche – disposto più a diventare un eccellente strumento di conquista anche per la sua stessa schiavitù, per quella disciplina interiore, volontaria, per quella passione all’obbedienza, che ne facevano un popolo modello – e che, malgrado tutti questi grandi vantaggi, si è visto ridotto a giocare, per tanti secoli di seguito, il ruolo di un popolo vittima, oppresso e decimato più o meno da tutti gli Stati vicini, perfino anche dalla piccola Svezia; di un popolo che non domandava di meglio che di invadere e a destra e a sinistra e ovunque, e che, invece di ciò, è stato condannato a trovarsi sempre invaso; perché infine, la maggior parte delle guerre che insanguinarono l’Europa dalla Riforma, fino ai nostri giorni, ebbero per teatro la Germania, ciò che, naturalmente, già dal solo punto di vista della tranquillità e degli interessi materiali, è dovuto dispiacere molto ai Tedeschi, nello stesso tempo che ciò doveva urtare molto la loro vanità nazionale.
Ne è risultato, molto lentamente e molto impercettibilmente, prima, è vero, un sentimento naturale e necessario di reazione contro la causa di tutta questa vergogna e di tutte queste disgrazie, contro la divisione della Germania in una moltitudine di Stati – non contro lo Stato in generale. Non era la reazione di un popolo che amava e che voleva la libertà, contro il dispotismo interno dello Stato che gli impediva di gioirne; era quella di un popolo che, sentendosi l’inclinazione e la potenza naturale della conquista, aspirava ad una forma politica capace di soddisfare questo desiderio istintivo e di mettere in azione questa potenza. Perciò, non vi era che una sola forma, quella di un grande Stato unitario, che abbracciasse patriotticamente tutta la Germania, e anche più di quella, tutti i paesi che i Tedeschi hanno preso l’abitudine, storica e scientifica al tempo stesso, di considerare come parti integranti della grande patria tedesca. È ancora oggi il sogno di tutti i pangermanisti.
Ma, per la realizzazione di questo sogno, occorreva un organo, e questo organo non poteva essere altro che uno Stato tedesco, già abbastanza potente per conto suo, e che doveva diventarlo maggiormente attraverso l’incremento dei mezzi che avrebbe ricevuto, più tardi, dalla Germania intera. È chiaro che, poiché l’unità, sempre più desiderata, fin dalla seconda metà del diciottesimo secolo, dagli spiriti più patriottici della Germania, aveva conformemente a tutto il carattere nazionale, per ultimo fine la potenza, è chiaro, dico, che questa unificazione e centralizzazione nazionale della Germania, non poteva essere realizzata che dallo Stato, e non da un movimento spontaneo delle popolazioni tedesche stesse, un simile movimento poteva, sì, produrre la prosperità materiale e la libertà, ma non la potenza politica di una nazione, a meno che il movimento popolare, ispirato piuttosto da quella passione di grandezza politica che dall’amore della libertà, non tendesse e non sfociasse da solo alla creazione di un grande Stato, così come lo desiderano oggi i democratici socialisti della Germania, i quali, evidentemente, si sforzano di trascinarla su questa strada.
Ma era assolutamente impossibile che le popolazioni tedesche marciassero spontaneamente su questa strada. Perché, per fondare il grande Stato unitario, esse dovevano prima abbattere quella moltitudine di piccoli Stati, di piccoli prìncipi, tra i quali la Germania si trovava divisa, ed era un’impresa, un’azione di cui i popoli tedeschi erano, e si mostrano ancora, almeno fino a questo momento, assolutamente incapaci. Per abbatterli per mezzo del loro proprio movimento, essi non avevano, non hanno ancora oggi, che un unico mezzo, la \emph{rivolta}, e noi abbiamo visto che la rivolta è stata sempre estranea, per non dire profondamente antipatica, a quella eccellente natura tedesca, tutta impastata di rispetto, di sottomissione e di rassegnazione, piena di una venerazione tanto istintiva quanto ponderata, verso tutte le autorità, e di una devozione senza limiti per i suoi prìncipi.
Questa virtù politica è talmente radicata nel cuore dell’immensa maggioranza dei Tedeschi, che il grande patriota Ludwig Börne, quando aveva appena quarant’anni, scriveva queste terribili parole: “Gli altri popoli possono essere \emph{schiavi}; li si può mettere in catene e dominarli con la violenza; ma i Tedeschi sono dei lacchè, non si ha nemmeno bisogno di incatenarli, li si può lasciar correre senza pericolo”.
Il dottor Johann Jacoby, anch’esso uno dei più grandi e dei più degni patrioti della Germania, e che ancora oggi è uno dei capi più riconosciuti del Partito della democrazia socialista, al quale ha dato appena ultimamente la sua piena adesione, ha ripetuto, più volte, la stessa cosa, benché in termini molto più parlamentari e gentili.
Ecco, ad esempio, le parole che ha pronunciato davanti agli elettori a Berlino, il 5 giugno 1848, allorché il movimento rivoluzionario di cui la Francia, come sempre, aveva preso l’iniziativa, era penetrato in Germania, e delle quali il linguaggio era, in generale, ancora molto ardito:
“Ovunque in Germania – con la sola eccezione del Baden – la rivoluzione si è liberamente arrestata davanti al trono vacillante; prova che il popolo tedesco, anche volendo porre un limite al potere sovrano dei prìncipi, non è minimamente disposto a cacciarli”.
E dieci anni più tardi, ricco di notizie e di ben crudeli esperienze, e più convinto che mai, ecco quelle che ha pronunciate in una assemblea di elettori nel novembre 1858 a Koenigsberg: “Rispetto al re! Se mai un’epoca, l’anno 1848 ci ha insegnato fino a quale profondità l’elemento monarchico ha spinto delle radici nel cuore del popolo. Rendendo alla monarchia questo omaggio che gli è dovuto, noi non tradiamo il principio dell’eguaglianza dei diritti, noi diamo soltanto soddisfazione a un’esigenza, perfettamente giusta, fondata sia sul bisogno del nostro popolo che sullo sviluppo della nostra patria”.
Le prime parole che ho appena citato furono pronunciate dall’illustre capo del partito democratico della Germania nel bel mezzo della rivoluzione, mentre tutti i troni vacillavano realmente e mentre non c’era bisogno che di una semplice manifestazione di volontà da parte del popolo tedesco per farli cadere. Il dr. Jacoby, repubblicano di pensiero e di cuore ma, nello stesso tempo, osservatore coscienzioso, testimonio attivo di tutto ciò che succedeva attorno a lui, ha constatato, non senza dolore, senza dubbio, che il popolo tedesco, ridiventato categoricamente padrone del suo destino durante quei pochi mesi di fermento nazionale, non ha voluto essere libero, ha voluto, al contrario, restare suddito dei suoi prìncipi, non perché essi erano dei buoni prìncipi – tutti sanno quanto essi sono stati e sono rimasti ridicoli ed orribili – ma perché aveva preso l’abitudine profondamente nazionale al loro giogo. Se il dr. Jacoby aggiunge che il popolo tedesco voleva, nello stesso tempo, porre delle condizioni e dei limiti al loro potere assoluto, non bisogna prendere queste parole troppo sul serio. In un altro discorso pronunciato molto più tardi (il 30 gennaio 1868, davanti un’assemblea di elettori a Berlino), egli stesso dice: “\emph{Parliamo di movimenti popolari, del risveglio della coscienza politica nel popolo, delle risoluzioni, delle manifestazioni e delle rivendicazioni popolari; ma dobbiamo tuttavia confessare a noi stessi che non è che una minima frazione del popolo} (senza dubbio la borghesia radicale, che resta propriamente al di fuori del popolo) \emph{che prende parte alle nostre lotte per la libertà}”.
Nel suo secondo discorso, pronunciato a Koenigsberg nel 1858, cioè dieci anni dopo la rivoluzione del 1848 – dopo dieci anni della reazione più terribile che abbia mai infierito in Germania, e che sarebbe stata capace di stancare la pazienza e la fede di ogni altro popolo che il tedesco – il venerabile patriota constata, più esplicitamente che mai, la profondità delle radici che il sentimento monarchico, cioè quello della schiavitù volontaria, ha spinto nella coscienza, nella natura del popolo tedesco. Egli lo chiama un bisogno di questo popolo, e confessa che è una necessità dello sviluppo della patria tedesca.
In una parola, con ogni sorta di reticenza e di riguardi imposti, senza dubbio, sia dalle circostanze che dalle abitudini di un temperamento più calmo, e da uno spirito più contemplativo e meno irascibile, il dr. Johann Jacoby ha completamente confermato la terribile sentenza pronunciata contro il popolo tedesco dal suo grande compatriota e predecessore, il dr. Ludwig Börne. Questo popolo non ha mai amato molto la libertà, e, a meno di avvenimenti straordinari e, probabilmente, esterni, quali una rivoluzione sociale che scoppia in Francia o in qualche altro paese del meridione dell’Europa, o anche in Inghilterra, non soltanto sarà incapace di rovesciare lui stesso i suoi tiranni, ma non desidererà nemmeno la loro caduta. Le ragioni che glielo impediranno saranno sempre il culto dell’autorità, la devozione per il principe, la fede nello Stato e il rispetto incallito per tutti i funzionari e i rappresentanti dello Stato; infine, questa mania della disciplina volontaria e dell’obbedienza ragionata, sviluppata in lui da tutta la sua storia, e, come abbiamo visto, soprattutto dagli ultimi tre secoli, avendo il protestantesimo consacrato, con la sua benedizione, in Germania, ma soltanto in Germania, tutte quelle disposizioni nazionali che fanno del popolo tedesco il popolo più liberamente asservito e, oggi, il più minaccioso per la libertà del mondo.
Una volta dati tutti questi elementi, si comprende che l’unità della Germania, così necessaria alla realizzazione della sua potenza politica, non poteva essere il risultato di un movimento liberale spontaneo della nazione stessa, ma solo quello della conquista; senza dubbio non della conquista straniera, ma dell’assorbimento violento di tutti i piccoli Stati della Germania in uno Stato, a paragone più potente, e se non ugualmente o completamente, almeno in gran parte germanico. Non è questo il luogo di dimostrare perché, né l’Austria né la Baviera, spossate e paralizzate del resto dalle loro precedenti lotte così come dalle loro reciproche gelosie, e colpite a morte dal principio dell’ultra-montanismo cattolico, al quale, per loro propria disgrazia, erano rimasti troppo fedeli, non erano ormai capaci di rendere questo grande servizio alla Germania, servizio che reclama l’azione di uno Stato tutto nuovo, per niente, o assai poco, compromesso dalla storia. Questo Stato nuovo, lo sanno tutti, fu la Prussia.
La storia dello Stato brandeburgo-prussiano, fino al 1807, non fu che quella dei suoi prìncipi, prima margravi, elettori di Brandeburgo e vassalli della Polonia per la Prussia, divenuti nel 1701 re di Prussia, e subito dopo, i protettori e, come tali, i comproprietari della Polonia, gli iniziatori incontestabili di quella spartizione che, oggi, i democratici socialisti della Germania maledicono con più energia che sincerità. Fino alla grande catastrofe di Jena, non vi fu, propriamente, una nazione prussiana. Era un agglomerato di popolazioni eterogenee, in parte slave, e in particolare polacche, in parte tedesche, e che non erano unite fra loro, come, ad esempio, quelle del Brandeburgo, con quelle della Prussia, che attraverso la persona del sovrano.
\bigskip
[Frammento formante un seguito dell’\emph{Impero knut-germanico}. Novembre-Dicembre 1872. Traduzione italiana in M. Bakunin, \emph{Opere complete}, vol. III, seconda ed., Catania 1999, pp. 210-262. Le note, in larga parte, sono state escluse].
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\begin{center}
Biblioteca anarchica
\bigskip
\includegraphics[width=0.25\textwidth]{logo-en}
\bigskip
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\strut
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\begin{center}
Michail Bakunin
Scritto contro Marx
1872
\bigskip
Consultato il 30 novembre 2017 su \href{https://www.edizionianarchismo.net/library/michail-bakunin-scritto-contro-marx}{www.edizionianarchismo.net}
Edizioni Anarchismo – Opuscoli provvisori N. 69\forcelinebreak Prima edizione: maggio 2015
\bigskip
\textbf{bibliotecaanarchica.org}
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%+
% Name:
% bias_parity_error_spec_1.3.tex
%
% History:
% 2010 Jul 19, created (v0.1), Glenn E. Allen
% 2010 Aug 18, removed maxpix and fixed maxerr (v0.2), GEA
% 2010 Aug 19, added a figure showing the number of errors per frame
% (v0.3), GEA
% 2012 Nov 02, described what to do for CC mode (v0.4), GEA
% 2012 Nov 20, (v1.0), GEA
% 2013 Nov 14, changed maxerr min to 1 from 0 (v1.3), GEA
%-
\documentclass{article}
\usepackage{/nfs/inconceivable/d0/SRC/LATEX/STY/cxo_memo_logo}
\usepackage[dvips]{graphics}
\usepackage{epsfig}
\usepackage{/nfs/inconceivable/d0/SRC/LATEX/STY/gea}
\usepackage{pstricks}
\newrgbcolor{red}{1 0 0}
\begin{document}
% 1. Header
\memobasic{
Jonathan McDowell, SDS Group Leader }{
Glenn E.\ Allen, SDS }{
Bias-parity error spec }{
1.3 }{
http://space.mit.edu/CXC/docs/docs.html\#berr }{
/nfs/inconceivable/d0/SDS/SPECS/BERR/bias\_parity\_error\_spec\_1.3.tex }
% 2. Tool name
\section{Bias-parity errors}
% 3. Description
\subsection{ Description }
Some observations are adversely affected by bias-parity errors. To explore
the properties of these errors, 16,304 bias-parity error files were obtained
from the archive for the interval from the beginning of the mission through
July 8, 2010. Figure~\ref{fig01} shows histograms of the total number and
the ``valid'' number (see sec.~\ref{proc}) of errors for each file. The
results for the valid errors are also listed in Table~1. The results below
the horizontal line in the middle of the table are the results for the
twelve files that contain errors associated with the ``FEP0 problem.'' The
number of errors, if any, per frame of data is typically very small
(Fig.~\ref{fig02} and Table~2). The only bias-parity error files that have
more than 10 errors per frame are the twelve files associated with the FEP0
problem. As shown in Figure~\ref{fig03}, the number of bias-parity errors
varies with time. There is a correlation between the number of errors and
the number of pixels on which the errors occur (Fig.~\ref{fig04}). Of the
16,304 files, there are only seven where the number of valid errors is not
equal to the number of pixels affected by the errors. Six of these seven
files are ones associated with FEP0 problem for which the number of errors
is comparable to or greater than 262,144, the maximum number of pixels that
can be affected by the problem. The seventh file is for {\tt OBS\_ID} 7649,
where all but one of the 7,439 errors are reported for the
pixel $( {\tt CCD\_ID}, {\tt CHIPX}, {\tt CHIPY} ) = ( 8, 786, 356 )$.%
%
\footnote{These errors are valid and are not associated with the FEP0
problem.}
%
The distribution of the valid errors in chip coordinates is shown in
Figure~\ref{fig05}. Inspection of this figure suggests that there is a
periodic pattern every 32 pixels in {\tt CHIPX}.%
%
\footnote{The FEP reads the bias-parity error data in 32-bit words.}\ \
%
Figures~\ref{fig06} and \ref{fig07} confirm the existence of a periodic
pattern. As shown in Figure~\ref{fig08}, there is a similar, but much less
pronounced, 32-pixel periodicity in the {\tt CHIPX} values of the errors
associated with the FEP0 problem. A much more prominent feature of the FEP0
errors is that they only occur in columns with odd values of {\tt CHIPX}
(Fig.~\ref{fig09}) and in rows with values of ${\tt CHIPY} \ge 513$
(Fig.~\ref{fig08}).
The remainder of this spec describes how the tool {\tt acis\_build\_badpix}
handles bias-parity error files.
% 4. Input
\subsection{ Input }
\begin{enumerate}
\item
One or more Level 0 bias-parity error file (acis*berr0.fits)
\item
A Level 0 parameter-block file (acis*pbk0.fits)
\end{enumerate}
% 5. Output
\subsection{ Output }
\begin{enumerate}
\item
A bad-pixel file that includes, among other things, a list of the pixels
with valid bias-parity errors (acis*bpix1.fits).
\end{enumerate}
% 6. Parameters
\subsection{ Parameters }
\begin{enumerate}
\item
{ \tt berrfile,f,a,"",,,"Name(s) of input bias-parity error file(s)" }
\item
{ \tt berrext,s,h,"BERR",,,"Name of bias-parity error extension" }
\item
{ \tt pbkfile,f,a,"",,,"Name of input parameter-block file" }
\item
{ \tt \red{maxerr,i,h,10,1,100}%
%
\footnote{A maximum value of 100 is large enough to be well above the
maximum number of valid errors per frame for files that are not
associated with the FEP0 problem (Fig.~\ref{fig02} and Table~2) and
small enough to be well below the number of errors per frame in the
first frame associated with the FEP0 problem for the twelve FEP0 {\tt
OBS\_ID}s in Table~1.}%
%
,"Maximum number of valid
bias-parity errors per frame" }
\item
{ \tt outfile,f,a"",,,"Name of output bad-pixel file" }
\end{enumerate}
% 7. Processing
\subsection{ Processing }
\label{proc}
Perform the following tests before processing begins.
%
\begin{itemize}
\item
Verify that each {\tt berrfile} exists and has an an extension where the
value of {\tt EXTNAME} is identical to the value specified by {\tt
berrext}. If one or both of these conditions is not true, then exit
with an error message.
\item
Verify that the {\tt pbkfile} exists. If it does not, then exit with an
error message.
\item
Verify that {\tt maxerr} is in the specified range.
\item
If {\tt clobber = no}, then verify that the {\tt outfile} does not
exist. If it does, then exit with an error message.
\end{itemize}
Perform the following steps, in sequence, for each bias-parity error file.
Note that each file corresponds to a single CCD for an observation.
\begin{enumerate}
\item
Ignore invalid bias-parity errors. Invalid errors are those for which
{\tt{DATAMODE = VFAINT}} and for which the coordinates%
%
\footnote{As defined here, all errors associated with the FEP0 problem,
except for those at $({\tt CCDX},{\tt CCDY}) = (0,{\tt ROWCNT})$, are
valid.}
%
\begin{itemize}
\item
$( {\tt CCDX}, {\tt CCDY} ) = ( 0, {\tt ROWCNT} )$ or
\item
$( {\tt CCDX}, {\tt CCDY} ) = ( 1, {\tt ROWCNT} )$ or
\item
$( {\tt CCDX}, {\tt CCDY} ) = ( 1022, 0 )$ or
\item
$( {\tt CCDX}, {\tt CCDY} ) = ( 1023, 0 )$.
\end{itemize}
%
Here {\tt DATAMODE} is a keyword in the {\tt berrfile}, {\tt CCDX} and
{\tt CCDY} are elements of columns with the same names in the {\tt
berrfile} and {\tt ROWCNT} is a keyword in the {\tt pbkfile}.
\item
If a {\tt berrfile} includes one or more valid bias-parity errors, then
set the {\tt FEP\_ID} equal to the value of the keyword of the same name
in the {\tt berrfile} and use the information in the binary table of the
{\tt pbkfile} to find the corresponding {\tt CCD\_ID}.
\item
A FEP is identified as having suffered from the FEP0 problem if
%
\begin{itemize}
\item
the ${\tt FEP\_ID} = 0$,
\item
the errors have ${\tt CCDY} \ge 0$ (if the ${\tt DATAMODE} = {\tt
CC33\_FAINT}$ or {\tt CC33\_GRADED}) or have ${\tt CCDY} \ge 512$
(if the {\tt DATAMODE} is anything else), and
\item
the total number of valid errors per frame, in the appropriate {\tt
CCDY} range, is greater than {\tt maxerr} for any frame.
\end{itemize}
\item
If a {\tt berrfile} includes one or more valid bias-parity errors that
are not associated with the FEP0 problem, then the extension of the {\tt
outfile} that is associated with {\tt CCD\_ID} includes one or more
entries such that
%
\begin{itemize}
\item
{\tt SHAPE} is computed as usual,
\item
{\tt COMPONENT} is computed as usual,
\item
${\tt CHIPX} = {\tt CCDX} + 1$,
\item
${\tt CHIPY} = {\tt CCDY} + {\tt STARTROW} + 1$ \hspace*{0.25in} (if
${\tt DATAMODE} = {\tt FAINT}$, {\tt FAINT\_BIAS}, {\tt GRADED}, or
{\tt VFAINT}), or \\
%
$1 \le {\tt CHIPY} \le 1024$ \hspace*{1.0in} (if ${\tt DATAMODE} =
{\tt CC33\_FAINT}$ or {\tt CC33\_GRADED}),
\item
${\tt TIME} = {\tt TIME}_{\rm berr}$,
\item
${\tt TIME\_STOP} = {\tt TSTOP}$, and
\item
{\tt STATUS} has bit 2 (of 0-31) set to one.
\end{itemize}
%
Here, {\tt CCDX} and {\tt CCDY} are the coordinates of the bias-parity
error, ${\tt TIME}_{\rm berr}$ is the {\tt TIME} associated with the
error, and {\tt STARTROW} and {\tt TSTOP} are keywords in the {\tt
pbkfile}.
\item
If a {\tt berrfile} contains valid bias-parity errors associated with
the FEP0 problem, then the extension of the {\tt outfile} that is
associated with {\tt CCD\_ID} includes an entry such that%
%
\footnote{An examination of the twelve bias-parity error files that
include errors associated with the FEP0 problem (\ie\ ones for the {\tt
OBS\_ID}s that are below the line in Table~1), reveals that the only
errors reported are errors associated with the FEP0 problem. There is
no evidence that there are other valid errors in the files.}
%
\begin{itemize}
\item
{\tt SHAPE} is determined as usual,
\item
{\tt COMPONENT} is computed as usual,
\item
$1 \le {\tt CHIPX} \le 1024$,
\item
$513 \le {\tt CHIPY} \le 1024$ \hspace*{0.86in} (if ${\tt DATAMODE}
= {\tt FAINT}$, {\tt FAINT\_BIAS}, {\tt GRADED}, or {\tt VFAINT}),
or \\
%
$1 \le {\tt CHIPY} \le 1024$ \hspace*{1.0in} (if ${\tt DATAMODE} =
{\tt CC33\_FAINT}$ or {\tt CC33\_GRADED}),
\item
${\tt TIME} = {\tt TIME}_{\rm berr}$,
\item
${\tt TIME\_STOP} = {\tt TSTOP}$,
and
\item
{\tt STATUS} has bit 13 (of 0-31) set to one.
\end{itemize}
%
Here, ${\tt TIME}_{\rm berr}$ is the {\tt TIME} associated with the
first frame in which there are more than {\tt maxerr} valid bias-parity
errors and {\tt TSTOP} is a keyword in the {\tt pbkfile}.
\end{enumerate}
% 8. Caveats
\subsection{ Caveats }
\begin{enumerate}
\item
The values of {\tt TIME} in the bias-parity error files appear to be the
{\tt TIME}s of the mid points of the frames. Therefore, perhaps the
values of {\tt TIME} in the output file should be ${\tt TIME}_{\rm stat}
- {\tt TIMEPIXR}_{\rm stat} \times {\tt TIMEDEL}_{\rm stat}$ instead of
${\tt TIME}_{\rm berr}$, where ${\tt TIME}_{\rm stat}$ is the time
associated with the relevant {\tt EXPNO}.
\end{enumerate}
% 9. Figures and table
% 9.1. Table 1
\begin{center}
\begin{tabular}{ccl}
\multicolumn{3}{c}{Table 1. Histogram of the number of valid bias-parity
errors} \\
\hline \hline
No.\ valid errors & No.\ files & {\tt OBS\_ID}(s) \\
\hline
0 & 14079 & {\ldots} \\
1 & 2055 & {\ldots} \\
2 & 124 & {\ldots} \\
3 & 23 & {\ldots} \\
4 & 6 & 2977, 5771, 9581, 10052, 10806, 11011 \\
5 & 1 & 4195 \\
6 & 2 & 9893, 11058 \\
7 & 1 & 9924 \\
7439 & 1 & 7649 \\
\hline
127003 [3550]\ \ \ \ & 1 & 62340 \\
136481 [625]\ \ \ \ \ & 1 & 62338 \\
139559 [139522] & 1 & 965 \\
139756 [139744] & 1 & 510 \\
149668 [149668] & 1 & 62502 \\
186595 [186383] & 1 & 62333 \\
200635 [4827]\ \ \ \ & 1 & 62327 \\
238050 [146756] & 1 & 62353 \\
265784 [118226] & 1 & 18 \\
336595 [79091]\ \ & 1 & 62363 \\
1043209 [139813]\ \ & 1 & 1383 \\
3286241 [101649]\ \ & 1 & 333 \\
\hline
Total & 16304 & {\ldots} \\
\hline \hline
%
\multicolumn{3}{l}{\parbox{5.0in}{The numbers inside the square brackets
in the first column are the number of errors in the first frame that has
an error. These values are well above the maximum allowed value for
{\tt maxerr}.}}
%
\end{tabular}
\end{center}
% 9.2. Table 2
\vspace*{1.0\baselineskip}
\begin{center}
\begin{tabular}{ccl}
\multicolumn{3}{c}{Table 2. Histogram of the number of valid bias-parity
errors per frame} \\
\hline \hline
No.\ valid errors per frame & No.\ frames & {\tt OBS\_ID}(s) \\
\hline
1 & 9613 & {\ldots} \\
2 & 90 & {\ldots} \\
3 & 13 & {\ldots} \\
4 & 1 & 5771 \\
5 & 1 & 4195 \\
6 & 2 & 9893, 11058 \\
7 & 1 & 9924 \\
\hline
Total & 9721 & {\ldots} \\
\hline \hline
%
\multicolumn{3}{l}{\parbox{5.0in}{The very large number of frames with
no valid errors is omitted. The data in the files that are associated
with the FEP0 problem are also omitted. Therefore, the values for the
number of frames are the differences between the red and green
histograms in Figure~\ref{fig02}. }}
%
\end{tabular}
\end{center}
% 9.3. Fig 1
\begin{figure}
\hbox{\psfig{file=FIGS/n_errs_hist.ps,angle=-90,width=6.5in}}
%
\caption{Histograms of the number of bias-parity errors in the bias-parity
error files. The black histogram includes all telemetered bias-parity
errors. The red histogram includes only the valid errors (see
sec.~{\ref{proc}}). The bin at the right-hand side of the plot
indicates the number of files that have at least 200 errors.
%
\label{fig01}}
\end{figure}
% 9.4. Fig 2
\begin{figure}
\hbox{\psfig{file=FIGS/err_rate_hist.ps,angle=-90,width=6.5in}}
%
\caption{Histograms of the number of bias-parity errors per frame of data.
The black histogram includes all telemetered bias-parity errors. The
red histogram includes only the valid errors (see sec.~\ref{proc}). The
green histogram includes only the valid errors that are associated with
the FEP0 problem. The bin at the right-hand side of the plot indicates
the number for frames that have at least 30 errors. All twelve of the
files associated with the FEP0 problem have at least one frame with 30
or more errors (Table~1). The dotted, vertical line is the default value for {\tt
maxerr}.
%
\label{fig02}}
\end{figure}
% 9.5. Fig 3
\begin{figure}
\hbox{\psfig{file=FIGS/n_errs_v_time.ps,angle=-90,width=6.5in}}
%
\caption{The number of valid bias-parity errors as a function of time.
Each data point is the sum over a 365-day interval. The day is the
mission elapsed time (\ie\ is relative to 1998-01-01T00:00:00). The
data associated with the FEP0 problem and with {\tt OBS\_ID} 7649 are
excluded. As noted by Peter Ford, there is a correlation between the
number of bias-parity errors and the number of threshold crossings.
%
\label{fig03}}
\end{figure}
% 9.6. Fig 4
\begin{figure}
\hbox{\psfig{file=FIGS/n_errs_v_n_pix.ps,angle=-90,width=6.5in}}
%
\caption{The number of pixels on which valid bias-parity errors occur v.\
the number of valid errors. The dashed line is the line along which the
number of pixels equals the number of errors. It is not possible for a
data point to lie above this line (\ie\ to have more pixels with
bias-parity errors than errors). The cluster of points near the upper,
right-hand corner are those associated with the FEP0 problem. The
dotted, horizontal line at 262,144 represents the maximum number of
pixels that can be affected by the FEP0 problem. The point near the
middle of the lower edge is for {\tt OBS\_ID} 7649. A bias-parity error
file for this observation had 7,439 errors, all but one of which
occurred at the location $( {\tt CCD\_ID}, {\tt CHIPX}, {\tt CHIPY} ) =
( 8, 786, 356 )$.
%
\label{fig04}}
\end{figure}
% 9.7. Fig 5
\begin{figure}
\hbox{\psfig{file=FIGS/valid_coords.ps,angle=-90,width=6.5in}}
%
\caption{A plot of the chip coordinates at which valid bias-parity errors
occur. Note that all CCDs are included. The data in the files that are
associated with the FEP0 problem are excluded. A periodic pattern in
{\tt CHIPX} is evident.
%
\label{fig05}}
\end{figure}
% 9.8. Fig 6
\begin{figure}
\hbox{\psfig{file=FIGS/n_valid_v_coords_1024.ps,angle=-90,width=6.5in}}
%
\caption{Histograms of the number of valid bias-parity errors as a
function of {\tt CHIPX} (black) and {\tt CHIPY} (red). Note that all
CCDs are included. The data in the files that are associated with the
FEP0 problem are excluded. The spikes at ${\tt CHIPX} = 786$ and ${\tt
CHIPY} = 356$ are associated with the 7,438 errors at this location for
{\tt OBS\_ID} 7649. A periodic pattern in {\tt CHIPX} is evident.
%
\label{fig06}}
\end{figure}
% 9.9. Fig 7
\begin{figure}
\hbox{\psfig{file=FIGS/n_valid_v_coords_32.ps,angle=-90,width=6.5in}}
%
\caption{Histograms of the number of valid bias-parity errors as a
function of {\tt CHIPX} (black) and {\tt CHIPY} (red). The coordinates
are modulo 32. Note that all CCDs are included. The data in the files
that are associated with the FEP0 problem are excluded. The spikes at
coordinates of 18 and 2 are associated with the 7,438 errors at ${\tt
CHIPX} = 786$ and ${\tt CHIPY} = 356$ for {\tt OBS\_ID} 7649. Errors
occur almost exclusively on one of the last four columns in each set of
32 columns.
%
\label{fig07}}
\end{figure}
% 9.10. Fig 8
\begin{figure}
\hbox{\psfig{file=FIGS/n_fep0_v_coords_1024.ps,angle=-90,width=6.5in}}
%
\caption{Histograms of the number of bias-parity errors as a function of
{\tt CHIPX} (black) and {\tt CHIPY} (red) for the errors associated with
the FEP0 problem. Note that all CCDs are included. A periodic pattern
in {\tt CHIPX} is evident. No errors are reported for pixels that have
${\tt CHIPY} < 513$.
%
\label{fig08}}
\end{figure}
% 9.11. Fig 9
\begin{figure}
\hbox{\psfig{file=FIGS/n_fep0_v_coords_32.ps,angle=-90,width=6.5in}}
%
\caption{Histograms of the number of bias-parity errors as a function of
{\tt CHIPX} (black) and {\tt CHIPY} (red) for the errors associated with
the FEP0 problem. The coordinates are modulo 32. Note that all CCDs
are included. No errors are reported for pixels that have even values
of {\tt CHIPX}.
%
\label{fig09}}
\end{figure}
% 10. Finish
\end{document}
|
https://defelement.com/img/element-serendipity_Hdiv-hexahedron-2-11.tex
|
defelement.com
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application/x-tex
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crawl-data/CC-MAIN-2022-21/segments/1652662522309.14/warc/CC-MAIN-20220518183254-20220518213254-00530.warc.gz
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http://kleine.mat.uniroma3.it/e/93-78.latex
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\documentstyle12pt!{article}
\title{DYNAMICAL SYSTEMS AND\\ FACTORS OF FINITE AUTOMATA}
\author{Petr K\accent23urka \vspace{8pt}\\
Dept. of Mathematical Logic and Philosophy of Mathematics,\\
Faculty of Mathematics and Physics, Charles University\\
Malostransk\'{e} n\'{a}m\v{e}st\'{\i} 25, 118 00 Praha 1,
Czechia\\
{\small fax: (422) 532 742, email: kurka@cspguk11} }
\date{}
\newcommand{\mez}{\vspace{10pt}}
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\newtheorem{dfn}{Definition}
\newtheorem{lem}{Lemma}
\newtheorem{pro}{Proposition}
\newtheorem{thm}{Theorem}
\newtheorem{cor}{Corollary}
\newtheorem{exm}{Example}
\begin{document}
\maketitle
\begin{abstract}
We conceive finite automata as dynamical systems on discontinuum
and investigate their factors. Factors of finite automata include
many well-known simple dynamical systems, e.g. hyperbolic
systems and systems with finite attractors. In the quadratic
family on the real interval, factors of finite automata include
all systems with finite number of periodic points, as well as
systems at the band-merging bifurcations. On the other hand the
system with a non-chaotic attractor, which occurs at the limit of
the period doubling bifurcations (at the edge of chaos), is not
of this class. Next we propose as another simplicity criterion
for dynamical systems the property of having chaotic limits
(every point belongs to a set, whose $\omega$-limit is
chaotic). We show that any factor of a finite automaton has
chaotic limits but not vice versa. \mez
\noindent
key words: edge of chaos, discontinuum, renormalization.
\end{abstract}
\section{Introduction}
Studies in chaotic dynamics suggest that chaotic dynamical
systems are usually rather simple, the most notable example being
the shift map. Another class of simple dynamical systems is
distinguished by the existence of periodic orbits, which attract
all points. Systems with really complex and interesting
dynamics are found at the edge of chaos (see Langton
\cite{kn:Langton}). They are characterized by long transient
periods, strong dependence on initial conditions and the power of
universal computations. In the quadratic family on the real
interval, the systems at both period doubling and band merging
bifurcations have been shown by Crutchfield and Young
\cite{kn:Crutch} to generate simple regular languages. On the
other hand the system at their common limit generates a
non-regular language.
The feeling that chaotic means simple has been supported by a
recent result of Brooks et al. \cite{kn:Brooks}. A standard
Devaney's \cite{kn:Devaney} definition reads that a chaotic
system is one, which is topologically transitive, whose periodic
points are dense, and which is sensitive to initial conditions.
Brooks et al. \cite{kn:Brooks} prove that on infinite metric
spaces, the first two conditions imply the third. In light of
this result it is natural to relax the definition of chaotic
system to topological transitivity and density of periodic
points. According to this relaxed definition, finite dynamical
systems, which are orbits of periodic points, are chaotic too.
One might try to characterize simple systems by the condition,
that all points have chaotic $\omega$-limit sets. This would not
do, however, since even in the shift system, there are many
complex subshifts like Morse sequences. We define therefore a
system with chaotic limits as one, whose each point is included
in a set, whose $\omega$-limit set is chaotic. This works well in
the quadratic family: all systems at the period doubling and band
merging bifurcations have chaotic limits, while the system at
their common limit has not.
The simplest systems with chaotic limits are the shift map
$\sigma$ on $2^{N}$ defined by $\sigma(u)_{i}=u_{i+1}$, which
itself is chaotic, and its inverse $\sigma^{-1}_{0}$ defined by
$\sigma^{-1}_{0}(u)_{i+1} = u_{i}$,\ $\sigma^{-1}_{0}(u)_{0} =
0$, whose limit is the fixed point 0. Both these systems are
instances of finite automata. We conceive a finite automaton as a
dynamical system:
a finite control connected to infinite input and output tapes. At
each time step the automaton reads a symbol from the input tape
and writes a symbol to the output tape. The state of the whole
system consists of the inner state of the control and the content
of both tapes. The shift map is an automaton which works only
with the input tape, while its inverse works only with the output
tape. The state space of a finite automaton is a discontinuum,
i.e. a countable product of finite spaces.
Another simplicity criterion for dynamical systems is
based on the fact, that every dynamical system on a
compact metric space is a factor of a dynamical system on
discontinuum (see Balcar and Simon (\cite{kn:Balcar},
Proposition 5.12). In computer science there is a hierarchy
ranging from finite automata, stack automata, Turing automata,
and cellular automata to neural networks. All these automata can
be regarded as dynamical systems on discontinuum. Considering
their factors, we obtain a hierarchy of dynamical systems on
compact metric spaces. Factors of finite automata are at the
bottom of this hierarchy. This works again in the quadratic
family: all systems at the period doubling and band merging
bifurcations are factors of finite automata, while the system at
their common limit is not. We show that every factor of a finite
automaton has chaotic limits, while there are systems with
chaotic limits, which are not factors of finite automata.
In Crutchfield and Young \cite{kn:Crutch} and Troll
\cite{kn:Troll}, the complexity of dynamical systems has been
studied via complexity of languages generated by finite
partitions. Our concepts of systems with chaotic limits, and
factors of finite automata offer an alternative and complementary
approach.
\section{Systems with chaotic limits}
\begin{dfn} A dynamical system $(X,f)$ is a continuous map
$f: X \rightarrow X$ of a compact metric space $X$ to itself. A
homomorphism $\varphi: (X,f) \rightarrow (Y,g)$ of dynamical
systems is a continuous mapping $\varphi:X \rightarrow Y$ such
that $g \varphi = \varphi f$. We say that $(Y,g)$ is a factor of
$(X,f)$, if $\varphi$ is a factorization (i.e. a surjective map).
\begin{picture}(200,55)
\put(110,45){\arleft{f}{X}}
\put(110,15){\ardown{\varphi}{\varphi}}
\put(110,5) {\arleft{g}{Y}}
\end{picture}
\end{dfn}
\noindent
The $n$-th iteration $f^{n}:X \rightarrow X$ of $f$ is defined by
$f^{0}(x)=x$, $f^{n+1}(x)=f(f^{n}(x))$. The orbit ${\cal O}(x) =
\{f^{i}(x): i \geq 0\}$ of $x$ is the set of its iterates. A
point $x \in X$ is periodic with period $n>0$ if $f^{n}(x)=x$ and
$f^{i}(x) \neq x$ for $0<i<n$. A fixed point is a periodic point
with period 1. A subset $A \subseteq X$ is invariant, if $f(A)
\subseteq A$. It is strongly invariant, if $f(A)=A$. The
$\omega$-limit set of a set $A \subseteq X$ is defined by
$\omega(A)= \bigcap_{n} \overline{ \bigcup_{m>n} f^{m}(A)}$. It
is easy to see that if $A$ is nonempty, then $\omega(A)$ is a
nonempty, closed, strongly invariant set, so $f$ restricted to
$\omega(A)$ is a dynamical system.
\begin{lem}
Let $\varphi: (X,f) \rightarrow (Y,g)$ be a homomorphism, and $A
\subseteq X$. Then $\varphi(\omega_{f}(A)) =
\omega_{g}(\varphi(A))$.
\end{lem} \label{omega}
Proof: If $x \in \omega_{f}(A)$, then there exist $x_{i} \in A$
and $n_{i}$ with $f^{n_{i}}(x_{i}) \rightarrow x$, so
$\varphi(x_{i}) \in \varphi(A), g^{n_{i}}(\varphi(x_{i}))
\rightarrow \varphi(x)$, and therefore $\varphi(x) \in
\omega_{g}(\varphi(A))$. If $y \in \omega_{g}(\varphi(A))$, then
there exist $x_{k} \in A$ and $n_{k}$ with $g^{n_{k}}
\varphi(x_{k}) \rightarrow y$. There exists a convergent
subsequence $f^{n_{k_{i}}}(x_{k_{i}}) \rightarrow x \in
\omega_{f}(A)$, so $\varphi f^{n_{k_{i}}}(x_{k_{i}})
\rightarrow \varphi(x)$. It follows $y = \varphi(x)$, and
therefore $y \in \varphi(\omega_{f}(A))$. $\Box$
\begin{dfn}
A dynamical system $(X,f)$ is chaotic, if the set of its periodic
points is dense in $X$ and if for any open nonempty sets $U,V
\subseteq X$ there exists $k>0$ such that $f^{k}(U) \cap V \neq
0$ (topological transitivity). The system $(X,f)$ has chaotic
limits, if for each $x \in X$ there exists $A \subseteq X$ such
that $x \in A$ and $\omega(A)$ is chaotic.
\end{dfn}
\noindent
In particular a finite system is chaotic iff it is an orbit of a
periodic point, and any finite system has chaotic limits. If
$\omega(x)$ is a periodic orbit for each $x \in X$, then $(X,f)$
is a system with chaotic limits. Moreover if $X$ or $\omega(X)$
is chaotic, then $(X,f)$ has again chaotic limits.
\begin{pro}
A factor of a chaotic dynamical system is chaotic. A factor of a
system with chaotic limits has chaotic limits.
\end{pro}
Proof: Suppose that $\varphi: (X,f) \rightarrow (Y,g)$ is a
factorization and $(X,f)$ is chaotic. Let $U \subseteq Y$ be a
nonempty open set. Then $\varphi^{-1}(U)$ is a nonempty open set
and there is a periodic point $x$ in it. It follows that
$\varphi(x)$ is a periodic point in $U$. If $U,V \subseteq Y$
are nonempty open sets, then so are $\varphi^{-1}(U)$ and
$\varphi^{-1}(V)$, so there exists $x \in f^{k} \varphi^{-1}(U)
\cap \varphi^{-1}(V)$. It follows $\varphi(x) \in g^{k}(U) \cap
V$, so $(Y,g)$ is chaotic. Suppose now that $(X,f)$ has chaotic
limits, and let $y \in Y$. There exists $x \in X$ with
$\varphi(x)=y$ and $x \in A \subseteq X$ such that $\omega(A)$ is
chaotic. It follows that $y \in \varphi(A)$ and by Lemma
\ref{omega}, $\omega_{g}(\varphi(A)) = \varphi(\omega_{f}(A))$ is
chaotic. $\Box$
\section{Finite automata}
\begin{dfn}
Let $A,Q,B$ be finite sets, and $Z=\{...-1,0,1,...\}$ the set of
integers. The discontinuum (over $A,Q,B$) is the space
\ X = \{u \in (A \cup Q \cup B)^{Z} : u_{i} \in A \mbox{ for }
i>0,\; u_{0} \in Q,\; u_{i} \in B \mbox{ for } i<0 \} \!
with metric
\ \varrho(u,v) = 2^{-n} \; \mbox{ where } \;
n = \inf\{i \geq 0: u_{i} \neq v_{i} \; \mbox{ or } \;
u_{-i} \neq v_{-i} \} \!
\end{dfn}
\begin{pro}
Let $X$ be a discontinuum. Then $X$ is a compact metric space.
For each compact metric space $Y$ there is a factorization
$\varphi : X \rightarrow Y$. For every dynamical system $(Y,g)$
there exists a dynamical system $f$ on $X$ and a factorization
$\varphi : (X,f) \rightarrow (Y,g)$.
\end{pro}
See Balcar and Simon \cite{kn:Balcar} for a proof.
\begin{dfn}
Let $A,Q,B$ be finite sets (input alphabet, set of inner states,
and output alphabet), and $f_{A}:Q \times A \rightarrow Q$,
$f_{B}:Q \rightarrow B$ input and output functions. A finite
automaton over $A,Q,B$ is a dynamical system $f$ on the
discontinuum $X$ (over $A,Q,B$) defined by\\
\hspace*{10pt} $f(u)_{-1} = f_{B}(u_{0}),\; f(u)_{0} =
f_{A}(u_{0},u_{1}),\; f(u)_{i} = u_{i+1} \; \mbox{ for }\; -1
\neq i \neq 0$\\
$(X,f)$ is a finite input automaton (without output tape) if $B$
is a singleton. It is a finite output automaton (without input
tape), if $A$ is a singleton.
\end{dfn}
\noindent
Thus $\{u_{i}:i>0\}$ is the input tape, $\{u_{i}:i<0\}$ is the
output tape, and\\
$f(...u_{-2},u_{-1},u_{0},u_{1},u_{2}...) =
(...u_{-1},f_{B}(u_{0}),f_{A}(u_{0},u_{1}),u_{2},u_{3}...)$.
\begin{thm}
Every finite automaton has chaotic limits.
\end{thm}
Proof: Let $w \in X$ and define $Q_{0}= \{q \in Q: (\forall
m)(\exists n >m)(f^{n}(w)_{0} = q) \}$. Let $k$ be the first
integer such that for all $n \geq k$ there is $f^{n}(w)_{0} \in
Q_{0}$. Define $W=\{v \in X: (\forall i \leq k)(v_{i}=w_{i})\;\;
\& \;\;(\forall i \geq k)(f^{i}(v)_{0} \in Q_{0}) \}$. We shall
prove that $\omega(W)$ is chaotic. Denote $Y = \{v \in X :
(\forall n \geq 0)(f^{n}(v)_{0} \in Q_{0})\}$. Then $Y$ is an
invariant set and $\omega(W) \subseteq \bigcap \{f^{n}(Y): n \geq
0\}$ since $f^{k}(W) \subseteq Y$. Let $u \in \bigcap
\{f^{n}(Y): n \geq 0\}$, and pick some $n>0$. There is $v \in Y$
with $f^{n}(v)=u$, and there exists $m \geq k$ with $f^{m}(w)_{0}
=v_{0}$. Define $s \in W$ by $s_{i}=w_{i}$ for $i \leq m$, $s_{i}
= v_{m+i}$ for $i > m$. Then $\varrho(f^{m+n}(s),u) < 2^{-n}$,
so $u \in \omega(W)$. Thus $\omega(W) = \bigcap \{f^{n}(Y) :n
\geq 0\}$. Let $U \subseteq X$ be an open set and $u \in U \cap
\omega(W)$. We shall find a periodic point in $U \cap \omega(W)$.
There exists $n$ such that the $n$-th cylinder around $u$ is
contained in $U$: $u \in \{v \in \omega(W): (\forall :i: \leq
n)(v_{i}=u_{i}) \} \subseteq U \cap \omega(W)$. There exists $u'
\in Y$ such that $u=f^{n}(u')$. Then there exists $u'' \in Y$
such that $u'_{i}=u''_{i}$ for $0 \leq i \leq 2n$ and
$f^{m}(u'')_{0} = u''_{0}$ for some $m>2n$. Define $s \in X$ by
$s_{0}=u''_{0}$, $s_{km+i}=u''_{i}$, $s_{-km-i}=f^{m}(u'')_{-i}$
for $1 \leq i \leq m$, and $k \geq 0$. Then $s \in \omega(W)$ is
a periodic point, and $f^{n}(s)$ is a periodic point in $U \cap
\omega(W)$. Thus periodic points are dense in $\omega(W)$. To
prove the topological transitivity, let $U,V$ be open sets, $u
\in U \cap \omega(W)$, $v \in V \cap \omega(W)$. There is again
$n$ such that the $n$-th cylinders around $u$ and $v$ are
contained in $U$ and $V$ respectively. Then there are $u',v' \in
Y$ such that $u=f^{n}(u')$, $v=f^{n}(v')$. There exists $u'' \in
Y$ such that $u'_{i} = u''_{i}$ for $0 \leq i \leq 2n$, and
$f^{m}(u'')_{0} =v'_{0}$ for some $m >2n$. Define $s \in X$ by
$s_{i}=u''_{i}$ for $i \leq m$ and $s_{i}=v'_{i-m}$ for $i > m$.
Then $f^{m+n}(s) \in f^{m}(U) \cap V \cap \omega(W)$. $\Box$
\begin{cor}
A factor of a finite automaton has chaotic limits.
\end{cor}
\begin{pro}
A subshift of finite type is a factor of a finite input
automaton. \end{pro}
Proof: Let $A$ be a finite alphabet and $M$ a square $A \times A$
matrix with entries from $2=\{0,1\}$. Let $Q=A$, $B=\{0\}$, and
define $f_{A}$ so that for each $a,b \in A$ $(\exists c \in
A)(f_{A}(a,c)=b) \Leftrightarrow M(a,b)=1$. Define $\Sigma_{M} =
\{u \in A^{N}: (\forall i \geq 0)(M(u_{i},u_{i+1})=1) \}$,
$\sigma: \Sigma_{M} \rightarrow \Sigma_{M}$ by $\sigma(u)_{i} =
u_{i+1}$, and
$\varphi:X \rightarrow \Sigma_{M}$ by $\varphi(u)_{i} =
(f^{i}(u))_{0}$. Then $\varphi : (X,f) \rightarrow
(\Sigma_{M},\sigma)$ is a factorization. $\Box$ \mez
\noindent
Since a closed hyperbolic set with a local product structure (see
Shub \cite{kn:Shub}) is a factor of a subshift of finite type, it
is also a factor of a finite automaton.
\begin{thm} \label{attractor}
A dynamical system $(Y,g)$ is a factor of a finite output
automaton if and only if $\omega(Y)$ is finite.
\end{thm}
Proof: Let $(X,f)$ be a finite output automaton. Then $f_{A}: Q
\rightarrow Q$. Denote $Q_{0} \subseteq Q$ the set of periodic
points of $f_{A}$, and $f_{A}^{-1} :Q_{0} \rightarrow Q_{0}$ the
inverse map to $f_{A}$. Then $u \in \omega(X)$ iff there exists
$q \in Q_{0}$ such that $u_{0}=q$ and $(\forall i >0)(u_{-i} =
f_{B} f_{A}^{-i}(q))$. Thus $\omega(X)$ is a finite set. If
$\varphi : (X,f) \rightarrow (Y,g)$ is a factorization, then
$\omega(Y) = \varphi(\omega(X))$ is finite too. Suppose now that
$\omega(Y)$ is finite. Since it is strongly invariant, it
consists just of periodic points of $(Y,g)$, and there exists a
map $g^{-1}: \omega(Y) \rightarrow \omega(Y)$ inverse to $g$. For
$p \in \omega(Y)$ denote $t_{p}>0$ its period. We shall prove
that for every $p \in \omega(Y)$ there exists its closed,
$g^{t_{p}}$-invariant neighbourhood, which is disjoint with
$\omega(Y)-\{p\}$. Suppose by contradiction, that it is not the
case. For $A \subseteq X$, $\varepsilon > 0$ denote
$B_{\varepsilon}(A) = \{y \in Y: (\exists z \in
A)(\varrho(y,z)<\varepsilon) \}$. For each $k>0$ the closure of
$\bigcup_{n \geq 0} g^{nt_{p}}(B_{1/k}(p))$ is a closed
$g^{t_{p}}$-invariant neighbourhood of $p$, and therefore meets
$\omega(Y)-\{p\}$. It follows that there exists a sequence $y_{k}
\in B_{1/k}(p)$, such that $g^{n_{k}t_{p}}(y_{k}) \in
B_{1/k}(\omega(Y)-\{p\})$ for some $n_{k}>0$. Let $W$ be a
neighbourhood of $p$ disjoint with $\omega(Y)-\{p\}$. There
exists an open neighbourhood $U$ of $p$ with $g^{t_{p}}(U)
\subseteq W$, and also an open neighbourhood $V$ of $\omega(Y)-
\{p\}$ disjoint with $W$. For each $k$ let $m_{k}<n_{k}$ be the
first integer, for which $g^{m_{k}t_{p}}(y_{k}) \not\in U$, and
therefore $g^{m_{k}t_{p}}(y_{k}) \in Y-U-V$. Since $Y-U-V$ is
compact, there is a convergent subsequence
$g^{m_{k_{i}}t_{p}}(y_{k_{i}}) \rightarrow y \in Y-U-V$, and it
follows $y \in \omega(Y)$, which is a contradiction. So we have a
closed neighbourhood $V_{p}$ of $p$ disjoint with $\omega(Y)-
\{p\}$, for which $g^{t_{p}}(V_{p}) \subseteq V_{p}$. Let us
prove, that $W_{p} = \{y \in Y: \lim_{k \rightarrow \infty}
g^{kt_{p}}(y) = p\}$ is an open set. If $y \in W_{p}$, there is
$k>0$ for which $g^{kt_{p}}(y) \in int(V_{p})$ and there is a
neighbourhood $U$ of $y$ with $g^{kt_{p}}(U) \subseteq V_{p}$,
so $U \subseteq W_{p}$. Since $W_{p} \cap W_{q} = 0$ for
different $p,q \in \omega(Y)$, and $\bigcup \{ W_{p}: p \in
\omega(Y)\} = Y$, $W_{p}$ are also closed.
Construct a finite automaton $(X,f)$ with alphabets $A=\{0\}$, $Q
= \omega(Y)$, $B= Q \cup \{0\}$ (0 is a symbol not occurring in
$Q$). Define transition and output functions by $f_{A}(p,0) =
g(p)$, $f_{B}(p)=g(p)$. For $p \in Q$, $k \geq 0$ define $X_{pk}
= \{u \in X : \max \{j \geq 0 : u_{-j} \neq g^{-j}(p)\} = k+1
\}$, $X_{p\infty} = \{u \in X : (\forall j \geq 0)(u_{-j} =
g^{-j}(p) \}$. Then $f : X_{pk} \rightarrow X_{g(p),k+1}$ is a
homeomorphism and has an inverse $f^{-1}$. Let $W_{p0} = W_{p} \cap
\overline{Y-g(Y)}$. If $W_{p0} \neq 0$ define $\varphi$ on
$X_{p0}$ so that $\varphi(X_{p0}) = W_{p0}$ ($X_{p0}$ is a
discontinuum and $W_{p0}$ is closed). If $W_{p0} = 0$, define
$\varphi(X_{p0})= \{p\}$. If $u \in X_{g(p),k+1}$, define
$\varphi(u) = g \varphi f^{-1}(u)$ by induction on $k$. If $u \in
X_{p\infty}$, define $\varphi(u) = p$.
Then $\varphi: (X,f) \rightarrow (Y,g)$ is a factorization.
$\Box$ \mez
\noindent
A set $A \subseteq X$ is an attractor (see Devaney
\cite{kn:Devaney}), if it has a neighbourhood $U$ such that
$f(U) \subseteq int(U)$, and $A=\omega(U)$. Thus Theorem
\ref{attractor} says that a system is a factor of a finite output
automaton iff all its attractors are finite.
\begin{dfn}
A sum of dynamical systems $(X_{0},f_{0})$ and $(X_{1},f_{1})$ is
a dynamical system $(X,f)$, where $X = X_{0} \cup X_{1}$ is the
disjoint union, and $f(x) = f_{i}(x)$ if $x \in X_{i}$.
\end{dfn}
\begin{pro} \label{sum}
The sum of dynamical systems, which are factors of finite
automata, is itself a factor of a finite automaton.
\end{pro}
Proof: Let $\varphi_{0}: (X_{0},f_{0}) \rightarrow
(Y_{0},g_{0})$, $\varphi_{1}: (X_{1},f_{1}) \rightarrow
(Y_{1},g_{1})$,
be factorizations of finite automata. Define a finite automaton
$(X,f)$ by $A= A_{0} \times A_{1}$, $Q = Q_{0} \cup Q_{1}$,
(disjoint union) $B = B_{0} \times B_{1}$. Pick some $b_{0} \in
B_{0}$, $b_{1} \in B_{1}$ and define
\ \begin{array}{lll}
f_{A}(q,(a_{0},a_{1})) = f_{A_{0}}(q,a_{0}), &\;
f_{B}(q) = (f_{B_{0}}(q),b_{1}) & \mbox{ if }\; q \in Q_{0}\\
f_{A}(q,(a_{0},a_{1})) = f_{A_{1}}(q,a_{1}), &\;
f_{B}(q) = (b_{0},f_{B_{1}}(q)) & \mbox{ if }\; q \in Q_{1}
\end{array} \!
Let $(Y,g)$ be the sum of $(Y_{0},g_{0})$ and $(Y_{1},g_{1})$.
Define $\varphi : (X,f) \rightarrow (Y,g)$ by
$\varphi(u) = \varphi_{0} \pi_{0}(u)$ if $u_{0} \in Q_{0}$,
$\varphi(u) = \varphi_{1} \pi_{1}(u)$ if $u_{0} \in Q_{1}$. Here
$\pi_{i}:X \rightarrow X_{i}$ are the projections.
\section{Clopen-regular systems}
If $\alpha$ is a finite set, denote $\alpha^{*}$ the set of words
over $\alpha$. For a word $u \in \alpha^{*}$ denote $:\alpha:
\geq 0$ its length and $u_{i}$ its $i+1$st letter, so $u =
u_{0}...u_{:u:-1}$. Subsets of $\alpha^{*}$ are called languages.
See Hopcroft and Ullmann \cite{kn:Hop} for the definition of a
regular language.
\begin{dfn}
Let $(X,f)$ be a dynamical system and $\alpha$ a finite set of
subsets of $X$. Define the language generated by $\alpha$ as \
L(f,\alpha) = \{ u \in \alpha^{*}: (\exists x \in X)(\forall i <
:u:)(f^{i}(x) \in u_{i}) \} \!
The system $(X,f)$ is clopen-regular if $L(f,\alpha)$ is regular
for every finite clopen cover $\alpha$ of $X$.
\end{dfn}
\noindent
A subset $A$ of a metric space $X$ is clopen, if it is both
closed and open. A set $\alpha$ is a cover of $X$ if its union is
$X$. It is a partition, if it is a cover, whose different sets
are disjoint. Let $X$ be discontinuum (over $A,Q,B$), $w \in X$
and $n>0$. Then the $n$-cylinder $w!_{n} = \{v \in X : (\forall
i \in Z)(:i: \leq n \Rightarrow v_{i}=w_{i}) \}$ of $w$ is a
clopen set (it is a ball with centre $w$). The set $\alpha_{n} =
\{w!_{n}: w \in X\}$ of all $n$-cylinders is a finite clopen
partition.
\begin{pro}
Let $(X,f)$ be a dynamical system on discontinuum such that
$L(f,\alpha_{n})$ is regular for each $n>0$ ($\alpha_{n}$ is the
partition of $n$-cylinders). Then $(X,f)$ is clopen-regular.
\end{pro}
Proof: Let $\beta$ be a finite clopen cover. For each $u \in X$
there exists $n_{u}>0$ such that if $u \in B \in \beta$, then
$u!_{n_{u}} \subseteq B$, and if $u \not \in B \in \beta$ then
$u!_{n_{u}} \cap B = 0$. The set $\{ u!_{n_{u}} : u \in X \}$
is an open cover of $X$. Since $X$ is compact, there is a finite
subcover $\{u!_{n_{u}}: u \in I\}$. Let $n= \max\{n_{u}: u \in
I\}$. Then for each $B \in \beta$ there is a finite set $J_{B}
\subseteq \alpha_{n}$ such that if $A \in J_{B}$ then $A
\subseteq B$, and if $A \not\in J_{B}$, then $A \cap B = 0$.
Since $L(f,\alpha_{n})$ is regular, $L(f,\beta)$ is regular too.
$\Box$
\begin{pro}
A factor of a clopen-regular system is clopen-regular.
\end{pro}
Proof: Let $\varphi : (X,f) \rightarrow (Y,g)$ be a
factorization, and $\alpha$ a clopen cover of $Y$. Then
$\varphi^{-1}\alpha = \{\varphi^{-1}(A): A \in \alpha \}$ is a
clopen cover of $X$ and $L(f,\varphi^{-1}\alpha) = L(g,\alpha)$.
$\Box$
\begin{pro}
Any finite automaton is clopen-regular.
\end{pro}
Proof: Let $\alpha_{n}$ be the clopen partition of $n$-cylinders.
For $A,B \in \alpha_{n}$ define $M(A,B)=1$ if $f(A) \cap B \neq
0$ and $M(A,B)=0$ otherwise. Then $L(f,\alpha_{n}) = \{u \in
\alpha^{*}_{n}: (\forall i<:u:-1) (M(u_{i},u_{i+1})=1) \}$. This
is a regular language. $\Box$
\begin{cor}
Any factor of a finite automaton is clopen-regular.
\end{cor}
\begin{exm}
There exists a chaotic dynamical system which is not a factor of
any finite automaton.
\end{exm}
Proof: Let $X=\{u \in 2^{N}: 0^{n}1^{m}0 \prec u \Rightarrow n
\leq m \}$. Here $2=\{0,1\}$ and $\prec$ means substring. Thus $u
\in X$ if every string of $n$ zeros in $u$ is immediately
followed by a string of at least $n$ ones. Then $X$ is a closed,
shift-invariant subset of $2^{N}$, and it is easy to see that
$(X,\sigma)$ is chaotic. However, it is not clopen-regular.
Consider the partition
$\alpha_{0} = \{ \{u:u_{0}=0\}, \{u:u_{0}=1\} \}$. Then
$L(\sigma,\alpha_{0}) = \{u \in 2^{*}: 0^{n}1^{m}0 \prec u
\Rightarrow n \leq m \}$ consists just of all substrings of
elements of $X$ and is not regular. $\Box$
\begin{exm}
There exists a dynamical system $(X,f)$, such that $\omega(x)$ is
a fixed point for all $x \in X$, but $(X,f)$ is not a factor of a
finite automaton.
\end{exm}
Proof: Let $M \subseteq N = \{0\}^{*}$ be a nonregular set of
positive integers. Define $X = \{u \in 3^{Z}: i<j \Rightarrow
u_{i} \leq u_{j}\;\; \&\;\; 01^{m}2 \prec u \Rightarrow m \in M
\}$, where $3=\{0,1,2\}$. Thus $u \in X$ if it is nondecreasing,
and when it contains a finite number of ones, then their number
belongs to $M$. Again, $X$ is a closed shift-invariant set. Its
only fixed points are constant sequences $\overline{0},
\overline{1}, \overline{2}$, and for each $x \in X$, $\omega(x)$
is one of them. However, $(X,\sigma)$ is not clopen-regular. If
$\alpha_{0}$ is the partition of the $0$-cylinders, then
$L(\sigma,\alpha_{0}) = \{u \in 3^{*}: i<j
\Rightarrow u_{i} \leq u_{j}\;\; \& \;\; 01^{m}2 \prec u
\Rightarrow m \in M \}$ is again the language of finite
substrings of elements of $X$, which is not regular. $\Box$ \mez
\noindent
This example does not contradict Theorem \ref{attractor}, since
$\sigma(X)=X$ and therefore $\omega(X)=X$ is infinite. Consider
$X_{1}=\{u \in X: u_{1} \geq 1 \}$ Then $X_{1}$ is a
closed shift-invariant subset of $X$ with only two fixed points.
When we factorize them, we get a system with a single fixed
point, which is $\omega$-limit of all other points, and still the
system is not a factor of a finite automaton. This shows that the
Theorem \ref{attractor} cannot be substantially strengthened.
\section{Unimodal systems}
\begin{dfn} A symmetric real function $g$ defined on $I=-1,1!$
is unimodal, if it is continuously differentiable,
$g(-1)=g(1)=-1$, $g(0)>-1$ and $g'(x)=0$ iff $x=0$.
(We speak about unimodal system, if $g(I) \subseteq I$, i.e. if
$g(0) \leq 1$.) \end{dfn}
\begin{pro} Let $g:I \rightarrow R$ be a symmetric unimodal
function with $g(0)>0$. Then there is a unique $0<p<1$ with $g(-
p)=g(p)=p$. Define the renormalization of $g$ as ${\cal R}g(x) =
- g^{2}(px)/p$. Then ${\cal R}g: I \rightarrow R$ is a
symmetric unimodal function.
\end{pro}
Proof: Clearly $g'(x)>0$ for $x<0$, and $g'(x)<0$ for $x>0$.
Since $g(x)-x$ is positive for $x=0$ and negative for $x=1$,
there is a unique fixed point $p>0$, and $g(-p)=p$. Clearly
${\cal R}g(\pm 1) = - g^{2}(\pm p)/p=-1$. For $x \in (-p,p)$
there is $g(x)>p$, so $g'(g(x))<0$. The equation $(g^{2})'(x)=
g'(g(x)) g'(x)=0$ has in $-p,p!$ unique solution $0$, so the
equation $({\cal R}g)'(x)=0$ has in $-1,1!$ the unique solution
$0$. Since $g$ is decreasing for $x>0$, and $0<p$, we have $g(0)
>p$, and $g^{2}(0)<p$. It follows ${\cal R}g(0) = -g^{2}(0)/p >
-1$. $\Box$
\begin{thm} \label{renorm}
Let $g$ be a symmetric unimodal system with $g(0)>0$. If ${\cal
R}g(0)\leq 1$, and if ${\cal R}g$ is a factor of a finite
automaton, then $g$ is also a factor of a finite automaton.
\end{thm}
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\put(65,45){\arleft{f}{X}}
\put(65,15){\ardown{\varphi}{\varphi}}
\put(65,5) {\arleft{g^{2}}{I_{0}}}
\put(205,45){\arleft{h}{X''}}
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\end{picture}
\noindent
Proof: Let $p_{0}$ be the positive fixed point of $g$. There is
an increasing sequence $p_{k} \in (0,1)$ such that $g(-p_{k})$ =
$g(p_{k})$ = $-p_{k-1}$ for $k>0$. Denote $I_{-\infty}=\{-1\}$,
$I_{k}=-p_{-k},-p_{-k+1}!$ for $k<0$, $I_{0}=-p_{0},p_{0}!$,
$I_{k}=p_{k-1},p_{k}!$ for $k>0$, and $I_{\infty}=\{1\}$. Then
$g(I_{-k}) = g(I_{k}) = I_{-k+1}$ for $k>0$. Since ${\cal R}g(I)
\subseteq I$, we have $g^{2}(I_{0}) \subseteq I_{0}$, and
$g(I_{0}) \subseteq I_{1}$. By the assumption there exists
a finite automaton $(X,f)$ and a factorization $\varphi:(X,f)
\rightarrow (I_{0},g^{2})$. We construct a finite automaton
$(X',h)$. Suppose $A=\{0,...,m-1\}$ and define $A'=\{0,...,m\}$,
$Q'=\{(q,i): q \in Q, i\in \{-1,0,1,\sharp\}\}$, $B'=B$. For $x
\in Q'$ denote $\lfloor x \rfloor$ its first component, and
$\lceil x \rceil$ the second, so that $x=(\lfloor x
\rfloor,\lceil x \rceil)$. Define
\ \begin{array}{ll}
X_{-\infty} & = \{u \in X':\; \lceil u_{0} \rceil=-1,
(\forall j >0)(u_{j}=m) \}, \\
X_{k} & = \{u \in X':\; \lceil u_{0} \rceil = \mbox{sgn}(k),
\min\{j > 0:u_{j} \neq m\} = :k: \},\;\; :k: > 0 \\
X_{\infty} & = \{u \in X':\; \lceil u_{0} \rceil=1, (\forall j
>0)(u_{j}=m) \} \\
X_{i} & = \{u \in X':\; \lceil u_{0} \rceil = i \} \;\;
\mbox{ for }\;\; i \in \{0,\sharp\} \end{array} \!
Define $h_{B} : Q' \rightarrow B'$, $h_{A}: Q' \times A'
\rightarrow Q'$ by $h_{B}(x) = f_{B}(\lfloor x \rfloor)$, \
\begin{array}{lll}
h_{A}(x,m) & = (\lfloor x \rfloor, -1) & \mbox{ if } \;
\lceil x \rceil \in \{-1,1\} \\
h_{A}(x,j) & = (\lfloor x \rfloor, 0) & \mbox{ if } \;
\lceil x \rceil \in \{-1,1,\sharp\},\; j<m \\
h_{A}(x,j) & = (f_{A}(\lfloor x \rfloor,j), \sharp) & \mbox{ if }
\; \lceil x \rceil = 0,\; j<m \\
h_{A}(x,m) & = h_{A}(x, m-1) & \mbox{ if }
\; \lceil x \rceil \in \{0,\sharp\} \end{array} \!
Then $h(X_{-k}) = h(X_{k}) = X_{-k+1}$, $h(X_{0}) \subseteq
X_{\sharp}$, $h(X_{\sharp}) = X_{0}$. Denote
$X''=\{u \in X': (\forall k>0)(u_{k}=m \Rightarrow \lceil u_{0}
\rceil \in \{0,\sharp\} \;\; \&\;\; (\forall 0<j<k)(u_{j}=m ))
\}$. Thus $m$'s are allowed only at the beginning of the input
tape and only if $\lceil u_{0} \rceil \in \{-1,1\}$. $X''$ is a
closed and invariant set, and there is a factorization
$\chi:(X',h) \rightarrow (X'',h)$ defined by \\
$\chi(u)_{k} = m-1 \mbox{ if } k>0, \; u_{k}=m, \mbox{ and }
\lceil u_{0} \rceil \in \{0,\sharp\} \mbox{ or } (\exists
0<j<k)(u_{j}<m)$ \\
$\chi(u)_{k} = u_{k} $ otherwise.
We construct a projection $\psi: (X'',h) \rightarrow (I,g)$. Let
$g_{0}:-1,g(0)! \rightarrow -1,0!$, $g_{1}:-1,g(0)!
\rightarrow 0,1!$ be the two inverse functions for $g$. Then
define by induction
\ \begin{array}{lll}
\psi(u) = \varphi(...u_{-4}u_{-2}\lfloor u_{0} \rfloor
u_{1}u_{3}...) & \mbox{ if } & \lceil u_{0} \rceil =0 \\
\psi(u) = g_{0}^{k} \psi h^{k}(u) & \mbox{ if } & \lceil u_{0}
\rceil = -1 \mbox{ and } \lceil h^{k}(u)_{0} \rceil = 0 \\
\psi(u) = g_{1} \psi h(u) & \mbox{ if } & \lceil u_{0}
\rceil \in \{1,\sharp\}\\
\psi(u) = -1 & \mbox{ if } & u \in X_{-\infty}\\
\psi(u) = 1 & \mbox{ if } & u \in X_{\infty} \end{array} \!
Then clearly $\psi h(u) = g \psi(u)$ whenever $\lceil u_{0}
\rceil \neq 0$. For $\lceil u_{0} \rceil = 0$ observe that both
$\psi h(u)$ and $g \psi(u)$ belong to $p,1!$. Since $g$ is
decreasing on $p,1!$ it suffices to show $g \psi h(u) = g^{2}
\psi(u)$. Since $\lceil h(u)_{0} \rceil \neq 0$, we have $g \psi
h(u)$ = $\psi h^{2}(u)$ =\\
$\psi h (... u_{-2},u_{-1},f_{B}(\lfloor u_{0} \rfloor),
(f_{A}(\lfloor u_{0} \rfloor,u_{1}),\sharp),u_{2},u_{3}, ...)$
=\\ $\psi (... u_{-2},u_{-1},f_{B}(\lfloor u_{0} \rfloor),
f_{B}f_{A}(\lfloor u_{0} \rfloor,u_{1}),
(f_{A}(\lfloor u_{0} \rfloor,u_{1}),0), u_{3},u_{4} ...)$ =\\
$\varphi(... u_{-4},u_{-2},f_{B}(\lfloor u_{0} \rfloor),
f_{A}(\lfloor u_{0} \rfloor, u_{1}),u_{3},u_{5} ...)$ =\\
$\varphi f (...u_{-4}u_{-2} \lfloor u_{0} \rfloor u_{1}u_{3}...)$
= $g^{2} \varphi (...u_{-4}u_{-2} \lfloor u_{0} \rfloor
u_{1}u_{3}...)$ = $g^{2} \psi (u)$. $\Box$ \mez
\begin{lem} \label{increase}
Let $g : I \rightarrow I$ be an increasing continuous function
such that $g(x) > x$ iff $x \in (-1,1)$. Then $(I,g)$ is a factor
of a finite automaton.
\end{lem}
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\put(78,0){$\underline{0}1$} \put(92,3){\vector(1,0){35}}
\put(137,0){$0\underline{1}$} \put(152,3){\vector(1,0){40}}
\put(196,0){$01\underline{1}$} \put(222,3){. . .}
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\put(65,15){ \begin{picture}(250,25)
\put(3,12){$\varphi$} \put(15,25){\vector(0,-1){23}}
\put(68,12){$\varphi$} \put(80,25){\vector(0,-1){23}}
\put(153,12){$\varphi$} \put(145,25){\vector(0,-1){23}}
\put(218,12){$\varphi$} \put(210,25){\vector(0,-1){23}}
\end{picture} }
\put(65,5){ \begin{picture}(250,10) \put(-15,3){. . .}
\put(10,0){$I_{-1}$} \put(40,7){$g$} \put(29,3){\vector(1,0){40}}
\put(75,0){$I_{0}$} \put(105,7){$g$}
\put(92,3){\vector(1,0){40}} \put(140,0){$I_{1}$}
\put(170,7){$g$} \put(157,3){\vector(1,0){40}}
\put(205,0){$I_{2}$} \put(222,3){. . .} \end{picture} }
\end{picture}
\noindent
Proof: For $k \in Z$ denote $I_{k}=g^{k}(0),g^{k+1}(0)!$ ($f$ is
a homeomorphism), $I_{-\infty} = \{-1\}$, $I_{\infty}=\{1\}$.
Define $A=Q=B=\{0,1\}$, $f_{B}(i)=i$, and $f_{A}(i,j) =
\max\{i,j\}$. We have closed sets
\ \begin{array}{lll}
X_{-\infty} & = \{u \in X: (\forall i \geq 0)(u_{i}=0) \}\\
X_{k} & = \{u \in X: \min\{i \geq 0: u_{i}=1\} = -k+1 \} , &
k \leq 0 \\
X_{k} & = \{u \in X: \max\{i \leq 0: u_{i}=0\} = -k \} , &
k > 0 \\
X_{\infty} & = \{u \in X: (\forall i \leq 0)(u_{i}=1) \}
\end{array} \!
For $k \in Z$ define a projection $\pi_{k}: X \rightarrow 2^{N}$
by $\pi_{k}(u)_{i} = 0$ if $0 \leq i < -k$, $\pi_{k}(u)_{i} =
u_{-k-i-1}$ if $i \geq \max\{0,-k\}$. (Thus $\pi_{-1}(u) =
(0,u_{-1},u_{-2}...)$, $\pi_{1}(u) = (u_{-2}u_{-3}...)$. It is
easy to see that $\pi_{k+1}f(u)=\pi_{k}(u)$ for $u \in X_{k}$.
Since $I_{0}$ is compact, there exists a factorization $\psi :
2^{N} \rightarrow I_{0}$. Define $\varphi(u) = g^{k} \psi
\pi_{k}(u)$ for $u \in X_{k}$, $\varphi(u)=-1$ for $u \in X_{-
\infty}$, and $\varphi(u) = 1$ for $u \in X_{\infty}$. Then
$\varphi: (X,f) \rightarrow (I,g)$ is a factorization. $\Box$
\begin{pro} \label{negative}
Let $(I,g)$ be a unimodal system with $g(0) \leq 0$. Then it is a
factor of a finite automaton.
\end{pro}
Proof: There is at most one fixed point in $(-1,0!$. If there is
none, we get the result by Theorem \ref{attractor}. Suppose there
is a fixed point $-1<p \leq 0$. Then $I_{0}=-1,p!$ and
$I_{1}=p,0!$ are invariant sets for $g$. $(I_{0},g)$ is a factor
of a finite automaton by Lemma \ref{increase}. $(I_{1},g)$ is a
factor of a finite automaton by Theorem \ref{attractor}. Their
sum is a factor of a finite automaton by Proposition \ref{sum}.
But $(-1,0!,g)$ is a factor of this sum, so
there is a factorization $\varphi : (X,f) \rightarrow
(-1,0!,g)$. Define an automaton $(X',f')$ by $A'=A$, $B'=B$,
$Q'=Q \times 2$, $f'_{A}(q,i)=(f_{A}(q),0)$, $f'_{B}(q,i) =
f_{B}(q)$. Define a factorization $\varphi':(X',f) \rightarrow
(I,g)$ by $\varphi'(u) = \varphi(...u_{-1},q,u_{1}...)$ if
$u_{0}=(q,0)$, $\varphi'(u) = g^{-1}_{1} \varphi f(u)$ if
$u_{0}=(q,1)$. $\Box$
\begin{thm}
Let $(I,g)$ be a symmetric unimodal system with a finite number
of periodic points. Then it is a factor of a finite automaton.
\end{thm}
Proof: If $g(0)>0$, then there exists ${\cal R}(g)$ and $I$ is
its invariant set (otherwise $g$ would have infinite number of
periodic points). If ${\cal R}g(0)>0$, we construct further
renormalizations. Since $g$ has only a finite number of periodic
points, there exists $k \geq 0$, with ${\cal R}^{k}g(0) \leq 0$.
By Proposition \ref{negative}, ${\cal R}^{k}g$ is a factor of a
finite automaton, and by Theorem \ref{renorm}, so is $g$. $\Box$
\begin{pro}
Let $(I,g)$ be a symmetric unimodal system with $g(0)=1$. Then
$g$ is a factor of a finite automaton.
\end{pro}
Proof: Define a closed cover $\alpha= \{-1,0!,0,1!\}$, and a
mapping $\varphi: 2^{N} \rightarrow I$ by
$\varphi(u) = x \in I$ iff $(\forall i \geq 0)(g^{i}(x) \in
\alpha_{i} \}$. It follows from the results in Collet and Eckmann
\cite{kn:Collet}, that $\varphi$ is a surjective mapping, and
$\varphi: (2^{N},\sigma) \rightarrow (I,g)$ is a factorization.
$\Box$
\begin{cor}
Let $(I,g)$ be a symmetric unimodal system at a band-merging
bifurcation, i.e. ${\cal R}^{k}g(0)=1$ for some $k$. Then it is a
factor of a finite automaton.
\end{cor}
\begin{exm}
A symmetric unimodal system at the common limit of period
doubling and band merging bifurcations has not chaotic limits.
\end{exm}
Proof: There exists an infinite closed invariant set $Y \subseteq
I$, which is topologically transitive but has no periodic point.
The set of periodic points $P \subseteq I$ is infinite too, and
its closure is $P \cup Y$. Moreover, for any finite $A \subseteq
P$ there exists $U \subseteq I$ with $Y \subseteq U$ and
$\omega(U) \cap A = 0$ (see Collet and Eckmann
\cite{kn:Collet} and Falconer \cite{kn:Fal} for more details).
Let $y \in Y$ and $y \in A \subseteq I$. If $\omega(A) \subseteq
Y$, then it has no periodic point. If $\omega(A) \cap P \neq 0$,
then $\omega(A)$ is not topologically transitive. In either case
$\omega(A)$ is not chaotic. $\Box$
\pagebreak
\begin{thebibliography}{99}
\bibitem{kn:Balcar} B.Balcar, P.Simon: Appendix on general
topology. Handbook of Boolean Algebras (J.D.Monk and R.Bonnet,
eds.), Elsevier Science Publishers B.V., (1989) 1241.
\bibitem{kn:Brooks} J.Brooks, G.Cairns, G.Davis, P.Stacey: On
Devaney's definition of chaos. The American Mathematical Monthly,
99,4 (1992) 332.
\bibitem{kn:Collet} P.Collet, J.P.Eckmann.: Iterated Maps on
the Interval as Dynamical Systems. Birkhauser, Basel (1980).
\bibitem{kn:Crutch} J.P.Crutchfield, K.Young: Computation at the
onset of chaos. in: Complexity, Entropy and the Physics of
Information, SFI Studies in the Sciences of Complexity, vol VIII
(W.H.Zurek, ed.), Addison Wesley (1990) 223.
\bibitem{kn:Devaney} R.L.Devaney: An Introduction to Chaotic
Dynamical Systems. Addison-Wesley, Redwood City (1989).
\bibitem{kn:Fal} K.J.Falconer: The Geometry of Fractal Sets.
Cambridge University Press, Cambridge (1985).
\bibitem{kn:Hop} J.E.Hopcroft, J.D.Ullmann: Introduction to
Automata Theory, Languages, and Computation. Addison-Wesley,
Menlo Park (1990).
\bibitem{kn:Langton} Ch.G.Langton: Life at the edge of chaos.
in: Artificial Life II. SFI Studies in the Sciences of
Complexity, vol. X (Ch.G.Langton, Ch.Taylor, J.D.Farmer,
S.Rasmunsen, eds.) Addison-Wesley, Redwood City (1992).
\bibitem{kn:Shub} M.Shub: Global Stability of Dynamical
Systems. Springer-Verlag, Berlin (1987).
\bibitem{kn:Troll} J.Troll: Formal language characterization
of transitions to chaos of truncated horseshoes. Technische
Universit\"{a}t Berlin, SFB 288, No 13, 1992.
\end{thebibliography}
\end{document}
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\begin{document}
\title{Microbial contamination of hands with or without the use of electric
toilet seats with water spray (bidets) after defecation}
\author[1]{Shigeharu Oie}%
\author[1]{Mai Suetomi}%
\affil[1]{Sanyo-Onoda City University}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
\textbf{Objective:} Electric toilet seats with water spray (bidets) are
gaining in popularity all over the world. However, the extent of
reduction in microbial contamination of hands with the use of bidets
after defecation is not known. \textbf{Methods:} The microbe
contamination of hands with and without the use of bidets after
defecation with the participation of 32 nursing students was studied.
Double gloves were worn on the dominant hand and four layers of toilet
paper were used to wipe the buttocks after defecation and the microbe
contamination of the second glove (outer glove) of the double gloves was
examined. The volunteers were free to select flow volume, wash time of
the bidet and even the type of bidet for use was left up the individual.
\textbf{Results:} Without the use of a bidet, the average value \selectlanguage{ngerman}±
standard deviation of the number of microbe attached to the gloves was
39,449.3 ± 77,768.3 colony forming units (cfu) / glove; however, it was
4,146.9 ± 11,427.7 cfu / glove when a bidet was used.The number of
microbe adhering to gloves was significantly reduced when a bidet was
used (p \textless{}0.0001, Wilcoxon singed-rank test).
\textbf{Conclusion: It was discovered that reduction of microbe
contamination of hands was possible with the use of bidets after
defecation.}%
\end{abstract}\selectlanguage{ngerman}%
\sloppy
\textbf{INTRODUCTION}
Electric toilet seats with water spray (bidets) were developed in Japan
and the use of bidets is spreading throughout the world. However, it has
not been made clear on whether the use of bidets has any effect on the
hygiene of hands. Studies on the effectiveness of bidets in the
prevention of microbial contamination of hand after defecation have been
done only with \emph{in vitro} experiments.\textsuperscript{1}Therefore,
this experiment examined the microbial contamination of the hands of 32
volunteers after defecation with and without the use of bidets.
\textbf{METHODS}
The number of microbe adhering to gloves after defecation of 32 nursing
students (17 males and 15 females) with and without the use of bidets
was examined. Double gloves (Plastic Glove No. 2500 Kyowa Ltd., Osaka,
Japan) were worn and the number of microbe adhering to the gloves after
wiping with four layers of toilet paper was examined. Four sheets of
toilet paper were used because a survey conducted by the Japan Sanitary
Equipment Industry Association with 1,748 subjects on the number of
sheets and the length of toilet paper for wiping revealed that 4 sheets
of toilet paper was the most frequently used
amount.\textsuperscript{2}The outer gloves of the double gloved hands
that held the toilet paper were peeled and placed into bottles
containing 200 mL of normal saline and were subjected to sonication at
36 kHz (Since Sonic 100, Ikemoto Scientific Technology Co., Ltd., Japan)
for 5 min. \textsuperscript{3,4}Each sample was diluted 10-fold,
100-fold and 1000-fold in sterile saline; four aliquots (0.25 mL each)
of each dilution and of an undiluted sample were plated on four
trypticase soy agar (TSA) . In addition, the remaining saline sample
(\emph{ca.} 200 mL) in the bottle was filtered through a 0.22micrometer membrane
filter (diameter, 5 cm; Nippon Thermo Scientific, Wilmington, NC, USA),
which was placed on TSA plates.\textsuperscript{4} These TSA were
cultured aerobically at 35 for 48 hr. In the case where the undiluted
inocula on TSA became less than 5 colony forming units (cfu), the cfu
with the membrane filtration technique on TSA were counted. This
experiment was conducted with the participation of volunteer nursing
students from the Ube Frontier University (Ube City, Yamaguchi
Prefecture). Therefore, permission was obtained from the Ube Frontier
University Ethics Review Committee (Title: Hands and finger
contamination after defecation - comparison of use with and without warm
water washing toilet seats (bidets) -, Approval date; November 8, 2017,
Examination certificate management number; 17007).
\textbf{RESULTS}
In the pre-experiment (5 subjects), when the cfu of microorganism
attached to gloves after defecation cultured aerobically with TSA and
anaerobically with GAM agar were compared, all five individuals had more
cfu with TSA. Therefore, in this experiment, anaerobic culture with GAM
agar was not performed, and only aerobic culture with TSA was performed.
Table 1 shows the number of microbe attached to gloves after defecation
with and without the use of bidets. The average \selectlanguage{ngerman}± standard deviation of
the colony forming units (cfu) attached to gloves after defecation
without using a bidet was 39,449.3 ± 77,768.3 / glove, however, it was
4,146.9 ± 11,427.7 / glove when a bidet was used. The amount of microbe
adhering to the glove after defecation was significantly reduced when a
bidet was used (\emph{p} \textless{} 0.0001, Wilcoxon singed-rank test)
(Table 1).
\textbf{DISCUSSION}
We have already reported the effectiveness of bidets with \emph{in
vitro} experiments. Namely, a model of the buttocks was smeared with
artificial diarrheal feces containing \emph{Serratia marcescens}, and
wiped by the participants wearing disposable gloves with 4 sheets of
toilet paper after the use and non-use of bidets. Subsequently, the
presence of \emph{S. marcescens} on the surface of the gloves was
quantified. After using the bidets, the mean count ± standard deviation
of \emph{S. marcescens} was 0.067 ± 0.249 cfu/ glove, and it was 4,275 ±
6,069 cfu/ glove when bidets was not used. The results obtained were
that the cfu of \emph{S. marcescens} was significantly lower when the
bidets were used (\emph{p} \textless{} 0.00001) prior to wiping the
artificial diarrheal feces. Although the effect of bidets in this
fieldwork was not as significant as that of the previous \emph{in
vitro}experiment, the effectiveness of bidets was confirmed as in the
previous\emph{in vitro} experiment. It is estimated that microbial
contamination from feces of hand after defecation has a major impact on
the spread of intestinal infections such as norovirus gastroenteritis,
\emph{Clostridioides difficile}related infections, and enterohemorrhagic
\emph{Escherichia coli}infections.\textsuperscript{5-10} For example,
outbreaks resulting from food handlers who are infected or subclinical
infected with the norovirus and does not sufficiently wash or disinfect
their hands after using the toilet, then handling
food.\textsuperscript{11-14}Accordingly, hand hygiene after defecation
is of course important,\textsuperscript{15} but it is also important to
prevent fecal contamination of the hand after defecation as much as
possible. In this experiment, the use of bidets was found to be
effective in reducing microbial contamination of fingers after
defecation. Although bidets were originally developed for medical use,
they are presumed to be also effective in the prevention of spreading
intestinal infections.
In conclusion, the use of electric toilet seats with water spray
(bidets) was an effective method in reducing faces adhering to hands at
the time of defecation.
\textbf{CONFLICT OF INTEREST}
The authors declare no conflict of interest.
\textbf{AUTHORS CONTRIBUTIONS}
SO developed the design of the study, participated in date collection,
planned and performed date analysis, drafted the article. MS
participated in the design of the study, participated in date collection
and analysis, critically revised the article.
\textbf{REFERENCES}
\begin{enumerate}
\tightlist
\item
Oie S, Aoshika H, Arita E, Kamiya A. The use of electric toilet seats
with water spray is efficacious in maintaining hand hygiene in
experimental model. \emph{Jpn J Infect Dis.} 2018;71(4):306-308.
\item
Japan Sanitary Equipment Industry Association. ``A present status
survey on the use of toilet paper.''
\textless{}http://www.sanitary-net.com.com/trend/research/toiletpaper2016.html\textgreater{},
accessed 8 November, 2017.
\item
Jeng DK, Lin LI, Hervey LV. Importance of ultrasonication conditions
in recovery of microbial contamination from material surfaces. \emph{F
Appl Bacteriol} . 1990;68(5): 479-484.
\item
Oie S, Huang Y, Kamiya A, Konishi H, Nakazawa T. Efficacy of
disinfectants against biofilm cells of
methicillin-resistant\emph{Staphylococcus aureus} . \emph{Microbios} .
1996;85(345):223-230.
\item
Lyman WH, Walsh JF, Kotch JB, Weber DJ, Gunn E, Vinjé J. Prospective
study of etiologic agents of acute gastroenteritis outbreaks in child
care centers. \emph{J Pediatr.} 2009;154(2):253-257.
\item
Wu HM, Fomek M, Schwab KJ, et al. A norovirus outbreak at a
long-term-care facility: the role of environmental surface
contamination. \emph{Infect Control Hosp Epidemiol.} 2005;26
(10):802-810.
\item
Worsley MA. Infection control and prevention of \emph{Clostridium
difficile} infection. \emph{J Antimicrob Chemother.} 1998;41(Suppl
C):59-66.
\item
Ekanem EE, DuPont HL, Pickering LK, Selwyn BJ, Hawkins CM.
Transmission dynamics of enteric bacteria in day-care centers.\emph{Am
J Epidemiol} . 1983;118 (4):562-572.
\item
Black RE, Dykes AC, Anderson KE, et al. Handwashing to prevent
diarrhea in day-care centers. \emph{Am J Epidemiol} . 1981;113
(4)\textbf{:} 445-451.
\item
Salama MF, Jamal WY, Mousa HA, Al-Abdulghani KA, Rotimi VO. The effect
of hand hygiene compliance on hospital-acquired infections in an ICU
setting in a Kuwaiti teaching hospital. \emph{J Infect Public Health}
. 2013;6 (1):27-34.
\item
U.S. Department of Health and Human Services CDC. ``Updated Norovirus
outbreak management and disease prevention guidelines.'' \emph{MMWR
Morb Mortal Wkly Rep.} 2011 March 4;60(3). \textless{}
https://www.cdc.gov/mmwr/pdf/rr/rr6003.pdf\textgreater{} , accessed 8
January, 2020.
\item
Mathijs E, Stals A, Baert L, et al. A review of known and hypothetical
transmission routes for noroviruses. \emph{Food Environ Virol} .
2012;4 (4):131-152.
\item
Hall AJ, Wikswo ME, Pringle K, Gould LH, Parashar UD. Division of
Viral Diseases, National Center for Immunization and Respiratory
Diseases (CDC). Vital signs: foodborne norovirus outbreaks - United
States, 2009-2012. \emph{MMWR Morb Mortal Wkly
Rep.}2014;63(22):491-495.
\item
Tsuchiya Y, Sahara A, Jinbo T, et al. A foodborne outbreak of
norovirus caused by bread. \emph{Jap J Food
Microbiol.}2015;32(3):153-158.
\item
Green LR, Selman CA, Radke V, et al. Food worker hand washing
practices: an observation study. \emph{J Food Prot} . 2006;69
(10):2417-2423.
\end{enumerate}
\textbf{Table 1. Contamination of hand after defecation with or without
the use of toilet seats with water spray (bidets)*}\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Experiment participant no. & Colony forming units (cfu)/glove & Colony
forming units (cfu)/glove & Sex\tabularnewline
\midrule
\endhead
& When bidet not used & When bidet used &\tabularnewline
1 & 4.1\selectlanguage{ngerman}×10\textsuperscript{5} & 5.4\selectlanguage{ngerman}×10\textsuperscript{4} &
Male\tabularnewline
2 & 1.7\selectlanguage{ngerman}×10\textsuperscript{5} & 664 & Male\tabularnewline
3 & 1.0\selectlanguage{ngerman}×10\textsuperscript{5} & 3.4\selectlanguage{ngerman}×10\textsuperscript{4} &
Male\tabularnewline
4 & 8.5\selectlanguage{ngerman}×10\textsuperscript{4} & 2.4\selectlanguage{ngerman}×10\textsuperscript{4} &
Male\tabularnewline
5 & 7.8\selectlanguage{ngerman}×10\textsuperscript{4} & 131 & Male\tabularnewline
6 & 7.2\selectlanguage{ngerman}×10\textsuperscript{4} & 115 & Female\tabularnewline
7 & 7.1\selectlanguage{ngerman}×10\textsuperscript{4} & 328 & Female\tabularnewline
8 & 5.6\selectlanguage{ngerman}×10\textsuperscript{4} & 38 & Female\tabularnewline
9 & 2.4\selectlanguage{ngerman}×10\textsuperscript{4} & 310 & Male\tabularnewline
10 & 2.4\selectlanguage{ngerman}×10\textsuperscript{4} & 720 & Male\tabularnewline
11 & 2.2\selectlanguage{ngerman}×10\textsuperscript{4} & 5 & Male\tabularnewline
12 & 2.1\selectlanguage{ngerman}×10\textsuperscript{4} & 7.2\selectlanguage{ngerman}×10\textsuperscript{3} &
Male\tabularnewline
13 & 1.8\selectlanguage{ngerman}×10\textsuperscript{4} & 352 & Female\tabularnewline
14 & 1.7\selectlanguage{ngerman}×10\textsuperscript{4} & 816 & Female\tabularnewline
15 & 1.7\selectlanguage{ngerman}×10\textsuperscript{4} & 4.8\selectlanguage{ngerman}×10\textsuperscript{3} &
Male\tabularnewline
16 & 1.5\selectlanguage{ngerman}×10\textsuperscript{4} & 1.0\selectlanguage{ngerman}×10\textsuperscript{3} &
Male\tabularnewline
17 & 1.4\selectlanguage{ngerman}×10\textsuperscript{4} & 420 & Male\tabularnewline
18 & 1.1\selectlanguage{ngerman}×10\textsuperscript{4} & 66 & Male\tabularnewline
19 & 1.0\selectlanguage{ngerman}×10\textsuperscript{4} & 134 & Male\tabularnewline
20 & 7.0\selectlanguage{ngerman}×10\textsuperscript{3} & 1.5\selectlanguage{ngerman}×10\textsuperscript{3} &
Female\tabularnewline
21 & 5.0\selectlanguage{ngerman}×10\textsuperscript{3} & 848 & Female\tabularnewline
22 & 4.0\selectlanguage{ngerman}×10\textsuperscript{3} & 172 & Female\tabularnewline
23 & 4.0\selectlanguage{ngerman}×10\textsuperscript{3} & 360 & Male\tabularnewline
24 & 2.0\selectlanguage{ngerman}×10\textsuperscript{3} & 38 & Male\tabularnewline
25 & 2.0\selectlanguage{ngerman}×10\textsuperscript{3} & 15 & Female\tabularnewline
26 & 2.0\selectlanguage{ngerman}×10\textsuperscript{3} & 63 & Male\tabularnewline
27 & 1.0\selectlanguage{ngerman}×10\textsuperscript{3} & 29 & Female\tabularnewline
28 & 1.0\selectlanguage{ngerman}×10\textsuperscript{3} & 265 & Female\tabularnewline
29 & 320 & 97 & Female\tabularnewline
30 & 244 & 18 & Female\tabularnewline
31 & 228 & 124 & Female\tabularnewline
32 & 184 & 75 & Female\tabularnewline
Mean \selectlanguage{ngerman}± standard deviation ** & 39,449.3 \selectlanguage{ngerman}± 77,768.3 & 4,146.9 \selectlanguage{ngerman}± 11,427.7
&\tabularnewline
\bottomrule
\end{longtable}
* Wiped with 4 layers of toilet paper.
** \emph{p} \textless{}0.0001 (Wilcoxon signed-rank test)
\selectlanguage{english}
\FloatBarrier
\end{document}
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\title{An Anarchist Response to “An Anarchist Response to Crime”}
\date{2011}
\author{Bob Black}
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According to “Scott,” the existing system of crime control is wrong, and contrary to anarchism, because it includes, among other evils, punishment, police, courts, and prisons. In contrast, his anarchist response to crime includes, among other improvements, punishment, police, courts, and prisons. After all, “Anarchists believe that the only true justice lies in personal freedom,” and what better ways to realize personal freedom than to restrict personal freedom by punishment, police, courts, and prisons?
“In society, there are only two ways to maintain peace: Cooperation and Coercion.” (Not so, but let that pass.) You might think that Scott is about to say that anarchist societies maintain peace through cooperation, whereas state societies maintain peace through coercion — but you would be wrong. If Scott implies that state societies maintain peace only through coercion, he is obviously wrong. People are mostly peaceful and mostly law-abiding in all societies, mostly for other reasons than coercion. Cooperation is even now the main source of social order, as anarchists such as Kropotkin and Malatesta observed. And you might think that Scott will argue that under anarchy, social order will be sustained by cooperation only — but you would again be wrong. But not as wrong as he is.
Scott is highly misleading when he makes statements like this: “Historically, societies with disparities in wealth and prosperity have always relied on coercion to keep those who have been robbed from taking back what is rightfully theirs.” This seeming statement of fact is morally rigged, because it mixes up “is” and “ought.” Societies with disparities in wealth and prosperity (what is a disparity in “prosperity” if not a disparity in wealth?) have always relied upon coercion to enforce all laws — that is true by definition — not just those which prohibit expropriating the expropriators, if indeed there are any such laws. The law of theft, for instance, applies in principle to everyone, however unequally it is in fact enforced. It applies to theft from the poor (which is usually committed by the poor), and to some of the ways the rich swindle each other. It applies to acts which have nothing to do with the just distribution of wealth, such as murder, drug use, reckless driving, indecent exposure, and animal cruelty.
In discussing Scott’s essay, when I refer to existing law enforcement and legal procedures I am referring to the current United States legal system, except where I indicate that I am drawing on comparative historical and cross-cultural data.
\section{What is Crime?}
Scott has his private idiosyncratic idea of what crime “is,” which really refers to how he would rewrite rather than abolish the criminal code. In real life, a crime is an act prohibited by the state (or an omission of an act mandated by the state) where this act or omission is subject to punishment by the state after the offender is arrested by the police, prosecuted by a public prosecutor, and convicted after a court proceeding by a judge with or without a jury. All crimes are by definition crimes against the state, whether or not they may also, or may not, affect private interests. So defined, the “anarchist response to crime” is self-evident: to abolish crime by abolishing the state. Scott’s proposed anarchist penal code is therefore literally nonsense.
Crime should be left to the state, and left behind when the state is left behind. The question is what to do about undesirable behavior. Now what is bad behavior to some people is not bad behavior to others. Scott, however, has a universal formula for justice, in the grand tradition of anarchists like Plato: “everyone must be entitled to life, liberty, and the fruits of their [sic] labor and no one should be allowed to take these things away from anyone else. Crime is any action which would deprive someone of equal access to these things.” Deprive them of these things, or deprive them of “equal access to” these things? What does it mean to have “equal access to” life? Is Scott anti-abortion? Beyond that, this generality is as abstract, and as vacuous, as proclaiming inalienable rights to life, liberty and the pursuit of happiness. This is a political philosophy, not a code of conduct. As Scott phrases it, Herbert Spencer or Ayn Rand could agree with it, but they had different ideas about what counts as the fruits of one’s labor. Their ideas were better thought out than his.
Scott does go on to try to infuse a little content into these principles: “An Anarchist society recognizes only three types of crime: (1) Chauvinistic Crimes, (2) Economic Crimes, and (3) Violent Crimes.” A strange way to rank these categories! What on earth are Chauvinistic Crimes? “Chauvinistic Crimes are those actions that deprive us of freedom or the fruits of our labor because of social prejudices, religious dogma, or personal malice or animosity.” But acts which deprive us of these things are either Economic Crimes or Violent Crimes regardless why they are committed. Scott’s Chauvinist Crimes are another of his borrowings from the law of the state: they are “hate crimes.” But currently, hate itself, or even the expression of hatred, is not a crime: it is only what is called an aggravating circumstance, something which justifies a harsher punishment when it is the motivation for something otherwise a crime already. But according to Scott, in an anarchist society, there is no punishment!
There will be no punishment — however, “there will still be people who want to exploit and victimize others for their own personal satisfaction as well as some reactionaries who want to establish a new system [I thought that was the old system] of domination, exploitation, and social control. To deal with these criminal personalities a society must be able to segregate them from the general population so they cannot harm anyone.” Criminal personalities? Aside from psychopaths, whose numbers are negligible, criminals have the same kinds of personalities as everybody else, except that some of them are above average in impulsivity. To speak of criminal personalities is literally reactionary: it echoes the discredited criminology of a century ago. To attribute crime to individual psychological defects flatly contradicts Scott’s opinion that most crime has social sources. In general, the only thing special about criminals is that they have committed crimes. And even that doesn’t make them special, because everyone has committed crimes. “Reactionaries” are not mentally ill, they will merely be political dissidents — just as anarchists are now. Criminologists used to talk about “anarchist personalities,” as one type of criminal personalities. Are we to follow their example?
Scott is obviously oblivious to the self-contradictory, not to say Orwellian quality of his language — such as this:
“Too often the term justice has been abused to imply retribution, punishment, correction or other forms of coercion or social control. Anarchists believe that the only true justice lies in personal freedom. \dots{} our goal is to insure social peace by segregating those who threaten [society] rather than debating and imposing and imposing an arbitrary view of justice based upon the whims and ambitions of parliamentarians, bureaucrats, and autocratic juries.”
So, anarchists don’t believe in “social control,” but they believe in locking up troublemakers who threaten social peace. Pardon me, but if that isn’t social control, what is? The only true justice lies in personal freedom, Scott says, from which it logically follows that one good way to assure true justice is to eliminate the personal freedom of criminals.
\section{How is Social Peace Achieved?}
In state societies, social peace is achieved — not very well, however — by specialized law enforcers (called police) who arrest suspected criminals and take them before tribunals (called courts) which, sometimes in collaboration with ad hoc citizen bodies (called juries), may determine that the accused did something contrary to social peace (called a judgment or verdict of guilt of a crime). Scott will have none of that. In an anarchist society, specialized law enforcers (called popular militia) arrest suspected criminals and take them before tribunals (called popular tribunals) which may impose a “term of banishment” (or even, as he later indicates, imprisonment). Scott’s anarchist criminal justice system is only a simplified, and probably worse version of the existing criminal justice system, which has at least addressed many considerations of which Scott must be totally unaware.
“Historically,” Scott relates, “Anarchist societies have replaced professional military and police forces with a part time popular militia which looks out for the safety of the community and would take a person accused of a crime and their accuser before a popular tribunal where any dispute could be arbitrated and any criminal act could be adjudicated and rectified.” No “Anarchist societies” ever did any such thing. The only genuinely anarchist socially viable societies so far have been primitive band and tribal societies, and none of them, as far as the historical and ethnographic evidence reveals, ever had anything remotely resembling this system. Nor was any such system in effect in the territories briefly controlled by anarchists in parts of Russia and Spain during their respective revolutions. What Scott describes is much closer — actually, it is very close — to the Cuban popular tribunals under Castro, which are agencies for the imposition of the Communist dictatorship. So much for the appeal to history.
All Scott has done is change the names of the law-enforcing institutions. Put “popular” in front and presto! a coercive institution is an anarchist institution. There is nothing anarchist about replacing full-time cops with part-time cops. Scott’s militias, he tells us, “work much like a neighborhood watch except they serve the community rather than being an instrument of police control and manipulation over [sic] the community.” Scott knows nothing about “neighborhood watch” except that he likes the feel-good sound of the phrase. Neighborhood watch refers to neighbors who have agreed to keep an eye on each other’s houses and report anything suspicious to the police. The participants don’t patrol the streets, much less arrest people. They aren’t an alternative to the police, they are adjuncts of the police. They are the eyes and ears of the police. They expand the scope of state control.
“Anarchist societies,” even if they are face-to-face communities, obviously are not organized so as to be directly capable of arresting suspects. The militia does that, in their name, and takes suspects and their accusers before a popular tribunal. In current society, the police cannot make an arrest without probable cause to believe that the suspect committed a crime, and their determinations are immediately reviewed by a judge. There is nothing like that in Scott’s scheme. As in a police state, the militia’s discretion is absolute. If Scott is to be taken at his word, all it takes is a denunciation to get someone arrested and sent before a “tribunal.” That was the system in Nazi Germany and the Stalinist U.S.S.R., although there the trial was often dispensed with. Individuals made extensive use of the opportunity to get rid of their enemies.
“Popular militias,” Scott relates, “are made up of volunteers from the community and are delegated their responsibility by the community who [sic] can revoke it at will.” In what way is the entire community institutionalized so as to undertake these functions? A general assembly? Is it going to pass upon the applications of each job applicant? Impractical and time-consuming: the assembly has too many other matters to decide. Or will it allow the militia to be self-appointed? There are some people who should never be allowed to be cops, and some of them will be the most eager to volunteer.
Among the other appalling features of this system is that every allegation of wrongdoing is either ignored by the militia or else processed as a possible crime, however trivial it may be. It implies the total criminalization of all deviance. This is not an anarchist utopia, it is a totalitarian nightmare. If my upstairs neighbor won’t stop playing his stereo so loudly, my only options are lumping it or calling the police. There is no provision for forms of alternate dispute resolution more suitable to minor problems between people, such as mediation and (non-binding) arbitration. These methods are in fact characteristic of stateless primitive societies, of which Scott is apparently ignorant.
When Scott speaks of his dispute resolution system indiscriminately as “arbitration” and “adjudication,” he betrays his ignorance of the difference. His system is, in fact, adjudication, involving an authoritative judgment by a third party not chosen by the disputants, coercively applying a general, pre-existing law. He likens his system to labor arbitration. If he knew anything about labor arbitration, he would keep quiet about such similarities, as most workers are highly dissatisfied with the results of labor arbitrations. But his system is not arbitration, not even binding arbitration, because it lacks critical features of arbitration, where (1) the parties choose the arbitrator, and (2) the parties choose the law to be applied (i.e., the collective bargaining agreement). Under Scott’s system, the decision-makers — “tribunals” — are already constituted, and they apply a generally applicable, pre-existing law (consisting of Chauvinistic Crimes, Economic Crimes, and Violent Crimes). (Scott makes heavy use of initial capital letters, as if to give his fancies some substantive reality.) This is no more anarchist than the status quo.
What Scott calls a tribunal is not what this word suggests, an individual or a panel which performs such functions as screening cases and presiding over the proceedings — in other words, judges. The judge is the only feature of the existing criminal justice system which Scott leaves out, but if you maintain everything else about the system but eliminate the judges, leaving them out makes for a system just as bad as the existing one, except that it is much worse. Somebody has to preside over the proceedings, and the person who does that is known as a judge. But who is he and how is he selected and just what are his powers? Scott has left a lot out of his anarchist response to crime, if that’s what it is.
The militia, as noted, is responsible for making arrests, “but, it is the tribunal that is responsible for questioning them as soon as they are apprehended. Tribunals are groups selected at random from members of the community by lottery. They function much like a jury in hearing evidence and making a decision based upon that evidence.” The questioning — the trial — commences immediately: nobody evaluates cases to determine if they are meritorious enough to go to trial. The tribunal doesn’t function “much like a jury.” The tribunal is a jury. In fact, it is more than a jury, it is judge and jury combined. Scott supposes that he is proposing something radically new when he says that juries are to be randomly selected from the community. Juries under the current system are already selected randomly from voter registration records, motor vehicle records, even public assistance (= welfare) records. The only difference between Scott’s jury and a real jury is that a real jury is subject to some control by the judge. Scott’s jurors are not, and so his reference to current “autocratic juries” is senseless, since real juries have far less autonomy than Scott’s juries. It was a jury like this which condemned Socrates to death.
Scott does say that ”If a person feels they [sic] have been treated unfairly they [sic] have the right to seek arbitration.” If this means what it says, there is a procedure of sorts for appeal, but, is this real arbitration? Where the parties choose an arbitrator? Why should the accuser, the winner, acquiesce in arbitration? If he doesn’t, this is appellate judicial review of a criminal conviction, just like what we have now, not arbitration. Can the arbitrator reverse the verdict of the jury? We are by now far removed from the realm of anarchist, popular justice in any plausibly imaginable form. Many disputes are now dealt with, not by invoking the criminal law, but by filing civil actions. “Anarchist societies,” however, “have no lawsuits \dots{}” Neither do totalitarian societies.
So far, Scott’s anarchist criminal justice system bears an uncanny resemblance to the current criminal justice system, except that, when it departs from it, it is more arbitrary and unfair. But the resemblance is even closer. There will be “forensic and detective collectives,” to undertake criminal investigations of unwitnessed crimes: “The type of crime that would fall under this heading would be murders, burglaries, and violent or economic crimes where the perpetrator or perpetrators concealed their identities.” A Detective Collective? I might think that Scott has written a parody of anarchism except that to do that he would have to have had a sense of humor.
When he encounters a problem with his criminal justice system, Scott’s solution is always to conjure up a “collective” to handle the matter. Scott is as ignorant of real-life police practices as he is of criminal law. His idea of forensic experts and detective work is a fantasy straight out of Sherlock Holmes and J. Edgar Hoover. Forensic evidence (almost always, this just has to do with matching fired bullets with guns, or testing to identify drugs) almost never solves crimes, be it street crimes or white-collar crimes, although it occasionally strengthens the case against a defendant whom there was already reason to prosecute. Detectives almost exclusively concern themselves with pumping their informants for information so as to set up arrests in victimless-crime cases, usually drug cases. There would be no detectives in an anarchist society.
“In a modern society, we must expect the need for forensic and detective collectives to investigate major crimes.” If so, that is one more argument against modern society. Who would be qualified to staff these collectives except former police detectives (who vastly outnumber private investigators, who are themselves usually ex-police) and police crime lab technicians? They would be counter-revolutionary hotbeds. Such people should not be imprisoned, as Scott advocates, but they should be put out of business for good, not empowered. An anarchist society could — and should — dispense with detectives, and could probably do without a forensic “collective” too. Such collectives, Scott tells us, “would serve several communities.” They are, then, specialized agencies detached from communities. The state is also a collective whose specialized agencies, detached from communities, attend to various particular purposes. And to their own.
Scott is ignorant of how real detectives operate. They don’t start with the crime, as in mystery stories, and trace it back to the criminal. Detectives start with the suspects and work forward to the crime. This often works well because most crime takes place among people who know each other. “The types of crime that would fall under this heading [unwitnessed crimes] would be murders, burglaries, and violent or economic crimes where the perpetrator or perpetrators conceal their identities.” Scott seems to assume that most crimes of these types are committed by strangers, and this is the popular view, but it is, to a surprising extent, wrong. Few homicides are committed by strangers. Few rapes are committed by strangers. A remarkably high proportion of what Scott would call Economic Crimes, such as burglary and robbery, are committed by relatives, neighbors and acquaintances of the victim.
To say that “anyone so predatory as to do such things must be quickly segregated from society to protect the community,” is savagely punitive in a way far beyond how the current system treats many of these cases. Here’s an example of a typical “burglary.” A loans his bicycle to his friend B. B fails to return it. A, losing patience, kicks in B’s door and retrieves his bicycle. B is at home and tries to stop A, but A pushes him aside. Legally, A has committed two major felonies: burglary and robbery. (It is legally irrelevant that A owns the bicycle, because larceny — robbery is larceny by force or intimidation — is a crime against possession, not title [ownership].) But realistically, what A has done might be called self-help repossession. Among people uncontaminated by law school, some would think that A was justified. Others would think that A had a legitimate grievance but went too far. Few people would think that A should be “quickly segregated,” and under the current system, he wouldn’t be. Once again the current system turns out to be more humane and reasonable than Scott’s.
“In an Anarchist society there is no punishment for crime, only social remedies [isn’t punishment for crime a social remedy?]. The only social remedy for an economic crime is 100\% restitution.” This is blatantly inadequate, because it means that you might as well steal: if you don’t get caught, you keep the goods, and if you do get caught, all you have to do is give them back. Laissez-faire libertarians similarly argue that whatever else might be inflicted in the way of punishment, there should be full restitution as far as possible. That is eminently just. The only problem is that it is usually impossible. Stolen money is spent, and stolen goods are consumed or fenced. The kinds of criminals that Scott is thinking of are almost always poor. That, after all, has something to do with why they commit Economic Crimes. If their assets are insufficient, “they may be asked [!] to do labor if this is not enough to correct for what they have damaged or stolen.” They won’t be “asked,” they will be told. Which means a return to involuntary servitude, the chain gang, temporary slavery, a punishment which the current system no longer employs. I daresay nobody before Scott ever thought that forced labor had a place in an anarchist society.
Now Scott claims that his version of anarchy, which is some sort of mutualism — a bastardized cross between socialism and capitalism — is so just and so egalitarian that there would be little incentive to commit Property Crimes, which he supposes would be committed only by kleptomaniacs, slackers and “idiots,” since why should anyone steal since there are well-paying jobs for everyone? He is apparently unaware that many embezzlers, swindlers and con-artists have, or could have, well-paying jobs. This is too funny for words, but even if he is right, the question remains, how to deal with the people who, from whatever motives and for whatever reasons, nonetheless steal or otherwise violate the sanctity of property. His essay is about how to deal with the antisocial residue of anarchist utopia, however big or small it may be. So is mine.
I pause at this point to take up the problem of Scott’s notion of “punishment.” He repeatedly states that in his anarchist society, there is no punishment, while he then goes on to endorse practices and institutions — including forced labor and prisons — which everybody recognizes to be punishments. Scott equates punishment with retribution. Although the word is sometimes used in that restrictive way, retribution is usually understood to be, not synonymous with punishment, but rather as one of the rationales for punishment. I am not sure that even punishment as retribution could have no place in an anarchist society, but in any event, retribution is only one of the generally recognized purposes of punishment.
There are three other major (and several minor) justifications for punishment. One is deterrence, which just means discouragement. Scott seems to assume that deterrence would be a justification for punishment, since he objects to capital punishment because it does not deter. There is specific deterrence and general deterrence. Specific deterrence punishes the offender in order to deter him from doing it again. It is the usual rationale for parents punishing their children. General deterrence means using punishment to make an example of the offender to discourage others from committing the same crime. Deterrence seems to play no role in Scott’s penology.
Another rationale is rehabilitation. The idea here is to change the criminal in such a way that he will commit no more crimes. Of all the rationales for punishment, this one is the most sinister, and the most discredited, because it is open-ended, not to mention that it is totally ineffective. Punishment as retribution or deterrence comes to an end, when the criminal has gotten his just deserts (retribution) or he has been punished just enough to discourage others from doing what he did (deterrence). But rehabilitation justifies indefinite incarceration, since nobody knows if a prisoner has been rehabilitated, and the authorities, playing it safe, prolong the prisoner’s incarceration (they will get bad publicity if, released, he commits more crimes). Often the prisoner, once released, is not so much rehabilitated as just being an old and broken man, not up for committing crimes because he is not up for anything. Scott explicitly rejects rehabilitation — one of the few points in which we are in agreement.
Which leads to the third rationale for punishment: incapacitation. Here the idea is to put the criminal in such a situation (usually, prison) that he is physically incapable of committing more crimes. Scott is enthusiastic about incapacitation, although he pretends, or is perhaps unaware, that what it justifies is punishment. He is big on “segregating” malefactors from the rest of us. He says that they are then in no position to victimize the general population, without noticing that they are in a position to victimize each other, which is very common in prisons (murder, theft, anal rape, etc.) Academic advocates of incapacitation espouse “selective incapacitation” — because we can’t lock up everybody — that is, the incapacitation of only those criminals who commit a highly disproportionate number of crimes. These criminologists know that most convicted criminals will never, as they say, recidivate, commit more crimes, but a small number of them will. Unfortunately, social scientists are unable to distinguish the criminals who will recidivate from the much larger number who will not. I think it is not unfair to say that Scott knows absolutely nothing about these matters. But not knowing anything doesn’t stop him from endorsing prisons. To the best of my knowledge, he is the first anarchist to do so. Let us hope he is the last.
\section{Do We Need Prisons?}
I would have thought that all anarchists would say “no.” For fifty years, radicals, including anarchists, have campaigned against prisons. Until now, nobody suspected that there could be prisons in an anarchist society. Anarchists such as Kropotkin and Berkman, based on personal experience, wrote some of the most eloquent critiques of imprisonment to be found. But Scott says they are indispensable. The “most violent elements of society” should be placed in “centers of incarceration” — his euphemism for prisons — for how long, he doesn’t specifically say, they must be committed to “the prison system,” “without any early release that might threaten the society.” However, we cannot allow these prisoners (Scott calls them “parasites,” a Stalinist slur) to sponge off the rest of us. It isn’t enough to lock them up: they must pay for their punishment and work off their debts to society.
The prison must be “fully self-sufficient.” This was indeed the goal (never quite realized) of the earliest prisons, in New York. Scott admits that this will not happen. Slave labor is known to be inefficient. The kind of people who end up in prison are the kind of people with few if any marketable skills. It should be obvious that prison bureaucrats would make their highest priority, getting the most possible work out of the prisoners, and keeping them from escaping, not reforming or rehabilitating them. Scott’s anarchist prisons would be the same. Except that they would be controlled by a Prison Guards Collective, a Screws’ Collective. What kind of people would volunteer to be prison guards? The only people who would want to be prison guards are the very people who should never be allowed to be prison guards. Most would probably be former prison guards — there will be a lot of them — as such people, who are generally of low intelligence, uneducated, and without marketable skills, are usually good for nothing else. No anarchist, except possibly Scott, would ever stoop to taking her turn as a prison guard. But apparently, for Scott, anything goes when it comes to organizing a collective. If you call it a collective, or call it “popular,” anything goes.
Remarkably, Scott goes on to say that “the most violent people in society” cannot be rehabilitated — I agree — and must be banished. Scott is troubled, however, by the fact that those who are banished will relocate to other communities and resume their predatory behavior. But since Scott posits that his anarchist society is also a modern society, we must suppose that the Internet will still be available for posting and disseminating information. Already the state maintains, for instance, registers of child molesters, including where they live, which anybody can access. An anarchist community which has been provoked so far as to expel somebody, and this should only happen in a very serious case, could, and should, post a warning, an all-points bulletin for all other communities. It will then be between the criminal and the community he wants to join, whether he will be allowed to join that community.
But there is another possibility. The incorrigible malefactor might be put to death. Scott objects to capital punishment because it does not, he supposes, deter crime. I am a lot more familiar with the social science research on capital punishment than Scott is, and as I read it, it does says that capital punishment is not a deterrent. But what this means is, not that capital punishment doesn’t deter murder (this is the only crime for which capital punishment is constitutionally permissible), it means that it doesn’t deter murder any more effectively than does the next most serious punishment, life imprisonment. I’ve studied this research and I find it convincing. But that is not the last word on the matter.
I am utterly opposed to capital punishment, inflicted by the state. I am not, however, opposed to killing intolerable people, as a last resort. Chronic troublemakers should be banished or, if they won’t go away and stay away, killed. Based on my extensive historical and ethnographic studies, which have especially focused on non-state band, tribal and chiefdom-type anarchist societies, I know that all of them — all of them — provide for capital punishment in some circumstances. But none of them maintain prisons. Capital punishment is compatible with anarchism, provided that the state does not inflict it. Prisons are incompatible with anarchism.
If an anarchist society was really put to the choice whether to imprison certain criminals (presumably for life), or, if for some reason it didn’t banish them, to execute them, I say execute them. Because an anarchist society is, I believe, the best possible form of society, though not a perfect one, and if we set one up, nobody should be allowed to wreck it. Capital punishment is regrettable, but it doesn’t compromise the anarchist nature of an anarchist society. Maintaining police and prisons doesn’t just compromise an anarchist society, it abolishes it as an anarchist society. That is a far too high a price to pay just to keep a few dirt-bags alive.
Scott’s anarchist prisons are so horrifying that to debunk him, he does not need to be criticized, merely quoted:
“The best disposition for those who are incarcerated is [for them] to be held separately for sleeping purposes and released for daily work periods. Those who do not choose to work should remain in isolation. Large areas of incarceration facilities should be devoted to food production for use at the facility. Hard work at the facility makes the time pass more quickly and uses up a person’s energy so there is less violence between those who are incarcerated. Those who endanger the lives of other people in the prison should not be allowed on work details. We cannot expect incarceration facilities to be self-sustaining. [He’s right about that.] They will be a liability the community will just have to accept as part of the price of their freedom.”
Except that the community should not accept that “liability,” if it wants to remain an anarchist community. The very idea of taking a turn at being a prison guard is nauseating to any real anarchist. The idea of a Screws’ Collective to do the community’s dirty work is even more disgusting, and it institutionalizes a danger to anarchism. Scott’s suggestion that, as anarchism gets established, the need for prisons will eventually wither away, is about as convincing as the Marxist-Leninist idea that, as socialism gets established, the state will eventually wither away. We know how that turned out. The state will never wither away. It must be smashed.
\section{A Different Orientation}
I’ve criticized Scott on many particular points. Until I read his essay, I would never have thought it possible for any self-styled anarchist to advocate a system of police, kangaroo courts, plus prisons with forced labor. I would have taken that to be a bad joke. And it is bad, but, it isn’t a joke. I have taken it upon myself to smack it down. It so happens that I have some relevant credentials and education in subjects such as criminal law and criminology (the sociology of law). But any well-informed anarchist who understands what anarchism means, as Scott doesn’t, would have come up with most of my criticisms.
The reason why Scott (who is obviously an excitable, college-type twentysomething leftist middle-class white boy) has got his anarchist response to crime totally wrong, is that he has started out by asking the wrong question. The real question has nothing to do with crime and punishment. Those are statist issues, not anarchist issues. Anarchism is about how people could live together as harmoniously as possible. An anarchist society is not concerned with crime and punishment. An anarchist society is concerned with conflict and dispute resolution.
This is not the place for me to reiterate what I’ve written and published about dispute resolution, and how certain of the several forms of dispute resolution might find a place in an anarchist society. The reader is welcome to look them up online, or write to me for them at [email protected]. Although Scott tosses around words like “arbitration,” he doesn’t know what they mean. But I do.
The “anarchist response to crime” is not to bother with crime, which, by definition, anarchy abolishes, but rather to resolve problems between people, or at least, to provide means for their resolution, such as mediation and arbitration, or if all else fails, banishment or execution. The possibilities of such methods should be exhausted before resorting to Scott’s cops, courts and prisons. The only difference between Scott’s criminal justice system and the existing criminal justice system is that his is a lot worse. The English and American common law judges have been pondering for almost a thousand years issues which have not even occurred to Scott. Their worst critic — and that would be me — would have to acknowledge, as I do, that there is some wisdom in what they have come up with.
Surely a statement like this (the italics are mine) is nothing if not repugnant: “We must accept that it may take a few generations of experience in the new society \emph{and a lot of incarcerations} before society at large is purged of the bad influences of capitalism, authoritarianism, and chauvinism.” Or, I would add: purged of the bad influences of leftism, cultural studies (feminist, black, queer, etc.) and moralism. The Marxists promised us that after a few generations (they were vague about the timetable) the state would wither away. They never delivered on their promise. Scott promises that it will only take “a few generations” for anarcho-cops, anarcho-courts and anarcho-prisons to wither away. If these really persist for, say, a hundred years or more, they will never wither away, they will have to be destroyed by an anarchist revolution against a police state that calls itself anarchist. I would rather they never get set up in the first place.
\section{\textbf{Appendix}: The Anarchist Response to Crime}
\begin{flushright}
Scott of the Insurgency Culture Collective
\end{flushright}
\begin{quote}
In \emph{The Descent of Man}, [Charles Darwin] gave some powerful pages to illustrate its proper, wide sense. He pointed out how, in numberless animal societies, the struggle between separate individuals for the means of existence disappears, how struggle is replaced by co-operation, and how that substitution results in the development of intellectual and moral faculties which secure to the species the best conditions for survival. He intimated that in such cases the fittest are not the physically strongest, nor the cunningest, but those who learn to combine so as to mutually support each other, strong and weak alike, for the welfare of the community. “Those communities”, he wrote, “which included the greatest number of the most sympathetic members would flourish best, and rear the greatest number of offspring” (2\textsuperscript{nd} edit., p. 163).
— Peter Kropotkin, \emph{Mutual Aid: A Factor In Evolution}, 1902.
\end{quote}
\textbf{Mutual Aid:} The idea that the evolution of Humanity as a sentient species and the emergence of Human Civilization were the result of solidarity for the needs of our fellow community members, cooperation and mutual support to overcome our mutual obstacles, defend against our mutual adversaries and create a society in which all who cooperate will mutually benefit. Mutual Aid is the basis of the village community, the labor syndicate (Union), cooperative and collective businesses, mutualist credit unions, mutual insurance and various mutual aid societies where people volunteer to help others.
In society, there are only two ways to maintain peace: Cooperation and Coercion. Authoritarian societies and societies which advocate a Social Contract (Constitutional Government) believe that people should give up part of their freedom and submit to the whim and violence of Police, Military and Government Spy and Covert Operations in order to feel safe. Societies which practice Mutual Aid believe that people in a community cooperate to insure that no person is victimized by another, that community standards of civility, mutual respect and mutual freedom are observed, and that persons who threaten the community must be opposed and are not welcome in the community. Historically, Mutual Aid has been the predominant means of maintaining Social Peace in every community and culture except those where one group tried to steal away more than their fair share of the resources of the community. The only way for them to get away with this is through violence, theft or fraud. Historically, cultures with disparities in wealth and prosperity have always relied on coercion to keep those who have been robbed from taking back what is rightfully theirs.
\subsection{What Is Crime?}
Anarchists believe that we are all born free, that no one can tell us what to do or how to think, and that we are always solely responsible for our own actions. For everyone to peacefully coexist in a free society and have an opportunity to get out of life what they put into it everyone must be entitled to life, liberty, and the fruits of their labor and no one should be allowed to take these things away from anyone else. Crime is any action which would deprive someone of equal access to these things. An Anarchist society recognizes only three types of crime: (1) Chauvinistic Crimes, (2) Economic Crimes, and (3) Violent Crimes. Chauvinistic Crimes are those actions that deprive us of freedom or the fruits of our labor because of social prejudices, religious dogma, or personal malice or animosity. Economic crimes are those that deprive us of the fruits of our labor by theft, fraud, or vandalism. Violent crimes are those that deprive us of our life, freedom, or the fruits of our labor through deadly force, physical abuse, or coercion.
Anarchists believe that most crime is a product of social deprivations, inequalities, and abuses inherent to Authoritarian, Capitalistic, and Chauvinistic socioeconomic systems. By doing away with these systems we can begin to do away with the problems they create. But, there will still be people who want to exploit and victimize others for their own personal satisfaction as well as some reactionaries who want to establish a new system of domination, exploitation, and social control. To deal with these criminal personalities a society must be able to segregate them from the general population so they cannot harm anyone.
Too often the term justice has been abused to imply retribution, punishment, correction or other forms of coercion or social control. Anarchists believe that the only true justice lies in personal freedom. In a free society the need is to protect the society from crime without obstructing freedom of choice. Anarchists are not interested in vengeance, only peace. Therefore, our goal is to insure social peace by segregating those who threaten it rather than debating and imposing an arbitrary view of justice based upon the whims and ambitions of parliamentarians, bureaucrats, and autocratic jurists.
\subsection{How Is Social Peace Achieved?}
Anarchists believe in cooperation rather than competition, direct democracy rather than authority, and mutual aid rather than policemen. These are the basis of the Anarchist system of social peace. Historically, Anarchist societies have replaced professional military and police forces with a part time popular militia which looks out for the safety of the community and would take a person accused of a crime and their accuser before a popular tribunal where any dispute could be arbitrated and any criminal act could be adjudicated and rectified. The militias work much like a neighborhood watch except they serve the community rather than being an instrument of police control and manipulation over the community. Popular tribunals work much like binding arbitration in a labor dispute. Popular militias are made up of volunteers from the community and are delegated their responsibility by the community who can revoke it at will. They are delegated the responsibility of bringing conflicting parties or accused persons and accusers before a tribunal but, it is the tribunal that is responsible for questioning them as soon as they are apprehended. Tribunals are groups selected at random from members of the community by lottery. They function much like a jury in hearing evidence and making a decision based on that evidence. No person should be convicted of a crime without evidence against them. Since the standards of the community are simple, the delegated responsibilities of tribunals are simple. It is simply their delegated responsibility to determine who did what to whom. The community at large decides the term of banishment for violent crimes based on their severity and threat to the community. If a person feels they have been treated unfairly they have the right to seek arbitration.
In a modern society we must expect the need for forensic and detective collectives to investigate major crimes. These would work with local militias whenever a crime was discovered but, not witnessed. The types of crime that would fall under this heading would be murders, burglaries, and violent or economic crimes where the perpetrator or perpetrators concealed their identities. Forensic and detective collectives would serve several communities. In an anarchist society, crimes requiring investigation would be rare, but must be pursued quickly because anyone so predatory as to do such things must be quickly segregated from society to protect the community.
Anarchist communities are protected by mutual aid rather than a police state. Since the safety of all people in the community is dependent on zero tolerance to violent predatory behavior, all members of the community cooperate to identify such incidents so the individuals involved can be dealt with. This value is instilled in all members of the community beginning when they can first begin to understand “getting along with each other” as young children and everyone is held accountable for their actions regardless of age. To discourage violence among the young, competition is discouraged in favor of personal progression and individuals are encouraged to specialize their learning in areas of personal interest after they master basic communication and arithmetic skills. Progress is based on demonstrating aptitude rather than the age of a student.
A community is a group of free individuals who cooperate to achieve a quality of life greater than what they could achieve separately. The community members have the right to protect their community and must take responsibility for doing so. They also have the responsibility of respecting each others freedom. This value must be instilled in children as they grow up. All members of the community must recognize that their participation in the community is subject to this value and that they will be held accountable by other community members if they violate this trust.
\subsection{How Is Crime Remedied?}
An Anarchist society has no victimless crime because all vices are legal and enjoyed only by those who chose to participate. There is no underground economy because there is no economic incentive for one. The commercial aspects of the current underground economy are legal so the violent aspects are either unnecessary or easily remedied by zero tolerance against violent crime and mutual aid. If people have a personal problem with compulsive behavior or a physical addiction, they can receive free counseling, peer support, or medical treatment to help them correct their problems. Persons who chose to provide vice services are free to do so without being exploited because there are no bosses, business managers, police, politicians, pimps, madams, gangsters, or any other authority coercing them out of their hard earned income. They enjoy the same protection in society as any other honest worker and have the same rights.
Anarchist societies have no lawsuits because social problems are dealt with by arbitration, real property is collectively owned and administered, and personal property is collectively insured. Real property includes the land and resources which are owned by the community, all factories, production facilities, and other work sites which are owned by those who work at each site, and all public infrastructure which may be owned by a single community or cooperatively owned by several communities who share its use. Personal property includes any possessions a person may accumulate in exchange for their labor. All housing is owned solely by the occupant since Anarchist societies have no landlords and housing production is financed by pooling personal incomes into mutual credit funds. All multifamily housing operates like a co-op where people own their own units and cooperate in the upkeep of the building. Since there are no landlords or bankers housing costs are based on the cost of production not profit and interest. Since inheritance is limited to personal property and everyone who wants to work can have a job, a person’s ability to pay for housing and other personal property is limited by the amount of work they do and there are no great disparities in the amount or value of personal property any person or household can amass in a lifetime. In an Anarchist society capitalism is abolished and the cartels which artificially inflate the value of gemstones, metals, artwork, etc. are abolished so things of beauty are possessed for the sake of beauty and truly rare artifacts are only affordable if many workers pool their resources for their mutual enjoyment or for the enjoyment of the community at large. This eliminates any incentive for tort lawsuits which are motivated by greed rather than need.
Anarchist societies have little chauvinism because most chauvinism is a product of competition, superstition, and social control mechanisms which are discouraged by community cooperation, mutual aid, and free school education. Intolerance of chauvinistic ideas and behavior is not chauvinism; it is mutual aid.
Anarchist societies have little economic crime because no one is truly poor, no one is very rich. It is not economically possible for a single person to amass valuables or wealth worth the risk of larceny and it is unlikely that anything stolen could be sold for a significant amount or that anything valuable could be easily sold without the need for a group of people as prospective buyers. People have what they earn from their own labor and they only have to work as much as they want to. Without capitalism, any job would require less work to earn a living than stealing. Most of the remaining economic criminals would either be those who enjoy the act of taking from others more than the revenue, persons antagonistic to individuals or the community, and idiots with no common sense.
In an Anarchist society there is no punishment for crime, only social remedies. The only social remedy for an economic crime is 100\% restitution. This means that a person’s possessions which can be bartered are forfeit and they may be asked to do labor if this is not enough to correct for what they have damaged or stolen. It is not necessary for a person to be incarcerated to provide restitution or remedial labor. Incarceration of nonviolent criminals only creates violent criminals. Their alternative, if they chose, is banishment from the community until such time as they chose to provide full restitution. Anarchists believe in free association which means that you can associate with whomever you chose but, cannot be forced into an association against your will. Free association means that the community has the right to expel undesirable individuals who threaten the community or refuse to meet their personal responsibility to make amends for their criminal actions. In a modern society where the person cannot be released into other communities without putting them at risk, banishment must mean incarceration for a non-negotiable period of time dependent on the severity of their crime if full restitution is beyond their ability to pay through voluntary work. Again, this is unlikely since Anarchist societies do not produce large concentrations of wealth like stocks and bonds that are worth more than a person could possibly earn by honest labor.
Anarchist societies have little violent crime because there is no underground economy, poverty, or social injustice to breed violent behavior. Most conflicts are settled by arbitration and mediation without violence and rowdiness is moderated by mutual aid. People are able to channel their aggressive feelings into constructive activities like athletics if they chose. All that remains are crimes of passion and predatory behavior. No society can hope to prevent either one of these so we must be prepared to deal with these problems when they arise.
Since Anarchist societies provide free counseling, arbitration, and mediation, we must accept that most crimes of passion would result where a person refused to deal with a problem before it got out of hand. All persons must be held responsible for their actions regardless of their mental state if the safety of the society is to be maintained. Crimes of passion must therefore be treated like any other violent crime based on the severity of their criminal actions. The only appropriate social correction for violent crime is banishment because violence must be segregated from society in order for the people in the community to live peacefully. Economic criminals who reject the judgement of their society do not have the right to live in it and must be banished. Likewise, those who act violently against other members of society do not wish to live peacefully and cooperatively as a part of the society. They place themselves above the good of the community and do not have the right to live in it. As with economic crime, banishment must mean incarceration.
In an Anarchist society everyone has freedom of choice. Crime is therefore a choice. We do not dictate how each person should live, but we must recognize that an injury to one is an injury to all. There can be no tolerance of one of our community members being hurt by another person without the rest of us being threatened. Social peace is an essential element of an Anarchist society because the only function of violence and predatory behavior is to institute slavery, injustice, and exploitation. Those who do not respect the social peace should not be a part of the community. Without this assurance, no society of free individuals can exist. By creating a free society we reject the idea that we need to subject our behavior to an outside authority; that we need someone else to take care of us and to tell us what to do. We discard the coercion of the old police state and its illusion of order which leaves no one but the members of the community itself to assume responsibility for their own lives. If we fail in our responsibility to protect the social peace, people will be hurt and subjected to the coercive force of violence which is the foundation of all autocratic, fascist, and feudal tyranny. This understanding must be instilled in the youngest members of the community, enforced equally by all members of the community, and applied equally to all members of the community regardless of age, gender, ethnicity, sexual orientation, or lifestyle.
\subsection{Do We Need Prisons?}
Not long ago there was a time when being banished from a community meant expulsion to large expanses of land between frontier towns, feudal merchant centers, or city states. In those areas a person had to fend for themselves and they were at the mercy of any predator (human or animal) who came upon them until they could come into another community who would agree to accept them. These islands of sanctuary were all independent and many areas were beyond their influence. In a modern society with most of the world populated and communities mostly adjacent to each other there are no more frontiers to which a person can be banished where they will not still be in the same society. There are no city gates where a person would be instantly recognized as an undesirable and locked out. If we release a predator, we release them to prey on someone else. In an Anarchist society where violent crime will become increasingly rare, the number of violent criminals will be a lot less than it is now. Since we cannot banish them to a frontier, we must banish them to the only artificial frontier which exists: the prison system. Their limited numbers will actually enable the society to incarcerate all its violent criminals without any early release that might threaten the society.
Since banishment must mean incarceration in modern society, incarceration will necessarily concentrate the most violent elements of society and place a demand for resources on the community to feed, clothe, and shelter those who are banished. It would be as immoral for those banished to be parasites on the society as it is for capitalists and other economic criminals. It is therefore necessary that centers of incarceration fully compensate for the resources they consume and be fully self-sufficient whenever possible. This can best be accomplished by allowing those who are banished to have limited liberty within the prison in exchange for contributing useful labor to their prison community. It is not likely that the most violent people in society can be contained and organized to sustain themselves without some coercion and social control. We must therefore concede that those who reject the benefits of the Anarchist society and chose to live apart from it should not expect Anarchist benevolence when they are banished. Neither should they expect punishment or rehabilitation. Those who are banished must be denied visitation from the Anarchist society which they have rejected. For all practical purposes they are dead.
However, Anarchists do not believe in a death penalty for any crime. First, death is not a corrective measure. When a person is killed, it in no way changes the act of the violent criminal nor makes the people anymore safe than merely segregating the violent criminal. Therefore, the death penalty is merely a political act. Its sole function is to enable the government to legally murder someone as an example to a group of people it wishes to coerce for reasons beyond the interest of public safety. Second, death is not a deterrent. It is impossible to use the threat of violence to coerce a determined violent criminal into not committing an act of violence because violence is either spontaneous or premeditated. People who go to the trouble to plan crimes of violence do not believe they will be caught. Some people may feel that segregation of violent criminals is somehow inhumane but, only the most inhumane individuals will require segregation. This is especially true of the criminally insane who pose an even greater threat to the social peace than premeditated killers. Any prison system which remains must have a special facility for the criminally insane. All criminally insane violent criminals will have to be kept in isolation. Anarchists believe that a society with social justice and free mental health care will greatly reduce the number of mentally ill people, including those who are criminally insane.
The best disposition for those who are incarcerated is to be held separately for sleeping purposes and released for daily work periods. Those who do not chose to work should remain in isolation. Large areas of incarceration facilities should be devoted to food production for use at the facility. Hard work at the facility makes the time pass more quickly and uses up a person’s energy so there is less violence between those who are incarcerated. Those who endanger the lives of other people in the prison should not be allowed on work details. We cannot expect incarceration facilities to be self-sustaining. They will be a liability the community will just have to accept as part of the price of their freedom. In an Anarchist society the number of people who are banished and incarcerated would be only a fraction of those incarcerated under the legal, economic, and social system that now exists.
Anarchist societies do not come into being over night. We must accept that many of the bad people from the old capitalist, authoritarian, and chauvinistic society will still be around when an Anarchist society is still in the process of being organized. An Anarchist society must be prepared for many of these people to reject the new society and must set an example with them that the Anarchist society is both more fair and more uncompromising in dealing with issues of crime and social peace. We must be prepared to liberate all those who are now incarcerated for actions no longer treated as criminal and act without mercy in incarcerating all those who will not respect the social peace in the new Anarchist society. We must accept that it may take a few generations of experience in the new society and a lot of incarcerations before the society at large is purged of the bad influences of capitalism, authoritarianism, and chauvinism. It is the ultimate goal of an Anarchist society to do away with prisons altogether. We can begin by releasing all those unnecessarily incarcerated under the current system and closing those prisons where they were held. Afterwards, as society is transformed and prison populations dwindle we can systematically close and dismantle all the remaining prisons as the need to banish violent criminals is minimized.
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The Anarchist Library
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Anti-Copyright
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Bob Black
An Anarchist Response to “An Anarchist Response to Crime”
2011
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Response to “The Anarchist Response to Crime” by Scott of the Insurgency Culture Collective.
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Pesëdhjetë vjet pas ekzekutimit të emigrantëve italianë Sako dhe Vanzeti, Guvernatori i Masaçusetit, Dukaki, ngre një komision me qëllim që të kontrollohet paanësia e gjyqit të tyre, dhe rezultoi se që të dy nuk u gjykuan në mënyrë të drejtë. Lajmi shkaktoi në Boston një furtunë të vogël reagimesh\dots{}
Në 50-vjetorin e ekzekutimit, gazeta N.Y.Times përmendte se:«Plani i Kryetarit të Bashkisë, të shpallë të Martën e ardhshme dita e ‘’Sakos dhe Vanzetit’’, u anulua për mënjanimin e debatit, sipas zëdhënësit të Bashkisë». Duhet të ekzistojë një arsye e rëndësishme, përderisa një çështje 50-vjeçare, tashmë më tepër se 75-vjeçare , të shkaktojë ndjenja kaq të forta. Konsideroj se kjo ndodh ngaqë diskutimi rreth Sakos e Vanzetit , sjell në dritë, në mënyrë të pashmangshme, probleme që na shqetësojnë edhe sot: si sistemi i drejtësisë, lidhja ndërmjet gjakndezjes së një lufte dhe lirive politike, dhe veçanërisht idetë zjarrvënëse të anarkizmit, domethënë zhdukjen e kufijve shtetëror dhe si rrjedhim edhe të luftës, eliminimin e varfërisë, zhvillimin e demokracisë së plotë. Çështja e Sakos dhe Vanzetit nxori në shesh gënjeshtrën e parullave të mëdha, ku shkruhet “barazi para ligjit”, të cilat zbukurojnë sallat tona të gjyqeve. Ata dy njerëz, peshkatari i rëndomtë dhe këpucari, nuk u trajtuan në mënyrë të drejtë nga sistemi amerikan, pasi drejtësia nuk është e barabartë për të varfrit dhe të pasurit, për të huajt dhe për vendasit, për radikalët dhe për racionalët, për njerëzit me ngjyrë dhe për te bardhët. Dhe ka mundësi padrejtësia sot, të funksionojë më me modesti dhe në mënyrë më të komplikuar, në krahasim me kushtet që mbizotëronin për çështjen Sako e Vanzeti, por esenca vazhdon të mbetet po ajo. Në rastin e tyre padrejtësia ishte skandaloze. Presupozohet se dënoheshin për vjedhje dhe vrasje, por në mendjet e tyre, në sjelljen e prokurorit, të gjykatësit dhe të jurisë ishte e qartë se rol vendimtar luajti të qenit “makaronas”, emigrantë, punëtorë të varfër, radikalë.
Ja një fragment nga hetimi policor:
-Polici: Je qytetar iShBA?
-Sako:Jo
-Polici: Je komunist?
-Sako: Jo
-Polici: Anarkist?
-Sako: Jo
-Polici: Beson tek qeveria jonë?
- Sako: Po, por disa gjëra do ti doja ndryshe.
Ç’lidhje kishin këto pyetje me vjedhjen e një fabrike këpucësh në Breindrin e Jugut në Masaçuseti dhe me vrasjen e një brigadieri dhe të një roje? Natyrisht, Sako gënjente kur thoshte nuk jam komunist, anarkist. Përse thoshte gënjeshtra në polici? Për të njëjtën arsye që një Hebre thoshte gënjeshtra në Gestapo. Për të njëjtën arsye qe një njeri ngjyrë thoshte gënjeshtra në hetuesi në Afrikën e Jugut. Për të njëjtën arsye që një antiregjimist thoshte gënjeshtra në sigurimin e Bashkimit Sovjetik(E njëjta ndodhte dhe në sigurimin e shtetit në Shqipëri, tashmë të gjithë ne e dimë se si i merrte të famshmet deklaratat e rreme nga të akuzuarit, dhe se si i detyronin të pranonin një faj që nuk kishin kryer). Ata të gjithë e dinin se nuk kishte drejtësi për ta. Ka ekzistuar ndonjëherë drejtësia në sistemin amerikan për një të varfër, për një njeri me ngjyrë, për një radikal? Tetë anarkistë të Çikagos u dënuan me vdekje më 1886 pas trazirave në Heimarket (për të cilat përgjegjëse ishte policia), jo se kishte të dhëna që vërtetonin pjesëmarrjen e tyre në sulmet ndaj një rajoni policie, as edhe më të voglën. Por sepse ata ishin liderë të lëvizjes anarkiste në Çikago.
E. Debs dhe njëmijë të tjerë, mos vallë u burgosën gjatë Luftës së Parë Botërore në bazë të ligjit për agjitacion, sepse ishin agjentë? E pa mundur. Ata ishin socialistë që i kundërviheshin luftës. Gjatë legalizimit të dënimit të Debs me 10-vjet heqje lirie, gjykatësi i gjykatës së shkallës së lartë, Oliver Holms, bëri të qartë për ç’arsye duhej të dënohej Debs-i, duke përsëritur fjalët e të akuzuarit: “shtresa e lartë gjithmonë shpallte luftëra dhe shtresa e ulët gjithmonë jepte betejat’’\dots{}
Është e mundur sot, në frymën e luftës ‘’kundër terrorizmit’’, një Mysliman të trajtohet në mënyrë të drejtë dhe të barabartë nga ligji? Përse policia nxori zvarrë nga makina një komshiun tim brazilian, që ishte ezmer dhe ngjante me mysliman nga Lindja e Mesme, pavarësisht se nuk kishte shkelur ligjin, dhe e morën në hetim dhe e poshtëruan? Përse njerëzit me ngjyrë dhe varfanjakët përbëjnë në proporcion të zhdrejtë pjesën më të madhe të dy milionë të burgosurve në burgjet amerikane dhe të gjashtë milionë njerëzve që gjenden jashtë me kusht ose në arrest shtëpie? Një studim tregoi se 70\% e të burgosurve në burgjet e New York-ut vjen nga 7 lagjet e qytetit, lagje varfërie dhe dëshpërimi. Fatkeqësia e dallimeve klasore është prezente në çdo dekadë, në çdo shekull të historisë sonë.
Ndërkohë që çështja Sako dhe Vanzeti ishte në shqyrtim e sipër , një i pasur nga Milton-i , në jug të Boston-it, qëlloi dhe vrau një njeri që mblidhte dru brenda kufijve të tokave të tij. U mbajt 8 ditë në arrest dhe më pas lirua me garanci një shumë të hollash dhe nuk iu ngrit asnjë akuzë. Prokurori e quajti çështjen “vrasje me arsye”. Tjetër ligj për të pasurit dhe tjetër për të varfrit-karakteristikë kronike e sistemit tonë.
Por varfëria e Sako-s dhe Vanzeti-t nuk ishte krimi kryesor i tyre. Ata ishin , italianë, emigrantë, anarkistë. Më pak se 2 vjet kishin kaluar nga Lufta e Parë Botërore dhe ata kishin protestuar kundër luftës. Refuzuan të rekrutoheshin. U bënë dëshmitarë të histerisë kundrejt radikalëve dhe emigrantëve, të bastisjeve të shtëpive nga agjentët e prokurorisë së përgjithshme të ministrisë së drejtësisë, të mbajtjes në izolim të personave të ndryshëm dhe rrahjes së tyre me çomange.
Në Boston arrestuan 500 veta, i lidhën me zinxhirë dhe i ekspozonin nëpër rrugë. Luixhi Galeani-n, redaktor i gazetës anarkiste Cronaca Suvversiva\footnote{Pjesë nga libri i Howard Zinn: A Power Cannot Suppress( Një fuqi që Qeveritë nuk mund ta mposhtin), City Lights, 2006. Bën fjalë për një çështje gjyqësore që lidhet me një krim në Masacusheti(1920-1927). Pas vjedhjes së një fabrikë këpucësh dhe vrasjet e një brigadieri dhe të një roje, policia arrestoi emigrantët italianë, anarkistët Nicola Sacco (1891-1927) dhe Bartolomeo Vanzzeti (1888-1927). U gjykuan, u dënuan dhe u ekzekutuan në Boston më 1927.}, tek e cila ishin abonentë edhe Sako me Vanzeti-n e arrestuan dhe e ekstraduan menjëherë. Por ndodhi diçka edhe më e tmerrshme. Një anarkist ,punëtor shtypshkronje, i quajtur Andrea Salsedo, shok i Sako-s dhe Vanzeti-t, u rrëmbye në New York nga agjentë të FBI-së (përdor fjalën rrëmbim për të përshkruar arrestimin e pa ligjshëm te një personi) dhe u mbajt në zyrat e shërbimit në katin e 14-të të ndërtesës Park Row. Nuk e lejonin ti telefononte familjes , miqve, apo ndonjë avokati, e morën në hetim dhe e rrahën, sipas të thënave të njërit që u arrestua bashkë me të. Gjatë javës së 8-të të arrestimit, më 3 Maj 1920, trupi i Salsedo-s ,i transformuar, u gjet në trotuarin pranë ndërtesës Park Row dhe sipas FBI-së ai u vetëvra duke u hedhur nga dritarja e dhomës ku mbahej, në katin e 14-ë. Kjo ndodhi vetëm 2 ditë para arrestimit të Sako-s dhe Vanzeti-t.
Sot pas disa raporteve të Kongresit më 1975, jemi në dijeni të detajeve të planit Cointelpro\footnote{Croanca Sovversiva: Gazetë e pavarur, anarkiste amerikane që u themelua nga Luigi Galleani, 6 Qershor 1903. Botonte artikuj vetëm në italisht dhe arriti të kishte 5000 abonent.} që ushtronte FBI-a sipas të cilës agjentët e saj hynin në shtëpi dhe zyra, duke realizuar përgjime, përvetësime, ushtronin dhunë deri në vdekje dhe bashkëpunuan me policinë e Çikagos për vrasjen e dy liderëve të organizatës Black Panther\footnote{Counter Intelligence Program: Projekt antispiunazhi i FBI 1956-1971. Përfshinte udhëzime për të përgjuar Ku Kluks Klan, partinë komuniste, ekstremistët me ngjyrë,partinë socialiste punëtore, etj.} më 1969. FBI-a dhe CIA kanë shkelur ligjin shumë herë. Për ta nuk ka dënim veç. Nuk ka arsye të besojmë se liritë politike në këtë vend do jenë nën mbrojtje në këtë frymë histerike që u kultivua pas 9 Shtatorit dhe që vazhdon deri sot. Brenda kufijve u kryen arrestime në masë, paraburgime pa arsye, ekstradime, përgjime e gjëmime pa asnjë autorizim. Jashtë kufijve u kryen ekzekutime pa gjyq, tortura, bombardime, luftë dhe pushtim ushtarak.
Gjyqi i Sako-s dhe Vanzeti-t filloi menjëherë pas përvjetorit Memorial Day\footnote{Organizata Pantera e Zezë u krijua në Kaliforni më 1966. Në gjirin e saj kishte disa Afroamerikanë të majtë, mbështetës të luftës së armatosur. Por programi zyrtar i saj ishte më konservator jo revolucionar.}, një vit e gjysmë pas orgjive të vdekjes dhe patriotizmit të Luftës së Parë Botërore, dhe ndërsa gazetat dridheshin nga tamburet e luftës dhe të propagandës shoviniste. Në ditën e 12-të të gjyqit u përmend në shtyp se tre trupa ushtarësh u transportuan nga fushat e betejës të Francës në Brokton, dhe se i gjithë qyteti mori pjesë në ceremoni patriotike. Këto shkruheshin në gazeta, të cilat natyrisht që kishin mundësinë anëtarët e jurisë ti lexonin. Sako u mor në hetim nga prokurori Kaxhman.
–Pyetje: Ndjeve dashuri për këtë vend javën e fundit të Majit të vitit 1917?
-Sako: Kjo është e vështirtë ti përgjigjem me një fjalë, z. Kaxhman.
–Pyetje: ekzistojnë dy fjalë që mund të përdorësh, z.Sako, po ose jo. Kë do zgjedhësh?
-Sako: Po -Pyetje: Dhe për të treguar këtë dashuri për Shtetet Bashkuara të Amerikës, kur tu kërkua të rekrutohesh, ti ia mbathe në Meksikë?
Në ditët e para të gjyqit, gjykatësi Thier (i cili, duke biseduar në një shoqëri golfi, përmendi të akuzuarit duke i quajtur :”ata bastardët anarkistë”), i tha jurisë: “Zotërinj, ju kërkoj të ofroni shërbimet tuaja këtu me të njëjtën frymë patriotike, kurajë dhe besnikëri ndaj detyrës, ashtu si vepruan ushtarët tanë në luftë”.
Ndjenjat që zgjuan një bombë që shpërtheu në shtëpinë e Prokurorit të Përgjithshëm Palmer në kohën e luftës, si ato që lindën nga goditja e 9 shtatorit, krijuan një atmosferë të nderë në kuadër të së cilës u flijuan liritë politike. Sako dhe Vanzeti kishin kuptuar se çfarë do lloji argumenti juridik të përdornin avokatët e tyre, nuk do të mbizotëronin kundrejt realitetit të egër të drejtësisë klasore.
Sako, duke iu referuar vendimit të dënimit të tij, deklaroi para gjyqit: «E di se është pasojë e luftës klasore ndërmjet të shtypurve dhe pasanikëve\dots{}Kjo është arsyeja që ndodhem sot në bankën e të akuzuarit, sepse unë i përkas klasës së shtypur»
Një mendim i tillë duket dogmatik dhe i thjeshtëzuar. Nuk mund të shpjegosh në këtë mënyrë të gjitha vendimet e gjykatave. Por, përderisa nuk disponojmë një teori që të mbulojë të gjitha rastet, pozicionimi i thjeshtë por i pa tundur e i argumentuar i Sako-s na ndihmon më tepër të kuptojmë funksionimin e sistemit ligjor, në kundërshtim me mendimin që konsideron se një çështje gjyqësore është një përballje ndërmjet të barabartëve dhe bazohet në kërkimin e të vërtetës objektive.\footnote{Festë zyrtare në SHBA. U vendos më 1868. Fillimisht i ishte dedikuar kujtesës së ushtarëve që ranë në luftën civile amerikane, por më pas iu dedikua të gjithë ushtarëve të Amerikës që vriten në luftë.}
Vanzeti e dinte se argumentet juridikë nuk do ta shpëtonin. Nga momenti që miliona Amerikanë nuk organizoheshin, ai dhe shoku i tij, Sako, do të ekzekutoheshin. Jo me fjalë por betejë. Jo thjeshtë dëshirë por pretendime. Jo me lutje kundrejt Qeverisë por me uzurpime fabrikash. Jo me ryshfete, duke vaisur ingranazhet e një sistemi gjoja të drejtë , për të funksionuar më mirë, por grevë të përgjithshme, me qëllim që të ndalojë së funksionuari.
Kjo nuk ndodhi. Mijëra vetë demonstruan dhe protestuan, jo vetëm në Nju Jork, në Boston, në Çikago, në San Françisko por edhe në Londër, në Paris, në Buenos Ajros, në Afrikën e Jugut. Kjo nuk mjaftoi. Natën e ekzekutimit të Sako-s dhe Vanzeti-t, mijëra vetë demonstruan në Çarlstoun, por u mbajtën larg burgut nga forcat e shumta të rendit. Demonstrues u arrestuan. Mitrolozë u vendosën nëpër tarraca dhe projektorë të mëdhenj vrojtonin gjithë zonën.
Një turmë e madhe u mblodhën në Union Square, më 23 Gusht 1927. Pak minuta pas mesnate, dritat e burgut luhateshin, ndërsa të dy burrat ekzekutoheshin në karrigen elektrike. Gazeta New York World përshkroi këtë skenë si më poshtë: «Turma reagoi me një dënesë të thellë. Pesëmbëdhjetë me njëzet gra humbën ndjenjat. Të tjerë, të përdhosur, u ulën në trotuar dhe mbulonin kokat e tyre me duar. Burra që mbështetën kokën tek supet e njëri-tjetrit dhe qanë.»
Krimi i Sako-s dhe Vanzeti-t ishte anarkizmi i tyre, një filozofi që edhe sot na befason si rrufe me të vërtetën e saj esenciale: jemi një të gjithë, kufijtë nacionalë dhe urrejtja nacionale duhen zhdukur, lufta është e palejueshme, frytet e tokës duhet të ndahen dhe kjo botë mund të bëhet realitet vetëm me luftën e organizuar kundër pushtetit. Çështja e Sako-s dhe Vanzeti-t për ne sot nuk është thjesht një tragjedi, por edhe na frymëzon. Anglishtja e tyre nuk ishte e përkryer. Por kur flisnin, fjalët e tyre jehonin si poezi. Vanzeti rrëfen për shokun e tij, Sako:
«Sako është shpirt njeriu, pishtar, personalitet, është Njeri, një Njeri i dashuruar me natyrën dhe me njerëzimin. Një Njeri që flijoi çdo gjë në altarin e lirisë dhe të dashurisë për njerëzit: paratë, çlodhjen, ambiciet mondane, gruan dhe fëmijët e tij, veten, dhe jetën e tij\dots{}Natyrisht, mund të kem më tepër intelekt se ai, si thonë disa, të jem orator më i mirë,por shumë herë në të kaluarën, duke dëgjuar zërin e tij të ngrohtë të tingëllojë me ndershmëri madhështore, mendoja flijimin e tij madhor duke sjellë në mendje heroizmin e tij, ndjehesha i vogël, i vogël përball madhështisë së tij dhe inkurajoja veten time ti rezistonte lotëve, mundohesha të qetësoja zemrën time, që rrihte fort, që të mos qante para tij. Atë Njeri e quajtën kriminel dhe kryetar bande dhe e dënuan».
Më e keqja nga të gjitha , ata dy Njerëz ishin Anarkist, domethënë ishin të infektuar nga një ide e çmendur për demokraci të plotë, ku nuk do të kishte as ksenofobi as varfëri, dhe besonin se në mungesë të këtyre shkaqeve lufta ndërmjet kombeve do shfarosej.
Sako i shkroi djalit të tij, Dante-s: «Bir, në vend që të qash, të jesh i fortë, që të mbështesësh nënën tënde\dots{} dërgoje për një shëtitje në natyrën e qetë, mblidhni lule, çlodhuni nën hijen e pemëve\dots{} Por, mos harro, Dante, në këtë lojë lumturie mos mendo vetëm për veten tënde\dots{}ndihmo të persekutuarit dhe viktimat, sepse ata janë miqtë e tu më të mirë\dots{}Në këtë luftë për të jetuar do njohësh dashurinë e vërtetë dhe do dashurohesh».
Pa dyshim, anarkizmi dhe dashuria e tyre për njerëzimin i dënoi. Kur arrestuan Vanzeti-n kishte në xhep një trakt, që fliste për një takim që do bëhej për pesë ditë. Ky trakt shumë mirë mund të shpërndahej edhe sot, në të gjithë botën, është shumë aktual, ashtu si ditën e arrestimit të tyre. Në të thuhej:
\bigskip
Ke luftuar në çdo luftë. Ke punuar për çdo kapitalist. Je endur në të gjithë botën. Ke shijuar, veç, frytet e punës tënde dhe dobitë e fitoreve të tua? Je i kënaqur me thërrimet? Të buzëqesh e tashmja? Të premton e ardhmja diçka më të mirë? Ke gjetur një cep në këtë botë ku të jetosh e të vdesësh si njeri? Për këto pyetje, për këtë çështje, për luftën për jetën, do flasë Bartolomeo Vanzeti.
\bigskip
Ky takim nuk u realizua kurrë. Por, fryma e atyre njerëzve vazhdon të posedoj edhe sot të gjithë ata që besojnë dhe duan dhe luftojnë kudo në botë.
% begin final page
\clearpage
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\begin{center}
Biblioteka Anarkiste
\strut
\end{center}
\strut
\vfill
\begin{center}
Howard Zinn
Çështja e Sako dhe Vanzeti
\bigskip
http:\Slash{}\Slash{}utopi09.blogspot.gr\Slash{}2009\Slash{}05\Slash{}ceshtja-sako-dhe-vanzeti.html
\bigskip
\textbf{biblioteka-anarkiste.net}
\end{center}
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\end{document}
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\begin{document}
\title{\vskip-60pt Computer Science 271 \\
Software I: Utilities and Internals}
\author{Dr. Stephen Bloch \\
office 112 Alumn\ae\ Hall \\
phone 877-4483 \\
email {\tt [email protected]} \\
office hours 11--12 TTh, 1--4 W, or by appointment}
\maketitle
\section{Subject Matter}
This course will explain the basic concepts common to many computer
operating systems and introduce you to a great number of tools and
features provided by operating systems, especially Unix, which is
currently the most popular at academic and research institutions and
just coming into widespread use elsewhere.
The Unix operating system has more personality than most, not
because of how it works but because the people who built (and continue
to build) it left such a distinctive mark on it with their senses of
beauty, humor, and responsible behaviour. These have led to a system
which, once you've grasped its fundamental philosophy, allows you both
to make efficient use of your time and to have fun at it.
The creators of Unix used computers
all day, every day, and wanted to use them as efficiently as possible.
These people loved elegance and simplicity, and hated re-inventing the
wheel, so they built a number of simple tools that could be combined as
needed in billions of ways. They also loved whimsy, so you will find a
lot of puns and jokes built into the system. On the other hand, they
believed strongly in personal responsibility, so destructive pranks,
invasions of privacy, and insults are strongly discouraged --- usually
not by rules, but by peer pressure. Unix has evolved from a computer
system to a philosophy and finally to a community. I hope, among other
things, to make you productive and civilized members of that community.
A disadvantage of building the whole system out of simple tools is that
you need to learn a lot of simple tools before you can do anything. So
in the first half of the semester you'll read a lot of documentation and
try your skill on small examples. In the second half of the semester
the emphasis will shift somewhat from reading about Unix tools to
actually using them.
Many of the people in this class are taking CSC 270 concurrently.
You'll need to learn the same Unix tools and commands for both courses,
but whereas for 270 it will suffice to learn only their simplest, most basic
uses, in this class we'll discuss each tool and command in greater detail.
\pagebreak[3]
\section{Texts}
In the course of the semester I expect you to read most of the book
{\em A Student's Guide to Unix}, by Harley Hahn. This very engaging,
fun book discusses Unix philosophy and many common tools and commands.
It does not cover Unix internals and programmers'
tools, so I expect you to learn about those through online documentation
later in the semester. You can also learn a lot from the Net, and I may
give out other reading assignments by email or in magazines.
\section{Grading}
As I write this (a week before classes start), I envision five homework
assignments, each worth 10\% of the semester grade,
a midterm worth 20\%, and a final exam worth 30\%.
This may change slightly.
% These numeric grades will be converted to letter grades as follows:
% I'll draw a curve showing the distribution of numeric grades, and look
% for naturally-occurring ``clumps''. For each clump, especially the
% top and bottom ones, I'll examine some exam and
% homework papers to decide what letter grade seems appropriate. This
% method corrects for excessively hard or excessively easy assignments
% while not penalizing anybody for having genius classmates.
Exams must be taken at the scheduled time, unless arranged in advance
or prevented by a documented medical or family emergency. If you have
three or more exams scheduled on the same date, or
a religious holiday that conflicts with an exam or assignment due date,
please notify me in writing within the first two
weeks of the semester in order to receive due consideration.
% (and I'd
% prefer it if you let me know earlier --- you should know within the
% first week of class when all your exams are).
Exams not taken without one of
the above excuses will be recorded with a grade of 0.
Homework and programming
assignments will be accepted late, with a penalty of 1/3 per 24 hours
or portion thereof after they're due. An hour late is 33\% off, 25
hours late is 67\% off, and after 48 hours don't bother turning it in.
It's still a good idea to do as much of it as you can, however,
because I'll assume on the exams that you've done the homework.
\section{Ethics}
A proven case of cheating or plagiarism will result in a zero for the
assignment, an ``F'' for the course, or even dismissal from the
University, depending on the severity of the case.
All work on an exam must be entirely the work of the one
person whose name is at the top of the page.
For homework assignments, you are permitted (and encouraged) to
discuss how to solve the problem with me or with classmates, but each
student must write the detailed solution separately.
And yes, I can tell the difference between two students
``using the same approach'' and one student copying from another.
\section{Schedule}
This class meets every Tuesday and Thursday from 3:00 PM to
4:15 PM, except on University holidays or if I cancel class.
% \subsection{Floating Events}
All dates in the following schedule are tentative, except those fixed
by the University; if some topic listed here as taking one lecture in
fact takes two lectures to cover adequately, or {\em vice versa},
the schedule will shift slightly.
% In no case will an assignment be due earlier than indicated in the
% following schedule, but some may be due later; this will be announced
% in class a reasonable time in advance. I'll try to keep an updated
% version of this schedule available online.
You are expected to have read the specified chapters in the textbook
before the lecture that deals with that topic; this way I can
concentrate my time on answering questions and clarifying subtle or
difficult points in the textbook, rather than on reading the textbook
to you, which will bore both of us. {\bf Please read the textbook and
documentation!}
\medskip
\begin{tabbing}
{\bf Date(s) \hskip20pt} \=
{\bf Assignment} \=
{\bf Reading \hskip10pt} \=
{\bf Subject} \kill
{\bf Date(s)} \>
{\hskip-20pt \bf Assignment} \>
{\bf Reading} \>
{\hskip40pt \bf Lecture Subject} \\
%
%
30 Aug \> \> \> Administrivia, accounts, \& passwords \\
1 Sep \> HW1 \> 1--4 \> What is an operating system? What is Unix? \\
6 Sep \> \> \> Rosh Hashanah --- no class \\
8 Sep \> \> 6--9 \> Basic commands and online documentation \\
13 Sep \> \> 10,11 \> The Shell \\
15 Sep \> \> \> Yom Kippur --- no class \\
16 Sep \> \> \> Last day to add classes \\
20 Sep \> \> 12--14 \> Communicating with Human Beings \\
22 Sep \> HW1 due \> 19 \> Text editors ({\tt ex, vi, emacs, sed, awk}) \\
27--29 Sep \> HW2 \> 15--18 \> Filters, pipes, and combining programs \\
30 Sep \> \> \> Last day to drop classes or change to P/F option \\
4--6 Oct \> \> 20--22 \> The Unix file system \\
11 Oct \> \> \> The Shell-Program Interface \\
13 Oct \> HW2 due \> {\tt man} pages \> The {\tt stdio} library \\
18 Oct \> \> \> Midterm exam \\
20 Oct \> HW3 \> {\tt man} pages \> The {\tt dbx} debugger \\
25--27 Oct \> \> {\tt man} pages \> The {\tt make} compilation control
utility \\
1 Nov \> HW4 \> {\tt man} pages \> Process control: {\tt fork, exec, wait} \\
3 Nov \> \> {\tt man} pages \> low-level I/O \\
4 Nov \> \> \> Last day to withdraw from classes \\
8--10 Nov \> HW3 due \> {\tt man} pages \> The {\tt lex} scanner preprocessor \\
15--17 Nov \> HW5 \> {\tt man} pages \> The {\tt rcs} version control utility \\
22 Nov \> \> 23--24 \> The Net \\
24 Nov \> \> \> Thanksgiving --- no class \\
29 Nov \> HW4 due \> 24--25 \> The Net, continued \\
1--8 Dec \> \> {\tt man} pages \> pot luck --- \LaTeX ? \\
13 Dec \> HW5 due \> \> Review for Final Exam \\
20 Dec \> \> \> Final Exam 3:30--5:30
\end{tabbing}
\end{document}
Homework assignments
HW1: try things and show that you can do stuff
HW2: write a shell script using filters, I/O redirection, etc.
HW3: write a program using I/O & command-line arguments (say, "tr")
HW4: write a shell with built-in commands and searched-for commands.
HW5: extend that shell with pipes, detached processes, access to
environment variables. Extra credit: suggest and implement other nifty
features.
Things I want to cover eventually:
make
lex?
level 2 I/O
level 1 I/O
fork, exec, wait
ls
rm, cp, mv
cat, more
man, help, docs?
(yp)passwd
finger, who
mail, write, phone
trn
vi
ed, ex
shells, shell substitutions, aliases, filec, command files
chmod
compilers
sed, awk?
grep, egrep, fgrep
stdin, stdout, I/O redirection, pipes
file system
Un*x philosophy
search paths
T 30 Aug Administrivia, Un*x philosophy, file system,
cmds ls,rm,cp,mv,cat,more,man,help,(yp)passwd,finger,mail
Th 1 Sep stdin/stdout, I/O redirection, pipes, grep et al
T 6 Sep Rosh Hashanah -- no class
Th 8 Sep vi, ed, ex
T 13 Sep Shells, command files, shell substitutions, aliases, filec, chmod
Th 15 Sep Yom Kippur -- no class
F 16 Sep Last day to add
T 20 Sep trn? (if I have a class newsgroup)
Th 22 Sep
T 27 Sep
Th 29 Sep
F 30 Sep Last day to drop or change to P/F
T 4 Oct
Th 6 Oct
T 11 Oct
Th 13 Oct
T 18 Oct
Th 20 Oct
T 25 Oct Midterm exam?
Th 27 Oct
T 1 Nov
Th 3 Nov
F 4 Nov Last day to withdraw
T 8 Nov
Th 10 Nov
T 15 Nov
Th 17 Nov
T 22 Nov
Th 24 Nov Thanksgiving -- no class
T 29 Nov
Th 1 Dec
T 6 Dec
Th 8 Dec
T 13 Dec Thursday make-up classes
W 14 Dec--T 20 Dec final exams
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\[\mathop{{H^{{-}}_{{\ell}}}\/}\nolimits\!\left(\eta,\rho\right)=\frac{-ie^{{-%
\pi\eta}}\rho^{{\ell+1}}}{(2\ell+1)!\mathop{C_{{\ell}}\/}\nolimits\!\left(\eta%
\right)}\int_{0}^{\infty}\left(\frac{\mathop{\exp\/}\nolimits\!\left(-i(\rho%
\mathop{\tanh\/}\nolimits t-2\eta t)\right)}{(\mathop{\cosh\/}\nolimits t)^{{2%
\ell+2}}}+i(1+t^{2})^{\ell}\mathop{\exp\/}\nolimits\!\left(-\rho t+2\eta%
\mathop{\mathrm{arctan}\/}\nolimits t\right)\right)dt,\]
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%%
%% Der LaTeX-Begleiter, zweite Auflage (September 2005)
%%
%% Beispiel 12-2-9 von Seite 720.
%%
%% Copyright (C) 2005 Frank Mittelbach, Michel Goossens,
%% Johannes Braams, David Carlisle, and Chris Rowley
%%
%% Uebersetzung: Copyright (C) 2005 Claudia Krysztofiak,
%% Rebecca Stiels und Frank Mittelbach
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%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
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\pagestyle{empty}
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%% Für das Beispiel im Buch:
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\begin{document}
\citen{LGC97,LWC99,test97,vLeunen:92} aber
\cite[\S5]{Knuth-CT-a}
\end{document}
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http://dowobeha.github.io/papers/mclc08.slides.tex
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\documentclass{beamer}
\DeclareMathOperator*{\argmax}{arg\,max}
\usepackage{beamerthemesplit}
\usepackage{amsmath}
\usepackage{pstricks,pst-node,pst-tree}
\def\Pr{\mbox{\bf \sf P}}
\newcommand{\prob}[1]{{\bf \sf P}(#1)}
\newcommand{\empirprob}[1]{{\bf \sf \tilde P}(#1)}
\newcommand{\modelprob}[2]{{\bf \sf \hat P}_{#1}(#2)}
\newcommand{\condprob}[2]{{\bf \sf P}( #1 \,|\, #2 )}
\title{An Open-Source Hierarchical Phrase-Based Machine Translation System}
\author{Lane Schwartz \\ \texttt{[email protected]}}
\institute{University of Minnesota}
\date{}
\begin{document}
\frame{\titlepage}
\frame{\tableofcontents}
\section{Background}
\frame { \frametitle{Background}
Translation is one of the oldest problems in computer science. {\\ \ }
\pause
\begin{itemize}[<+->]
\item Rule-based translation
{\\ \ }
\uncover<+->{\\Requires highly trained bilingual linguists}
\uncover<+->{\\And lots and lots of time for them to develop rules}
\uncover<+->{\\Hard to extend to new domains}
{\\ \ }
\item Statistical translation \uncover<+->{$\leftarrow$ We'll use this approach :)}
\end{itemize}
}
\section{Statistical Methods}
\frame { \frametitle{Parallel Corpora}
Statistical translation requires large parallel texts.
\pause
\begin{itemize}[<+->]
\item Corporate documentation
\item International news organizations
\item Governments
\begin{itemize}
\item United Nations
\item Canada
\item European Union \uncover<+->{$\leftarrow$ We'll use this data :)}
\end{itemize}
\end{itemize}
}
\frame { \frametitle{Words}
\begin{itemize}[<+->]
\item Word-by-word translation
%{\\ \ }
\item Word alignments
\begin{itemize}
\item Align words by hand
\uncover<+->{\\tedious and time-consuming}
\item Automatic alignment
\uncover<+->{\\uses EM on a parallel corpus; \\see Och \& Ney (2000)}
\uncover<+->{\\Many researchers use the freely available GIZA++ tool to automatically extract word alignments}
\end{itemize}
%{\\ \ }
\item Word alignments can be used in more sophisticated translation models.
\end{itemize}
}
\frame { \frametitle{Phrases}
\begin{itemize}[<+->]
\item Phrases may work better than words
\item Phrase-based translation
\begin{itemize}
\item Phrase table
\item Reordering model
\end{itemize}
\item Phrases can be automatically extracted from word alignments.
\end{itemize}
}
\frame { \frametitle{Statistical Models}
\begin{itemize}[<+->]
\item Traditional noisy-channel approach \\[\baselineskip]
\uncover<+->{\[ \argmax_{e} \condprob{e}{f} = \argmax_{e} \prob{e,f} \]}
\uncover<+->{\[ \argmax_{e} \condprob{e}{f} = \argmax_{e} \prob{e} \times \condprob{f}{e} \] \\[\baselineskip]}
\item Log-linear approach \\[\baselineskip]
\uncover<+->{\[ weight = \prod_{i}{\phi_{i}^{\lambda_{i}}} \]}
\end{itemize}
}
\frame { \frametitle{Log-linear features}
So what features should our log-linear model use? \pause
\begin{itemize}
\item<2-> P$_{lm}(e)$
\item<2-> $\condprob{f}{e}$
\item<3-> $\condprob{e}{f}$
\item<3-> $\condprob{f_w}{e_w}$
\item<3-> $\condprob{e_w}{f_w}$
\end{itemize}
\uncover<2-> { Features used in noisy channel approach... \\ }
\uncover<3-> { ...and other features empirically found to be useful!}
%\uncover<2-> {
% $\alpha$ is a source language phrase. \\
% $\gamma$ is a target language phrase.
%}
}
\section{Hierarchical phrase-based translation}
\frame { \frametitle{Hierarchical phrase-based translation}
\begin{itemize}
\item<1-> Phrase-based translation
\begin{itemize}
\item Phrase table
\item Reordering model
\end{itemize}
\item<2-> What if we treat translation as a parsing task? \\
\uncover<3->{ $\rightarrow$ Phrase table becomes synchronous context free rules \\ }
\uncover<4->{ $\rightarrow$ Reordering model becomes implicit in rule applications }
\end{itemize}
}
\frame { \frametitle{Chiang (2007)}
Hierarchical phrase-based translation model \pause
\begin{itemize}[<+->]
\item Database of synchronous context-free rules
\item Only two nonterminals!!!
\begin{itemize}
\item X \uncover<+->{ Used in extracted grammar rules }
\item S \uncover<+->{ Allows for serial combination of phrases }
\end{itemize}
%\item<2-> What if we treat translation as a parsing task? \\
%\uncover<3->{ $\rightarrow$ Phrase table becomes synchronous context free rules \\ }
%\uncover<4->{ $\rightarrow$ Reordering model becomes implicit in rule applications }
\end{itemize}
}
\frame { \frametitle{Our System}
\begin{itemize}[<+->]
\item Open source implementation of Chiang (2007)
\item Implemented in Java
\item Designed to be easily extended
\item Data structures map onto the hypergraph architecture of Huang \& Chiang (2005)
\begin{itemize}
\item { This allows n-best lists to be easily obtained }
\item { N-best lists are needed during parameter tuning }
\end{itemize}
\item Uses off-the-shelf minimum error rate trainer\\
for log-linear parameter training
\end{itemize}
}
\frame { \frametitle{Our System}
What make this system unique? \pause
\begin{itemize}[<+->]
\item There are two other known implementations of a hierarchical phrase-based system
\item Of the other two...,
\begin{itemize}
\item { CMU SAMT - Open source, but doesn't implement cube pruning algorithm. C++ }
\item { Chiang's Hiero - Closed source, does implement cube pruning algorithm. Python }
\end{itemize}
\item Our system...
\begin{itemize}
\item { Open source}
\item { Implements cube pruning algorithm. }
\item { Java }
\end{itemize}
\end{itemize}
}
\frame { \frametitle{Our System}
Code available through anonymous svn at {\tt http://sf.net/projects/nlp-parsers} \\[\baselineskip]
Questions? \\[\baselineskip]
{\tt [email protected]}
}
\end{document}
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\[\mathop{M_{\frac{3}{4}+n,\frac{1}{4}}\/}\nolimits\!\left(z^{2}\right)=(-1)^{n}%
\frac{n!}{(2n+1)!}\frac{e^{-\frac{1}{2}z^{2}}\sqrt{z}}{2}\mathop{H_{2n+1}\/}%
\nolimits\!\left(z\right),\]
|
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%&LaTeX
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\begin{document}
\begin{thebibliography}{1}
\bibitem{Akhmediev_etal2016} Akhmediev, N., Kibler, B., Baronio, F., Belic, M., Zhong, W. P., Zhang, Y. Q., et al. (2016). Roadmap on optical rogue waves and extreme events. \textit{J. Opt.}, \textit{18}(6), 37 pp.
\end{thebibliography}
\end{document}
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\documentstyle[12pt]{article}
\pagestyle{empty}
\textwidth11cm
\textheight22cm
\parindent0cm
\parskip0.2cm plus0.1cm minus0.05cm
\begin{document}
\begin{center}
{\large \bf
%Please insert here the title of your contribution!
A Multigrid Algorithm for Immersed Interface Problems
}
\bigskip
%Please insert here the address(es) of the author(s)!
%\begin{center}
{\bf Prof. Loyce Adams}
%Collaborators:
Dept. Applied Mathematics
University of Washington
[email protected]
\end{center}
\bigskip
%Please insert here the abstract!
Many physical problems involve interior interfaces across which
the coefficients in the problem, the solution and or its derivatives,
the flux, or the source term has jumps. These interior interfaces may
or may not align with a underlying Cartesian grid. Zhilin Li, in his
dissertation, showed how to discretize such problems using only a
Cartesian grid and the known jump conditions to second order accuracy.
In this talk, we describe how to apply the multigrid algorithm in this
context. In particular, the restriction, interpolation, and coarse grid
problem will be described and numerical results will be given for several
groundwater flow problems.
\end{document}
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http://www.mat.univie.ac.at/~gerald/ftp/articles/StepScatJac2.tex
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%% @texfile{
%% filename="StepScatJac2.tex",
%% version="1.0",
%% date="Sept-2007",
%% cdate="20070812",
%% filetype="LaTeX2e",
%% journal="Zh. Mat. Fiz. Anal. Geom. 4-1, 33-62 (2008)",
%% url="http://jmage.ilt.kharkov.ua/abstract.php?uid=jm04-0033e",
%% copyright="Copyright (C) I.Egorova, J.Michor, and G.Teschl"
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\begin{document}
\title[Scattering Theory for Steplike Quasi-Periodic Background]{Scattering Theory for
Jacobi Operators with General Steplike Quasi-Periodic Background}
\author[I. Egorova]{Iryna Egorova}
\address{Institute for Low Temperature Physics\\ 47,Lenin ave\\ 61164 Kharkiv\\ Ukraine}
\email{\href{mailto:[email protected]}{[email protected]}}
\author[J. Michor]{Johanna Michor}
\address{Imperial College\\
180 Queen's Gate\\ London SW7 2BZ\\ and International Erwin Schr\"odinger
Institute for Mathematical Physics\\ Boltzmanngasse 9\\ 1090 Wien\\ Austria}
\email{\href{mailto:[email protected]}{[email protected]}}
\urladdr{\href{http://www.mat.univie.ac.at/~jmichor/}{http://www.mat.univie.ac.at/\string~jmichor/}}
\author[G. Teschl]{Gerald Teschl}
\address{Faculty of Mathematics\\ University of Vienna\\
Nordbergstrasse 15\\ 1090 Wien\\ Austria\\ and International Erwin Schr\"odinger
Institute for Mathematical Physics\\ Boltzmanngasse 9\\ 1090 Wien\\ Austria}
\email{\href{mailto:[email protected]}{[email protected]}}
\urladdr{\href{http://www.mat.univie.ac.at/~gerald/}{http://www.mat.univie.ac.at/\string~gerald/}}
\dedicatory{To Vladimir Aleksandrovich Marchenko and Leonid Andreevich Pastur,
our teachers and inspiring colleagues.}
\thanks{Zh. Mat. Fiz. Anal. Geom. {\bf 4-1}, 33--62 (2008).}
\thanks{Work supported by the Austrian Science Fund (FWF) under Grants No.\ Y330 and J2655.}
\keywords{Inverse scattering, Jacobi operators, quasi-periodic, steplike}
\subjclass[2000]{Primary 47B36, 81U40; Secondary 34L25, 39A11}
\begin{abstract}
We develop direct and inverse scattering theory for Jacobi operators
with steplike coefficients which are asymptotically close to
different finite-gap quasi-periodic coefficients on different sides.
We give a complete characterization of the scattering data, which
allow unique solvability of the inverse scattering problem in the
class of perturbations with finite first moment.
\end{abstract}
\maketitle
\section{Introduction}
In this paper we consider direct and inverse scattering theory for Jacobi operators with
steplike quasi-periodic finite-gap background, using the Marchenko \cite{mar} approach.
Scattering theory for Jacobi operators is a classical topic with a long tradition. Originally developed
on an informal level by Case in \cite{dinv4}, the first rigorous results for the case of a
constant background were given by Guseinov \cite{gu} with further extensions by
Teschl \cite{tivp}, \cite{tjac}. The case of periodic backgrounds was completely
solved in \cite{voyu} (who in fact handle almost periodic operators with a homogenous
Cantor type spectrum) respectively \cite{emtqps} using different approaches. Moreover,
the case of a steplike situation, where the coefficients are asymptotically close to
two different quasi-periodic finite-gap operators, was solved in \cite{emtstep} (see
also \cite{baeg}, \cite{eg}) under the restriction that the two background operators are isospectral.
It is the purpose of the present paper to remove this restriction.
We should also mention that scattering theory for Jacobi operators is directly
applicable to the investigation of the Toda lattice with initial data in the above mentioned classes. See
for example \cite{bdmek}, \cite{dkkz}, \cite{vdo} for steplike constant backgrounds,
and \cite{emtist}, \cite{emtsr}, \cite{kateptr}, \cite{katept}, and \cite{mtqptr} for periodic backgrounds.
For further possible applications and additional references we refer to the discussion in \cite{emtstep}.
Finally, let us give a brief overview of the remaining sections.
After recalling some necessary facts on algebro-geometric quasi-periodic finite-gap
operators in Section~\ref{secQP}, we construct the transformation operators and
investigate the properties of the scattering data in Section~\ref{secSD}. In Section~\ref{secGLM}
we derive the Gel'fand-Levitan-Marchenko equation and show that it uniquely determines
the operator. In addition, we formulate necessary conditions for the scattering data to uniquely
determine our Jacobi operator. Our final Section~\ref{secINV} shows that our necessary
conditions for the scattering data are also sufficient.
\section{Step-like finite-band backgrounds}
\label{secQP}
First we need to recall some facts on quasi-periodic finite-band Jacobi operators
which contain all periodic operators as a special case. We refer to
\cite[Chapter~9]{tjac} and \cite{emtqps} for details.
Let $H_q^\pm$ be two quasi-periodic finite-band Jacobi operators,\footnote{Everywhere in this
paper the sub or super index "$+$" (resp.\ "$-$") refers to the background on the right
(resp.\ left) half-axis.}
\be
H_q^\pm f(n) = a_q^\pm(n) f(n+1) + a_q^\pm(n-1) f(n-1) + b_q^\pm(n) f(n),
\quad f\in\ell^2(\Z),
\ee
associated with the Riemann surface of the square root
\begin{equation}\label{defP}
P_\pm(z)= -\prod_{j=0}^{2g_\pm+1} \sqrt{z-E_j^\pm}, \qquad
E_0^\pm < E_1^\pm < \cdots < E_{2g_\pm+1}^\pm,
\end{equation}
where $g_\pm\in \N$ and $\sqrt{.}$ is the standard root with branch
cut along $(-\infty,0)$. In fact, $H_q^\pm$ are uniquely determined by
fixing a Dirichlet divisor
$\sum_{j=1}^{g^\pm}(\mu_j^\pm, \si_j^\pm)$, where
$\mu_j^\pm\in[E_{2j-1}^\pm,E_{2j}^\pm]$ and $\si_j^\pm\in\{-1, 1\}$.
The spectra of $H_q^\pm$ consist of $g_\pm+1$ bands
\be \label{0.1}
\si_\pm:=\sig(H_q^\pm) = \bigcup_{j=0}^{g_\pm}
[E_{2j}^\pm,E_{2j+1}^\pm].
\ee
We will identify the set
$\C\setminus\sig(H_q^\pm)$ with the upper sheet of the Riemann surface.
The upper and lower sides of the cuts over the spectrum are denoted by
$\siu$ and $\sil$ and the symmetric points on these cuts by
$\lau$ and $\lal$, that is,
\begin{equation}\nn
f(\lam^u)=\lim_{\epsilon \downarrow 0}f(\lam + i\epsilon), \quad
f(\lam^l)=\lim_{\epsilon \downarrow 0}f(\lam - i\epsilon), \quad
\lam \in \sig_\pm.
\end{equation}
We will develop the scattering theory for the operator
\be \label{0.2}
H f(n)=a(n-1) f(n-1) + b(n) f(n)+ a(n) f(n+1), \quad n\in\Z,
\ee
whose coefficients are asymptotically close to the
coefficients of $H_q^\pm$ on the corresponding half-axes:
\be \label{hypo}
\sum_{n = 0}^{\pm \infty} |n| \Big(|a(n) -
a_q^\pm(n)| + |b(n) - b_q^\pm(n)| \Big) < \infty.
\ee
The special case $H_q^- = H_q^+$ has been exhaustively studied in \cite{emtqps}
(see also \cite{voyu}) and the case where $H_q^-$ and $H_q^+$ are in the
same isospectral class $\si_-=\si_+$ was treated in \cite{emtstep}.
Several results are straightforward generalizations, in such
situations we will simply refer to \cite{emtqps}, \cite{emtstep} and
only point out possible differences.
Let $\psi_q^\pm(z,n)$ be the Floquet solutions of the spectral equations
\be\label{0.12}
H_q^\pm \psi(n)=z \psi(n), \qquad z\in\C,
\ee
that decay for $z\in\C\setminus\si_\pm$ as $n\to \pm\infty$.
They are uniquely defined by the condition $\psi_q^\pm(z,0)=1$,
$\psi_q^\pm(z,\cdot)\in\ell^2(\Z_\pm)$. The solution $\psi_q^+(z,n)$
(resp.\ $\psi_q^-(z,n)$) coincides with the upper (resp.\ lower)
branch of the Baker--Akhiezer functions of $H_q^+$ (resp.\ $H_q^-$),
see \cite{tjac}. The second solutions $\breve \psi_q^\pm(z,n)$ are
given by the other branch of the Baker--Akhiezer
functions and satisfy $\breve \psi_q^\pm(z,\cdot)\in\ell^2(\Z_\mp)$ as
$z\in\C\setminus\si_\pm$. Their Wronskian is equal to
\beq\label{2.9}
W_q^\pm(\breve{\psi}_q^\pm(z), \psi_q^\pm(z)) =
\pm\frac{1}{\rho_\pm(z)},
\eeq
where
\begin{equation}\label{0.5}
\rho_\pm(z)=\frac{\prod_{j=1}^{g_\pm}(z-\mu_j^\pm)}{ P_\pm(z)}
\end{equation}
satisfy by our choice of the branch for the square root
\be \label{0.10}
\im(\rho_\pm(\lau))>0, \quad \im(\rho_\pm(\lal))<0,
\quad \la\in\si_\pm.
\ee
In \eqref{2.9} the following notation is
used
\beq \label{new11}
W_{q,n}^\pm(f,g):=a_q^\pm(n) \left(f(n)
g(n+1) - f(n+1)g(n)\right).
\eeq
Note that $\psi_q^\pm(z,n)$,
$\breve\psi_q^\pm(z,n)$ have continuous limits as
$z\to\laul\in\siul_\pm\setminus\partial\si_\pm$, where
$$\partial\si_\pm=\{E_0^\pm,...,E_{2g_\pm+1}^\pm\},$$
and they satisfy the symmetry property
\be \label{0.6}
\psi_q^\pm(\lal,n)= \ol{\psi_q^\pm(\lau,n)}=\breve\psi_q^\pm(\lau,n), \quad \lam\in\si_\pm.
\ee
The points $(\mu_j^\pm,\si_j^\pm)$, $1\le j\le g_\pm$, form the divisors of poles of the
Baker--Akhiezer functions. Correspondingly, the sets of Dirichlet
eigenvalues $\{\mu_1^\pm,...,\mu_{g_\pm}^\pm\}$ can
be divided in three disjoint subsets
\begin{align}
\begin{split}
M^\pm &= \{\mu_j^\pm \,|\, \mu_j^\pm \in \R\backslash\sig_\pm \mbox{
is a pole of } \psi_q^\pm(z,1)\},\\
\breve{M}^\pm &= \{ \mu_j^\pm\,|\,\mu_j^\pm
\in \R\backslash\sig_\pm \mbox{ is a pole of } \breve{\psi}_q^\pm(z,1)\},\\
\hat{M}^\pm &= \{ \mu_j^\pm \,|\, \mu_j^\pm \in \partial \si_\pm \}.
\end{split}
\end{align}
In order to remove the singularities of $\psi_q^\pm(z,n)$, $\breve\psi_q^\pm(z,n)$
we introduce
\begin{align}\label{0.63}
\begin{split}
\delta_\pm(z) &:= \prod_{\mu^\pm_j\in M_\pm} (z - \mu^\pm_j),\\
\hat \delta_\pm(z) &:= \prod_{\mu^\pm_j\in M_\pm}
(z-\mu_j^\pm) \prod_{\mu^\pm_j \in \hat M_\pm} \sqrt{z -
\mu^\pm_j},\\
\breve \delta_\pm(z) &:= \prod_{\mu^\pm_j\in
\breve M_\pm} (z-\mu_j^\pm) \prod_{\mu^\pm_j \in \hat M_\pm} \sqrt{z
- \mu^\pm_j},
\end{split}
\end{align}
where $\prod =1$ if there are no multipliers, and set
\be
\tilde\psi_q^\pm(z,n)=\delta_\pm(z) \psi_q^\pm(z,n),\quad
\hat\psi_q^\pm(z,n)=\hat\delta_\pm(z) \psi_q^\pm(z,n).
\ee
\begin{lemma}\label{lem1.1}
The Floquet solutions $\psi_q^\pm$, $\breve\psi_q^\pm$ have the following properties:
\begin{enumerate}
\item
The functions $\psi_q^\pm(z,n)$ (resp.\ $\breve\psi_q^\pm(z,n)$) are
holomorphic as functions of $z$ in the domain $\mathbb{C}\setminus
(\si_\pm\cup M_\pm)$ (resp.\ $\mathbb{C}\setminus (\si_\pm\cup\breve
M_\pm)$), take real values on the set $\mathbb{R}\setminus
\sigma_\pm$, and have simple poles at the points of the set $M_\pm$
(resp.\ $\breve M_\pm$). They are continuous up to the boundary
$\sipmu\cup \sipml$ except at the points in $\hat M_\pm$ and
satisfy the symmetry property \eqref{0.6}. For $E \in \hat M_\pm$,
they satisfy
\[
\psi_q^\pm(z,n)=O\left(\frac{1}{\sqrt{z-E}}\right), \quad
\breve\psi_q^\pm(z,n) =O\left(\frac{1}{\sqrt{z-E}}\right), \quad
z\to E\in \hat M_\pm.
\]
Moreover, the estimate
\begin{equation}\label{new7}
\hat\psi_q^\pm(z,n) - \hat\psi_q^\pm(E,n) = O(\sqrt{z-E}), \qquad E\in\pa\si_\pm,
\end{equation}
is valid.
\item
The following asymptotic expansions hold as $z \rightarrow \pm
\infty$
\begin{equation} \label{1.12}
\psi_q^\pm(z,n) = z^{\mp n}\Big(\vprod{j=0}{n-1} a_q^\pm(j)
\Big)^{\pm 1} \Big(1 \pm \frac1z \vsum{j=0}{n-1} b_q^\pm(j +
{\scriptstyle{1 \atop 0}}) + O(\frac{1}{z^2})\Big),
\end{equation}
where
\begin{equation*}
\vprod{j=n_0}{n-1}f(j) = \left\{ \begin{array}{c@{\ }l}
\prod\limits_{j=n_0}^{n-1} f(j), & n > n_0, \\ 1, & n=n_0,\\
\prod\limits_{j=n}^{n_0-1} f(j)^{-1}, & n < n_0, \end{array} \right.
\quad
\vsum{j=n_0}{n-1} f(j) = \left\{ \begin{array}{c@{\ }l} \sum\limits_{j=n_0}^{n-1}
f(j), & n > n_0, \\ 0, & n = n_0, \\ -\sum\limits_{j=n}^{n_0-1} f(j), & n < n_0.\end{array}
\right.
\end{equation*}
\item
The functions $\psi_q^\pm(\la,n)$ form a complete orthogonal system
on the spectrum with respect to the weight
\be \label{1.121}
d\omega_\pm(\la) = \frac{1}{2\pi\I} \rho_\pm(\la) d\la,
\ee
namely
\begin{equation}
\oint_{\sig_\pm}\overline{\psi_q^\pm(\lam,m)}\psi_q^\pm(\lam,n)d\omega_\pm(\la)
= \delta(n,m), \label{1.14}
\end{equation}
where
\be \label{1.141}
\oint_{\si_\pm}f(\la) d\la := \int_{\sipmu} f(\lau) d\la - \int_{\sipml} f(\lal) d\la.
\ee
Here $\delta(n,m)=1$ if $n=m$ and $\delta(n,m)=0$ else is the Kronecker
delta.
\end{enumerate}
\end{lemma}
\section{Scattering data}
\label{secSD}
Now let $H$ be a steplike operator with coefficients
$a(n)$, $b(n)$ satisfying \eqref{hypo}. The two solutions $\psi_\pm(z,n)$ of the spectral
equation
\be \label{0.11}
H \psi = z \psi, \quad z\in\C,
\ee
which are asymptotically close to the Floquet solutions $\psi_q^\pm(z,n)$ of the background
equations \eqref{0.12} as $n\to\pm\infty$, are called Jost solutions. They can
be represented as (see \cite{emtqps})
\be \label{3.16}
\psi_\pm(z,n) = \sum_{m=n}^{\pm \infty} K_\pm(n,m) \psi_q^\pm(z, m),
\ee
where the
functions $K_\pm(n, .)$ are real valued and satisfy the estimate
\be \label{estimate K q}
|K_\pm(n,m)| \leq C_\pm(n) \sum_{j=[\frac{m+n}{2}] }^{\pm \infty}
\Big(|a(j)-a_q^\pm(j)| + |b(j)-b_q^\pm(j)|\Big), \quad \pm m
> \pm n>0.
\ee
The functions $C_\pm(n) > 0$ decrease monotonically as
$n\rightarrow \pm \infty$.
Moreover, we have
\begin{align} \label{0.13}
\begin{split}
a(n) &= a_q^+(n)\frac{K_+(n+1, n+1)}{K_+(n,n)}, \\
a(n) &= a_q^-(n)\frac{K_-(n, n)}{K_-(n+1,n+1)}, \\
b(n) &= b_q^+(n) + a_q^+(n)\frac{K_+(n, n+1)}{K_+(n,n)} -
a_q^+(n-1) \frac{K_+(n-1, n)}{K_+(n-1,n-1)}, \\
b(n) &= b_q^-(n) + a_q^-(n-1)\frac{K_-(n, n-1)}{K_-(n,n)} - a_q^-(n)
\frac{K_-(n+1, n)}{K_-(n+1,n+1)},
\end{split}
\end{align}
which implies (cf.\ \cite{emtqps}) the following asymptotic behavior
of the Jost solutions as $z\to\pm \infty$ using \eqref{3.16}, \eqref{1.12},
\be \label{B4jost}
\psi_\pm(z,n) = z^{\mp n}K_\pm(n,n)
\Big(\vprod{j=0}{n-1}a_q^\pm(j)\Big)^{\pm 1} \Big(1 + \Big(B_\pm(n)
\pm \vsum{j=1}{n} b_q^\pm(j- {\scriptstyle{0 \atop 1}})
\Big)\frac{1}{z} + O(\frac{1}{z^2}) \Big), \ee where
\beq
\label{0.14}
B_\pm(n)= \sum_{m=n\pm 1}^{\pm\infty} (b_q^\pm(m)-b(m)).\eeq
For $\la \in \siu_\pm\cup\sil_\pm$ a second pair of solutions of \eqref{0.11} is given
by
\be
\breve\psi_\pm(\la,n)=\sum_{m=n}^{\pm \infty} K_\pm(n,m) \breve\psi_q^\pm(\la, m),
\quad \la \in \siu_\pm\cup\sil_\pm,
\ee
which cannot be continued to the complex plane.
Note that $\breve\psi_\pm(\la,n)=\overline{\psi_\pm(\la,n)}$, $\la \in \sig_\pm$,
and from \eqref{hypo}, \eqref{3.16} we conclude
\be\label{0.62}
W(\overline{\psi_\pm(\la)}, \psi_\pm(\la)) = W_q^\pm(\breve{\psi}_q^\pm(\la), \psi_q^\pm(\la)) =
\pm \rho_\pm(\la)^{-1}.
\ee
The Jost solutions $\psi_\pm$ are holomorphic in the domains
$\mathbb{C}\setminus \left(\si_\pm\cup M_\pm\right)$ and inherit
almost all properties of their background counterparts listed in
Lemma~\ref{lem1.1}. As before, we set
\be\label{0.64}
\tilde\psi_\pm(z,n)=\delta_\pm(z)
\psi_\pm(z,n),\quad \hat\psi_\pm(z,n)=\hat\delta_\pm(z) \psi_\pm(z,n).
\ee
The following Lemma is proven in \cite{emtqps}.
\begin{lemma}\label{lem2.1}
The Jost solutions have the following properties.
\begin{enumerate}
\item
For all $n$, the functions $\psi_\pm(z,n)$ are holomorphic in the
domain $\mathbb{C}\setminus (\si_\pm\cup M_\pm)$ with respect to $z$
and continuous up to the boundary $(\sipmu\cup
\sipml)\setminus\pa\si_\pm$, where \be \label{symm}
\psi_\pm(\lau,n)=\overline{\psi_\pm(\lal,n)}, \quad \la \in
(\sipmu\cup \sipml)\setminus\pa\si_\pm. \ee The functions
$\psi_\pm(z,n)$ are real valued for $z \in \mathbb{R}\setminus
\sigma_\pm$ and have simple poles at $\mu_j \in M_\pm$. Moreover,
$\hat\psi_\pm$ are continuous up to the boundary $\sipmu\cup
\sipml$.
\item
At the band edges we have for $ \la\in\siul_\pm$
\beq\label{new3}\begin{array}{lll}
&\psi_\pm(\la,n) -\overline{\psi_\pm(\la,n)}=o(1), &
E\in\pa\si_\pm\setminus\hat M_\pm, \\
&\psi_\pm(\la,n) +\overline{\psi_\pm(\la,n)}=o\Big(\frac{1}{\sqrt{\la - E}}\Big),&
E\in\hat M_\pm.\end{array}\eeq
\end{enumerate}
\end{lemma}
Next, we introduce the sets
\be \label{2.5}
\si^{(2)}:=\si_+\cap\si_-, \quad
\si_\pm^{(1)}=\clos\,(\si_\pm\setminus\si^{(2)}), \quad
\si:=\si_+\cup\si_-,
\ee
where $\si$ is the (absolutely) continuous
spectrum of $H$ and $\si_+^{(1)}\cup \si_-^{(1)}$ resp.\
$\si^{(2)}$ are the parts which are of multiplicity one resp.\ two.
We will denote the interior of the spectrum by $\inte(\si)$, that is,
$\inte(\si):=\si\setminus\pa\si$.
In addition to the continuous part, $H$ has a finite number of
eigenvalues situated in the gaps, $\si_d=\{\la_1,...,\la_p\} \subset \R \setminus \si$
(see, e.g., \cite{tosc}).
For every eigenvalue we introduce the corresponding norming constants
\be \label{norming}
\ga_{\pm, k}^{-1}=\sum_{n \in
\Z}|\tilde\psi_\pm(\la_k, n)|^2, \quad 1 \leq k \leq p.
\ee
Moreover, $\tilde{\psi}_{\pm}(\la_k, n) = c_k^{\pm} \tilde{\psi}_{\mp}(\la_k, n)$
with $c_k^+ c_k^- = 1$.
Let
\beq\label{2.8}
W(z):=W(\psi_-(z), \psi_+(z))
\eeq
be the Wronskian of two Jost solutions. This function is meromorphic in
the domain $\mathbb{C}\setminus\si$ with possible poles at the
points $M_+\cup M_-\cup(\hat M_+\cap\hat M_-)$
and with possible square root singularities at the points $\hat
M_+\cup\hat M_-\setminus (\hat M_+\cap \hat M_-)$. Set
\beq \label{2.10}
\tilde W(z) =W(\tilde\psi_-(z), \tilde\psi_+(z)), \quad \hat W(z) =
W(\hat\psi_-(z), \hat\psi_+(z)),
\eeq
then $\hat W(\la)$ is holomorphic in
the domain $\mathbb{C}\setminus\mathbb{R}$
and continuous up to the boundary. But unlike to $W(z)$
and $\tilde W(z)$, the function $\hat W(\la)$ may not take real
values on the set $\mathbb{R}\setminus\si$ and complex conjugated
values on the different sides of the spectrum. That is why it is
more convenient to characterize the spectral properties of the
operator $H$ by means of the function $\tilde W$, which can have
singularities at the points of the sets $\hat M_+\cup\hat M_-$.
We will study the precise character of these singularities in
Lemma~\ref{lem2.3} below.
Note that outside the spectrum the function $\tilde W(z)$ vanishes precisely at the
eigenvalues. However, it might also vanish inside the spectrum at points in $\pa\si_-\cup\pa\si_+$.
We will call such points virtual levels of the operator $H$,
\beq\label{2.363}
\si_v:= \{ E\in\si:\ \hat W(E)=0\},
\eeq
and we will show that $\si_v \subseteq \pa\si\cup(\pa\si_+^{(1)}\cap\pa\si_-^{(1)})$
in Lemma~\ref{lem2.3}.
All other points $E$ of the set $\pa\si_+\cup\pa\si_-$ correspond to
the generic case $\hat W(E)\neq 0$.
Our next aim is to derive the properties of the scattering matrix. Introduce the
scattering relations
\be\label{6.16}
T_\mp(\la) \psi_\pm(\la,n)
=\overline{\psi_\mp(\la,n)} + R_\mp(\la)\psi_\mp(\la,n),
\quad\la\in\simpul,
\ee
where the transmission and reflection coefficients are defined as usual,
\be\label{6.17}
T_\pm(\la):= \frac{W(\overline{\psi_\pm(\la)}, \psi_\pm(\la))}{W(\psi_\mp(\la), \psi_\pm(\la))},\quad
R_\pm(\la):= - \frac{W(\psi_\mp(\la),\overline{\psi_\pm(\la)})}{W(\psi_\mp(\la),\,\psi_\pm(\la))}, \quad\la\in \sipmul.
\ee
The equalities in \eqref{6.17} imply the identity
$$
\frac{1}{T_+(\la) \rho_+(\la)} = \frac{1}{T_-(\la) \rho_-(\la)} =W(\la), \quad \la\in\si^{(2)},
$$
where $W(\la)$ is the Wronskian of two Jost solutions \eqref{2.8}.
This Wronskian plays an important role in the characterization
of the properties of the scattering matrix. Namely, the following result is valid.
\begin{lemma}\label{lem2.3}
The entries of the scattering matrix have the following properties:
{\bf I}.
$$
\begin{array}{lcl}
{\bf (a)}&T_\pm(\lau) =\overline{T_\pm(\lal)},& \la\in\si_\pm, \\
& R_\pm(\lau) =\overline{R_\pm(\lal)},&\la\in\si_\pm, \nn\\
{\bf (b)}&\displaystyle{\frac{T_\pm(\la)}{\overline{T_\pm(\la)}}} = R_\pm(\la),&
\la\in\si_\pm^{(1)},\nn\\
{\bf (c)}& 1 - |R_\pm(\la)|^2 =
\displaystyle{\frac{\rho_\pm(\la)}{\rho_\mp(\la)}}\,|T_\pm(\la)|^2,&\la\in\si^{(2)},\\
{\bf (d)}&\overline{R_\pm(\la)}T_\pm(\la) +
R_\mp(\la)\overline{T_\pm(\la)}=0,& \la\in\si^{(2)}.
\end{array}
$$
{\bf II}.
The functions $T_\pm(\la)$ can be extended analytically to the domain
$\mathbb{C} \setminus (\si\cup M_\pm\cup\breve M_\pm)$ and satisfy
\be \label{2.18}
\frac{1}{T_+(z) \rho_+(z)} = \frac{1}{T_-(z) \rho_-(z)} =W(z).
\ee
The function $W(z)$ has the following properties:
{\bf (a)} The function $\tilde W(z) = \delta_+(z)\delta_-(z) W(z)$
is holomorphic on $\mathbb{C}\setminus\si$ with simple zeros at the eigenvalues $\la_k$, where
\be \label{2.11}
\bigg(\frac{ d\tilde W}{d z}(\la_k)\bigg)^2
=\frac{1}{\ga_{+,k}\ga_{-,k}}.
\ee
Moreover,
\be \label{6.9}
\overline{\tilde W(\lau)}=\tilde W(\lal), \quad \la\in\si,
\qquad \tilde W(z)\in\mathbb{R}, \quad
z\in\mathbb{R}\setminus \sigma.
\ee
{\bf (b)} The function $\hat W(z) = \hat\delta_+(z) \hat\delta_-(z)
W(z)$ is continuous on the set $\mathbb{C}\setminus\si$ up to the
boundary $\siu\cup\sil$. It can have zeros on the set
$\pa\si\cup(\pa\si_+^{(1)}\cap\pa\si_-^{(1)})$ and does not vanish
at the other points of the spectrum $\si$. If $\hat W(E)=0$ as
$E\in\pa\si\cup(\pa\si_+^{(1)}\cap\pa\si_-^{(1)})$, then
\be \label{estim}
\frac{1}{\hat W(\la)} = O\left(\frac{1}{\sqrt{\la -
E}}\right),\quad\mbox{for } \la \in \si \mbox{ close to } E.
\ee
Moreover,
\be \label{estim2}
\frac{1}{\hat W(z)} = O\left((z-E)^{-1/2-\eps}\right),\quad
\mbox{for } z \mbox{ close to } E.
\ee
{\bf (c)} In addition,
\be \label{T infty}
T_+(\infty)=T_-(\infty)>0.
\ee
%$T_\pm(z) = C(1 + o(1)), \quad C\in\R\setminus \{0\}, \quad z\to\infty$.
{\bf III}.
{\bf (a)} The reflection coefficients $R_\pm(\la)$ are continuous functions on
$\inte(\sipmul)$.
{\bf (b)} If $E\in\pa\si_+\cap \partial\si_-$ and $\hat W(E)\neq 0$, then the functions $R_\pm(\la)$
are also continuous at $E$. Moreover,
\be\label{P.1}
R_\pm(E) = \left\{ \begin{array}{c@{\quad\mbox{for}\quad}l}
-1 & E\notin\hat M_\pm,\\
1 & E\in\hat M_\pm. \end{array}\right.
\ee
\end{lemma}
\begin{proof}
{\bf I}.
The symmetry property {\bf (a)} follows from formulas (\ref{6.17}) and (\ref{symm}).
For {\bf (b)}, use \eqref{6.17} and observe that $\psi_\mp(\la)$ are real valued for
$\la\in\inte(\si_\pm^{(1)})$.
Let $\la\in\inte(\si^{(2)})$.
By (\ref{6.16}),
$$
|T_\pm|^2 W(\psi_\mp,\overline{\psi_\mp}) = (|R_\pm|^2 -1)
W(\psi_\pm,\overline{\psi_\pm}),
$$
and property {\bf (c)} follows from (\ref{0.62}). The
consistency condition {\bf (d)} can be derived directly from
definition (\ref{6.17}).
{\bf II}.
The identity (\ref{2.18}) follows from (\ref{6.17}).
{\bf (a)} The Wronskian inherits the properties of $\psi_\pm(z)$,
so it remains to show (\ref{2.11}).
If $\hat W(z_0)=0$ for $z_0\in\mathbb{C}\setminus\si$, then
\beq\label{D.1}
\tilde\psi_\pm(z_0,n)=c^\pm\tilde\psi_\mp(z_0,n)
\eeq
for some constants $c^\pm$ (depending on $z_0$), which satisfy $c^-c^+ =1$.
In particular, each zero of $\tilde W$ (or $\hat W$) outside the continuous spectrum
is a point of the discrete spectrum of $H$ and vice versa.
Let $\ga_{\pm,j}$ be the norming constants defined in (\ref{norming})
for some point of the discrete spectrum
$\la_j$. By virtue of \cite{tjac}, Lemma~2.4,
\begin{align}\nn \label{der W q}
\frac{d}{dz}W(\tilde {\psi}_-(z), \tilde{\psi}_+(z)) \Big|_{\la_j} &=
W_n(\tilde {\psi}_-(\la_j), \tfrac{d}{dz}\tilde{\psi}_+(\la_j))
+W_n(\tfrac{d}{dz} \tilde {\psi}_-(\la_j), \tilde{\psi}_+(\la_j))\\
&= - \sum_{k \in \Z} \tilde {\psi}_-(\la_j, k)
\tilde{\psi}_+(\la_j, k)
= - \frac{1}{c_j^{\pm}\gamma_{\pm, j}}.
\end{align}
Since $c_j^-c_j^+=1$, we obtain (\ref{2.11}).
{\bf (b)} Continuity of $\hat W$ up to the boundary follows from the corresponding
property of $\hat \psi_\pm(z,n)$. We begin with the investigation of
the possible zeros of this function on the spectrum.
First let $\la_0\in\inte(\si^{(2)}):= \si^{(2)}\setminus\pa\si^{(2)}$,
that is, $\hat\delta_-\neq 0$ and $\hat\delta_+\neq 0$. Suppose
$W(\la_0) = 0$, then $\psi_+(\la_0,n)=c\,\psi_-(\la_0,n)$ and
$\overline{\psi_+(\la_0,n)}=\bar c\, \overline{\psi_-(\la_0,n)}$,
i.e. $W(\psi_+,\overline {\psi_+})=|c|^2 W(\psi_-,\overline
{\psi_-})$. But this implies opposite signs for $\rho_+, \rho_-$
by (\ref{0.62}), $\sign \rho_+(\la_0)= -\sign$ $\rho_-(\la_0)$,
which contradicts (\ref{0.10}).
Let $\la_0\in\inte(\si^{(1)}_\pm)$ and $\tilde W(\la_0) =0$. The
point $\la_0$ can coincide with a pole $\mu\in M_\mp$. But
$\psi_\pm(\la_0,n)$ and $\overline{\psi_\pm(\la_0,n)}$ are linearly
independent and bounded, and $\tilde\psi_\mp(\la_0,n)\in\mathbb{R}$.
If $W(\la_0)=0$, then
$\tilde\psi_\mp=c_1^{\pm}\,\psi_\pm=c_2^\pm\,\overline{\psi_\pm}$
which implies $W(\psi_\pm,\overline{\psi_\pm})(\la_0)=0$, a contradiction.
In the general mutual location of the background spectra the case
$\la_0=E\in (\pa\si^{(2)}\cap\inte(\si_\pm))\subset\inte(\si)$ can occur. If
$\hat W(E)=0$, then $W( \psi_\pm, \hat\psi_{\mp})(E)=0$, where
$\hat\psi_{\mp}$ are defined by (\ref{0.64}). The values of
$\hat\psi_{\mp}(E,\cdot)$ are either purely real or purely imaginary,
therefore $W( \overline{\psi_\pm}, \hat\psi_{\mp})(E)=0$, that is,
$\overline{\psi_\pm(E,n)}$ and $\psi_\pm(E,n)$ are linearly
dependent, which is impossible at inner points of the set $\si_\pm$.
Thus, the virtual level $\si_v$ of $H$ defined in \eqref{2.363} can only
be located on the set $\pa\si_-\cap\pa\si_+$, that is,
\be\label{in}
\si_v \subseteq \pa\si\cup\big(\pa\si_-^{(1)}\cap\pa\si_+^{(1)}\big).
\ee
To prove \eqref{estim}, take $E\in\si_v$ and assume for example $E\in\si_+$.
By \eqref{6.16} and \eqref{2.18},
\[
\frac{\hat\delta_+(\la)\hat\psi_-(\la,n)}{\hat\delta_-(\la)\rho_+(\la)W(\la)}=
\hat\delta_+(\la) \overline{\psi_+(\la,n)}
+R_+(\la)\hat\psi_+(\la,n).
\]
Choose $n_0$ such that $\hat\psi_-(E,n_0)\neq 0$.
By continuity we also have $\hat\psi_-(\la,n_0)\neq 0$ in a small vicinity of $E$.
Then
\[
\frac{\hat\delta_+(\la) \overline{\psi_+(\la,n_0)}
+R_+(\la)\hat\psi_+(\la,n_0)}{\hat\psi_-(\la,n_0)}=O(1),\quad\la\to
E.
\]
Accordingly,
\[
\frac{1}{\hat W(\la)}=O\bigg(\frac{\prod_{j=1}^{g_+}(\la -
\mu_j^+)}{\hat\delta^2_+(\la)\sqrt{\la-E}}\bigg)=O\left(\frac{1}{\sqrt{\la
- E}}\right), \quad \la\in\si_+,
\]
which proves (\ref{estim}). To see (\ref{estim2}) note that
$$
g(z,n)=\frac{\psi_+(z,n)\psi_-(z,n)}{W(z)}
$$
is a Herglotz function. Moreover, we can assume that $\mu_j \ne E$ and
choose $n$ such that $\psi_\pm(E,n_0)\ne 0$. Hence it remains to show
the corresponding estimate for $g(z)=g(z,n_0)$. Since the continuous
spectrum of $H$ is purely absolutely continuous, we deduce from Stieltjes
inversion formula that
$$
g(z) = \frac{1}{\pi} \int_{E-\delta}^{E+\delta} \frac{\im(g(\la))}{\la-z} d\la + \tilde g(z),
\qquad \delta>0,
$$
where $\tilde g(z)$ is holomorphic near $E$. By (\ref{estim}) we infer
$(\la-E)^{1/2+\eps}\im(g(\la))$ is H\"older continuous and the result follows
from \cite[Eq. (29.8)]{Mu}.
{\bf (c)} Equation (\ref{T infty}) follows from (\ref{B4jost}).
{\bf III}. {\bf (a)} follows from the corresponding properties of
$\psi_\pm(z)$ and from {\bf II}, {\bf (b)}. To show {\bf III}, {\bf (b)} we
use that by (\ref{6.17}) the reflection coefficients have the
representation
\beq\label{2.n}
R_\pm(\la)=-\frac{W(\ov{\psi_\pm(\la)},\psi_\mp(\la))}
{W\left(\psi_\pm(\la),\psi_\mp(\la)\right)}=\mp\frac{W(\ov{\psi_\pm(\la)},
\psi_\mp(\la))}{W(\la)}
\eeq
and are continuous on both sides of the
set $\inte(\si_\pm)\setminus (M_\mp\cup\hat M_\mp)$.
Moreover,
$$
|R_\pm(\la)|=\bigg|\frac{W(\ov{\hat\psi_\pm(\la)},\hat\psi_\mp(\la))}{\hat W(\la)}\bigg|,
$$
where the denominator does not vanish on the set $\si_\pm\setminus\si_v$. Hence
$R_\pm(\la)$ are continuous on this set since both numerator and denominator are.
Next, let $E\in\pa\si_\pm \setminus \si_v$ (in particular $\hat
W(E)\ne 0$). Then, if $E\notin \hat M_\pm$, we use (\ref{2.n}) in
the form
\beq \label{2.n1}
R_\pm(\la)= -1 \mp \frac{\hat{\de}_\pm(\la)
W(\psi_\pm(\la)-\ov{\psi_\pm(\la)},\hat\psi_\mp(\la))} {\hat W(\la)},
\eeq
which shows $R_\pm(\la) \to -1$ since
$\psi_\pm(\la)-\ov{\psi_\pm(\la)} \to 0$ by Lemma~\ref{lem2.1}, (2).
This settles the first case in (\ref{P.1}). Similarly, if
$E\in\hat M_\pm$, we use (\ref{2.n}) in the form
\beq \label{2.n2}
R_\pm(\la)= 1 \pm \frac{\hat{\de}_\pm(\la)
W(\psi_\pm(\la)+\ov{\psi_\pm(\la)},\hat\psi_\mp(\la))} {\hat
W(\la)},
\eeq
which shows $R_\pm(\la) \to 1$ since
$\hat{\de}_\pm(\la)=O(\sqrt{\la - E})$ and
$\psi_\pm(\la)+\ov{\psi_\pm(\la)} = o\big(\frac{1}{\sqrt{\la - E}}\big)$
by Lemma~\ref{lem2.1}, (2). This settles the second case in (\ref{P.1}) as well.
\end{proof}
\section{The Gel'fand-Levitan-Marchenko equation}
\label{secGLM}
The aim of this section is to derive the inverse scattering problem
equation (the Gel'fand-Levitan-Marchenko equation) and to discuss
some additional properties of the scattering data which are
consequences of this equation.
\begin{theorem}
The inverse scattering problem (the GLM) equation has the form
\be \label{glm1 q}
K_\pm(n,m) + \sum_{l=n}^{\pm \infty}K_\pm(n,l)F_\pm(l,m) =
\frac{\delta(n,m)}{K_\pm(n,n)}, \qquad \pm m \geq \pm n,
\ee
where
\begin{align} \nn
F_\pm(m,n) &= \oint_{\sig_\pm} R_\pm(\lam) \psi_q^\pm(\lam,m)
\psi_q^\pm(\lam,n) d\omega_\pm\\ \label{glm2 q} & +
\int_{\sig_\mp^{(1),u}} |T_\mp(\lam)|^2 \psi_q^\pm(\lam,m)
\psi_q^\pm(\lam,n) d\omega_\mp + \sum_{k=1}^p \ga_{\pm,k}
\tilde\psi_q^\pm(\la_k,n) \tilde\psi_q^\pm(\la_k,m).
\end{align}
\end{theorem}
\begin{proof}
Consider a closed contour $\Gamma_\epsilon$ consisting of a large circular
arc and some contours inside this arc, which envelope the spectrum
$\sigma$ at a small distance $\varepsilon$ from the spectrum.
Let $\pm m \geq\pm n$. The residue theorem, \eqref{1.121},
\eqref{B4jost}, \eqref{2.11}, and equality
$\tilde \psi_\mp(\la_k,n)=c_j^\mp \tilde \psi_\pm(\la_k,n)$ imply
\begin{align} \nn
\frac{1}{2\pi\I} \oint_{\Gamma_\epsilon}
\frac{\psi_\mp(\lam,n)\psi_q^\pm(\lam,m)} {W(\la)} d\lam &=
\frac{\delta(n,m)}{K_\pm(n,n)} + \sum_{k=1}^p
\res_{\la_k}\bigg(\frac{\tilde \psi_\mp(\lam,n) \tilde \psi_q^\pm(\lam,m)}
{\tilde W(\la)} \bigg)\\ \label{4.3} &= \frac{\delta(n,m)}{K_\pm(n,n)} -
\sum_{k=1}^p \ga_{\pm,k} \tilde\psi_\pm(\la_k,n)
\tilde\psi_q^\pm(\la_k,m),
\end{align}
since the integrand is meromorphic on $\C\backslash \si$ with simple
poles at the eigenvalues $\la_k$ and at $\infty$ if $m=n$. It is
continuous till the boundary except at the points
$E\in \partial \sigma_+ \cup \partial \sigma_-$ where
\begin{equation}
\frac{\psi_\mp(\lam,n)\psi_q^\pm(\lam,m)} {W(\la)} = O
\left(\frac{1}{\sqrt{\lam - E}}\right), \quad E \in \partial
\sigma_+ \cup \partial \sigma_-,
\end{equation}
by \eqref{estim}. On the other hand, as $\epsilon \rightarrow 0$,
\begin{align} \label{4.5}
\begin{split}
& \frac{1}{2\pi\I} \oint_{\si}
\frac{\psi_\mp(\lam,n)\psi_q^\pm(\lam,m)}
{W(\lam)} d\lam = \\
&\quad = \frac{1}{2\pi\I} \oint_{\sig_\pm} \frac{\big(\ol{\psi_\pm(\lam,n)}
+ R_\pm(\lam)\psi_\pm(\lam,n)\big)\psi_q^\pm(\lam,m)}
{T_\pm(\lam) W(\lam)} d\lam \\
&\qquad + \frac{1}{2\pi\I} \oint_{\sig_\mp^{(1)}} \frac{\psi_\mp(\lam,n)\psi_q^\pm(\lam,m)}
{W(\lam)} d\lam \\
&\quad = \oint_{\sig_\pm} \ol{\psi_\pm(\lam,n)}\psi_q^\pm(\lam,m)d\omega^\pm
+ \oint_{\sig_\pm}
R_\pm(\lam)\psi_\pm(\lam,n)\psi_q^\pm(\lam,m)d\omega^\pm\\
&\qquad + \frac{1}{2\pi\I}\int_{\sig_\mp^{(1),u}}\psi_q^\pm(\lam,m)
\bigg(\frac{\psi_\mp(\lam,n)}{W(\lam)} -
\frac{\ol{\psi_\mp(\lam,n)}}{\ol{W(\lam)}}
\bigg)d\lam.
\end{split}
\end{align}
It remains to treat the last integrand. By \eqref{6.16} and Lemma~\ref{lem2.3},~{\bf I},
\begin{equation} \nn
\ol{\psi_\mp(\lam,n)} = T_\mp(\lam)\psi_\pm(\lam,n) - R_\mp(\lam)\psi_\mp(\lam,n)
= T_\mp(\lam)\psi_\pm(\lam,n) - \frac{T_\mp(\lam)}{\ol{T_\mp(\lam)}}\psi_\mp(\lam,n),
\end{equation}
and therefore
\begin{equation} \nn
\frac{\psi_\mp(n)}{W} -
\frac{\ol{\psi_\mp(n)}}{\ol{W}}
= \frac{\ol{W}\ol{T_\mp} + W T_\mp}{|W|^2\ol{T_\mp}}\psi_\mp(n) -
\frac{T_\mp}{\ol{W}}\psi_\pm(n) = - \frac{T_\mp}{\ol{W}}\psi_\pm(n),
\end{equation}
since $\ol{W}\ol{T_\mp} + W T_\mp = 2 \re(W T_\mp)=0$ on $\sig_\mp$. In summary, \eqref{4.3}
and \eqref{4.5} yield
\begin{align} \nn
\frac{\delta(n,m)}{K_\pm(n,n)} &= K_\pm(n,m)
+ \oint_{\sig_\pm} R_\pm(\lam)\psi_\pm(\lam,n)\psi_q^\pm(\lam,m)d\omega^\pm \\ \nn
&+ \int_{\sig_\mp^{(1),u}} |T_\mp(\lam)|^2\psi_\pm(\lam,n)\psi_q^\pm(\lam,m)d\omega^\mp
+ \sum_{j=1}^p \ga_{\pm,j} \tilde \psi_\pm(\la_j,n) \tilde \psi_q^\pm(\la_j,m),
\end{align}
and applying \eqref{3.16} finishes the proof.
\end{proof}
As it is shown in \cite{emtqps}, the estimate \eqref{estimate K q} for $K_\pm(n,m)$
implies the following estimates for $F_\pm(n,m)$.
\begin{lemma}\label{lem4.1}
The kernel of the GLM equation satisfies the following properties.\\
{\bf IV}. There exist functions $C_\pm(n)>0$ and $ q_\pm(n)\geq 0$,
$n\in\Z_\pm$, such that $C_\pm(n)$ decay as $n\to\pm\infty$,
$|n| q(n) \in \ell^1(\Z_\pm)$, and
\begin{align} \label{fourest}
\begin{split}
&|F_{\pm}(n, m)|\leq C_\pm(n)\sum_{j=n+m}^{\pm \infty} q(j), \\
&\sum_{n = n_0}^{\pm \infty}|n| \big| F_{\pm}(n,n) -
F_{\pm}(n \pm 1, n \pm 1)\big| < \infty, \\
&\sum_{n = n_0}^{\pm \infty}|n| \big|a_q^\pm(n) F_{\pm}(n,n+1) -
a_q^\pm(n-1) F_{\pm}(n - 1, n)\big| < \infty.
\end{split}
\end{align}
\end{lemma}
In summary, we have obtained the following necessary conditions for
the scattering data:
\begin{theorem}\label{theor1}
The scattering data
\begin{align}\label{4.6}
\begin{split}
{\mathcal S} &= \Big\{ R_+(\la),\,T_+(\la),\,
\la\in\si_+^{\mathrm{u,l}}; \,
R_-(\la),\,T_-(\la),\, \la\in\si_-^{\mathrm{u,l}};\\
& \qquad \la_1,\dots, \la_p \in\mathbb{R} \setminus (\si_+\cup\si_-),\,
\ga_{\pm, 1}, \dots, \ga_{\pm, p} \in\mathbb{R}_+\Big\}
\end{split}
\end{align}
satisfy the properties {\bf I-III} listed in Lemma~\ref{lem2.3}. The
functions $F_\pm(n,m)$, defined in (\ref{glm2 q}), satisfy property
{\bf IV} in Lemma~\ref{lem4.1}.
\end{theorem}
In fact, the conditions on the scattering data given in Theorem~\ref{theor1}
are both necessary and sufficient for the solution of the
scattering problem in the class (\ref{hypo}). The sufficiency of
these conditions as well as the algorithm for the solution of the
inverse problem will be discussed in the next section.
\section{The inverse scattering problem}
\label{secINV}
Let $H_q^\pm$ be two arbitrary quasi-periodic Jacobi operators
associated with sequences $a_q^\pm(n), b_q^\pm(n)$ as introduced in
Section~\ref{secQP}. Let $\mathcal{S}$ be given scattering data with
corresponding kernels $F_\pm(n,m)$ satisfying the necessary
conditions of Theorem~\ref{theor1}.
First we show that the GLM equations (\ref{glm1 q}) can be solved for
$K_\pm(n,m)$ if $F_\pm(n,m)$ are given.
\begin{lemma}\label{lem5.4}
Under condition {\bf IV}, the GLM equations (\ref{glm1 q}) have
unique real-valued solutions $K_\pm(n,\cdot)\in \ell^1(n,\pm\infty)$
satisfying the estimates
\beq \label{5.100}
|K_\pm(n,m)|\leq
C_\pm(n)\sum_{j=\left[\frac{n+m}{2}\right]}^{\pm\infty} q(j),
\quad\pm m>\pm n.
\eeq
Here the functions $q_\pm(n)$ and $C_\pm(n)$ are of the same
type as in (\ref{fourest}).
Moreover, the following estimates are valid
\begin{align} \label{invest}
\begin{split}
&\sum_{n = n_0}^{\pm \infty}|n| \big| K_{\pm}(n,n) -
K_{\pm}(n \pm 1, n \pm 1)\big| < \infty, \\
&\sum_{n = n_0}^{\pm \infty}|n| \big|a_q^\pm(n) K_{\pm}(n,n+1) -
a_q^\pm(n-1) K_{\pm}(n - 1, n)\big| < \infty.
\end{split}
\end{align}
\end{lemma}
\begin{proof}
The solvability of (\ref{glm1 q}) under condition (\ref{fourest})
and the estimates (\ref{5.100}), \eqref{invest} follow
completely analogous to the corresponding
result in \cite[Theorem 7.5]{emtqps}. To prove
uniqueness, first note that the GLM equations are generated by
compact operators. Thus, it is sufficient to prove that the
equation
\beq \label{5.102}
f(m)+\sum_{\ell=n}^{\pm\infty} F_\pm(\ell,m)
f(\ell) =0
\eeq
has only the trivial solution in the space
$\ell^1(n,\pm\infty)$. The proof is similar for the "$+$" and "$-$"
cases, hence we give it only for the "$+$" case. Let $f(\ell)$, $\ell > n$,
be a nontrivial solution of (\ref{5.102}) and set $f(\ell)=0$ for
$\ell \leq n$. Since $F_+(\ell,n)$ is real-valued, we can assume that
$f(\ell)$ is real-valued. Abbreviate by
\beq \label{5.103}
\widehat f(\la)
=\sum_{m \in \mathbb{Z}} \psi_q^+(\la,m) f(m)
\eeq
the generalized Fourier transform, generated by the spectral
decomposition (\ref{1.14}) (cf.\ \cite{T}).
Recall that $\widehat f(\la)\in L^1_{loc} (\siu_+\cup\sil_+)$.
Multiplying (\ref{5.102}) by $f(m)$, summing over $m \in \Z$,
and applying \eqref{1.14}, (\ref{glm2 q}), (\ref{5.103}), and
condition {\bf I}, {\bf (a)}, we have
\begin{align}
\begin{split}
& 2 \int_{\si_+^u}|\widehat f(\la)|^2 d\omega_+(\la) + 2 \re
\int_{\si_+^u}R_+(\la) \widehat f(\la)^2 d\omega_+(\la) \\ \label{5.104}
& \quad +\int_{\si_-^{(1),u}}\widehat f(\la)^2 |T_-(\la)|^2 d\omega_-(\la)
+ \sum_{k=1}^p \ga_{+,k} \bigg(\sum_{n \in \mathbb{Z}} \tilde \psi_q^+(\la_k,n) f(n) \bigg)^2=0.
\end{split}
\end{align}
The last two summands in (\ref{5.104}) are nonnegative since
$\widehat f(\la) \in\mathbb{R}$ for $\la\in\si_-^{(1)}$
and $\tilde \psi_q^+(\la_k)\in \R$.
We estimate the first two integrands by
\[
|\widehat f(\la)|^2 + \re R_+(\la) \widehat f(\la)^2 \geq |\widehat f(\la)|^2 - |R_+(\la)
\widehat f(\la)^2|
\geq \big(1-|R_+(\la)|\big)|\widehat f(\la)|^2
\]
and drop the last summand in (\ref{5.104}), thus obtaining
\beq \label{5.105}
2\int_{\si^{(2),\mathrm{u}}} (1-|R_+(\la)|)|\widehat f(\la)|^2 d\omega_+(\la)
+ \int_{\si_-^{(1),\mathrm{u}}} \widehat f(\la)^2 |T_-(\la)|^2 d\omega_-(\la) \leq 0.
\eeq
Here we also used that
\[
\int_{\si_+^{(1),\mathrm{u}}}(1-|R_+(\la)|) |\widehat f(\la)|^2
d\omega_+(\la) = 0,
\]
which follows from condition {\bf I}, {\bf (b)}. Since $|R_+(\la)|<1$
for $\la\in \inte(\si^{(2)})$ and
$\omega_-(\la)>0$ for $\la\in\inte(\si_-^{(1)})$ we conclude that
\[
\widehat f(\la)=0 \quad \mbox{for}\quad \la\in\si^{(2)}\cup
\si_-^{(1)}= \si_-.
\]
The function $\widehat f(z)$ can be defined by formula (\ref{5.103})
as a meromorphic function on $\mathbb{C}\setminus\si_+$. By our
analysis it is even meromorphic on $\mathbb{C}\setminus\si^{(1)}_+$
and vanishes on $\si_-$. Thus $\widehat f(z)$ and hence also $f(m)$
are equal to zero.
\end{proof}
Next, define the sequences $a_\pm, b_\pm$ by
\begin{align} \label{5.1}
\begin{split}
a_+(n) &= a_q^+(n)\frac{K_+(n+1, n+1)}{K_+(n,n)}, \\
a_-(n) &= a_q^-(n)\frac{K_-(n, n)}{K_-(n+1,n+1)}, \\
b_+(n) &= b_q^+(n) + a_q^+(n)\frac{K_+(n, n+1)}{K_+(n,n)}
- a_q^+(n-1) \frac{K_+(n-1, n)}{K_+(n-1,n-1)}, \\
b_-(n) &= b_q^-(n) + a_q^-(n-1)\frac{K_-(n, n-1)}{K_-(n,n)} - a_q^-(n)
\frac{K_-(n+1, n)}{K_-(n+1,n+1)},
\end{split}
\end{align}
and note that estimate (\ref{invest}) implies
\beq \label{5.2}
n\left\{|a_\pm(n)-a_q^\pm(n)| + |b_\pm -
b_q^\pm(n)|\right\}\in\ell^1(\Z_\pm).
\eeq
\begin{lemma}\label{lem5.7}
The functions $\psi_\pm(z,n)$, defined by
\beq \label{Dop}
\psi_\pm(z,n) =\sum_{m=n}^{\pm\infty}
K_\pm(n,m) \psi_q^\pm(z,m),
\eeq
solve the equations
\beq \label{5.3}
a_\pm(n-1)\psi_\pm(z,n-1)+b_\pm(n)\psi_\pm(z,n)+a_\pm(n)\psi_\pm(z,n+1)=z\psi_\pm(z,n),
\eeq
where $a_\pm(n), b_\pm(n)$ are defined by (\ref{5.1}).
\end{lemma}
\begin{proof}
Consider the two operators\footnote{We don't know that $ H_\pm$ is limit
point at $\mp\infty$ yet, but this will not be used.}
$$
(H_\pm y)(n)= a_\pm(n-1)y_\pm(n-1)+b_\pm(n)y_\pm(n)+a_\pm(n)y_\pm(n+1),\quad
n\in\mathbb{Z}.
$$
Define two discrete integral operators
$$
\left ({\mathcal K}_\pm f\right)(n) =\sum_{m=n}^{\pm\infty} K_\pm(n,m) f(m).
$$
Then (cf.\ \cite{emtqps}) the following identity is valid
$$
H_\pm{\mathcal K}_\pm={\mathcal K}_\pm\,H_q^\pm,
$$
which implies (\ref{5.3}).
\end{proof}
The remaining problem is to show that $a_+(n)\equiv a_-(n)$,
$b_+(n)\equiv b_-(n)$ under conditions {\bf II} and {\bf III} on the
scattering data $\mathcal{S}$.
\begin{theorem}\label{theor2}
Let the scattering data ${\mathcal S}$, defined as in (\ref{4.6}),
satisfy conditions {\bf I}, {\bf (a)--(c)}, {\bf II}, {\bf III}, {\bf (a)},
and {\bf IV}. Then each of the GLM equations (\ref{glm1 q}) has
unique solutions $K_\pm(n,m)$, satisfying the estimate
(\ref{invest}). The functions $a_\pm(n), b_\pm(n)$, defined by
(\ref{5.1}), satisfy (\ref{5.2}).
Under the additional conditions {\bf III}, {\bf (b)} and {\bf I}, {\bf (d)},
these functions coincide, $a_+(n)\equiv a_-(n)=a(n)$, $b_+(n)\equiv
b_-(n)=b(n)$, and the data ${\mathcal S}$ are the scattering data
for the Jacobi operator associated with the sequences $a(n), b(n)$.
\end{theorem}
The proof of Theorem~\ref{theor2} takes up the remaining
section and is split into several lemmas for the convenience of the
reader.
To prove uniqueness of the reconstructed potential we follow the
method proposed in \cite{mar}. Recall that, by Lemma~\ref{lem1.1}
(iii), the functions $\psi_q^\pm(\lam,n)$ form an orthonormal basis
with corresponding generalized Fourier transform. Split the kernel
of the GLM equation (\ref{glm2 q}) into three summands $F_\pm(m,n)=
F_{r,\pm}(m,n) + F_{h,\pm}(m,n) +F_{d,\pm}(m,n)$ and set \be
G_\pm(n, m) := \sum_{l=n}^{\pm \infty}K_\pm(n,l) F_{r,\pm}(l,n). \ee
Then one obtains as in \cite[Theorem 8.2]{emtqps} that the functions
$h_\mp(\la, n)$, defined by
\begin{align} \label{5.11}
\begin{split}
h_\mp(\lam, n) &= \frac{1}{T_\pm(\lam)}\Bigg(
\frac{\breve{\psi}_q^\pm(\lam,n)}{K_\pm(n, n)} + \sum_{m = n\mp1}^{\mp
\infty}G_\pm(n, m) \breve{\psi}_q^\pm(\lam,m) \\
&\quad \mp \int_{\sig_\mp^{(1),u}} |T_\mp(\xi)|^2 \psi_\pm(\xi,n)
\frac{W_{q,n-1}^\pm(\psi_q^\pm(\xi), \breve{\psi}_q^\pm(\lam))} {\xi-\lam}
d\omega_\mp(\xi)\\
&\quad \pm \sum_{k=1}^p \gamma_{\pm,
k} \tilde \psi_\pm(\lam_k, n) \frac{W_{q,n-1}^\pm(\tilde \psi_q^\pm(\lam_k),
\breve{\psi}_q^\pm(\lam))} {\lam - \lam_k }\Bigg),
\end{split}
\end{align}
satisfy
\be \label{5.10}
T_\pm(\lam)h_\mp(\lam, n) = \ol{\psi_\pm(\lam, n)} + R_\pm(\lam) \psi_\pm(\lam, n),
\quad \lam \in \sig_\pm^{u,l}.
\ee
Despite the fact that $h_\mp(\la,n)$ are defined via the background solutions
corresponding to the opposite half-axis $\mathbb{Z}_\pm$, they share a series
of properties with $\psi_\mp(\la,n)$.
Namely, we prove
\begin{lemma}\label{lem5.1}
Let $h_\mp(z,n)$ be defined by formula (\ref{5.11}) on the set $\sipmul$.
\begin{enumerate}
\item
The functions $\tilde h_\mp(z,n)= \de_\mp(z) h_\mp(z,n)$
admit analytic extensions to the domain $\mathbb{C}\setminus\si$.
\item
The functions $\tilde h_\mp(z,n)$
are continuous up to the boundary $\siul$ except possibly at the points $\pa\si_+\cup\pa\si_-$.
Furthermore,
\begin{align} \label{5.30}
\begin{split}
&\tilde h_\mp(\lau,n)=\tilde h_\mp(\lal,n)\in \R, \qquad
\la\in\mathbb{R}\setminus\si_\mp,\\
& \tilde h_\mp(\lau,n)=\overline{\tilde h_\mp(\lal,n)}, \qquad \la\in\inte(\si_\mp).
\end{split}
\end{align}
\item
For large $z$ the functions $h_\mp(z,n)$ have the following asymptotic
behavior
\be \label{h infty}
h_{\mp}(z, n) = \frac{z^{\pm n}}{K_\pm(n,n)T_\pm(\infty)}
\Big(\vprod{j=0}{n-1}a_q^\pm(j)\Big)^{\mp1}\Big(1+O(\frac{1}{z})\Big),
\quad z \rightarrow \infty.
\ee
\item
We have
\begin{align*}
W^\pm(h_\mp(z),\psi_\pm(z)):=&a_\pm(n)\big(h_\mp(z,n)\psi_\pm(z,n+1)-
h_\mp(z,n+1)\psi_\pm(z,n)\big)\\
\equiv& \pm W(z),
\end{align*}
where $W(z)$ is defined by (\ref{2.18}).
\end{enumerate}
\end{lemma}
\begin{remark}\label{rem5}
Note that we did not establish the connection between the function
$W(z)$ and the functions $W^\pm(\psi_+(z,n),\psi_-(z,n))$,
which can depend on $n$, because $\psi_+$ and $\psi_-$ are
the solutions of Jacobi equations corresponding to possibly
different operators $H_+$ and $H_-$.
\end{remark}
\begin{proof}
(i). To show that $\tilde h_\mp(z,n)$ have analytic extensions to
$\mathbb{C}\setminus\si$, we study each term in (\ref{5.11}) separately.
First of all, note that due to the representation
\beq \label{2.19}
T_\pm(z) = \frac{1}{\rho_\pm(z) W(z)} =
\frac{\hat\de_\mp(z)}{\breve \de_\pm(z)}
\frac{\sqrt{\prod_{j=0}^{2g_\pm+1} (z-E_j^\pm)}}{\hat W(z)},
\eeq
the functions $\tilde\zeta_\mp(z,n)= \de_\mp(z) \zeta_\mp(z,n)$, where
\beq \label{5.141}
\zeta_\mp(z,n):=\frac{\breve{\psi}_q^\pm(z,n)}{T_\pm(z)},
\eeq
can be continued analytically to $\mathbb{C}\setminus\si$. This also
holds for the second term since $G_\pm(n,\cdot)\in \ell^1(\mathbb{Z})$ are
real-valued.
Next we discuss the properties of the Cauchy-type integral in the
representation (\ref{5.11}). We represent the third summand in (\ref{5.11})
multiplied by $T_\pm^{-1}(z)$ as
\beq \label{5.123}
\Theta_\mp(z,n):=\mp \frac{1}{2\pi\I} \int_{\si_\mp^{(1),\mathrm{u}}}
\theta_\mp(z,\xi,n)\frac{d\xi}{\xi - z},
\eeq
where
\begin{align}\nn
\theta_\mp(z,\xi,n) &= -\frac{\de_\mp(\xi)^2}{\rho_\mp(\xi) |\tilde
W(\xi)|^2} \tilde\psi_\pm(\xi,n)
W_{q,n-1}^\pm(\tilde\psi_q^\pm(\xi,\cdot), \zeta_\mp(z,\cdot))\\
\label{5.13} & = -\frac{|\hat\de_\mp(\xi)|^2}{\rho_\mp(\xi) |\hat
W(\xi)|^2} \frac{|\hat\de_\pm(\xi)|^2}{\hat\de_\pm(\xi)^2}
\hat\psi_\pm(\xi,n) W_{q,n-1}^\pm(\hat\psi_q^\pm(\xi,\cdot),
\zeta_\mp(z,\cdot)).
\end{align}
By property {\bf II}, {\bf (a)} the function $\hat W(\xi)$ has no zeros in the interior of
$\si_\mp^{(1),\mathrm{u}}$. Thus, for $z\notin \si_\mp^{(1)}$, the functions $\theta_\mp(z,.,n)$
are bounded in the interior of $\si_\mp^{(1)}$ and the only possible singularities can arise
at the boundary. We claim
\beq\label{5.131}
\theta_\mp(z,\xi,n)= \begin{cases}
O(\sqrt{\xi - E}) & \mbox{ for } E\notin\si_v,\\
O\big(\frac{1}{\sqrt{\xi - E}}\big) & \mbox{ for } E\in\si_v,
\end{cases}
\qquad E\in\pa\si_\mp^{(1)},\; z\neq E.
\eeq
This follows from $\frac{|\hat\delta_\mp(\xi)|^2}{\rho_\mp(\xi)}=O(\sqrt{\xi - E})$
together with $\hat W(\xi) = O(1)$ if $E\notin\si_v$ and
$1/\hat W(\xi) = O(1/\sqrt{\xi - E})$ by {\bf II}, {\bf (b)} if $E\in\si_v$.
Therefore, $\theta_\mp$ are integrable and the third summand of (\ref{5.11})
also inherits the properties of $\zeta_\mp(z,n)$.
Finally, the last summand in (\ref{5.11}) again inherits the properties of
$\tilde\zeta_\mp(z,n)$ except for possible additional poles at the eigenvalues $\la_k$.
However, these cancel with the zeros of $\tilde W(z)$ at $z=\lam_k$.
(ii). We consider the boundary values next. The only nontrivial term is of course
the Cauchy-type integral (\ref{5.123}) as $z\to\la\in\inte(\si_\mp^{(1)})$.
First of all observe that by \eqref{2.9} and \eqref{2.18},
\[
\frac{W_{q,n-1}^\pm(\tilde\psi_q^\pm(\la),\breve\psi_q^\pm(z))}{T_\pm(z)} \to (\de_\pm W)(\la),
\]
where the functions $\de_\pm W$ are bounded and nonzero for $\la\in\inte(\si_\mp^{(1)})$ by
{\bf II}, {\bf (a)}. Hence the Plemelj formula applied to (\ref{5.123}) gives
\[
\Theta_\mp(\la,n) = \pm \frac{\tilde\psi_\pm(\la,n)}{2\de_\pm(\la)
\rho_\mp(\la) \overline{W(\la)}} \mp
\dashint_{\si_\mp^{(1),
\mathrm{u}}}\frac{\theta_\mp(\la,\xi,n)}{\xi - \la}d\xi, \quad
\la\in\inte(\si_\mp^{(1),\mathrm{u}}),
\]
where both terms are finite. Here $\dashint$ denotes the principle value integral.
Therefore, the boundary values away from $\pa\si_+\cup\pa\si_-$ exist and we have
\beq \label{5.14}
h_\mp(\lau,n)= \overline{h_\mp(\lal,n)}, \quad\la\in\si_+\cup\si_-.
\eeq
By property {\bf I}, {\bf (b)},
\beq \label{5.16}
h_\mp=T_\pm^{-1}\left(R_\pm\psi_\pm +\overline{\psi_\pm}\right) =
\frac{\psi_\pm}{\ov{T_\pm}} +\frac{\overline{\psi_\pm}}{T_\pm}\in\mathbb{R},
\quad \la\in\si_\pm^{(1)},
\eeq
from which
\beq \label{5.15}
h_\mp(\lau,n)= h_\mp(\lal,n) ,\quad \la\in\si_\pm^{(1)},
\eeq
follows. Combining (\ref{5.14}) and (\ref{5.15}) yields (\ref{5.30}).
(iii). Since the last two terms in (\ref{5.11}) are $O(z^{-1})$, the asymptotic behavior
follows from \eqref{B4jost} and {\bf II}, {\bf (c)}.
%\beq \zeta_\mp(z,n)=z^{\mp n}\left(C_\mp(n) + o(1))\right), \quad z\to\infty. \eeq
(iv). From (\ref{5.10}), \eqref{0.62}, and (\ref{2.18}) we obtain
\beq \nonumber
W^\pm(h_\mp(\la), \psi_\pm(\la))=\frac{W^\pm(\ol{{\psi}_\pm(\la)}, \psi_\pm(\la))}{T_\pm(\la)} =
\frac{1}{T_\pm(\la)\rho_\pm(\la)} = \pm W(\la), \quad \la\in \si_\pm.
\eeq
Hence equality holds for all $z\in\mathbb{C}$ by analytic continuation.
\end{proof}
\begin{corollary}\label{col7}
The functions $\tilde h_\mp(z,n)$ admit analytic extensions to
$\mathbb{C}\setminus\si_\mp$.
\end{corollary}
\begin{proof}
Property (i) of Lemma \ref{lem5.1} holds for
$z\in\mathbb{C}\setminus \si$. Relation (\ref{5.30}) implies that
$\tilde h_\mp$ have no jumps across $z\in\inte(\si_\pm^{(1)})$. To
finish the proof we need to show that the possible remaining
singularities at $E\in\pa\si_\pm^{(1)}\cap\pa\si$ are removable.
This follows from (cf.\ \eqref{2.19})
\beq \label{5.142}
\hat\zeta_\mp(z,n)= \frac{\hat W(z)}{\sqrt{\prod_{j=0}^{2g_\pm+1}
(z-E_j^\pm)}} \breve\de_\pm(z) \breve\psi_q^\pm(z,n)
\eeq
which shows
$\tilde\zeta_\mp(z,n)=O((z-E)^{-1/2})$ and hence
$\tilde h_\mp(z,n)= O((z-E)^{-1/2})$ for $E\in\si_\pm^{(1)}\cap\pa\si$.
However, let us emphasize at this point that the behavior of
$h_\pm(z,n)$ at the remaining edges is a more subtle question
to be discussed later.
\end{proof}
Eliminating $\overline{\psi_\pm}$ from
$$
\left\{\begin{array}{lll}
\overline{ R_\pm(\la)}\,\overline{\psi_\pm(\la,n)} + \psi_\pm(\la,n)&=&\overline{h_\mp(\la,n)}\,
\overline{T_\pm(\la)}\\[2mm]
R_\pm(\la)\,\psi_\pm(\la,n) + \overline{\psi_\pm(\la,n)} &=&h_\mp(\la,n)\,T_\pm(\la)
\end{array}\right.
$$
yields
$$
\psi_\pm(\la,n)\left(1 - |R_\pm(\la)|^2\right) =\overline{h_\mp(\la,n)}\,
\overline{T_\pm(\la)} -
\overline{R_\pm(\la)}\,h_\mp(\la,n)\,T_\pm(\la).
$$
We apply {\bf I}, {\bf (c)}, {\bf II}, and the consistency condition
{\bf I}, {\bf (d)} to obtain
\begin{align} \nonumber
T_\mp(\la)\psi_\pm(\la,n) &=\overline{h_\mp(\la,n)} - \frac{\overline{R_\pm(\la)}
T_\pm(\la)}{\ov{T_\pm(\la)}} h_\mp(\la,n)\\ \label{4.26}
&=\overline{h_\mp(\la,n)} + R_\mp(\la) h_\mp(\la,n),
\quad\la\in\si^{(2)}.
\end{align}
This equation together with (\ref{5.10}) gives us a system from
which we can eliminate the reflection coefficients $R_\pm$. We obtain
\beq\label{5.20}
T_\pm(\la) \big(\psi_\pm(\la)\psi_\mp(\la) -
h_\pm(\la)h_\mp(\la)\big)=
\psi_\pm(\la)\overline{h_\pm(\la)} -
\overline{\psi_\pm(\la)}h_\pm(\la), \quad
\la\in\si^{(2),\mathrm{u,l}}.
\eeq
Now introduce the function
\beq \label{5.211}
G(z):= G(z,n) = \frac{\psi_+(z,n)\psi_-(z,n) - h_+(z,n)h_-(z,n)}{W(z)}
\eeq
which is well defined in the domain $z\in \mathbb{C}\setminus
\left(\si\cup\si_d\cup M_+\cup M_- \right)$.
By (\ref{5.20}) and \eqref{2.18},
\beq \label{5.22}
G(\la) = \left(\psi_\pm(\la)\overline{h_\pm(\la)} -
\overline{\psi_\pm(\la)}h_\pm(\la)\right) \rho_\pm(\la),
\quad\la\in\si^{(2),\mathrm{u,l}},
\eeq
so we need to study the properties of $G(z,n)$ as a function of $z$.
Our aim is to prove that $G(z,n)=0$, which will follow
from the next lemma.
\begin{lemma}\label{lem5.2}
The function $G(z,n)$, defined by \eqref{5.211}, has the following properties.
\begin{enumerate}
\item
$G(\lau,n) = G(\lal,n)\in\mathbb{R}$ for $\la\in\mathbb{R}\setminus (\pa\si_-\cup\pa\si_+\cup\si_d)$.
\item
It has removable singularities at the points $\pa\si_-\cup\pa\si_+\cup\si_d$,
where $\si_d:=\{\la_1,...,\la_p\}$.
\end{enumerate}
\end{lemma}
\begin{proof}
(i). We can rewrite $G(z,n)$ as
\beq\label{5.25}
G(z,n)= \frac{\tilde\psi_+(z,n)\tilde\psi_-(z,n) -
\tilde h_+(z,n)\tilde h_-(z,n)}{\tilde W(z)},
\eeq
where $\tilde h_\pm(z,n)=\de_\pm(z)h_\pm(z,n)$ as usual.
The numerator is bounded near the points under consideration and the
denominator does not vanish there.
Thus $G(z,n)$ has no singularities at the points $(M_+\cup M_-) \setminus \si_d$.
Furthermore, by Lemma~\ref{lem5.1}, {\bf II}, {\bf (a)}, and Lemma~\ref{lem2.1}
we know that $G(z,n)$ has continuous limiting values on the sets
$\si_-$ and $\si_+$, except possibly at the edges, and satisfies
$$
G(\lau,n) =\overline{G(\lal,n)},\quad \la\in\si_+ \cup \si_-.
$$
Hence, if we can show that these limits are real, they will be equal and
$G(z,n)$ will extend to a meromorphic function on $\mathbb{C}$, that is, (i) holds.
To this aim we first observe that \eqref{5.30}, \eqref{5.22}, and Lemma~\ref{lem2.1}
imply
\beq\label{5.24}
G(\lau,n) = G(\lal,n)\in\mathbb{R}, \quad \la\in\inte(\si^{(2)}).
\eeq
Thus, it remains to prove
\beq\label{5.26}
G(\lau,n) = G(\lal,n)\in\mathbb{R}
\quad \mbox{for}\quad \la\in\inte(\si_-^{(1)})\cup\inte(\si_+^{(1)}).
\eeq
Let us show that $G(\la,n)$ has no jump on the set
$\inte(\si_-^{(1)})\cup\inte(\si_+^{(1)})$. We abbreviate
\beq\label{5.28}
\left[G\right] :=G(\la)
-\overline{G(\la)}=\left[\frac{\psi_+\psi_-}{W}\right] -
\left[\frac{h_+h_-}{W}\right], \quad \la\in\si_\pm^{(1),\mathrm{u}},
\eeq
and drop some dependencies until the end of this lemma for notational simplicity.
Let $\la\in\inte(\si_\mp^{(1),\mathrm{u}})$, then $\psi_\pm,h_\pm\in\mathbb{R}$
and $\overline T_\mp=-(\overline W\,\rho_\mp)^{-1}$.
By (\ref{2.18}), {\bf (I)}, {\bf (b)}, and
(\ref{5.10}) we obtain for $\la\in\inte(\si_\mp^{(1)})$
\beq \label{5.29}
\left[\frac{\psi_+\psi_-}{W}\right]= \psi_\pm \left[\frac{\psi_\mp}{W}\right] = \rho_\mp\psi_\pm
\left(\psi_\mp T_\mp+ \overline\psi_\mp \overline T_\mp\right)=
\rho_\mp h_\pm \psi_\pm |T_\mp|^2.
\eeq
Since $\rho_\pm\in\mathbb{R}$ for $\la\in\inte(\si_\mp^{(1),\mathrm{u}})$, (\ref{2.18}) implies
$$
\left[\frac{h_\mp}{W}\right] = \rho_\pm \left[h_\mp T_\pm\right].
$$
The only non-real summand in (\ref{5.11}) is the
Cauchy-type integral. The Plemelj formula applied to this
integral gives
$$
\left[h_\mp T_\pm\right]= -
\rho_\mp\psi_\pm |T_\mp|^2 W(\psi_q^\pm,\breve\psi_q^\pm)=
\rho_\mp \psi_\pm|T_\mp|^2 \frac{1}{\rho_\pm},
$$
and by (\ref{5.29}) we get
\beq\label{5.301}
\left[\frac{h_+h_-}{W}\right]=\left[\frac{\psi_+\psi_-}{W}\right]
= \rho_\mp \psi_\pm h_\pm |T_\mp|^2,\quad \la\in\inte(\si_\mp^{(1)}).
\eeq
Since $\tilde W\neq 0$ for $\la\in\inte(\si_\mp^{(1)})$, the function
$$
\rho_\mp \psi_\pm h_\pm |T_\mp|^2= - \frac{\delta_\mp^2}{\rho_\mp}
\frac{\tilde\psi_\pm \tilde h_\pm}{|\tilde W|^2}
$$
is bounded on the set under consideration. Finally,
(\ref{5.301}) and (\ref{5.28}) imply (\ref{5.26}).
(ii). Now we prove that the function $G(z,n)$ has removable
singularities at the points $\pa\si_-\cup\pa\si_+\cup\si_d$. We divide
this set into four subsets
\beq \label{5.32}
\Omega_1^\pm=\pa\si^{(2)}\cap\inte(\si_\mp), \quad
\Omega_2=\pa\si^{(2)}\cap\pa\si, \quad \Omega_3^\pm=\pa\si_\pm^{(1)}\cap\pa\si_\pm, \quad
\Omega_4=\si_d. \eeq
Since all singularities of $G$ are at most isolated poles, it is
sufficient to show that
\beq \label{5.35}
G(z)=o\big((z - E)^{-1}\big)
\eeq
from some direction in the complex plane.
$\Omega_1$: Consider $E \in \Omega_1^+$ (the case $E \in \Omega_1^-$ being
completely analogous). We will study $\lim_{\la \rightarrow E}G(\la,n)$ as $\la \in \inte(\si^{(2)})$
using \eqref{5.22} with the ``$-$'' sign. Note that $\psi_-=O(1)$, $\rho_-=O(1)$, and $\hat W(E)\neq 0$.
Moreover, we obtain from Lemma~\ref{lem2.1} respectively {\bf II} that
$$
\psi_+(\la) = \left\{ \begin{array}{cl} O(1), & E \notin \hat M_+,\\
O\left(\frac{1}{\sqrt{\la - E}}\right), & E \in \hat M_+, \end{array} \right.
\quad
\frac{1}{T_+(\la)} = \left\{ \begin{array}{cl} O\left(\frac{1}{\sqrt{\la - E}}\right),
& E \notin \hat M_+,\\
O(1), & E \in \hat M_+, \end{array} \right.
$$
which shows
$$
h_-(\la)=\frac{\ov{\psi_+(\la)}+R_+(\la)\psi_+(\la)}{T_+(\la)}=
O\left(\frac{1}{\sqrt{\la - E}}\right)
$$
for $\la \in \si^{(2)}$. Inserting this into \eqref{5.22} shows
$G(\la,n)=O\big(\frac{1}{\sqrt{\la - E}}\big)$
and finishes the case $E\in \Omega_1$.
$\Omega_2$: For $E \in \pa\si^{(2)}\cap\pa\si$, we use \eqref{5.22}
and take the limit $\la \rightarrow E$ from $\si^{(2)}$. First of all,
observe that
$$
\breve\de_-\left(R_-\psi_- +\ol\psi_-\right)=\left\{\begin{array}{ll}
O(1) & E\in \si_v,\\
o(1) & E\notin\si_v.\end{array}\right.
$$
The case $E\in\si_v$ is evident. If $E\notin \si_v$ then \eqref{new3} and \eqref{P.1}
yield
$$\breve\de_-\left(R_-\psi_- +\ol\psi_-\right)=
\left\{\begin{array}{cl} \breve\de_-\big((\psi_- - \ol\psi_-) +(R_- + 1)\psi_-\big)
, & \quad E\notin \hat M_-\\
\big(\breve\de_-(\psi_- + \ol\psi_-) +(R_- -
1)\breve\de_-\psi_-\big), & \quad E\in\hat
M_-\end{array}\right. =o(1).
$$
Therefore, both for virtual and non-virtual levels the estimate
\beq\label{new4}
\breve\de_-\left(R_-\psi_- +\ol\psi_-\right)\hat W=o(1),\quad E\in\pa\si_-,
\eeq
is valid. Inserting \eqref{5.10} into the summand $\ol\psi_+h_+\rho_+$ of
\eqref{5.22} (for the second summand we use an analogous approach) we obtain
(recall \eqref{defP})
\begin{align} \nn
\ol\psi_+h_+\rho_+ &=\ol\psi_+\rho_+ \rho_- (\ol \psi_- + R_-
\psi_-) W = \frac{\ol\psi_+\breve\de_+}{P_+P_-} \hat \de_+
\hat \de_- \breve\de_- (\ol \psi_- + R_- \psi_-) W\\ \label{new2}
&= \frac{\ol\psi_+\breve\de_+}{P_+P_-}
\breve\de_-\left(R_-\psi_- +\ol\psi_-\right)\hat W.
\end{align}
Combining the estimate
$$
\frac{\ol\psi_+\breve\de_+}{P_+P_-}=O\bigg(\frac{1}{\la -E}\bigg)
$$
with \eqref{new4} we have $G(z)=o\big((z-E)^{-1}\big)$ as desired.
$\Omega_3$: Suppose that $E \in \pa \si_-^{(1)}\cap\pa\si_-$ (the case $E
\in \pa \si_+^{(1)}\cap\pa\si_+ $ is again analogous). Now we
cannot use \eqref{5.22}, so we proceed directly from formula
\eqref{5.211} estimating the summands $\frac{\psi_+\psi_-}{W}$ and
$\frac{h_+h_-}{W}$ separately. We investigate the limit as
$\la\to E$ from the set $\inte(\si_-^{(1)})$.
By Lemma~\ref{lem2.1} and \eqref{estim} we have
\beq \label{5.53}
\frac{\psi_+\psi_-}{W}=\frac{\hat \psi_+\hat \psi_-}{\hat W} =
O\left(\frac{1}{\sqrt{\la - E}}\right),
\eeq
hence the first summand has the desired behavior. To estimate the second summand,
we split the function $h_-(\la,n)$ according to
\[
h_-(\la,n) =h_1(\la,n) +h_2(\la,n),
\]
where
\[
h_1(\la,n)=W_{q,n-1}^+(\zeta_-(\la,\cdot),
d_-(\la,n,\cdot)), \quad h_2(\la,n)=h_-(\la,n) - h_1(\la,n),
\]
\be \label{5.55}
d_-(\la,n,.):=\int_{\sig_-^{(1),u}}
\frac{|T_-(\xi)|^2 \psi_+(\xi,n) \psi_q^+(\xi,\cdot) } {\xi-\lam
}d\omega_-(\xi).
\ee
It follows from the proof of Lemma \ref{lem5.1}
that $h_2(\la)=O(\zeta_-(\la))$ for $\la\to E$. Recall that at the
point under consideration singularities
$E\in\{\mu_1^+, \dots, \mu_{g_+}^+\} \cup \hat M_-$ might occur (in the case
$\pa\si_-^{(1)}\cap\pa\si$ one can have $E\in M_+\cup\breve M_+$ and
in the case $\pa\si_-^{(1)}\cap\pa\si_+^{(1)}$ one can have
$E\in\hat M_+$). Introduce
\beq\label{new9}
\phi_q^+(z,n):=\breve\de_+(z)\breve\psi_q^+(z,n)
\eeq
and recall that \eqref{new7} implies
\beq\label{new8}
\phi_q^+(z,n) - \phi_q^+(E,n)=O(\sqrt{z - E}).
\eeq
Then (see \eqref{defP} and \eqref{0.63}) we have
\be \label{5.56}
\frac{h_+ \zeta_-}{W}=O\bigg(\frac{h_+\breve{\psi}_q^+}{W T_+}\bigg)=
O\bigg(\frac{h_+\hat\de_+\breve\de_+\breve{\psi}_q^+}{P_+}\bigg)=
O\bigg(\frac{h_+ \hat\de_+}{P_+}\bigg)\phi_q^+.
\ee
Now we
distinguish two cases: (a) $E\in \pa\si_-^{(1)}\cap\pa\si_+^{(1)}$
and (b) $E\in\pa\si_-^{(1)}\cap\pa\si$.
Case (a). By \eqref{5.10} and \eqref{new4} we have
\beq\label{new13}
\hat\de_+h_+=\frac{(R_-\psi_- +
\ol\psi_-)\hat\de_+}{T_-} = \frac{\hat W\breve\de_-(R_-\psi_- +
\ol\psi_-)}{P_-} =o\bigg(\frac{1}{\sqrt{\la - E}}\bigg),
\eeq
therefore
\be \label{5.80}
\frac{h_+(\la)\zeta_-(\la)}{W(\la)}=o\bigg(\frac{1}{\sqrt{\la -
E}}\bigg) \frac{\phi_q^+(\la)}{P_+(\la)}.
\ee
As a consequence
of $\frac{\phi_q^+}{P_+}=O\big(\frac{1}{\sqrt{\la - E}}\big)$ we
obtain
\be \label{5.82}
\frac{h_+h_2}{W}=o\bigg(\frac{1}{\la -E}\bigg),
\quad E\in\pa\si_-.
\ee
Next, we have to estimate
\beq\label{new14}
\frac{h_+h_1}{W}=W_{q,n-1}^+\Big(\frac{h_+\zeta_-}{W},d_-\Big).
\eeq
By \eqref{new8} we can represent \eqref{5.80} as
\be \label{5.801}
\frac{h_+(\la)\zeta_-(\la)}{W(\la)}= o\bigg(\frac{1}{\sqrt{\la - E}}\bigg)
\bigg(\frac{\bar{\psi}_q^+(E)}{\sqrt{\la - E}} + O(1)\bigg).
\ee
Then \eqref{new14} implies
\begin{align} \label{5.83}
\begin{split}
\frac{h_+(\la,n)h_1(\la,n)}{W(\la)}&=o\bigg(\frac{1}{\sqrt{\la - E}}\bigg)\bigg(O(d_-(\la,n)) +
O(d_-(\la,n-1))\\
&\quad +\frac{O\left(W_{q,n-1}^+\left(\phi_q^+(E),
d_-(\la)\right)\right)}{\sqrt{\la-E}}\bigg).
\end{split}
\end{align}
To estimate $d_-$ in the first two summands we distinguish between
the resonance case, $E\in\si_v$, and non-resonance, $E \notin\si_v$.
First let $E\notin \si_v$, that is, $\hat W(E)\neq 0$. From \eqref{5.13} and \eqref{5.131}
we see that the integrand is bounded as $\la\to E\notin\si_v$, then $d_-(\la)=O(1)$ by \cite{Mu}.
If $E\in\si_v$, then \eqref{estim} (see also \eqref{5.13}) yields
$$
|T_-(\xi)|^2\rho_-(\xi)
\psi_+(\xi,\cdot)
\psi_q^+(\xi,\cdot)=O\left(\frac{1}{\sqrt{\xi-E}}\right)
$$
and \cite[Eq. (29.8)]{Mu} implies
\be \label{5.62}
d_-(\la)=o\left(\frac{1}{\sqrt{\la - E}}\right).
\ee
For the estimate of the last summand in \eqref{5.83} we use \eqref{5.13} and \eqref{5.55} to
represent the integrand in $W_{q,n-1}^+\left(\breve \psi_q^+(E), d_-(\la)\right)$ as
\begin{align*}
&|T_-(\xi)|^2\rho_-(\xi) \psi_+(\xi,n)
W_{q,n-1}^+\left(\psi_q^+(\xi),
\phi_q^+(E)\right)\\
&\hspace{1cm} =O\bigg(\frac{\sqrt{\xi - E}} {|\hat
W(\xi)|^2}W_{q,n-1}^+\big(\hat\psi_q^+(\xi),
\phi_q^+(E)\big)\bigg).
\end{align*}
It follows from \eqref{new7} and \eqref{new9} that
$$
W_{q,n-1}^+(\hat\psi_q^+(\xi),\phi_q^+(E))=O\big(\sqrt{\xi -
E}\big),
$$
which implies together with \eqref{estim} the boundedness of the
integrand near $E$. Thus, \beq\label{new12}
W_{q,n-1}^+\left(\phi_q^+(E), d_-(\la)\right)=O(1), \eeq and
combining \eqref{5.82}, \eqref{5.83}, \eqref{new12}, and
\eqref{5.62} finishes case (a).
Case (b). Now we do not have estimate \eqref{new4} (cf.\ {\bf III}, {\bf (b)}) at our disposal,
but we can proceed as in \eqref{5.56}, \eqref{new13} since $P_+(E)\neq 0$ and arrive at
\beq\label{new16}
\frac{h_+ \zeta_-}{W}=O(h_+\hat\de_+)=O\bigg(\frac{\hat W\breve\de_-(R_-\psi_- +
\ol\psi_-)}{P_-}\bigg)=O\bigg(\frac{\hat W}{\sqrt{\la - E}}\bigg).
\eeq
This estimate is sufficient to conclude that \eqref{5.82} is valid in case (b) as well.
For $h_1$, we use the following estimate (cf. \eqref{5.62} and \eqref{new16}) instead of \eqref{new14}:
$$
\frac{h_+h_1}{W}=O\left(\frac{h_+\zeta_-}{W}\right)O\left(d_-\right)=
O\left(\frac{\hat W}{\sqrt{\la - E}}\right)o\left(\frac{1}{\sqrt{\la - E}}\right).
$$
Combining this with \eqref{5.82} finishes case (b).
$\Omega_4$: Finally we have to show that the singularities of $G(z,n)$ at the
points of the discrete spectrum are removable. Since
$\tilde W(z)$ has simple zeros at $z=\la_k$, it suffices by \eqref{5.25} to show that
\beq \label{5.71}
\tilde h_+(\la_k,n)\tilde h_-(\la_k,n) =
\tilde\psi_-(\la_k,n)\tilde\psi_+(\la_k,n).
\eeq
By Lemma~\ref{lem5.1}, the functions $\tilde h_\mp=\de_\mp h_\mp$
given in (\ref{5.11}) are continuous at the points $\breve M_\pm$. Since
$(\de_\mp T_\pm^{-1})(\la_k)=0$ and
$(\de_\mp T_\pm^{-1}\breve\psi_q^\pm)(\la_k)=0$, only the last
summand in (\ref{5.11}) is non-zero.
We compute the limit of this summand as $\la \rightarrow \la_k$ using (\ref{2.18}),
\beq \label{5.77}
\tilde h_\mp(\la_k) =-\ga_{\pm,k} \tilde\psi_\pm(\la_k) \frac{d\tilde W(\la_k)}{d\la},
\eeq
and apply (\ref{2.11}) to obtain (\ref{5.71}).
\end{proof}
The identity $G(z,n)\equiv0$ implies
\beq\label{new17}
\psi_+(z,n) \psi_-(z,n)- h_+(z,n)h_-(z,n) \equiv 0, \quad \forall n \in \Z.
\eeq
For $z \rightarrow \infty$ we obtain by (\ref{1.12}) and (\ref{Dop})
$$
\psi_+(z,n)\psi_-(z,n)=K_+(n,n)K_-(n,n)\vprod{j=0}{n-1}\frac{a_q^+(j)}{a_q^-(j)}(1+o(1)).
$$
Formulas \eqref{h infty} and \eqref{T infty} imply
$$
h_+(z,n)h_-(z,n)=\frac{1}{T_+(\infty)^2 K_+(n,n)K_-(n,n)}
\vprod{j=0}{n-1}\frac{a_q^-(j)}{a_q^+(j)}(1+o(1))
$$
and by \eqref{new17},
$$
K_+(n,n)K_-(n,n)\vprod{j=0}{n-1}\frac{a_q^+(j)}{a_q^-(j)}=\frac{1}{T_+(\infty)}.
$$
The value on the left hand side does not depend on $n$, so using \eqref{5.1} we conclude
\be\label{new18}
a_+(n) = a_-(n) \equiv a(n), \quad \forall n \in \Z.
\ee
It remains to prove $b_+(n)=b_-(n)$.
If we eliminate the reflection coefficient $R_\pm$ from \eqref{5.10} at $n$ and
\eqref{4.26} at $n+1$ we obtain
\begin{align}
\begin{split}
&G_1(\la,n):=\frac{\psi_+(\lam,n) \psi_-(\lam,n+1)
-h_+(\lam,n+1) h_-(\lam,n)}{W(\lam)}\\
&= \rho_+(\la)
\big(\overline{h_\pm(\lam,n+1)} \psi_\pm(\lam,n)
- \overline{\psi_\pm(\lam,n)} h_\pm(\lam,n+1)\big), \quad \la\in\si^{(2),\mathrm{u,l}}.
\end{split}
\end{align}
Proceeding as for $G(\lam,n)$ in Lemma~\ref{lem5.2} we can show that that the function
$G_1(z,n)$ is holomorphic in $\C$. From \eqref{h infty}, \eqref{Dop}, \eqref{T infty},
\eqref{1.12}, \eqref{new18}, and the Liouville theorem we conclude that
$$
\frac{\psi_+(z,n) \psi_-(z,n+1)-h_+(z,n+1) h_-(z,n)}{W(z)}= -1/a(n).
$$
We compute the asymptotics of
\[
\bar W(z,n) := a(n) \left(\psi_+(z,n) \psi_-(z,n+1) - h_+(z,n+1) h_-(z,n) \right)\\
= - W(z)
\]
as $z \rightarrow \infty$ and obtain (compare (\ref{B4jost}))
\be
0= \bar W(z,n) - \bar W(z,n-1) = (b_+(n) - b_-(n))K_+(0,0)K_-(0,0).
\ee
This implies in particular $b_+(n) = b_-(n) \equiv b(n)$, hence the proof of Theorem~\ref{theor2} is finished.
{\bf Acknowledgments.}
I.E. and J.M. gratefully acknowledge the extraordinary hospitality of the
Faculty of Mathematics of the University of Vienna during their stay in 2007,
where parts of this paper were written.
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\end{document}
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\bibitem{Nof_etal2012} Nof, D., Zharkov, V., Arruda, W., Pichevin, T., Van Gorder, S., \& Paldor, N. (2012). Comments on {\textquotedblleft}On the Steadiness of Separating Meandering Currents{\textquotedblright}. \textit{J. Phys. Oceanogr.}, \textit{42}(8), 1366--1370.
\end{thebibliography}
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% A Sample Thesis for the University of Calgary
% =============================================
% This is a sample LaTeX document to build a University of Calgary
% graduate thesis according to the guidelines of the Faculty of
% Graduate Studies, available here:
% https://grad.ucalgary.ca/current-students/thesis-based-students/thesis/building-thesis
% To use this sample for your own thesis, rename this file, make any
% changes necessary, then add the content of your thesis to the
% included files frontmatter.tex, chapter1.tex, etc.
% First, we load the UCalgary Memoir Thesis class ucalgmthesis,
% available at https://github.com/rzach/ucalgmthesis
% This class in turn loads the memoir class for book design. All its
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% We'll need some colored links, so we load xcolor and hyperref. But
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% For black (hidden) links, replace the above with:
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% Note that per UCalgary's thesis guidelines, links must be blue or
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% If you prefer hyperref's boxes around links (which don't print), you
% can also change their color. With boxes around links, you probably
% don't want everything in the table of contents to be a link, so we
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% following command instead:
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% default, but it's nice to also have chapter and section numbers for
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% can take these out or use your own favorite theorem package.
\usepackage{amsmath,amsthm}
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\theoremstyle{definition}
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% For author-year references, you probably want to use natbib with a
% bibliography style appropriate for your discipline; or check out
% biblatex!
\usepackage[round]{natbib}
\bibliographystyle{plainnat}
% The blindtext package produces the ``lorem ipsum''
% texts in this sample and can safely be removed.
\usepackage{blindtext}
% Now we put in the information for the thesis title page.
% Full Name
\author{Jane Mary Doe}
% Full Title
\title{An Important Contribution to the Literature}
% Official name of the degree
\degree{Doctor of Philosophy}
% The full name of the graduate program (not the department!). For
% interdisciplinary degrees, the home graduate program is listed
% first, followed by the word "and," then the other graduate program
% is listed
\prog{Graduate Program in Philosophy}
% The month (for the final version: when you file, not when you defended)
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% The year
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% Tell hyperref to put author and title into the PDF metadata
\hypersetup{pdfinfo={Title={\thetitle},Author={\theauthor}}}
% If you want memoir to produce endnotes, turn them on here
\makepagenote
% Often you only want to output a single chapter so you can send it to
% your supervisor. Use includeonly and make sure everything you don't
% always want compiled to PDF is include'd from a separate file. For
% instance, to produce a PDF only of chapter 1, endnotes and
% bibliography, say
% \includeonly{chapter1,backmatter}
% To compile only the title page, which you need when submitting your
% thesis, say
% \includeonly{titlepage}
% and then copy the resulting PDF to a separate file.
% Memoir by default numbers document divisions from sections up. If
% you want subsections numbered as well, uncomment the following line:
% \maxsecnumdepth{subsection}
\begin{document}
\frontmatter
% titlepage.tex just makes the titlepage; it's in its own file so you
% can typeset it alone using includeonly.
\include{titlepage}
% frontmatter.tex contains the abstract, preface, acknowledgments, and
% the commands to produce the table of contents, list of tables, etc.
\include{frontmatter}
% The main matter of the thesis contains the actual content, separated
% into chapters.
\mainmatter
\include{chapter1}
\include{chapter2}
% The back matter includes commands to produce endnotes, index,
% glossary, bibliography, and the like.
\backmatter
\include{backmatter}
% The appendix contains material that would clutter up the main text,
% such as program code, survey instruments, or interview transcripts.
% Remove it if you don't have an appendix.
\appendix
\include{appendix}
\end{document}
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revision and extension of 04-24
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Determinantal point process, fermion point process,
Gibbs point process, Papangelou intensity, stochastic domination,
percolation
---------------0409141008843
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\pagestyle{myheadings} \markboth{Georgii and Yoo}{Determinantal point
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\begin{document}
\title{Conditional Intensity and Gibbsianness\\ of Determinantal
Point Processes}
\author{ Hans-Otto Georgii\footnotemark[1] \ and Hyun Jae
Yoo\footnotemark[2] }
\date{}
%\subjclass{Primary: 60K35; Secondary: 82B43 }
\maketitle
\begin{abstract}
The Papangelou intensities of determinantal (or fermion) point
processes are investigated. These exhibit a monotonicity property
expressing the repulsive nature of the interaction, and satisfy a
bound implying stochastic domination by a Poisson point process.
We also show that determinantal point processes satisfy the
so-called condition $(\S_{\l})$ which is a general form of
Gibbsianness. Under a continuity assumption, the Gibbsian
conditional probabilities can be identified explicitly.
\end{abstract}
\noindent
{\bf Keywords}. {Determinantal point process, fermion point process,
Gibbs point process, Papangelou intensity, stochastic domination,
percolation}\\
{\bf Running head}. {Determinantal point processes}
\footnotetext[1]{Mathematisches Institut der Universit\"{a}t
M\"{u}nchen, Theresienstra{\ss}e 39, 80333 M\"{u}nchen, Germany.
E-mail: [email protected]}
\footnotetext[2]{University College , Yonsei University, 134
Shinchon-dong, Seodaemoon-gu, Seoul 120-749, Korea. E-mail:
[email protected]}
%\today
\section{Introduction}
The aim of this paper is to investigate the dependence structure
of determinantal (also called fermion) point processes,
abbreviated DPP's. These are point processes on a locally compact
metric space $\SP$ with a particular repulsive dependence
structure induced by the fact that their correlation functions are
given by suitable determinants. More explicitly, the correlation
function $\r(\a)$ at a finite configuration $\a$ is the
determinant of the matrix obtained by evaluating a positive
definite integral kernel at the points of $\a$; see Subsection
\ref{subsec:DPP} for details.
Since their invention by Macchi \cite{M}, DPP's have attracted
much interest from various viewpoints. Spohn \cite{Sp1, Sp2}
investigated the dynamics of the so-called Dyson's model, a model
of interacting Brownian particles on the real line with pair force
$1/x$, or pair interaction $-\log x$. Its invariant measure is a
typical DPP having the sine kernel as defining integral kernel.
Rather recently, the theory of DPP's has been developed
much further. Soshnikov \cite{So} established the full existence
theorem for DPP's, discussed many examples occurring in various
fields of physics and mathematics, and derived various further
results for DPP's with translation-invariant kernels, including
mixing properties and central limit theorems.
Shirai and
Takahashi \cite{ST1} also dealt with the existence theorem and
extended the theory to some generalized DPP's including
Boson processes. They also established some particular properties
such as limit theorems, ergodic properties, and the Gibbs property
of the corresponding discrete model \cite{ST2}. In a series of
papers, Borodin and Olshanski studied the DPP's appearing in the
representation of the infinite symmetric group, see \cite{BO} and
the references therein. Lyons and Steif \cite{L, LS} investigated
the ergodic and stochastic domination properties of DPP's on
discrete lattices. The Glauber dynamics leaving some DPP's
invariant was studied by Shirai and the second author \cite{SY}.
In this paper we ask for the dependence properties of DPP's. Our leading
questions are the following:
\begin{itemize}
\item[--]What can be said about the repulsive nature of the interaction?
\item[--]When are determinantal point processes Gibbsian?
\end{itemize}
Unfortunately, to answer these questions we need to exclude the
interesting case when $1$ belongs to the spectrum of the
underlying integral operator, and in general we can only establish
a weak form of Gibbsianness. To prove full Gibbsianness we need to
impose a natural though restrictive continuity assumption. A key
quantity we consider is the conditional intensity in the sense of
Papangelou, which is a function $c(x,\x)$ of points $x\in\SP$ and
configurations $\x$. Its intuitive meaning is that, for a suitable
reference measure $\l$ on $\SP$, $c(x,\x)\l(dx)$ is the
conditional probability of having a particle in $dx$ when the
configuration $\x$ is given. We will show that, locally on
relatively compact regions, Papangelou intensities always exist,
are given by ratios of determinants, and are decreasing functions
of $\x$ (Theorem~\ref{thm:PapMon}). This monotonicity is a natural
expression of the repulsiveness of DPP's. In particular, it
implies negative correlations of local vacuum events stating that
some local regions contain no particles
(Corollary~\ref{cor:Monoton}). We also show that the local
Papangelou intensities are bounded from above. This implies
stochastic domination of DPP's by Poisson point processes and, for
$\SP=\R^d$, the absence of percolation in the associated Boolean
model when the underlying integral kernel is small enough
(Corollaries~\ref{cor:PoissonDom} and \ref{cor:NoPerc}).
Next we will show that the Papangelou
intensities of DPP's exist not only locally but also globally
(Theorem~\ref{thm:Sigma}). This means that all DPP's are Gibbsian
in a general sense, in that one can write down natural versions of
their conditional distributions in local regions when the
configuration outside of this region is fixed, and these
conditional distributions are absolutely continuous with respect
to the Poisson point process. It is a more difficult question to
decide whether the associated conditional Hamiltonians can be
expressed in terms of the underlying integral kernel in
the natural way one expects. Here we only have a partial
result, stating that this holds whenever these natural
versions are continuous almost everywhere (Theorem~\ref{thm:Gibbs}).
The last condition holds in particular when $\SP=\R^d$
and the associated interaction kernel has finite range and is
continuous and small enough (Proposition~\ref{prop:a.e.continuity}).
In the next section we set up the stage. That is, in
Subsection~\ref{subsec:DPP} we recall the definition of DPP's
together with some basic facts, while Subsection~\ref{subsec:PI}
contains a discussion of the Papangelou intensity and its
significance. Our results are stated in Section~\ref{sec:results}.
The proofs follow in Section~\ref{sec:proofs}. In the Appendix we
collect some useful facts and discuss in particular the question
of how to make a proper choice of integral kernels.
\vspace{0cm plus 4cm}
\section{Preliminaries}
\subsection{Determinantal point processes}
\label{subsec:DPP}
In this section we describe the general setting and recall the
definition of determinantal point processes (DPP). For a more
complete account of DPP's we refer to the survey \cite{So} and the
articles \cite{L, LS, ST1, ST2}.
Let $E$ be any locally compact metric space serving as the state
space of the points, $\cB$ the Borel $\s$-algebra on $\SP$, and
$\cB_0$ the system of all \emph{relatively compact} Borel sets in
$\SP$. Also, let $\l$ be a diffuse, locally finite reference
measure on $(\SP,\cB)$. The standard case is when $\SP=\R^d$ and
$\l$ is Lebesgue measure.
Let $\cX$ be the space of all locally finite subsets (configurations) in
$\SP$, i.e.,
\[
\cX:=\{\x \sub \SP:| \x \cap \L|<\infty \text{ for all
}\L \in \cB_0\}\,,
\]
where $|A|$ denotes the cardinality of a set $A$. Later on, we
will exploit the fact that $\cX$ is partially ordered by
inclusion. Given any $\L \sub \SP$, we write $\cX_\L:=\{\x \in\cX:
\x \sub\L\}$ for the set of all configurations in $\L$, and
$r_\L:\x \to\x_\L:= \x \cap\L$ for the corresponding projection
from $\cX$ onto $\cX_\L$. Also let $N_\L:\x \to | \x \cap \L|$ be
the associated counting variable on $\cX$, and $\cF_\L$ be the
smallest $\s$-algebra on $\cX$ such that $N_\D$ is measurable for
all relatively compact Borel sets $\D \sub \L$. We write $\cF$ for
$\cF_{\SP}$. Each configuration $\x \in \cX$ can be identified
with the integer-valued Radon measure $\sum_{x\in \x }\d_x$ on
the Borel $\s$-algebra on $\SP$. The vague topology for the latter
then induces a topology on $\cX$ turning $\cX$ into a Polish
space. It is well-known that $\cF$ is the associated Borel
$\s$-algebra \cite{DV, Sh}. A \emph{point process} is a
probability measure $\m$ on $(\cX,\cF)$. We write $\m_\L:= \m\circ
r_\L^{-1}$ for its marginal on $\cX_\L$.
Next let $\cX_0=\{\a\in\cX: |\a|<\infty\}$ be the set of all
\emph{finite} configurations in $\SP$. $\cX_0$ is equipped with
the trace $\s$-algebra $\cF_0=\cF|_{ \cX_0}$ and the
\emph{$\l$-sample measure} $L$ defined by the identity
\begin{equation}\label{eq:L}
\int_{\cX_0} f(\a)\,L(d\a) =
\sum_{m=0}^{\infty}\frac{1}{m!}\int_{\SP^m} f(\{x_1,\ldots,
x_m\})\, \l(dx_1)\cdots \l(dx_m)
\end{equation}
for any measurable function $f:\cX_0\to\R_+$. For any $\L\subset\SP$ we
let $L_\L(d\a) = 1_{\{\a\subset\L\}}L(d\a)$ be the restriction of $L$ to
$\cX_\L$. Here we use the notation $1_A$ for the indicator function of
a set $A$.
Recall that a point process $\m$ is said to have the
\emph{correlation function} $\r:\cX_0\to \R_+$ if $\r$ is
measurable and satisfies
\begin{equation}\label{eq:corrfct}
\int_\cX \ \sum_{ \a\in \cX_0:\, \a \sub \x} u( \a) \ \m(d \x )=
\int_{\cX_0} u( \a) \r( \a)\,L(d \a)
\end{equation}
for any measurable $u:\cX_0\to \R_+$. (For a general account of
the interrelationship $\m\leftrightarrow \r$ between point
processes and correlation functions we refer to the recent paper
\cite{KK}.) The \emph{Poisson point process $\p^z$ with (locally
integrable) intensity function $z:\SP\to [0,\infty[$} is the
unique point process having correlation function $\r^z(\a
)=\prod_{x\in \a}z(x)$. Equivalently, $\p^z$ is the unique point
process such that, for each $\L \in\cB_0$, the projection
$\p^z_\L$ has the Radon-Nikodym density $\x\to e^{-\int_\L
z\,d\l}\prod_{x\in \x}z(x)$ relative to $L_\L$. The characteristic
feature of the determinantal point processes to be considered here
is that their correlation function is given by suitable
determinants. Given a function $K:\SP\times\SP \to\C$, we write
\begin{equation}\label{eq:Kmatrix}
K(\a,\a)=\big(K(x,y)\big)_{x,y\in\a}
\end{equation}
for the matrix obtained by evaluating $K$ at a finite configuration
$\a\in\cX_0$.
%: Def DPP
\begin{define}\label{def:DPP} Let $K(x,y)$, $x,y\in \SP$, be the
integral kernel of a positive\footnote{We use the terms
``positive operator'' and ``positive definite
matrix'' always in the weak sense, in that $0$ may belong to the
spectrum.} Hermitian integral operator $K$ on $L^2(\SP,\l)$. A
point process $\m$ with correlation function
\[
\r(\a)=\det K(\a,\a)
\]
is called a \emph{determinantal point process} (abbreviated DPP)
with \emph{correlation kernel} $K$.
\end{define}
The DPP's defined above are also known as \emph{fermion point
processes}; see \cite{ST1} for the boson case where the
determinant is replaced by the permanent, and more general
determinantal processes. In fact, there exist interesting examples
of DPP's for non-Hermitian kernels such as the discrete Bessel
kernel; see \cite{BOO}, for example. In this paper, however, we
confine ourselves to the Hermitian case. On the technical side, we
note that the matrices \eqref{eq:Kmatrix} involve the values of
the integral kernel $K(x,y)$ not only for $\l^{\otimes 2}$-almost
all $(x,y)\in\SP^2$ but also on the diagonal of $\SP^2$, which is
a $\l^{\otimes 2}$-nullset because $\l$ is diffuse. So one needs
to make a proper choice of $K(x,y)$ which is \emph{positive
definite a.e.}, in that $K(\a,\a)$ is positive definite for
$L$-almost all $\a\in \cX_0$ (implying that the correlation
function $\r$ is indeed nonnegative $L$-a.e.). In Lemma
\ref{lem:loc_trace_formula} will be explained how this can be done
.
Concerning the existence of DPP's, we state the following theorem
from \cite{So}, see also \cite{M, DV, ST1}. $I$ stands for the
identity operator, and the ordering $S\le T$ between operators
means that $T-S$ is a positive operator.
%
\begin{thm}[Macchi, Soshnikov]\label{thm:frpf}
A Hermitian locally trace class operator $K$ on $L^2(\SP,\l)$
defines a DPP $\m$ if and only if $0\le K\le I$, and in this case
$\m$ is unique.
\end{thm}
%
Any DPP $\m$ is locally
absolutely continuous with respect to the $\l$-sample measure $L$
and admits explicit expressions for the local densities. To be
specific, for each $\L \in \cB_0$ let $P_\L: L^2(\SP,\l)\to
L^2(\L,\l_\L)$ be the projection operator and $K_\L:=P_\L KP_\L$
the restriction of $K$ onto $L^2(\L,\l_\L)$. That is, $K_\L$
admits the kernel $K_\L(x,y)=1_\L(x)K(x,y)1_\L(y)$. Suppose that
$\m$ is the unique DPP for an operator $K$ as in Theorem
\ref{thm:frpf}. Then the density function of $\m_\L$ with respect
to $L_\L$, the so-called Janossy density \cite{DV} of $\m$, is
given by \cite{ST1, So}
\begin{equation}\label{eq:density_function}
\s_\L(\x)=\det(I-K_\L)\det J_{[\L]}(\x,\x), \quad \x\in\cX_\L;
\end{equation}
here $J_{[\L]}:=K_\L(I-K_\L)^{-1}$, and the normalization
constant $\det(I-K_\L)$ is to be understood as a Fredholm
determinant \cite{Si}. A priori, this formula requires that $0\le
K_\L<I$. However, one can show that \eqref{eq:density_function}
still makes sense when $\|K_\L\|=1$; see \cite[p.~935]{So}. In view
of \eqref{eq:density_function}, we call $J_{[\L]}$ the local
interaction operator and its kernel the local interaction kernel
for $\L$. Again, Lemma \ref{lem:positive_kernel} allows to choose
the kernel $J_{[\L]}$ in such a way that all matrices
$J_{[\L]}(\x,\x)$ are positive definite. Finally, we note that the
correlation function $\r$ can be recovered from the local
densities $(\s_\L)$ by
\[
\r(\a)=\int_{\cX_\L}\s_{\L}(\a\x)\,L_\L(d\x)
\]
for $\a\in \cX_\L$, where $\a\x$ is shorthand for $\a\cup\x$.
\subsection{Papangelou intensities}
\label{subsec:PI}
Here we summarize some facts concerning the reduced (compound)
Campbell measure of a point process $\m$ as well as its Papangelou
intensity which describes the local dependence of particles.
%
\begin{define}\label{def:redCampb}
(a) The \emph{reduced} (or modified) \emph{Campbell measure} of a
point process $\m$ is the measure $\CM$ on the product space
$(\SP\times\cX, \cB\otimes\cF)$ defined by
\[
\CM(A) = \int \m(d\x ) \sum_{x\in \x } 1_A(x, \x \sm x)\,, \quad A\in
\cB\otimes\cF,
\]
where $\x \sm x:=\x \sm\{ x\}$.
(b) The \emph{reduced compound Campbell measure} of $\m$ is the measure $\CCM$
on the product space $(\cX_0\times\cX, \cF_0\otimes\cF)$ satisfying
\[
\CCM(B) = \int \m(d\x ) \sum_{\a\in\cX_0:\,\a\subset \x } 1_B(\a, \x \sm \a)\,,
\quad B\in \cF_0\otimes\cF.
\]
\end{define}
%
It is well-known and easy to check that the reduced Campbell
measure of the Poisson point process $\p^z$ is given by
$\CM[\p^z](dx,d\x)=z(x) \l(dx)\p^z(d\x)$, and a classical result
of Mecke \cite{Mecke} states that $\p^z$ is the only point process
with this property. This fact suggests the following concept.
\begin{define}
A point process $\m$ is said to satisfy \emph{condition} $(\S_\l)$
if $\CM \ll \l\otimes\m$. Any Radon-Nikodym density $c$ of $\CM$
relative to $\l\otimes\m$ is then called (a version of) the
\emph{Papangelou (conditional) intensity} (abbreviated PI) of
$\m$.
\end{define}
%
More explicitly, $c$ is a PI of $\m$ if
\begin{equation}\label{eq:Papint}
\int \m(d\x ) \sum_{x\in \x } f(x, \x \sm x) = \int \l(dx) \int
\m(d\x )\, c(x,\x ) f(x,\x )
\end{equation}
for all measurable functions $f:\SP\times\cX \to \R_+$.
Another way of stating this is that the intensity
measure of $\m$ has a density $\r_1$ relative to $\l$, and the
\emph{reduced Palm distribution $\m^x$ of $\m$ at
$x$} (which is defined by the desintegration formula $\CM(dx,d\x) = \l(dx)\r_1(x)\,\m^x(d\x)$) is absolutely
continuous with respect to $\m$ with density $c(x,\cdot)/\r_1(x)$ for $\l$-a.a. $x\in\{\r_1>0\}$. Intuitively,
$c(x,\x )\l(dx)$ is the conditional probability for a particle in the differential region $dx$ given the
configuration $\x $. Also, if
\[
Gh(\x ) = \int \l(dx)\ c(x,\x ) \big[h(\x \cup x)-h(\x )\big] +
\sum_{x\in \x }\big[h(\x \sm x)-h(\x )\big]
\]
is the formal generator of a birth-and-death process with
birth rate $c(x,\x )\l(dx)$ for a particle in $dx$ and
death rate $1$ for each particle, \eqref{eq:Papint} is
equivalent to the reversibility equation $\int g\, Gh\,
d\m = \int h\, Gg\, d\m$; to see this it is sufficient to set
$f(x,\x )=g(\x )h(\x \cup x)$.
The following remark lists some further consequences of condition $(\S_\l)$.
In particular, it shows that $(\S_\l)$ processes are Gibbsian in a
general sense.
%: Remark
\begin{rem}\label{rem:MWM}
For any $\m$ satisfying condition $(\S_\l)$ the following conclusions hold.
\smallskip
(a) The reduced compound Campbell measure $\CCM$ is absolutely
continuous with respect to $L\otimes\mu$ with a Radon-Nikodym density
$\hat c$ satisfying $\hat c(\emptyset,\xi) =1$ and
\begin{equation}\label{eq:compPapdens}
\hat c(\a,\x ) = c(x_1,\x) \prod_{i=2}^n
c(x_i,x_1 \ldots x_{i-1}\x) \quad\text{when }\a=\{x_1,\ldots, x_n\};
\end{equation}
here $x_1 \ldots x_{i-1}\x = \{x_1, \ldots, x_{i-1}\}\cup \x$. In
particular, the right-hand side of \eqref{eq:compPapdens} is almost
surely symmetric in $x_1,\ldots, x_n$. $\hat c$ is called the
\emph{compound Papangelou intensity} (CPI). Explicitly, the relation
$\hat c=d\CCM/d( L\otimes\mu)$ means that
\begin{equation}\label{eq:compPapint}
\int \m(d\x ) \sum_{\a\in\cX_0:\,\a\subset \x } f(\a, \x \sm \a) =
\int L(d\a) \int \m(d\x )\, \hat c(\a,\x )\, f(\a,\x )
\end{equation}
for any measurable $f:\cX_0\times\cX \to \R_+$, and follows easily from
\eqref{eq:Papint} by induction on $|\a|$.
\smallskip
(b) For an $f$ depending only on $\a$, a comparison of
\eqref{eq:compPapint} and \eqref{eq:corrfct} shows that the correlation
function and the CPI of $\m$ are related to each other by
\[
\r(\a) = \int \m(d\x)\, \hat c(\a,\x)\quad\text{for $L$-almost all $\a$.}
\]
\smallskip
(c) Let $\L\in\cB_0$. Applying \eqref{eq:compPapint} to $f(\a,\x)=
g(\a)h(\x) 1_{\{\a\subset\L, \,N_\L(\x)=0\}}$ for any
$\cF_\L$-measurable $g:\cX\to\R_+$ and $\cF_{\L^c}$-measurable
$h:\cX\to\R_+$ and taking conditional expectations we find
\[
\begin{split}
&\int \E_\m(g|\cF_{\L^c})\,h\, d\m = \int g h\, d\m
= \int f \,d\CCM\\
&=\int \m(d\x)\,h(\x)\ \m(N_\L{=}0\,|\,\cF_{\L^c})(\x) \int L_\L(d\a)\,
g(\a)\,\hat c(\a,\x_{\L^c})
\end{split}
\]
Hence
\begin{equation}\label{eq:condexpect}
\E_\m(g|\cF_{\L^c})(\x) = \m(N_\L{=}0\,|\,\cF_{\L^c})(\x)\ \int g\; \hat
c(\cdot, \x_{\L^c}) \,dL_\L
\end{equation}
for $\m$-almost all $\x$ and any $\cF_\L$-measurable $g$. In particular,
for $g\equiv 1$ we find that $\m(N_\L{=}0\,|\,\cF_{\L^c})>0$ almost surely for
each $\L\in\cB_0$, a property introduced by Papangelou \cite{Papangelou}
as condition $(\S)$, and by Kozlov \cite{Kozlov} as the condition of
non-degenerate vacuum.
\end{rem}
The observations in the preceding remark are due to Matthes, Warmuth and
Mecke \cite[Section 3]{MWM} and give one part of their theorem below;
cf. also \cite[Theorem 2$'$\,]{NZ}.
\begin{thm}[Matthes, Warmuth and Mecke]\label{thm:MWM}
A point process $\m$ satisfies condition $(\S_\l)$ with PI $c$ if and
only if, for each $\L\in\cB_0$, $\m$ is absolutely continuous relative
to $L_\L\otimes\m_{\L^c}$ with a density $\g_\L$ satisfying
$\g_\L(x\x)=0$ whenever $\g_\L(\x)=0$ and $x\in\L\sm\x$. In this case,
for $L_\L\otimes\m_{\L^c}$-almost all $\x \in\cX$ we have
\begin{equation}\label{eq:condPapdens}
\g_\L(\x ) = Z_\L(\x _{\L^c})^{-1}\; \hat c(\x_\L,\x _{\L^c})
\end{equation}
with $0< Z_\L(\x _{\L^c}) = \int \hat c(\cdot,\x _{\L^c})\,dL_\L
<\infty$, and $c(x,\x ) = \g_\L(x\x )/\g_\L(\x )$ for
$\l\otimes\m$-almost all $(x,\x )\in \L\times\cX$.
\end{thm}
%
More explicitly, Equation \eqref{eq:condPapdens} means that for
each bounded measurable function $f:\cX\to\R$, the conditional
expectation $\E_\m(f\,|\,\cF_{\L^c})(\x )$ has the version
\begin{equation}\label{eq:condProb}
G_\L(f\,|\,\x ) := Z_\L(\x _{\L^c})^{-1} \int f(\a\x _{\L^c})\, \hat
c(\a,\x _{\L^c})
L_\L(d\a).
\end{equation}
\begin{rem}\label{rem:locMWM}
Theorem \ref{thm:MWM} has a counterpart for the restriction of a
point process $\m$ to a local region $\L\in\cB_0$. Let $\l_\L$
be the restriction of $\l$ to the $\s$-algebra $ \cB_\L$ of Borel
subsets of $\L$. Then $\m_\L$ satisfies condition $(\S_{\l_\L})$
with a PI $c_\L$ if and only if $\mu_\L$ is absolutely continuous
with respect to $L_\L$ with a density $\s_\L$ having an increasing
zero-set $\{\s_\L=0\}$. In this case, $\s_\L =
\s_\L(\emptyset)\,\hat c_\L(\cdot,\emptyset)$ $L_\L$-almost
everywhere, and $c_\L(x,\xi) = \s_\L(x\x)/\s_\L(\x)$ for
$\l_\L\otimes\m_\L$ almost all $(x,\x)\in \L\times\cX_\L$. This
follows from the above by noting that $\m_\L$, regarded as a
measure on $(\cX, \cF)$ supported on $\{N_{\L^c}=0\}$, is trivial
on $\cF_{\L^c}$; cf. also \cite[Proposition 3.1]{GK}.
\end{rem}
\section{Results}
\label{sec:results}
Our results on DPP's are based on the following standing
assumption on the underlying correlation operator $K$.
\begin{ass}\label{hyp:H} $K$ is a Hermitian integral
operator on $L^2(\SP,\l)$ such that
\begin{enumerate}
\item $K$ is of local trace class, and \item $\text{spec\,}K\sub[0,1[\,$;
i.e., $0\le K\le I$ in the operator ordering, and $\|K\|<1$.
\end{enumerate}
We write $\m$ for the unique DPP with correlation kernel $K$.
\end{ass}
Let us comment on these assumptions. First, $K$ is
necessarily a Carleman operator~\cite{HS}, in that its
integral kernel satisfies $K(x,\cdot)\in L^2(\SP,\l)$ for
$\l$-almost all $x\in E$; this will be shown in Lemma
\ref{lem:loc_trace_formula}(b). Secondly, it follows from (b)
that $J:=K(I-K)^{-1}$ exists as a bounded
operator; we call $J$ the \emph{(global) interaction operator}.
Since the Carleman operators form a right ideal
in the space of bounded operators on $L^2(\SP,\l)$
\cite[Theorem 11.6]{HS}, hypothesis (H) ensures that $J$ is
also a Carleman operator. Moreover, since $K$ is supposed
to be of local trace class, so is $J$; for, if $\L\in
\cB_0$ then $J_\L:=P_\L J P_\L\le (1-\|K\|)^{-1} K_\L$,
whence $\Tr J_\L\le (1-\|K\|)^{-1}\Tr K_\L<\infty$.
Assumption (a) implies further that, for each $\L\in \cB_0$,
the local operators $K_\L$ and $J_\L$ as well as
the local interaction operator $J_{[\L]}:=K_\L(I-K_\L)^{-1}$
satisfy the conditions of Lemma~\ref{lem:positive_kernel}.
So, their kernel functions can and will be chosen in such a
way that all associated matrices $K_\L(\a,\a)$, $J_\L(\a,\a)$
and $J_{[\L]}(\a,\a)$ defined in \eqref{eq:Kmatrix} are
positive definite. Finally, we note that necessarily
$0\in \text{spec\,}K$ because $K_\L$, being trace class, is
compact and thus has eigenvalues tending to zero.
Our first result describes the local behavior of DPP's under (H).
%: Thm1
\begin{thm}\label{thm:PapMon}
For each $\L\in\cB_0$,
$\m_\L$ satisfies condition $(\S_{\l_\L})$, and a version
of its CPI $\,\hat c_\L$ is given by
\begin{equation}\label{eq:cLformula}
\hat c_\L(\a,\x)= \det J_{[\L]}(\a\x,\a\x)/\det J_{[\L]}(\x,\x)\,;
\end{equation}
the ratio is defined to be zero whenever the denominator vanishes.
This version also satisfies the inequalities
\begin{equation}\label{eq:cLinequality}
\hat c_\L(\a,\x)\ge\hat c_\L(\a,\eta)\quad\text{and}\quad 0\le \hat c_\L(\a,\x)\le
\det J_{[\L]}(\a,\a) \le \prod_{x\in\a}J_{[\L]}(x,x)
\end{equation}
whenever $\x\sub\eta$ and $\a\sub\L\sm\eta$.
\end{thm}
Here are some consequences of the theorem. Let us look first at
the local CPI $\,\hat c_\L$ in \eqref{eq:cLformula}.
Let $\L,\D\in\cB_0$ with $\L\subset\D$ be given,
and $f:\cX_\L\to\R_+$ an arbitrary
measurable function. Then, combining \eqref{eq:cLformula} with
Remark \ref{rem:locMWM} and \eqref{eq:condProb} we find that
\begin{equation}\label{eq:locCondProb}
\begin{split}
\E_\m(f\,|\,\cF_{\D\sm\L})(\x) &= G_{\L,\D}(f\,|\,\x)\\
&:= Z_{\L,\D}(\x_{\D\sm\L})^{-1} \int L_\L(d\a) \, f(\a)\,\hat
c_\D(\a,\x_{\D\sm\L})
\end{split}
\end{equation}
for $\m$-almost all $\x\in\cX$. Let us comment on these
conditional probabilities.
%: Remark G_L,D
\begin{rem}\label{rem:G_L,D}
(a) For any $\x\in\cX_{\D\sm\L}$, the normalization constant
$$
Z_{\L,\D}(\x)= \int L_\L(d\a) \,\hat
c_\D(\a,\x)
$$
is finite. In fact, $Z_{\L,\D}(\x)\le \det(I+J_\L)$.
Moreover, $Z_{\L,\D}(\x)$ is non-zero whenever $\det
J_{[\D]}(\x,\x)>0$ because $L_\L(\{\emptyset\})=1$. This means
that $G_{\L,\D}(\,\cdot\,|\,\x)$ is a well-defined probability measure on $\cX_\L$
for \emph{all} such $\x$.
(b) For all $\x$ with $D:=\det J_{[\D]}(\x,\x)>0$, $G_{\L,\D}(\,\cdot\,|\,\x)$
is a DPP with interaction kernel
$J_{\L,\D}^\x(x,y):=D^{-1} \det J_{[\D]}(x\x,y\x)$, $x,y\in\L$.
(The last matrix is defined in obvious analogy
to \eqref{eq:Kmatrix}.) This observation is analogous to
the fact observed in \cite{ST1} that the reduced Palm
measures $\m^x$ of $\m$ are again determinantal with correlation kernel $K^x(y,y')=K(x,x)^{-1}\det K(yx,y'x)$.
\end{rem}
Turning to the inequalities \eqref{eq:cLinequality}, we emphasize that
the monotonicity of the functions $\hat c_\L(\a,\cdot)$ expresses the
repulsive nature of the particle interaction in an infinitesimal way.
As a matter of fact, this
monotonicity is analogous to the inequality
\[
\r(\a_1)\r(\a_2)\ge \r(\a_1\cup\a_2)\r(\a_1\cap\a_2),\quad
\a_1,\,\a_2\in \cX_0,
\]
derived in \cite{ST1} for the correlation function $\r$ of $\m$,
and follows in the same way from an inequality for determinants of
Hermitian matrices; see \eqref{eq:det3} below. The following
corollary provides an integral version of this repulsiveness.
\begin{cor}\label{cor:Monoton}
For any $\L\subset\D\in\cB_0$ and any measurable
function $f:\cX_\L\to\R_+$, the ratio $G_{\L,\D}(f\,|\,\x
)/G_{\L,\D}(N_\L{=}0\,|\,\x )$ is decreasing in $\x\in\cX_{\D\sm\L} $.
In particular, $G_{\L,\D}(N_\L{=}0\,|\,\cdot)$ is increasing, and for
$\L\sub\D_1\sub\D_2\in\cB_0$ we have
\begin{equation}\label{eq:Monoton}
\m(N_\L{=}0\,|\,N_{\D_2\sm\L}{=}0)\le \m(N_\L{=}0\,|\,N_{\D_1\sm\L}{=}0) \le
\m(N_\L{=}0)\,.
\end{equation}
\end{cor}
The statement of the corollary is weaker than one may hope. In
fact, one might guess that $G_{\L,\D}(f\,|\,\x )$ is decreasing in
$\x$ for any increasing $\cF_{\L}$-measurable function $f$. (The
corollary implies this assertion only for $f=1_{\{N_\L\ge 1\}}$).
However, we have some doubts whether this can be expected to hold
in general. For if $f$ depends only on some part $\L_0$ of $\L$,
then an increase of $\x$ may repel some particles from
$\L\setminus\L_0$, giving a chance to some additional particles in
$\L_0$, so that $G_{\L,\D}(f\,|\,\x )$ will increase. So, the
situation is less satisfactory for point processes than in the
discrete case; cf. Theorem 6.5 of \cite{L}. Nevertheless,
\eqref{eq:Monoton} implies that, for disjoint $\L,\D\in\cB_0$, the
events $\{N_\L=0\}$ and $\{N_\D=0\}$ are negatively correlated;
see Proposition 2.7 of \cite{ST2} for the corresponding result in
the discrete case.
Next we exploit the domination bound $c_\L(x,\x)\le
J_{[\L]}(x,x)$, which will imply that $\m$ is
stochastically dominated by a Poisson process.
Recall that a point process $\n$ is \emph{stochastically dominated}
by a point process $\n'$, written $\n\preceq\n'$, if
\[
\int f\,d\n\le \int f\,d\n'
\]
for every increasing measurable function $f:\cX\to\R$. Here, $f$
is said to be increasing if $f(\x)\le f(\eta)$ whenever
$\x\subset\eta$. The intensity function of the dominating Poisson
process shall be given by $z(x)=J(x,x)$, where $J(x,y)$ is a
\emph{properly chosen} integral kernel of $J$. To understand the
necessity of a proper choice one should note again that the
diagonal in $\SP^2$ is a $\l^{\otimes 2}$-nullset because $\l$ is
diffuse; the behavior of the integral kernel on the diagonal that
enters in the definition of $z(x)$ is therefore a priori unrelated
to the operator $J$ (except when the kernel is continuous which we
do not require here). However, a natural way of determining the
kernel function on the diagonal is in terms of the local trace
formula
\begin{equation}\label{eq:locTrace1}
\Tr\,(J_\L)=\int_\L J(x,x)\;\l(dx)\quad\text{for all }\L\in\cB_0,
\end{equation}
and such a choice is possible according to Lemma \ref{lem:loc_trace_formula}.
The function $z(x):=J(x,x)$ is then locally $\l$-integrable, and
the Poisson point process $\p^{J}$ with intensity function $z(x)$ is well-defined.
\begin{cor}\label{cor:PoissonDom}
$\m\preceq\p^J$.
\end{cor}
%
In the case when $\SP=\R^d$ and $\l$ is Lebesgue measure, the last
result implies in particular that there is no percolation in the
Boolean model associated to $\m$ when $J(x,x)$ is small enough. Let
$b_R(x)$ denote the closed ball of radius $R<\infty$ in $\R^d$
centered at $x$, and for $\x \in\cX$ let
\[
B_R(\x )=\bigcup_{x\in \x }b_R(x)
\]
the associated Boolean set. $B_R(\x )$ splits into connected
components called \emph{clusters}. A cluster is called
\emph{infinite} if it consists of infinitely many points of $\x $,
or equivalently, if its diameter is infinite. It is well-known
\cite{G, MR} that, for $d\ge 2$, there exists a critical threshold
$0<z_c\equiv z_c(d,R)<\infty$ for Poisson percolation: For the
Poisson point process $\p^z$ with constant intensity function
$z>0$, one has
\begin{equation*}
\p^z\big(\,\exists \text{ infinite cluster of }B_R(\cdot)\,\big)=
\begin{cases} 0 &\text{if }z<z_c\,,\\1 &\text{if }z>z_c\,.\end{cases}
\end{equation*}
For $d=1$ one has $z_c=+\infty$ \cite[Theorem 3.1]{MR}.
\begin{cor}\label{cor:NoPerc}
Let $\SP=\R^d$ and $\l$ be Lebesgue measure.
If $$z(J):=\limsup_{|x|\to \infty} J(x,x)<z_c$$ then
$\m(\,\exists \text{ infinite cluster of }B_R(\cdot)\,)=0$.
\end{cor}
We now address the question of whether DPP's are Gibbsian. In view of
Remark \ref{rem:MWM} and Theorem \ref{thm:MWM}, the following
result implies that $\m$ is Gibbsian at least in a general sense.
%: Thm2
\begin{thm}\label{thm:Sigma}
$\m$ satisfies condition $(\S_\l)$. Its CPI is given by
\begin{equation}\label{eq:cJ-lim}
\hat c(\a,\x) = \lim_{n\to\infty} \hat c_{\D_n}(\a,\x_{\D_n})\quad
\text{for $L\otimes\m$-almost all $(\a,\x)$,}
\end{equation}
where $\hat c_{\D_n}$ is given by \eqref{eq:cLformula}
and $(\D_n)$ is any
sequence in $\cB_0$ that increases to $\SP$. In particular,
$\m(N_\L{=}0\,|\,\cF_{\L^c}) >0$ $\m$-almost surely for
each $\L\in\cB_0$ and, for any $\cF_\L$-measurable $f:\cX\to\R_+$, the ratio
\[
\E_{\m}(f\,|\,\cF_{\L^c})/\m(N_\L{=}0\,|\,\cF_{\L^c})
\]
of conditional expectations has a decreasing version.
\end{thm}
%
Two remarks are in order. First, in view of the comments in
Remark \ref{rem:G_L,D}(b) and below \eqref{eq:Papint},
the first assertion can be restated as an absolute continuity
between DPP's: the DPP $\m^x$ with correlation
kernel $K^x$ is absolutely continuous with respect to the
DPP $\m$ for $K$ with density $c(x, \cdot)/K(x,x)$.
Next, and more importantly, combining \eqref{eq:cJ-lim}
with \eqref{eq:cLformula} and \eqref{eq:condProb} we
obtain at least an implicit formula for the conditional probabilities
of $\m$ given the events outside of a
local region. But the question remains of whether the CPI, and
thereby the conditional probabilities, of $\m$
can be identified in a more specific way. In fact, if we make
a proper choice of the integral kernel $J(x,y)$ as
in Lemma \ref{lem:loc_trace_formula}, a natural candidate for $\hat c$ is
\begin{equation}\label{eq:candidate}
\hat c_*(\a,\x) = \lim_{\D\uparrow\SP} \det J(\a\x_\D,\a\x_\D)/\det J(\x_\D,\x_\D)\,.
\end{equation}
This limit does exist because the ratio on
the right-hand side is decreasing in $\D$, as follows from inequality
\eqref{eq:det3} in the Appendix. (As before, we set a ratio of determinants
equal to zero if the denominator vanishes.) In contrast to
\eqref{eq:cJ-lim}, the determinants in \eqref{eq:candidate}
involve $J$ itself rather than $J_{[\D_n]}$.
Now our question is the following: \emph{When is it true that
$\hat c=\hat c_*$ a.e. for $L\otimes\m$?}
Unfortunately, we are unable to settle the question above
in the same generality as this was done in the lattice
case by Shirai and Takahashi \cite[Theorem 6.2]{ST2}.
Their argument exploits the symmetry between occupied and
empty lattice sites and therefore does not carry over to our
continuous setting. (Formally, this is reflected by
their condition $\text{spec\,} K\sub\; ]0,1[$ which is never
satisfied in the continuous case.) The following
theorem gives a partial answer, at least.
%: Thm Gibbs
\begin{thm} \label{thm:Gibbs}
In general, the inequality $\hat c\le \hat c_*$ holds
$L\otimes\m$-almost everywhere. If $\hat c_*$ is continuous
$L\otimes\m$-a.e. then $\hat c= \hat c_*$
$L\otimes\m$-a.e., i.e., $\hat c_*$ is a version
of the CPI of $\m$.
\end{thm}
Proposition \ref{prop:a.e.continuity} below will provide
sufficient conditions for the almost-everwhere continuity
to hold. First let us comment on the significance of this result.
\begin{rem}\label{rem:potential}
If $\hat c= \hat c_*$ a.e. then $\m$ is a
Gibbs measure for a specification $G$ defined in terms of $J$
as follows. For each $\L\in\cB_0$ and any
$\x\in\cX_{\L^c}$ satisfying $\det J(\z,\z)>0$ for all finite
$\z\sub\x$, let $G_\L(\cdot\,|\,\x)$ be defined by
inserting $\hat c _*$ into \eqref{eq:condProb}. In fact,
$G_\L(\cdot\,|\,\x)$ is a Gibbs distribution for the Hamiltonian
$H_\L(\cdot\,|\,\x)= -\log \hat c _*(\cdot,\x)$ on $\cX_\L$,
$\x\in\cX_{\L^c}$. (If desired, one can express the Hamiltonian in
terms of a many-body potential $\Phi$, but this is not
particularly useful.) These Gibbs distributions altogether form a
Gibbsian specification $G=(G_\L)_{\L\in\cB_0}$ in the sense of
Preston \cite[pp. 16, 17]{PrLNM}; this has been proved by Gl\"otzl
\cite{Gloetzl2} in a general setting, and in \cite{Y} for the
particular case of DPP's. In particular, if $\hat c_*$ is a.e.
continuous then the conditional expectations
$\E_\m(g|\cF_{\L^c})$ in \eqref{eq:condexpect} have a.e.\ continuous
versions. This is Gibbsianness in the best sense one
can expect for a point process.
Conversely, suppose $\m $ is a Gibbs measure for some Hamiltonian
$H$. Then $\hat c^H(\a,\x)$ $:=\exp[-H_\a(\a\,|\,\x_{\a^c})]$ is a
version of its CPI \cite{NZ} and will typically satisfy the continuity
condition $\hat c^H(\a,\x) = \lim_{\D\ua\SP}\hat c^H(\a,\x_\D)$.
If one assumes that the function $\hat c =\lim_{n\to\infty} \hat c
_{\D_n}$ in \eqref{eq:cJ-lim} has the same continuity property,
one can conclude that $\hat c =\hat c _*$ a.e. For, Proposition
\ref{prop:local_convergence} below implies that $\lim_{n\to\infty} \hat
c _{\D_n}(\a,\x_\D) =\hat c _*(\a,\x_\D)$ a.e.
for all $\D\in\cB_0$.
\end{rem}
The next proposition describes a case in which the condition of
almost-everwhere continuity in Theorem \ref{thm:Gibbs} is satisfied.
%: Prop a.e.continuity
\begin{prop}\label{prop:a.e.continuity}
Suppose $E=\R^d$, $\l$ is Lebesgue measure and, in addition to (H),
\begin{enumerate}
\item $J:=K(I-K)^{-1}$ has a continuous integral kernel $J(x,y)$, $x,y\in\R^d$;
\item $J$ has finite range $R<\infty$, in that $J(x,y)=0$ for $|x-y|>R$;
\item $\m$ does not percolate, in that
$\m \big(\,\exists \text{ \rm infinite cluster of }B_R(\cdot) \,\big)=0$.
\end{enumerate}
Then $\hat c_*$ is continuous $L\otimes\m$-almost everywhere.
Specifically,
\begin{equation}\label{eq:cJ-subcr}
\hat c _*(\a,\x)=\det J(\a\x_W,\a\x_W)/ \det
J(\x_W,\x_W)\ 1_{\{\diam W(\a,\x)<\infty\}}\,,
\end{equation}
where $W(\a,\x)$ is the
union of the clusters of $B_R(\a\x)$ hitting $\a$, and
$\x_W:=\x_{W(\a,\x)}$ is the restriction of $\x$ to $W(\a,\x)$.
\end{prop}
Under the conditions of this proposition, the Gibbsianness of DPP's has
already been derived by the second author in \cite{Y} by different
methods.
\begin{ex}\label{ex:Example}
Typical examples of operators satisfying the assumptions
of Proposition \ref{prop:a.e.continuity} are
obtained by Fourier transforms: Let $\hat j\ge0$ be an integrable
function on $\R^d$,
\[
j(x):=(2\p)^{-d} \int_{\R^d}e^{ix\cdot t}\;\hat j(t)\,dt
\]
its (inverse) Fourier transform, and $J(x,y):=j(x-y)$. We assume
that $j(\cdot)\in L^1(\R^d)$. By Bochner's theorem and Young's
inequality \cite[p. 29]{RS}, $J$ then defines a positive bounded
operator on $L^2(\R^d)$. The associated correlation operator
$K:=J(I+J)^{-1}$ is the convolution operator for the function $k$
satisfying $\hat k = \hat j/(1+\hat j)$. The validity of
hypothesis (H) is evident,
and the continuity assumption (a) of Proposition
\ref{prop:a.e.continuity} also holds by definition. To satisfy
the finite range condition (b), let $j:=\ph\,\chi_R$ or,
equivalently, $\hat j=\hat \ph\star \hat \chi_R$, where $0\le
\hat\ph\in L^1(\R^d)$, $\chi_R(x)=\prod_{i=1}^d(1-|x_i|/R)^+$, and
$\star$ denotes convolution. By Corollary \ref{cor:NoPerc}, the
non-percolation assumption (c) holds when $d=1$ or
$j(0)<z_c(d,R)$.
To construct non-translation-invariant examples, let $\psi\ge0$ be any
bounded measurable function on $\R^d$
and $M_\psi$ the associated multiplication operator on $L^2(\R^d,\l)$.
Let $J$ be a finite range operator as above
and $L:=JM_\psi J$. $L$ has the kernel $L(x,y)=\int
j(x-z)\psi(z)j(z-y)\,dz$. Obviously, $L(x,y)$ is of finite range
because so is $j$, and not translation-invariant except when $\psi$ is
constant almost everywhere.
\end{ex}
Let us also comment on the particular case of renewal processes
which deserves special interest.
\begin{ex}\label{ex:renewal}
Let $\SP=\R$ and $K:f\to k\star f$ the convolution operator for the function
$k(x)= \r e^{-a|x|}$, where $\r,a>0$ are such that $\r <a/2$. (The last
condition means that $\|k\|_1<1$, and thus $\|K\|<1$ by Young's inequality.)
In the setting of the preceding example, this corresponds to setting
$\hat k(t) = 2\r a/(a^2+t^2)$. Hence
\[
\hat j(t) = \frac{\hat k(t)}{1-\hat k(t)}
=\frac{2\r a}{\s^2+t^2}
\]
with $\s^2:= a^2-2\r a$, and therefore $j(x)=(\r a/\s) e^{-\s|x|}$. The
associated integral kernel can be written in the form
\[
J(x,y):=j(x-y) = u(x\wedge y)\, v(x\vee y)
\]
with $x\wedge y=\min(x,y)$, $x\vee y=\max(x,y)$, $u(x)= e^{\s x}$, and
$v(x)= (\r a/\s) e^{-\s x}$. Therefore, if $\a=\{x_1,\ldots,x_n\}$ with
$x_1<\cdots<x_n$ then
\[
\det J(\a,\a) = u(x_1)\, v(x_n)\, \prod_{i=1}^{n-1}d(x_{i+1}-x_i)
\]
with $d(x_{i+1}-x_i)= \det \begin{pmatrix}v(x_i)&v(x_{i+1})\\
u(x_i)&u(x_{i+1}) \end{pmatrix} = (2\r a/\s) \sinh\big(\s(x_{i+1}-x_i)\big)$, as
is easily verified by induction on $n=|\a|$. Together with \eqref{eq:candidate}
we find that
\[
c_*(x,\x) = {d\big(\ell_x(\x)\big)\, d\big(r_x(\x)\big)}\big/
{d\big(\ell_x(\x)+r_x(\x)\big)}\,,
\]
where $\ell_x(\x)$ and $r_x(\x)$ are the distances from $x$ to the nearest
points of $\x$ on the left, respectively on the right. This relationship still
holds if $d(\cdot)$ is multiplied with an exponential factor to obtain a probability
density. That is, we have
\[
c_*(x,\x) = {f\big(\ell_x(\x)\big)\, f\big(r_x(\x)\big)}\big/{f\big(\ell_x(\x)+r_x(\x)\big)}
\]
for the probability density $f(x) = e^{-ax}d(x)$ on $[0,\infty[$.
The right-hand side is the PI of the stationary renewal process $\m_f$
with spacing density $f$, and $\m_f$ is the only translation invariant
point process having this PI. As $c_*$ is continuous,
we conclude from Theorem \ref{thm:Gibbs} that
$\m_f$ is the unique DPP for $K$. In this way we recover a well-known
result of Macchi \cite{M}; see also
\cite{DV}. According to Soshnikov \cite{So}, the densities $f$ of the
form above are the only possible spacing
distributions of determinantal renewal processes. (We remark that
Soshnikov also gave a complete
characterization of all kernels $K(x,y)$ on $\SP=[0,\infty[$ which
are such that the associated DPP's have
independent spacings, see also Example~6.7 of \cite{ST1}.
The previous comments can be extended to this setting.)
\end{ex}
\section{Proofs}
\label{sec:proofs}
Let us start with the proof of Theorem \ref{thm:PapMon}. Its key
ingredients are equation \eqref{eq:density_function} for the
Janossy densities of $\m$, and the determinant inequalities of
Lemma \ref{lem:determinant-relation} in the Appendix.
We assume throughout this section that hypothesis (H) is satisfied.
\medskip
\Proof[ of Theorem \ref{thm:PapMon}] Fix any $\L\in\cB_0$.
>From Eq. (\ref{eq:density_function}) we know that
$\m_\L$ is absolutely continuous relative to $L_\L$ with
density $\s_\L(\x)\propto \det J_{[\L]}(\x,\x)$.
Inequality \eqref{eq:det2} implies that the zero
set $\{\s_\L=0\}$ is increasing. Remark \ref{rem:locMWM} thus
tells us that $\m_\L$ satisfies condition $(\S_{\l_\L})$ with
PI given by \eqref{eq:cLformula}. This proves the
first statement of the theorem.
For the proof of \eqref{eq:cLinequality} let $\x\sub\eta\in \cX_\L$
and $\a\in\cX_0$ with $\a\sub \L\sm\eta$.
Choosing the kernel function of $J_{[\L]}$ as in Lemma
\ref{lem:positive_kernel}, we get that $J_{[\L]}(\a\eta,\a\eta)$ is
positive definite. Inequality \eqref{eq:det3} thus asserts that
\[
\det J_{[\L]}(\a\eta,\a\eta)\det J_{[\L]}(\x,\x) \le \det
J_{[\L]}(\eta,\eta) \det J_{[\L]}(\a\x,\a\x),
\]
and this gives the
first inequality in \eqref{eq:cLinequality}. In particular, we
have $\hat c_\L(\a,\x)\le c_\L(\a,\emptyset)$ for the empty configuration
$\emptyset$. But the last quantity equals $\det
J_{[\L]}(\a,\a)$ by definition. An application of inequality \eqref{eq:det2}
then gives the last estimate.\EndProof
To exploit the upper bound in \eqref{eq:cLinequality} we will
use the following comparison lemma.
\begin{lem}\label{lem:monotonicity}
For any $\L \subset \D\in \cB_0$,
$J_{[\L]}\le P_\L J_{[\D]}P_\L\le J_\L$ in the operator ordering.
In particular,
\begin{equation}\label{eq:det-monotone}
\det J_{[\L]}(\x,\x) \le
\det J_{[\D]}(\x,\x)\le \det J_\L(\x,\x)
\end{equation}
for $L_\L$-almost all $\x\in \cX_\L$.
\end{lem}
\Proof We prove only the inequality $J_{[\L]}\le J_\L$ which
implies in particular that $P_\L J_{[\D]}P_\L\le P_\L J_\D P_\L
=J_\L$. The proof of the relation $J_{[\L]}\le P_\L J_{[\D]}P_\L$
is similar. Since $J=K (I-K )^{-1}$ and
$L(I-L)^{-1}=-I+(I-L)^{-1}$ for any contraction $L$, the
inequality $J_{[\L]}\le J_\L$ is equivalent to
\[
P_\L(I-K_\L )^{-1}P_\L\le P_\L(I-K )^{-1}P_\L.
\]
But this follows from Lemma \ref{lem:basic-order} as applied to
$P=P_\L$ and $T=I-K $, because $P_\L(I-K_\L
)^{-1}P_\L=P_\L(P_\L(I-K )P_\L)^{-1}P_\L$.
To prove the determinantal inequalities \eqref{eq:det-monotone},
we apply Lemma \ref{lem:positive_kernel} to the positive trace
class operators $J_{[\L]}$, $P_\L J_\D P_\L-J_{[\L]}$, and
$J_\L-P_\L J_\D P_\L$. We then see that the kernels of $J_{[\L]}$,
$J_\D$, and $J_\L$ can be chosen in such a way that, for each
$\x\in \cX_\L$, $J_{[\L]}(\x,\x)\le J_\D(\x,\x)\le J_\L(\x,\x)$
as operators on $\C^{|\x|}$. By Lemma \ref{lem:indistinguishable},
these kernels are indistinguishable from the corresponding kernels
obtained by applying Lemma \ref{lem:positive_kernel} to
$J_{[\L]}$, $J_\D$, and $J_\L$ directly. For the latter kernels,
the same operator inequalities thus hold for $L_\L$-almost all
$\x\in \cX_\L$, at least. To complete the proof it is therefore
sufficient to note that the determinant is increasing relative to
the operator ordering; see \cite[Corollary III.2.3]{B}.\EndProof
We are now ready for the proofs of Remark~\ref{rem:G_L,D} and
Corollaries~\ref{cor:Monoton} to \ref{cor:NoPerc}.
\medskip
\Proof[ of Remark \ref{rem:G_L,D}] (a) Let us start with a
slightly simpler estimate. Combining the last bound in
\eqref{eq:cLinequality} with the second inequality in
\eqref{eq:det-monotone} (for $\x=\{x\}$) and using \eqref{eq:L}
and the trace formula \eqref{eq:trace-formula} we find
\[
Z_{\L,\D}(\x)\le \exp\int_\L J_\L(x,x)\,\l(dx)= \exp \Tr J_\L <\infty
\]
because $J_\L$ is trace class by (H).
To obtain the sharper bound stated in Remark \ref{rem:G_L,D}(a)
we use the next to last inequality in \eqref{eq:cLinequality} and
the second inequality in \eqref{eq:det-monotone} (for $\x=\a$)
to obtain
\[
Z_{\L,\D}(\x)\le \int L_\L(d\a)\,\det J_\L(\a,\a)= \det(I+J_\L).
\]
To get the last identity one can use the argument on p. 930 of \cite{So}
by combining Lidskii's theorem \cite[p. 50]{Si} with the trace formula
\eqref{eq:trace-formula}. (A similar argument implies that the Janossy densities
in \eqref{eq:density_function} integrate to $1$.)
We note that $\det(I+J_\L)\le \exp\Tr (J_\L)$ by \cite[eq. (3.6)]{Si}.
(b) For fixed $\x$ as stated, $G_{\L,\D}(\,\cdot\,|\,\x)$ -- considered as a measure
on $\cX_\L$ -- is defined by an $L_\L$-density of the form
\[
\s^\x_{\L,\D}(\a)\propto \hat c_\D(\a, \x) = \det
J_{[\D]}(\a\x,\a\x)/\det J_{[\D]}(\x,\x)\,,\quad \a\in\cX_\L.
\]
In view of the identity \eqref{eq:det-ratio}, the last expression is equal to
$\det J_{\L,\D}^\x(\a,\a)$. Comparing this observation with
\eqref{eq:density_function} we see that $G_{\L,\D}(\,\cdot\,|\,\x)$
is a determinantal process with interaction kernel $J_{\L,\D}^\x$,
defining a positive Hermitian operator on $L^2(\L,\l_\L)$. The associated
correlation operator is
$K_{\L,\D}^\x:=J_{\L,\D}^\x(I+J_{\L,\D}^\x)^{-1}$.\EndProof
\medskip
\Proof[ of Corollary \ref{cor:Monoton}] In view of Eq. (\ref{eq:locCondProb}),
\[
G_{\L,\D}(f\,|\,\x )\,\big/\, G_{\L,\D}(N_\L{=}0\,|\,\x )= \int L_\L(d\a)\,
f(\a) \, \hat c_\D(\a,\x)
\]
for $\m_\D$-almost all $\x\in\cX_{\D\sm\L}$. Since $f\ge0$,
Theorem \ref{thm:PapMon}(b) together with equation
\eqref{eq:compPapdens} implies that the integrand on the
right-hand side is a decreasing function of $\x$. In particular,
for $f\equiv1$ we find that $G_{\L,\D}(N_\L{=}0\,|\,\cdot)$ is
increasing. To prove \eqref{eq:Monoton} we note that
\[
\begin{split}
&\m(N_\L{=}0\,|\,N_{\D_2\sm\L}{=}0)= G_{\L,\D_2}(N_\L{=}0\,|\,\emptyset )\\
&\le
\E_{\m}\big(G_{\L,\D_2}(N_\L{=}0\,|\,\cdot)\big|\cF_{\D_1\sm\L}\big)(\emptyset)\\
&= \m(N_\L{=}0\,|\,\cF_{\D_1\sm\L})(\emptyset)
=\m(N_\L{=}0\,|\,N_{\D_1\sm\L}{=}0)
\end{split}
\]
because $G_{\L,\D_2}(N_\L{=}0\,|\,\emptyset )\le
G_{\L,\D_2}(N_\L{=}0\,|\,\cdot )$. The final inequality follows by
setting $\D_1=\L$.\EndProof
\medskip
\Proof[ of Corollary \ref{cor:PoissonDom}] We show first that
$\m_\L\preceq\p^J_\L$ for any $\L\in\cB_0$. Consider the PI $c_\L$
of $\m_\L$. Combining \eqref{eq:cLinequality} (for $\a=\{x\}$)
with \eqref{eq:det-monotone} (for $\x=\{x\}$) we find that
$c_\L(x,\x)\le J_\L(x,x)$ for all $x\in \L$ and $\x\in \cX_\L$.
On the other hand, it is
well-known and easy to check that the Poisson point process
$\p^J_\L$ has the PI $c_\L^J(x,\x)=J(x,x)$ on $\L$; cf.
\cite{Mecke, NZ}. Moreover, since $J(x,x)=J_\L(x,x)$ for $\l$-a.a.
$x\in \L$ by the construction of $J(x,x)$ in Lemma
\ref{lem:loc_trace_formula}, we may also regard $J_\L(x,x)$ as the
PI of $\p^J_\L$. Thus we can conclude that the PI of $\m_\L$ at a
configuration $\x\in \cX_\L$ is not larger than the PI of
$\p^J_\L$ evaluated at any larger configuration $\eta\in\cX_\L$,
as long as $x\notin\eta$. This, however, is precisely the
hypothesis of the point-process counterpart of the well-known
FKG-Holley-Preston inequality for lattice systems. This continuous
counterpart was obtained first by Preston \cite{Pr}; an
alternative simplified proof can be found in \cite[Theorem
1.1]{GK}. It asserts that, under the above condition on the PI's,
$\m_\L\preceq\p^J_\L$, as required.
To get rid of the locality restriction we argue as follows. For
any compact $\L$, a celebrated theorem of Strassen \cite{Strassen}
provides us with a probability measure $m_\L$ on $\cX\times\cX$
having marginals $\m_\L$ resp. $\p^J_\L$ and being supported on
the set $D:=\{(\x,\eta)\in\cX\times\cX:\x\sub\eta\}$. Note that
$D$ is closed when $\cX\times\cX$ is equipped with the product of
the vague topology on $\cX$. By a standard compactness criterion
for point processes \cite[Proposition 9.1.V]{DV}, the measures
$m_\L$ admit a weak limiting measure $m$ as $\L$ increases to
$\SP$. By construction, $m$ has marginals $\m$ resp. $\p^J$, and
$m(D)=1$ because $D$ is closed. This implies that
$\m\preceq\p^J$.\EndProof
\Proof[ of Corollary \ref{cor:NoPerc}] By assumption, there exists
some $z<z_c$ such that $J(x,x)\le z$ for all $x$ outside of some
compact region. Therefore, $\p^J$-almost surely there exists no
infinite cluster outside of this region, and therefore no infinite
cluster anywhere. As the existence of an infinite cluster is an
increasing event, the absence of percolation carries over to $\m$,
by Corollary \ref{cor:PoissonDom}.\EndProof
%: Pf Thm 3.6
Next we turn to the proof of Theorem~\ref{thm:Sigma}. We will use
a martingale argument to derive property $(\S_\l)$ from the local
property $(\S_{\l_\L})$ of Theorem~\ref{thm:PapMon}.
\medskip
\Proof[ of Theorem~\ref{thm:Sigma}] We only need to show
that $\m$ satisfies condition $(\S_\l)$ with CPI
\eqref{eq:cJ-lim}; the remaining assertions then follow
from Theorem \ref{thm:PapMon} and Remark
\ref{rem:MWM}(c). Let $(\D_n)$ be any increasing sequence
in $\cB_0$ exhausting $\SP$, $\L\in\cB_0$ a fixed set,
and $n$ so large that $\L\sub\D_n$. Consider the product
space $\cX_\L\times\cX$, equipped with the probability
measure $\n_\L:=\p_\L^1\otimes\m$ and the $\s$-algebras
$\cG_n= (\cF|_{\cX_\L})\otimes\cF_{\D_n}$. Now, Theorem
\ref{thm:PapMon} asserts that, on $\cG_n$, the restriction of
$\CCM[\m]$ to $\cX_\L\times\cX$ is absolutely
continuous with respect to $\n_\L$ with Radon-Nikodym
density $R_n:=e^{\l(\L)}\,\hat c_{\D_n}$.
The sequence
$(R_n)$ is therefore a nonnegative martingale relative to
$\n_\L$. By \eqref{eq:cLinequality} and
\eqref{eq:det-monotone},
$R_n$ satisfies the bound
\[
R_n(\a,\x)\le e^{\l(\L)}\,\det J_{[\D_n]}(\a,\a)
\le S(\a):= e^{\l(\L)}\,\det J_{\L}(\a,\a)
\]
for $\n_\L$-almost all $(\a,\x)\in\cX_\L\times\cX$.
As we have seen in the proof of Remark \ref{rem:G_L,D}(a),
$S$ is integrable relative to $\p_\L^1$.
As a consequence, $(R_n)$ converges $\n_\L$-almost surely and
in $L^1(\n_\L)$-norm to a limit $R$. By the
norm-convergence, $R$ is a Radon-Nikodym density of $\CCM[\m]$
relative to $\n_\L$ on the limiting $\s$-algebra
$\s(\bigcup_n\cG_n)= (\cF|_{\cX_\L})\otimes\cF$. Finally we
replace $\p_\L^1$ with $L_\L$ by dropping the
constant factor $e^{\l(\L)}$, and use the fact that
$\cX_\L\uparrow\cX_0$ as $\L \uparrow\SP$. We then get the
desired result that $\CCM[\m]\ll L\otimes\m$ with density
\eqref{eq:cJ-lim}.\EndProof
Our proof of Theorem \ref{thm:Gibbs} will be based on the
following convergence result. As before, we say that a kernel
function $t(x,y)$ of an operator $T$ is \emph{positive definite
almost everywhere} if the matrix $t(\a,\a)$ is positive definite
for $L$-almost all $\a\in \cX_0$.
%: Prop
\begin{prop}\label{prop:local_convergence}
Given any sequence $(\D_n)$ in $\cB_0$ increasing to $\SP$, there
exist integral kernels $J_{[n]}(x,y)$ for $J_{[n]}:=J_{[\D_n]}$
such that the following holds:
\begin{enumerate}
\item Each $J_{[n]}(x,y)$ is positive definite a.e. and satisfies
the trace formula
\begin{equation}\label{eq:locTrace2}
\Tr\,(P_\L J_{[n]}P_\L)=\int_\L J_{[n]}(x,x)\,\l(dx)
\end{equation}
for all $\L\subset\D_n$. \item The limit
\[
J(x,y)=\lim_{n\to \infty} J_{[n]}(x,y)
\]
exists for all $x,y\in\SP\sm\cN$, where $\cN\in \cB$ is a
$\l$-nullset. Moreover, this limit defines an integral kernel of
$J$, is positive definite a.e., and satisfies the trace formula
\eqref{eq:locTrace1}.
\end{enumerate}
\end{prop}
Note that, by Lemma \ref{lem:indistinguishable}, the kernels
$J_{[n]}(x,y)$ and $J(x,y)$ constructed here are indistinguishable
from those obtained directly from Lemmas \ref{lem:positive_kernel}
and \ref{lem:loc_trace_formula}.
\bigskip
\Proof
In view of hypothesis (H) and Lemma \ref{lem:loc_trace_formula},
$K$ admits an integral kernel $K(x,y)$ with the properties
(a)--(c) of that lemma. In particular, $K(x,y)$ is positive
definite a.e., and there exists a $\l$-nullset $\cN\in \cB$ such
that $k_x:=K(\cdot,x)\in L^2(\SP,\l)$ whenever $x\notin \cN$. For
each $n$ we choose the integral kernel
$K_n(x,y):=1_{\D_n}(x)K(x,y)1_{\D_n}(y)$, $x,y\in\D_n$, of
$K_n:=K_{\D_n}$. Also, for each power $l\ge 2$ we set
$K^l(x,y):=(k_x,K^{l-2} k_y)$ and $K_n^l(x,y):=(k_x,P_n(K_n)^{l-2}
k_y)$, where $(\cdot,\cdot)$ is the inner product in $L^2(\SP,\l)$
and $P_n:=P_{\D_n}$. These are well-defined for $x,y\notin \cN$,
and define versions of the integral kernels of $K^l$ resp.
$(K_n)^l$.
Now, since $\|K_{n}\|\le \|K\|<1$, we can write
$J_{[n]}=\sum_{l\ge1}(K_n)^l$ and $J=\sum_{l\ge1}K^l$\,; these
series converge in operator norm, and the convergence
is uniform in $n$. In particular, this implies the
absolute convergence of the series $\sum_{l\ge 1}K_n^l(x,y)$
and $\sum_{l\ge 1}K^l(x,y)$ for $x,y\notin \cN$,
again uniformly in $n$. Obviously, these series define
integral kernels of $J_{[n]}$ and $J$, respectively. They
are positive definite a.e. because $K(x,y)$ is.
To prove the trace formula \eqref{eq:locTrace1} we introduce the
partial sum $J^{(m)}=\sum_{l=1}^mK^l $.
Obviously, as $m\to \infty$, the sequence $P_\L J^{(m)}P_\L$
increases and converges in operator norm to $J_\L$, which is of
trace class. Using \cite[Theorem 2.16]{Si}, we conclude that $P_\L
J^{(m)}P_\L\to J_\L$ in trace norm as $m\to \infty$. Hence
\[
\Tr\big(J_\L\big)=\lim_{m\to \infty}\,\sum_{l=1}^m\Tr\big(P_\L K^l
P_\L\big)\,.
\]
Inserting the trace formulas of Lemma \ref{lem:loc_trace_formula}(c)
and taking the limit $m\to \infty$ we arrive at
\eqref{eq:locTrace1}. Formula \eqref{eq:locTrace2} follows in the same way by considering $J_{[n]}$ resp.
$K_n$ instead of $J$ resp. $K$.
It remains to show that $J_{[n]}(x,y)\to J(x,y)$ when $x,y\notin\cN$.
By the uniform absolute convergence of these series, it is enough
to check that $K_{n}^l(x,y)\to K^l(x,y)$ for all $l\in\N$.
The case $l=1$ is trivial. For $l=2$ we have
$K_{ n}^2(x,y)=(k_x,P_{n} k_y)$
when $\D_n\ni x,y$, and this converges to $(k_x,
k_y)=K^2(x,y)$. In the case $l\ge 3$ we note that $K_n$
converges strongly to $K$ as $n\to \infty$. Since $\|K_n\|\le1$,
it follows that $(K_{n})^{l-2}$ converges strongly to $K^{l-2}$,
whence $K_{n}^l(x,y)=(k_x,(K_{n})^{l-2}k_y)$
converges to $(k_x,K^{l-2}k_y)=K^l(x,y)$. This
completes the proof.\EndProof
\Proof[ of Theorem \ref{thm:Gibbs}] Consider the CPI
\[
\hat c (\a,\x) = \lim_{n\to\infty} \hat c _{\D_n}(\a,\x_{\D_n})\,.
\]
that occurs in \eqref{eq:cJ-lim}. We know that this limit exists
for $L\otimes\m $-almost all $(\a,\x)\in\cX_0\times\cX$. In fact,
we may define $\hat c _{\D_n}(\a,\x_{\D_n})$ in terms of the
integral kernels $J_{[n]}$ of Proposition
\ref{prop:local_convergence} by setting $\hat c
_{\D_n}(\a,\x_{\D_n})=\det J_{[n]}(\a\x_{\D_n},\a\x_{\D_n}) / \det
J_{[n]}(\x_{\D_n},\x_{\D_n})$. On the other hand, for each
$\L\in\cB_0$ we conclude from \eqref{eq:cLinequality} that $\hat
c_{\D_n}(\a,\x_{\D_n}) \le \hat c _{\D_n}(\a,\x_{\L})$ for
$L\otimes \m$-a.a. $(\a,\x)$ as soon as $\D_n\supset\L$ . Hence
\[
\hat c (\a,\x) \le \liminf_{n\to\infty} \hat c_{\D_n}(\a,\x_\L)\,.
\]
Now, Proposition \ref{prop:local_convergence} implies that for
$L\otimes L_\L$-a.a. $(\a,\x_\L)$
\[
\hat c _{\D_n}(\a,\x_\L)\to \hat c _*(\a,\x_\L)= \det
J(\a\x_\L,\a\x_\L)/\det J(\x_\L,\x_\L)
\]
as $n\to\infty$, provided that $\det J(\x_\L,\x_\L)>0$. In view of
\eqref{eq:density_function} and \eqref{eq:det-monotone}, the last
proviso holds true for $\m$-almost all $\x$. Hence $\hat c
(\a,\x) \le \hat c _*(\a,\x_\L)$ for $L\otimes\m$-almost all
$(\a,\x)$. As we have noticed after \eqref{eq:candidate},
$\hat c_*(\a,\x_\L)$ is a decreasing function of $\L$, and its limit is
equal to $\hat c _*(\a,\x)$ by definition. This proves that
$\hat c \le \hat c_*$ almost everywhere.
Suppose next that $\hat c_*$ is continuous
$L\otimes\m$-everywhere. Consider the DPP's $\m^{J_\D}$ for the
interaction operators $J_\D=P_\D J P_\D$, and thus for the
correlation operators $K_{[\D]}=J_\D(I+J_\D)^{-1}$,
$\L\sub\D\in\cB_0$. According to Theorem 6.17 of \cite{ST1}, or
Lemma 4.3 of \cite{Y} in the case of a discontinuous kernel of
$J$, $\m^{J_\D}$ converges weakly to $\m $ as $\D$ increases to
$\SP$. Let $f$ be any bounded continuous function on
$\cX_0\times\cX$ such that $f(\a,\x)=0$ unless $\a\sub\L$ and
$|\a\x_\L|\le k$ for some number $k$. The portmanteau theorem
\cite[Proposition A2.3.V]{DV} then implies that
\[
\int f \,\hat c _*\, d(L_\L\otimes\m ) = \lim_{\D\ua\SP} \int f
\,\hat c _* \,d (L_\L\otimes\m^{J_\D})\,.
\]
But $\m^{J_\D}$ is supported on $\cX_\D$, and for almost every
$\a\in \cX_\L$ and $\x\in \cX_\D$ we have $\hat c_*(\a,\x)=\hat
c^{J_\D}_*(\a,\x):=\det J_\D(\a\x,\a\x)/\det J_\D(\x,\x)$. By
Remark \ref{rem:locMWM}, $\hat c^{J_\D}_*$ is a CPI of
$\m^{J_\D}$. Eq. \eqref{eq:compPapint} thus shows that
\[
\int f \,\hat c _*\,d (L_\L\otimes\m^{J_\D}) = \int \m^{J_\D}(d\x
) \sum_{\a\in\cX_0:\,\a\subset \x } f(\a, \x \sm \a)\,.
\]
The integrand on the right-hand side is still a bounded continuous
function of $\x$. Letting $\D\ua\SP$ we thus find that
\[
\int f \,\hat c _*\, d(L_\L\otimes\m )= \int f\, d\CCM[\m
]|_{\cX_\L\times \cX}\,.
\]
As $f$, $k$ and $\L$ were arbitrarily chosen, it follows that
$\hat c _*$ is a CPI of $\m $.\EndProof
Finally we prove Proposition \ref{prop:a.e.continuity} on the a.e.
continuity of $\hat c_*$.
\medskip
\Proof[ of Proposition \ref{prop:a.e.continuity}] Fix any $\L\in\cB_0$,
$\a\in\cX_\L$, and consider the function $\hat c_*(\a,\cdot)$. For
$\x\in \cX$ let $W(\a,\x)$ be the union of all clusters of
$B_R(\a\x)$ hitting $\a$, and write $\x_W=\x_{W(\a,\x)}$. By the
finite range assumption, $J(x,y)=0$ whenever $x\in \a\x_W$ and
$y\in \x\sm \x_W$. Hence, if $W(\a,\x)$ is finite then, for any
local $\D\supset W(\a,\x)$, the matrix $J(\a\x_\D,\a\x_\D)$
consists of the two diagonal blocks $J(\a\x_W,\a\x_W)$ and
$J(\x_{\D\sm W},\x_{\D\sm W})$. Thus
\[
\det J(\a\x_\D,\a\x_\D)= \det J(\a\x_W,\a\x_W)\, \det J(\x_{\D\sm
W},\x_{\D\sm W})\,.
\]
Dividing this by the analogous equation for $\a=\emptyset$ we
arrive at \eqref{eq:cJ-subcr}. By the continuity of the kernel $J$,
it follows that $\hat c_*(\a,\cdot)$ is continuous on the open
set of configurations having no infinite cluster, which has full measure
by assumption.\EndProof
\renewcommand{\thesection}{\Alph{section}}
\setcounter{section}{0}
\section{Appendix}
Here we collect some general facts on positive matrices and
operators. Some of them are standard and listed here for ease of
reference. (We include their simple proofs for the convenience of
the readers.) Some others are more subtle and do not seem to
appear in the literature, at least not in the form we need. We
start with a classical lemma on determinants of finite matrices.
The inequalities \eqref{eq:det2} and \eqref{eq:det3} are a key ingredient
of our arguments; \eqref{eq:det2} is known as Fischer's inequality. To state
the lemma we consider a finite index set $\G$ and any complex matrix
$A=(a_{ij})_{i,j\in \G}$. For any two subsets $\a,\b\sub \G$ we let
$A_{\a,\b}=(a_{ij})_{i\in \a,j\in \b}$ be the associated submatrix.
\begin{lem}\label{lem:determinant-relation}
If $A$ is Hermitian and positive definite then
\begin{equation}\label{eq:det2}
\det A \le \det A_{\a,\a} \,\det A_{\b,\b}
\end{equation}
when $\G=\a\cup\b$ is partitioned into two nontrivial subsets, and
\begin{equation}\label{eq:det3}
\det A \;\det A_{\b,\b} \le \det A_{\a\cup\b,\a\cup\b}
\,\det A_{\b\cup\g,\b\cup\g}
\end{equation}
when $\G=\a\cup\b\cup\g$ is partitioned into three nontrivial subsets.
For $\G=\a\cup\b$ and general $A$ with invertible $A_{\b,\b}$ we have
\begin{equation}\label{eq:det-ratio}
\det A/\det A_{\b,\b}= \det \,(a^\b_{kl})^{\phantom{\b}}_{k,l\in
\a}
\end{equation}
with $a^\b_{kl} = \det A_{\b\cup\{k\}, \b\cup\{l\}}/\det A_{\b,\b}$.
\end{lem}
\Proof If $\G=\a\cup\b$ and $A_{\b,\b}$ is invertible we can write
\[
A=\begin{pmatrix}A_{\a,\a}&A_{\a,\b}\\A_{\b,\a}&A_{\b,\b}\end{pmatrix} =
\begin{pmatrix}A_{\a,\a}-A_{\a,\b}A_{\b,\b}^{-1}A_{\b,\a}&
A_{\a,\b}A_{\b,\b}^{-1}\\0&I\end{pmatrix}
\begin{pmatrix}I&0\\ A_{\b,\a}&A_{\b,\b}\end{pmatrix}\,,
\]
where $I$ is the identity matrix. Hence
\begin{equation}\label{eq:det1}
\det A /\det A_{\b,\b}=
\det(A_{\a,\a}-A_{\a,\b}A_{\b,\b}^{-1}A_{\b,\a})
\end{equation}
Now, if $A$ is Hermitian and positive definite then
$A_{\a,\b}A_{\b,\b}^{-1}A_{\b,\a}\ge0$, and the determinant is monotone
with respect to the
operator ordering. This implies \eqref{eq:det2} for invertible $A_{\b,\b}$. For general $A_{\b,\b}$ one can approximate
$A_{\b,\b}$ by invertible matrices. To prove \eqref{eq:det3} one can assume that
$\det A_{\b,\b}>0$ and then divide both sides
by $\det^2 A_{\b,\b}$. In view of \eqref{eq:det1}, \eqref{eq:det3} then takes the form
\[
\begin{split}
&\det (A_{\a\cup\g,\a\cup\g}-A_{\a\cup\g,\b}A_{\b,\b}^{-1}A_{\b,\a\cup\g}) \\
&\qquad\qquad\le
\det(A_{\a,\a}-A_{\a,\b}A_{\b,\b}^{-1}A_{\b,\a})\,
\det(A_{\g,\g}-A_{\g,\b}A_{\b,\b}^{-1}A_{\b,\g})
\end{split}
\]
which follows from \eqref{eq:det2}. To verify \eqref{eq:det-ratio} we
have to show that the right-hand sides of \eqref{eq:det1} and
\eqref{eq:det-ratio} are identical. However, applying \eqref{eq:det1}
to the matrix $A_{\a\cup\{k\}, \a\cup\{l\}}$ it is easily seen that $a^\b_{kl}$
is precisely the $kl$-entry of the matrix
on the right-hand side of \eqref{eq:det1}.\EndProof
The second subject of this appendix is the proper choice of
integral kernels. Note that we need to evaluate such integral
kernels at the points of configurations in $\SP$. This leads us to
the following concept. Let us say that two functions
$t_1,t_2:\SP^2\to\C$ are \emph{indistinguishable} ($L$-almost
everywhere) if
\[
L\Big(\a\in\cX_0: t_1(x,y)\ne t_2(x,y)\text{ for some }x,y\in\a\Big)=0\,.
\]
The lemma below shows the significance of trace formulas for indistinguishability.
As before, we write $T_\L=P_\L TP_\L$.
\begin{lem}\label{lem:indistinguishable}
Let $T$ be a local trace class integral operator on $L^2(\SP,\l)$ and $t_1,t_2$
be two integral kernels of $T$ satisfying
\[
\Tr\, T_\L=\int_{\L}t_i(x,x)\,\l(dx)
\]
for all $\L\in\cB_0$, $i=1,2$. Then $t_1$ and $t_2$ are indistinguishable.
\end{lem}
\Proof Since both $t_1$ and $t_2$ are integral kernels of $T$, we have
$t_1=t_2$ almost everywhere with respect to $\l^{\otimes 2}$.
On the other hand, since the local trace formula holds for each $\L\in\cB_0$,
it follows that $t_1=t_2$ almost everywhere also with respect to
$\bar\l:= \l(x: (x,x)\in \,\cdot\,)$. So, the set $\cN=\{t_1\ne t_2\}$ is a
nullset for both $\l^{\otimes 2}$ and $\bar\l$.
This proves the lemma because
\[
\hat\cN:= \{\a\in\cX_0: (x,y)\in\cN\text{ for some }x,y\in\a\}
\]
is then a nullset for $L$.\EndProof
As for the existence of suitable integral kernels, we consider
first the case of trace class operators. (For $\SP=\R^d$, the
trace formula \eqref{eq:trace-formula} appears also in \cite[Lemma
2]{So}.) Recall that a function $t:\SP\times\SP\to\C$ is called
\emph{positive definite} if for any $n\in \N$,
$\{c_i\}_{i=1}^n\subset\C$ and $\{x_i\}_{i=1}^n\subset \SP$,
\begin{equation}\label{eq:positivity}
\sum_{i,j=1}^n \ol{c}_i\,t(x_i,x_j)\,c_j\ge 0.
\end{equation}
\begin{lem}\label{lem:positive_kernel}
Let $T\ge 0$ be any trace class operator on $L^2(\SP,\l)$. Then
$T$ admits a positive definite integral kernel $t(x,y)$ satisfying
\begin{equation}\label{eq:trace-formula}
\Tr(P_\L T^k P_\L)=\int_{\SP^k}1_\L(x_1)\,t(x_1,x_2)\cdots
t(x_k,x_1)\,\l(dx_1)\cdots\l(dx_k)
\end{equation}
for all $k\ge 1$ and $\L\in\cB$.
\end{lem}
\Proof Since $T$ is positive and of trace class, there exists a
Hilbert-Schmidt operator $S$ such that $T=S^*S$. Let $s(x,y)$ be
an integral kernel function of $S$ and $s^*(x,y):=\ol{s(y,x)}$ the
associated kernel of $S^*$. The Hilbert-Schmidt norm of $S$
satisfies $\|S\|_2^2=\int_{\SP^2}|s(x,y)|^2\l(dx)\l(dy)<\infty$.
There exists therefore a $\l$-nullset $\cN \subset\SP$ such that
$s(\cdot,y)\in L^2(\SP,\l)$ for $y\notin \cN $. Define $t(x,y)=\int
s^*(x,z)s(z,y)\,\l(dz)$ if $x,y\notin \cN $ and $t(x,y)=0$ otherwise.
Then $t$ is an integral kernel of $T$, and for
$\{c_i\}_{i=1}^n\subset\C$ and $\{x_i\}_{i=1}^n\subset \SP$ one
has
\[
\sum_{i,j=1}^n \ol{c}_i\, t(x_i,x_j)c_j=\int \big|\sum_{j=1}^n
c_j\,s(z,x_j)\big|^2\,\l(dz)\ge 0.
\]
On the other hand,
\[
\Tr\,T=\Tr\,S^*S=\|S\|_2^2=\int_{\SP^2}|s(x,y)|^2\l(dx)\l(dy)=\int_\SP
t(x,x)\l(dx),
\]
proving \eqref{eq:trace-formula} for $k=1$ and $\L=\SP$. To check
the case $\L\sub\SP$, it is sufficient to note that $SP_\L$ admits
the kernel $s(x,y)1_\L(y)$. The case of powers $T^k$ with $k>1$
follows similarly because $T^k=(S^{(k)})^*S^{(k)}$ with
$S^{(k)}=S^*S\cdots S^\sharp$, where $S^\sharp=S$ if $k$ is even
and $S^\sharp=S^*$ if $k$ is odd.\EndProof
Next we need to extend Lemma \ref{lem:positive_kernel} to integral
operators which are only local trace class.
\begin{lem}\label{lem:loc_trace_formula}
Let $T\ge 0$ be a bounded local trace class integral operator
on $L^2(\SP,\l)$. Then one can choose its integral
kernel $t(x,y)$ such that the following properties hold:
\begin{enumerate}
\item $t(\a,\a)\ge 0$ for $L$-a.a. $\a\in \cX_0$;
\item $t(x,y)$ is a Carleman
kernel, i.e., $t_x:=t(\cdot,x)\in L^2(\SP,\l)$ for $\l$-a.a. $x\in \SP$;
\item For any $\L\in \cB_0$, $\Tr(T_\L)=\int_\L t(x,x)\,\l(dx)$ and
\[
\Tr(P_\L T^k P_\L)=\int_\L (t_x,T^{k-2} t_x)\,\l(dx)
\]
for $k\ge 2$, where $(\cdot,\cdot)$ stands for the inner product in $L^2(\SP,\l)$.
\end{enumerate}
\end{lem}
\Proof
For each $\D\in\cB_0$ we choose an integral kernel $t_\D$ of
$T_\D$ according to Lemma \ref{lem:positive_kernel}. For any
$\L\sub\D$, $1_\L(x)t_\D(x,y)1_\L(y)$ is also an integral kernel
of $T_\L$ which satisfies the assumptions of Lemma
\ref{lem:indistinguishable}. As in the proof of that lemma, we
thus find a set $\cN_{\L,\D}$ which is a nullset for both
$\l^{\otimes 2}$ and $\bar\l$ such that $t_\L=t_\D$ on
$\L^2\sm\cN_{\L,\D}$.
Now let $(\D_n)_{n\ge1}$ be a sequence in $\cB_0$ increasing to
$\SP$, and consider the set $\cN=\bigcup_{n\ge1}\cN_{\D_n,\D_{n+1}}$.
For $(x,y)\notin\cN$ we let $t(x,y)$ be the common value of all
$t_{\D_n}(x,y)$ with $\D_n\ni x,y$, and define $t=0$ on $\cN$.
Since $T$ is supposed to admit an integral kernel $\tilde t$, it is then
clear that
\[
\int_{\SP^2}\ol{f(x)}\,\big[t(x,y)-\tilde t(x,y)\big] \,g(y)\, \l(dx)\l(dy) = 0
\]
whenever $f,g\in L^2(\SP,\l)$ vanish outside some $\D_n$, and
hence that $t=\tilde t$ $\l^{\otimes 2}$-a.e., meaning that $t$ is
also a kernel for $T$. By construction, $t$ is indistinguishable
from $t_{\D_n}$ under $L_{\D_n}$, and $t_{\D_n}$ is positive
definite. This yields assertion (a).
To prove (b) and (c) we proceed as follows.
Let $T_n:=T_{\D_n}$ for brevity. Since $T$ is bounded,
$P_\L T_n^k P_\L$ converges strongly to $P_\L T^k
P_\L$ as $n\to \infty$. In particular, it converges weakly.
Since also both $P_\L T_n^k P_\L $ and $P_\L T^k P_\L
$ are bounded from above by the trace class operator
$\|T\|^{k-1}T_\L$, it follows that the sequence $(P_\L
T_n^k P_\L)_{n\ge 1}$ converges to $P_\L T^k P_\L$
in trace norm \cite[Theorem 2.16]{Si}. Hence
\begin{equation}\label{eq:tr_convergence}
\Tr(P_\L T^kP_\L)=\lim_{n\to \infty}\Tr(P_\L T_n^kP_\L).
\end{equation}
However, $t_{\D_n}$ has been chosen to satisfy the identity
\begin{equation}\label{eq:locTrace3}
\Tr(P_\L T_n^kP_\L)=
\int_{\D_n^k}1_\L(x_1)\,t_{\D_n}(x_1,x_2)\cdots
t_{\D_n}(x_k,x_1)\,\l(dx_1)\cdots\l(dx_k),
\end{equation}
and we have seen that $t_{\D_n}$ can be replaced by $t$
in this integral. Hence, statement (c) will be proved
once we have shown that the right-hand side of
\eqref{eq:locTrace3} converges to the integrals in (c).
For $k=1$, this is evident from the above. In the case
$k=2$, \eqref{eq:locTrace3} means that
\[
\Tr(P_\L T_n^2
P_\L)=\int_{\SP^2}1_\L(x_1)1_{\D_n}(x_2)\,|t(x_1,x_2)|^2\,\l(dx_1)\l(dx_2).
\]
The integrand is nonnegative and increases to $1_\L(x_1)|t(x_1,x_2)|^2$
as $n\to \infty$. On the other hand, $\Tr(P_\L T_n^2 P_\L)\le
\|T\|\Tr(P_\L T_n P_\L)=\|T\|\Tr(T_\L)<\infty$ for all $n$ with
$\D_n\supset \L$. The monotone convergence theorem thus shows that $1_\L(x_1)|t(x_1,x_2)|^2$ is integrable on $\SP^2$. This proves statement (c)
for $k=2$, and also assertion (b) by Fubini's theorem.
Finally, let $k\ge3$. Eq.~\eqref{eq:locTrace3} can then be rewritten
in the form
\[
\Tr(P_\L T_n^kP_\L)=
\int_{\L}(t_x,T_n^{k-2}t_x)\, \l(dx),
\]
and the integrand is bounded by $(t_x,T_n^{k-2}t_x)\le \|T\|^{k-2}(t_x,t_x)$
uniformly in $n$. We also know from the case $k=2$ that this
upper bound is locally integrable. We know further that
$(t_x,T_n^{k-2}t_x)$ converges to
$(t_x,T^{k-2}t_x)$ for all $x$ with $t_x\in L^2(\SP,\l)$, and thus
for $\l$-a.a. $x$. Again, these functions are bounded by
$\|T\|^{k-2}(t_x,t_x)$. Together with \eqref{eq:tr_convergence},
this gives the trace formula in (c) for $k\ge3$. The proof is
therefore complete.\EndProof
A final useful tool is the following projection-inversion lemma
appearing without proof in \cite[p. 18]{OP}; see
\cite[Corollary 5.3]{ST2} for the matrix version.
\begin{lem}\label{lem:basic-order}
Let $T$ be any bounded positive operator with bounded inverse
$T^{-1}$. Then for any projection $P$,
\[
PT^{-1}P\ge P(PTP)^{-1}P.
\]
\end{lem}
\Proof Since $T$ is positive and invertible, any restriction of
$T$ to some subspace is invertible in this subspace. This means
that the operators $R:=P(PTP)^{-1}P$ and
$S:=P^\bot(P^\bot T^{-1}P^\bot)^{-1}P^\bot$ are
well-defined, where $P^{\bot}=I-P$. The key
observation is the decomposition formula
\begin{equation}\label{eq:decomposition}
PT^{-1}P=R+PT^{-1}ST^{-1}P\,.
\end{equation}
To see this we observe that $P^\bot T^{-1}(P^\bot+P)TP=0$.
Multiplying with $S$ from the left we find $P^\bot
TP=-S T^{-1}PTP$. Inserting this into the identity
$PT^{-1}(PTP+P^\bot TP)=P$ we get
\[
PT^{-1}\Big(I-ST^{-1}\Big)PTP=P.
\]
Multiplying with $R$ from the right and rearranging we
arrive at \eqref{eq:decomposition}. As the second operator on the
right-hand side of \eqref{eq:decomposition} is positive, the lemma
follows.\EndProof
\medskip\small
\noindent{\it Acknowledgments}. We are grateful to the
referees whose remarks helped to improve this paper. H.J.Y. would
like to thank Prof. T. Shirai and Prof. Y. Takahashi for inviting
him to Kanazawa University. Part of this work was done during this
stay. We also thank Prof. Y. M. Park for informing us about
reference \cite{OP}. H.J.Y. was supported by Korea Research
Foundation Grant (KRF-2002-015-CP0038).
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\end{document}
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Interacting particle systems, spectral gap,
Poincare inequality, Log-Sobolev inequality, Conservative spin systems,
Continuous spin systems
---------------0201210008946
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\newcommand{\mykeywords}{Interacting particle systems, spectral gap,
Poincaré inequality, Log-Sobolev inequality, Conservative spin systems,
Continuous spin systems}
\newcommand{\mysubjclass}{
60K35 Interacting random processes,
82B44 Disordered systems,
82B20 Lattice systems,
46-99 Functional analysis,
60J60 Diffusion processes,
26D10 Inequalities involving derivatives, differential and integral operators}
\title{Glauber versus Kawasaki for spectral gap\\ and logarithmic Sobolev
inequalities\\ of some unbounded conservative spin systems}
\date{University of Toulouse\\ \medskip \small \today}
\author{D.~Chafaï}
%
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%
\begin{document}
\maketitle
\begin{abstract}
Inspired by the recent results of C. Landim, G. Panizo and H.-T. Yau
\cite{landim-panizo-yau} on spectral gap and logarithmic Sobolev
inequalities for unbounded conservative spin systems, we study uniform
bounds in these inequalities for Glauber dynamics of Hamiltonian of the form
$$
\sum_{i=1}^n V(x_i)+V\biggl(\MSX\biggr), \quad (x_1,\ldots,x_n)\in\dR^n
$$
Specifically, we examine the case $V$ is strictly convex (or
small perturbation of strictly convex) and, following
\cite{landim-panizo-yau}, the case $V$ is a bounded perturbation of
a quadratic potential. By a simple path counting argument for the
standard random walk, uniform bounds for the Glauber dynamics
yields, in a transparent way, the classical $L^{-2}$ decay for the
Kawasaki dynamics on $d$-dimensional cubes of length $L$. The
arguments of proofs however closely follow and make heavy use of
the conservative approach and estimates of \cite{landim-panizo-yau},
relying in particular on the Lu-Yau martingale decomposition and
clever partitionings of the conditional measure.
\end{abstract}
%
\section*{Introduction}
%
Let $Q$ be a probability measure on $\dR^n$. In the sequel, we denote
by $\moy{Q}{f}$ the expectation of $f$ with respect to $Q$,
$\var{Q}{f}:=\moy{Q}{f^2}-\moy{Q}{f}^2$ the variance of $f$ for $Q$,
and $\ent{Q}{f}$ the entropy of a non negative measurable function $f$
with respect to $Q$, defined by
$$
\ent{Q}{f}:=\int\! f\log f dQ - \int\! f dQ \;\log \int\! f dQ.
$$
We say that $Q$ satisfies a Poincaré inequality if there exists a positive
constant $\cP$ such that for any smooth function $f:\dR^n\to\dR$,
\begin{equation}\label{in:def-ts}
\var{Q}{f} \leq \cP\, \moy{Q}{\ABS{\GR f}^2},
\end{equation}
where $\ABS{\GR f}^2:=\sum_{i=1}^n \ABS{\pd_i f}^2$. Similarly, we say that
$Q$ satisfies a logarithmic Sobolev inequality if there exists a positive
constant $\cL$ such that for any smooth function $f$,
\begin{equation}\label{in:def-ls}
\ent{Q}{f^2} \leq \cL\, \moy{Q}{\ABS{\GR f}^2}.
\end{equation}
This inequality strengthen the Poincaré inequality \eqref{in:def-ts} since for
$\veps$ small enough,
$$
\ent{Q}{(1+\veps f)^2}=2\veps^2\var{Q}{f}+\cO(\veps^3),
$$
which gives $2\cP \leq \cL$. Let $\cH\in\cC^2(\dR^n,\dR)$ such that
$$
Z_{\cH}:=\int_{\dR^n}\!\!e^{-\cH(x)}\,dx < +\infty.
$$
The probability measure $Q$ defined by
$dQ(x)=(Z_{\cH})^{-1}\exp\PAR{-\cH(x)}\,dx$ is the symmetric invariant measure
of the diffusion process $(X_t)_{t\geq 0}$ on $\dR^n$ driven by the S.D.E.
$$
dX_t = \sqrt{2}\,dB_t - \GR \cH(X_t)\,dt,
$$
where $(B_t)_{t\geq 0}$ is a standard brownian motion on $\dR^n$.
In this context, we say that the probability measure $Q$ is associated
with the ``Hamiltonian'' $\cH$. It is well known that $Q$ satisfies
the Poincaré inequality \eqref{in:def-ts} with a constant $\cP$ if and
only if the infinitesimal generator $\GI:=\LA-\GR\cH\cdot\GR$
possesses a spectral gap greater than $\cP^{-1}$. In the other hand, a
famous Theorem of Gross states that $Q$ satisfies the logarithmic
Sobolev inequality \eqref{in:def-ls} if and only if the diffusion
semi-group generated by $\GI$ is hyper-contractive. A celebrated
result of Bakry and Émery ensures that when there exists a constant
$\rho>0$ such that for any $x\in\dR^n$,
$$
\Hess{\cH}(x)\geq \rho\,\bI_{p}
$$
as quadratic forms on $\dR^n$, i.e. $\cH$ is uniformly strictly convex or
$Q$ is log-concave, then $Q$ satisfies to \eqref{in:def-ts} and
\eqref{in:def-ls} with constants $\cP=\rho^{-1}$ and $\cL=2\,\rho^{-1}$
respectively. Moreover, $Q$ satisfies to \eqref{in:def-ts} with a constant
$\cP$ if and only if
$$
\cP\moy{Q}{(\GI f)^2} \geq \moy{Q}{\ABS{\GR f}^2}
$$
for any smooth function $f$. The reader may find an introduction to
logarithmic Sobolev inequalities and related fields in \cite{our-ls-2000}.
We are interested in the present work to particular ``Hamiltonians''
$H\in\cC^2(\dR^{n+1},\dR)$. Let $M\in\dR$ and define $H_M\in\cC^2(\dR^n,\dR)$
by
\begin{equation}\label{eq:defhm}
H_M(x_1,\ldots,x_n):=H\biggl(x_1,\ldots,x_n,\MSX\biggr).
\end{equation}
Assume that $Z_{H_M}<\infty$. Our aim is to establish Poincaré and
logarithmic Sobolev inequalities for probability measures on $\dR^n$ of the
form
\begin{equation}\label{eq:defnum}
d\si_M(x_1,\ldots,x_n):=(Z_{H_M})^{-1}\,\exp\PAR{-H_M(x)}\,dx_1\cdots dx_n,
\end{equation}
with constants $\cP$ and $\cL$ which does not depend on $n$ and $M$. This
investivation is motivated by the study of certain conditional probability
measures. Namely, if the probability measure $\mu$ on $\dR^{n+1}$ given by
\begin{equation}\label{eq:defmu}
d\mu(x):=(Z_H)^{-1}\,\exp\PAR{-H(x_1,\ldots,x_{n+1})}\,dx_1\cdots dx_{n+1}
\end{equation}
is well-defined, i.e. $Z_H<+\infty$, then for any $M\in \dR$, one can define
the conditional probability measure $\mu_M$ by
\begin{equation}\label{eq:defmum}
\mu_M:=\mu\biggl(\;\cdot\;\Bigr\vert\;\sum_{i=1}^{n+1} x_i=M\biggr),
\end{equation}
and we get, for any $f\in\cC_b(\dR^{n+1},\dR)$,
\begin{equation}\label{eq:mum2num}
\moy{\mu_M}{f}=\int_{\dR^n}\! f\biggl(x_1,\ldots,x_n,\MSX\biggr)\,
d\si_M(x_1,\ldots,x_n).
\end{equation}
Thus, $\si_M$ can be viewed as the translation of the conditional
probability measure $\mu_M$ under the affine hyperplane of $\dR^{n+1}$
of equation $x_1+\cdots+x_{n+1}=M$. Alternatively, and following
Caputo in \cite{caputo}, the conditional probability measure $\mu_M$
can be defined from the probability measure $\mu$ given in
\eqref{eq:defmu} by adding an infinite potential outside of the affine
constraint $x_1+\cdots+x_{n+1}=M$. Namely for any bounded continuous
function $f:\dR^{n+1}\to\dR$
$$
\moy{\mu_M}{f}=\lim_{\be\to+\infty} \moy{\mu_{M,\be}}{f}.
$$
where $\mu_{M,\be}$ denotes the probability measure on $\dR^{n+1}$
defined by
$$
d\mu_{M,\be}(x)
:= \cZ_{\mu_{M,\be}}^{-1}\,e^{-\be\,\PAR{M-x_1-\cdots-x_{n+1}}^2}\,d\mu(x).
$$
A simple change of variable in $\moy{\mu_{M,\be}}{f}$ gives that
$$
\lim_{\be\to+\infty} \moy{\mu_{M,\be}}{f}=
\int_{\dR^n}\! f\biggl(x_1,\ldots,x_n,\MSX\biggr)\,d\si_M(x_1,\ldots,x_n),
$$
This weak limit definition of $\mu_M$ was used by Caputo in
\cite{caputo} in order to study the case of a convex Hamiltonian $H$.
We do not use it in our approach. Notice that if
$f\in\cC_b(\dR^n,\dR)$, we get from \eqref{eq:mum2num} that
\begin{equation}\label{eq:mumeqnum}
\moy{\si_M}{f}
=\int_{\dR^{n+1}}\!f(x_1,\ldots,x_n)\, d\mu_M(x_1,\ldots,x_{n+1}).
\end{equation}
Observe that \eqref{eq:mum2num} gives $\moy{\mu_M}{x_1+\cdots+x_{n+1}}=M$.
Thus, when $H$ is a symmetric function, $\si_M$ and $\mu_M$ are exchangeable
measures, i.e. invariant by any permutation of the coordinates. This holds for
example when $H(x)=V(x_1)+\cdots+V(x_{n+1})$. Moreover, $\MSX$ and $x_j$ have
then the same law under $\si_M$ for any $j$ in $\{1,\ldots,n\}$ and we get
\begin{equation}\label{eq:mum-num-moy}
\moy{\mu_M}{x_1}=\cdots=\moy{\mu_M}{x_{n+1}}
=\moy{\si_M}{x_1}=\cdots=\moy{\si_M}{x_n}
=\frac{M}{n+1}.
\end{equation}
Thus, the mean of $\mu_M$ and $\si_M$ does not depend on $H$ in this case.
Let us see now how to translate \eqref{in:def-ts} and \eqref{in:def-ls} for
$\si_M$ in terms of $\mu_M$. One can observe that for any $i\in\{1,\ldots,n\}$
\begin{multline*}
\pd_i\BPAR{f\BPAR{x_1,\ldots,x_n,\MSX}} \\
=(\pd_i f)\BPAR{x_1,\ldots,x_n,\MSX}-(\pd_{n+1} f)\BPAR{x_1,\ldots,x_n,\MSX}.
\end{multline*}
By replacing the coordinate $x_{n+1}$ by any of the $x_1,\ldots,x_n$ in
\eqref{eq:mum2num}, we obtain the following proposition
\begin{prop}\label{pr:num-mum}
Let $H:\dR^{n+1}\to\dR$ and assume that for any permutation $\pi$ of the
coordinates, the probability measure $\si_M^\pi$ on $\dR^n$ defined by
\eqref{eq:defnum} and associated to $H\circ \pi$ satisfies to Poincaré
(resp. logarithmic Sobolev) inequality with a constant $\cP$ (resp. $\cL$)
which does not depend on $n$, $M$ and $\pi$. Then, if $\mu_M$ is the
associated conditional probability measure defined by \eqref{eq:defmum}, we
get for any smooth $f:\dR^{n+1}\to\dR$
\begin{equation}\label{in:ts-ij}
\var{\mu_M}{f}
\leq
\frac{\cP}{n+1}
\;\moy{\mu_M}{\sum_{1\leq i,j\leq n+1}\ABS{\pd_i f-\pd_j f}^2},
\end{equation}
and respectively
\begin{equation}\label{in:ls-ij}
\ent{\mu_M}{f^2}
\leq
\frac{\cL}{n+1}
\;\moy{\mu_M}{\sum_{1\leq i,j\leq n+1}\ABS{\pd_i f-\pd_j f}^2}.
\end{equation}
\end{prop}
These inequalities leads to constants in $L^2$ for the ``Kawasaki
dynamics'' associated to $\mu_M$. Namely, consider a finite box
$\La:=\{1,\ldots,L\}^d\subset\dZ^d$ on the lattice $\dZ^d$ and $n$
such that $\dR^\La\simeq\dR^{n+1}$ (i.e. $n+1=\ABS{\La}=L^d$). There
exists a constant $C>0$ depending only on $d$ such that for any
$a\in\dR^\La$
\begin{equation}\label{in:compdirf}
\frac{1}{\ABS{\La}}\sum_{i,j\in\La}(a_i-a_j)^2
\leq
C\;L^2\;\sum_{\SSK{i,j\in\La\\\ABS{i-j}=1}}(a_i-a_j)^2,
\end{equation}
Therefore, it is straightforward to deduce from \eqref{in:ts-ij} and
\eqref{in:ls-ij} that for a constant $C>0$ which does not depend on
$n$ and $M$, one have
\begin{equation}\label{in:ts-l2}
\var{\mu_M}{f}
\leq C\,L^2\; \sum_{\SSK{k,l\in\La\\\ABS{k-l}=1}}
\moy{\mu_M}{\ABS{\pd_i f-\pd_j f}^2},
\end{equation}
and
\begin{equation}\label{in:ls-l2}
\ent{\mu_M}{f^2} \leq
C\,L^2\;
\sum_{\SSK{k,l\in\La\\\ABS{k-l}=1}}
\moy{\mu_M}{\ABS{\pd_i f-\pd_j f}^2}.
\end{equation}
Inequality \eqref{in:compdirf} follows from a classical path counting argument
(see for example section 4.2 of \cite{saloffcoste}). However, let us gives
briefly a proof. For any $i,j$ in $\La$, consider the path $\Ga_{ij}$ inside
$\La$ joining $i$ and $j$ obtained by adjusting the $d$ coordinates one after
the other. We have $\ABS{\Ga_{ij}}\leq dL$ and for each $k,l$ in $\La$ with
$\ABS{k-l}=1$, the number of such paths containing the edge $(k,l)$ is bounded
above by $c_d\,L^{d+1}$ where $c_d>0$ is a constant depending only on $d$. Now
by Cauchy-Schwarz's inequality
$$
(a_i-a_j)^2
=
\SBRA{\sum_{(k,l) \in \Ga_{i,j},\,\ABS{k-l}=1}\!\!(a_k-a_l)}^2
\leq
dL \sum_{(k,l) \in \Ga_{i,j},\,\ABS{k-l}=1} (a_k-a_l)^2,
$$
and therefore
$$
\sum_{i,j\in\La} (a_i-a_j)^2
\leq
dL \sum_{\SSK{\ABS{k-l}=1\\k,l\in \La}}
(a_k-a_l)^2\sum_{\SSK{i,j\in\La\\\Ga_{i,j}\ni(k,l)}}\!\!\!1
\leq
dc_d L^{d+2} \sum_{\SSK{\ABS{k-l}=1\\k,l\in \La}} (a_k-a_l)^2,
$$
which gives the desired result \eqref{in:compdirf}.
A simple example is given by uniformly strictly convex $H$ with a constant
$\rho$ in $\dR^{n+1}$. Namely, if there exists a constant $\rho>0$ such that
for any $x\in\dR^{n+1}$, $\Hess{H}(x)\geq \rho \bI_{n+1}$ as quadratic forms
on $\dR^{n+1}$, then, an easy calculus gives for any $x\in\dR^n$ and
$h\in\dR^n$
$$
\DP{(\Hess{H_M})(x) h,h}_{\dR^n}
\geq \rho
\sum_{i=1}^n h_i^2 + \rho \PAR{-\sum_{i=1}^n h_i}^2 \geq \rho \sum_{i=1}^n h_i^2.
$$
Thus, $H_M$ is uniformly strictly convex with the same constant
$\rho$, and therefore, by the Bakry-Émery criterion, $\si_M$ satisfies
to Poincaré and logarithmic Sobolev inequalities with a constant
$\rho^{-1}$ and $2\,\rho^{-1}$ respectively, which does not depend on
$n$ and $M$. The hypotheses of Proposition \ref{pr:num-mum} are
full-filled since by the same calculus, $(H\circ\pi)_M$ is also
uniformly strictly convex with a constant $\rho$. A more simple
example is given by
$$
H(x)=V(x_1)+\cdots+V(x_{n+1})
$$
where $V$ is in $\cC^2(\dR,\dR)$ with $V''>\rho>0$. Let us
consider now another convex Hamiltonian example on $\dR^{n+1}$ defined
by
$$
H(x):=\frac{1}{2(n+1)}\,\sum_{i,j=1}^{n+1} V_{\{i,j\}}(x_i-x_j),
$$
where $V_{\{i,j\}}$ are in $\cC^2(\dR,\dR)$ and even. This is a so called
mean-field Hamiltonian when all the $V_{\{i,j\}}$ are equal. We have for any
$i,j$ in $\{1,\ldots,n+1\}$
$$
(n+1)\,\pd^2_{ij} H(x)=
\begin{cases}
\sum_{\SSK{k=1\\k\neq i}}^{n+1} V''_{\{i,k\}}(x_i-x_k) & \text{ if } i=j\\
-V''_{\{i,j\}}(x_i-x_j) & \text{ if } i\neq j
\end{cases}
$$
Therefore, if $V''_{\{i,j\}}(u)\geq 0$ for any $u\in\dR$ and any
$i,j\in\{1,\ldots,n+1\}$, i.e. $V_{\{i,j\}}$ is convex, the
Gershgorin-Hadamard theorem implies that for any $x\in\dR^{n+1}$,
$\Hess{H}(x)\geq 0$ as a quadratic form, and thus $H$ is convex on
$\dR^{n+1}$. Unfortunately, since $\sum_{j=1}^{n+1} \pd^2_{ij} H(x)=0$ for
any $i\in\{1,\ldots,n+1\}$, the null space of $\Hess{H}$ contains $\Vo_{n+1}$
and therefore, the measure $\mu$ on $\dR^{n+1}$ defined by
$d\mu(x):=\exp\PAR{-H(x)}\,dx$ cannot be normalised into a probability measure
since $Z_\mu:=\mu(\dR^{n+1})=+\infty$. Nevertheless, suppose that there
exists a constant $\rho>0$ such that $V''_{\{i,j\}}(u)\geq \rho$ for any
$u\in\dR$ and any $i,j\in\{1,\ldots,n\}$. Then, $u\in\dR\mapsto
V_{\{i,j\}}(u)-\rho u^2/2$ is convex and the latter implies that
$$
\Hess{H}(x) \geq \rho\,\bI_{n+1}-(n+1)^{-1}\rho\,\Mo_{n+1},
$$
as quadratic forms. Thus, by writing
$\dR^{n+1}=\dR\Vo_{n+1}\overset{\perp}{\oplus}\cH_n$ where $\cH_n$ is the
hyperplane of equation $h_1+\cdots+h_{n+1}=0$, we get that the spectrum of
$\Hess{H}(x)$ is of the form
$$
\{0=\la_1(x)<\la_2(x)\leq\cdots\leq\la_{n+1}(x)\}
$$
with $\la_2(x)\geq n(n+1)^{-1}\rho$. Hence, one can define the probability
measure $\si_M$ on $\dR^n$ as in \eqref{eq:defnum} for any $M$ in $\dR$.
Moreover $\si_M$ is uniformly log-concave with a constant $n(n+1)^{-1}\rho$ and
therefore the conditional measure $\mu_M$ can be defined from $\si_M$ as a
probability measure by equation \eqref{eq:mum2num}, despite the fact that
$\mu$ is not a probability measure on $\dR^{n+1}$. The particular case
$V_{\{i,j\}}=V$ with $V$ even and uniformly convex is considered for example
in \cite{malrieu-projection}, in terms of the associated S.D.E., in order to
study the granular media equation.
As we seen, when $H$ is uniformly strictly convex with a constant
$\rho>0$, the hypotheses of Proposition \ref{pr:num-mum} are
full-filled and hence, inequalities \eqref{in:ts-l2} and
\eqref{in:ls-l2} hold. It is quite natural to ask if \eqref{in:ts-l2}
and \eqref{in:ls-l2} remains true for symmetric but non convex
Hamiltonians $H$. In this direction, the Bakry-Émery criterion allows
the following perturbative statement due to Ivan Gentil. The proof,
prototype of which can be found in \cite{ledoux-lsrev}, is taken from
\cite{hel-bod} and is postponed to section \ref{se:pr:pr:ivan}.
\begin{prop}[Perturbative result]\label{pr:ivan}
Let $H(x)=V(x_1)+\cdots+V(x_{n+1})$ with
$$
V(u)=\frac{u^2}{2}+F(u)
$$
where $F:\dR\to\dR$, and let $\si_M$ be the probability measure on
$\dR^n$ defined by \eqref{eq:defnum}, namely
$$
\si_M(dx_1,\ldots,dx_n)
=(Z_{\si_M})^{-1}
\int_{\dR^{n}}\!\exp\BPAR{-\sum_{i=1}^n V(x_i)-V(\MSX)}\,dx_1\cdots dx_n.
$$
Then, for \NI{F} small enough, there exists a positive constant $\cP$
depending only on \NI{F} such that for any $n$, any $M$ and any smooth
$f:\dR^n\to\dR$,
\begin{equation}\label{in:ivan}
\var{\si_M}{f} \leq \cP\,\moy{\si_M}{\ABS{\GR f}^2}.
\end{equation}
\end{prop}
Proposition \ref{pr:ivan} remains valid if we replace, in the definition of
$\si_M$, the square function $u\mapsto u^2/2$ by a smooth convex function
$u\mapsto \Phi(u)$, provided that there exists real constants $\al$ and $\be$
such that $0<\al\leq\be\leq 2\al$ and $\al\leq \Phi''(u) \leq \be$ for every
$u\in\dR$. The constant $\cP$ becomes in this case
$e^{2\,\OSC{F}}/\PAR{2\al\,e^{-2\,\OSC{F}}-\be}$ for
$\OSC{F}<\log\sqrt{2\al/\be}$.
The exchangeability of the underlying measure $\mu_M$ indicates that the
perturbative approach by mean of Helffer's method which sees $\si_M$ as a
quasi-product measure with small interactions is not relevant : any reduction
of $F$ in the interaction term
$$
V\BPAR{\MSX}
$$
affects the product term $\sum_{i=1}^n V(x_i)$. Helffer's method was
essentially developed for spins systems with \emph{boundary conditions} for
which the measure is not exchangeable. For our measure $\si_M$, one can expect
in contrast that the symmetries of $H_M$ induces a stronger result, as for
many mean field models. In this direction, Landim, Panizo and Yau have
recently established in \cite{landim-panizo-yau} that $\mu_M$ satisfies
inequalities \eqref{in:ts-l2} and \eqref{in:ls-l2} when $H$ is of the form
$H(x)=V(x_1)+\cdots+V(x_{n+1})$ where $V(u)=u^2/2+F(u)$ with $F$ and $F'$
bounded and Lipschitz. A simple example is given by $F(x)=P(\sin(Q(x)))$
where $P$ and $Q$ are fixed polynomials in $\dR[X]$. Their proof relies on
Lu-Yau's markovian decomposition \cite{lu-yau} and on Local Central Limit
Theorem estimates \cite{kipnis-landim}.
Following closely \cite{landim-panizo-yau}, we are actually able to
show that measure $\si_M$ itself satisfies to \eqref{in:def-ts} and
\eqref{in:def-ls} with a constants which does not depend on $n$ and
$M$, as stated in our main result, which follows.
\begin{thm}\label{th:num-quad+bd}
Let $H(x)=V(x_1)+\cdots+V(x_{n+1})$ with $V(u)=u^2/2+F(u)$ and let $\si_M$
be the probability measure on $\dR^n$ defined by \eqref{eq:defnum}, namely
$$
\si_M(dx_1,\ldots,dx_n) =(Z_{\si_M})^{-1}
\int_{\dR^{n}}\!\exp\BPAR{-\sum_{i=1}^n V(x_i)-V(\MSX)}\,dx_1\cdots dx_n.
$$
Then, if $F$ is bounded and Lipschitz, there exists a positive constant
$\cP$ depending only on \NI{F} and \NI{F'} such that for any $n$ and $M$ and
any smooth $f:\dR^n\to\dR$,
\begin{equation}\label{in:nu-quad+bd-ts}
\var{\si_M}{f} \leq \cP\,\moy{\si_M}{\ABS{\GR f}^2}.
\end{equation}
Moreover, if $F''$ is also bounded, there exists a positive constant
$\cL$ depending only on \NI{F}, \NI{F'} and \NI{F''} such that for
any $n$ and $M$ and any smooth $f:\dR^n\to\dR$,
\begin{equation}\label{in:nu-quad+bd-ls}
\ent{\si_M}{f^2} \leq \cL\, \moy{\si_M}{\ABS{\GR f}^2}.
\end{equation}
\end{thm}
As a Corollary, we recover from Proposition \ref{pr:num-mum} and
\eqref{in:compdirf} the $L^2$ factor for the Kawasaki dynamics (cf.
\eqref{in:ts-l2} and \eqref{in:ls-l2}) obtained by
\cite{landim-panizo-yau}.
The rest of the paper is divided as follows. The first section gives
the proof of Proposition \ref{pr:ivan}, which relies only on the
Bakry-Émery criterion. In Section \ref{se:prelims}, we give some
preliminaries to the proof of Theorem \ref{th:num-quad+bd}. Lemma
\ref{le:cov-estims} gives some covariance bounds taken from
\cite{landim-panizo-yau}. This Lemma allows us to derive the ``one
spin Lemma'' \ref{le:onespin} by a simple application of the
Bakry-Émery criterion. Section \ref{se:qd+bd:ip} is devoted to the
derivation of the Poincaré inequality \eqref{in:nu-quad+bd-ts} and
section \ref{se:qd+bd:ls} to the derivation of the logarithmic Sobolev
counterpart \eqref{in:nu-quad+bd-ts}. The proofs make heavy use of
the LCLT based estimates of \cite{landim-panizo-yau} throughout Lemmas
\ref{le:cvg} and \ref{le:ceg}, but our induction in $n$ is quite
different.
It is quite natural to ask if Theorem \ref{th:num-quad+bd} remains
valid if we replace the quadratic potential $u^2/2$ by a uniformly
strictly convex potential $\Phi$. We believe that this is true, at
least for $\Phi$ such that $0<\al \leq \Phi''(u)\leq \be$. In an
other direction, one can ask if our method remains valid for discrete
spins systems similar to those presented in \cite{martinelli-99}. It
is not clear at all for us.
%
\section{Proof of Proposition \ref{pr:ivan}}\label{se:pr:pr:ivan}
%
We give here a proof of Proposition \ref{pr:ivan}, which relies only on the
Bakry-Émery criterion. Let $\si_M^*$ the probability measure on $\dR^n$
defined by
$$
(Z_{\si_M^*})^{-1}\,\exp\BPAR{-\sum_{i=1}^n
V(x)-\frac{1}{2}\,\BPAR{\MSX}^2\,}\,dx_1\cdots dx_n.
$$
If $\si_M^*$ satisfies a Poincaré inequality with a constant $c>0$,
then $\si_M$ satisfies a Poincaré inequality with a constant
$c\exp\PAR{2\,\OSC{F}}$. Now, for any smooth function
$f:\dR^n\to\dR$,
$$
\moy{\si_M^*}{(\GI f)^2}=\sum_{i,j=1}^n\moy{\si_M^*}{\ABS{\pd^2_{ij} f}^2}
+\bmoy{\si_M^*}{\sum_{i=1}^n\PAR{1+F''(x_i)}\,\ABS{\pd_i f}^2}
+\bmoy{\si_M^*}{\BPAR{\sum_{i=1}^n \pd_i f}^2}.
$$
In another hand, for any $i\in\{1,\ldots,n\}$ and any
$x_1,\ldots,x_{i-1},x_{i+1},\ldots,x_n$, the Bakry-Émery criterion gives that
the one dimensional probability measure
$$
\rho_i(dx_i):=(Z_{\rho_i})^{-1}\,
\exp\BPAR{-V(x_i)-\frac{1}{2}\BPAR{\MSX}^2\,}\,dx_i
$$
satisfies a Poincaré inequality with a constant $(1/2)\,\exp(2\,\OSC{F})$,
hence, by the Bakry-Émery criterion applied reversely, we get for any smooth
function $f:\dR^n\to\dR$, by summing over $i$
$$
\sum_{i=1}^n\moy{\rho_i}{\ABS{\pd^2_{ii} f}^2} +
\sum_{i=1}^n\moy{\rho_i}{\PAR{2+F''(x_i)}\,\ABS{\pd_i f}^2} \geq
2\,e^{-2\,\OSC{F}}\sum_{i=1}^n\moy{\rho_i}{\ABS{\pd_i f}^2}.
$$
Notice that
$\rho_i=\LAW{\si_M^*}{x_i\,\vert\,x_1,\ldots,x_{i-1},x_{i+1},\ldots,x_n}$.
Therefore, by taking the expectation with respect to $\si_M^*$, we get
\begin{align*}
\moy{\si_M^*}{(\GI f)^2}
&\geq \PAR{2\,e^{-2\,\OSC{F}}-1}\,\sum_{i=1}^n\moy{\si_M^*}{\ABS{\pd_i f}^2}\\
&=: \PAR{2\,e^{-2\,\OSC{F}}-1}\,\moy{\si_M^*}{\ABS{\GR f}^2}.
\end{align*}
Thus, for $\OSC{F}$ sufficiently small ($<\log\sqrt{2}$), one can take
$$
\cP=\frac{e^{2\,\OSC{F}}}{2\,e^{-2\,\OSC{F}}-1},
$$
which is optimal when $F\equiv0$ (pure Gaussian case).
%
\section{Preliminaries to the proof of Theorem \ref{th:num-quad+bd}}
\label{se:prelims}
%
Let $\ga_{n,M}$ the Gaussian measure of mean $M/(n+1)$ and covariance matrix
$\PAR{\bI_n+\Mo_n}^{-1}$. If $B(x):=\sum_{i=1}^n
F(x_i)+F\BPAR{M-x_1-\cdots-x_n}$, on can write
$$
d\si_M(x_1,\ldots,x_n)
=(Z_{n,M})^{-1}\,\exp\PAR{-B(x)}\,d\ga_{n,M}(x_1,\ldots,x_n).
$$
Thus, $\si_M$ is a bounded perturbation of $\ga_{n,M}$, which is
log-concave with a constant $\rho$ equal to $1$, and therefore,
$\si_M$ satisfies to Poincaré and logarithmic Sobolev inequalities
with constants depending only on \NI{B} (i.e. $\NI{F}$ and $n$). Our
goal is to show that the dependence in $n$ can be dropped by taking
into account \NI{F'} and \NI{F''}. The presence of the bounded part
$F$ in $V$ and the non-product nature of $\si_M$ does not allow any
direct approach based on the Bakry-Émery criterion.
Observe that $\cov{\ga_{n,M}}{x_1}{x_2}=-(n+1)^{-1}$, and we can then expect
the same decrease in $n$ for $\cov{\si_M}{V'(x_1)}{V'(x_2)}$. This is actually
the case, as stated in the following Lemma. Notice that since $\si_M$ is
exchangeable and since $\MSX$ and $x_i$ have the same law under $\si_M$, we
have $\var{\si_M}{x_1}=-n\cov{\si_M}{x_1}{x_2}$, as for $\ga_{n,M}$.
\begin{lem}\label{le:cov-estims}
Let $\si_M$ be the probability measure on $\dR^n$ ($n>2$) defined in Theorem
\ref{th:num-quad+bd} and $\mu_M$ the associated conditional measure defined
by \eqref{eq:defmum}. Assume that $F$ and $F'$ are bounded, then there
exists a constant $C>0$ depending only on \NI{F} and \NI{F'} such that for
any $M\in\dR$
\begin{equation}
\label{in:cov-estim1}
\ABS{\cov{\si_M}{V'(x_1)}{V'(x_2)}} =
\ABS{\cov{\mu_M}{V'(x_1)}{V'(x_2)}} \leq \frac{C}{n},
\end{equation}
and for any $\al\in\dR$
\begin{equation}\label{in:cov-estim2}
\begin{split}
\var{\si_M}{\sum_{i=1}^n V'(x_i)+V'(\MSX)}
&=\var{\si_M}{\sum_{i=1}^n F'(x_i)+F'(\MSX)}\\
&=\var{\mu_M}{\sum_{i=1}^{n+1} F'(x_i)} \leq nC.
\end{split}
\end{equation}
\end{lem}
\begin{proof}
Inequality \eqref{in:cov-estim2} follows from \eqref{eq:mum2num} and
\cite[Corollary 5.4]{landim-panizo-yau}.
For \eqref{in:cov-estim1}, just write
$$
\cov{\si_M}{V'(x_1)}{V'(x_2)}
=\cov{\si_M}{x_1}{x_2}
+2\,\cov{\si_M}{x_1}{F'(x_2)}
+\cov{\si_M}{F'(x_1)}{F'(x_2)},
$$
and use \eqref{eq:mum2num} and \cite[Corollary 5.3]{landim-panizo-yau} to
estimate each term. Actually, one can derive the estimates of
$\cov{\si_M}{x_1}{F'(x_2)}$ and $\cov{\si_M}{x_1}{x_2}$ directly by using
the symmetries of $\si_M$.
\end{proof}
Inequality \eqref{in:cov-estim1} of Lemma \ref{le:cov-estims} allows
us to establish the following one spin result, which is the first step
in our proof of Poincaré and logarithmic Sobolev inequalities for
$\si_M$ by induction on $n$ by mean of the Lu-Yau Markovian
decomposition. In the other hand, inequality \eqref{in:cov-estim2}
will be usefull, as we will see in sections \ref{se:qd+bd:ip} and
\ref{se:qd+bd:ls}, for the induction itself.
\begin{lem}[One spin Lemma]\label{le:onespin}
Let $\si_M$ be the probability measure on $\dR^n$ defined in Theorem
\ref{th:num-quad+bd}. If $F$ is bounded and Lipschitz, there exists a
constant $A>0$ depending only on \NI{F} and \NI{F'} and not on $n$ and $M$
such that for any $n$ and $M$ and any smooth $f:\dR\to\dR$,
$$
\ent{\si_M}{f(x_1)^2} \leq 2A\,\moy{\si_M}{f'(x_1)^2},
$$
and
$$
\var{\si_M}{f(x_1)} \leq A\,\moy{\si_M}{f'(x_1)^2}.
$$
\end{lem}
\begin{proof}[Proof of Lemma \ref{le:onespin}]\label{le:pr:onespin}
As we already noticed, it is clear that the desired inequalities are true
with a constant depending on $n$ and $\NI{F}$, so we just have to see what
happens for large values of $n$. We have in mind the use of the Bakry-Émery
criterion. The Hamiltonian of the probability measure in $x_1$ is given by
\begin{multline*}
\vphi_{M,n}(x_1):=V(x_1)+\log Z_{M,n} %\\
- \log \int\!\exp\PAR{-\sum_{i=2}^n V(x_i)-V(\MSX)}\, dx_2\cdots dx_n.
\end{multline*}
We first observe that we can forget the $F(x_1)$ part in $V(x_1)$, which is
payed by a factor $\exp(2\,\OSC{F})$ in $A$. Hence, we simply have, after an
integration by parts
\begin{equation*}
\vphi_{M,n}''(x_1)=1-\cov{\si_{M-x_1}(dx_2,\ldots,dx_n)}{V'(x_2)}{V'(x_3)}.
\end{equation*}
Now, \eqref{in:cov-estim1} gives $\vphi_{M,n}''(x_1) \geq 1-Cn^{-1}$, where
$C$ is a positive constant depending only on \NI{F} and \NI{F'} and not on
$n$ and $M$. Thus, we are able to apply the Bakry-Émery criterion for large
values of $n$. Hence, the proof is completed, with a constant $A$ depending
only on \NI{F} and \NI{F'} and not on $M$ and $n$.
\end{proof}
Obviously, one can replace $x_1$ in $f$ and $f'$ by $M-x_1-\cdots-x_n$ or by
any $x_i$ for $i\in\{1,\ldots,n\}$. Moreover, according to
\eqref{eq:mumeqnum}, on can replace $\moyf{\si_M}$ by $\moyf{\mu_M}$.
%
\section{Derivation of the Poincaré inequality}\label{se:qd+bd:ip}
%
This section is devoted to the derivation of inequality
\eqref{in:nu-quad+bd-ts} of Theorem \ref{th:num-quad+bd}. The proof
relies on the one spin Lemma \ref{le:onespin} and on the crucial Lemma
\ref{le:cvg} which allows us to use the Lu-Yau Markovian
decomposition.
\begin{proof}[Proof of \eqref{in:nu-quad+bd-ts}]\label{th:pr:nu-quad+bd:ts}
As we already noticed, the result is true with a constant depending
on $n$, so that if we denote by $\cP_n$ the maximum of best Poincaré
constants in dimension less than or equal to $n$, we just have to
show that the non decreasing sequence of constants $(\cP_n)_{n\geq
1}$ is bounded.
Let us denote by $\si$ the measure $\si_M$ and by $\sik{k}$ the measure
$\si_M$ given $x_1,\ldots,x_k$ for $k\in\{0,\ldots,n\}$ and by $f_k$ the
conditional expectation
$$
\moy{\si}{f\vert x_1,\ldots,x_k}=\moy{\sik{k}}{f}.
$$
Notice that $\sik{k}$ is nothing else but
$\si_{M-x_1-\cdots-x_k}(dx_{k+1},\ldots,dx_n)$. Moreover, $f_n=f$ and by
convention $\si^{(0)}:=\si$ and thus $f_0=\moy{\mu}{f}$. For a \emph{fixed}
function $f$, we can always choose the order of the coordinates
$x_1,\ldots,x_n$ such that $\moy{\si}{\ABS{\pd_k f}^2}$ becomes a \emph{non
increasing} sequence in $k\in\{1,\ldots,n\}$. This gives
$$
\sum_{i=k+1}^n \frac{1}{n-k}\,\moy{\si}{\ABS{\pd_i f}^2} \leq
\moy{\si}{\ABS{\pd_{k+1} f}^2}.
$$
Following Lu-Yau \cite{lu-yau}, we have the following Markovian
decomposition of the variance
$$
\var{\si}{f} := \moy{\si}{f^2}-\moy{\si}{f}^2
=\sum_{k=1}^n\moy{\si}{(f_k)^2-(f_{k-1})^2}
=\sum_{k=1}^n\moy{\si}{\var{\sik{k-1}}{f_k}}.
$$
Since measure $\sik{k-1}$ integrates coordinates $x_k,\ldots,x_n$ and
function $f_k$ depends only on coordinates $x_1,\ldots,x_k$, the quantity
$\var{\sik{k-1}}{f_k}$ is actually a variance for a one spin function.
Therefore, by the one spin Lemma \ref{le:onespin}, there exists a constant
$A>0$ depending on \NI{F} and \NI{F'} but not on $n$ and $M$ such that
$$
\var{\si}{f} \leq A\,\sum_{k=1}^n \moy{\si}{\ABS{\pd_k f_k}^2}.
$$
Our aim is to express the right hand side of the previous inequality in
terms of $\ABS{\pd_k f}^2$. Notice that the $k=n$ term in the sum is trivial
since $f_n=f$. By definition of $f_k$, we get for any $k\in\{1,\ldots,n-1\}$
$$
\pd_k f_k=\moy{\sik{k}}{\pd_k f}-\bcov{\sik{k}}{f}{V'(\MSX)}.
$$
At this stage, we notice that by $n-k$ integrations by parts, we have
$$
\bcov{\sik{k}}{f}{V'(\MSX)}
=\frac{1}{n-k}\, \sum_{i=k+1}^n\cov{\sik{k}}{f}{V'(x_i)}
-\frac{1}{n-k}\,\sum_{i=k+1}^n \moy{\sik{k}}{\pd_i f}.
$$
Therefore, we can write by denoting $S_k:=\sum_{i=k+1}^n V'(x_i)+V'(\MSX)$
$$
\pd_k f_k =\moy{\sik{k}}{\pd_k f} -\frac{1}{n-k+1}\,\cov{\sik{k}}{f}{S_k}
+\frac{1}{n-k+1}\,\sum_{i=k+1}^n \moy{\sik{k}}{\pd_i f}.
$$
Now, by the Cauchy-Schwarz inequality
$$
\ABS{\pd_k f_k}^2
\leq 3\,\moy{\sik{k}}{\ABS{\pd_k f}^2}
+\frac{3}{(n-k)^2}\,\cov{\sik{k}}{f}{S_k}^2
+\frac{3}{n-k}\,\sum_{i=k+1}^n\moy{\sik{k}}{\ABS{\pd_i f}^2}.
$$
This gives by summing over all $k$ in $\{1,\ldots,n-1\}$ (the case $k=n$
is trivial)
\begin{align*}
\sum_{k=1}^{n-1}\moy{\si}{\ABS{\pd_k f_k}^2}
\leq\;&3\,\moy{\si}{\ABS{\GR f}^2}
+3\,\sum_{k=1}^{n-1}
\frac{1}{(n-k)^2}\,\moy{\si}{\cov{\sik{k}}{f}{S_k}^2}\\
&+3\,\sum_{k=1}^{n-1}
\frac{1}{n-k}\,\sum_{i=k+1}^n\moy{\si}{\ABS{\pd_if}^2}.
\end{align*}
The monotonicity of $\moy{\si}{\ABS{\pd_i f}^2}$ yields
$$
\sum_{k=1}^{n-1}
\moy{\si}{\ABS{\pd_k f_k}^2} \leq\;6\,\moy{\si}{\ABS{\GR f}^2}
+3\,\sum_{k=1}^{n-1}\frac{1}{(n-k)^2}\,\moy{\si}{\cov{\sik{k}}{f}{S_k}^2}.
$$
By inequality \eqref{in:cvg} of Lemma \ref{le:cvg}, there exists a
positive constant $C$ depending only on \NI{F} and \NI{F'} such that for any
$\veps>0$, there exists a positive constant $C_\veps$ depending only on
\NI{F}, \NI{F'} and $\veps$ such that for any $k\in\BRA{1,\ldots,n-1}$
$$
\cov{\sik{k}}{f}{S_k}^2 \leq (C_\veps+\veps (n-k)C)\,\var{\sik{k}}{f}
+(n-k)C_\veps\,\sum_{i=k+1}^n\moy{\sik{k}}{\ABS{\pd_i f}^2}.
$$
Therefore, by the monotonicity of $\moy{\si}{\ABS{\pd_i f}^2}$
again
\begin{equation}\label{in:pr:estim:grad-grad-var-var}
\begin{split}
\sum_{k=1}^{n-1}\moy{\si}{\ABS{\pd_k f_k}^2}
\leq\;&C'_\veps\,\moy{\si}{\ABS{\GR f}^2}
+C'_\veps\,\sum_{k=1}^{n-1}%
\frac{1}{(n-k)^2}\,\moy{\si}{\var{\sik{k}}{f}} \\
&+\veps
C'\,\sum_{k=1}^{n-1}\frac{1}{n-k}\,\moy{\si}{\var{\sik{k}}{f}}.
\end{split}
\end{equation}
Recall that $\cP_n$ is the maximum of best Poincaré constants in dimension
less than or equal to $n$. The last sum of the right hand side (RHS) of
\eqref{in:pr:estim:grad-grad-var-var} can be bounded above as follows
$$
\sum_{k=1}^{n-1}\frac{1}{n-k}\moy{\si}{\var{\sik{k}}{f}}
\leq \cP_{n-1} \moy{\si}{\ABS{\GR f}^2}.
$$
It remains to examine the first sum of the RHS of
\eqref{in:pr:estim:grad-grad-var-var}. The Jensen inequality yields
$$
\moy{\si}{\var{\sik{k}}{f}} \leq \var{\si}{f},
$$
and therefore, we get for any $p\in\{1,\ldots,n-1\}$
\begin{align*}
\sum_{k=1}^{n-1}\frac{1}{(n-k)^2}\,\moy{\si}{\var{\sik{k}}{f}}
&=\var{\si}{f}\sum_{k=1}^{n-p-1}\frac{1}{(n-k)^2}
+\sum_{k=n-p}^{n-1}\frac{1}{(n-k)^2}\,\moy{\si}{\var{\sik{k}}{f}}\\
&\leq\var{\si}{f}\sum_{k=p+1}^{n-1}\frac{1}{k^2}
+\sum_{k=1}^{p}\frac{1}{k^2}\,\moy{\si}{\var{\sik{n-k}}{f}}.
\end{align*}
At this stage, we observe that for every $k$ in $\{1,\ldots,p\}$,
$$
\moy{\si}{\var{\sik{n-k}}{f}}
\leq \cP_{p} \sum_{i=n-k+1}^n \moy{\si}{\ABS{\pd_i f}^2}
\leq p\cP_{p}\,\moy{\si}{\ABS{\pd_{n-p+1} f}^2}.
$$
We are now able to collect our estimates of the RHS of
\eqref{in:pr:estim:grad-grad-var-var}. Putting all together, we have
obtained that
$$
\sum_{k=1}^{n-1}\moy{\si}{\ABS{\pd_k f_k}^2}
\leq
(C'_\veps+p\pi^2\cP_{p}C'_\veps+\veps C'\cP_{n-1})\,\moy{\si}{\ABS{\GR f}^2}
+(C'_\veps R_p)\var{\si}{f},
$$
where $R_p:=\sum_{k=p+1}^{n-1}k^{-2}$. Therefore, for somme
$C''_{p,\veps}>0$,
$$
(1-AC'_\veps R_p)\,\var{\si}{f}
\leq (C''_{p,\veps}+\veps AC'\cP_{n-1})\,\moy{\si}{\ABS{\GR f}^2}.
$$
Now, we may choose $\veps < 1/(AC')$ and then $p$ large enough (always
possible when $n$ is sufficiently large) to ensure that
$$
R_p < \min\PAR{\frac{1}{AC'_\veps},\frac{1-\veps AC'}{AC'_\veps}}.
$$
This gives two positive constants $\al$ and $\be$ with $\be<1$ depending
only on \NI{F} and \NI{F'} such that for large values of $n$, one has
$\cP_n \leq \al + \be\,\cP_{n-1}$, and therefore $\sup_{n} \cP_n < +\infty$.
\end{proof}
Let us give now the crucial Lemma which allows us to use the Markovian
decomposition of Lu-Yau, by splitting the covariance term into a
variance term and a gradient term. The proof makes heavy use of
estimates taken from \cite{landim-panizo-yau}.
\begin{lem}\label{le:cvg}
Let $\si_M$ be the probability measure on $\dR^n$ defined in Theorem
\ref{th:num-quad+bd}. Assume that $F$ is bounded and Lipschitz, then there
exists a positive constant $C$ depending only on $\NI{F}$ and $\NI{F'}$ such
that for any $\veps>0$, there exists a positive constant $C_\veps$ depending
only on $\NI{F}$, $\NI{F'}$ and $\veps$ such that for any $n\in\dN^*$, any
$M\in\dR$ and any smooth function $f:\dR^n\to\dR$
\begin{equation}\label{in:cvg}
\cov{\si_M}{f}{S}^2
\leq (C_\veps+\veps n C)\,\var{\si_M}{f}
+nC_\veps\,\moy{\si_M}{\ABS{\GR f}^2},
\end{equation}
where $S:=\sum_{i=1}^n V'(x_i)+V'(\MSX)$.
\end{lem}
\begin{proof}[Proof of Lemma \ref{le:cvg}]\label{le:pr:cvg}
Notice that we just have to study what happens for small values of $\veps$
and large values of $n$, since for any $\veps>0$ and any $n\leq n_\veps$, we
get by the Cauchy-Schwarz inequality and \eqref{in:cov-estim2} that
$$
\cov{\si_M}{f}{S}^2 \leq n_\veps C\,\var{\si_M}{f} =:
C_\veps\,\var{\si_M}{f}.
$$
We have in mind the use of the partitioning result of
\cite{landim-panizo-yau}. If ${\mu_M}$ denotes the conditional measure on
$\dR^{n+1}$ associated to $\si_M$ as in \eqref{eq:mum2num}, we have
$$
\cov{{\si_M}}{f}{S(x_1,\ldots,x_n)}^2
=\bcov{{\mu_M}}{f}{\sum_{i=1}^{n+1}F'(x_i)}^2.
$$
Now, for $n$ large enough, one can then subdivide the set
$\{1,\ldots,n+1\}$ into $\ell$ adjacent subsets $I_i$ of size $K$ or $K+1$.
We have in mind to take $K^{-1}\leq\veps$, which is always possible when $n$
is large enough. We can write with this decomposition
$$
\bcov{{\mu_M}}{f}{\sum_{i=1}^{n+1} F'(x_i)} =
\bcov{{\mu_M}}{f}{\sum_{i=1}^\ell\sum_{k\in I_i} F'(x_k)}.
$$
For any $(i,x)\in\BRA{1,\ldots,\ell}\times\dR^{n+1}$, we define the
``total spin on $I_i$'' by $M_i(x):=\sum_{k\in I_i} x_k$. On $\dR^{I_i}$,
one can define the conditional measure $\mu_{M_i}$ with total spin $M_i$,
as in \eqref{eq:defmum}. To lighten the notations, we denote this measure by
$\muMi$. We get from the latter by the Cauchy-Schwarz inequality
\begin{equation}\label{in:cvg-step-1}
\begin{split}
\bcov{{\mu_M}}
{f}{\sum_{i=1}^{n+1}F'(x_i)}^2
\leq\;&2\,\bcov{{\mu_M}}{f}
{\sum_{i=1}^\ell\sum_{k\in I_i}\PAR{F'(x_k)-\moy{\muMi}{F'}}}^2\\
&+ 2\,\bcov{{\mu_M}} {f}{\sum_{i=1}^\ell\ABS{I_i}\moy{\muMi}{F'}}^2
\end{split}
\end{equation}
By the Cauchy-Schwarz inequality again and by \eqref{eq:mumeqnum},
the second term of the RHS of \eqref{in:cvg-step-1} can be bounded
above by
$$
\var{\si_M}{f}\bvar{\mu_M}{\sum_{i=1}^\ell\ABS{I_i}\moy{\muMi}{F'}}.
$$
Now, according to \cite[ineq. (3.10)]{landim-panizo-yau}, the last
variance in the RHS is bounded above by $nC/K$ for $n$ sufficiently large,
which can be rewritten as $\veps nC$. We turn now to the control of the
first term of the RHS of \eqref{in:cvg-step-1}. Since
$\moyf{{\mu_M}}=\moyf{{\mu_M}} \circ \moyf{\muMi}$, we get
$$
\bcov{{\mu_M}}
{f}
{\sum_{i=1}^\ell\sum_{k\in I_i}\PAR{F'(x_k)-\moy{\muMi}{F'}}}
=\sum_{i=1}^\ell\bmoy{{\mu_M}}{\bcov{\muMi}{f}{\sum_{k\in I_i} F'(x_k)}}.
$$
Thus, the Cauchy-Schwarz inequality yields
$$
\bcov{{\mu_M}}
{f}
{\sum_{i=1}^\ell\sum_{k\in I_i}\PAR{F'(x_k)-\moy{\muMi}{F'}}}^2
\leq
\ell\,
\sum_{i=1}^\ell\bmoy{{\mu_M}}{\bcov{\muMi}{f}{\sum_{k\in I_i} F'(x_k)}^2}.
$$
Again by the Cauchy-Schwarz inequality, we get
$$
\bcov{\muMi}{f}{\sum_{k\in I_i} F'(x_k)}^2
\leq
\var{\muMi}{f}\bvar{\muMi}{\sum_{k\in I_i}F'(x_k)}.
$$
By virtue of \eqref{in:cov-estim2} applied to $\muMi$, we obtain
$$
\bcov{\muMi}{f}{\sum_{k\in I_i} F'(x_k)}^2
\leq C\,\ABS{I_i}\,\var{\muMi}{f}.
$$
Now, for any $i$, let $r_i=\max\{k,\,k\in I_i\}$
and $J_i:=I_i\bs\{r_i\}$ and $\siMi$
the probability measure on $\dR^{J_i}$ associated with the Hamiltonian
$$
\sum_{k\in J_i} V(x_k)+V(M_i-\sum_{k\in J_i} x_k).
$$
Equation \eqref{eq:mumeqnum} simply gives
$$
\var{\muMi}{f} = \var{\siMi}{f(\vphi_i(x))},
$$
where $\vphi_i:\dR^{n+1}\to\dR^n$ is defined by
$$
(\vphi_i(x))_k
:=
\begin{cases}
x_k & \text{if $k\neq r_i$}\\
M_i-\sum_{l\in J_i} x_l & \text{if $k=r_i$}
\end{cases}
$$
Recall that $\cP_K$ is the maximum of the best Poincaré constants for
$\si_M$ in dimensions less than or equal to $K$. We get by definition of
$\cP_K$ that
\begin{align*}
\var{\siMi}{f}
&\leq\cP_K\sum_{k\in J_i}
\moy{\siMi}{\ABS{(\pd_k f)(\vphi_i)-(\pd_{r_i}f)(\vphi_i)}^2}\\
&=\cP_K\sum_{k\in J_i}
\moy{\muMi}{\ABS{\pd_k f-\pd_{r_i}f}^2}.
\end{align*}
Hence, by the Cauchy-Schwarz inequality, we get
$$
\var{\siMi}{f}
\leq
2\cP_K\,\bmoy{\muMi}{\sum_{k\in J_i} \ABS{\pd_k f}^2} +
2(\ABS{I_i}-1)\cP_K\,\moy{\muMi}{\ABS{\pd_{r_i} f}^2},
$$
Summarising, since $\cP_K$ depends only on $K$, \NI{F}, \NI{F'},
we have obtained that the first term of the right hand side of
\eqref{in:cvg-step-1} is bounded above by
$$
nC_K\cP_K\,\moy{\mu_M}{\ABS{\GR f}^2},
$$
which can be rewritten by virtue of \eqref{eq:mumeqnum} as
$n\,C'_\veps\,\moy{{\si_M}}{\ABS{\GR f}^2}$. This concludes the proof of
\eqref{in:cvg} and Lemma \ref{le:cvg}.
\end{proof}
%
\section{Derivation of the Logarithmic Sobolev inequality}\label{se:qd+bd:ls}
%
This section is devoted to the derivation of inequality
\eqref{in:nu-quad+bd-ls} of Theorem \ref{th:num-quad+bd}. As for the
Poincaré inequality \eqref{in:nu-quad+bd-ts}, the proof relies on the
one spin Lemma \ref{le:onespin} and on a crucial Lemma \ref{le:ceg}
which allows us to use the Lu-Yau Markovian decomposition.
\begin{proof}[Proof of the logarithmic Sobolev inequality
\eqref{in:nu-quad+bd-ls} of Theorem
\ref{th:num-quad+bd}]\label{th:pr:nu-quad+bd:ls}
We follow here the same scheme used for the Poincaré inequality. For any
smooth non negative function $g:\dR^n\to\dR^+$, we have the
following decomposition of the entropy
\begin{align*}
\ent{\si}{g} :&= \moy{\si}{g\log g}-\moy{\si}{g}\log\moy{\si}{g}\\
&=\sum_{k=1}^n \moy{\si}{g_k\log g_k-g_{k-1}\log g_{k-1}}\\
&=\sum_{k=1}^n \moy{\si}{\ent{\sik{k-1}}{g_k}}.
\end{align*}
Alike for the variance, measure $\sik{k-1}$ integrates on
$x_k,\ldots,x_n$ and function $f_k$ depends only on
$x_1,\ldots,x_k$, so that $\ent{\sik{k-1}}{g_k}$ is actually an
entropy for a one spin function. Therefore, by the one spin Lemma
\ref{le:onespin}, there exists a positive constant $A$ depending on
\NI{F} and \NI{F'} but not on $n$ and $M$ such that
$$
\ent{\si}{g}
\leq 2A\,\sum_{k=1}^n \bmoy{\si}{\frac{\ABS{\pd_k g_k}^2}{4g_k}},
$$
By taking $g=f^2$ for a smooth function $f:\dR^n\to\dR$, we get
$$
\ent{\si}{f^2}
\leq 2A\,\sum_{k=1}^n \bmoy{\si}{\frac{\ABS{\pd_k (f^2)_k}^2}{4(f^2)_k}}.
$$
By imitating the method used for the Poincaré inequality, we get
that
$$
\frac{\ABS{\pd_k (f^2)_k}^2}{4(f^2)_k}
\leq 3\,\frac{\ABS{\moy{\sik{k}}{f\pd_k f}}^2}{\moy{\sik{k}}{f^2}}
+\frac{6}{(n-k)^2}\,\frac{\cov{\sik{k}}{f^2}{S_k}^2}{\moy{\sik{k}}{f^2}}
+\frac{3}{n-k}\,\sum_{i=k+1}^n
\frac{\ABS{\moy{\sik{k}}{f\pd_i f}}^2}{\moy{\sik{k}}{f^2}}.
$$
The Cauchy-Schwarz inequality yields
$$
\frac{\ABS{\moy{\sik{k}}{f\pd_k f}}^2}{\moy{\sik{k}}{f^2}}
\leq\moy{\sik{k}}{\ABS{\pd_k f}^2}.
$$
Therefore, the Jensen inequality and the monotonicity of
$\moy{\si}{\ABS{\pd_i f}^2}$ yield
$$
\sum_{k=1}^{n-1}\moy{\si}{\frac{\ABS{\pd_k (f^2)_k}^2}{4(f^2)_k}}
\leq\; 6\,\moy{\si}{\ABS{\GR f}^2}
+6\,\sum_{k=1}^{n-1}\frac{1}{(n-k)^2}\,
\moy{\si}{\frac{\cov{\sik{k}}{f^2}{S_k}^2}{\moy{\sik{k}}{f^2}}}.
$$
By inequality \eqref{in:ceg} of Lemma \eqref{le:ceg}, there
exists a positive constant $C$ depending only on \NI{F}, \NI{F'} and
\NI{F''} such that for any $\veps>0$, there exists a positive
constant $C_\veps$ depending only on \NI{F}, \NI{F'}, \NI{F''} and
$\veps$ such that for any $n$ and $M$
$$
\frac{\cov{\sik{k}}{f^2}{S_k}^2}{\moy{\sik{k}}{f^2}}
\leq (C_\veps+\veps(n-k)C)\,\ent{\sik{k}}{f^2}
+(n-k)C_\veps\,\sum_{i=k+1}^n\moy{\sik{k}}{\ABS{\pd_i f}^2}.
$$
Hence, we are now able to proceed as the same way as for the Poincaré
inequality.
\end{proof}
As for the derivation of the Poincaré inequality, we give now the
crucial Lemma which allows us to use the Markovian decomposition of
Lu-Yau.
\begin{lem}\label{le:ceg}
Let $\si_M$ be the probability measure on $\dR^n$ defined in Theorem
\ref{th:num-quad+bd}. Assume that $F$, $F'$ and $F''$ are bounded, then
there exists a positive constant $C$ depending only on $\NI{F}$, $\NI{F'}$
and $\NI{F''}$ such that for any $\veps>0$, there exists a positive constant
$C_\veps$ depending only on $\NI{F}$, $\NI{F'}$, $\NI{F''}$ and $\veps$ such
that for any $n\in\dN^*$, any $M\in\dR$ and any smooth function
$f:\dR^n\to\dR$ such that $\moy{\si_M}{f^2}=1$
\begin{equation}\label{in:ceg}
\cov{\si_M}{f^2}{S}^2
\leq (C_\veps+\veps n C)\,\ent{\si_M}{f^2}
+nC_\veps\,\moy{\si_M}{\ABS{\GR f}^2},
\end{equation}
where $S(x):=\sum_{i=1}^n V'(x_i)+V'(\MSX)$.
\end{lem}
\begin{proof}[Proof of Lemma \ref{le:ceg}]\label{le:pr:ceg}
We follow the same scheme as for \eqref{in:cvg}, by replacing the
Cauchy-Schwarz inequality by the entropy inequality. Since $f^2$ is
a density with respect to $\si_M$, we can write
$$
\cov{\si_M}{f^2}{S}=\moy{\si_M}{\PAR{S-\moy{\si_M}{S}}\,f^2},
$$
and hence, we get by the entropy inequality that for any $\be>0$
$$
\cov{\si_M}{f^2}{S} \leq
\be^{-1}\,\log\moy{\si_M}{\exp\PAR{\be\PAR{S-\moy{\si_M}{S}}}}
+\be^{-1}\,\moy{\si_M}{f^2\log f^2}.
$$
By \eqref{eq:mum2num} and \cite[Lemma 6.1]{landim-panizo-yau},
the first term of the right hand side is bounded above by $nC\be$
where $C$ depends only on \NI{F}, and \NI{F''}. This yields by
considering the minimum in $\be>0$
$$
\cov{\si_M}{f^2}{S}^2\leq nC\,\moy{\si_M}{f^2\log f^2}.
$$
Thus, for any fixed $\veps>0$, we just have to study what happens
for large values of $n$ since $nC\leq n_\veps C=:C_\veps$ for $n\leq
n_\veps$. After rewritting \eqref{in:ceg} in terms of ${\mu_M}$, we
get by Cauchy-Schwarz's inequality
\begin{equation}\label{in:ceg-step-1}
\begin{split}
\bcov{{\mu_M}}
{f^2}{\sum_{i=1}^{n+1}F'(x_i)}^2
\leq\;&
2\,\bcov{{\mu_M}}
{f^2}{\sum_{i=1}^\ell\sum_{k\in I_i}\PAR{F'(x_k)-\moy{\muMi}{F'}}}^2\\
&+2\,\bcov{{\mu_M}}{f^2}{\sum_{i=1}^\ell\ABS{I_i}\moy{\muMi}{F'}}^2.
\end{split}
\end{equation}
Let us treat the first term of the right hand side of
\eqref{in:ceg-step-1}. It can be rewritten as
$$
2\,\sum_{i=1}^\ell
\bmoy{\mu_M}{\moy{\muMi}{f^2}\bcov{\muMi}{f_i^2}{\sum_{k\in I_i} F'(x_k)}},
$$
where $f_i^2 :=f^2/\moy{\muMi}{f^2}$. Thus, by the Cauchy-Schwarz
inequality, the first term of the RHS of \eqref{in:ceg-step-1} is
bounded above by
$$
2\,\ell\,\sum_{i=1}^\ell
\bmoy{{\mu_M}}
{\moy{\muMi}{f^2}\bcov{\muMi}{f_i^2}{\sum_{k\in I_i} F'(x_k)}^2},
$$
where we used the Jensen inequality with respect to the density
$\moy{\muMi}{f^2}$. Now, by the entropy inequality and by
\cite[Lemma 6.1]{landim-panizo-yau}
$$
\moy{\muMi}{f^2}
\bcov{\muMi}{f_i^2}{\sum_{k\in I_i} F'(x_k)}^2
\leq C\,\ABS{I_i}\,\ent{\muMi}{f^2}.
$$
At this stage, the argument used for the Poincaré inequality can
be rewritten exactly in the same way, by replacing the variance by
the entropy and $\cP_K$ by $\cL_K$. It gives finally that the first
term of the RHS of \eqref{in:ceg-step-1} is bounded above by
$$
nC_K\cL_K\,\moy{\mu_{M}}{\ABS{\GR f}^2}.
$$
The latter can be rewritten by virtue of \eqref{eq:mumeqnum} as
$n\,C'_\veps\,\moy{{\si_M}}{\ABS{\GR f}^2}$. It remains to bound
the last term of the RHS of \eqref{in:ceg-step-1}. Let $\be_0$ as
in \cite[Lemma 6.5]{landim-panizo-yau} and $\de\in(0,2)$. By a
simple rewriting of \cite[Lemma 4.5]{landim-panizo-yau}, one gets
that if $\ent{\mu_M}{f^2} \leq \de(n+1)\be_0^2$ with $n$ and $K$
large enough
$$
\bcov{{\mu_M}}
{f^2}{\sum_{i=1}^\ell\ABS{I_i}\moy{\muMi}{F'}}^2
\leq \de n C\,\ent{\mu_M}{f^2}.
$$
In another hand, if $\ent{\mu_M}{f^2} \geq \de(n+1)\be_0^2$, one gets
$$
\bcov{{\mu_M}} {f^2}{\sum_{i=1}^\ell\ABS{I_i}\moy{\muMi}{F'}}^2 \leq \de n
C_K\,\ent{\mu_M}{f^2} + C_{K,\de}\,n\,\moy{\mu_M}{\ABS{\GR f}^2}.
$$
This last estimate is based on a simple rewriting of \cite[Lemma
4.5]{landim-panizo-yau} together with the following straightforward but
essential version of \cite[Lemma 4.6]{landim-panizo-yau} :
$$
\moy{\nu_{I_i\cup I_j,M}}{(m_i-m_j)^2f^2} \leq C_1(K)\,\moy{\nu_{I_i\cup
I_j,M}}{f^2} + C_2(K)\,\cL_{2K}\,\bmoy{\nu_{I_i\cup I_j,M}}{\sum_{k\in
I_i\cup I_j} \ABS{\pd_k f}^2},
$$
where $\nu_{I_i\cup I_j,M}$ is the conditional measure on
$I_i\cup I_j$, $m_i=\ABS{I_i}^{-1}\sum_{k\in I_i}$, and $C_1(K)\to
0$ when $K\to+\infty$.
Summarising, we get that for any $\de\in (0,2)$ and for $n$ and $K$
large enough, the last term of the RHS of \eqref{in:ceg-step-1} is
bounded above as follows
$$
\bcov{{\mu_M}} {f^2}{\sum_{i=1}^\ell\ABS{I_i}\moy{\muMi}{F'}}^2
\leq %
n\de C_K\,\ent{{\mu_M}}{f^2}
+nC_{K,\de}\cL_{2K}\,\moy{\mu_M}{\ABS{{\GR}f}^2},
$$
which can be rewritten by virtue of \eqref{eq:mumeqnum} as $\veps
n C'\,\ent{{\si_M}}{f^2} + nC''_\veps\,\moy{\si_M}{\ABS{\GR f}^2}$.
This achieves the proof of \eqref{in:ceg} and Lemma \ref{le:ceg}.
\end{proof}
%
\section*{Acknowledgments}
%
The author would like to warmly acknowledge Prof. Michel Ledoux for
helpful discussions and encouraging comments, and Doct. Ivan Gentil
for some discussions at the beginning of this work.
%%% Bib
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% \MRhref is called by the amsart/book/proc definition of \MR.
\providecommand{\MRhref}[2]{%
\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
}
\providecommand{\href}[2]{#2}
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\begin{center}
\hrule
\end{center}
\noindent
\textbf{E-mail}: \url{mailto:[email protected]}.\\
\textbf{URL} : \url{http://www.lsp.ups-tlse.fr/Chafai/}\\
\textbf{Postal Adress}:
Laboratoire de Statistique et Probabilités, U.M.R.
C.N.R.S. C5583, Université Paul Sabatier, 118 route de Narbonne, 31062
Toulouse CEDEX 4, France.\\
\textbf{Keywords}: \mykeywords.\\
\textbf{Subj. Class. MSC-2000} : \mysubjclass.
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