Science in the Crop Circles
Crop Circle Positional Math
Charles William Johnson
Before I present the analyses of some crop
circles that I wrote during the mid-90s, I would like to suggest a few
ideas regarding one of the recent crop circles, the one cited at Wilton
Windmill in Wiltshire on the 22nd of May 2010. Below is contrast rendering
of it. To view its majesty, please, visit the marvelous web-site www.cropcircleconnector.com.
Wilton Windmill, nr Wilton, Wiltshire. Reported 22nd May 2010
The reason that I quoted the lyrics of an
Irving Berlin song in the presentation of the section on crop circles
on the Earth/matriX web-site is to emphasize the fact that whoever the
individuals are who are making the numerous crop circles throughout
the world appear to attempt to better themselves every time a new circle
you can do I can do better; I can do anything better than you.”
-[Irving Berlin, 1946]
The Wiltshire crop circle falls within that
attempt to constantly improve upon the previous circles. In general,
the crop circles appear to represent the product of some kind of competition,
one trying to better the other. Behind that betterment, however, may
exist a designed purpose, in teaching us how to identify the meanings
encoded into the crop circles. Let us see if that may be true.
This particular crop circle as a few analysts
have stated supposedly represents ASCII numbers. Let us consider the
possibility that the dashes along the radii of the twelve sectors of
the circle represent do not represent ASCII numbers, but rather sequential
natural numbers as in 1,2,3,4,5,6,7,8,9,0. The sequence runs from the
center of the circle to its circumference outwardly.
No doubt, many of the crop circles appear
to reflect encoded mathematical and geometrical patterns. At least,
that is what different analysts today propose in searching for the meanings
of the crop circles. Many of the mathematical and geometrical analyses
that can be viewed on various web-sites such the www.cropcircleconnector.com
are extremely suggestive regarding the use of pi, phi, the Fibonacci
series, among many other aspects of geometry and math.
However, in my mind, finding the expression
of pi within a circle or even that phi, or the Golden Ratio, or a Fibonacci
series of numbers could result from the nature of the geometrical figures
employed and not from some conscious intelligent design. In other words,
possibly there is no intelligent design behind a given circle in relation
to some other geometrical figure, say a square, but simply that those
geometrical figures contain relationships of pi as such given their
For those crop circles that are evidently
made by human beings on this planet, well, we may consider from the
start that they represent a conscious, intelligent design. But, for
some of the most complex crop circles, measuring hundreds of meters
in expansive size, which are not so obviously made by human beings,
the existence of a conscious intelligent design comes into question.
Are some of the crop circles being produced by beings not of this Earth,
residents from afar, possibly from another solar system in another galaxy.
One would want to be able to identify those particular conscious, intelligent
designs as distinct from the ones being made by human beings here on
Is it possible, then, to distinguish between
a conscious, intelligent design made by human beings from one made by
beings other than of this Earth. That is the task at hand in my mind.
The crop circle that I have chosen to initiate this discussion, in my
view, presents a conscious intelligent design that does not obey the
general reasoning about geometry and math as we are taught in school.
The fact that many analysts identify the design as one reflecting the
ASCII Code, and not simply natural numbers, attests to this idea.
In order to identify an intelligent design
or pattern within math and geometry, one might analyze the apparently
random dashes within the Wiltshire crop circle cited above. In my view,
this crop circle portrays a definite pattern that suggests the existence
of a consciously intelligent design unlike the way we generally think
on Earth. The dashes at first sight, as they appear, suggest a random
placement, but upon closer consideration, they obey an intelligent,
conscious design based on the natural numbers.
In this analysis, I shall examine the natural
numbers coming out of this design as of the binary system and as of
the ASCII Code. For, no matter what, both the binary numbers and the
ASCII Code numbers are ultimately based upon the natural numbers.
But, the natural numbers within the Wiltshire
crop circle are based on a positional math; depending upon the position
of the dashes within the geometry of the crop circle, certain values
are assigned to each dash, and therefore to each sector of the circle.
Those assigned values of the natural numbers, can then be employed to
derive an analysis based upon the binary numbers and the ASCII Code
numbers reflected and derived thereof. But, before I can explain the
translation from the natural numbers to the binary and ASCII numbers,
it is necessary to examine the design of the natural numbers and their
pattern within this particular crop circle.
Let us suppose for a moment that this particular
crop circle does not represent ASCII Code numbers or binary numbers,
but merely natural numbers; plain and simple. So, let us suppose that
whoever is communicating through the selective placement of dashes within
the different sectors of the cited crop circle is employing an easily
identifiable numerical pattern. The idea would be that if one is attempting
to communicate to others, the designed pattern should be simple and
easily accessible, not complex and obscure.
With the idea of simplicity, one could then
assign a number to each dash according to the positional placement of
the dash along the radii defining the different sectors.
The apparent division of the sectors in the
circle suggests a pairing of 24 smaller sectors within each larger sector
which are identifiably 12. In the following illustration, I have darkened
the apparent six diameter lines that trace out twelve smaller sectors,
two to each larger sector. This division comes from viewing the crop
circle at first glance, which I would recommend viewing on the cropcircleconnector-dot-com
In a sense, then, there appears to be a misleading
view of the crop circle made by those who made that particular crop
circle. It were as though the makers of this circle were attempting
to fool us into thinking that this is the way in which the design of
the circle should be viewed. This obtains because there are no identifiable
lines between the two smaller sectors in each of the twelve larger sectors.
The darkened lines of the diameters of separating the twelve larger
sectors are what are emphasized in the rendering of the crop circle
itself. One need only consult once again the image of this circle that
appears on page one of this essay. The definitely drawn lines between
the larger sectors determine ones approach to an analysis of the small
curved dashes registered within the sectors, emanating from the lines
drawn by the six diameters.
If one does not fall into the temptation of
the apparent design as presented by the makers of this circle, then
it is possible to draw the twelve sectors in a distinct manner from
that suggested. The pairing of the dashes along the invisible radii/diameters
creates a different pattern of twelve different large sectors and twenty-four
This distinct view, with the diameters darkened
along the non-existing lines of the diameters between the smaller sectors
creates an alternative pattern that is easily identifiable. And, the
alternative pattern puts into perspective the curved dashes that now
lie along the darkened lines of the newly drawn six diameters. It may
be noticed now that the curved dashes along the alternative six diameter
lines reflect positions of the numbers 1 through 8. The curved dashes
spread out from the centerpoint of the circle towards its circumference,
with the smaller dashes in the minor sectors and the larger curved dashes
within the major sectors.
The alternative presentation, with the imaginary
diameter lines expressly drawn in, creates different pairs of smaller
sectors. The apparent random placement of the dashes as they appeared
on the initial rendering of the circle, no longer appear to be random
at all. Quite the opposite, the sets of curved dashes along the alternative
darkened diameter lines now appear to obey a very simple rule.
The small curved dashes start on either side
of the alternative darkened lines and run from 1 to 8 along those lines,
from the center to the circumference, in a progressive manner, alternating
on either side of a specific diameter line.
The next two illustrations present this perspective
in the analysis. The first illustration shows how the alternate lines
of the diameters separating the sectors are now drawn in a different
manner than as suggested by the original design of the crop circle.
And, in the second illustration I show how one may view the small curved
dashes that run along these alternative diameters, running from a positional
value of one through eight [1,2,3,4,5,6,7,8] ---with the center of
the circle being zero . Note, there is no positional dash for the
number nine on any of the sectors. So, the natural numbers chosen for
the design of this particular crop circle are the natural numbers zero
Once the alternative sectors are paired in
the previous manner as shown on the illustrations, it becomes obvious
that each sector contains a complete set of natural numbers. Each darkened
diameter line has on either side or the other one of the natural numbers
from one to eight. No pair of smaller sectors lacks a specific natural
number. In this sense, the pattern is obvious and complete in that
it presents a distinct placement and arrangement of the natural numbers
along the six diameter lines.
The following illustration shows how each
particular pair of smaller sectors contains the complete number of curved
dashes positioned to represent numerical values of 1,2,3,4,5,6,7,8.
Each of the eight natural numbers lies on either side of a specific
alternative diameter line. Each pair of smaller sectors, in this manner,
contains a complete set of the natural numbers one through eight.
Once the pattern of eight curved dashes per
pair of smaller sectors is identified, it then becomes possible to assign
a numerical value to the presence or absence of a curved dash along
the six alternate diameter lines.
When a particular dash is present, then that
positional numerical value is registered. When there is no particular
dash present, in other words, when a dash is absent, then a zero is
assigned to the placement with the series of natural numbers as shown
in the following illustration.
I have chosen a random example to illustrate
this point. Along the alternate diameter line of sector six, there
appear five curved dashes above the diameter line and three curved dashes
below it. Therefore, these numbers would be written as follows:
10040678 [curved dashes above the diameter
02305000 [curved dashes below the diameter
The first number tells us that the curved dashes appear
for the positions of 1,4,6,7,8 above the line, and for the positions
of 2,3,5 for the curved dashes below the line. Yet, in order to identify
the numerical pattern, it is possible to represent the absence of a
curved dash either above or below the line with a zero.
By doing so, it is now possible to compute
different patterns within the sets of numerical values. In other words,
the numbers 10040678 and 02305000 may be summed, multiplied, subtracted
and/or divided by one another in search of meaningful patterns of historically
significant numbers or, scientifically significant numbers.
Each pair of smaller sectors contains a complete
set of eight curved dashes along the diameter lines as illustrated.
One would necessarily ask why would such a
complex-looking crop circle has such a unique and simple resolution
based on simple math. One must ask why did the makers of the circle
emphasize the original diameter lines which do not allow one to easily
identify the basic pattern within the circle’s design. One can only
imagine that the purpose might be that of deception, making it harder
for the viewer to discern the underlying pattern within the circle’s
One may suspect that the combination of numerical
values arranged in the manner cited here contains information that should
reveal to us some inner meaning to the design. In other words, by combining
the different sets of curved dashes along the different diameter lines,
numerical values are being suggested that have some kind of meaning
that we should resolve. Otherwise, one could expect a more simple design
by merely placing the eight curved dashes along each diameter line without
any alternating placement or positioning.
In other words, the positional math contains
a specific meaning that may not be obvious to us at first glance. However,
upon viewing the positional math and its subsequent pattern, one does
recall the positional math of the Maya Long Count. For example, were
we to assign the Maya Long Count numbers to the positional math of the
cited crop circle, then, the numerical values coming into relationship
with one another would be extremely complex compared to the elementary
assignment of values one through eight. For example, compute what the
positional values would be were they to represent the Maya Long Count
fractal values: 36, 72, 144, 288, 576, 1152, 2304, and 4608 for the
eight positions/placements. That would be mind-blowing to say the least.
In my view, the crop circle represents a teaching
aid, a learning tool, a manner for viewing the geometrical designs that
are being created with a certain degree of flexibility. It is somewhat
like creating a common language.
Each particular crop circle appears to reflect
its own mathematical and geometrical design and corresponding method
of analysis. Therefore, it is necessary to approach each crop circle
from its own internal logic, thus avoiding imposing our own way of thinking,
such as looking for specialized systems of numbers as in the ASCII Code.
There may be other crop circles which do reflect
the ASCII Code, but this particular circle can be resolved as of basic
math and natural numbers.
Once the numbers are derived into pairs, it
is obvious that each pair sums to 12345678.
Note that Sector One Pair and Sector Ten Pair
present the same paired values [10040670; 02305008]. This would suggest
a beginning and an end to a cycle or half-cycle. Then, Sector Two Pair
and Sector Eleven Pair are the same paired values [12040670; 00305008],
suggesting the first step to each cycle or half-cycle. The repetition
of numerical values confirms the existence of a consciously designed
pattern; in that the numbers are not randomly situated.
From the previous list of pairs, it becomes
obvious that each pair sums to 12345678. Consider the following computations.
One may simply note the presence/absence of the numerals 1 through 8
at any position within the paired small sectors as illustrated. The
zero represents the absence of a natural number [ 1 through 8], and
not the centerpoint zero of the circle.
Obviously the pattern of positional math based
on the 1-to-8 count derives seven and its reciprocal, which is a significant
ancient reckoning number. If the numerical positioning values included
the number nine, then other significant numerical values would derive
other than seven and its reciprocal. [See my essay on the earthmatrix-dot-com
web-site about ancient reckoning and the number seven and its reciprocal
for reckoning time.] All of the numerical values derived as previously
shown through multiplication represent historically significant numerical
series. To explore their meaning would require a lengthy essay. I suggest
reading some of the essays on the earthmatrix-dot-com web-site.
/ 1.2345678 = 5.67000465 [
Nineveh number 567, 1134, 2268]
Given that there are eight positional levels
within the cited crop circle, one could relate this particular number
to many different aspects of matter-energy. For example, an initial
aspect that comes to mind concerns the eight shells of an atom. In fact,
the fractal value that appears in Sector Pairs One and Ten concerning
the fractal 02305008 suggests the mass difference factor between a proton
and a neutron [2.30558c]. (See the Earth/matriX essays regarding this
But then again, the 02305000 value suggests
a similarity to the Maya Long Count fractal value of 2304c. For example,
the final Sector Twelve Pair value of 02340000 suggests a relationship
to the Maya Long Count: 234, 468, 936, 1872, which involves considerations
about the coming 2012 period of 1872000 days. One cannot help but note
the relationship of Sector 12 to the year of 2012 and a common fractal
numerical common shared by both in terms of multiples.
Numerous observations could be made regarding
the possible socio-historical meaning of the different values cited
for the sectors within the crop circle or, even their scientific meaning.
But, such an analysis must wait its turn. For now, I only want to treat
the idea of methodology of positional math within the crop circle, and
not so much what the actual values suggested in the paired numbers may
Similarly, one would have to consider the
non-paired numbers which are suggested by the designed sectors in the
crop circles, through addition, [multiplication] subtraction, and/or
Copyrighted by Charles William Johnson. All rights reserved. Reproduction
by any means prohibited.
Earth/matriX: Science in the Crop Circles
view the full analysis of this crop circle in relation to binary and ASCII
numbers view the pdf version. Click