HOW BUTTERFLIES CAUSE HURRICANES
Published: October 25, 1987
(Page 2 of 2)
One of the strengths of Mr. Gleick's book is his artful use of examples such as this to demonstrate the ubiquity of chaos. The visits of the Voyager spacecraft to Jupiter and Saturn have shown that some of the satellites of those planets spin chaotically. Instead of turning regularly on an axis, they tumble about, never quite repeating themselves. It is the same with the movement of stars within a galaxy; they do not revolve about the center, as the planets of the solar system turn about the sun, but instead move in large ellipselike orbits which never quite repeat themselves. The periodic motions that are the hallmarks of classical mechanics give way to chaotic motion.
You can see the transformation when a spinning top, as it runs down, scrabbles about on its side. In quite different connections, chaos explains why plagues of gypsy moths recur sporadically, as do outbreaks of measles. Mr. Gleick neatly makes the case that these are also systems in which the rules of time succession are well determined, but in which chaos can spring from order.
He draws other, much deeper connections, of which the most startling is the one between chaos and the study of geometrical systems with fractional dimensions (called ''fractal''), neither one-dimensional (as on a line) nor two-dimensional (as on a plane) and so on. It is strange that these two quite novel (and fashionable) fields had quite different origins 20 years ago, but have since been discovered to be linked.
They touch in several places; here is one. Take weather forecasting by computer. If forecasts are limited in time because the starting point is poorly defined, why not build more weather stations to collect more data? There might be benefits in doing that, but the problem would remain that even the refined network could not yield an exact description of the present state of the atmosphere, with the result that predictions of the future would again be all over the place. On a different scale, the small problem would persist.
Exactly the same happens with the classical problem of fractional dimensions, that of measuring the length of a stretch of coastline. Just how long is the coastline of Martha's Vineyard? The answer will depend on how you measure it. Using a yardstick along the low-water mark will give one answer; a foot-long ruler (forcing the measurement of shoreline puddles) will give another. And however the scale of the measurement is refined, its crudity persists - ever smaller puddles remain unmeasured. If Martha's Vineyard were a triangle with an unindented coastline and were doubled in size, the length of the coastline would also be doubled. But the coastline is irregular and indented, and doubling the size of the island would more than double the length of the coasts, though the island's area would increase even faster.
Mr. Gleick also ambitiously tackles the origins of chaos in the brooding of the Frenchman Jules Henri Poincare a century ago about the geometry of space of different kinds. That the underlying issues are geometrical is beyond dispute. If two similar states of today's weather yield two very different states of the weather 10 days from now, that must surely say something important about the space in which the system moves. Mr. Gleick also credits Soviet mathematicians with their important work - at a time when excitement about chaos was rising in the United States - on the turbulence that can be observed in pans of heated liquid, in the Gulf Stream or in the atmosphere, all of which is now being neatly welded into a coherent whole.
I HAVE but two quibbles. The first, minor in the circumstances, is with Mr. Gleick's practice of seeking to bring his tale to life by overdramatizing anecdotal material. He has Mitchell Feigenbaum of Los Alamos National Laboratory walking the streets at night, smoking cigarettes and worrying his neighbors; people ''bumping into each other'' in hotel lobbies; direct quotes from the distant past that seem to spring from more recent tape recordings; and a fondness for sections that begin with sentences such as ''Smale made a bad conjecture.''
The second quibble is more substantial. Is this a revolution in science or something else? Mr. Gleick is right to say that 20 years ago the chaosmongers were a small band of scattered people, mostly mathematicians and physicists, but I suspect that he may have overestimated the degree to which they were intellectually embattled, constrained by the weight of past convention. On balance, they have quickly vindicated themselves, while their views have been welcomed both by applied scientists and by those seeking even deeper connections than have so far come to light. There can hardly ever have been an easier revolution. It has also been great fun, as Mr. Gleick shows well enough.