Chaos - James Gleick [143]
H. Bruce Stewart, an applied mathematician at Brookhaven National Laboratory on Long Island: Apparently random recurrent behavior in a simple deterministic (clockwork-like) system.
Roderick V. Jensen of Yale University, a theoretical physicist exploring the possibility of quantum chaos: The irregular, unpredictable behavior of deterministic, nonlinear dynamical systems.
James Crutchfield of the Santa Cruz collective: Dynamics with positive, but finite, metric entropy. The translation from mathese is: behavior that produces information (amplifies small uncertainties), but is not utterly unpredictable.
And Ford, self-proclaimed evangelist of chaos: Dynamics freed at last from the shackles of order and predictability…. Systems liberated to randomly explore their every dynamical possibility…. Exciting variety, richness of choice, a cornucopia of opportunity.
John Hubbard, exploring iterated functions and the infinite fractal wildness of the Mandelbrot set, considered chaos a poor name for his work, because it implied randomness. To him, the overriding message was that simple processes in nature could produce magnificent edifices of complexity without randomness. In nonlinearity and feedback lay all the necessary tools for encoding and then unfolding structures as rich as the human brain.
To other scientists, like Arthur Winfree, exploring the global topology of biological systems, chaos was too narrow a name. It implied simple systems, the one-dimensional maps of Feigenbaum and the two– or three– (and a fraction) dimensional strange attractors of Ruelle. Low-dimensional chaos was a special case, Winfree felt. He was interested in the laws of many-dimensional complexity—and he was convinced that such laws existed. Too much of the universe seemed beyond the reach of low-dimensional chaos.
The journal Nature carried a running debate about whether the earth’s climate followed a strange attractor. Economists looked for recognizable strange attractors in stock market trends but so far had not found them. Dynamicists hoped to use the tools of chaos to explain fully developed turbulence. Albert Libchaber, now at the University of Chicago, was turning his elegant experimental style to the service of turbulence, creating a liquid-helium box thousands of times larger than his tiny cell of 1977. Whether such experiments, liberating fluid disorder in both space and time, would find simple attractors, no one knew. As the physicist Bernardo Huberman said, “If you had a turbulent river and put a probe in it and said, ‘Look, here’s a low-dimensional strange attractor,’ we would all take off our hats and look.”
Chaos was the set of ideas persuading all these scientists that they were members of a shared enterprise. Physicist or biologist or mathematician, they believed that simple, deterministic systems could breed complexity; that systems too complex for traditional mathematics could yet obey simple laws; and that, whatever their particular field, their task was to understand complexity itself.
“LET US AGAIN LOOK at the laws of thermodynamics,” wrote James E. Lovelock, author of the Gaia hypothesis. “It is true that at first sight they read like the notice at the gate of Dante’s Hell…” But.
The Second Law is one piece of technical bad news from science that has established itself firmly in the nonscientific culture. Everything tends toward disorder. Any process that converts energy from one form to another must lose some as heat. Perfect efficiency is impossible. The universe is a one-way street. Entropy must always increase in the universe and in any hypothetical isolated system within it. However expressed, the Second Law is a rule from which there seems no appeal. In thermodynamics that is true. But the Second Law has had a life of its