Chaos - James Gleick [118]
“Here was one coin with two sides. Here was order, with randomness emerging, and then one step further away was randomness with its own underlying order.”
SHAW AND HIS COLLEAGUES had to turn their raw enthusiasm into a scientific program. They had to ask questions that could be answered and that would be worth answering. They sought ways of connecting theory and experiment—there, they felt, was a gap that needed to be closed. Before they could even begin, they had to learn what was known and what was not, and this itself was a formidable challenge.
They were hindered by the tendency of communication to travel piecemeal in science, particularly when a new subject jumps across the established subdisciplines. Often they had no idea whether they were on new or old territory. One invaluable antidote to their ignorance was Joseph Ford, an advocate of chaos at the Georgia Institute of Technology. Ford had already decided that nonlinear dynamics was the future of physics—the entire future—and had set himself up as a clearinghouse of information on journal articles. His background was in nondissipative chaos, the chaos of astronomical systems or of particle physics. He had an unusually intimate knowledge of the work being done by the Soviet school, and he made it his business to seek out connections with anyone who remotely shared the philosophical spirit of this new enterprise. He had friends everywhere. Any scientist who sent in a paper on nonlinear science would have his work summarized on Ford’s growing list of abstracts. The Santa Cruz students found out about Ford’s list and made up a form postcard for requesting prepublication copies of articles. Soon the preprints flooded in.
They realized that many sorts of questions could be asked about strange attractors. What are their characteristic shapes? What is their topological structure? What does the geometry reveal about the physics of the related dynamical systems? The first approach was the hands-on exploration that Shaw began with. Much of the mathematical literature dealt directly with structure, but the mathematical approach struck Shaw as too detailed—still too many trees and not enough forest. As he worked his way through the literature, he felt that the mathematicians, deprived by their own traditions of the new tools of computing, had been buried in the particular complexities of orbit structures, infinities here and discontinuities there. The mathematicians had not cared especially about analog fuzziness—from the physicist’s point of view, the fuzziness that surely controlled real-world systems. Shaw saw on his oscilloscope not the individual orbits but an envelope in which the orbits were embedded. It was the envelope that changed as he gently turned the knobs. He could not give a rigorous explanation of the folds and twists in the language of mathematical topology. Yet he began to feel that he understood them.
A physicist wants to make measurements. What was there in these elusive moving images to measure? Shaw and the others tried to isolate the special qualities that made strange attractors so enchanting. Sensitive dependence on initial conditions—the tendency of nearby trajectories to pull away from one another. This was the quality that made Lorenz realize that deterministic long-term weather forecasting was an impossibility. But where were the calipers to gauge such a quality? Could unpredictability itself be measured?
The answer to this question lay in a Russian conception, the Lyapunov exponent. This number provided a measure of just the topological qualities that corresponded to such