Chaos - James Gleick [88]
But Feigenbaum had discovered universality and created a theory to explain it. That was the pivot on which the new science swung. Unable to publish such an astonishing and counterintuitive result, he spread the word in a series of lectures at a New Hampshire conference in August 1976, an international mathematics meeting at Los Alamos in September, a set of talks at Brown University in November. The discovery and the theory met surprise, disbelief, and excitement. The more a scientist had thought about nonlinearity, the more he felt the force of Feigenbaum’s universality. One put it simply: “It was a very happy and shocking discovery that there were structures in nonlinear systems that are always the same if you looked at them the right way.” Some physicists picked up not just the ideas but also the techniques. Playing with these maps—just playing—gave them chills. With their own calculators, they could experience the surprise and satisfaction that had kept Feigenbaum going at Los Alamos. And they refined the theory. Hearing his talk at the Institute for Advanced Study in Princeton, Predrag Cvitanović, a particle physicist, helped Feigenbaum simplify his theory and extend its universality. But all the while, Cvitanović pretended it was just a pastime; he could not bring himself to admit to his colleagues what he was doing.
Among mathematicians, too, a reserved attitude prevailed, largely because Feigenbaum did not provide a rigorous proof. Indeed, not until 1979 did proof come on mathematicians’ terms, in work by Oscar E. Lanford III. Feigenbaum often recalled presenting his theory to a distinguished audience at the Los Alamos meeting in September. He had barely begun to describe the work when the eminent mathematician Mark Kac rose to ask: “Sir, do you mean to offer numerics or a proof?”
More than the one and less than the other, Feigenbaum replied.
“Is it what any reasonable man would call a proof?”
Feigenbaum said that the listeners would have to judge for themselves. After he was done speaking, he polled Kac, who responded, with a sardonically trilled r: “Yes, that’s indeed a reasonable man’s proof. The details can be left to the r-r–rigorous mathematicians.”
A movement had begun, and the discovery of universality spurred it forward. In the summer of 1977, two physicists, Joseph Ford and Giulio Casati, organized the first conference on a science called chaos. It was held in a gracious villa in Como, Italy, a tiny city at the southern foot of the lake of the same name, a stunningly deep blue catchbasin for the melting snow from the Italian Alps. One hundred people came—mostly physicists, but also curious scientists from other fields. “Mitch had seen universality and found out how it scaled and worked out a way of getting to chaos that was intuitively appealing,” Ford said. “It was the first time we had a clear model that everybody could understand.
“And it was one of those things whose time had come. In disciplines from astronomy to zoology, people were doing the same things, publishing in their narrow disciplinary journals, just totally unaware that the other people were around. They thought they were by themselves, and they were regarded as a bit eccentric in their own areas. They had exhausted the simple questions you could ask and begun to worry about phenomena that were a bit more