Chaos - James Gleick [21]
As the 1960s went on, individual scientists made discoveries that paralleled Lorenz’s: a French astronomer studying galactic orbits, for example, and a Japanese electrical engineer modeling electronic circuits. But the first deliberate, coordinated attempt to understand how global behavior might differ from local behavior came from mathematicians. Among them was Stephen Smale of the University of California at Berkeley, already famous for unraveling the most esoteric problems of many-dimensional topology. A young physicist, making small talk, asked what Smale was working on. The answer stunned him: “Oscillators.” It was absurd. Oscillators—pendulums, springs, or electrical circuits—were the sort of problem that a physicist finished off early in his training. They were easy. Why would a great mathematician be studying elementary physics? Not until years later did the young man realize that Smale was looking at nonlinear oscillators, chaotic oscillators, and seeing things that physicists had learned not to see.
SMALE MADE A BAD CONJECTURE. In the most rigorous mathematical terms, he proposed that practically all dynamical systems tended to settle, most of the time, into behavior that was not too strange. As he soon learned, things were not so simple.
Smale was a mathematician who did not just solve problems but also built programs of problems for others to solve. He parlayed his understanding of history and his intuition about nature into an ability to announce, quietly, that a whole untried area of research was now worth a mathematician’s time. Like a successful businessman, he evaluated risks and coolly planned his strategy, and he had a Pied Piper quality. Where Smale led, many followed. His reputation was not confined to mathematics, though. Early in the Vietnam war, he and Jerry Rubin organized “International Days of Protest” and sponsored efforts to stop the trains carrying troops through California. In 1966, while the House Un-American Activities Committee was trying to subpoena him, he was heading for Moscow to attend the International Congress of Mathematicians. There he received the Fields Medal, the highest honor of his profession.
The scene in Moscow that summer became an indelible part of the Smale legend. Five thousand agitated and agitating mathematicians had gathered. Political tensions were high. Petitions were circulating. As the conference drew toward its close, Smale responded to a request from a North Vietnamese reporter by giving a press conference on the broad steps of Moscow University. He began by condemning the American intervention in Vietnam, and then, just as his hosts began to smile, added a condemnation of the Soviet invasion of Hungary and the absence of political freedom in the Soviet Union. When he was done, he was quickly hustled away in a car for questioning by Soviet officials. When he returned to California, the National Science Foundation canceled his grant.
Smale’s Fields Medal honored a famous piece of work in topology, a branch of mathematics that flourished in the twentieth century and had a particular heyday in the fifties. Topology studies the properties that remain unchanged when shapes are deformed by twisting or stretching or squeezing. Whether a shape is square or round, large or small, is irrelevant in topology, because stretching can change those properties. Topologists ask whether a shape is connected, whether it has holes, whether it is knotted. They imagine surfaces not just in the one–, two–, and three-dimensional universes of Euclid, but in spaces of many dimensions, impossible to visualize. Topology is geometry on rubber sheets. It concerns the qualitative