Chaos - James Gleick [31]
At the institute, Yorke enjoyed an unusual freedom to work on problems outside traditional domains, and he enjoyed frequent contact with experts in a wide range of disciplines. One of these experts, a fluid dynamicist, had come across Lorenz’s 1963 paper “Deterministic Nonperiodic Flow” in 1972 and had fallen in love with it, handing out copies to anyone who would take one. He handed one to Yorke.
Lorenz’s paper was a piece of magic that Yorke had been looking for without even knowing it. It was a mathematical shock, to begin with—a chaotic system that violated Smale’s original optimistic classification scheme. But it was not just mathematics; it was a vivid physical model, a picture of a fluid in motion, and Yorke knew instantly that it was a thing he wanted physicists to see. Smale had steered mathematics in the direction of such physical problems, but, as Yorke well understood, the language of mathematics remained a serious barrier to communication. If only the academic world had room for hybrid mathematician/physicists—but it did not. Even though Smale’s work on dynamical systems had begun to close the gap, mathematicians continued to speak one language, physicists another. As the physicist Murray Gell-Mann once remarked: “Faculty members are familiar with a certain kind of person who looks to the mathematicians like a good physicist and looks to the physicists like a good mathematician. Very properly, they do not want that kind of person around.” The standards of the two professions were different. Mathematicians proved theorems by ratiocination; physicists’ proofs used heavier equipment. The objects that made up their worlds were different. Their examples were different.
Smale could be happy with an example like this: take a number, a fraction between zero and one, and double it. Then drop the integer part, the part to the left of the decimal point. Then repeat the process. Since most numbers are irrational and unpredictable in their fine detail, the process will just produce an unpredictable sequence of numbers. A physicist would see nothing there but a trite mathematical oddity, utterly meaningless, too simple and too abstract to be of use. Smale, though, knew intuitively that this mathematical trick would appear in the essence of many physical systems.
To a physicist, a legitimate example was a differential equation that could be written down in simple form. When Yorke saw Lorenz’s paper, even though it was buried in a meteorology journal, he knew it was an example that physicists would understand. He gave a copy to Smale, with his address label pasted on so that Smale would return it. Smale was amazed to see that this meteorologist—ten years earlier—had discovered a kind of chaos that Smale himself had once considered mathematically impossible. He made many photocopies of “Deterministic Nonperiodic Flow,” and thus arose the legend that Yorke had discovered Lorenz. Every copy of the paper that ever appeared in Berkeley had Yorke’s address label on it.
Yorke felt that physicists had learned not to see chaos. In daily life, the Lorenzian quality of sensitive dependence on initial conditions lurks everywhere. A man leaves the house in the morning thirty seconds late, a flowerpot misses his head by a few millimeters, and then he is run over by a truck. Or, less dramatically, he misses a bus that runs every ten minutes—his connection to a train that runs every hour. Small perturbations in one’s daily trajectory can have large consequences. A batter facing a pitched ball knows that approximately the same swing will not give approximately the same result, baseball being a game of inches. Science, though—science was different.
Pedagogically speaking, a good share of