Chaos - James Gleick [99]
“But when it was seen in experiments, that’s when it really became exciting. The miracle is that, in systems that are interesting, you can still understand behavior in detail by a model with a small number of degrees of freedom.”
It was Hohenberg, in the end, who brought the theorist and the experimenter together. He ran a workshop at Aspen in the summer of 1979, and Libchaber was there. (Four years earlier, at the same summer workshop, Feigenbaum had listened to Steve Smale talk about a number—just a number—that seemed to pop up when a mathematician looked at the transition to chaos in a certain equation.) When Libchaber described his experiments with liquid helium, Hohenberg took note. On his way home, Hohenberg happened to stop and see Feigenbaum in New Mexico. Not long after, Feigenbaum paid a call on Libchaber in Paris. They stood amid the scattered parts and instruments of Libchaber’s laboratory. Libchaber proudly displayed his tiny cell and let Feigenbaum explain his latest theory. Then they walked through the Paris streets looking for the best possible cup of coffee. Libchaber remembered later how surprised he was to see a theorist so young and so, he would say, lively.
THE LEAP FROM MAPS TO FLUID FLOW seemed so great that even those most responsible sometimes felt it was like a dream. How nature could tie such complexity to such simplicity was far from obvious. “You have to regard it as a kind of miracle, not like the usual connection between theory and experiment,” Jerry Gollub said. Within a few years, the miracle was being repeated again and again in a vast bestiary of laboratory systems: bigger fluid cells with water and mercury, electronic oscillators, lasers, even chemical reactions. Theorists adapted Feigenbaum’s techniques and found other mathematical routes to chaos, cousins of period-doubling: such patterns as intermittency and quasiperiodicity. These, too, proved universal in theory and experiment.
The experimenters’ discoveries helped set in motion the era of computer experimentation. Physicists discovered that computers produced the same qualitative pictures as real experiments, and produced them millions of times faster and more reliably. To many, even more convincing than Libchaber’s results was a fluid model created by Valter Franceschini of the University of Modena, Italy—a system of five differential equations that produced attractors and period-doubling. Franceschini knew nothing of Feigenbaum, but his complex, many-dimensional model produced the same constants Feigenbaum had found in one-dimensional maps. In 1980 a European group provided a convincing mathematical explanation: dissipation bleeds a complex system of many conflicting motions, eventually bringing the behavior of many dimensions down to one.
Outside of computers, to find a strange attractor in a fluid experiment remained a serious challenge. It occupied experimenters like Harry Swinney well into the 1980s. And when the experimenters finally succeeded, the new computer experts often belittled their results as just the rough, predictable echoes of the magnificently detailed pictures their graphics terminals were already churning out. In a computer experiment, when you generated your thousands or millions of data points, patterns made themselves more or less apparent. In a laboratory, as in the real world, useful information had to be distinguished from noise. In a computer experiment data flowed like wine from a magic chalice. In a laboratory experiment you had to fight for every drop.
Still, the new theories of Feigenbaum and others would not have captured so wide a community of scientists on the strength of computer experiments alone. The modifications, the compromises, the approximations needed