Chaos - James Gleick [142]
Uncomprehension; resistance; anger; acceptance. Those who had promoted chaos longest saw all of these. Joseph Ford of the Georgia Institute of Technology remembered lecturing to a thermodynamics group in the 1970s and mentioning that there was a chaotic behavior in the Duffing equation, a well-known textbook model for a simple oscillator subject to friction. To Ford, the presence of chaos in the Duffing equation was a curious fact—just one of those things he knew to be true, although several years passed before it was published in Physical Review Letters. But he might as well have told a gathering of paleontologists that dinosaurs had feathers. They knew better.
“When I said that? Jee-sus Christ, the audience began to bounce up and down. It was, ‘My daddy played with the Duffing equation, and my granddaddy played with the Duffing equation, and nobody seen anything like what you’re talking about.’ You would really run across resistance to the notion that nature is complicated. What I didn’t understand was the hostility.”
Comfortable in his Atlanta office, the winter sun setting outside, Ford sipped soda from an oversized mug with the word chaos painted in bright colors. His younger colleague Ronald Fox talked about his own conversion, soon after buying an Apple II computer for his son, at a time when no self-respecting physicist would buy such a thing for his work. Fox heard that Mitchell Feigenbaum had discovered universal laws guiding the behavior of feedback functions, and he decided to write a short program that would let him see the behavior on the Apple display. He saw it all painted across the screen—pitchfork bifurcations, stable lines breaking in two, then four, then eight; the appearance of chaos itself; and within the chaos, the astonishing geometric regularity. “In a couple of days you could redo all of Feigenbaum,” Fox said. Self-teaching by computing persuaded him and others who might have doubted a written argument.
Some scientists played with such programs for a while and then stopped. Others could not help but be changed. Fox was one of those who had remained conscious of the limits of standard linear science. He knew he had habitually set the hard nonlinear problems aside. In practice a physicist would always end up saying, This is a problem that’s going to take me to the handbook of special functions, which is the last place I want to go, and I’m sure as hell not going to get on a machine and do it, I’m too sophisticated for that.
“The general picture of nonlinearity got a lot of people’s attention—slowly at first, but increasingly,” Fox said. “Everybody that looked at it, it bore fruit for. You now look at any problem you looked at before, no matter what science you’re in. There was a place where you quit looking at it because it became nonlinear. Now you know how to look at it and you go back.”
Ford said, “If an area begins to grow, it has to be because some clump of people feel that there’s something it offers them—that if they modify their research, the rewards could be very big. To me chaos is like a dream. It offers the possibility that, if you come over and play this game, you can strike the mother lode.”
Still, no one could quite agree on the word itself.
Philip Holmes, a white-bearded mathematician and poet from Cornell by way of Oxford: The complicated, aperiodic, attracting orbits of certain (usually low-dimensional) dynamical systems.
Hao Bai-Lin, a physicist in China who assembled many of the historical papers of chaos