Solving the Mathematical Riddle of Chaos

Mitchell Feigenbaum’s exploration of (seemingly) random relationships.

  1. A premature summery Sunday takes Cornell University by surprise, and students head off to sun themselves at Treman State Park. The waterfall trail is closed, supposedly because of hazardous winter conditions. But not everyone is playing by the rules. High above the falls, a man stands at streamside, just where the smooth flow of water begins to speed and shudder. He is sweating slightly in sports coat and corduroys and puffing on a cigarette. Suddenly, in what might be a demented high-speed parody of a tennis spectator, he starts turning his head from side to side, over and over again.

    His companions have walked ahead toward the quieter pools upstream, but Mitchell Feigenbaum is totally absorbed. ''You can focus on something, a bit of foam or something,'' he says. ''If you move your head fast enough, you can all of a sudden discern the whole structure of the surface, and you can feel it in your stomach.'' He takes another pull on his cigarette. ''But for anyone with a mathematical background, if you look at this stuff, or you see clouds with all their puffs on top of puffs, or you stand at a sea wall in a storm, you know that you really don't know anything.''

    Here, where the water flashes over the rocks in indistinguishable eddies and cascades, chaos begins, and traditionally that is where science stops. For as long as the world has had physicists inquiring into the laws of nature, it has had a sense of deep ignorance about chaos—disorder, turbulence, in water, in the atmos...