Chaos - James Gleick [57]
A geometrical shape has a scale, a characteristic size. To Mandelbrot, art that satisfies lacks scale, in the sense that it contains important elements at all sizes. Against the Seagram Building, he offers the architecture of the Beaux-Arts, with its sculptures and gargoyles, its quoins and jamb stones, its cartouches decorated with scrollwork, its cornices topped with cheneaux and lined with dentils. A Beaux-Arts paragon like the Paris Opera has no scale because it has every scale. An observer seeing the building from any distance finds some detail that draws the eye. The composition changes as one approaches and new elements of the structure come into play.
Appreciating the harmonious structure of any architecture is one thing; admiring the wildness of nature is quite another. In terms of aesthetic values, the new mathematics of fractal geometry brought hard science in tune with the peculiarly modern feeling for untamed, uncivilized, undomesticated nature. At one time rain forests, deserts, bush, and badlands represented all that society was striving to subdue. If people wanted aesthetic satisfaction from vegetation, they looked at gardens. As John Fowles put it, writing of eighteenth-century England: “The period had no sympathy with unregulated or primordial nature. It was aggressive wilderness, an ugly and all-invasive reminder of the Fall, of man’s eternal exile from the Garden of Eden…. Even its natural sciences…remained essentially hostile to wild nature, seeing it only as something to be tamed, classified, utilised, exploited.” By the end of the twentieth century, the culture had changed, and now science was changing with it.
So science found a use after all for the obscure and fanciful cousins of the Cantor set and the Koch curve. At first, these shapes could have served as items of evidence in the divorce proceedings between mathematics and the physical sciences at the turn of the century, the end of a marriage that had been the dominating theme of science since Newton. Mathematicians like Cantor and Koch had delighted in their originality. They thought they were outsmarting nature—when actually they had not yet caught up with nature’s creation. The prestigious mainstream of physics, too, turned away from the world of everyday experience. Only later, after Steve Smale brought mathematicians back to dynamical systems, could a physicist say, “We have the astronomers and mathematicians to thank for passing the field on to us, physicists, in a much better shape than we left it to them, 70 years ago.”
Yet, despite Smale and despite Mandelbrot, it was to be the physicists after all who made a new science of chaos. Mandelbrot provided an indispensable language and a catalogue of surprising pictures of nature. As Mandelbrot himself acknowledged, his program described better than it explained. He could list elements of nature along with their fractal dimensions—seacoasts, river networks, tree bark, galaxies—and scientists could use those numbers to make predictions. But physicists wanted to know more. They wanted to know why. There were forms in nature—not visible forms, but shapes embedded in the fabric of motion—waiting to be revealed.
Strange Attractors
Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.
—LEWIS F. RICHARDSON
TURBULENCE WAS A PROBLEM with pedigree. The great physicists all thought about it, formally or informally. A smooth flow breaks up into whorls and eddies. Wild patterns disrupt the boundary between fluid and solid. Energy drains rapidly from large-scale motions to small. Why? The best ideas came from mathematicians; for most physicists, turbulence was too dangerous to waste time on. It seemed almost unknowable. There was a story about the quantum theorist Werner Heisenberg, on his deathbed, declaring that he will have two questions for God: why relativity,