Chaos - James Gleick [77]
In practice the renormalization group was far from foolproof. It required a good deal of ingenuity to choose just the right calculations to capture the self-similarity. However, it worked well enough and often enough to inspire some physicists, Feigenbaum included, to try it on the problem of turbulence. After all, self-similarity seemed to be the signature of turbulence, fluctuations upon fluctuations, whorls upon whorls. But what about the onset of turbulence—the mysterious moment when an orderly system turned chaotic. There was no evidence that the renormalization group had anything to say about this transition. There was no evidence, for example, that the transition obeyed laws of scaling.
AS A GRADUATE STUDENT at M.I.T., Feigenbaum had an experience that stayed with him for many years. He was walking with friends around the Lincoln Reservoir in Boston. He was developing a habit of taking four– and five-hour walks, attuning himself to the panoply of impressions and ideas that would flow through his mind. On this day he became detached from the group and walked alone. He passed some picnickers and, as he moved away, he glanced back every so often, hearing the sounds of their voices, watching the motions of hands gesticulating or reaching for food. Suddenly he felt that the tableau had crossed some threshold into incomprehensibility. The figures were too small to be made out. The actions seemed disconnected, arbitrary, random. What faint sounds reached him had lost meaning.
The ceaseless motion and incomprehensible bustle of life. Feigenbaum recalled the words of Gustav Mahler, describing a sensation that he tried to capture in the third movement of his Second Symphony. Like the motions of dancing figures in a brilliantly lit ballroom into which you look from the dark night outside and from such a distance that the music is inaudible…. Life may appear senseless to you. Feigenbaum was listening to Mahler and reading Goethe, immersing himself in their high Romantic attitudes. Inevitably it was Goethe’s Faust he most reveled in, soaking up its combination of the most passionate ideas about the world with the most intellectual. Without some Romantic inclinations, he surely would have dismissed a sensation like his confusion at the reservoir. After all, why shouldn’t phenomena lose meaning as they are seen from greater distances? Physical laws provided a trivial explanation for their shrinking. On second thought the connection between shrinking and loss of meaning was not so obvious. Why should it be that as things become small they also become incomprehensible?
He tried quite seriously to analyze this experience in terms of the tools of theoretical physics, wondering what he could say about the brain’s machinery of perception. You see some human transactions and you make deductions about them. Given the vast amount of information available to your senses, how does your decoding apparatus sort it out? Clearly—or almost clearly—the brain does not own any direct copies of stuff in the world. There is no library of forms and ideas against which to compare the images of perception. Information is stored in a plastic way, allowing fantastic juxtapositions and leaps of imagination. Some chaos exists out there, and the brain seems to have more flexibility than classical physics in finding the order in it.
At the same time, Feigenbaum was thinking about color. One of the minor skirmishes of science in the first years of the nineteenth century was a difference of opinion between Newton’s followers in England and Goethe in Germany over the nature of color. To Newtonian physics, Goethe’s ideas were just so much pseudoscientific meandering. Goethe refused to view color as a static quantity, to be measured in a spectrometer and pinned down like a butterfly to cardboard. He argued that color is a matter of perception. “With light poise and counterpoise, Nature oscillates within her prescribed limits,” he wrote, “yet thus arise