Chaos - James Gleick [86]
While he was computing, he was thinking. What new mathematics could produce the multiple scaling patterns he was observing? Something about these functions must be recursive, he realized, self-referential, the behavior of one guided by the behavior of another hidden inside it. The wavy image that had come to him in a moment of inspiration expressed something about the way one function could be scaled to match another. He applied the mathematics of renormalization group theory, with its use of scaling to collapse infinities into manageable quantities. In the spring of 1976 he entered a mode of existence more intense than any he had lived through. He would concentrate as if in a trance, programming furiously, scribbling with his pencil, programming again. He could not call C division for help, because that would mean signing off the computer to use the telephone, and reconnection was chancy. He could not stop for more than five minutes’ thought, because the computer would automatically disconnect his line. Every so often the computer would go down anyway, leaving him shaking with adrenalin. He worked for two months without pause. His functional day was twenty-two hours. He would try to go to sleep in a kind of buzz, and awaken two hours later with his thoughts exactly where he had left them. His diet was strictly coffee. (Even when healthy and at peace, Feigenbaum subsisted exclusively on the reddest possible meat, coffee, and red wine. His friends speculated that he must be getting his vitamins from cigarettes.)
In the end, a doctor called it off. He prescribed a modest regimen of Valium and an enforced vacation. But by then Feigenbaum had created a universal theory.
UNIVERSALITY MADE THE DIFFERENCE between beautiful and useful. Mathematicians, beyond a certain point, care little whether they are providing a technique for calculation. Physicists, beyond a certain point, need numbers. Universality offered the hope that by solving an easy problem physicists could solve much harder problems. The answers would be the same. Further, by placing his theory in the framework of the renormalization group, Feigenbaum gave it a clothing that physicists would recognize as a tool for calculating, almost something standard.
But what made universality useful also made it hard for physicists to believe. Universality meant that different systems would behave identically. Of course, Feigenbaum was only studying simple numerical functions. But he believed that his theory expressed a natural law about systems at the point of transition between orderly and turbulent. Everyone knew that turbulence meant a continuous spectrum of different frequencies, and everyone had wondered where the different frequencies came from. Suddenly you could see the frequencies coming in sequentially. The physical implication was that real-world systems would behave in the same, recognizable way, and that furthermore it would be measurably the same. Feigenbaum’s universality was not just qualitative, it was quantitative; not just structural, but metrical. It extended not just to patterns, but to precise numbers. To a physicist, that strained credulity.
Years later Feigenbaum still kept in a desk drawer, where he could get at them quickly, his rejection letters. By then he had all the recognition he needed. His Los Alamos work had won him prizes and awards that brought prestige and money. But it still rankled that editors of the top academic journals had deemed his work unfit for publication for two years after he began submitting it. The notion of a scientific breakthrough so original and unexpected that it cannot be published seems a slightly tarnished myth. Modern science, with its vast flow of information and its impartial system of peer review, is not supposed to be a matter of taste. One editor who sent back a Feigenbaum manuscript recognized years later that he had rejected a paper that was a turning point