Chaos - James Gleick [42]
Nowhere were these values as severely codified as in France, and there Bourbaki succeeded as its founders could not have imagined. Its precepts, style, and notation became mandatory. It achieved the unassailable Tightness that comes from controlling all the best students and producing a steady flow of successful mathematics. Its dominance over École Normale was total and, to Mandelbrot, unbearable. He fled Normale because of Bourbaki, and a decade later he fled France for the same reason, taking up residence in the United States. Within a few decades, the relentless abstraction of Bourbaki would begin to die of a shock brought on by the computer, with its power to feed a new mathematics of the eye. But that was too late for Mandelbrot, unable to live by Bour-baki’s formalisms and unwilling to abandon his geometrical intuition.
ALWAYS A BELIEVER in creating his own mythology, Mandelbrot appended this statement to his entry in Who’s Who: “Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads-by–choice are essential to the intellectual welfare of the settled disciplines.” This nomad-by–choice, who also called himself a pioneer-by–necessity, withdrew from academe when he withdrew from France, accepting the shelter of IBM’s Thomas J. Watson Research Center. In a thirty-year journey from obscurity to eminence, he never saw his work embraced by the many disciplines toward which he directed it. Even mathematicians would say, without apparent malice, that whatever Mandelbrot was, he was not one of them.
He found his way slowly, always abetted by an extravagant knowledge of the forgotten byways of scientific history. He ventured into mathematical linguistics, explaining a law of the distribution of words. (Apologizing for the symbolism, he insisted that the problem came to his attention from a book review that he retrieved from a pure mathematician’s wastebasket so he would have something to read on the Paris subway.) He investigated game theory. He worked his way in and out of economics. He wrote about scaling regularities in the distribution of large and small cities. The general framework that tied his work together remained in the background, incompletely formed.
Early in his time at IBM, soon after his study of commodity prices, he came upon a practical problem of intense concern to his corporate patron. Engineers were perplexed by the problem of noise in telephone lines used to transmit information from computer to computer. Electric current carries the information in discrete packets, and engineers knew that the stronger they made the current the better it would be at drowning out noise. But they found that some spontaneous noise could never be eliminated. Once in a while it would wipe out a piece of signal, creating an error.
Although by its nature the transmission noise was random, it was well known to come in clusters. Periods of errorless communication would be followed by periods of errors. By talking to the engineers, Mandelbrot soon learned that there was a piece of folklore about the errors that had never been written down, because it matched none of the standard ways of thinking: the more closely they looked at the clusters, the more complicated the patterns of errors seemed. Mandelbrot provided a way of describing the distribution of errors that predicted exactly the observed patterns. Yet it was exceedingly peculiar. For one thing, it made it impossible