Chaos - James Gleick [40]
Within the most disorderly reams of data lived an unexpected kind of order. Given the arbitrariness of the numbers he was examining, why, Mandelbrot asked himself, should any law hold at all? And why should it apply equally well to personal incomes and cotton prices?
In truth, Mandelbrot’s background in economics was as meager as his ability to communicate with economists. When he published an article on his findings, it was preceded by an explanatory article by one of his students, who repeated Mandelbrot’s material in economists’ English. Mandelbrot moved on to other interests. But he took with him a growing determination to explore the phenomenon of scaling. It seemed to be a quality with a life of its own—a signature.
INTRODUCED FOR A LECTURE years later (“…taught economics at Harvard, engineering at Yale, physiology at the Einstein School of Medicine…”), he remarked proudly: “Very often when I listen to the list of my previous jobs I wonder if I exist. The intersection of such sets is surely empty.” Indeed, since his early days at IBM, Mandelbrot has failed to exist in a long list of different fields. He was always an outsider, taking an unorthodox approach to an unfashionable corner of mathematics, exploring disciplines in which he was rarely welcomed, hiding his grandest ideas in efforts to get his papers published, surviving mainly on the confidence of his employers in Yorktown Heights. He made forays into fields like economics and then withdrew, leaving behind tantalizing ideas but rarely well-founded bodies of work.
In the history of chaos, Mandelbrot made his own way. Yet the picture of reality that was forming in his mind in 1960 evolved from an oddity into a full-fledged geometry. To the physicists expanding on the work of people like Lorenz, Smale, Yorke, and May, this prickly mathematician remained a sideshow—but his techniques and his language became an inseparable part of their new science.
The description would not have seemed apt to anyone who knew him in his later years, with his high imposing brow and his list of titles and honors, but Benoit Mandelbrot is best understood as a refugee. He was born in Warsaw in 1924 to a Lithuanian Jewish family, his father a clothing wholesaler, his mother a dentist. Alert to geopolitical reality, the family moved to Paris in 1936, drawn in part by the presence of Mandelbrot’s uncle, Szolem Mandelbrojt, a mathematician. When the war came, the family stayed just ahead of the Nazis once again, abandoning everything but a few suitcases and joining the stream of refugees who clogged the roads south from Paris. They finally reached the town of Tulle.
For a while Benoit went around as an apprentice toolmaker, dangerously conspicuous by his height and his educated background. It was a time of unforgettable sights and fears, yet later he recalled little personal hardship, remembering instead the times he was befriended in Tulle and elsewhere by schoolteachers, some of them distinguished scholars, themselves stranded by the war. In all, his schooling was irregular and discontinuous. He claimed never to have learned the alphabet or, more significantly, multiplication tables past the fives. Still, he had a gift.
When Paris was liberated, he took and passed the month-long oral and written admissions examination for École Normale and École Polytechnique, despite his lack of preparation. Among other elements, the test had a vestigial examination in drawing, and Mandelbrot discovered a latent facility for copying the Venus de Milo. On the mathematical sections of the test—exercises in formal algebra and integrated analysis—he managed to hide his lack of training with the help of his geometrical intuition. He had realized that, given an analytic problem, he could almost always think of it in terms of some shape in his mind.