In the back of the cab, Benoît Mandelbrot was at work. We had an appointment in Manhattan together, and the Polish-born, Franco-American mathematician did not like the geometry of the route the taxi driver was taking.
“Why don’t you go down Second Avenue?” he asked the driver. Cross on 25th, he ordered. Go left at Park — no, not here. It was a running commentary — and was causing a small explosion in the front seat. But Mandelbrot didn’t care.
“Look, it’s just a matter of elegance,” he explained. “I’d like him to do it with a minimum of motion — an elegant solution.” I joked that he was trying to solve a ‘travelling salesman’ problem in the back of a cab. “I already solved it,” he chuckled.
That was vintage Mandelbrot: an indomitable will, leavened with some humour, pushing into other people’s business. He died October 14 in Cambridge, Mass., at the age of 85. In life he was the archetypal campaigner — the scientist who, when his reason convinced him of a fact, would not back down. This was the man, after all, who fought the cliquish math world for half a century to earn respect for the branch of mathematics he created, fractal geometry; who, from his base as an industrial researcher at IBM’s Yorktown Heights lab made a career of tweaking posh academic noses (he was 75 before he earned tenure at Yale); who, as early as 1962, argued that the math on Wall Street was all wrong and would lead to the kind of financial disaster that hit in 1987 and again in 2008. He was, he liked to say, a ‘maverick’ — a forceful frontiersman of science who relished a good, intellectual fight. But in the bigger picture, he was more: an exemplar of the kind of independent, inter-disciplinary researcher that is all too rare—and necessary—in the big business of science that characterizes our age.
The research enterprise, whether in universities or corporate labs, is a complex affair. Science is huge: $935 billion in the developed world alone in 2008, according to the Organisation for Economic Cooperation and Development. It is powerful, shaping fundamental policy debates from climate change to management of the economy. And it is divided into thousands of narrow specialities, each one a small world of received wisdom, rigid hierarchies, and strict entry requirements.
In that realm, a number theorist is not welcome to publish on high energy physics, and a biochemist is not often invited to a conference of economists, however much their tangential perspectives on the topic might possibly stimulate some new thinking. “The specialization of science is an inevitable accompaniment of progress; yet it is full of dangers, and it is cruelly wasteful,” wrote J. Robert Oppenheimer, the Manhattan Project leader (and a friend to the younger Mandelbrot.)
Mandelbrot built a career fighting against that trend towards specialization. He was a mathematician who told hydrologists how to build dams, a computer scientist who studied financial markets. He analyzed the noise on telephone lines, the branching of bronchia in the lungs, the shape of coastlines and clouds, the distribution of word frequencies in literature and of stars and galaxies in the universe.
To be sure, he had a method. Wherever there was a phenomenon with large amounts of data and huge variation from one point in the data to another — a stock market chart, a hospital EKG readout, a telescope’s CCD output — he had a mathematical tool for it, fractal geometry. It was a tool to study what he called roughness, or irregularity. It showed an underlying and often unexpected unity among phenomena in nature and society.
“The complexity of the world is absolutely boundless, and the number of tools you can use to get a handle on it is extremely small,” Mandelbrot once told me. “Very often the problem consists in taking a tool from one field, and applying it elsewhere… What I think has been my contribution in a broad sense is to take a problem of roughness in nature and to, in part, identify and to, in part, invent new tools to handle it. Some of these tools were used in the past. Some of them were never used.”
A fractal, a term he coined while leafing through one of his sons’ Latin grammars (it comes from ‘broken’), is a shape or pattern that can be seen repeating over and over at different scales in the same object or set of data – the way the florets in broccoli are a small-scale image of the whole vegetable, or the way stars cluster into galaxies which in turn group into in galaxy clusters, or the way the fluctuations of stock prices during an hour can, statistically speaking, look similar to the way they move around in a day or a month. Today, this math is used in data-compression algorithms on the Internet, in computer graphics, and in financial market analysis, among many other fields. It is also familiar to millions through the Mandelbrot Set, a psychedelic-looking mathematical shape that appears on screen-savers and T-shirts, or through the fractals-made-easy modules now incorporated into numerous high school and college math courses.
He was particularly troublesome to economists. Working at IBM, he began to look at the way financial markets work. He concluded that the data didn’t fit the theories of the academic economists; their mathematical formulae — in Modern Portfolio Theory, Black-Scholes options pricing, the Capital Asset Pricing Model — were based on a series of embedded assumptions that were plainly false. Sure, the equations were easy to use and produced decent results most of the time; but when they failed (which was more often than the experts liked to admit) there were the crashes and bankruptcies. In the aftermath of the 2008 crash, his views have seemed more prescient than ever. Said one Nobel-winning economist, the late Paul A. Samuelson: “On the scroll of great non-economists who have advanced economics by quantum leaps, next to John von Neumann we read the name of Benoît Mandelbrot.” (The Nobel Prize committee never agreed.)
The world’s problems seem to grow by the year — energy supply, climate, pandemics, financial turmoil. We still need specialists, but we also need creative agitators who cross from one field to another fertilizing ideas and shaking up the received wisdom. Now, more than ever, we need scientists like Mandelbrot.
Author: Richard Hudson is the CEO & Editor of Science|Business. He co-authored with Mandelbrot (who was an IMS Fellow) a 2004 book, The (Mis)Behavior of Markets: A fractal view of risk, ruin and reward. This obituary is reprinted by permission: The Wall Street Journal
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