Wandering Visionary in Math’s Far Realms

http://www.nytimes.com/2012/10/31/books/the-fractalist-benoit-b-mandelbrots-math-memoir.html

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“When I find myself in the company of scientists,” W. H. Auden wrote, “I feel like a shabby curate who has strayed by mistake into a drawing room full of dukes.” Benoit B. Mandelbrot (1924-2010) had the kind of beautiful, buzzing mind that made even gifted fellow scientists feel shabby around the edges. Mandelbrot is said to have revitalized visual geometry and coined the term “fractal” to refer to a new class of mathematical shapes that uncannily mimic the irregularities found in nature.

He prized roughness and complication. “Think of color, pitch, loudness, heaviness and hotness,” he once said. “Each is the topic of a branch of physics.” He dedicated his life to studying roughness and irregularity through geometry, applying what he learned to biology, physics, finance and many other fields.

He was never easy to pin down. He hopscotched so frequently among disciplines and institutions — I.B.M., Yale, Harvard — that in his new memoir, “The Fractalist,” he rather plaintively asks, “So where do I <em>really</em> belong?” The answer is: nearly everywhere.

As “The Fractalist” makes plain, Mandelbrot led a zigzag sort of life, rarely remaining in one place for long. He was born in Warsaw to a middle-class Lithuanian Jewish family that prized intellectual achievement. His mother was a dentist; his father worked in the clothing business. Both loved knowledge and ideas, and their relatives included many fiercely brainy men.

“I grew up,” Mandelbrot writes, “in what may be called a house of mathematics.”

The family fled to Paris in 1936, in time to escape Hitler’s advances. Looking back on dear friends who didn’t make it out, he laments their procrastination. Some, he writes, “had been detained by their precious china, or inability to sell their Bösendorfer concert grand piano, or unwillingness to abandon the park view from their windows.” He’d learned a lesson about not being tied down.

Once in Paris, he was mentored by a brilliant mathematician uncle. Family members split up — Mandelbrot and his brother lived for a while in various parts of France — to avoid the Nazis until France was liberated. Back in school, he learned he was, as he puts it, “a taupin, linguistically an extreme form of the American ‘nerd.’ ”

He also discovered that he had what he calls a “freakish gift” for solving complex mathematical problems by reducing them to familiar geometric shapes in his mind. He compared the disparate shapes that filled his head to a well-populated zoo.

He studied at the prestigious École Polytechnique in Paris, and later at the California Institute of Technology, Princeton and M.I.T. At M.I.T. he got to know the young Noam Chomsky and debated going into linguistics.

“But the more I watched,” he writes, “the clearer it became that linguistics was to be dominated by Chomsky.” He kept moving.

Mandelbrot ultimately settled at I.B.M., an association that lasted 35 years. He took frequent leaves, teaching at many colleges, including Yale, where he was a professor for 17 years. He refused to get bogged down solely in math.

“I realized that mathematics cut off from the mysteries of the real world was not for me, so I took a different path,” he writes. He wanted to play with what he calls “questions once reserved for poets and children.”

His work on fractals was inspired, in no small part, by his childhood love of maps; he began to think about creating “random coastlines from a simple formula,” as he put it. The arrival of computer graphics greatly aided his quest. He ultimately described what became known as the Mandelbrot set, famous, he writes, for being “the most complex object in mathematics,” and inspired decades of trippy graphic representations.

Many memoirists write their books too early in their lives. Others, like Mandelbrot, wait too long. “The Fractalist” was composed shortly before he died in 2010 at 85; he never had a chance to make final revisions.

I’m not sure they would have greatly helped. His memoir has a distant quality, a vagueness and rigidity that perhaps came with age. Few of this book’s milieus are evoked with any kind of liveliness or precision. I would have liked to know what it was like to work at I.B.M. during its “Mad Men”-era heyday, for example. But most of what Mandelbrot provides are generalities.

To read “The Fractalist” is to examine a brain — Mandelbrot’s — that can seem to reside in a jar. There is almost nothing about his wife, his two sons or his other interests (if he had any), besides music. His ego is perhaps too apparent. To put my complaints in Mandelbrotian terms, this book lacks a sort of glorious roughness. It reads like a lightly annotated curriculum vitae.

Having said that, I must say my ears pricked up at more than a few nice moments. He’s amusing about how his dialect-heavy French accent — he compares it to Cockney — made him self-conscious. He is good on being an “impoverished oddball” while at school in France, and he nails why dress codes can be a godsend for children.

“Without that dress code,” he writes, “the differences between rich and poor students would have been intolerably conspicuous.”

He communicates the reverence he felt toward men like Norbert Wiener, then a professor at M.I.T., and John von Neumann, then a professor at the Institute for Advanced Study at Princeton. Mandelbrot perceived them, he writes, “as made of stardust.” He refers to von Neumann, more than once, as Johnny. He quotes a friend who called Mandelbrot and his wife’s first automobile, a grasshopperlike Citroën 2CV, “the Platonic essence of a car.”

Beautiful minds don’t always write beautiful books. Life isn’t fair that way. But “The Fractalist” evokes the kinds of deceptively simple questions Mandelbrot asked — “What shape is a mountain, a coastline, a river or a dividing line between two river watersheds?” — and the profound answers he supplied.