Wednesday, October 20, 2010

Wednesday Math, Vol. 130: Benoit Mandelbrot, 1924-2010

Benoit Mandelbrot coined the word fractal. Even non-mathematicians might remember fractals. They were a popular culture fad about thirty years ago, fading from view around the same time as sociobiology and Gödel Escher Bach. Fractals may not be bandied about in coffee shops anymore, but the idea is still bearing fruit in computer science, math and biology.

What is a fractal? Is it a noun or an adjective, like in the title of Mandelbrot’s most famous book The Fractal Geometry of Nature?

Mandelbrot was vague at first. Without a definitive statement, some wag declared “fractals are the mathematical proof for the existence of paisley.”

By the time of his death last Thursday, the definition had been refined to self-similarity, systems with small pieces that look like the whole. Think of tree branches or blood vessels. A nautilus shell, if shrunken and rotated just the right amount, will be almost identical to removing the last chamber the critter inhabited.

Benoit Mandelbrot is considered a French or Franco-American mathematician, but he was born in Warsaw in 1927 into a family of Lithuanian Jews, the family name Yiddish for “almond bread”. They left Warsaw in 1936 for Paris. When the war came, they moved again, leaving their son in the care of a rabbi. He spent much of the war in hiding.

After the war, he attended colleges studying math and aeronautics in France and the U.S., getting a Ph.D at the University of Paris. Instead of the teaching route, Mandelbrot took work at IBM’s Thomas J. Watson Research Center in Yorkton Heights, New York. The standard mathematical path to glory is solving some open problem that has stumped the finest minds for decades or centuries. Mandelbrot found fame pondering a poorly defined concept of his own making for a very long time, usually a one-way ticket to Eccentric Palookaville. Could math replicate the messy shapes and patterns created by living things that grew following instructions stored in self-replicating cells?

Jonathan Miller said in The Body In Question everything must be understood first in metaphor. The heart was a drum until someone invented the pump, and no one could have dreamed the better metaphor before the pump’s invention. The computer was both Mandelbrot’s metaphor and major tool. Mandelbrot didn’t so much “prove” his main thesis as show it was plausible. Computer graphics took huge strides forward in creating natural looking landscapes and biological textures based on simple instructions repeated at different scales many, many times.

On self-similarity, the last word goes to Sally Draper, precocious daughter of Don Draper of Mad Men, from an episode this season, discussing eternity with her creepy friend Glenn.

Sally Draper: “When I think about forever I get upset. Like the Land O Lakes butter has that Indian girl, sitting holding a box? And it has a picture of her on it, holding a box, with a picture of her on it, holding a box. Have you ever noticed that?”

Creepy Glenn: “I wish you wouldn’t have said that.”


susan s. said...

And before Land O Lakes, there was the Morton Salt Girl. Thanks, Matty. I love looking at fractals.

Peregrin said...