“I have never done anything like others,” Benoit Mandelbrot (1924-2010) once said.
That statement is proven time and time again in his autobiography: The Fractalist.
Mandelbrot is independent almost to a fault, his book an interesting memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at physics, engineering, arts, medicine, finance, and biology.
Nearly all common patterns in nature are rough. They have aspects that are exquisitely irregular and fragmented—not merely more elaborate than the marvelous ancient geometry of Euclid but of massively greater complexity. For centuries, the very idea of measuring roughness was an idle dream. This is one of the dreams to which I have devoted my entire scientific life.
Let me introduce myself. A scientific warrior of sorts, and an old man now, I have written a great deal but never acquired a predictable audience. So, in this memoir, please allow me to tell you who I think I am and how I came to labor for so many years on the first-ever theory of roughness and was rewarded by watching it transform itself into an aspect of a theory of beauty.
Mandelbrot was full of insight.
What shape is a mountain, a coastline, a river or a dividing line between two river watersheds? … Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
While that sounds obvious it wasn't at the time. In showing that triangles, squares, and circles are more prevalent in textbooks than reality, he brought to life the discipline now known as fractal geometry, a general theory of “roughness.”
Mandelbrot was fascinating, in part, because he never stayed in one place very long.
An acquaintance of mine was a forceful dean at a major university. One day, as our paths crossed in a busy corridor, he stopped to make a comment I never forgot: “You are doing very well, yet you are taking a lonely and hard path. You keep running from field to field, leading an unpredictable life, never settling down to enjoy what you have accomplished. A rolling stone gathers no moss, and—behind your back—people call you completely crazy. But I don’t think you are crazy at all, and you must continue what you are doing. For a thinking person, the most serious mental illness is not being sure of who you are. This is a problem you do not suffer from. You never need to reinvent yourself to fit changes in circumstances; you just move on. In that respect, you are the sanest person among us.”
Quietly, I responded that I was not running from field to field, but rather working on a theory of roughness. I was not a man with a big hammer to whom every problem looked like a nail. Were his words meant to compliment or merely to reassure? I soon found out: he was promoting me for a major award.
Is mental health compatible with being possessed by barely contained restlessness? In Dante’s Divine Comedy, the deceased sentenced to eternal searching are pushed to the deepest level of the Inferno. But for me, an eternal search across countless scientific fields beyond obvious connection managed to add up to a happy life. A rolling stone perhaps, but not an unresponsive one. Overactive and self-motivated, I loved to roll along, stopping to listen and preach in lay monasteries of all kinds—some splendid and proud, others forsaken and out of the way.
He had a different way of looking at things. For example, he saw math problems as geometry.
I would raise my hand and describe my findings: “Monsieur, I see an obvious geometric solution.” I quickly grasped the most abstract problem that the teacher could contrive. And then — with no effort, conscious search, or delay — I continued along a path that somehow avoided every difficulty…. I managed to be examined on the basis of speed and good taste in, first, translating algebra back into geometry, and then thinking in terms of geometric shapes. My analytic skills remained so-so, but that did not matter — the hard work was done by geometry, and it sufficed to fill in short calculations that even I could manage.
Ultimately, The Fractalist is proof that “force of character and independence” can take some to great heights.