I had something in common with Benoît Mandelbrot. He was Lithuanian and he lived awhile in Princeton. But that’s where the similarity ends. He passed on at the age of 85 lately, but left a word in our vocabulary for us all to pass on.
What in the world is a fractal?
Fractal is something Mandelbrot discovered. Fractals are everywhere, but it took this wondering mathematician looking very hard to find them.
A closer look
How long is the shoreline of Great Britian, he wondered. A simple observation and a simple measurement yield a simple answer. But that answer didn’t satisfy Benoît. Upon closer examination of the intricacies of the shoreline, another number arose in answer. Closer yet inspection of each steadily closer examination yielded yet another larger number. As observations got more detailed, Mandelbrot got the idea that the length of the English coast must be infinite.
The surfaces and edges of many natural things seem to yield the same result. Mandelbrot postulated that surfaces aren’t smooth but rather are fractal. That is, closer inspection of smooth surfaces or straight edges are neither, but contain randomly repeating yet irregular patterns. That’s as simply stated as I can think of to say it.
And I don’t pretend to understand the mathematics of fractals nor the theory of chaos, which Mandelbrot ushered into the science of the universe. Speaking of the universe, fractal patterns describe, among other things, the clustering of galaxies and how the brains of mammals fold as they grow. Perhaps yours or mine too. It may be an oversimplification to say that Mandelbrot brought some sense of order to things that appear, at first glance, disordered and random. But maybe that’s not right either. Like I said, I don’t pretend to understand it all that well.
Not so fast
But he surely gave science a lot to think about….and for scientists not to jump to conclusions without looking more closely. I’ve had a lot to say about that lately, on subjects in the world of science.
So, when you are about to jump to some foregone conclusion brought to you by someone’s casual observation, think fractal. And find out what you may be missing.
Benoît Mandelbrot is gone from the world at 85, but not gone from our renewed perspectives of the world in which we live.