The Mandelbrot Set: Infinities Within Infinities

I was very surprised to learn that the two most accomplished scientists I know don’t know about the Mandelbrot Set. I have known about it for a long time, and recently saw a great show about it on PBS while I was pedaling on the stationary bike at the health club.

But these guys had not heard of it. Imagine that.

So without mentioning names, I have to say, everyone who wishes to be a scientist should know all about the Mandelbrot Set. It is the model we need to reproduce mathematically the patterns we find in nature. But don’t ask me, ask cardiac surgeons and paleogeologists.

Here’s the nub: If you map the coastline of an island — England, let’s say — with a one-mile yardstick, you get a certain number of miles. If you use a one-foot yardstick you get a much higher figure. If you use a one-centimeter yardstick, it’s higher still.

The simplest Mandelbrot formulas create infinitely complex patterns within infinitely complex patterns, just as the branches of a tree resemble the veins in the leaves.

Then some guy whose landlord restricted the size of his antenna used Mandelbrot principles to increase the power of his antenna by bending it in Mandlebrot patterns. This is the basis of cell phone technology. The tiny antenna receives a wide range of electromagnetic waves.

Benoit Mandelbrot is clearly onto something, and I have to say, as a former hippie, that a Mandlebrot Set, when you set it on constant magnfication, resembles a journey through a womb lined with Persian-carpet-Paisley designs, infinite complexity within infinite complexity — the kind of thing that would keep hippies occupied for hours on end, without drawing any conclusions of any value, except to say “Wow!”

In fact I think Mandelbrot’s astonishing success affirms many of the hippies’ ideas about infinities within infinities, but I’d be surprised if you could find anyone who understood what they were, exactly, at the time or any time later. It’s a fuzzy period in a lot of people’s memories, especially those who were on the scene.

That’s why the scientists should know about these things. They’re the ones who can do something with it.