Benoit Mandelbrot is dead and I don‘t feel so good myself.

If there was ever any soul on earth who understood what it meant to live on the edge, it was Benoit Mandelbrot.

The man’s name is synonymous with fractals, which are, for those in the know, the class of mathematical entities in which any portion of the set is substantially similar to the set as a whole. For everyone else, grab a leaf and look at it closely. Note how the angles between the veins and the proportional distances between branchings of those veins is quite similar to how the leaves are distributed on the twigs of the tree it came from, and how those twigs are arranged on the branches, and the branches on the trunk.

Fractals form at the interfaces between domains. In the case of trees, the interface is the very concrete interface between domain of tree and the domains of air and soil. Between any domains, no matter how concrete or abstract those domains, there is a fractal surface. And the math that governs the topology of that boundary is ridiculously simple — no matter how ridiculously complicated it looks.

It’s because of what I learned from Mandelbrot and his intellectual kin that I learned to watch the interfaces between things — between substances, between individuals, between groups of people, between states of being, between abstract categories — to look for that telltale stutter, the flickers, the swirling interlocking textures, the alien landscape that‘s what you get when you put any “gray area” between black and white absolutes under a microscope.

You can see it yourself when you look at the interfaces between, say, legal and illegal, between your money and the government’s money. The more complicated the rules are, the more you know someone has taken the wrong approach to describing the interface, because the math itself is simple, simple, simple. Measuring the coastline of an island, the boundary between earth and sea, by picking up and laying down a one-millimeter ruler again and again wherever the last wave ended is an exercise in gritty, freezing, salty, damp frustration. And, when you add all those millimeters up, you will get a coastline longer than the circumference of the earth. I’m not kidding about that.

When Mandelbrot made his journey from living to dead, I wonder if he remembered to eschew the millimeter-long ruler in favor of enjoying the intricate interlocking textures he discovered that certainly must describe the boundary between here and the hereafter.


October 16, 2010 · by xalieri · Posted in Everything Else  


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