Saturday, October 23, 2010


A week late but I couldn't let this pass without notice.

Benoit Mandelbrot died of pancreatic cancer on October 16. He was 85.

You may never have heard of him but you may well have heard of the Mandelbrot set, an illustration/example of his great accomplishment: He basically invented the field of fractal geometry. No, he didn't originate it, but he put it on a firm foundation.

The mathematics of fractals can be extremely complex, but essentially they are about addressing "roughness" in a quantitative, rigorous, way.

For an example of what one related issue is, consider the coastline of, say, Massachusetts. How long is it? Using a kilometer-long ruler, you could draw a line wrapping around the coast and come up with a figure, a rough figure. Now do the same with a meter-long ruler and you can measure into small areas of bays and inlets where your kilometer-long ruler wouldn't fit. You'll come up with a bigger number. Do it again with an centimeter-long ruler and you'll get a bigger number still. Do it with a millimeter-long ruler - and you get the idea.

So how long is the coastline of Massachusetts? It depends on the roughness of your measurement.

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