Friday, June 29, 2007

Wild Randomness

In history, modernists argue that the course of human events is shaped by many trends, economic and social, enacted in the lives of millions of forgotten individuals; the historian’s task is to trace these trends. By contrast, traditionalists, now coming back into fashion, contend that history was shaped and dominated by a few great men, Caesar or Napoleon, Newton or Einstein, for example. In the first, mild view, the birth or death of no single individual is crucial to the story of mankind; in the second, wild view, it most certainly is. Another example: Under a microscope, the edge of a sharp razor blade looks a bit ragged. It has random pits and bumps, but they appear to be minor imperfections on an approximately straight edge. You can easily spot the dominant trend. This is mild variation. By contrast, consider the rugged coastline of Brittany: Does it really have an “average” outline, like that of the razor blade? Only from the very great height of a satellite, where the familiar map shape can be imagined; but from closer up, in an airplane or from a tower, the tortuous, random details of promontories and bays, crags and hollows obscure the image. This coastline is wild. Yet a third example, this time in electronics. If you run a steady electrical current through copper wire, you can “hear” it on a loudspeaker as a steady, white noise—the static of mild variation, due to the thermal excitation of the electrons. But if you try to run computer data down a very long wire, you will pick up irregular, intermittent “pops” and crackles on the line. Engineers call this 1/f noise, and it is the bane of computer communications, causing transmission errors. It cannot be predicted or prevented; it can only be accommodated, with error-correcting software. That is wild variation.

Wild randomness is uncomfortable. Its mathematics is unfamiliar and in many cases remains to be developed. It looks difficult, often requiring elaborate computer simulations rather than a quick punch on a calculator. Unfortunately, the world has not been designed for the convenience of mathematicians. There is much in economics that is best described by this wilder, unpleasant form of randomness—perhaps because economics is about not just the physics of wheat, weather, and crop yields, but also the mercurial moods and unmeasurable anticipations of wheat farmers, traders, bakers, and consumers.

Benoit Mandelbrot
and Richard L. Hudson

Benoit Mandelbrot’s Wiki Page

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