July 6, 2009

Randomness

Please read this fascninating piece from the July 3rd Wall Street Journal by Leonard Mlodinow, professor of randomness at Cal Tech.

This is an extremely thought provoking article, and I believe it gets at the heart of how we get oursevles into our current financial mess.

Here is an excerpt from the article:

In sports, the championship contenders are usually pretty evenly matched. But in baseball, even if one assumes that the better team has a lopsided 55/45 edge over the inferior one, the lesser team will win the seven-game World Series 40% of the time. That might seem counterintuitive, but you can look at it as follows. If you play a best-of-one game series, then, by our assumption, the lesser team will win 45% of the time. Playing a longer series will cut down that probability. The problem is that playing a seven-game series only cuts it down to 40%, which isn’t cutting it down by much. What if you demand that the lesser team win no more than 5% of the time—a constraint called statistical significance? The World Series would have to be the best of 269 games, and probably draw an audience the size of that for Olympic curling. Swap baseball for marketing, and you find a mistake often made by marketing departments: assuming that the results of small focus groups reflect a trend in the general population.

We find false meaning in the patterns of randomness for good reason: we are animals built to do just that. Suppose, for example, that you sit a subject in front of a light which flashes red twice as often as green, but otherwise without pattern. After the subject watches for a while, you offer the subject a reward for each future flash correctly predicted. What is the best strategy?

A nonhuman animal in this situation will always guess red, the more frequent color. A different strategy is to match your proportion of red and green guesses to the proportion you observed in the past, that is, two reds for every green. If the colors come in some pattern that you can figure out, this strategy will enable you to be right every time. But if the colors come without pattern you will do worse. Most humans try to guess the pattern, and in the process allow themselves to be outsmarted by a rat. (Those trying to time the market lately might wish they had let the rat take charge.) Looking for order in patterns has allowed us to understand the patterns of the universe, and hence to create modern physics and technology; but it also sometimes compels us to submit bids on eBay because we see the face of Jesus in a slice of toast.

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