13 August 2007

Logic vs. Conventional Wisdom

This NYT article is a great example of how conventional wisdom doesn't always stand up to logic. The subject is the great disparity in the average number of sexual partners between men and women. Some surveys produce self-reported results with men having an average of 7 partners to women's 4. That's a 75% difference. That's big. But, it makes sense with what we think about the reproductive strategies of men and women, right? You know, men want to reproduce as often as possible to guarantee the continued existence of their genes. Women, on the other hand, want a stable relationship to help raise the kids, thereby ensuring that they reach reproductive age and pass on her genes. This makes women jealous and men infidel. Right?

Sure, except that it's logically impossible. The math professor in the article, David Gale of UC Berkeley, provides the following example:

"By way of dramatization, we change the context slightly and will prove what will be called the High School Prom Theorem. We suppose that on the day after the prom, each girl is asked to give the number of boys she danced with. These numbers are then added up giving a number G. The same information is then obtained from the boys, giving a number B.

Theorem: G=B

Proof: Both G and B are equal to C, the number of couples who danced together at the prom. Q.E.D.”

For a closed population, that has to be true. Like, logically. Think about it.

The moral for today, kids: Conventional wisdom may not be as wise as originally thought.

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