Saturday, June 19, 2004

Simple answers and Reagan

Menken said "For every human problem, there is a neat, simple solution; and it is always wrong."

Everyone knows Fermat's last problem: For positive integers a,b, and c, the equation a^n + b^n = c^n has no solutions for n greater than 2. It is a deceptively simple problem, unsolved for hundreds of years until Wiley's proof recently. Wiley's proof is hard, and relies on the efforts of generations of mathematicians. I don't understand the proof myself, but the answer is quite simple: a child can understand it.

Another problem: tie a lot of strings together at some large knot, so that the whole thing looks rather like an octopus. How do you pick the pair of strings which together stretch out farther than all other pairs? Answer: Pick any string and dangle the bundle from it. Pick the string that hangs down the farthest, and dangle the bundle from it. Holding onto that one, grab the string that hangs down farthest now. Those two span farther together than any other pair of strings you could have picked. Pretty obvious, right? Proving it might be a bit harder than most of us would care for, but it isn't that tough; and most of us would have tried the solution as our first guess.

I've read a few retrospectives of Reagan which claimed he was much smarter than he looked. I have my doubts: I still remember my shock when during the course of a televised debate he said "The Shah (of Iran) did our bidding." You don't say things like that out loud--it gives ammunition to the opponents of leaders of friendly countries, who then have to thumb their noses at us for a while to re-establish domestic credibility. (And as far as I can tell it wasn't completely true, either.) And of course there was the klutzy handling of the Lebanese intervention: it was never quite clear why we were still hanging around.

But you don't have to be brilliant to be right. And he was right to call the Soviet Union "an evil empire." And he was right to consider it fragile and susceptible to sustained pressure. And he was wrong to think that American troops in Lebanon would be some kind of talisman for peace.

Menken was a fool. Sometimes the simple solution is wrong, but sometimes it is right. Never mind the source--Reagan, Clinton, Bush--is the answer true or false?

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