

MindlessBy Steven E. Landsburg
The movie A Beautiful Mind is a lovely fiction, based ever so loosely on Sylvia Nasar's far lovelier and decidedly nonfictional biography of the mathematician John Forbes Nash Jr. The movie's not bad, for what it isbut there is a good deal that it isn't. The book, though, is superb. Fortunately, the overlap is so slight that you can enjoy them in either order. Like Nash, though with far less cause for optimism, I came to Princeton in my youth hoping to make an important contribution to mathematics. I've known dozens of the mathematicians and economists whose portraits Nasar paints with uncanny accuracy. Reading her book, I hear voices from my past, and they all sound familiar. Nash at Princeton in A Beautiful Mind. What is he thinking? It's not just the people she's got right; it's also the places, the milieu, the social structure. No place on earth feels quite like the math common room at Princeton, where great minds and ambitious young scholars meet for tea, making both a glorious history and an exhilarating future seem palpably present. Nasar's book shows exactly how that room feels. As for the moviewell, as I said, it's a lovely fiction. In more ways than one. Many critics have noted that the movie bowdlerizes Nash's life, omitting mention of his bisexuality and divorce, among other things. But those omissions at least serve a dramatic purpose. Far more unsettling is that the movie rewrites not just Nash's life but his thought. Take the bizarre and ludicrous scene apparently inventedwhere Nash, out drinking with his fellow graduate students, achieves the flash of insight that he's been desperately seeking for months. If he and his friends all hit on the same woman, Nash reasons, they'll devastate one another's chances while letting other, slightly less desirable, women get away. "Adam Smith needs revision!" he declares triumphantly. To his baffled classmates, he explains: "Adam Smith said the best result comes from everyone in the group doing what's best for himself, right? Adam Smith was wrong!" The message: Sometimes it's better to cooperate! Well, duh. Does anyone believe that the benefits of cooperation could have eluded the astute Adam Smith? Isn't this the same Adam Smith who famously remarked that "people of the same trade seldom meet together, even for merriment or diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices"? Surely Smith would have appreciated the value of a contrivance among horny graduate students to stay out of one another's way. Competition is often destructive. Everybody knows that. The remarkable exception, enshrined in Smith's enduring metaphor of the Invisible Hand, is that in the presence of free competitive markets, functioning price systems, and welldefined property rights, the "best result" (in a sense that can be defined precisely) does come from everyone in the group doing what's best for himself. That's not obvious, but it's true. It was proved, as a matter of pure mathematics, by economists like Gerard Debreu, Kenneth Arrow, and Wilson Professor Emeritus of Economics Lionel McKenzie, beginning around the time Nash was supposedly having that fateful drink. Surely that would have been good enough for Nash, who through all his breakdowns never lost his respect for mathematical reasoning. In the real world, as opposed to the movie, Nash complemented Smith without supplanting him. The Invisible Hand tells you that good things happen when people compete in free markets. Nash laid the gametheoretic mathematical foundations for figuring out what happens when people compete in other ways. It turns out that without markets, many different things can happen, not all of them good. That means we should have more respect for markets, not less. What the fictionalized Nash should have saidand the real Nash would have saidis that mating competitions can turn out badly because mates are not allocated through a competitive price system. But thank goodness other goodsfrom hamburgers to locomotivesare allocated by prices, yielding the desirable outcomes that Adam Smith promised us all along. According to social critics who can't be bothered to learn the subject they're criticizing, the Invisible Hand works only in highly stylized settings, where consumers have perfect information and transaction costs are negligible. Quite the contrary: Modern economics demonstrates the robust power of markets to deliver optimal outcomes in a rich array of environments. The key tool in this analysis is Nash's notion of equilibrium: a situation where everyone does the best he can subject to what everyone else is doingthat is, "everyone in the group doing what's best for himself." In the presence of competitive price systems, a Nash equilibrium is usually a desirable outcome. "Adam Smith needs revision" indeed! It's said that Einstein, on being asked whether he kept a notebook to write down all his ideas, replied: "I've only had three ideas in my life!" Nash had approximately the same number, and they were very good ideas, though not as good as Einstein's. Besides his Nobel Prizeworthy work in game theory, Nash solved some impressively difficult problems in pure mathematicsshowing, for example, that certain abstractly defined geometric objects are in a sense more concrete than anybody had a right to expect. But solving problems is not the same thing as laying new foundations, unifying vast areas of mathematics and uncovering deep analogies between disparate fields. In Nash's time, more than the usual number of mathematical giants walked the earthmen like Andre Weil, Alexandre Grothendieck, JeanPierre Serre, and Nash's old friend John Milnor. Despite all the hype associated with the movieand despite the brilliance of his workNash was never quite in their league. Had he never been plagued by schizophrenia, might Nash have joined the pantheon? The question is probably as meaningless as asking what I could have accomplished with an extra hundred points of I.Q. With a different brain, he would have been a different man. To me, the most moving and insightful moment in Nasar's book comes when Nash receives a visitor who asks: "How could you, a mathematician, a man devoted to reason and logical proof . . . how could you believe that extraterrestrials are sending you messages?" Nash replies: "Because the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously." Nash's delusions were perhaps the necessary price for his particular brilliance, just as the movie's biographical inaccuracies and omissions are perhaps the necessary price for its particular charm. But why distort Nash's ideas? If you don't care about getting the ideas right, why would you care about John Nash? Ideas, after all, are what make minds beautiful.
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