An occasional column of faculty opinion
Mindless
By Steven E. Landsburg
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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 is-but 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 movie-well, 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 invented-where 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!
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Author Sylvia Nasar signs copies of her book, A Beautiful
Mind, during a campus visit. |
Mind-ful
Sylvia Nasar, the bestselling author of A Beautiful Mind-the
biography of Nobel Prize-winning mathematician John Nash Jr. that
was turned into the Academy Award-winning movie of the same name-told
a standing-room-only crowd at Rush Rhees Library that the story
of the recovering schizophrenic was too compelling to ignore.
"There are so many stories throughout history on the spectacular
rise and tragic fall," Nasar said. "But few have such
a stunning third act as the story of John Nash."
"The fact that he could come back from the depths of this
awful disease speaks directly to the strengths of the human spirit."
A journalist and economist, Nasar is a former writer for The
New York Times, Fortune magazine, and U.S. News &
World Report.
She was one of several guest speakers for the spring 2002 edition
of the Neilly Series, sponsored by the Andrew H. and Janet Dayton
Neilly Endowed Fund of the River Campus Libraries.
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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 well-defined
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 game-theoretic 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 said-and the real Nash would have said-is
that mating competitions can turn out badly because mates are not allocated
through a competitive price system. But thank goodness other goods-from hamburgers
to locomotives-are 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 doing-that
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 Prize-worthy work in game theory,
Nash solved some impressively difficult problems in pure mathematics-showing,
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
earth-men like Andre Weil, Alexandre Grothendieck, Jean-Pierre Serre, and Nash's
old friend John Milnor. Despite all the hype associated with the movie-and despite
the brilliance of his work-Nash 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.
Landsburg is adjunct associate professor of economics at the University.
This essay originally appeared in the Wall Street Journal. © Steven E.
Landsburg
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