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A Beautiful Mind

You may have seen the film, or read the book. A Beautiful Mind, the Oscar-winning portrayal of the life of John Forbes Nash Jr. released earlier this year, was notable for presenting schizophrenia in an informative and sympathetic light. It highlighted the difficulties faced by individuals and their carers, while also giving the positive - albeit Hollywood-embellished - message that recovery is possible, even from severe mental illness.

What was so remarkable about John Nash? In 1994 Nash, along with two others, won the Nobel Prize in Economics for his contribution to non-cooperative game theory. In particular he devised the concept of "Nash equilibrium," a fundamental concept in the theory of games which provides a novel insight into human behaviour. Although his subsequent research in mathematics might be considered more significant - indeed, Nash himself regarded his work in game theory as comparatively unimportant - this insight was revolutionary in changing our understanding of the way people interact with one another. The Nash equilibrium concept is used across a range of disciplines from economics and political science to biology.

So what is Nash equilibrium? Suppose you and I play a game of noughts and crosses. If you get three in a line first, you win and I lose. But if I can block your line and get three in a row myself, I win and you lose. The players in a game such as this are interdependent: the outcome for each one - win, lose or draw - depends on the other player's moves as well as their own. Nash equilibrium is a means of predicting the outcome of such a game. It looks for a strategy, or game plan, for each player such that each does the best he or she can, taking as given what the opponent is doing. So, given your way of playing the game, I choose the strategy that maximises the benefit to me, while at the same time you choose the strategy that is best for you given what I am doing. In effect it is a kind of stability condition: once this situation is reached there is no reason for either player to change their behaviour.

Nash proved mathematically that such an equilibrium outcome (or perhaps a number of them) exists in a wide range of games. It enables predictions to be made as to how players will act in situations involving conflict and co-operation. The "players" might be firms competing in a market, countries considering pre-emptive military strikes, suspects deciding whether to fink on their accomplices or animals competing for survival. Subsequent work in evolutionary biology has demonstrated that the Nash outcome can arise from a simple survival and replication mechanism even though the players - in this case, organisms or even genes - make no conscious decisions.

But this prize-winning work, carried out at the age of just twenty-one, is not the only remarkable fact about John Nash. At the age of thirty his promising career as a mathematician was interrupted by a schizophrenic breakdown, resulting in a series of involuntary hospital admissions during which he was treated with neuroleptic drugs and insulin coma. Over the next three decades Nash gradually recovered; he emerged from his delusions and began to work on mathematical problems once again. He developed the ability to criticise his own thinking and to reject his voices, deciding not to listen to them. As Nash wrote in 1995, "Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation." This he achieved eventually without medication, which he stopped taking in 1970: in 1996 he said, "I emerged from irrational thinking ultimately without medicine other than the natural hormones of aging."

While the importance of his work was becoming recognised during the 1970s and 1980s, Nash himself remained in obscurity. Princeton students referred to him as "the phantom": a mysterious figure who wandered around the university campus, scribbling cryptic formulas on chalkboards, tolerated but largely ignored. By the early 1990s, however, his condition was transformed and he was once again interacting with colleagues. There was nevertheless some reluctance to award him the honours that would usually be forthcoming for research of this importance. The first attempt to elect Nash to a Fellowship of the Econometric Society, the club of leading economic theorists, was turned down. The award of the Nobel Prize itself would appear - the deliberations are cloaked in secrecy - to have been dogged by controversy. Yet despite his years in obscurity and the stigma of his illness, Nash's contribution to economics was recognised, and the man himself welcomed back into the academic community, by the award of the Nobel Prize eight years ago.

To what extent are Nash's genius and schizophrenia connected? Attractive as the image of the "mad genius" might be, the question is difficult to answer. Nash was noted for his novel ideas and unconventional approaches to mathematics: could this be related to his non-conformist and ultimately disconnected thoughts and behaviour? Nash himself commented, "To some extent, sanity is a form of conformity." Nash's reported response to George Mackey, professor of mathematics at Harvard University, following his first psychotic episode is also suggestive. When asked how, as a mathematician, a man devoted to reason and logical proof, he could believe that extraterrestrials were sending him messages, Nash is said to have replied, "Because the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."

In addition to its Oscar-winning performances and the achievements of John Nash, A Beautiful Mind should also be remembered for publicising some positive but largely unrecognised aspects of mental illness. First, that despite sometimes devastating consequences mental illness may not be entirely negative, but may be associated with particular talents and insights. Secondly, that recovery is possible and can ultimately be achieved by the individuals themselves.

[For further details about the life of John Nash see the biography by Sylvia Nasar, A Beautiful Mind, and the PBS website www.pbs.org/wgbh/amex/nash/index.html . For an introduction to game theory see Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life, by Avinash Dixit and Barry Nalebuff.]