On A Beautiful Mind

I recently finished reading A Beautiful Mind, a biography by Sylvia Nasar. As best stated by the author: “This is the story of John Forbes Nash. Ir. It is a story about the mystery of the human mind, in three acts: genius, madness, reawakening. ”

Below are key excerpts from the book that I found particularly insightful:

The young genius from Bluefield, West Virginia – handsome, arrogant, and highly eccentric — burst onto the mathematical scene in 1948. Over the next decade, a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind’s survival, Nash proved himself, in the words of the eminent geometer Mikhail Gromov, “the most remarkable mathematician of the second half of the century.” Games of strategy, economic rivalry, computer architecture. the shape of the universe, the geometry of imaginary spaces, the mystery of prime numbers —all engaged his wide-ranging imagination. His ideas were of the deep and wholly unanticipated kind that pushes scientific thinking in new directions.

Nash’s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn’t merely that his mind worked faster, that his memory was more retentive,or that his power of concentration was greater. The flashes of intuition were non-rational. Like other great mathematical intuitionists —Georg Friedrich Bernhard Riemann. Jules Henri Poincare, Srinivasa Ramanujan — Nash saw the vision first. constructing the laborious proofs long afterward. But even after he’d try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. Donald Newman, a mathematician who knew Nash at MIT in the 1950s, used to say about him that “everyone else would climb a peak by looking for a path somewhere on the mountain. Nash would climb another mountain altogether and from that distant peak would shine a searchlight back onto the first peak.”

As was to become increasingly obvious over the months that followed, Princeton’s approach to its graduate students, with its combination of complete freedom and relentless pressure to produce, could not have been better suited to someone of Nash’s temperament and style as a mathematician, nor more happily designed to elicit the first real proofs of his genius. Nash’s great luck, if you want to call it luck, was that he came onto the mathematical scene at a time and to a place tailor-made for his particular needs. He came away with his independence, ambition, and originality intact, having been allowed to acquire a truly first-class training that was to serve him brilliantly.

Sometimes one person’s best choice is the same no matter what the others do. That is called a dominant strategy for that player. At other times, one player has a uniformly bad choice — a dominated strategy — in the sense that some other choice is best for him irrespective of what the others do. The search for equilibrium should begin by looking for dominant strategies and eliminating dominated ones. But these are special and relatively rare cases. In most games each player’s best choice does depend on what the others do, and one must turn to Nash’s construct. Nash defined equilibrium as a situation in which no player could improve his or her position by choosing an alternative available strategy, without implying that each person’s privately held best choice will lead to a collectively optimal result. He proved that for a certain very broad class of games of any number of players, at least one equilibrium exists —so long as one allows mixed strategies. But some games have many equilibria and others, relatively rare ones that fall outside the class he defined, may have none. Today, Nash’s concept of equilibrium from strategic games is one of the basic paradigms in social sciences and biology. It is largely the success of his vision that has been responsible for the acceptance of game theory as, in the words of The New Palgrave, “a powerful and elegant method of tackling a subject that had become increasingly baroque, much as Newtonian methods of celestial mechanics had displaced the primitive and increasingly ad-hoc methods of the ancients.”

All through the childhood, adolescence, and brilliant student career. Nash had seemed largely to live inside his own head, immune to the emotional forces that bind people together. His overriding interest was in patterns, not people. and his greatest need was making sense of the chaos within and without by employing, to the largest possible extent, the resources of his own powerful, fearless. fertile mind. His apparent lack of ordinary human needs was, if anything, a matter of pride and satisfaction to him, confirming his own uniqueness. He thought of himself as a rationalist, a free thinker, a sort of Spock of the starship Enterprise. But now, as he entered early adulthood, this unfettered persona was shown to be partly a fiction or at least partly superseded. In those first years at MIT, he discovered that he had some of the same wishes as others. The cerebral, playful, calculating, and episodic connections that had once sufficed no longer served. In five short years, between the ages of twenty-four and twenty-nine, Nash became emotionally involved with at least three other men. He acquired and then abandoned a secret mistress who bore his child. And he courted —or rather was courted by —a woman who became his wife.

Although Nash appeared unscathed, the arrest was a turning point in his life. Aloof, ambitious, coolly indifferent to others as he often appeared, Nash was by no means a true loner. Living in a tolerant ivory tower, he had been lulled into believing that he could do as he liked. Now he learned, in a particularly brutal fashion, that the emotional connections he sought threatened to destroy all else that he valued — his freedom, his career, his reputation, success on society’s terms. Contradictory imperatives can engender tremendous fear. And fear can be subtly destructive.

Nash’s lifelong quest for meaning, control, and recognition in the context of a continuing struggle, not just in society, but in the warring impulses of his paradoxical self, was now reduced to a caricature. Just as the over-concreteness of a dream is related to the intangible themes of waking life, Nash’s search for a piece of paper, a carte d’identite, mirrored his former pursuit of mathematical insights. Yet the gulf between the two recognizably related Nashes was as great as that between Kafka, the controlling creative genius, struggling between the demands of his self-chosen vocation and ordinary life, and K, a caricature of demands of his self-chosen vocation and ordinary life, and K, a caricature of Kafka, the helpless seeker of a piece of paper that will validate his existence. rights, and duties. Delusion is not just fantasy but compulsion. Survival, both of the self and the world, appears to be at stake. Where once he had ordered his thoughts and modulated them, he was now subject to their peremptory and insistent commands.

Nash’s remission did not come about as many people later assume because of some new treatment. “I emerged from irrational thinking,” he said in 1996, “ultimately, without medicine other than the natural hormonal changes of aging.” He described the process as one that involved both a growing awareness of the sterility of his delusional state and a growing capacity for rejecting delusional thought.

On a closing note:

Unlike a game of Hex, outcomes in real life aren’t predetermined by the first or even the fiftieth move. The extraordinary journey of this American genius, this man who surprises people, continues. The self-deprecating humor suggests greater self-awareness. The straight-from-the-heart talk with friends about sadness, pleasure. and attachment suggests a wider range of emotional experiences. The daily effort to give others their due, and to recognize their right to ask this of him, bespeaks a very different man from the often cold and arrogant youth. And the disjunction of thought and emotion that characterized Nash’s personality, not just when he was ill, but even before are much evident today. In deed, if not always in word, Nash has come to a life in which thought and emotion are more closely entwined, where getting and giving are central, and relationships are more symmetrical. He may be getting and giving are central, and relationships are more symmetrical. He may be less than he was intellectually, he may never achieve another breakthrough, but he has become a great deal more than he ever was— “a very fine person,” as Alicia put it once.

A highly recommended biography.

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