A Beautiful Mind Part 1

A Beautiful Mind.

by Sylvia Nasar.

Foreword

(Adapted from remarks at John Nash's 80th birthday Festschrift).

IN J JUNE 2006, I went to St. Petersburg to track down the forty-year-old mathematician who had solved the Poincare Conjecture. Reputedly a hermit with wild hair and long nails who lived in the woods on mushrooms, he was up for a Fields Medal and a $1 million cash prize but had gone into hiding, not just from the media but from the math community. Meanwhile, some folks in Beijing were claiming that they'd beaten him to the punch. It was a great story - if only we could find him. 2006, I went to St. Petersburg to track down the forty-year-old mathematician who had solved the Poincare Conjecture. Reputedly a hermit with wild hair and long nails who lived in the woods on mushrooms, he was up for a Fields Medal and a $1 million cash prize but had gone into hiding, not just from the media but from the math community. Meanwhile, some folks in Beijing were claiming that they'd beaten him to the punch. It was a great story - if only we could find him.

After four frustrating days in Russia, my colleague and I hadn't found a soul who had seen or talked to the guy or his family in years. Then, when we had pretty much thrown in the towel, we stumbled on his mother's apartment more or less by accident and, voila, there was the "hermit," dressed in a sports jacket and Italian loafers, evidently having lunch and watching soccer on TV.

He gestured for us to sit down and explain what we wanted.

"My name is Sylvia Nasar," I began. "I'm a journalist from New York and I'm working on ..."

He interrupted: "You're a writer?"

I nodded.

"I didn't read the book," he said, "but I saw the movie with Russell Crowe."

The point is that, no matter where in the world you are, you'd have to be a real hermit not to know the inspiring story of John Nash.

There are lots of stories about the rise and fall of remarkable individuals. But there are very few stories, much less true stories, with a genuine third act. Nash's story had - has - such a third act. Act III of Nash's life story is his miraculous reawakening.

It is that third act that makes Nash's story resonate with people all over the world - most especially with those who suffer from devastating mental illnesses or love someone who does.

At one point in the movie, when it looks as if things were all over for Nash, his wife, Alicia, takes John's hand, places it over her heart, and says, "I have to believe that something extraordinary is possible."

Something extraordinary was possible.

Of all the letters I've received from readers, my favorite came from a homeless man. It arrived in a dirty envelope with no return address, and it was scrawled on neon orange paper. It was signed "Berkeley Baby." It would never have made it past the New York Times mailroom after the anthrax scare.

The letter writer turned out to have been the night rewrite editor on the metro desk at the New York Times before he was diagnosed with paranoid schizophrenia in the mid-1970s. Since then, he had adopted the name Berkeley Baby and lived on the streets of Berkeley, California, near the university, a forlorn, sad figure not unlike the Phantom of Fine Hall.

He wrote, "John Nash's story gives me hope that one day the world will come back to me too."

The world came back to John Nash after more than thirty years, and it was the third act of his life that drew me to his story in the first place. In the early 1990s, I was an economics reporter at the New York Times. I was interviewing a Princeton professor about some trade statistics when he mentioned a rumor that a "crazy mathematician" who hung around the math building might be on the short list for a n.o.bel prize in economics. "You don't mean the Nash of the Nash equilibrium?" I asked. He told me to call a couple of people in the math department to learn more. By the time I put down the phone, I realized that this was a fairy tale, Greek myth, and Shakespearean tragedy rolled into one.

I didn't write the story immediately. Lots of people wind up on short lists for the n.o.bel and never win, so writing about him in a newspaper would have been an invasion of privacy. In any case, someone else got the prize in 1993. The next year, however, I saw Nash's name in the n.o.bel announcement. I ran over to my editor to pitch the story and actually made him cry.

It was a difficult story to get. n.o.body who knew any facts was willing to go on the record or even talk to me. Martha Legg, Nash's sister, finally broke the silence about the nature of the illness that had wrecked his life.

Lloyd Shapley, another pioneer of game theory, described Nash as a graduate student in the late 1940s, when he wrote his seminal papers on game theory: "He was immature, he was obnoxious, he was a brat. What redeemed him was a keen, logical, beautiful mind.

So now you know to whom I owe the t.i.tle of the biography.

Because Nash's story is so familiar, I'd like to share some of the less familiar parts, including how the book came to be and some of the things that happened after the book and movie broke off.

In June 1995, I found myself in Jerusalem. By then, I had written a book proposal, gotten a publisher, and was about to spend a year at the Inst.i.tute for Advanced Study. Unfortunately, I'd never met my subject or exchanged more than a few words with him on the phone. When I found out that Nash was going to a game theory conference in Jerusalem, I thought I'd go too.

Some will remember what Nash said about John von Neumann, who had given him some of the worst advice ever given to a doctoral student. Fortunately, Nash had ignored von Neumann's advice. Unfortunately for me, he had also decided to ignore the advice of many of his friends and supporters to cooperate with his biographer.

"Dear Mrs. Nasar," a typical note began. "I have decided to take a position of Swiss neutrality ..."

Everyone knows the phrase "It takes a village." It had taken someone weeks of dogged reporting to put together a six-line CV and a short list of Nash's publications. It took hundreds of sources to piece together his whole story. No single individual, not even Alicia or his sons, knew the whole story.

It turned out to be possible to st.i.tch together thousands of bits and pieces - gathered from hundreds of interviews, dozens of letters, and a smattering of doc.u.ments - into a narrative. It worked partly because the mathematics community is like a Greek chorus - watching, commenting, remembering, filling in the background, explaining the action.

But ultimately it worked because John Nash was always a star and, all his life, people around him couldn't take their eyes off him, couldn't stop thinking about him. How many of us, years from now, will live as brightly in the memories as he has for so long ... and long before the fairy tale ending.

And, of course, it worked because Alicia never stopped believing that something extraordinary is possible. She wanted his story told because she thought it would be inspiring for people with mental illnesses.

A friend once asked Nash where Alicia was. John answered "Having dinner with Sylvia." After a pause, he added, "I hope they aren't talking about me."

Actually, Alicia was extremely protective of Nash's privacy and incredibly discreet. There was only one exception: we were in the bas.e.m.e.nt of her bank, sifting through the contents of her safety deposit box looking for photos. She came across these little 2 x 2 snapshots of her and John with Felix Browder at the UC Berkeley swimming pool. That was the beefcake shot that convinced Graydon Carter not to kill the book excerpt in Vanity Fair. (Brian Grazer told me he'd bought the rights to the book because Graydon told him to.) Alicia was holding the picture and chuckling: "Doesn't he have the greatest legs?!"

Nash never did agree to give me an interview for the book.

Post-publication meetings between biographers and their living subjects, authorized or not, often take place in lawyers' offices. Ours did not.

Instead, we met at a Broadway play, Amy's View, starring Judi Dench. Nash told us that it was his first Broadway play. He and Alicia liked Proof better. I was sitting behind them and could see their shoulders shaking with laughter. David Auburn, the playwright of Proof, told me that he got the idea of turning the sisters into daughters of a mad mathematician from John's story.

Watching someone get his life back is an incredibly sweet experience - even little things like driving again or having coffee at Starbucks. When I asked Nash, for a New York Times story about n.o.bel prize winners and how they spent their prize money, how the prize had affected his life, he said, well, now he could buy a $2 cup of coffee at Starbucks. "Poor people can't do that," he'd observed.

Watching someone get his life back and in the process touch the lives of millions of people is equally remarkable. People have told me that they'll never again pa.s.s someone on the street with matted hair and filthy clothes who's shouting at the air without telling themselves that he or she is someone's child or sibling, someone with a past, and maybe someone, like John Nash, with a future. That's the power of stories.

The first time I went to the movie set, Ron Howard was filming the wedding scene on the Lower East. All the princ.i.p.als were there because a New York Times reporter was going to interview us all.

I met Akiva Goldsman, the screenwriter without whom the movie would never have been made, much less won an Oscar. It was Goldsman's brilliant idea to have the audience see the world through Nash's eyes for the first half of the movie. Stepping into Nash's shoes and then having the rug pulled out from under them, the movie audience was not only drawn into the story but experienced what it's like not to be able to distinguish between reality and delusion.

After Ron Howard screened the movie for John and Alicia, I called them. "So, John, what did you think?"

I don't remember all of his exact words, but I do recall that he mentioned liking three things: First of all, that it was funny.

Second, John being an action movie fan, that the pacing was fast.

Third ...

"I think Russell Crowe looks a little like me."

Just in case you think Nash was kidding himself, at a Q&A with Ron Howard at New York University's film school, some mathematicians from the Courant Inst.i.tute came up to Ron Howard to tell him that John Nash actually had looked like Russell Crowe in the white T-s.h.i.+rt scene.

The movie turned Nash into a celebrity. I was on a flight to Mumbai where I was meeting Amartya Sen, also a n.o.bel laureate in economics, at a game theory conference. The woman to my left had just asked me why I was going to India when the flight attendant came by with an Indian newspaper, and there was a photograph of John Nash, the keynote speaker, on the front page, right next to one of Sen. All I had to do was to point. In Mumbai, as in Beijing and other places he was invited to speak, he was mobbed by hundreds of reporters and well-wishers.

Nash's story appealed to children and teenagers who were thrilled by the notion that someone really young - and quirky - could accomplish amazing things and outsmart the older generation. And it made math seem cool.

Dear Mr. Nash,

Hi! I am 9 years old. My name is Ellie. I am a girl. I really admire you. You are my roll [sic] model for a lot of things. I think you are the smartest person who ever lived. I really wish to be like you. I would love to study math. The only problem with that is that I am not very good at math. I can do it. I like it. I am just not good at it. Was that what it was like for you when you were a kid? Please write back. Love, Ellie

P.S. I LOVE your name.

- Sylvia Nasar

Prologue

Where the statue stood Of Newton with his prism and silent face, The marble index of a mind for ever Voyaging through strange seas of Thought, alone.

- WILLIAM W WORDSWORTH

JOHN F FORBES N NASH, JR. - mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine - had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon s.h.i.+rt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll's, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repet.i.tive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. "How could you," began Mackey, "how could you, a mathematician, a man devoted to reason and logical proof... how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer s.p.a.ce to save the world? How could you ... ?"

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispa.s.sionate as that of any bird or snake. "Because," Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, "the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."1 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,2 Nash proved himself, in the words of the eminent Nash proved himself, in the words of the eminent geometer Mikhail Gromov, "the most remarkable mathematician of the second half of the century." geometer Mikhail Gromov, "the most remarkable mathematician of the second half of the century."3 Games of strategy, economic rivalry, computer architecture, the shape of the universe, the geometry of imaginary s.p.a.ces, the mystery of prime numbers - all engaged his wide-ranging imagination. His ideas were of the deep and wholly unantic.i.p.ated kind that pushes scientific thinking in new directions. Games of strategy, economic rivalry, computer architecture, the shape of the universe, the geometry of imaginary s.p.a.ces, the mystery of prime numbers - all engaged his wide-ranging imagination. His ideas were of the deep and wholly unantic.i.p.ated kind that pushes scientific thinking in new directions.

Geniuses, the mathematician Paul Halmos wrote, "are of two kinds: the ones who are just like all of us, but very much more so,.and the ones who, apparently, have an extra human spark. We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue."4 Nash's genius was of that mysterious variety more often a.s.sociated 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 astonis.h.i.+ng 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 s.h.i.+ne a searchlight back onto the first peak." Nash's genius was of that mysterious variety more often a.s.sociated 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 astonis.h.i.+ng 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 s.h.i.+ne a searchlight back onto the first peak."5 No one was more obsessed with originality, more disdainful of authority, or more jealous of his independence. As a young man he was surrounded by the high priests of twentieth-century science - Albert Einstein, John von Neumann, and Norbert Wiener - but he joined no school, became no one's disciple, got along largely without guides or followers. In almost everything he did - from game theory to geometry - he thumbed his nose at the received wisdom, current fas.h.i.+ons, established methods. He almost always worked alone, in his head, usually walking, often whistling Bach. Nash acquired his knowledge of mathematics not mainly from studying what other mathematicians had discovered, but by rediscovering their truths for himself. Eager to astound, he was always on the lookout for the really big problems. When he focused on some new puzzle, he saw dimensions that people who really knew the subject (he never did) initially dismissed as naive or wrongheaded. Even as a student, his indifference to others' skepticism, doubt, and ridicule was awesome.

Nash's faith in rationality and the power of pure thought was extreme, even for a very young mathematician and even for the new age of computers, s.p.a.ce travel, and nuclear weapons. Einstein once chided him for wis.h.i.+ng to amend relativity theory without studying physics.6 His heroes were solitary thinkers and supermen like Newton and Nietzsche. His heroes were solitary thinkers and supermen like Newton and Nietzsche.7 Computers and science fiction were his pa.s.sions. He considered "thinking machines," as he called them, superior in some ways to human beings. Computers and science fiction were his pa.s.sions. He considered "thinking machines," as he called them, superior in some ways to human beings.8 At one point, he became fascinated by the possibility that drugs could heighten physical and intellectual performance. At one point, he became fascinated by the possibility that drugs could heighten physical and intellectual performance.9 He was beguiled by He was beguiled by the idea of alien races of hyper-rational beings who had taught themselves to disregard all emotion. the idea of alien races of hyper-rational beings who had taught themselves to disregard all emotion.10 Compulsively rational, he wished to turn life's decisions - whether to take the first elevator or wait for the next one, where to bank his money, what job to accept, whether to marry - into calculations of advantage and disadvantage, algorithms or mathematical rules divorced from emotion, convention, and tradition. Even the small act of saying an automatic h.e.l.lo to Nash in a hallway could elicit a furious "Why are you saying h.e.l.lo to me?" Compulsively rational, he wished to turn life's decisions - whether to take the first elevator or wait for the next one, where to bank his money, what job to accept, whether to marry - into calculations of advantage and disadvantage, algorithms or mathematical rules divorced from emotion, convention, and tradition. Even the small act of saying an automatic h.e.l.lo to Nash in a hallway could elicit a furious "Why are you saying h.e.l.lo to me?"11 His contemporaries, on the whole, found him immensely strange. They described him as "aloof," "haughty," "without affect," "detached," "spooky," "isolated," and "queer."12 Nash mingled rather than mixed with his peers. Preoccupied with his own private reality, he seemed not to share their mundane concerns. His manner - slightly cold, a bit superior, somewhat secretive - suggested something "mysterious and unnatural." His remoteness was punctuated by flights of garrulousness about outer s.p.a.ce and geopolitical trends, childish pranks, and unpredictable eruptions of anger. But these outbursts were, more often than not, as enigmatic as his silences. "He is not one of us" was a constant refrain. A mathematician at the Inst.i.tute for Advanced Study remembers meeting Nash for the first time at a crowded student party at Princeton: Nash mingled rather than mixed with his peers. Preoccupied with his own private reality, he seemed not to share their mundane concerns. His manner - slightly cold, a bit superior, somewhat secretive - suggested something "mysterious and unnatural." His remoteness was punctuated by flights of garrulousness about outer s.p.a.ce and geopolitical trends, childish pranks, and unpredictable eruptions of anger. But these outbursts were, more often than not, as enigmatic as his silences. "He is not one of us" was a constant refrain. A mathematician at the Inst.i.tute for Advanced Study remembers meeting Nash for the first time at a crowded student party at Princeton: I noticed him very definitely among a lot of other people who were there. He was sitting on the floor in a half-circle discussing something. He made me feel uneasy. He gave me a peculiar feeling. I had a feeling of a certain strangeness. He was different in some way. I was not aware of the extent of his talent. I had no idea he would contribute as much as he really did.13

But he did contribute, in a big way. The marvelous paradox was that the ideas themselves were not obscure. In 1958, Fortune Fortune singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory, calling him the most brilliant of the younger generation of new ambidextrous mathematicians who worked in both pure and applied mathematics. singled Nash out for his achievements in game theory, algebraic geometry, and nonlinear theory, calling him the most brilliant of the younger generation of new ambidextrous mathematicians who worked in both pure and applied mathematics.14 Nash's insight into the dynamics of human rivalry - his theory of rational conflict and cooperation - was to become one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel's ideas of genetic transmission, Darwin's model of natural selection, and Newton's celestial mechanics reshaped biology and physics in their day. Nash's insight into the dynamics of human rivalry - his theory of rational conflict and cooperation - was to become one of the most influential ideas of the twentieth century, transforming the young science of economics the way that Mendel's ideas of genetic transmission, Darwin's model of natural selection, and Newton's celestial mechanics reshaped biology and physics in their day.

It was the great Hungarian-born polymath John von Neumann who first recognized that social behavior could be a.n.a.lyzed as games. Von Neumann's 1928 article on parlor games was the first successful attempt to derive logical and mathematical rules about rivalries.15 Just as Blake saw the universe in a grain of sand, great scientists have often looked for clues to vast and complex problems in the small, familiar phenomena of daily life. Isaac Newton reached insights about the heavens by juggling wooden b.a.l.l.s. Einstein contemplated a boat paddling upriver. Von Neumann pondered the game of poker. Just as Blake saw the universe in a grain of sand, great scientists have often looked for clues to vast and complex problems in the small, familiar phenomena of daily life. Isaac Newton reached insights about the heavens by juggling wooden b.a.l.l.s. Einstein contemplated a boat paddling upriver. Von Neumann pondered the game of poker.

A seemingly trivial and playful pursuit like poker, von Neumann argued, might hold the key to more serious human affairs for two reasons. Both poker and economic compet.i.tion require a certain type of reasoning, namely the rational calculation of advantage and disadvantage based on some internally consistent system of values ("more is better than less"). And in both, the outcome for any individual actor depends not only on his own actions, but on the independent actions of others. might hold the key to more serious human affairs for two reasons. Both poker and economic compet.i.tion require a certain type of reasoning, namely the rational calculation of advantage and disadvantage based on some internally consistent system of values ("more is better than less"). And in both, the outcome for any individual actor depends not only on his own actions, but on the independent actions of others.

More than a century earlier, the French economist Antoine-Augustin Cournot had pointed out that problems of economic choice were greatly simplified when either none or a large number of other agents were present.16 Alone on his island, Robinson Crusoe doesn't have to worry about others whose actions might affect him. Neither, though, do Adam Smith's butchers and bakers. They live in a world with so many actors that their actions, in effect, cancel each other out. But when there is more than one agent but not so many that their influence may be safely ignored, strategic behavior raises a seemingly insoluble problem: "I think that he thinks that I think that he thinks," and so forth. Alone on his island, Robinson Crusoe doesn't have to worry about others whose actions might affect him. Neither, though, do Adam Smith's butchers and bakers. They live in a world with so many actors that their actions, in effect, cancel each other out. But when there is more than one agent but not so many that their influence may be safely ignored, strategic behavior raises a seemingly insoluble problem: "I think that he thinks that I think that he thinks," and so forth.

Von Neumann was able to give a convincing solution to this problem of circular reasoning for games that are two-person, zero-sum games, games in which one player's gain is another's loss. But zero-sum games are the ones least applicable to economics (as one writer put it, the zero-sum game is to game theory "what the twelve-bar blues is to jazz; a polar case, and a point of historical departure"). For situations with many actors and the possibility of mutual gain - the standard economic scenario - von Neumann's superlative instincts failed him. He was convinced that players would have to form coalitions, make explicit agreements, and submit to some higher, centralized authority to enforce those agreements.17 Quite possibly his conviction reflected his generation's distrust, in the wake of the Depression and in the midst of a world war, of unfettered individualism. Though von Neumann hardly shared the liberal views of Einstein, Bertrand Russell, and the British economist John Maynard Keynes, he shared something of their belief that actions that might be reasonable from the point of view of the individual could produce social chaos. Like them he embraced the then-popular solution to political conflict in the age of nuclear weapons: world government. Quite possibly his conviction reflected his generation's distrust, in the wake of the Depression and in the midst of a world war, of unfettered individualism. Though von Neumann hardly shared the liberal views of Einstein, Bertrand Russell, and the British economist John Maynard Keynes, he shared something of their belief that actions that might be reasonable from the point of view of the individual could produce social chaos. Like them he embraced the then-popular solution to political conflict in the age of nuclear weapons: world government.18 The young Nash had wholly different instincts. Where von Neumann's focus was the group, Nash zeroed in on the individual, and by doing so, made game theory relevant to modern economics. In his slender twenty-seven-page doctoral thesis, written when he was twenty-one, Nash created a theory for games in which there was a possibility of mutual gain, inventing a concept that let one cut through the endless chain of reasoning, "I think that you think that I think... ."19 His insight was that the game would be solved when every player independently chose his best response to the other players' best strategies. His insight was that the game would be solved when every player independently chose his best response to the other players' best strategies.

Thus, a young man seemingly so out of touch with other people's emotions, not to mention his own, could see clearly that the most human of motives and behavior is as much of a mystery as mathematics itself, that world of ideal platonic forms invented by the human species seemingly by pure introspection (and yet somehow linked to the grossest and most mundane aspects of nature). But Nash had grown up in a boom town in the Appalachian foothills where fortunes were made from the roaring, raw businesses of rails, coal, sc.r.a.p metal, and electric power. Individual rationality and self-interest, not common agreement on some collective good, seemed sufficient to create a tolerable order. The leap was a short one, from his observations of his hometown to his focus on the logical strategy necessary for the individual to maximize his own advantage and minimize his disadvantages. The Nash equilibrium, once it is explained, sounds obvious, but by formulating the problem of economic compet.i.tion in the way that he did, Nash showed that a decentralized decision-making process could, in fact, be coherent - giving economics an updated, far more sophisticated version of Adam Smith's great metaphor of the Invisible Hand. had grown up in a boom town in the Appalachian foothills where fortunes were made from the roaring, raw businesses of rails, coal, sc.r.a.p metal, and electric power. Individual rationality and self-interest, not common agreement on some collective good, seemed sufficient to create a tolerable order. The leap was a short one, from his observations of his hometown to his focus on the logical strategy necessary for the individual to maximize his own advantage and minimize his disadvantages. The Nash equilibrium, once it is explained, sounds obvious, but by formulating the problem of economic compet.i.tion in the way that he did, Nash showed that a decentralized decision-making process could, in fact, be coherent - giving economics an updated, far more sophisticated version of Adam Smith's great metaphor of the Invisible Hand.

By his late twenties, Nash's insights and discoveries had won him recognition, respect, and autonomy. He had carved out a brilliant career at the apex of the mathematics profession, traveled, lectured, taught, met the most famous mathematicians of his day, and become famous himself. His genius also won him love. He had married a beautiful young physics student who adored him, and fathered a child. It was a brilliant strategy, this genius, this life. A seemingly perfect adaptation.

Many great scientists and philosophers, among them Rene Descartes, Ludwig Wittgenstein, Immanuel Kant, Thorstein Veblen, Isaac Newton, and Albert Einstein, have had similarly strange and solitary personalities.20 An emotionally detached, inward-looking temperament can be especially conducive to scientific creativity, psychiatrists and biographers have long observed, just as fiery fluctuations in mood may sometimes be linked to artistic expression. In An emotionally detached, inward-looking temperament can be especially conducive to scientific creativity, psychiatrists and biographers have long observed, just as fiery fluctuations in mood may sometimes be linked to artistic expression. In The Dynamics of Creation, The Dynamics of Creation, Anthony Storr, the British psychiatrist, contends that an individual who "fears love almost as much as he fears hatred" may turn to creative activity not only out of an impulse to experience aesthetic pleasure, or the delight of exercising an active mind, but also to defend himself against anxiety stimulated by conflicting demands for detachment and human contact. Anthony Storr, the British psychiatrist, contends that an individual who "fears love almost as much as he fears hatred" may turn to creative activity not only out of an impulse to experience aesthetic pleasure, or the delight of exercising an active mind, but also to defend himself against anxiety stimulated by conflicting demands for detachment and human contact.21 In the same vein, Jean-Paul Sartre, the French philosopher and writer, called genius "the brilliant invention of someone who is looking for a way out." Posing the question of why people often are willing to endure frustration and misery in order to create something, even in the absence of large rewards, Storr speculates: In the same vein, Jean-Paul Sartre, the French philosopher and writer, called genius "the brilliant invention of someone who is looking for a way out." Posing the question of why people often are willing to endure frustration and misery in order to create something, even in the absence of large rewards, Storr speculates: Some creative people ... of predominately schizoid or depressive temperaments ... use their creative capacities in a defensive way. If creative work protects a man from mental illness, it is small wonder that he pursues it with avidity. The schizoid state ... is characterized by a sense of meaninglessness and futility. For most people, interaction with others provides most of what they require to find meaning and significance in life. For the schizoid person, however, this is not the case. Creative activity is a particularly apt way to express himself ... the activity is solitary ... [but] the ability to create and the productions which result from such ability are generally regarded as possessing value by our society. productions which result from such ability are generally regarded as possessing value by our society.22

Of course, very few people who exhibit "a lifelong pattern of social isolation" and "indifference to the att.i.tudes and feelings of others" - the hallmarks of a so-called schizoid personality - possess great scientific or other creative talent.23 And the vast majority of people with such strange and solitary temperaments never succ.u.mb to severe mental illness. And the vast majority of people with such strange and solitary temperaments never succ.u.mb to severe mental illness.24 Instead, according to John G. Gunderson, a psychiatrist at Harvard, they tend "to engage in solitary activities which often involve mechanical, scientific, futuristic and other non-human subjects ... [and] are likely to appear increasingly comfortable over a period of time by forming a stable but distant network of relations.h.i.+ps with people around work tasks." Instead, according to John G. Gunderson, a psychiatrist at Harvard, they tend "to engage in solitary activities which often involve mechanical, scientific, futuristic and other non-human subjects ... [and] are likely to appear increasingly comfortable over a period of time by forming a stable but distant network of relations.h.i.+ps with people around work tasks."25 Men of scientific genius, however eccentric, rarely become truly insane - the strongest evidence for the potentially protective nature of creativity. Men of scientific genius, however eccentric, rarely become truly insane - the strongest evidence for the potentially protective nature of creativity.26 Nash proved a tragic exception. Underneath the brilliant surface of his life, all was chaos and contradiction: his involvements with other men; a secret mistress and a neglected illegitimate son; a deep ambivalence toward the wife who adored him, the university that nurtured him, even his country; and, increasingly, a haunting fear of failure. And the chaos eventually welled up, spilled over, and swept away the fragile edifice of his carefully constructed life.

The first visible signs of Nash's slide from eccentricity into madness appeared when he was thirty and was about to be made a full professor at MIT. The episodes were so cryptic and fleeting that some of Nash's younger colleagues at that inst.i.tution thought that he was indulging a private joke at their expense. He walked into the common room one winter morning in 1959 carrying The New York Times The New York Times and remarked, to no one in particular, that the story in the upper left-hand corner of the front page contained an encrypted message from inhabitants of another galaxy that only he could decipher. and remarked, to no one in particular, that the story in the upper left-hand corner of the front page contained an encrypted message from inhabitants of another galaxy that only he could decipher.27 Even months later, after he had stopped teaching, had angrily resigned his professors.h.i.+p, and was incarcerated at a private psychiatric hospital in suburban Boston, one of the nation's leading forensic psychiatrists, an expert who testified in the case of Sacco and Vanzetti, insisted that Nash was perfectly sane. Only a few of those who witnessed the uncanny metamorphosis, Norbert Wiener among them, grasped its true significance. Even months later, after he had stopped teaching, had angrily resigned his professors.h.i.+p, and was incarcerated at a private psychiatric hospital in suburban Boston, one of the nation's leading forensic psychiatrists, an expert who testified in the case of Sacco and Vanzetti, insisted that Nash was perfectly sane. Only a few of those who witnessed the uncanny metamorphosis, Norbert Wiener among them, grasped its true significance.28 At thirty years of age, Nash suffered the first shattering episode of paranoid schizophrenia, the most catastrophic, protean, and mysterious of mental illnesses. For the next three decades, Nash suffered from severe delusions, hallucinations, disordered thought and feeling, and a broken will. In the grip of this "cancer of the mind," as the universally dreaded condition is sometimes called, Nash abandoned mathematics, embraced numerology and religious prophecy, and believed himself to be a "messianic figure of great but secret importance." He fled to Europe several times, was hospitalized involuntarily half a dozen times for periods up to a year and a half, was subjected to all sorts of drug and shock treatments, experienced brief remissions and episodes of hope that lasted only a few months, and finally became a sad phantom who haunted the Princeton University campus where he had once been a brilliant graduate student, oddly dressed, muttering to himself, writing mysterious messages on blackboards, year after year. brief remissions and episodes of hope that lasted only a few months, and finally became a sad phantom who haunted the Princeton University campus where he had once been a brilliant graduate student, oddly dressed, muttering to himself, writing mysterious messages on blackboards, year after year.

The origins of schizophrenia are mysterious. The condition was first described in 1806, but no one is certain whether the illness - or, more likely, group of illnesses - existed long before then but had escaped definition or, on the other hand, appeared as an AIDS-like scourge at the start of the industrial age.29 Roughly 1 percent of the population in all countries succ.u.mbs to it. Roughly 1 percent of the population in all countries succ.u.mbs to it.30 Why it strikes one individual and not another is not known, although the suspicion is that it results from a tangle of inherited vulnerability and life stresses. Why it strikes one individual and not another is not known, although the suspicion is that it results from a tangle of inherited vulnerability and life stresses.31 No element of environment - war, imprisonment, drugs, or upbringing - has ever been proved to cause, by itself, a single instance of the illness. No element of environment - war, imprisonment, drugs, or upbringing - has ever been proved to cause, by itself, a single instance of the illness.32 There is now a consensus that schizophrenia has a tendency to run in families, but heredity alone apparently cannot explain why a specific individual develops the full-blown illness. There is now a consensus that schizophrenia has a tendency to run in families, but heredity alone apparently cannot explain why a specific individual develops the full-blown illness.33 Eugen Bleuler, who coined the term schizophrenia schizophrenia in 1908, describes a "specific type of alteration of thinking, feeling and relation to the external world." in 1908, describes a "specific type of alteration of thinking, feeling and relation to the external world."34 The term refers to a splitting of psychic functions, "a peculiar destruction of the inner cohesiveness of the psychic personality." The term refers to a splitting of psychic functions, "a peculiar destruction of the inner cohesiveness of the psychic personality."35 To the person experiencing early symptoms, there is a dislocation of every faculty, of time, s.p.a.ce, and body. To the person experiencing early symptoms, there is a dislocation of every faculty, of time, s.p.a.ce, and body.36 None of its symptoms - hearing voices, bizarre delusions, extreme apathy or agitation, coldness toward others - is, taken singly, unique to the illness. None of its symptoms - hearing voices, bizarre delusions, extreme apathy or agitation, coldness toward others - is, taken singly, unique to the illness.37 And symptoms vary so much between individuals and over time for the same individual that the notion of a "typical case" is virtually nonexistent. Even the degree of disability - far more severe, on average, for men - varies wildly. The symptoms can be "slightly, moderately, severely, or absolutely disabling," according to Irving Gottesman, a leading contemporary researcher. And symptoms vary so much between individuals and over time for the same individual that the notion of a "typical case" is virtually nonexistent. Even the degree of disability - far more severe, on average, for men - varies wildly. The symptoms can be "slightly, moderately, severely, or absolutely disabling," according to Irving Gottesman, a leading contemporary researcher.38 Though Nash succ.u.mbed at age thirty, the illness can appear at any time from adolescence to advanced middle age. Though Nash succ.u.mbed at age thirty, the illness can appear at any time from adolescence to advanced middle age.39 The first episode can last a few weeks or months or several years. The first episode can last a few weeks or months or several years.40 The life history of someone with the disease can include only one or two episodes. The life history of someone with the disease can include only one or two episodes.41 Isaac Newton, always an eccentric and solitary soul, apparently suffered a psychotic breakdown with paranoid delusions at age fifty-one. Isaac Newton, always an eccentric and solitary soul, apparently suffered a psychotic breakdown with paranoid delusions at age fifty-one.42 The episode, which may have been precipitated by an unhappy attachment to a younger man and the failure of his alchemy experiments, marked the end of Newton's academic career. But, after a year or so, Newton recovered and went on to hold a series of high public positions and to receive many honors. More often, as happened in Nash's case, people with the disease suffer many, progressively more severe episodes that occur at ever shorter intervals. Recovery, almost never complete, runs the gamut from a level tolerable to society to one that may not require permanent hospitalization but in fact does not allow even the semblance of a normal life. The episode, which may have been precipitated by an unhappy attachment to a younger man and the failure of his alchemy experiments, marked the end of Newton's academic career. But, after a year or so, Newton recovered and went on to hold a series of high public positions and to receive many honors. More often, as happened in Nash's case, people with the disease suffer many, progressively more severe episodes that occur at ever shorter intervals. Recovery, almost never complete, runs the gamut from a level tolerable to society to one that may not require permanent hospitalization but in fact does not allow even the semblance of a normal life.43 More than any symptom, the defining characteristic of the illness is the profound feeling of incomprehensibility and inaccessibility that sufferers provoke in other people. Psychiatrists describe the person's sense of being separated by a "gulf which defies description" from individuals who seem "totally strange, puzzling, inconceivable, uncanny and incapable of empathy, even to the point of being sinister and frightening." inconceivable, uncanny and incapable of empathy, even to the point of being sinister and frightening."44 For Nash, the onset of the illness dramatically intensified a pre-existing feeling, on the part of many who knew him, that he was essentially disconnected from them and deeply unknowable. As Storr writes: For Nash, the onset of the illness dramatically intensified a pre-existing feeling, on the part of many who knew him, that he was essentially disconnected from them and deeply unknowable. As Storr writes: However melancholy a depressive may be, the observer generally feels there is some possibility of emotional contact. The schizoid person, on the other hand, appears withdrawn and inaccessible. His remoteness from human contact makes his state'of mind less humanly comprehensible, since his feelings are not communicated. If such a person becomes psychotic (schizophrenic) this lack of connection with people and the external world becomes more obvious; with the result that the sufferer's behavior and utterances appear inconsequential and unpredictable.45

Schizophrenia contradicts popular but incorrect views of madness as consisting solely of wild gyrations of mood, or fevered delirium. Someone with schizophrenia is not permanently disoriented or confused, for example, the way that an individual with a brain injury or Alzheimer's might be.46 He may have, indeed usually does have, a firm grip on certain aspects of present reality. While he was ill, Nash traveled all over Europe and America, got legal help, and learned to write sophisticated computer programs. Schizophrenia is also distinct from manic depressive illness (currently known as bipolar disorder), the illness with which it has most often been confounded in the past. He may have, indeed usually does have, a firm grip on certain aspects of present reality. While he was ill, Nash traveled all over Europe and America, got legal help, and learned to write sophisticated computer programs. Schizophrenia is also distinct from manic depressive illness (currently known as bipolar disorder), the illness with which it has most often been confounded in the past.

If anything, schizophrenia can be a ratiocinating illness, particularly in its early phases.47 From the turn of the century, the great students of schizophrenia noted that its sufferers included people with fine minds and that the delusions which often, though not always, come with the disorder involve subtle, sophisticated, complex flights of thought. Emil Kraepelin, who defined the disorder for the first time in 1896, described "dementia praec.o.x," as he called the illness, not as the shattering of reason but as causing "predominant damage to the emotional life and the will." From the turn of the century, the great students of schizophrenia noted that its sufferers included people with fine minds and that the delusions which often, though not always, come with the disorder involve subtle, sophisticated, complex flights of thought. Emil Kraepelin, who defined the disorder for the first time in 1896, described "dementia praec.o.x," as he called the illness, not as the shattering of reason but as causing "predominant damage to the emotional life and the will."48 Louis A. Sa.s.s, a psychologist at Rutgers University, calls it "not an escape from reason but an exacerbation of that thoroughgoing illness Dostoevsky imagined ... at least in some of its forms ... a heightening rather than a dimming of conscious awareness, and an alienation not from reason but from emotion, instincts and the will." Louis A. Sa.s.s, a psychologist at Rutgers University, calls it "not an escape from reason but an exacerbation of that thoroughgoing illness Dostoevsky imagined ... at least in some of its forms ... a heightening rather than a dimming of conscious awareness, and an alienation not from reason but from emotion, instincts and the will."49 Nash's mood in the early days of his illness can be described, not as manic or melancholic, but rather as one of heightened awareness, insomniac wakefulness and watchfulness. He began to believe that a great many things that he saw - a telephone number, a red necktie, a dog trotting along the sidewalk, a Hebrew letter, a birthplace, a sentence in The New York Times - The New York Times - had a hidden significance, apparent only to him. He found such signs increasingly compelling, so much so that they drove from his consciousness his usual concerns and preoccupations. At the same time, he believed he was on the brink of cosmic insights. He claimed he had found a solution to the greatest unsolved problem in pure mathematics, had a hidden significance, apparent only to him. He found such signs increasingly compelling, so much so that they drove from his consciousness his usual concerns and preoccupations. At the same time, he believed he was on the brink of cosmic insights. He claimed he had found a solution to the greatest unsolved problem in pure mathematics, the so-called Riemann Hypothesis. Later he said he was engaged in an effort to "rewrite the foundations of quantum physics." Still later, he claimed, in a torrent of letters to former colleagues, to have discovered vast conspiracies and the secret meaning of numbers and biblical texts. In a letter to the algebraist Emil Artin, whom he addressed as "a great necromancer and numerologist," Nash wrote: the so-called Riemann Hypothesis. Later he said he was engaged in an effort to "rewrite the foundations of quantum physics." Still later, he claimed, in a torrent of letters to former colleagues, to have discovered vast conspiracies and the secret meaning of numbers and biblical texts. In a letter to the algebraist Emil Artin, whom he addressed as "a great necromancer and numerologist," Nash wrote: I have been considering Algerbiac [sic] questions and have noticed some interesting things that might also interest you ... I, a while ago, was seized with the concept that numerological calculations dependent on the decimal system might not be sufficiently intrinsic also that language and alphabet structure might contain ancient cultural stereotypes interfering with clear understands [sic] or unbiased thinking... . I quickly wrote down a new sequence of symbols... . These were a.s.sociated with (in fact natural, but perhaps not computationally ideal but suited for mystical rituals, incantations and such) system for representing the integers via symbols, based on the products of successive primes.50

A predisposition to schizophrenia was probably integral to Nash's exotic style of thought as a mathematician, but the full-blown disease devastated his ability to do creative work. His once-illuminating visions became increasingly obscure, self-contradictory, and full of purely private meanings, accessible only to himself. His longstanding conviction that the universe was rational evolved into a caricature of itself, turning into an unshakable belief that everything had meaning, everything had a reason, nothing was random or coincidental. For much of the time, his grandiose delusions insulated him from the painful reality of all that he had lost. But then would come terrible flashes of awareness. He complained bitterly from time to time of his inability to concentrate and to remember mathematics, which he attributed to shock treatments.51 He sometimes told others that his enforced idleness made him feel ashamed of himself, worthless. He sometimes told others that his enforced idleness made him feel ashamed of himself, worthless.52 More often, he expressed his suffering wordlessly. On one occasion, sometime during the 1970s, he was sitting at a table in the dining hall at the Inst.i.tute for Advanced Study - the scholarly haven where he had once discussed his ideas with the likes of Einstein, von Neumann, and Robert Oppenheimer - alone as usual. That morning, an inst.i.tute staff member recalled, Nash got up, walked over to a wall, and stood there for many minutes, banging his head against the wall, slowly, over and over, eyes tightly shut, fists clenched, his face contorted with anguish. More often, he expressed his suffering wordlessly. On one occasion, sometime during the 1970s, he was sitting at a table in the dining hall at the Inst.i.tute for Advanced Study - the scholarly haven where he had once discussed his ideas with the likes of Einstein, von Neumann, and Robert Oppenheimer - alone as usual. That morning, an inst.i.tute staff member recalled, Nash got up, walked over to a wall, and stood there for many minutes, banging his head against the wall, slowly, over and over, eyes tightly shut, fists clenched, his face contorted with anguish.53 While Nash the man remained frozen in a dreamlike state, a phantom who haunted Princeton in the 1970s and 1980s scribbling on blackboards and studying religious texts, his name began to surface everywhere - in economics textbooks, articles on evolutionary biology, political science treatises, mathematics journals. It appeared less often in explicit citations of the papers he had written in the 1950s than as an adjective for concepts too universally accepted, too familiar a part of the foundation of many subjects to require a particular reference: "Nash equilibrium," "Nash bargaining solution," "Nash program," "De Giorgi-Nash result," "Nash embedding," "Nash-Moser theorem," "Nash blowing-up." foundation of many subjects to require a particular reference: "Nash equilibrium," "Nash bargaining solution," "Nash program," "De Giorgi-Nash result," "Nash embedding," "Nash-Moser theorem," "Nash blowing-up."54 When a ma.s.sive new encyclopedia of economics, When a ma.s.sive new encyclopedia of economics, The New Palgrave, The New Palgrave, appeared in 1987, its editors noted that the game theory revolution that had swept through economics "was effected with apparently no new fundamental mathematical theorems beyond those of von Neumann and Nash." appeared in 1987, its editors noted that the game theory revolution that had swept through economics "was effected with apparently no new fundamental mathematical theorems beyond those of von Neumann and Nash."55 Even as Nash's ideas became more influential - in fields so disparate that almost no one connected the Nash of game theory with Nash the geometer or Nash the a.n.a.lyst - the man himself remained shrouded in obscurity. Most of the young mathematicians and economists who made use of his ideas simply a.s.sumed, given the dates of his published articles, that he was dead. Members of the profession who knew otherwise, but were aware of his tragic illness, sometimes treated him as if he were. A 1989 proposal to place Nash on the ballot of the Econometric Society as a potential fellow of the society was treated by society officials as a highly romantic but essentially frivolous gesture - and rejected.56 No biographical sketch of Nash appeared in No biographical sketch of Nash appeared in The New Palgrave The New Palgrave alongside sketches of half a dozen other pioneers of game theory. alongside sketches of half a dozen other pioneers of game theory.57 At around that time, as part of his daily rounds in Princeton, Nash used to turn up at the inst.i.tute almost every day at breakfast. Sometimes he would cadge cigarettes or spare change, but mostly he kept very much to himself, a silent, furtive figure, gaunt and gray, who sat alone off in a corner, drinking coffee, smoking, spreading out a ragged pile of papers that he carried with him always.58 Freeman Dyson, one of the giants of twentieth-century theoretical physics, one-time mathematical prodigy, and author of a dozen metaphorically rich popular books on science, then in his sixties, about five years older than Nash, was one of those who saw Nash even' day at the inst.i.tute.59 Dyson is a small, lively sprite of a man, father of six children, not at all remote, with an acute interest in people unusual for someone of his profession, and one of those who would greet Nash without expecting any response, bur merely as a token of respect. Dyson is a small, lively sprite of a man, father of six children, not at all remote, with an acute interest in people unusual for someone of his profession, and one of those who would greet Nash without expecting any response, bur merely as a token of respect.

On one of those gray mornings, sometime in the late 1980s, he said his usual good morning to Nash. "I see your daughter is in the news again today," Nash said to Dyson, whose daughter Esther is a frequently quoted authority on computers. Dyson, who had never heard Nash speak, said later: "I had no idea he was aware of her existence. It was beautiful. I remember the astonishment I felt. What I found most wonderful was this slow awakening. Slowly, he just somehow woke up. n.o.body else has ever awakened the way he did."

More signs of recovery followed. Around 1990, Nash began to correspond, via electronic mail, with Enrico Bombieri, for many years a star of the Inst.i.tute's mathematics faculty.60 Bombieri, a das.h.i.+ng and erudite Italian, is a winner of the Fields Medal, mathematics' equivalent of the n.o.bel. He also paints oils, collects wild mushrooms, and polishes gemstones. Bombieri is a number theorist who has been working for a long time on the Riemann Hypothesis. The exchange focused on various conjectures and calculations Nash had begun related to the so-called Bombieri, a das.h.i.+ng and erudite Italian, is a winner of the Fields Medal, mathematics' equivalent of the n.o.bel. He also paints oils, collects wild mushrooms, and polishes gemstones. Bombieri is a number theorist who has been working for a long time on the Riemann Hypothesis. The exchange focused on various conjectures and calculations Nash had begun related to the so-called ABC conjecture. The letters showed that Nash was once again doing real mathematical research, Bombieri said: ABC conjecture. The letters showed that Nash was once again doing real mathematical research, Bombieri said: He was staying very much by himself. But at some point he started talking to people. Then we talked quite a lot about number theory. Sometimes we talked in my office. Sometimes over coffee in the dining hall. Then we began corresponding by e-mail. It's a sharp mind ... all the suggestions have that toughness ... there's nothing commonplace about those... . Usually when one starts in a field, people remark the obvious, only what is known. In this case, not. He looks at things from a slightly different angle.

A spontaneous recovery from schizophrenia - still widely regarded as a dementing and degenerative disease - is so rare, particularly after so long and severe a course as Nash experienced, that, when it occurs, psychiatrists routinely question the validity of the original diagnosis.61 But people like Dyson and Bombieri, who had watched Nash around Princeton for years before witnessing the transformation, had no doubt that by the early 1990s he was "a walking miracle." But people like Dyson and Bombieri, who had watched Nash around Princeton for years before witnessing the transformation, had no doubt that by the early 1990s he was "a walking miracle."

It is highly unlikely, however, that many people outside this intellectual Olympus would have become privy to these developments, dramatic as they appeared to Princeton insiders, if not for another scene, which also took place on these grounds at the end of the first week of October 1994.

A mathematics seminar was just breaking up. Nash, who now regularly attended such gatherings and sometimes even asked a question or offered some conjecture, was about to duck out. Harold Kuhn, a mathematics professor at the university and Nash's closest friend, caught up with him at the door.62 Kuhn had telephoned Nash at home earlier that day and suggested that the two of them might go for lunch after the talk. The day was so mild, the outdoors so inviting, the Inst.i.tute woods so brilliant, that the two men wound up sitting on a bench opposite the mathematics building, at the edge of a vast expanse of lawn, in front of a graceful little j.a.panese fountain. Kuhn had telephoned Nash at home earlier that day and suggested that the two of them might go for lunch after the talk. The day was so mild, the outdoors so inviting, the Inst.i.tute woods so brilliant, that the two men wound up sitting on a bench opposite the mathematics building, at the edge of a vast expanse of lawn, in front of a graceful little j.a.panese fountain.

Kuhn and Nash had known each other for nearly fifty years. They had both been graduate students at Princeton in the late 1940s, shared the same professors, known the same people, traveled in the same elite mathematical circles. Thev had not been friends as students, but Kuhn, who spent most of his career in Princeton, had never entirely lost touch with Nash and had, as Nash became more accessible, managed to establish fairly regular contact with him. Kuhn is a shrewd, vigorous, sophisticated man who is not burdened with "the mathematical personality." Not a typical academic, pa.s.sionate about the arts and liberal political causes, Kuhn is as interested in other people's lives as Nash is remote from them. Thev were an odd couple, connected not by temperament or experience but by a large fund of common memories and a.s.sociations.