Sylvia Nasar - May 13, 2002
BEHIND JOHN NASH AND A BEAUTIFUL MIND
Sylvia Nasar, Author, A Beautiful Mind
Dave Bayer, Mathematician; Scientific Advisor on the film, A Beautiful Mind
In conversation with Robert Osserman, Author, Poetry of the Universe
Osserman: There isn’t anyone in America who doesn’t know the story of John Nash, thanks to Sylvia Nasar's articles and books, the movie A Beautiful Mind, the feature on "60 Minutes" and a recent PBS documentary, "A Brilliant Madness." I’d like to start out by asking Sylvia to tell us about her background and how she got into this topic.
Nasar: I was an economics reporter for The New York Times. Like every economics graduate student, I knew what the Nash equilibrium was, but I’d never thought about the man at all. In 1993, I was on the phone gossiping about the Nobel Prize with a Princeton economist who’d just come back from Stockholm. He said, "They’re thinking about giving a prize in game theory, and if they do, there’s this crazy mathematician who’s been haunting the math building at Princeton for the last two decades. He might actually be on the short list." I said, "Who’s that?" He said, "Nash." I said, "Not the Nash of the Nash equilibrium?" He said, "Yes."
He had been one of the intellectual giants, not just in economics, but also in true mathematics, in his 20s in the 1950s. He had then succumbed to this terrible illness and had lived in poverty and obscurity for the last 30 years. That someone who had been so lost for so long could come back and recover from an illness that, as far as I knew, no one ever recovered from, and could then win a Nobel Prize for something he had done as a graduate student, was the most remarkable story I had come across as a journalist.
It wasn’t until a year and a half later, when I was sitting at my desk in the newsroom, reading the wires, that I saw Nash’s name. I couldn’t believe it. I ran over to the business editor, Glenn Kramon, and blurted out a few lines about who Nash was, what he had done, and this amazing fairy-tale turn in his life. Glenn’s face turned bright pink and tears welled up in his eyes. I thought, "Yes, I’m going to write this story."
There was an immediate obstacle. No one in the economics and mathematics communities who knew Nash would put the schizophrenia on the record. This is an illness that, even if you’ve won the Nobel Prize, is so stigmatized that people who care about you don’t want it to be in the newspaper. Two and a half weeks into the process I discovered that he had a sister, and she decided to break the silence. That is why it was possible to write that story for the Times.
Osserman: Dave Bayer was the mathematical consultant on the movie. Tell us about your connection with the project.
Bayer: I’d crossed paths with John Nash several times before this film. As a child, the most interesting math books I could find in my house were the two volumes of Martin Gardner’s columns in Scientific American from the 1950s. One of the articles describes a game of Hex, or Nash, depending what you call it, that Nash invented in grad school, and that all the grad students at Princeton were playing. I was fascinated. The second computer program I ever wrote was an attempt to play that game.
Later, my grad-school advisor was Heisuke Hironaka. As Sylvia chronicles in her book, during Nash’s illness Hironaka went to visit Nash, and one of the things he discussed was an idea about the resolution of singularities as a topic in algebraic geometry. Hironaka came back and suggested, “Maybe you should think about this problem." Then he mischievously suggested there was a chance it could drive me crazy.
Two summers ago, I was about to pack off to Berkeley from New York City for the summer and I got a call from the American Mathematical Society. Would I review the play "Proof"? I was fascinated by the play, which has a theme similar to that of the movie. I spent weeks writing what should have taken a day or so.
Director Ron Howard was looking for somebody to work with him on the film as a consultant. He read the review and approached me. I had a chance, as a result, to work on the film. People don’t run away and join the circus the same way they did a century ago. This is the modern-day equivalent.
Osserman: What did you do in the film, besides be Nash’s hands?
Bayer: The script was basically complete, but there were questions about what would be mathematically realistic in this scene, or what phrases would be possible. I read the script with Ron and screenwriter Akiva Goldsman, who listened to my responses, often with great humor. In pre-production, they were trying to imagine what Hex should be, if it was to be in the film. The set dressers came to imagine what each room should look like, taking pictures around Columbia – the messiest professors’ offices I could find. I would be available for these people to call on if they wanted to talk about math first.
The part I most enjoyed was doing all the blackboards in all the windows. There would be about an hour during which the scene would be lit. During that hour, I would work around the stand-ins and doodle on the windows or blackboard. Later in the movie the idea is that John Nash has been in a room crazy for three days working on the board.
Osserman: One of the key questions is the blurring of fact and fiction. They kept the name of the biography, the name of John Nash and his wife, Alicia. They made up all sorts of fictional parts, changed the names of all the other characters. They came up with this amalgam.
Nasar: When I look back on this whole debate, I think the real blurring of fact and fiction, in a destructive and mean-spirited way, took place in the entertainment media. Reviewers and reporters framed the debate in a rather specious way to suggest that the only intellectually honest film that could be made about a life would be virtually a documentary.
What makes this movie work, and the reason so many people were touched by it and felt that for the first time they understood what their child or their friend’s child was going through, was a fictional device that made the audience put itself in the shoes of someone with whom, ordinarily, it would be very hard to identify. When you are in Golden Gate Park in San Francisco and you look at somebody who is dressed in filthy clothes, pushing a shopping cart full of junk and talking to himself, it’s very hard to identify with somebody like that. This movie, by making you see the world through the eyes of someone who could not distinguish between delusion and reality – someone, however, who was also seen as worthy of love and respect – is what made this movie work.
The other question brought up repeatedly was, for the real John Nash, was his life a love story? Didn’t he and Alicia get divorced? The reason that the biography, 450 pages of tremendous detail, some of it not so attractive, is dedicated to Alicia Nash, is that their relationship was more complicated than in the movie. She was his student. She married him when he was a rising star. Soon afterwards he got sick. He had paranoid schizophrenia. He never thought he was sick when he was ill. She was the one taking care of him; she was the one making the tough calls about hospitalizing him. He blamed her. At a certain point, she couldn’t take it anymore and they got divorced. They lived apart for about five years. She never let him go; she was always in touch with him. She kept doing things for him.
In 1970, when he was at the end of the line – his mother had died, he was locked up in a big state hospital in Virginia – he wrote to Alicia, who was living at Princeton, raising their son on her own, and still young and very beautiful. He wrote to her and begged her to save him from future hospitalizations and homelessness. For some reason, she took him in. For years, during which there was no sign that he was ever going to get well, and certainly not that he would win a Nobel, Alicia got up at 4:30 in the morning to commute two hours to Manhattan to support her indigent, mentally ill ex-husband and their son, who was also diagnosed with schizophrenia. To me, if this is not love, I don’t know what is. Now the story has, with the exception of the continuing tragedy of their son’s illness, taken on this very romantic quality once again. Last year, John and Alicia got remarried. Yes, this is an amazing love story.
Osserman: David Gale, professor emeritus at UC Berkeley, sent me a neat example of the famous Nash equilibrium. This game is a three-person odds or evens. I count, "One, two, three, go," then we each put out one or two fingers. If you’re the only one to put out one finger, you get a dollar from the bank. If you’re the only one to put out two fingers, you get two dollars from the bank. Otherwise, everybody gets nothing. Shall we try it?
Each of us has put out one finger. Nobody gets a dollar. Sylvia has put out two fingers, and Dave and I have put out one each. Sylvia collects two bucks. This is an example of the Nash equilibrium; each one of us could not have done better if we’d changed, assuming the others stayed the same. Clearly Sylvia could not have done better; she got the maximum two bucks. If I had changed, Sylvia and I would both have had two fingers out. Dave would have collected a dollar, but I would still get nothing. The same would happen if he changed. It’s a position where none of us would have done any better by switching strategies if the others were the same.
It really gets interesting if you do this repeatedly. You have to come up with a mixed strategy: it’s like a pitcher choosing between balls and strikes and the occasional brushback. You have to figure out what percentage of each you want to do. Nash proved that if we keep switching there is equilibrium – some percentage of ones and twos that’s optimal. In this case, you can compute it exactly. Roughly two out of five times you would want to put out one finger, and three out of five you want to put out two.
Nash defined this concept, which nobody had previously thought of, and he proved his theorem. He took it to John von Neumann, who was the big star at that time in Princeton, one of the most famous mathematicians of the century. Neumann looked at it and said, "That’s trivial. That’s a fixed point theorem."
Nasar: You all must be wondering, For this they give a Nobel Prize in economics? We have to say why this is incredibly useful and revolutionary. Nash thought of this in the context of a search launched by von Neumann and other mathematicians in the 1920s for a general but truly rigorous mathematical theory of human conflict and cooperation. Mathematicians wanted to be able to say something insightful and useful about society. Von Neumann had a good theory only for a situation of all-out conflict, such as a game. This was his model for more complicated real-life situations like wars and economies, in which your loss is my gain. In economics and even in warfare, most real-life situations are not zero-sum games. There is almost always the possibility for mutual gain.
Von Neumann also had a good theory only for situations involving two players. Most real-life situations in economics and elsewhere have many players. Along comes Nash – a 21-year-old, arrogant, irreverent graduate student – with a theory that applies to any scenario, anywhere on the spectrum between all-out conflict and total cooperation and any number of players. He comes up with a definition of what a solution is and proves that, in any scenario, a situation exists in which no one can do any better, given the others’ choices.
He doesn’t tell you how to get there. This isn’t a theory that five minutes later you would then take and apply to nuclear strategizing at the RAND Corporation, or to predicting where the U.S. economy was going to be in five months. But it was the beginning, and it revolutionized economics, because it gave economists a useful way of talking about all competition and interaction, most of which takes place outside of markets.
Osserman: Nash’s theorem was an example of what mathematicians call an existence theorem; he proves that there is an equilibrium. It is not what is called a constructive theorem, which you could put on a computer to come up with the next equilibrium.
Nasar: But it created a foundation and a rock-solid conviction that you could go forward with models like this and use them. By the late 1970s, game-theoretic models, in which interdependent, strategic decision-making could be taken into account, swept economics. That’s why Nash got the Nobel.
Bayer: Not all triumphs are technological, virtuoso, or technique-oriented. Sometimes it’s an original point of view. The fact that it’s an existence result and not a constructive result might give insight into why people didn’t see it before him. He came into this with the mindset of other branches of mathematics and was going to look for existence proofs and constructive proofs on an equal basis.
Osserman: In the movie, a bunch of guys are trying to pick up a bunch of girls in a bar and are looking for the optimal strategy. Nash goes home to write up all this stuff, shows it to the professor, who looks at it and says, "Do you realize this overturns 150 years of economic theory?" Is there any truth to this? The way Nash describes it in his thesis, he’s generalizing the earlier work that had been done.
Nasar: Economists have had the price model – the Adam Smith model – to explain competition in markets. With non-cooperative games, the Nash equilibrium, economics has a second model to use to analyze competition outside of markets. The Adam Smith model is a subset of the more general Nash model.
Osserman: Was the code breaking in the movie real?
Bayer: It was real. We had long discussions about how to handle the code sequences. It’s a very visually fanciful scene. Akiva described it by saying that, in some sense, to suffer from schizophrenia is to pay overly acute attention to reality. Very high-functioning mathematicians who are nowhere near ill are also paying overly acute attention to reality, explaining to themselves, three times in a row, "Well, let’s see if the surface goes like this." It’s to switch from having that as a functional behavior to having that as a behavior over the edge. Codes were a beautiful vehicle that everyone could understand. Nash would go from real code breaking to imaginary code breaking as a way of being drawn off the map.
Nasar: Nash went from mathematics to numerology when he got sick. He was looking for patterns. He saw patterns and coincidences to which he attributed the same kind of meaning that he had earlier attributed to his insights about mathematics. He had been doing things like taking Rockefeller’s name and converting it into base 26 and then factoring it, thinking it would reveal secret connections. Almost the first sign that he was emerging from this illness in the 1980s was that he stopped doing that and started factoring very large numbers in pursuit of some real problems that he then got interested in.
Osserman: How is Nash’s son coping with the same illness? Is he too a genius?
Nasar: Nash’s son, who was diagnosed with schizophrenia at age 15, is mathematically gifted and actually was able to get a Ph.D. from Rutgers in mathematics. Had it not been for the illness, which was progressive, he would have had a fine career as a research mathematician. Is he a genius like his father? No. I don’t think anyone thinks that. The tragedy is that Johnny has now been sick for 25 years. He was never able to work. He lives with John and Alicia, who take care of him.
Osserman: Alicia Nash was studying physics when she met John. How did she earn a living while he was ill?
Nasar: She started working as an engineer at RCA and then became a programmer. She had gone to MIT with the fantasies so many young people did then – although not that many women – of the heroism of scientists, of becoming another Madame Curie. Instead, she married the rising star and she supported them by working as a programmer. She still works for New Jersey Transit in downtown Newark as a programmer and is the main source of support for her family.
Osserman: What were John Nash’s reactions to the book and the film?
Nasar: Ron Howard screened it for the Nashes around Thanksgiving. John said, "Ron Howard was in the room, and he had all these papers under his arm, and he kept saying, ‘I’ve really got some work. I can’t stay and watch this with you.’ But then, he never left. He watched us watching it." First of all, John loved the humor. Secondly, he loved the pace. John Nash is a real action movie kind of guy and he doesn’t like to sit still for drama. So he was very relieved that the pace of A Beautiful Mind was actually fast. The third thing he said was, "I think Russell Crowe looks a little bit like me."
Osserman: What was that math problem that Russell Crowe writes on the chalkboard in the classroom when Jennifer Connelly opens the window and asks the maintenance man to be quiet?
Bayer: I’ve heard so many friends and other mathematicians tell me that they thought they could solve the problem in Good Will Hunting while it was still on the board. Well, I couldn’t. I wanted them to play with the problems a little bit. I put myself in the character and thought, "What is it about multiple-variable calculus that gets near something of deep interest?" One aspect of topology is how to measure things when they have different shapes. There’s a fact in multiple variable calculus that’s nearly true, but not quite true; it fails if the space you’re working around is a strange shape. Georges de Rham noticed that if you viewed this defect as an attribute, you can actually use it as a tool to measure the shapes of spaces – this is de Rham cohomology.
The way I thought about it and the way the script turned out, John walks into this room, and he hasn’t been thinking about teaching this class at all, he’s just winging it. They asked to me write something that would be a hard problem to solve. I had Jennifer assume that the functions are rational functions and come up with one answer. Russell said, "Where on this page would I be looking to know right away that this wrong?" So I said, "Point here." He’s very technical. Then Jennifer asked me – these are my words, not hers – something to the effect of, "Are you making me look like a yahoo?" I said, "No, actually I tried it out on some colleagues and they fell for the trap. So you’re making a very high-level mistake." No one has ever explained it back to me yet like they got it.
Osserman: Aside from the essential story, do you find anything attractive about Nash’s personality?
Nasar: He has an almost childlike lack of guile, which is very charming. He also has an amazing lack of self-pity. I found on eBay a copy of the game he invented, which Parker Brothers had brought out in 1951 under the name of Hex. The day they got remarried, it was one of the presents I brought down to him. He was very taken by it, because the last time he had seen this game was in 1951. He said, "I had that game once, but I lost all of my possessions, including that game. That’s what happens when you’re mentally ill."
He also has a great sense of humor. We were at a cocktail party at the Institute for Advanced Study, and he was regaling Freeman Dyson with the box-office results. He said, "Well, I hope Universal is not keeping its books like Enron."
Osserman: One thing that impressed me when I read the book was your description of the behind-the-scenes discussions of the Nobel Prize committee.
Nasar: I went to Sweden to fill out the story of the Nobel. By interviewing many members of the Swedish Academy of Sciences, I discovered that the Nobel Prize to Nash had almost been voted down about an hour before it was supposed to be announced to the press. That was the time of the final vote by the members of the academy. There was a group of members who believed that if you had schizophrenia you could never recover, and that if you had schizophrenia, it so dehumanized you that "this is not the man who did the thing." Some extraordinary people on the Nobel Prize economics committee beat back that argument, and that’s why John Nash got his phone call from the executive secretary of the academy an hour and a half later.
Osserman: What’s your opinion about Nash’s claim that he willed himself to overcome his illness?
Nasar: What he’s talking about is something that everyone who has an illness like this and wants to reconnect with reality struggles with every day. When his symptoms began to die down, he was able to recognize which thoughts were delusional, and that the voices that he was hearing were in fact thoughts generated by his own mind. Because he did want to reconnect with reality, he was able to recognize and put aside, not act upon. It’s not that he willed it away. That’s not what his volition and personal struggle mean. What he wanted was incredibly important to where he is today. It’s not just medication or, in his case, the natural chemistry of aging. It’s also the person. That was one of things that make this story so meaningful to everyone who’s struggling with the illness.
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