A Beautiful Mind

by Sylvia Nasar

  18

  Experiments RAND, Summer 1952

  ONE AFTERNOON during Nash’s second summer in Santa Monica, he and Harold N. Shapiro, another mathematician from RAND, were swimming in the surf off Santa Monica Beach just south of the pier.1 The ocean was fairly rough. Below the breakwater, Santa Monica Beach was a narrow and steep strip of sand with breakers that were usually six to ten feet high. It was a favorite of body surfers.

  Nash and Shapiro were far from shore when they were caught in a powerful current that swept them farther out. Both men were strong swimmers. Nash was “built like a Greek god,” Shapiro recalled, and he, too, was sturdy and muscular. But Shapiro remembers being dragged under the waves, briefly overpowered by the current, and very frightened. Nash seemed to be struggling as well. “It was hard work getting back to shore,” Shapiro said. When the two young men finally reached the beach, they threw themselves on the sand, exhausted and breathing heavily. Shapiro recalled lying there, thinking how lucky they were not to have drowned. To his amazement, however, Nash jumped to his feet after a moment or two and announced he was going back into the water. “I wonder if that was an accident,” Nash said in a calm and detached tone. “I think I’ll go back in and see.”

  At the beginning of that second summer, Nash had driven cross-country from Bluefield to Santa Monica in a rusty old Dodge. He and John Milnor, who was by now a graduate student at Princeton, made the trip together, though Milnor drove his own car.2 Traveling with them were Nash’s younger sister Martha and Ruth Hincks, a journalism major at the University of North Carolina in Chapel Hill, who joined them at the last minute.3 They met in Chapel Hill, then drove on to Bluefield. Hincks remembers being warned not to let slip that Martha would be sharing the apartment with Milnor as well as Nash. She recalled in 1997 that this secretiveness struck her as strange. As they started out, Ruth drove with Nash, Martha with Milnor. Ruth was struck by Nash’s complete indifference to her. “I was slim, attractive, intelligent,” she recalled in 1997. Nash “never even noticed that I was there,” she said. She was also struck by the seemingly distant relationship between Nash and Milnor. “They just sort of stood around. They could have met the day before. They never referred to shared experiences. They didn’t seem to really know each other.” Even the relationship between brother and sister seemed “a little standoffish, not affectionate at all,” said Ruth. “I don’t think I saw any affection from anybody on that trip.”

  They traveled on U.S. 40, which took them through Kansas and Nebraska.4 They stopped once for a day in Grand Lakes, Colorado, where they all went horseback riding, and also in Salt Lake City, where they visited the Mormon Temple. The men put the young women in charge of divvying up all the motel, restaurant, and gas bills. All should have been fine for these young people, privileged as few were, in 1952, to be traveling cross-country on their own. Yet before the trip was over, Nash and Ruth had quarreled, and Martha, who had been riding with Milnor, was forced, reluctantly, to ride with her older brother for the remainder of the journey.5

  It started as a fine adventure. Martha had just graduated from Chapel Hill, and had traveled very little before.6 Tall and striking like her brother, Martha was extremely intelligent. In spite of a fierce determination not to be regarded as an egghead and an oddball, Martha had won a Pepsi-Cola scholarship by beating every boy at Beaver High on the SATs and had received invitations to apply to Radcliffe, Smith, and other top women’s schools. Her father, however, had turned down the scholarship on her behalf, saying that the family could afford tuition at a nearby school, and Martha wound up at St. Mary’s, a junior college attended mostly by well-to-do southern girls who brought fur coats with them, rode horses, and were themselves being groomed not for the job but for the marriage market. After graduating from St. Mary’s, she went on to the University of North Carolina, where she completed a teaching degree.

  John had persuaded his parents that it would be good for Martha to spend a summer in Santa Monica, suggesting that he could get more work done if Martha kept house for him.7 Martha, who had never been away from home except at college, was eager to go. Once the plans were made, John also made no secret of his hope that his sister and John Milnor would take an interest in each other.

  It was Nash who had proposed that they all travel together. Milnor and Nash, of course, had known each other since Milnor was a freshman at Princeton four years earlier. Though he had not yet completed his dissertation, Milnor had already been asked by Princeton to join its faculty. Nash confessed to Martha that he was jealous of Milnor’s abilities, but he was clearly also charmed by Milnor’s self-effacing personality, his brilliantly lucid mind, and the younger man’s lanky good looks.

  Ruth said her good-byes as soon as the quartet arrived in Santa Monica. Martha, Nash, and Milnor rented a small furnished apartment at the top of a rambling Spanish-style villa on Georgina Avenue, a stately street in the old section of Santa Monica and ten minutes’ walk via Palisades Park from RAND.8 Nobody did much cooking or housekeeping. A guest who had been invited for lunch said: “The place hadn’t been cleaned — ever. There were dust balls and dirty dishes. After looking around — they obviously hadn’t prepared a meal — I decided to ask for eggs. John pushed the remnants of a previously fried egg aside in the frying pan. ’Very nice people,’ I thought to myself.”9 Martha got a job in a bakery. She hardly saw her two roommates, who seemed to spend most of their waking hours inside the RAND headquarters, Martha tried to visit their offices one day but was barred by the guards because she had no security clearance.10 She and Milnor went out to dinner once in the first week or two, but despite their many hours together in the car, Milnor was uneasy and painfully tongue-tied, and it became clear to Martha that no romance was in the offing.11

  The two men worked mostly on their own. Milnor wrote a lovely paper called “Games Against Nature.”12 Nash dabbled with games that could be played using a computer.13 He was, by this time, chiefly concerned with mathematical problems that arise in the study of fluid dynamics. A paper on war games was merely a half-hearted effort, designed to justify his employment at RAND and to be hastily drafted before he returned to Cambridge at the beginning of September.14

  But Nash and Milnor did collaborate on one project, an experiment on bargaining involving hired subjects, that was to become, unexpectedly, a much-cited classic.15 The experiment, designed with two researchers from the University of Michigan who were also at RAND for the summer, anticipated by several decades the now-thriving field of experimental economics.

  The RAND experiments grew more or less directly out of the habit of playing games that the mathematicians indulged in their spare time. Inventing new games and trying them out, always with the inventors as subjects, had been a popular pastime at Princeton. Many of the players had, like Nash, only recently outgrown boyhood passions for chemistry and electricity experiments. The idea of recording the play to see whether people played the way the theory predicted was already a bit of a tradition at RAND, inaugurated by the famous Prisoner’s Dilemma experiment. Martha was astonished to learn that the volunteers were earning fifty dollars a day “to play games.”16

  The experiment, which was conducted over a two-day period, was designed to test how well different theories of coalitions and bargaining held up when real people were making the decisions.17 Von Neumann and Morgenstern, with their interest in games with many players,- focused on coalitions, groups of people who act in unison. They argued that rational players would calculate the benefits of joining every possible coalition and choose the best one — that is, the one that was most advantageous to them — whether they were business executives intent on collusion or workers who wanted to join a union.

  Nash, Milnor, and the other researchers hired eight subjects, college students and housewives. They devised different games, mostly with four rotating players, one with as many as seven. The game mimicked the general, “n-person” game of von Neumann’s theory. Subjects were told they could win cash by forming
coalitions, and the specific amounts that would be awarded to each possible coalition. To be eligible to win, however, the coalition partners had to commit in advance to a given division of the winnings.

  According to Al Roth, a leading experimental economist, the experiment yielded two insights that proved highly influential.18 For one thing, it drew attention to information possessed by participants: If the same players play the game repeatedly, the authors concluded, players tend to “regard a run of plays as a single play of a more complicated game.” Second, like the Prisoner’s Dilemma experiment devised by Melvin Dresher and Merrill Flood in 1950, it showed that players’ decisions were often motivated by concerns about fairness. In particular, in situations in which neither player had a privileged position, players typically opted to “split the difference.”

  For the designers of the experiment, however, the results merely cast doubt on the predictive power of game theory and undermined whatever confidence they still had in the subject. Milnor was particularly disillusioned.19 Though he continued at RAND as a consultant for another decade, he lost interest in mathematical models of social interaction, concluding that they were not likely to evolve to a useful or intellectually satisfying stage in the foreseeable future. The strong assumptions of rationality on which both the work of von Neumann and Nash were constructed struck him as particularly fatal. After Nash won the Nobel Prize in 1994, Milnor wrote an essay on Nash’s mathematical work in which he essentially adopted the widespread view among pure mathematicians that Nash’s work on game theory was trivial compared with his subsequent work in pure mathematics. In the essay, Milnor writes:

  As with any theory which constructs a mathematical model for some real-life problem, we must ask how realistic the model is. Does it help us to understand the real world? Does it make predictions which can be tested? …

  First let us ask about the realism of the underlying model. The hypothesis is that all of the players are rational, that they understand the precise rules of the game, and that they have complete information about the objectives of all of the other players. Clearly, this is seldom completely true.

  One point which should particularly be noticed is the linearity hypothesis in Nash’s theorem. This is a direct application of the von Neumann-Morgenstern theory of numerical utility; the claim that it is possible to measure the relative desirability of different possible outcomes by a real-valued function which is linear with respect to probabilities… . My own belief is that this is quite reasonable as a normative theory, but that it may not be realistic as a descriptive theory.

  Evidently, Nash’s theory was not a finished answer to the problem of understanding competitive situations. In fact, it should be emphasized that no simple mathematical theory can provide a complete answer, since the psychology of the players and the mechanism of their interaction may be crucial to a more precise understanding.20

  Nevertheless, decades later, economists, differing with Milnor, came to regard this “failure” of an experiment as a very worthwhile one. Casual as the experiment was in one sense, it became a model for a new method of economic research, one that had never before been tried in the two hundred years since Adam Smith dreamed up the Invisible Hand. The feeling was that even if the experiments weren’t sophisticated enough to show how people’s brains work, watching the way people played games could draw researchers’ attention to elements of interaction — such as signaling or implicit threats — that couldn’t be derived axiomatically.21

  By the time the experiment was run the relationship between Nash and Milnor had become strained, and Milnor had moved out of the Georgina Avenue apartment.

  Milnor says now that Nash made a sexual overture toward him. “I was very naive and very homophobic,” said Milnor. “It wasn’t the kind of thing people talked about then.”22 But what Nash felt toward Milnor may have been something close to love. A dozen years later, in a letter to Milnor, Nash wrote: “Concerning love, I know a conjugation: amo, amas, amat, amamus, amatis, amant. Perhaps amas is also the imperative, love! Perhaps one must be very masculine to use the imperative.”23

  19

  Reds Spring 1953

  Now, the thing I think would interest the committee very greatly, if you could possibly explain to them … Doctor… how you can account for what would seem to be an abnormally large percentage of communists at MIT?

  —ROBERT L. KUNZIG, Counsel HUAC, April 22, 1953

  THE COLD WAR promised to be the sugar daddy of the MIT mathematics department, but McCarthy ism — which blamed the setbacks in that war on sinister conspiracies and domestic subversion — threatened to devour it.

  While Nash and his graduate student friends were shooting each other down and playing games in the mathematics common room, FBI investigators were fanning out around Cambridge, rifling through trash cans, placing individuals under surveillance, and questioning neighbors, colleagues, students, and even children.1 Their targets, as Nash and everyone else at MIT would learn in early 1953, included the chairman and the deputy chairman of the MIT mathematics department, as well as a tenured full professor of mathematics, Dirk Struik — all three one-time members, indeed, leading members, of the Cambridge cell of the Communist Party. All three were subpoenaed by the House Un-American Activities Committee.2 It was a state of siege and everyone in the mathematics department felt the threat.

  At the time, Nash was no doubt far more preoccupied with the draft — not to mention growing complications of his personal life — than with the possible repercussions for himself of the persecution of his benefactors. Nevertheless, the whole episode was a warning that the world he and other mathematicians inhabited was an extremely fragile one. A congressional committee could destroy your career, just as your draft board could send you halfway around the world.

  The whole thing had begun as a farce.3 McCarthy’s original list of communists, announced in February 1950, was studded with academics, including the father of Nash’s friend Lloyd Shapley, Harvard astronomy professor Harlow Shapley, whom McCarthy incorrectly identified to reporters as “Howard Shipley, astrologer.” But as the red hunt gathered momentum, the entire scientific community felt vulnerable. Princeton’s Solomon Lefschetz would be identified as a possible communist sympathizer by an investigative body.4 Within a year, Robert Oppenheimer, head of the Manhattan Project, one of the most revered scientists in America and the director of the Institute for Advanced Study, would be humiliated by the McCarthyites.

  When the subpoenas were issued, nobody knew how MIT would handle the matter. Other universities had responded with immediate firings and suspensions.5 “McCarthyism was a big threat to these schools,” Zipporah Levinson, Norman Levinson’s widow, recalled. “During the war the government had started pouring money into them. The threat was that the research money would dry up. It was a bread-and-butter issue.”6 Martin and Levinson were certain that they were about to lose their jobs and wind up blacklisted for good, like so many others. Levinson talked about becoming a plumber and specializing in the repair of furnaces. The investigators had their eye on the three Browder boys — sons of former Communist Party head Earl Browder, who had all studied or were studying mathematics at MIT and were scholarship recipients, as well.7

  “MIT was turned topsy-turvy,” Mrs. Levinson recalled. “The faculty debated and debated how to prove that MIT was patriotic. There was strong pressure to name names.”8 As it turned out, Karl Compton, the president of the university and an outspoken liberal who was a supporter of the Chinese revolution and a critic of Chiang Kai-shek, may have felt that he himself would soon be subpoenaed. He hired a white-shoe Boston law firm, Choate, Hall & Steward, to defend Martin, Levinson, and the others for a minimal fee.9 By April, when Martin and Levinson were forced to testify, The Tech was running daily stories and anti-McCarthy sentiment was running high on campus.10

  There is no evidence that the FBI ever questioned Nash or any other students or faculty in the department, or asked for depositions, in an effort to establish a
link between Levinson’s and Martin’s Communist Party membership and classified defense research — a link that probably never existed, given that both left the party soon after the end of the war. The graduate students and junior faculty in the department stood on the sidelines and watched lives and careers ruined and homes, even car insurance, lost. “By that time, young people had prospects, jobs, optimism,” Mrs. Levinson recalled. “The younger people — Nash’s group — didn’t want to be too friendly. They were scared. They distanced themselves.”11

  Martin and several others named their former associates. Norman Levinson refused to name anyone who had not been previously named. “Ted and Izzy Amadur hemmed and hawed. Norman knew that Ted Martin and Izzy would cooperate. They spilled all the names. Norman said he’d talk freely about the party but that he wouldn’t name names. The lawyer told Norman, no you don’t have to say any names. He’d cooperate, but he wouldn’t give any names.”12 Martin gave a pathetic, frightened performance. Levinson’s testimony, by contrast, demonstrated the qualities of intellect and character that made him such a force in the mathematics community. In a series of forceful and eloquent answers to direct questioning, he managed at one and the same time to defend the youthful idealism that led him into the party, attack the intellectual poverty of communism, and, implicitly, call into question the committee’s assumption that communism was a threat to the nation. He spoke out against the hounding of former party members and asked the committee to take a stand against the blacklisting of Browder’s oldest son, Felix, who had finished his Ph.D. and was unable to obtain an academic post.