A tribute to Lloyd Shapley, Nobel Laureate mathematician

Lloyd Shapley, Nobel Laureate, mathematician, an inventor of theory of games passed away recently.

Source: Chapter 11, Lloyd, Princeton 1950 — Sylvia Nasat in “A Beautiful Mind”

When Lloyd Shapley first moved into the Graduate College, a few doors down from Nash in the fall of 1949, Lloyd Shapley had just turned twenty-six, five years and eleven days older than Nash. No one could have presented a stronger contrast with the childish, boorish, handsome, and uninhibited boy wonder from West Virginia.

Born and bred in Cambridge, Massachusetts, Shapley was one of five children of one of the most famous and revered scientists in America, the Harvard astronomer, Harlow Shapley. The senior Shapley was a public figure known to every educated household, and also one of the most politically active. In 1950, he was accorded the dubious honour of being the first prominent scientists to appear on the earliest of Senator John McCarthy’s famous list of crypto-communists.

Lloyd Shapley was a war hero. He was drafted in 1943. He refused an offer to become an officer. That same year, as a sergeant of the Army Air Corps, in Sheng-Du, China, Shapley got a Bronze Star for breaking the Japanese weather code. In 1945, he went back to Harvard, where he had begun to study mathematics before he was drafted, and finished his BA in mathematics in 1948.

When Shapley showed up at Princeton, von Neumann already considered him the brightest young star in game theory research. Shapley had spent the year after graduating from Harvard at the RAND Corporation, a think tank in Santa Monica that was attempting to use game theory applications to solve military problems, and came to Princeton while technically on leave from RAND. He was immediately recognized as brilliant and quite sophisticated in his thinking. One contemporary remembers that he “talked good math, knew a lot.” He did extraordinarily hard double crostics from The NewYork Times without using a pencil. He was a fiercely competitive and highly accomplished player of Kriegspiel and Go. Everybody knew “that ‘his game was strictly his own,” said another fellow student. “He went out of his way to find nonstandard moves. No one was going to anticipate them.” He was also well read. He played the piano beautifully. His manner suggested an acute awareness of pedigree and prospects. When Lefschetz wrote a letter telling him of a very generous grant if he came to Princeton, for example, Shapley replied loftily and hint of disdain, “Dear Leftschtez, The arrangements are satisfactory. Go ahead with the formalities, Shapley.”

Shapley was by no means as self-confident as his imperious note to Lefschetz implied. His appearance can only be described as rather strange. Tall, dark and so thin that his clothing hung from him like a scarecrow’s, Shapley reminded one young woman of a giant insect, another contemporary said he looked like a horse. His normally gentle demeanour and ironic banter hid a violent temper and a harshly self-critical streak. When challenged in some unexpected fashion, he could become hysterical, literally vibrating and shaking with fury. His perfectionism, which would later prevent him from publishing a large portion of his research, was extreme. He was, moreover, acutely self-conscious about being a few years older than some of the brilliant young men around the Princeton mathematics department.

Nash was one of the first students Shapley met at the Graduate College. For a time, they shared a bathroom. Both of them attended Tucker’s game theory seminar every Thursday, now run by Kuhn and Gale while Tucker was at Stanford. The best way to describe the impression Nash made on Shapley when the two first talked about mathematics is to say that Nash took Shapley”s breath away. Shapley, could, of course, see what the others saw — the childishness, brattiness, obnoxiousness — but he saw a great deal more. He was dazzled by what he would later describe as Nash’s “keen, beautiful, logical mind.” Instead of being alienated by the younger’s man’s odd manner and weird behaviour, he interpreted these simply as signs of immaturity. “Nash was spiteful, a child with a social IQ of 12, but Lloyd did appreciate talent,” recalled Martin Shubik.

Shapley’s greatest eccentricity at the time was his claim that he was on a twenty-five hour sleep cycle. He worked and sleeped at extremely odd hours, often transposing day and night. “Every once in a while, he’d disappear from sight,” another student recalled. “That’s what he said. We accepted anything.” Waking Stanley up when he was lost to the world became an ongoing prank. “A group of us was attending a regular seminar at the institute given by de Rham and Kodaira. We were always very anxious to go but only three or four of us had cars. Lloyd Shapley was one, but there was one difficulty. Lloyd like to sleep late and was often asleep at two o’clock in the afternoon. So we had to devise all sorts of ways to wake him. We dropped hot candle wax on him. I devised another method. We played 45 rpm records of Lloyd’s favourite Chinese music without the little insert so that it oscillated all over the place (and made excruciating noise), Nash once tried to wake Shapley by climbing on his bed, straddling him and dropping wster in his ear with an eyedropper.

John McCarthy, one of the inventors of artificial intelligence, also befriended Shapley and apparently aroused Nash’s jealousy. One day McCarthy got an inquiry from a Philadelphia haberdashery about a massive shirt order he had placed. How good was his credit, the company wanted to know? McCarthy, who hadn’t placed any such order, immediately suspected Nash and asked Shapley if Nash was the culprit. Shapley confirmed that this was highly likely. McCarthy asked the company for the original order. Sure enough, a postcard came back with Nash’s unmistakable scrawl in green ink, the colour Nash always used. Shubik and McCarthy cornered Nash and confronted him. “There was no denying what he had done. We threatened him with postal inspectors. The post office refused to merely bawl him out. “If we do anything, we will prosecute him,” they said. Concluding that Nash had learned his lesson, Shubik and McCarthy dropped the matter. Another time, he rigged up McCarthy’s bed so that it would collapse when McCarthy tried to crawl under the covers.

It was Shapley, who reacted to Nash’s absurd behaviour with amused tolerance, who proposed that they might channel his mischievous impulses in a more intellectually constructive way. So, Nash, Shapley, Shubik, and McCarthy, along with another student named Mel Hausner, invented a game involving coalitions and double=-crosses. They called the game, So Long Sucker!. The game is played with a pile of different colored poker chips. Nash and others crafted a complicated set of rules, designed to force players to join forces with one another to advance, but ultimately to double-cross one another in order to win. The point of the game was to produce psychological mayhem, and, apparently, it often did. McCarthy, remembers losing his temper after Nash cold-bloodedly dumped him on the second-to-last round and Nash was absolutely astonished that McCarthy could get so emotional. “But, I didn’t need you anymore,” Nash kept saying, over and over.

By and large, Shapley tried to play the role of the mentor. He came to Nash’s aid, for example, when Tucker demanded that Nash include a concrete example of an equilibrium point in his thesis and Nash couldn’t think of a good one. Shapley spent weeks working out an elaborate but convincing example of Nash’s equilibrium concept involving three-handed poker, another Shapley speciality.


-Nalin Pithwa







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