Nash returns to RAND for another summer of research in 1952. One afternoon, he and Harold Shapiro, another RAND mathematician, are swimming at Santa Monica Beach when they are swept under by a powerful current. The two men struggle back to shore, and Shapiro feels relieved that they fought their way out of the current; Nash, though, decides to go back into the water, saying, “I wonder if that was an accident […] I think I’ll go back in and see.”
1952 is a turning point for Nash. He begins to exhibit stranger, more erratic behavior, and he often seems to lose his grasp on reality, as evidenced by this incident with Harold Shapiro: Nash seems strangely unaware of the danger of wading back into the ocean.
Nash is living in Santa Monica with his younger sister Martha; her college friend, Ruth Hincks, a journalism student at the University of North Carolina; and John Milnor, a brilliant math student Nash knew at Princeton, where Milnor was an undergraduate student. Hincks later recalled that the journey the four of them made out to California from Bluefield was “strange,” noting the seemingly “distant” relationship between Nash, Milnor, and Martha. Nash persuades his parents to let Martha live with him in Santa Monica for a summer, since she has never been away from home except to go to college: secretly, though, Nash wishes to set Martha up with Milnor, though he is also “charmed” by Milnor—who has a “self-effacing personality,” “a brilliantly lucid mind,” and “lanky good looks”—himself. Later, Milnor would claim that Nash made a “sexual overture” toward him, and that their friendship fell apart shortly thereafter.
Though Nash plots to set up Milnor and Hincks, this matchmaking scheme seems to serve only as a cover-up for his own feelings for Milnor. Nash is beginning to find it difficult to disguise his attraction to other men, and these feelings seem to torment him, given his attempts to cover them up. Unfortunately, Nash’s flirtatious behavior with Milnor causes an irreversible rift in their relationship—which may have made Nash even more uncomfortable with his own feelings.
Martha and Milnor do not connect romantically in Santa Monica, but Nash and Milnor collaborate on a project for RAND, testing out theories of coalition and bargaining. Nash, Milnor, and other researchers recruit subjects to play different games with cash rewards. Though Milnor later became disillusioned with game theory—since the results of the experiment “cast doubt” on the usefulness of game theory in predicting real-life outcomes—Nash and Milnor’s research would serve a model for a new kind of economic research, encouraging researchers to attend closely to “elements of interaction” between players in actual game scenarios, rather than focusing solely on theoretical research.
Milnor is disappointed with the results of his and Nash’s experiment, which seems to have negative implications for the usefulness of game theory. However, the experiment has merit: it demonstrates that creating actual game scenarios to test out different ideas can be a helpful way to study game theory. Though many of Nash’s experiments and research ideas were controversial, many ultimately proved beneficial to the field of mathematics.