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By Root 2336 0

from intellect to athleticism, but he could hold off the taint of sissiness by staying with the more practical side of the mental world, or so he thought. The practical man—that was how he saw himself. At Far Rockaway High School he came upon a series of mathematics primers with that magical phrase in the title—Arithmetic for the Practical Man; Algebra for the Practical Man—and he devoured them. He did not want to let himself be too “delicate,” and poetry, literature, drawing, and music were too delicate. Carpentry and machining were activities for real men.

For students whose competitive instincts could not be satisfied on the baseball field, New York’s high schools had the Interscholastic Algebra League: in other words, math team. In physics club Feynman and his friends studied the wave motions of light and the odd vortex phenomenon of smoke rings, and they re-created the already classic experiment of the California physicist Robert Millikan, using suspended oil drops to measure the charge of a single electron. But nothing gave Ritty the thrill of math team. Squads of five students from each school met in a classroom, the two teams sitting in a line, and a teacher would present a series of problems. These were designed with special cleverness. By agreement they could require no calculus—nothing more than standard algebra—yet the routines of algebra as taught in class would never suffice within the specified time. There was always some trick, or shortcut, without which the problem would just take too long. Or else there was no built-in shortcut; a student had to invent one that the designer had not foreseen.

According to the fashion of educators, students were often taught that using the proper methods mattered more than getting the correct answer. Here only the answer mattered. Students could fill the scratch pads with gibberish as long as they reached a solution and drew a circle around it. The mind had to learn indirection and flexibility. Head-on attacks were second best. Feynman lived for these competitions. Other boys were president and vice president, but Ritty was team captain, and the team always won. The team’s number-two student, sitting directly behind Feynman, would calculate furiously with his pencil, often beating the clock, and meanwhile he had a sensation that Feynman, in his peripheral vision, was not writing—never wrote, until the answer came to him. You are rowing a boat upstream. The river flows at three miles per hour; your speed against the current is four and one-quarter. You lose your hat on the water. Forty-five minutes later you realize it is missing and execute the instantaneous, acceleration-free about-face that such puzzles depend on. How long does it take to row back to your floating hat?

A simpler problem than most. Given a few minutes, the algebra is routine. But a student whose head starts filling with 3s and 4¼s, adding them or subtracting them, has already lost. This is a problem about reference frames. The river’s motion is irrelevant—as irrelevant as the earth’s motion through the solar system or the solar system’s motion through the galaxy. In fact all the velocities are just so much foliage. Ignore them, place your point of reference at the floating hat—think of yourself floating like the hat, the water motionless about you, the banks an irrelevant blur—now watch the boat, and you see at once, as Feynman did, that it will return in the same forty-five minutes it spent rowing away. For all the best competitors, the goal was a mental flash, achieved somewhere below consciousness. In these ideal instants one did not strain toward the answer so much as relax toward it. Often enough Feynman would get this unstudied insight while the problem was still being read out, and his opponents, before they could begin to compute, would see him ostentatiously write a single number and draw a circle around it. Then he would let out a loud sigh. In his senior year, when all the city’s public and private schools competed in the annual championship at New York University, Feynman placed first.

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