Genius: The Life and Science of Richard Feynman

by James Gleick

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 41/4s, 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