“The Indefatigable Frog” July 1953

Professor Hardy, a mathematician, teaches his students about Zeno’s paradox through the story of a frog unable to reach the top of a well because he will always have half of the previous distance left to go. Professor Grote, a philosopher, disagrees with Hardy, believing that the frog will reach the top of the well. They rig up an experiment. A tube is closed at one end, which becomes hot. At the other end is a force field. The closer the frog gets to the force field, the smaller he becomes by half, thus doubling the distance he must travel to reach a photon beam that will shut off the force field. But during the experiment the frog becomes so small he seems to disappear. Grote enters the tube to investigate and Hardy locks him in, making him the frog of a new experiment. He, too, keeps getting smaller as the experiment progresses. Meanwhile, Hardy announces his victory to his students. Then a frog appears and a student says it validates his theory that the frog would become so small it would fall through the molecules of the tube, then regain its normal size in the absence of the force field. An angry full-sized Grote awaits Hardy outside. But he is most perturbed by the fact that the paradox remains unsolved. He suggests to Hardy that they come up with a new experiment that will work, and the story ends.