It happened to Archimedes in the bath. To Descartes it took place in bed while watching flies on his ceiling. And to Newton it occurred in an orchard, when he saw an apple fall. Each had a moment of insight. To Archimedes came a way to calculate density and volume; to Descartes, the idea of coordinate geometry; and to Newton, the law of universal gravity.

In our fables of science and discovery, the crucial role of insight is a cherished theme. To these epiphanies, we owe the concept of alternating electrical current, the discovery...