Biologist and mathematician D’Arcy Thompson advanced a strange new idea in his 1917 book On Growth and Form: He found that if you draw the outline of an animal or plant on an ordinary Cartesian grid, and then you put the grid through some mathematical transformation (stretching it, for example, so that its squares become rhombuses), very often the resulting shape is that of a related real creature. What can that mean? Thompson doesn’t really say. He thought that the biologists of his day overemphasized evolution in explaining the form and structure of living things; he preferred to look for...