Zero: The Biography of a Dangerous Idea

by Charles Seife

There were other schools of thought. The atomists, for example, believed that the universe is made up of little particles called atoms, which are indivisible and eternal. Motion, according to the atomists, was the movement of these little particles. Of course, for these atoms to move, there has to be empty space for them to move into. After all, these little atoms had to move around somehow; if there were no such thing as a vacuum, the atoms would be constantly pressed against one another. Everything would be stuck in one position for eternity, unable to move. Thus, the atomic theory required that the universe be filled with emptiness—an infinite void. The atomists embraced the concept of the infinite vacuum—infinity and zero wrapped into one. This was a shocking conclusion, but the indivisible kernels of matter in atomic theory got around the problem of Zeno’s paradoxes. Because atoms are indivisible, there is a point beyond which things could not be divided. Zeno’s hair-splitting doesn’t go on ad infinitum. After a number of strides, Achilles would be taking tiny steps that can’t get any smaller; eventually he would have to hurdle an atom that the tortoise doesn’t. Achilles would finally catch up to the elusive turtle. Another philosophy vied with the atomic theory, and instead of posing such bizarre concepts as the infinite vacuum, it turned the universe into a cozy nutshell. There was no infinity, no void—just beautiful spheres that surrounded the earth, which was natu...