Struggles with the Continuum (Part 1)

Is spacetime really a continuum? That is, can points of spacetime really be described—at least locally—by lists of four real numbers ? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances?

Rather than trying to answer this hard question, let’s look back at the struggles with the continuum that mathematicians and physicists have had so far.

The worries go back at least to Zeno. Among other things, he argued that that an arrow can...