Suppose space and time are non-discrete. Do we have good reason to think that they form an uncountable continuum of the real-number sort? One might first speculate: Perhaps points in space have coordinates that are triples of rational numbers (in some coordinate system)? That would, however, make it impossible to rotate an object by 45 degrees: the coordinates after such a rotation would no longer be rational numbers. And that's implausible. But there are bigger countable sets than that of rational numbers that one might invoke that would get out of problems like that. So why suppose our space and time have the structure of the real numbers?