... are there actually only a finite number of ways matter can rearrange itself? Or are configuration spaces "actually" described by real (or complex) numbers (

... are there actually only a finite number of ways matter can rearrange itself? Or are configuration spaces "actually" described by real (or complex) numbers (whether for things like distances or angles, or for things like the probability that a prepared quantum state will collapse to a given outcome)? If real (or complex) numbers are "real", then doesn't the fact that configuration states for some perceptually available region are described by R^(huge number) mean that merely traveling around in R^3 space, one _shouldn't_ expect to see repeats?