# Zeno's stadium paradox: If space is not continuous or discrete, what is it?

Zeno's paradoxes are paradoxical because they show that in a world of continuous time and space, there cannot be any motion, thus all motion that we see are some kind of illusion. His paradoxes then rely on the infinite divisibility of real numbers which would be identical to chopping up continuous space/time and coming to the conclusion that no task can ever be completed in any finite amount of time. The stadium paradox however shows that the idea of discrete space is problematic too, that discreteness of space which would solve the earlier paradoxes of Achilles and the tortoise, or the arrow paradox, cannot solve the stadium paradox.

The stadium paradox goes like this: Row A is occupying 3 quanta of space, while row B is moving right at maximum velocity, and row C is moving left at maximum velocity. In the time row B surpasses two quanta of space from A's perspective, row B also passes 4 quanta of space from C's perspective. If there is a discrete absolute space, this paradox is unsolvable. Relativity would solve this problem by contracting space at C from B's perspective and the same with A to a lesser degree. However, you cannot contract discrete space because that contradicts our assumption of discreteness, so space must be continuous in order to allow such a contraction. So to explain the general phenomenon that we observe, we must assume that space and consequently time are both discrete and continuous and the paradox remains.

What should one make out of this? Can this paradox be solved? If not, does it mean that there is no motion or dynamics in the world?