Zeno is still my favorite. To summarize in modern terms: in order for a particle to move 1 inch, it must first move 1/2 inch. Before it can move 1/2 inch, it must move 1/4 inch. Before it can move 1/4 inch, it must move 1/8 inch. And so on. The paradox is, if a particle has to traverse an infinite number of infinitely small spaces before it can move even one inch, how is it possible that it can move at all?
Some mathematicians pull out calculus to "disprove" the paradox, but to me it disproves nothing. For example, you can show, mathematically, that sum( 1/(2^N) ) = 1 as N goes from 1 to infinity. The problem is that you have to go to infinity before it will sum to 1. If space is infinitely divisible and a particle has to traverse an infinite number of subspaces in order to move just a nanometer, I still don't see how it's possible that it could move at all.
Some mathematicians pull out calculus to "disprove" the paradox, but to me it disproves nothing. For example, you can show, mathematically, that sum( 1/(2^N) ) = 1 as N goes from 1 to infinity. The problem is that you have to go to infinity before it will sum to 1. If space is infinitely divisible and a particle has to traverse an infinite number of subspaces in order to move just a nanometer, I still don't see how it's possible that it could move at all.