I really wanted to just throw this out there and wanted to see if anybody has 'solved' the problem. I'm sure some of you are content with the mathematical / calculus solution but here me out. For those not in the know, I will explain the paradox and you too can play along.

Zeno's paradoxes are generally two dimensional motion questions where (due to his interpretation of how motion works) one is shown to obviously not be able to move. The general gist goes as such. I will use a general movement example rather than Achilles and his arrow or a turtle:

- I need to walk towards a door. I am not at the door for the purpose of the example
- To get to the wall I need to walk 1/2 the distance, then 1/2 the remaining distance, and so on ad infinitum
- To summarise, in order for any finite motion to happen, infinite steps have to be traversed.

Now mathematics and simple logic tells us that this is resolved because the sum 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1, meaning that an infinite amount of infinisimal pieces amounts to a finite number. This is fine, but does not answer the question of how one can pass through infinite fractions of space, since one starts from 0 and infinity is not an attainable 'digit' gained by progressive increase of finite numbers.

Anyway I was discussing this with my friend the other day and he would refuse to give me an answer, so I eventually countered that "Well, considering that any distance smaller than a planck length is causally meaningless, one can argue that any distance can be summed up by a finite number of planck lengths, and thus can be traversed with ease". He agreed.

Do you? Or is there a more simple explanation?