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Comment by tshaddox | Hacker News Reader

No one seems to be bold enough to actually go this far, so I’ll make the claim:

Zeno’s paradox is wrong because its key premise is wrong: there aren’t infinitely many time intervals or distances, or arbitrarily small time intervals or distances.

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That just raises a new paradox: how can you jump across those discrete distances without passing through the space between?

If space is discrete, then there is no space in between. If you shift a bit to the right or left, it does not pass through some in between space, it disappears in one position and appears in one next to it.

Similar to Richard Feynman’s famous answer to the question “why do I feel the force of a magnet from several inches away?” What counts as a satisfying answer depends on the person, but the general answer is “that’s how the physical world works.” This one doesn’t particularly feel like a “paradox.”

With my feet, usually.

Solvitur ambulando, as St. Augustine and/or Lewis Carroll would say.

I would say it is the other way around, it is totally feasible to traverse an infinite number of intervals in a fixed time. As I also responded to a different comment, just assume space is E³. Would you want to argue that you can not move or reach the goal under that assumption?

But if it's an infinite number of spatial intervals, then it's also an infinite number of temporal intervals, so you can't argue they cancel without quantifying how fast they grow.

Sure, but we know from the setup and I think it is fair to just assume a constant velocity which gives us this countably infinite sequence of distances and times, both getting shorter geometrically. And their partial sums have a finite limit. In essence you seem to be stuck because you have to complete an infinite number of tasks, but that is just the wrong measure, i.e. you must measure the time or distance, not the number of tasks in order to determine if you can complete all the tasks. Just walk from start to goal, there is no task in Xeno's infinite task list where he could say that you did not complete it. The problem is that Xeno can not give you the complete list of tasks if he tries to enumerate them one by one, not that you can not complete them all. Instead of enumerating them, he should just tell you to visit all places 2^-n for all natural n, you walk one meter and are done.

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