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> Strictly speaking you don't even know whether space and time are not indefinitely divisible in our universe, there are good reasons to think so, but it is - a

by drdec 4y ago

> Strictly speaking you don't even know whether space and time are not indefinitely divisible in our universe, there are good reasons to think so, but it is - as far as I know - not a certainty. There are even good reasons to think that space does not exist in the same sense as temperature does not fundamentally exist and is something emerging from something more fundamental. Yes, I agree, our knowledge is imperfect and the truth may be different. > But whether or not our space and time are indefinitely divisible, just denying this assumption seems like the cheap way out for me, sidestepping the more fundamental issue that applies even if space and time are indefinitely divisible. Here we disagree. I think the whole point of the exercise from Zeno's point-of-view is to make you question your assumptions. > So let me offer you a different view that does not hinge on the divisibility of space and time. I didn't find your resolution very satisfying - it seemed to boil down to "motion is clearly possible by demonstration" and "you can't make an infinite list". Both of these things are part of Zeno's argument (the second in a different form). > And again, just walking to the goal will include any task that Xeno would ever have asked you to do When you get down to the quantum scale, is this still true? Does it even make sense to talk about a human moving a very small fraction of the width of an atom? > The list does not even have to be limited to countably many tasks as in the original paradox, it could contain uncountable many times, say the entire time between 11:11 and 11:12. Would it surprise you to learn that I think the universe is at most countable, if not finite?

danbruc 4y ago
Here we disagree. I think the whole point of the exercise from Zeno's point-of-view is to make you question your assumptions. Sure, but we also agree that it would be weird if it was impossible to move in Euclidean space, so I would say further questioning is warranted, what other assumptions are wrong that also resolve the paradox for Euclidean space. I didn't find your resolution very satisfying - it seemed to boil down to "motion is clearly possible by demonstration" and "you can't make an infinite list". Both of these things are part of Zeno's argument (the second in a different form). I would say the core of my argument is that Xeno essentially argues that you can not do an infinite number of things in finite time at that this is a wrong assumption. Look, I can not even finish telling you all the things you have to do, how could you possibly do them all? And as I said, just being in one place from 11:00 to 12:00 makes you do being at that place at all times between 11:00 to 12:00, independent of whether there are finitely many, countably many, or uncountably many instants in that interval. It is also noteworthy that doing something here is a pretty weak form of doing something, being at a place at some instant does not take any time at all or the smallest possible amount of time if time is not continuous. But similarly is moving infinitesimal distances in the original paradox a pretty weak form of doing something. But now that I think about it again, my argument can not replace your argument as I rely on the indefinit divisibility. So what I would really want to say is probably either space and time or not indefinitely divisibel, then Xeno can not make an infinite list of tasks to do, or space and time are indefinitely divisibel, but then it is also possible to do infinitely many tasks in finite time notwithstanding Xeno's inability to enumerate them. Would it surprise you to learn that I think the universe is at most countable, if not finite? Not really, I am also sympathetic towards ideas like loop quantum gravity. I also always liked - for no good reason - the idea of a closed universe but the observed flatness seems to point into a different direction. On the other hand someone pointed out to me some time ago that there are closed flat topologies, for example a torus, which I knew but never considered when thinking about the universe.

by drdec 4y ago

danbruc 4y ago

Here we disagree. I think the whole point of the exercise from Zeno's point-of-view is to make you question your assumptions. Sure, but we also agree that it would be weird if it was impossible to move in Euclidean space, so I would say further questioning is warranted, what other assumptions are wrong that also resolve the paradox for Euclidean space. I didn't find your resolution very satisfying - it seemed to boil down to "motion is clearly possible by demonstration" and "you can't make an infinite list". Both of these things are part of Zeno's argument (the second in a different form). I would say the core of my argument is that Xeno essentially argues that you can not do an infinite number of things in finite time at that this is a wrong assumption. Look, I can not even finish telling you all the things you have to do, how could you possibly do them all? And as I said, just being in one place from 11:00 to 12:00 makes you do being at that place at all times between 11:00 to 12:00, independent of whether there are finitely many, countably many, or uncountably many instants in that interval. It is also noteworthy that doing something here is a pretty weak form of doing something, being at a place at some instant does not take any time at all or the smallest possible amount of time if time is not continuous. But similarly is moving infinitesimal distances in the original paradox a pretty weak form of doing something. But now that I think about it again, my argument can not replace your argument as I rely on the indefinit divisibility. So what I would really want to say is probably either space and time or not indefinitely divisibel, then Xeno can not make an infinite list of tasks to do, or space and time are indefinitely divisibel, but then it is also possible to do infinitely many tasks in finite time notwithstanding Xeno's inability to enumerate them. Would it surprise you to learn that I think the universe is at most countable, if not finite? Not really, I am also sympathetic towards ideas like loop quantum gravity. I also always liked - for no good reason - the idea of a closed universe but the observed flatness seems to point into a different direction. On the other hand someone pointed out to me some time ago that there are closed flat topologies, for example a torus, which I knew but never considered when thinking about the universe.