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I said: >> Yes, one way to resolve the paradox is to allow time to be infinitely divisible like (Euclidean) space. Then you can describe where something is at

by drdec 4y ago

I said: >> Yes, one way to resolve the paradox is to allow time to be infinitely divisible like (Euclidean) space. Then you can describe where something is at any point in time. Then you said: > So I ask, are you willing to argue that if our spacetime was Euclidean, then we could not move? I'm sure how to move forward from there and I am not interested in discussing Zeno's paradox relative to Euclidean space and Newtonian mechanics about which we seem to be in violent agreement.

danbruc 4y ago
On the one hand you say, the reason we can move is that our space and time are not indefinitely divisible, on the other hand you say even in a hypothetical universe with indefinitely divisible space and time motion can exist.
- drdec 4y ago
  I'm saying my problem with Zeno's argument in setting up the paradox is assuming that spacetime is infinitely divisible. That doesn't mean that's the "reason we can move", it means that's why the argument is flawed. Now Euclidean space with Newtonian motion is a mathematical construction. It has infinitely divisible space and time. That allows for the resolution of Zeno's paradox. It was constructed to describe motion so this is not a surprise and not really interesting. The difference is that spacetime, aka reality[1], does not allow for space to be infinitely divided. So you can't apply Zeno's argument (which was his point). In summary, Zeno's paradox is resolved by infinitely divisible time in Newtonian mechanics. You can't apply Zeno's argument to spacetime, because his assumptions are not satisfied. (Hopefully no autocorrect issues, moved to my phone.) [1] Of course I am actually taking about our best models of reality, relatively and QM, which are works in progress and not even consistent. So I could be all wet in one hundred years.
  - danbruc 4y ago
    1. Zeno makes some assumptions and proves from them that it is impossible to move. 2. A quick experiment proves that you can move around anyway. 3. Therefore Zeno's reasoning must be wrong, either he assumed something false or his reasoning itself is flawed. 4. You say, Xeno's reasoning is fine, in the setting he describes it is indeed impossible to move, but Xeno has an unstated assumption - that space and time are indefinitely divisible - but in our universe, because our spacetime is not indefinitely divisible, Xeno's reasoning - which is fine if all assumptions are satisfied - just does not apply. This is where the paradox falls apart for me. There's no reason to assume that there is always a halfway there. 5. All assumptions of Xeno's reasoning are satisfied in a hypothetical universe with Euclidean space - and classical mechanics is some sense represents such universe - and because Xeno's reasoning is fine in principle if all the assumptions are satisfied and the hypothetical universe satisfies by assumption, Xeno's reasoning applies in the hypothetical universe and therefore you can not move in the hypothetical universe.

by drdec 4y ago

danbruc 4y ago

On the one hand you say, the reason we can move is that our space and time are not indefinitely divisible, on the other hand you say even in a hypothetical universe with indefinitely divisible space and time motion can exist.

drdec 4y ago
I'm saying my problem with Zeno's argument in setting up the paradox is assuming that spacetime is infinitely divisible. That doesn't mean that's the "reason we can move", it means that's why the argument is flawed. Now Euclidean space with Newtonian motion is a mathematical construction. It has infinitely divisible space and time. That allows for the resolution of Zeno's paradox. It was constructed to describe motion so this is not a surprise and not really interesting. The difference is that spacetime, aka reality[1], does not allow for space to be infinitely divided. So you can't apply Zeno's argument (which was his point). In summary, Zeno's paradox is resolved by infinitely divisible time in Newtonian mechanics. You can't apply Zeno's argument to spacetime, because his assumptions are not satisfied. (Hopefully no autocorrect issues, moved to my phone.) [1] Of course I am actually taking about our best models of reality, relatively and QM, which are works in progress and not even consistent. So I could be all wet in one hundred years.
- danbruc 4y ago
  1. Zeno makes some assumptions and proves from them that it is impossible to move. 2. A quick experiment proves that you can move around anyway. 3. Therefore Zeno's reasoning must be wrong, either he assumed something false or his reasoning itself is flawed. 4. You say, Xeno's reasoning is fine, in the setting he describes it is indeed impossible to move, but Xeno has an unstated assumption - that space and time are indefinitely divisible - but in our universe, because our spacetime is not indefinitely divisible, Xeno's reasoning - which is fine if all assumptions are satisfied - just does not apply. This is where the paradox falls apart for me. There's no reason to assume that there is always a halfway there. 5. All assumptions of Xeno's reasoning are satisfied in a hypothetical universe with Euclidean space - and classical mechanics is some sense represents such universe - and because Xeno's reasoning is fine in principle if all the assumptions are satisfied and the hypothetical universe satisfies by assumption, Xeno's reasoning applies in the hypothetical universe and therefore you can not move in the hypothetical universe.