I think this idea works, and it’s consistent with the way the ‘paradox’ was presented. I just need to point out that movements aren’t performed in steps, the intermediate positions are also continuous, so there are undoubtedly infinite positions to map with undoubtedly infinite instants. To me, that’s the “true” solution.
As I see it, the only reason the paradox presents halving steps is because it’s the easiest way to demonstrate that there are infinitely many steps. It doesn’t bother to show that there’s uncountably infinite steps because countable is sufficient.
But as I said, your proof (or disproof?) works for the argument as it was presented, so it’s good!
I much prefer the physics approach: disproof by experiment! “Look at my gavel. According to your theory, it has infinitely many steps to go through before it reaches the pad, so it can never hit the pad.” *bang* “Motion denied.”
I don’t think Planck length is a “minimum distance step” the way you imply it is. IIRC it’s a theoretical minimum uncertainty range, or something like that. But honestly I’m not really in the know about this whole subfield so I could be wrong.
But if we take this as fact - there exists a minimum distance step - then that means there can only ever be finitely many intermediate steps and the paradox is resolved.
I think this idea works, and it’s consistent with the way the ‘paradox’ was presented. I just need to point out that movements aren’t performed in steps, the intermediate positions are also continuous, so there are undoubtedly infinite positions to map with undoubtedly infinite instants. To me, that’s the “true” solution.
As I see it, the only reason the paradox presents halving steps is because it’s the easiest way to demonstrate that there are infinitely many steps. It doesn’t bother to show that there’s uncountably infinite steps because countable is sufficient.
But as I said, your proof (or disproof?) works for the argument as it was presented, so it’s good!
I much prefer the physics approach: disproof by experiment! “Look at my gavel. According to your theory, it has infinitely many steps to go through before it reaches the pad, so it can never hit the pad.” *bang* “Motion denied.”
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I don’t think Planck length is a “minimum distance step” the way you imply it is. IIRC it’s a theoretical minimum uncertainty range, or something like that. But honestly I’m not really in the know about this whole subfield so I could be wrong.
But if we take this as fact - there exists a minimum distance step - then that means there can only ever be finitely many intermediate steps and the paradox is resolved.
Removed by mod
Well now you’re just making shit up :P
Removed by mod