It's the thing where you're supposed to wonder how motion is possible if space or time can be endlessly divided: after all, how can you move through an infinite amount of slices of space to move a meter, or through infinite moments in time which all have you motionless?What do you make of Zeno's paradoxes? I don't like the explanation where asymptotically approaching a limit is somehow supposed to make anything believable. After all, the really distressing idea seems to be the potentially INFINITE amount of steps.However, it makes sense to me when I consider that reality isn't slices of distance or moments in time, but both of them interwoven in change itself. The more you divide the physical distance, the more you multiply the speed through each individual slice, so that the elapsed time always remains. Space and time interwoven is the constraint, and not misguided abstraction demanding reality itself to conform.
>I don't like k
>>17007471Time is maintained inside out while distance is maintained outside in
>>17007491Trying to move through infinite slices of distance makes no sense if elapsed time isn't there to maintain the big picture. A limit can never be reached, which is why it's a limit.
>>17007471>>17007497plank length unc
>>17007497The relevant concept is a supertask. A bouncing ball, losing half of its energy each bounce, bounces half as high each bounce, bounces for 1/2 the time of the last bounce, and therefore bounces an infinite number of times within a finite interval.>which is why it's a limitYou're making the usual mistake of treating infinity as a verb rather than a noun. Specifically, you're not seeing that the time to reach the next node halves as you reach the limit. Zeno didn't see this it seems.
>>17007471>>17007497>>17007540We do not have a lot of Zeno or Parmenides to work with, and what we do have is second hand (and from those least likely to understand them), but it is my opinion that they were not taking themselves seriously with the paradoxes, and were trying to show that narrative positions mattered in all things.So they would purposely paradox (change the narrator in the middle of making the story) so that the story would seem stupid, in order to show that those that were arguing from a materialist point of view shouldn’t be so sure of their narrative frames. And, as it turns out, the history of science vindicates them. Therefore, you shouldn’t get too involved in their arguments, and certainly should not bring the ideas of limits or of differential calculus into the discussion. They were simply changing the narrator as the story progressed.For example, they would start of with the narrator being someone watching the arrow fly through the air towards a target being Zeno himself in time AND space. They would put a limit on the story as the distance from the bow to the target, removing time from the equation and dealing only with space. But then they would switch to the point of view of the arrow going half that distance, then half again, then half again and so on to show that the arrow could not possibly make it to the target. Then they would make the statement that Zeno could not be shot with an arrow.Now this would be true assuming the arrow landed at Zeno’s feet, but that is not the story they started with.
(cont from) >>17007543Or they would have a race with Achilles and a Tortoise. They start off looking at the entire race as a spectator would. They give the Tortoise a head starts so the Tortoise is ahead of Achilles. Then they would change the narrator from the spectator to Achilles that is catching up to the Tortoise with a set distance between them, BUT THEN switch to the narrator of the Tortoise moving forward changing that distance, BUT THEN switch back to Achilles having to catch up to the new distance, BUT THEN switch back again to the Tortoise moving forward,… They would then make the conclusion that Achilles could NEVER cover the distance, because the Tortoise is always adding to it; Therefore Achilles would always be behind the Tortoise! NOTICE how they also changed to distance only, omitting time. But this makes no sense from the point of view of the spectator of the race, who is still in space AND time. So don’t get too drawn into slices or limits or Planck length! . That is not what they were trying to do.
