Harassment? Once there’s physical contact isn’t it assault?
SEE that is the THING! IT COULD NEVER HAVE TOUCHED IF YOU WATCHED IT HAPPEN
I have to wonder what Zeno would have thought of calculus
So how did you manage to lift your hand up in front of the graph? Checkmate theists.
Calculus.
Don’t even need calculus. You move the hand 1/2 of the way in 1/2 of the total time. Then 1/4 of the way in 1/4th of the total time… They just forgot to think about how the intervals of time those steps take are proportional to the size of the step.
But the amount of time is never zero for any step, and there are infinite steps.
The amount of time does, however, approach zero, so calculus solves the problem.
Let’s put it this way: you move your hand 1m in 1s. Looking at it like Zeno, there are infinite space-steps that total in 1m moved. And there are infinite time-steps that total in 1s. If there is no problem in having infinite space-steps covering a finite distance, what’s the problem with having infinite time-steps covering a finite time?
It’s more fundamentally philosophic than calculus, that’s why I said it’s unnecessary. You don’t need to know you can sum infinite “infinitesimal” parts and get a finite quantity, or how to do it. It’s just a simple reasoning to see there’s no paradox (in the “it’s impossible” sense) at all.
Black magic. Fucking glad I never had to use it after college.
Did the hand arrive at a known destination at a known timestamp?
If so, the potentially infinite iterations between a and b are irrelevant, because the observer decides what scope matters.
Not that anyone cares but I just realized that this is not actually paradoxical and I can prove it mathematically! (I think) Bear with me since I’ve like just barely learned this stuff this week.
Proof Let S be the set of all steps needed to be taken. It can be written as S = {(distance to be traveled)(2-n): n in the Natural numbers}. Thus, S shares cardinality with the natural numbers and is countably infinite.
However, time is continuous. Thus, it has the cardinality of the continuum (real numbers) which means any time interval contains an uncountably infinite amount of moments. Let us denote an arbitrary time interval as T.
Because | T | > | S | there is no injection from T to S. Thus if each step has only 1 time value, there will be moments of time left over, and since the hand is not in two places at once we know each step must have its own time value, so this must be the case.
Therefore, when moving in steps like this, one will run out of infinite steps before they run out of moments in time to complete those steps. Hence, any finite distance can be traversed in this way over some bounded interval of time. QED.
Basically, you can traverse any distance in any time interval as long as physics allows you to move at a fast enough speed. Even if it doesn’t, there may be a limit to how fast you can traverse the distance, but it is still bounded. You can traverse any finite distance like this before existence runs out of time.
(I’m still learning. So if there’s an error in my proof please be gentle lol)
I haven’t read the actual proof you wrote, but I think the paradox was shown to, well, not be a paradox multiple times in history. It was thought of long ago, when our understanding of mathematics and physics was more limited, and we didn’t have the tools to prove the flaws exist.
It’s pretty cool that a problem created so long ago can still be relevant, and that random people find it interesting enough to solve in Lemmy comments though! Keep learning and rock on!
I thought it was first halfway proved. And then an extra 1/4th proved. And then an additional 1/8th proved. And then the proof went an extra 1/16th. So if you can wait an infinite time, it will be proved.
Geometric series disagrees.
Bloody Ephebians. Shooting at tortoises.
She’s not my type.
