This Stumped Philosophers For Millennia 

Nice video, but why haven't you talked about the fourth paradox of Zeno - "The Stadium Paradox"?

Or the archimedian principle: For x < y, there is natural n such that nx > y. That induces a real interval covering. And it works, at least in analysis.

"takes minimum coverage of two distinct points to move. Otherwise how would you know with one?" Least i like to think about it.

Magic word - Planck distance

@@vsyovklyucheno Planck distance isn’t what is often popularly thought about it. It isn’t a smallest step like a distance of one cell in Conway’s Game of Life or other cellular automata. It’s just a scale at which we shouldn’t try to apply general relativity or quantum field theory, because they clash quite horribly here. In other cases, we can use approximations to get what we want, but on a Planck scale (which includes all Planck quantities) we can pretty much just wave our hands. We can do more if we suppose a more universal theory is true, like string theory. Then we just use insights from that theory to fill the paradoxical gaps in naively quantized GR. I like to think about the motion paradox in terms of an example from quantum mechanics (probably QFT too, but I’m not good with it at all). In QM, the state of the physical system already contains information about its position “distribution” (just apply the position operator) and its momentum “distribution” (apply the momentum operator) and moreover its evolution in the neighborhood of the current time instant is dictated by the state too: apply the hamiltonial operator to see the “velocity”. (Also one can reasonably do away with all those quotes.) In classical mechanics it’s often needed to have two different kinds of spaces: configuration space (for a moving ball that’s just its positions) and phase space (add velocities) and the dynamics are dictated by a state from a phase space. This doesn’t resolve the paradox as is but it says: no, there is difference which you evidence with this paradox that just a position isn’t enough. But when we encounter a framework like QM, we see sometimes we can have come with the phase space from the start! (Of course QM isn’t an “ultimate theory” (at least it’s superseded by QFT) but I don’t think one should wait for an ultimate theory for making sense of this paradox.)

The third paradox precisely exists to discredit the idea of velocity

Just to play the devil’s advocate here, but you cannot create such a sequence considering the time as a continuous variable in a set that is uncountably infinite. But this opens up the argument for taking infinitesimal steps along the time line, and given its density and continuity it is possible to have motion even with fixed frame points. Also this explains the half distance paradox, since although you’re taking an infinite amount of steps, you do them in an infinitesimal amount of time, just like you can take an infinite number of points and end up with a totally measurable line.

@@eu7059 Right, maybe we should modify the sequence to be something like this { 0, Sn -> 1 } where n is the most infinitesimal number in R+ (which excludes zero,) 1 is a representative and the final element in the sequence and -> represents all the numbers in the sequence that go from Sn to 1. Regardless of how the sequence is expressed though, I think my point still essentially stands.

my ans: 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256...=1 no paradox there and i am only 13 qed

Goofy Ahh nerd

@@SuperYoonHo Wow, very smart for your age! You have the potential to be on Harvard!

Well, both are technically not numbers that we attempt to assign arithmetic properties mainly just to see what happens. Sometimes we get cool and interesting properties that help us do math easier (sometimes we get x/0 or infinity-infinity)

Good luck to you! I hope you have great success.

The solution is that the motion has a minimum length - the Planck Length. This resolves the paradox because you actually cannot subdivide each distance infinitely.

@@elweewutroone I agree

i concur with this explanation.

No, he was right, this is starting at n = 0, but he is starting at n = 1, which will always result in a difference of 1 between the formulae.

He's applied the correct formula

I suggest the model very simply consists in representing motion as a series of fictitious stops. When you report the position of a moving object, like it's halfway along, or 1 km from its destination or start, or give a map reference, or whatever, then you're pretending it's stopped there. It's a very useful convention. When the distance is big enough and the motion slow enough, like a ship on the ocean or a star in the heavens, you can then use that information to make useful predictions. But you can also play tricks, as naughty old Zeno does, and argue you can't get anywhere because of all those stops. But reaching your friend is only miraculous if you take those "stops" along the way as the literal truth.

Intuitive calculus

I'd say it depends on where you are and how fast you're going, because the amount of time distortion you're experiencing changes. A second isn't always a second.

@@aguyontheinternet8436 are you entering to special relativity? If it is, i am saying on the same reference frame. If you also relate it with moments, again i say it is 1.

*Axiom of Frienship*

@@BriTheMathGuy I think you’ll find this leads to some contradictions though