Klimbatize wrote:

A vote for the IRC Revolution is a vote against JonSnow.

I gave them the ability to warp what have you done? (-10 votes for rules violation)

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Sold me.

Very tempted to say i was the buyer .

I hope you guys realize there is some legitimacy to the argument and it's not a closed case.

Here's the exact same problem. Suppose a ball is dropped from 10 feet in the air, and it always goes .9 of the height it fell from on the way back up.
Questions:
how many times will it bounce?
Will it stop bouncing?

According to calculus the sum of total distance traveled is finite, by the fact the sum of the distance is a geometric sum with r=.9 < 1. So it converges. The ball is traveling a constant acceleration, so a object moving at a constant acceleration over a finite distance will eventually pass that distance. Therefore according to calculus not only will the ball stop bouncing, but it will stop after a finite amount of time.

However simultanously, the ball will bounce an infinite number of times. So Zeno's like well if we let this case happen we arise at the situation that for every bounce there is one more bounce, but there is a last bounce. He argues this is a contradiction, so he says the above case is impossible, and the reason it's impossible is because of motion, so he comes to the conclusion continuous motion cannot happen.

The difference you're striking is putting it into the physical world, as opposed to this hypothetical world. In the world I created, it will always bounce 90% of the height it fell.

In the real world you are correct, these so called bounces will just be atomic vibration which will reach equilibrium with the surrounding atoms, the air, the earth etc... it won't cease vibrating but cease decreasing in energy level. Specifically it won't keep having a reduction eventually it's energy will be approaching less than/equal to the energy being put back into it by the surrounding atoms so it will plateau.

It's kind of like a super hot glass of water will get cooler if you leave it out, but it won't keep getting cooler indefinitely, it'll reach equilibrium, the same thing happens with these bounces, which eventually become vibration that reach an equilibrium vibration.

However we still can imagine the hypothetical situation, then attempt to see it's connection with continuous motion. I'll leave it at that, but this is a fun topic to think about.

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If each bounce retains 90% of the height from previous bounce, it WILL bounce infinite times. You will approach zero, but never reach it. You will, however, reach a point where the bounces become undetectable to the naked human eye.

Very true.. however by calculus they contend not only will it bounce an infinite number of times, but there will be a last bounce, and that last bounce will occur after a finite amount of time. Essentially you could sit there and watch an infinite number of bounces occur.

Zeno says this is impossible so comes to the conclusion motion is an illusion. (continous motion specifically, warping is possible still though)

Yes and no, there's real world ramifications. In this fantasy world, it doesn't have to be too different from our own world, we're just ignoring certain factors, just like sometimes in physics problems you have your weightless massless strings, and you exclude wind resistance. We're creating some ideal case so we can look at certain properties, mostly this is a commentary on continuous motion. The problem arises because of our assumption about the continuity of movement. If movement was discrete, like in video games, this problem wouldn't arise.

Basically if what you're saying wasn't stopping it from going .9*(the drop height) every time, suppose it just can, what would happen, and what conclusion can we draw. This situation is very parallel to the examples given in Syd's article. The tortoise and the hare, the football field example, etc...

There's a little more to it... Actually, in the fantasy world it does stop bouncing after it bounces an infinite number of times, which it does in a finite amount of time, hence Zeno's paradox. I'll just leave it at what i've said.

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Simply put: Zeno's paradox is only a paradox if you're a fucking retard who takes every one of those statements as fact despite being impossible in any sort of world that resembles ours closely enough to be of ANY importance.

Not really true at all, because none of those properties suddenly allow for continuous motion to work. What i mean is, sure in the bouncing ball scenario you can't always allow the ball to go .9*fall height, but the properties stopping it from doing so, have no bearing on the fact that continuous motion itself would make it paradoxical. Secondly, if you don't like the bouncing ball, you can just use the football field example.

Where for every segment a person travels there is one more segment to travel (like each bounce of the ball), and there will there be a last segment to travel (a last bounce), he will travel all infinite segments (infinite bounces will occur), in a finite amount of time. Note: (you can map each segment to a bounce)


Secondly not only does this seem impossible to perform an infinite number of tasks, (which if it's the case logically then it's the case that must be true, which is why Zeno said this world is an illusion), but also when you get down to it, and you go to the smallest units that make up all things in quantum physics, things are warping around.

I'll put it this way if you look up objections to Zeno's paradox, none of them are going to be bringing up what you're saying.

The properties you bring up stop the ball from doing what I'm saying is happening, but they don't give an answer to the ball's problem that arises due to continuous motion, they just prevent the scenario from happening in reality. Again if you don't like that scenario you can use the walking across the football field scenario.


To sum up Zeno's argument: As soon as you have continuous motion stuff like the ball example are hypothetically possible, Zeno argues that's a contradiction, ergo continuous motion can neither be hypothetically possible in ANY imaginable universe, and in particular not ours. He's arguing it creates a fundamental contradiction.

I will say this, I'm not totally convinced of Zeno's argument myself, but I want to present it and for it to be understood as it was supposed to be. He is bringing up a very intelligent point, Zeno was not by any means dumb. His thinking helped propel calculus, and changed philosophical views that still are impacted today. As much as i hate to say this, Zeno could very well be correct. I have a response I would offer but I'm not satisfied with my own response.