Lalala Zeno's paradox question lawl

I really wanted to just throw this out there and wanted to see if anybody has 'solved' the problem. I'm sure some of you are content with the mathematical / calculus solution but here me out. For those not in the know, I will explain the paradox and you too can play along.

Zeno's paradoxes are generally two dimensional motion questions where (due to his interpretation of how motion works) one is shown to obviously not be able to move. The general gist goes as such. I will use a general movement example rather than Achilles and his arrow or a turtle:

- I need to walk towards a door. I am not at the door for the purpose of the example
- To get to the wall I need to walk 1/2 the distance, then 1/2 the remaining distance, and so on ad infinitum
- To summarise, in order for any finite motion to happen, infinite steps have to be traversed.

Now mathematics and simple logic tells us that this is resolved because the sum 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1, meaning that an infinite amount of infinisimal pieces amounts to a finite number. This is fine, but does not answer the question of how one can pass through infinite fractions of space, since one starts from 0 and infinity is not an attainable 'digit' gained by progressive increase of finite numbers.

Anyway I was discussing this with my friend the other day and he would refuse to give me an answer, so I eventually countered that "Well, considering that any distance smaller than a planck length is causally meaningless, one can argue that any distance can be summed up by a finite number of planck lengths, and thus can be traversed with ease". He agreed.

Do you? Or is there a more simple explanation?

It's summer, I don't like math, can we just say a wizard did it?

Hold on. Let me ask Tim Robbins and Meg Ryan.

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Originally Posted by Rengori

It's summer, I don't like math, can we just say a wizard did it?

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Gandalf versus Dumbledore. To the death. Which will win, the mighty morphin' power wizard (reference to Dumbledore's actor dying between movies 1and2) or the breakdancing wizard?

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Originally Posted by Pureghetto

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Originally Posted by Rengori

It's summer, I don't like math, can we just say a wizard did it?

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Gandalf versus Dumbledore. To the death. Which will win, the mighty morphin' power wizard (reference to Dumbledore's actor dying between movies 1and2) or the breakdancing wizard?

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I thought he died between 2and3.

EDIT: nvm, he died Oct 2002, and the second movie was released Nov 2002.

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Originally Posted by Pureghetto

Anyway I was discussing this with my friend the other day and he would refuse to give me an answer, so I eventually countered that "Well, considering that any distance smaller than a planck length is causally meaningless, one can argue that any distance can be summed up by a finite number of planck lengths, and thus can be traversed with ease". He agreed.

Do you? Or is there a more simple explanation?

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According to a senior mathematics/theoretical physics guy at my university, space becomes granular once you get down to a certain size, and distance ceases to be a real concept. Grains are either adjacent or not. How this affects the paradox I'm not sure, but it does suggest that sufficiently small steps would no longer actually move you anywhere, since you'd be unable to traverse the singular grain of space in question.

But taking a staightforward look at the problem... you'd never reach the destination, because you're only ever getting closer. No matter how close you are, the next step will only take you half the remaining distance. Sure an infinite number of steps would get you there, but an infinite number of steps - or any other kind of incremental motion - is impossible.

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- To get to the wall I need to walk 1/2 the distance, then 1/2 the remaining distance, and so on ad infinitum

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I'll have to disagree. To get to the wall, you don't need to walk 1/2 the distance. Just walk the whole distance and be done with it. If you walk half the distance, then you know how long the other half is.

Tim loves Meg so Tim dances with Meg. Why waste time taking half-steps when he knows how far he needs to go to dance!? :p

This is calculus. If you use infanite series and limits, you will get to the door. Or you would just get bored and jump over to the door after a while.

This never made sense to me but I also hate math. How can I be walking 1/2 the distance if I made it to the door all the way?

I just thought it was a logical fallacy and kind of retarded. You can philosophize all you want, but some things just don't work the way we can reason they will, and I've never had a problem with just saying something's wrong because it's wrong. :p

All I know is that when the cheese is running low, it becomes Zeno's Cheese, because nobody wants to use it up so it gets cut into incrementally smaller parts.

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Originally Posted by I'm my own MILF

All I know is that when the cheese is running low, it becomes Zeno's Cheese, because nobody wants to use it up so it gets cut into incrementally smaller parts.

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It's like that whenever I'm sharing pie, cheesecake or ice cream with friends. The last slice keeps getting sub-divided, no-one wants to take the final piece. Until it gets stupidly small, and someone finally does the deed and finishes it off.

It's an example of mathematics and their virtual nonexistence in the three- (or four-, depending on if you count time) dimensional reality we occupy. They're a human created quantifier, and our system can't always be applied to the real world. Unless you want to invoke calculus, then it all becomes nice and harmonious.

The problem is that while calculus or arithmetic tells you that you can traverse infinite fractions of a whole distance, it doesn't tell you how a finite entity can traverse infinite fractions of a whole distance (1+1+1+...+1+1etc != infinity)

Big D seemed to start to make sense then he said it was impossible. Clearly it's possible as I keep moving around every day.

Well then is the passage of time not also "impossible"? If one is going to try and measure the passage of one second, numerically, eventually they would see that .9 seconds have elapsed. And after that, .99 seconds. And still after that, .999 seconds. With this logic, 1 second is an impossible goal. But time does flow, whether or not it seems impossible. Just like any human being can start at point A and reach point B without the universe exploding due to the paradoxical nature of it. Which is why you can't place our numerical restrictions on the physical world in every case. So I don't see an answer to your question unless you're willing to use calculus, which is another human tool to make the concept of infinity more applicable to reality. In the time case, if you're willing to use calculus, the passage becomes the sum of 9/(10^x), starting at 1 and going to infinity, and as with the whole .99999...=1 mess, the series converges at infinity and the passage of a second makes sense.

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Originally Posted by I Took the Red Pill

Well then is the passage of time not also "impossible"? If one is going to try and measure the passage of one second, numerically, eventually they would see that .9 seconds have elapsed. And after that, .99 seconds. And still after that, .999 seconds. With this logic, 1 second is an impossible goal. But time does flow, whether or not it seems impossible. Just like any human being can start at point A and reach point B without the universe exploding due to the paradoxical nature of it. Which is why you can't place our numerical restrictions on the physical world in every case. So I don't see an answer to your question unless you're willing to use calculus, which is another human tool to make the concept of infinity more applicable to reality. In the time case, if you're willing to use calculus, the passage becomes the sum of 9/(10^x), starting at 1 and going to infinity, and as with the whole .99999...=1 mess, the series converges at infinity and the passage of a second makes sense.

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Planck time - Wikipedia, the free encyclopedia

Ah, that Max Planck dude solved it all.

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Originally Posted by I Took the Red Pill

Well then is the passage of time not also "impossible"? If one is going to try and measure the passage of one second, numerically, eventually they would see that .9 seconds have elapsed. And after that, .99 seconds. And still after that, .999 seconds. With this logic, 1 second is an impossible goal. But time does flow, whether or not it seems impossible. Just like any human being can start at point A and reach point B without the universe exploding due to the paradoxical nature of it. Which is why you can't place our numerical restrictions on the physical world in every case. So I don't see an answer to your question unless you're willing to use calculus, which is another human tool to make the concept of infinity more applicable to reality. In the time case, if you're willing to use calculus, the passage becomes the sum of 9/(10^x), starting at 1 and going to infinity, and as with the whole .99999...=1 mess, the series converges at infinity and the passage of a second makes sense.

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*Brain Implodes*

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Originally Posted by I Took the Red Pill

Well then is the passage of time not also "impossible"? If one is going to try and measure the passage of one second, numerically, eventually they would see that .9 seconds have elapsed. And after that, .99 seconds. And still after that, .999 seconds. With this logic, 1 second is an impossible goal. But time does flow, whether or not it seems impossible. Just like any human being can start at point A and reach point B without the universe exploding due to the paradoxical nature of it. Which is why you can't place our numerical restrictions on the physical world in every case. So I don't see an answer to your question unless you're willing to use calculus, which is another human tool to make the concept of infinity more applicable to reality. In the time case, if you're willing to use calculus, the passage becomes the sum of 9/(10^x), starting at 1 and going to infinity, and as with the whole .99999...=1 mess, the series converges at infinity and the passage of a second makes sense.

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Absolutely, but in this hypothetical scenario it's a little different. The distance traveled with each step is smaller than the last; while you keep getting closer to the goal, you never travel far enough to reach it. Realistically, this is impossible to implement; the remaining distance to the goal soon becomes too small to measure, and too small actually to matter.

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Originally Posted by oddler

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- To get to the wall I need to walk 1/2 the distance, then 1/2 the remaining distance, and so on ad infinitum

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I'll have to disagree. To get to the wall, you don't need to walk 1/2 the distance. Just walk the whole distance and be done with it. If you walk half the distance, then you know how long the other half is.

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Like that, basically.

Or... wait. Have I totally misunderstood the question here?
All along, I've been assuming this is a theoretical situation whereby a person chooses to cover only half of the remaining distance, reducing how far is travelled in each increment.
Have I got this part wrong? Is the paradox actually saying that 'since every movement is comprised of infinite increments, it is theoretically impossible to traverse the entire distance'?
Because if so, then that fails at a fundamental level in the real world. Just because something can be expressed in terms of infinity, doesn't make it subject to the rule that 'the infinite can never be achieved'.

Spoiler: Perception may be warping what is actually happening.

It's not like you are ever going to get a non distance when dividing by half. So, eventually you will get there.

Now, our perception may just be speeding up the process.

D:?

Just about everyone who reads the paradox assumes that the person would take the same amount of time to cover the 1/8 and 1/4 distances that he took to cross the 1/2 distance.
Zeno never said anything of the sort.
Each shorter length of distance takes a shorter length of time to traverse so there would be no slowdown.

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Originally Posted by sockmonkey

Just about everyone who reads the paradox assumes that the person would take the same amount of time to cover the 1/8 and 1/4 distances that he took to cross the 1/2 distance.
Zeno never said anything of the sort.
Each shorter length of distance takes a shorter length of time to traverse so there would be no slowdown.

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Right but there's still infinite slices, and infinite of anything is impossible to achieve using finite increments. Hence the only solution I can come up with involves Planck measurements.

Thinking about planck measurements as the smallest possible distance gives the impression that the universe is made of really small 3d pixels

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Originally Posted by blackmage_nuke

Thinking about planck measurements as the smallest possible distance gives the impression that the universe is made of really small 3d pixels

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**4D pixels, but yeah lol, I suppose so.