I don't get it

isnt this just an introduction to series and sums?

youtu.be/PCu_BNNI5x4

what is paradoxical about a fast thing catching a slow thing? are western maths and science such total shit that this is somehow viewed as a complex problem?

Zeno's paradox proves that math is incompatible with reality

Yes, everyone knows this. Why are you telling me something I already know?

If you have a 10cm long stick and you split it into infinite pieces, the pieces will still only be 10cm combined

How does that relates to anything at all

Brainlet.

"dude what if life was like a turn-based game with tiles and a minimum movement distance and then like, a turtle is really slow, but it still moves a minimum of one tile, and it always moves first, and then some really fast guy (Achilles???) can never reach it because he's always one turn behind lol, what does that tells us about the nature of the universe"

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this paradox implies the existence of "infinity" which is a purely theoretical concept that doesnt exist in nature

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>western math
outed yourself as a brainlet right there

Literally nothing about this is viewed as a complex problem, not since 300 years ago at least.
The paradox arises from the hidden assumption that if a process takes infinite number of steps to achieve, the process must take infinite amount of time. Yet this is clearly false - Achilles will outrun the tortoise at some point in the future. This is infinite series - an infinite sum of positive numbers can sum up to a finite number.
Brainlet. Learn some math.

No it fucking doesn't, learn to think.

This proves you’re a retard

numbers dont even exist bbro

not even natural numbers? I could see your point about the reals.

The paradox is that before getting anywhere, you have to move half the distance first. To move half the distance, you first half to move half of that distance.
It's saying that you have to move an infinite amount of distances to move any distance. But each of those distances are infinitely small. The paradox is insisting on the actual, real existence of infinity.
So what the person you responded to is saying is that even though you can mathematically describe a distance as an infinite amount of infinitely small distances, that has no consequence on reality. Infinity doesn't exist; it's not a real number.

>the Planck length
pseud detected

> are western maths and science such total shit that this is somehow viewed as a complex problem?
no retard, it was 2000 years ago though

point out a natural number to me right now brainlet
yeah thought so

Natural numbers (and other real numbers) are representations of reality.
Infinity doesn't exist in reality for numerous mathematical and logical reasons.

Why do you say that? Doesn't the existence of the Planck length ultimately make the universe discrete and therefore restore the moving lines paradox?

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the absolute state of Yea Forums

>yfw it was just conceived as a bait for the ages and it worked brilliantly

5 is a natural number, and if you pretend you don't know what it is, you're dumber than a monkey.
>infinity doesn't exist in reality
That statement is very vague. Infinity is a concept of there being more things than any finite number, and there are many examples of it - like the amount of prime numbers.

I'm OP and I find this convincing.
Am I still not getting it?

The paradox arises because you are bounding time. Obviously Achilles catches up after some time x, but the paradox shows how the distance traveled in time x can be thought of as being composed of infinite parts (as can the time x) . How then can the sum of this infinite series of distances equal a finite distance? We know that in truth an infinite series can sum to a finite number, but it doesn't make sense. Infinity is beyond true comprehension.

But I can comprehend infinity.
It's just infinite lol what's so hard to grasp
No I still don't get what this ancient meme is about desu

If you understand infinity then explain this to me, because I still don't get it. On the frontiers of physics the sum of all natural numbers (1 plus 2 plus 3 plus 4....) is required to do certain calculations. In order to get the result we see in nature the value of this sum is - 1/12. In the real world that is the correct answer, how can that be?

Zeno was using this as a defense of his teacher Parmenides. Parmenides claimed that the universe was unchanging and that any “movement” we see is just a trick of the senses, so Zeno decided that this was a good example of how nothing actually “moved” but only appeared to.

Diogenes solved it.

By just walking away right?
Bruh that was like soooo badass and epic of him, me and all the kool kids love Diogenes and how epix and badass he wuz.

>hey dood, lern 2 tink
>doesnt understand one of the most simple paradoxes

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>I watched a numberophile youtube video I'm a full accomplished mathematician
plus.maths.org/content/infinity-or-just-112
lol you must be >18 to post here

Yes I have seen that video, and also have learned much more about the concept since then. I encourage you to dig deeper into the idea.

WHAT DOES IT FUCKING MEAN I DON'T GET IT
srsly what did Zeno meant whit this

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achilles-turtle parable

What's there to get?
Give the slower turtle a head start and eventually the faster man will catch up to it, and both will have exhausted their energy by then probably. Both velocities will approach zero.

we are always one turn behind the ever-moving universe, mankind can´t catch up

I have lost all faith in the intelligence of anyone on this board and am disappointed I ever managed to believe otherwise. This thread is unbearable.

>t. too afraid to voice his opinions or views and only spends time shitting on people who do

This implies that Achilles cannot change his destination while on the move. That is, every cycle he will try to reach the turtle's last known position. All he has to do is take an additional step before stopping.

ZENO PROVEN WRONG

The timeframe for Achilles to catch up to the turtle's previous position, and since we can't experience infinitely brief moments, there'll be an infinite moments of Achilles catching up to the turtle which we simply cannot perceive.

There's an infinite amount of decimals between 1 and 2, but that doesn't mean we can't simply advance to 2.

>Didn't read article nor comments
You must possess basic willingness to read to post on this board.

Daily reminder that some infinities are bigger than other infinities

Actually it doesn't, at the level of Planck lengths, particles don't physically move along in a continuous way, you can think of them more as LEDs in a grid being turned on and off simultaneously. There's nothing preventing a particle passing two particles in one unit of time as the actual movement is instantaneous at this level. It doesn't pass by other particles as objects appear to do on a macroscopic level.

Zeno btfo

Some greek didn't understand the relativity of motion.
The whole paradox falls flat if you consider the relative motion of one runner to the other. Then Achilles catches up to the tortoise if and only if physical space is an archimedian space.
I don't blame Zeno for not foreseeing this development but the people that keep bringing this up have no excuse.

Suppose Achilles can run 2 meters in 1 second, then 1m - 1/2s, 1/2m - 1/4s, etc.
Sum up all time intervals: 1+1/2+1/4+1/8+...= 2s. So the paradox states that Achilles can never reach the tortoise, but he runs actually just for 2 seconds(some finite time in general). The trick is that the sum of infinite terms(strictly mathematically it’s not a sum) is not necessarily infinite.