Someone explain to me what this means? It doesn't make any sense at all to me:

ITT: people who dont view the attached image

> the space between Achillies and the tortoise is infinite

Bullshit.

You could fit an infinite number of infinitely small points between Achilles and the tortoise.

Yes, but the problem still stands... Achilles would always overtake the tortoise. it's basic logic.

I think the general idea is that there's an infinite number of steps that could be taken, but the entire premise uses a bad example that would be subject to minimum unit lengths. It is a lot better represented in the golden spiral.

The obvious fact that Achilles would overtake the tortoise is the entire point of the paradox.

Everybody always knew that Achilles would overtake the tortoise. Zenos knew this, Plato knew this.

The point of the excercise, and the "paradox", is that this thing which we know will happen SEEMS like it should be impossible with intuitive logic of how adding the sum of an infinite number of objects should work.

To simplify, you can cut away the fluff from this paradox and simply it to:
If you add 1/2, and then 1/4th, and then 1/8th, and keep doing this forever (getting less each time), it somehow will still reach 1. How is that possible? It should always be getting closer but never reach, no matter how long you wait. That is the paradox!

However, in modern times we found the answer with limits

You are standing in front of a wall. If you can only step halfway to the wall with each step, will you ever reach the wall?
>>no
But if you take as many steps as you want, is there a place between you and the wall that you won't eventually reach?
>> no also.

So, like all stories where you doubt the stories from which you made the stories, this is a paradox. You never reach the wall but there is no place between you and the wall you won't eventually reach.

So you make a choice. If there is no difference in the intent between the story of covering every point between you and the wall and the story of reaching the wall then they are the same story.

Welcome to math. The flaming misuse of the story for rhetorical purposes.

The Socratic trio themselves solved it by noting that it was erroneous to state that space is infinitely sub-dividable while forgetting that time is as well.

>The point of the excercise, and the "paradox", is that this thing which we know will happen SEEMS like it should be impossible with intuitive logic of how adding the sum of an infinite number of objects should work.

But infinity is just a state... not a number... of course you can fill up the space between spaces with infinite space but the whole pretence of infinity is stupid to begin with - if I had a piece of paper and cut it up into infinitesimally small pieces, I would still only have a finite mass of paper which means that infinity can only exist as an idea, not a countable thing...

>So, like all stories where you doubt the stories from which you made the stories, this is a paradox. You never reach the wall but there is no place between you and the wall you won't eventually reach.

You will reach the wall, it would just take a fucking long time with extremely small increments.

They didn't understand math yet. It's okay. Not understanding the problem speaks for humanity's advancement more than your shortcomings.

It's a metaphor for a mathematical problem. Physical constraints like minimum distance or divisibility of time are just begging the question.

Paradoxes like this are a chance to learn something and improve yourself, but you're just trying to find some cheap cop-out to avoid the problem like some smartass 10 year old.

Think more abstractly. If you stop and think for a second Zeno's Paradox is just
"1/2+1/4+1/8+1/16...=1 seems to be true. why?"

In so far as Parmenides and his student Zeno actually believed their writings they did not in fact believe Achilles would overtake the rabbit.They are monists who believed there was only a single eternal substance not subject to any change or differentiation, and thus all movement, distinction, and essentially every other element of the world as we perceive it is illusory.

The various "paradoxes" Zeno contrived were meant to be proof of this thesis, by demonstrating that various things we perceive to occur in the world are not logically possible. Of course, even the Greeks themselves understood the issues with these paradoxes.

>Paradoxes like this are a chance to learn something and improve yourself, but you're just trying to find some cheap cop-out to avoid the problem like some smartass 10 year old.

I wouldn't be here if I didn't try and improve myself. Cool it.

I understand the pretence of the '"1/2+1/4+1/8+1/16...=1' scenario, being infinite until 0 reaches 1, but the idea of numbers are to quantify objects, not dwell on the imaginary objects within 0 and 1. This problem isn't a paradox, the idea of infinity is itself the paradox which has no real world application.

Actually even if you accept that infinity exists there still is no paradox because the problem can be solved with limits.

lol you're seriously dumb.

>the idea of infinity is itself the paradox which has no real world application.
this statement alone proves that you know absolutely nothing about modern mathematics and its applications

>the idea of infinity is itself the paradox which has no real world application.
That's the whole point, you are looking at this problem from a physical perspective, real world constraints do not apply to math, the infinite in this case it's not the time it takes to catch the turtle itself, but the amounts of sections in which you break time by taking half of it, this will take you to some intervals of time so small you can't really understand, because you exist in the real world, your brain works by electrical signals and this takes time, just like this, distance exists in the real world, and the study of this is physics, but we use math to understand it and this mixture of having to use math to a real life problem is what's confusing you.

I hope this helps, but just a heads up, the line between math and physics gets blurred the higher you go up in the study on physics, so understanding them both and being able to think in an abstract way and applying it to the real world it's going to help you a lot

How fucking autistic are you? The point of the whole fucking paradox is that mathematically (and intuitionally as I thought of this paradox in like 6th grade constantly) as you get closer to something the distance keeps getting smaller and smaller 1/100th 1/1000000000th 1/100000000000000000000000000000000000th so they were wondering how the fuck you ever reach something if you can get infinitely closer. Obviously we know there is a smallest distance now, but that wasn't obvious back then

jesus fucking christ you people are absolutely brain-dead. if you seriously can't get yourself in a more primitive mindset you have to have an iq

t. brainlet

>each racer starts running at some constant speed
Do you think this diagram depicts constant speed?

>I don't understand why this is a paradox... it's just incorrect.

The paradox comes from stating the situation in a different way.
Achilles and the tortoise start running (running, for a tortoise, is obviously something of an over-statement, but let it stand..)

Achilles runs to where the tortoise was when they both started sprinting across the lawn, however long that takes. But the tortoise has moved on a bit. So Achilles runs some more, and arrives at the second position of the tortoise, in a lot less time, but of course the tortoise has again moved on a bit.

Stated that way, it sounds as if Achilles will get infinitely close to the tortoise but never catch him.

Figuring out what is wrong in the way the question is posed is how you resolve the paradox.

Replace Achilles with an arrow for tragicomic effect.

Not op but wow, this comment is so dumb

You are reading the diagram wrong. Time is not a feature of the diagram, other then the same amount of time passing for Achilles and for Torto.

Hint: Do you think the diagram intends to show the tortoise slowing down? Why would it do that?

"The solution is to breed a faster tortoise."
-- Ibid, Son of user

it will make straight lines (a visual representation of constant speed) if the spacing between the four horizontal lines is made proportional to the time taken to move that distance

i don't think he says if the tortoise is driving a car or not
he could be driving a car. like a really fast car

Seriously? That's the whole point. You either have the passage of time going to 0 as the racers approach each other or speeds are going to 0 as the racers approach each other. Neither of those are congruent with reality.

Smallest distance has nothing to do with the problem. Also, there is no smallest distance. This was purely a math problem and it was resolved by calculus.

See:

I did not mention "smallest distance."

No, either time gets closer to 0 or distance gets closer to 0, speed remains constant

I think the issue here is that this is an old way of trying to explain the concept of infinite numbers between two variables. Kinda like an asymptote on a graph. It will get infinitiely closer, but will never touch.

It's just a shitty way of explaining it due to lack of proper understanding. That's my theory anyway.

Because the tortoise isn't travelling infinitesimally. The object, in this problem, will be easy to catch up to.

Retard. A 5 year old knows that things travelling faster than things will catch up to slower things.

This is probably one of the reasons the Greek civilisation crumbled - they spent all their time thinking about pointless bullshit.

Everyone keeps saying 'muh limits' smugly like they're above everyone else, but no one has even explained why 'muh limits' solves the paradox.

The paradox ignores the fact that, every time achilles reaches a new point, the distance between to the next point decreases. It's true that the number of points he has to reach is infinite, but the distance and time between each point approaches 0. If you were to model this as an infinite series, it would be convergent.

It explicitly says constant speed.

Yeah, this is a good way to explain it, and it's exactly where the term limit comes from, it's not about "where it is" but rather "where it's heading" if you don't know calculus congratulations on the intuition, good job.

It absolutely is a paradox until you have the properly basic info necessary to solve it. Like it or not, this problem was impossible to solve until the coriolis effect was invented, thus allowing Achilles to break common rules of conservation.

so he can reach the turle
but can he overtake it?

...Yes? This paradox only applies when he's behind the turtle, and has to "catch up" to it. Once he's at the turtle's level, he will logically pass it.

>implying the tortoise would let Achilles get him

Bitch would run like a motherfucking rocket, have you ever heard about tortoise soup?

youtube.com/watch?v=uhaNXlmMyTo

Except this is the physical universe and there aren't an infinite amount of points, there's only as many points as there are plank distances.

The paradox only deals with the point before overtaking. It does this by reducing the period of time before each step, with the total time approaching the point of overtaking and the value of each step approaching 0. As soon as the time exceeds that of the infinite sum, the turtle will be stuck in second place.

Plank distances are about our own observational limits. There could theoretically even be smaller distances, but we could never observe them.

>if you don't know calculus

Much appreciated.

achilles is running faster than the tortoise, but, the amount of time that achilles must spend reaching each of the tortise's milestones gets smaller and smaller
so, running the simulation, you might come to the conclusion that achilles cannot overtake the tortoise, as the tortoise makes a new milestone every time achilles reaches the previous one, but, the sum of the elapsed times are not infinite. If you add up all of the times that achilles spends reaching each milestone, you find out that all of the sums are bounded above.
If you only consider points in time before the least upper bound of the partial sums of the time, then you come to the conclusion that the tortoise is always in front of achilles. However, if you push the clock forward, beyond the least upper bound, you will find that achilles will have covered more total distance than the tortoise, with the addition of the tortoise's head start, so, in truth, achilles will overtake the tortoise.

If you can't observe something then it doesn't exist.

The assumption of the paradox is that all infinite sums are infinite, that the process of achilles catching up to the tortoise will take infinitely long because there are infinitely many steps. Once a person accepts that there exist infinite sums that fail to transcend all bounds, then the paradox resolves for them

This riddle is directly analogous to the following: "Hercules walks into a wall at a constant velocity. It takes a finite interval to walk halfway. Then another finite interval to get the next quarter of the way. This goes on to infinity."

If 1 meter is the total distance, and Hercules moves at 1 meter per second, the sum of the finite times traveled are :

.5s + .25s + .125s + .....

This infinite sum does NOT diverge, it converges to 1s. That's all there is to it.

The continuum was a mistake. Confess your sins and repent.

Not convincing

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