At what point did you realise that he indeed never can suroass the turtoise?

This is not the answer. If we didn't know about the planck length Zeno wouldn't have pointed towards it. We don't know if space is continuous past the planck length or not and if it is discrete that implies a grid that can be aligned to. The correct answer to Achilles/Tortoise paradox is from calculus with the sum of an infinite series.

>The correct answer to Achilles/Tortoise paradox is from calculus with the sum of an infinite series
NPC. Achilles moves at a constant rate and closes the distance in a finite time. Leave the infinity bullshit out of this

>Achilles moves at a constant rate and closes the distance in a finite time.
And the infinite series has a finite sum. Claiming the Planck length solves the paradox and reality is discrete is stupid and a total misunderstanding of quantum physics. If you can't even accept infinite sums from basic calculus you shouldn't be talking about quantum physics which is highly dependent on them

No you fucking idiot. The problem works on the assumption that time is being halved or something like that.

a planck length is not inherent to the sum of (1/2)^k from k=0 to infinity equalling 2. Get a degree you nutter.

>The problem works on the assumption that time is being halved or something like that.
No shit. If Achilles is moving at a constant rate it will take him half the time to cover half the distance. If that is the case the infinite sum converges to a finite value. It's only if Achilles slows down exponentially and take the same amount of time to cover an exponentially decreasing distance does the infinite sum diverge.

>It's only if Achilles slows down exponentially and take the same amount of time to cover an exponentially decreasing distance does the infinite sum diverge.
That's not the paradox though you absolute bellend.

Empirisism > Rationalism
It's time for you to pack up and leave.

I have never seen a more retarded sequence of posts in my life. Each one was more retarded than the last.

>a planck length is not inherent to the sum of (1/2)^k from k=0 to infinity equalling 2. Get a degree you nutter.
Exactly what I said here >If we didn't know about the planck length Zeno wouldn't have pointed towards it
The paradox was solved long before Planck

fuck you I see your point now, don't fucking @ me you cock gobbler.

You don’t have to model this scenario with infinite series bullshit. Instead of 1/2 + 1/4 + 1/8… = 1 how about 0.1 + 0.1 + … = 1? We know he reaches the tortoise because he travels at a certain rate and since the distance is finite, the rate allows them to complete the distance. It has nothing to do with infinity. Everyone knows the limit of the infinite series is 1, but to say that the infinite sum is EQUAL to 1 is hocus pocus. For an infinite sum to be completed you need an infinite calculator. Can an infinitely strong man lift an infinitely heavy stone? According to math NPC’s yes. Just ignore one infinity and focus on the other. Assume that which goes on forever can somehow be completed. Retarded

>That's not the paradox though you absolute bellend.
My bad I thought you were the guy arguing against the infinite sum. If Achilles moves at a constant rate the infinite sum described by his movement converges to a finite value and calculus solves the paradox

Zeno’s paradox is all well and good until you have to get to work

We can say that the distance Achilles moves past the start line is d_achillies(t) = 10t, d_tortoise(t) = t + 10

We want to find the value of t where d_achillies(t) = d_tortoise(t)
or when
10t = t + 10
9t = 10
t = 10/9
t = 1.1111....
And that after this d_achillies(t) > d_tortoise(t).

We can answer the paradox by asking what is the total time. The total time = 1 + 1/10 + 1/100... to infinity; this is the sum of a geometric series r^n where r = 1/10
(1/10)^0 = 1, (1/10)^1 = 1/10, (1/10)^2 = 1/100 etc..
This converges to 1 / (1 - (1/10)), or 1/(9/10) or 10/9 or 1.11111.....

>You don’t have to model this scenario with infinite series bullshit.
So what? The infinite sum models the scenario and gives the same value as the algebraic approach. Here is Zeno's actual paradox as recounted by Aristotle.
>That which is in locomotion must arrive at the half-way stage before it arrives at the goal.
Which clearly leads to an infinite sum.

That assumes the existence of the Continuum (TM). We don’t know if that’s true or not, so we shouldn’t assume it. There is no problem

It assumes the existence of the real numbers. If you don't assume they exist most polynomials don't have any zeroes, e and pi don't exist, and you can construct a right triangle with compass and straight edge with a hypotenuse that can't be measured.

If by continuum you also me the rationals it gets even worse since fractions would no longer exist

This is such a retarded scenario lol, all it proves is that the Ancient Greeks didn't know about asymptotes

Real numbers are bullshit. You can’t even define most irrational numbers.
>e and pi
So? I’ve never seen a perfect circle, have you?
>and you can construct a right triangle with compass and straight edge with a hypotenuse that can't be measured.
once again, this construction isn’t perfect. Or did you think it was actually possible to construct two sides of exactly the same length, and also connect them exactly at their endpoints with a completely straight line? Even by recognizing the existence of atomic lengths you realize the difficulty of this.
>If by continuum you also me the rationals
the infinite series only requires the rationals, so yes. What is the biggest number that has any significance in the real world? What is the largest n such that n can describe the physical state of reality in a meaningful way? The smallest number is probably the reciprocal of that, if not bigger or slightly smaller. Rational numbers don’t exist until they are constructed. There is no such thing as a number “line.” A line isn’t a collection of points but something on which points are constructed. You can zoom in on a line drawn by a pencil and find gaps. You’ve never seen a continuous line in your whole life. Your biology deceived you.

I mean you've just thrown out most of math and science to defend your position. I think that's a pretty clear win for me isn't it?
>You can zoom in on a line drawn by a pencil and find gaps.
No you can't. What is this zoom you're talking about? It's an abstraction just like the compass and straight edge of geometry you just threw out.

>I mean you've just thrown out most of math and science to defend your position
>appeal to authority
Wittgenstein called “most of math” you see today laughable, as well as many others. But people like to believe in things they don’t understand so it caught on.
>No you can't. What is this zoom you're talking about?
yes, you can. Microscopes exist. There are gaps even farther below that, at the atomic level. Your eyes do not see a continuum. It is an illusion, just as pixels on a screen form the illusion.

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If calculus proves space is continuous then playing Mario on my TV proves space is discrete. You just can’t perceive the pixels of the universe.

What cannot said must be passed over in silence.

based and wildbergerpilled

>yes, you can. Microscopes exist. There are gaps even farther below that, at the atomic level. Your eyes do not see a continuum. It is an illusion, just as pixels on a screen form the illusion.
Microscopes can't see atoms. And we're not talking about a line of pencil lead we're talking about a line of points. What physical device can see discrete points of space? If you've got one you're going to get a Nobel prize. Come forwards with it.

>Microscopes can't see atoms
I didn’t even imply that, but whatever.
vice.com/amp/en/article/8qxe7z/this-microscope-can-see-down-to-individual-atoms

The point was that the gaps exist whether or not you can see them.

>And we're not talking about a line of pencil lead we're talking about a line of points
What’s a point? Have you ever seen a line of continuous points? No
>What physical device can see discrete points of space?
just because it’s not detected yet doesn’t mean there aren’t discrete points of space. There’s no reason to assume either or. But infinity and continuity have never been truly observed.

>just because it’s not detected yet doesn’t mean there aren’t discrete points of space. There’s no reason to assume either or. But infinity and continuity have never been truly observed.
Ah now we've moved from claiming the continuum doesn't exist to we don't know if the continuum exists.

I've thought more about your gaps too and realized that admitting that there are gaps implies that space is a continuum. If space was discrete there would be no gaps or space between the points. Your own argument contradicts you.

>Ah now we've moved from claiming the continuum doesn't exist to we don't know if the continuum exists.
See >If space was discrete there would be no gaps or space between the points
That’s assuming space isn’t discrete at a much smaller level. Your arguments are retarded. Get IQ mogged. I won’t participate further in this discussion as the point has already been demonstrated to the audience.

>That’s assuming space isn’t discrete at a much smaller level.
So different levels of discreteness lol. Apply the argument at the lowest level two points in space should have no distance or gap between them if space is discrete. If there is no lowest level that is exactly the same as space being continuous.

>See
This you? >Real numbers are bullshit. You can’t even define most irrational numbers.
>There is no such thing as a number “line.” A line isn’t a collection of points but something on which points are constructed. You can zoom in on a line drawn by a pencil and find gaps. You’ve never seen a continuous line in your whole life

>Leave the infinity bullshit out of this
numbers of infinite magnitude is what solves the paradox

besides, wiles tile argument btfo's most discrete arguments

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and what does that even mean, thinking space is discrete is just not a good view, there are so many arguments against it

The distance along a vertical line between points one row apart would be greater than one unit but less than two units. And besides that's not Weyl's tile argument, he pointed out how the Pythagorean theorem wouldn't work in a discrete universe.

turns out that the smallest distances don’t have right angles, so the tile argument doesn’t hold. Sorry bud, next argument

Going further I'm going to say it is impossible to come up with a 2d grid where the distance between every point is a whole number multiple of some basic unit.

The grid here is supposed to be a grid of equilateral triangles where the length of each side is the smallest distance. But as I pointed out here it's easy to construct a length between two points that is not a multiple of that smallest distance.

>The distance along a vertical line between points one row apart would be greater than one unit but less than two units
And? Motion doesn’t exist at this level, there is no distance to be traveled, either these informational states are on or off. See the example of a screen with pixels. Part of the program is that pixels cannot be skipped. But there is no speed associated with moving a certain direction. You can go vertical or horizontal or diagonal, and the appropriate points will be selected at the appropriate time.

>turns out that the smallest distances don’t have right angles
lmfao, the tile argument works for any angle that is not infinitesimally small. Do you have any actual evidence for a "smallest unit of space"? If what you are saying is true then why dont you ride a rollercoaster with wheels that were constructed with discrete space calculations?

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>And? Motion doesn’t exist at this level, there is NO DISTANCE TO BE TRAVELED, either these informational states are on or off.
This just goes to what I said here >I've thought more about your gaps too and realized that admitting that there are gaps implies that space is a continuum. If space was discrete there would be no gaps or space between the points. Your own argument contradicts you.
We can both agree that is a fucking moron

Why would I agree that I’m a moron? Dumbass

>Why would I agree that I’m a moron? Dumbass
Because you fucking contradicted yourself.
>>If space was discrete there would be no gaps or space between the points
>That’s assuming space isn’t discrete at a much smaller level. Your arguments are retarded.
>Motion doesn’t exist at this level, there is no distance to be traveled
You can't even keep your own dumbass positions straight. Do you think there are gaps or not?

Distance is not a meaningful concept. It literally doesn’t exist at the fundamental level of reality. Everything about this world is an illusion. It will always be a mystery and will never make sense because it is designed that way. It CAN’T make absolute sense. You’re just building illusions upon illusions. There is nothing to know or find out. Where knowledge is, there is deception.

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>Where knowledge is, there is deception
asian nihlism is so cringe bros

>Distance is not a meaningful concept. It literally doesn’t exist at the fundamental level of reality.
Just more agreement with me saying this guy >here are gaps even farther below that, at the atomic level
is fucking dumb. Gaps between points in discrete space would not exist

there is no notion of gapness or distance until it emerges. It doesn’t exist at the fundamental level. When it does emerge, it is still discrete.

>atomic level = fundamental level
stop putting words in my mouth

So your statement about zooming in to see the gaps was totally wrong then? You admit it was wrong and contradicts your own position.

>only le potential infinity is real not actual
yikes

Me >If space was discrete there would be no gaps or space between the points. Your own argument contradicts you
You calling that my argument stupid >That’s assuming space isn’t discrete at a much smaller level. Your arguments are retarded
You using my same argument >Motion doesn’t exist at this level, there is no distance to be traveled
Rofl you're a fucking retard

It should be clear that my point was that any illusion of continuity that you can see can be taken away by zooming in using a microscope. I did not say that you can always zoom in on fundamental levels of reality and find gaps, because these can’t even be seen. Humans formed the idea of continuity by seeing lines that appear continuous when they are not. That is the whole point.

>It should be clear that my point was that any illusion of continuity that you can see can be taken away by zooming in using a microscope.
Rofl so the illusion can be broken by zooming in to see gaps or distance that you claim don't exist. This is a clown show

My point is that you can’t give a SINGLE observed example of continuity in the real world. You see the number line and think “wow it must be full of infinite points” when the continuous line is an illusion.
>b-but I can imagine it’s real in the Platonic world!
imagination is imagination

This is the only question that /sci/ and Yea Forums can come up with, and both failed to properly explain what it is
Even the threads on problem of consciousness is not this branched

Again I asked you here to come forward with this miracle machine that can see discrete points in space. But since you don't have it you have zero basis for calling the continuous line an illusion. It doesn't matter that you can imagine discrete points

>My point is that you can’t give a SINGLE observed example of continuity in the real world
but thats retarded, of course you cant see an infinite amount of things at the same time. Theres still reason to think that space is continuous though.
refute

Both discreteness and continuity are ultimately illusions. But you don’t need infinite sums to explain movement. You’re trying to explain macro-events on a micro level which is absurd. Achilles reaches the tortoise means that we see him reach the tortoise. We can say nothing beyond this.

>Both discreteness and continuity are ultimately illusions
and what isnt an illusion? is knowledge about space possible?

1) the tile argument is irrelevant as it assumes notions of distance, speed, and motion at the fundamental level
2) I have no evidence of discrete points, but I don’t have to assume this to do practical math. You have to assume the continuum to talk about the real numbers and infinite sums. I don’t need to talk about Achilles moving at Planck lengths or below, I can describe his speed as rates that we can actually measure and understand.

This is a bunch of lame bullshit you're throwing up to try and hide how wrong you are.
>But you don’t need infinite sums to explain movement.
Between points A and B you pass 1/2 then 1/4 then 1/8... that clearly leads to an infinite sum Zeno recognized that it did and came up with his paradox. Infinite summations from calculus provide an answer that agrees with the alternative algebraic formulation of the problem and both the calculus and algebra agree with empirical measurements. You've gave a bunch of dumbass objections and wound up contradicting yourself.

Infinite summations are the basis of calculus namely the integral is formulated as Riemann sum or to make it totally clear for you an INFINITE Riemann sum. There are plenty of physical problems that require calculus and integration