So I read something by Borges on the Zeno paradoxes and it occurs to me they are more troubling than I had previously...

677. There can be no "paradoxes" in the flux any more than there can be "magic", "miracles", "discontinuities" or things that "transcend" the flux. If a phenomenon seems "paradoxical" to you — i.e. the observation clashes with your theory — all it means is that your theory is weak, and must be revised. Baudrillard, for example, seeing paradoxes every other paragraph says nothing about the nature of the universe but only about his weak eyesight. All of Zeno's paradoxes are of this nature. Achilles would indeed not catch the tortoise if time and space were not related, but as it happens they are, so he quite obviously will, and the problem lies with the conceptions of Euclidean space and linear time, which though adequate to analyze a wide range of situations, nevertheless break down when strictly applied and followed to their ultimate conclusions, as Zeno did with his series of brilliant and famous thought experiments (which, by the way, I have still not seen anyone explain — all I've seen is pathetic attempts to dismiss them as trivial or fallacious). — So we see that in Zeno's case the "paradoxes" proceed not from weakness, as with Baudrillard — who goes as far as to invent paradoxes for physical phenomena that have long been adequately explained, just to make things seem a little more nebulous than they already are — but from strength: the intellectual strength of showing his contemporaries that their facile notions of space, time, etc. are not sufficient to describe reality, since when tested consistently they lead to self-contradictions, and must therefore be re-evaluated and revised. Which they have been, destroying the notion of any "paradoxes" involved, and affirming once again that there is nothing "magical" or "miraculous" about this world... for those with a sufficiently strong eyesight to see this. — At which point people began to realize that to solve Zeno's paradoxes we had to invent general relativity and quantum mechanics, among other things, which when taken to their ultimate conclusions also appear to make bollock-all sense, and the "paradox" circus began anew...

That has little to no bearing on the paradox. Infinity is infinity, regardless of which you're attempting to cross.

>There is no sound refutation for this
>When Zeno told a gathering this Diogenes proceeded to stand up and leave the room

other examples: present a hand then another, or kick a rock.

hey zero, lemme introduce you to a little thing we like to call CALCULUS.......

you are just considering smaller and smaller time intervals before A reaches T. hence, the distance between reaches 0. this is not proof that motion is false, but rather that the speed is finite.

similarly: take a square. shade half. shade half the unshaded side. repeat ad infinitum. you can see that there are infinite squares, but they add up to finite area. same thing with the time required for A to reach T.

Japanese arcades the best, yo.

132. Fondue sucks. It's just a pot of disgusting melted cheese in which you dip pieces of stale bread. The only reason subhumans are still eating it is because of all the apparatus on the table that makes them feel like children. Its continued popularity has nothing to do with culinary excellence but with subhuman childishness.

>*holds spork* dude diogenes is so funny xD hes so weird and random LOL *le upvote*

Why the need to call him a scammer? It's not like you'll see "Seller: 7H3 1CY U83RM4N" when your retarded ass is trying to get a good deal on a laptop.

Many philosophical paradoxes remain constrained to their own thought experiments, but this paradox has a real world solution in the form of calculus.

This paradox is often used during pre-calc courses to introduce students to the concept of integration. Try a youtube lecture on the subject.

Do you even know who Diogenes is?

"Refuted" not as in "proved incorrect" but "proved incongruous by contradictory evidence." Again I say, it's not perfectly sound, but it's funny.

Motion is an illusion you dip

That is literally the problem. Exactly what is wrong with the puzzle?

>try a youtube lecture on the subject

people are just confusing an epistemological antinomy not jiving with a simple ontological reality as some kind of great paradox

just read kant, the mind trying to apply a conceptual schema to a holistic situation that unsurprisingly intersects multiple conflicting categories of spatial intuition (continuous vs. discrete) can only flip between different subsidiary schemata. you can't intuit a line or movement along tha tline as BOTH continuous and composed of discrete divisible units at the same time in the same intuition

it's just a simple case of confusion between two different ways of looking at an object. the discreteness schema is continually looking for a new fraction (doesn't have to be half, can be 99.999999999999999999999%), which is always possible, and always possible to spatially intuit. the common sense and ordinary intuition is to imagine the obvious overtaking of a slow object by a fast object.

Its simple

maths and fractions and all that are just an idea

You are as bad as people who argue for Free Will with compatibalism. "Of course I have free will, I think my arm should go up and wouldn't ya know it the damn thing goes up"

kys empricist scum

>implying people here read

There are infinite series that sum to a finite number, this is the solution.

the map is not the territory

>8400598
I thought you guys were Infinite Jest fans. The whole tennis fight started over a similar issue

"Korzybski held that many people do confuse maps with territories, that is, confuse models of reality with reality itself"

>Of course I have free will, I think my arm should go up and wouldn't ya know it the damn thing goes up

That's literally what free will is.

"Oooh free will can only exist if it breaks the laws of physics blah blah blah anything that people freely will is not free will because muh physics

"I am the one that makes the definition of free will blah blah blah because I am the only person smart enough to realize that free will doesn't exist under my own definition of free will...that is why my autistic description of free will is obviously the correct one.

"UGHHHH PEOPLE ARE SOOOO STUPID. Why can't they see that free will isn't really because God doesn't exist and because the brain is all physics!! It's like they don't even know that I own the official narrow rigid useless strict definition that guarantees that free will is impossible

"I am so much smarter than everyone else. Haha guess they didn't know that I own the phrase "free will" and that they are all officially wrong about what it means :) Stupid fucking sheeple

"I guess you can't expect everyone to be a philosophical genius like me."

>It simply doesn't take an infinite amount of time to travel the infinite amount of points between zero and one.
but WHY doesn't it?

Math reconciles this with the concept of "aleph", basically a representation of infinite sets that also indicates their relative "largeness". So for example the infinite numbers between 1 and 2 are a lower degree aleph than the infinite integers

Convergence

this is why I'm afraid to start seriously reading philosophy

For one thing, the paradox in OP pic predicates that, unlike the time taken for the first half, the time for the second half never fully comes. Second, it assumes an infinite divisibility of time, about which Planck would like a word

inb4 >implying time exists in the first place

isoscelles triangle with 2 sides of one planck length just phoned, should I take a message?

Tell him hello and thanks but we're discussing time here. If he gets testy then remind him that he cannot exist.

In terms of distances it works out fine.

The series 1/2 + 1/4 + 1/8... has the limit of 1, meaning all the ever decreasing fractions together reach 1, and the distance can be covered.

Some of his other paradoxea are very cool as well and often overlooked. I like the arrow paradox: at a single point in time if an arrow's flight it's still, and this is true of any point in its flight. So how is it moving if it's still at every point?

Moving lines paradox covers discrete space.

Does it though? Tgere's multiple interpretations and it can easily be read as Zeno simply not understanding relative velocity, which is the traditional interpretation.

>That's literally what free will is
That is not a meaningful definition of free will. If that's free will, then computers have free will too.

There is no evidence that time is quantized.

i am not Veeky Forums enough to understand. What are the implications of relative velocity on the lines?

Simply that if you're moving 30kph towards someone moving 30kph towards you, your velocity in relation to each other is 60kph. Zeno thought this was a problem because the two moving rows are crossing each other twice as fast as they are the immobile row, but that simply isn't a problem in physics.

An alternative viewpoint is that the paradox refers to indivisible particles and quantised time, whereby one particle passing another always takes one quantum of time, so the rows can't pass at relatively different speeds. But it's often pointed out that the original text doesn't really imply those stipulations and like user said there's no evidence time is quantised, but even accepting that it is, an object doesn't glide between two places as one quantum of time passes, it essentially dissapears from one location to another next to it.

Another interpretation is that the lines of runners are lines of dimensionless points making up a single object, being single points they always take the same amount of time to pass another single point. So in that one time doesn't need to be quantised and the paradox becomes a point on one of the moving rows crossing a certain number of points on the immobile row yet twice as many on the other moving row. The issue with that version is that there would be the same number of dimensionless point across any length of the lines i.e. infinity, so it's not a paradox at all for a point to seemingly cross different amounts of other points, it's still crossed an infinite number of points in any case.

No, they don't. A computer cannot decide things because it's structure is not complex enough to have wildly unpredictable outputs.

>it can easily be read as Zeno simply not understanding relative velocity, which is the traditional interpretation.
If there is a traditional interpretation, it's based upon the thought of Parmenides (shout out to ) and in essence says motion is an illusion.

>but that simply isn't a problem in physics.
Physics is an illusion. As for the whole quantum woo shit, in a way space on some level being non divisable (quantised) might seem to propose a solution but I wouldn't hold my breath. It's interesting that some people simulataneously propose calculus and quantisation as solutions with no second thoughts too.

Comolexity and predictability are not correlated. See chaos/complexity theory.

I agree that computers being conscious is trite tho.

Aristotle refuted them pretty easily, by pointing out that there is a difference between an infinitely divisible distance (which all distances are) and a distance that is infinite in extension. Zeno's paradoxes were quickly dismissed in his time, but you blowhards are arguing about them in 2016.

>Zeno's paradoxes were quickly dismissed in his time
Except they weren't.

Frames of reference! This is basic physics.

>I agree that computers being conscious is trite tho

Then I sure hope you weren't the user I was replying to :^)

>Comolexity and predictability are not correlated.

There is generally a correlation isn't there? Could you elaborate more on this?

>So for example the infinite numbers between 1 and 2 are a lower degree aleph than the infinite integers

That's completely backwards. The 'Real' numbers between 1 and 2 are of higher cardinality than the integers.

And how exactly the the proposition of infinitesimals or epsilon-delta constructions resolve the fundamental problems the paradoxes reveal? Saying "well, we happen to be able to perform a number of useful calculations now and have systems to reason about and resolve them" doesn't counter the problem of there being no well defined final step given a continuous universe.

The distance between Achilles and the tortoise can be divided an infinite number of times, but the distance itself is not infinite.

Paradox solved. Rate and subscribe.

I'm (mirin my quads?) and I instantly came to that conclusion on my own, without ever reading your post or Aristotle.

Do I have the potential to be the next Aristotle?

Oh /: sorry I'm high

Right, and it's every man's responsibility to go around calling people fags and gooks and niggers, and the so-called "real" is someone else's fantasy.

This.

The more I consider Zeno's paradoxes the more I consider them to demonstrate the limitation of human conceptualization. We can imagine quantifying space by discrete points, but we can alternately consider space as a continuous reality without discrete differentiation. In reality, space is neither of these: they are only useful for approximation within human meaning. The Eleatics demonstrate through each of their paradoxes that concepts do not simply stand for things as such, but that they are their own thing and we must not confuse semantic similarity with ontological parity.

You guys realize that the paradox is the logical conclusion to Heraclitus's philosophy, right? Zeno didn't actually believe that distance is infinitely divisible. The paradoxes are reducto ad absurdums designed to show how Heraclitus was wrong in his view that there is a pluralistic ontology in which time and space are divided. Everyone arguing against the paradox is only proving his point. Figures the board with the massive hard on for Heraclitus doesn't actually know the historical and philosophical context.

wow if that is the case Zeno is even more of a genius than I thought

>wildly unpredictable outputs

How is a human choice a "wildly unpredictable output" ?

Indeterminism =/= Free will.

It's funny because physics actually solves the problem.

Basically there aren't an infinite number of divisions that space can be chopped up into. The Planck length, unthinkably smaller than even sub-atomic particles, is the smallest packet which could be defined as Space. There aren't an infinite number of divisions of space that the runner has to traverse to over-take the turtle.

Wrong but thanks for playing.

Not so sure on that, you're dismissing the entire field of physics to make the paradoxes work. And the different interpretations are really about how the paradox works rather than the response. So the one you picked out is saying Zeno was literally talking about two rows of runners, in which case relative velocity absolutely applies.

>It's funny because physics actually solves the problem.

no it doesn't

>The Planck length, unthinkably smaller than even sub-atomic particles, is the smallest packet which could be defined as Space.

Wrong. It is the smallest measurement of length used by physicists, not an absolute limit imposed by nature itself. Stay off the pop sci kids

Unfortunately I'm right, friend. It's common knowledge

>not an absolute limit imposed by nature itself.

lol, not him, but the mathematics of Zeno's paradox is an absolute limit imposed by nature itself?

Stop making a fool out of yourself fag.

>lol, not him, but the mathematics of Zeno's paradox is an absolute limit imposed by nature itself?

Did I say that? That literally has nothing to do with how physicists measure length, which is what I was clarifying. Nice try though

But that's not how people use free will. When christards use "free will" to explain why suffering exists, they mean it in the sense that your soul can metaphysically choose to be evil, not the unconstrained application of your inclinations.

it's a trivial point in the grand scheme of things
>ellipsis into already established members of the set
>'and so on' isn't vertically reflected
gross

This is the right answer. Ancient Greece had yet to discover acceleration. Their concept of speed was restricted to running faster, or running slower (velocity).

it's easier to digest and a more personal experience with the content creator, especially for those with a non-stem background. I never learned math well through books alone, having lecturers to bounce questions off of was helpful.

>you're dismissing the entire field of physics to make the paradoxes work
You're doing the same argument as Diogenes but going "muh physics!" instead of walking out. And no relative velocity does not apply as a solution, although some of the paradoxes are the same.

ISN'T THIS FROM THAT FUCKING JOHN GREEN BOOK

Didn't Einstein solve it?
Basically this paradox fails because it's imagined and drawn in a 2D/3D plain, where if you add time as a distance, Ulysses would've passed the turtle.

This doesn't seem like a mind bending paradox.
Do you guys have any other paradox that needs solving?

I mean, human brains are just complex enough that 99/100, you can't guess what someone will do next with any certainty

Calculus.

Convergence of a sequence...

This is literally calculus 1. Are you all retarded? Go take a math class instead of masturbating over your philosophy

>Continental """"""""""""""""""""philosophy""""""""""""""""""""

Infinite sums can have finite results

ie 2 = sum (x=1,...,n) 1/x

Actually it's from Infinite Jest. :^)

>Didn't Einstein solve it?
While it wasn't originally Einstein's idea, yeah space and time being the same thing and not separate does fuck it over since it changes one of the underlying assumptions.

What's interesting tho is they're event based paradoxes and we've now returned to event based thinking after the spacetime thing killed cartesianism.

Simple systems can produce complex results (chaos theory), Ian Stewart has written some very good texts that appeal to a broad range of understanding.

is this bait?

You occupy infinite space and move at infinite speed across infinite spaces, so its basic algebra at the end :^)

If I were to get one Borges book/collection/whatever what should it be?

Some infinities are larger than others

∞+2=essentially still ∞

therefore ∞

got em

You've contradicted yourself. Infinity encompass infinity +2
infinity +2 = infinity
Just as you cannot add two infinities. Are you are adding is the concept of infinities

Labyrinths

>Are you are adding is the concept of infinities
Arguable interpretation. All we are ever doing is adding concepts even with finite numbers if you want to go down that road. It's how you can have a consistent concept of infinity in a mathenatical sense.

There are different infinities and the questions around those are quite interesting.

Wasn't he just trying to prove Parmenides' monism and the impossibility of change? That makes more sense for me since he's recorded as being Parmenides' pupil and the conclusion of the paradox is that motion is impossible.

This is what I have learned.

>So is there a sound refutation of this?
Real life

Anyone can beat a turtle in a race

Turtle and the runner?

Lets assume that the turtle has a 100 m head start and moves with 1 m/s.
Let's assume that the runner has no head start and moves with 10 m/s.

When will the runner outrun the turtle.

The equation for the turtle is t(x) = 100 + X
The equation for the runner is r(x) = 10X.

100 + X = 10X

100 = 9X

X = 11.11111....

After X seconds (111.11111.... meters), they are at the same spot. Then the runner will outrun the turtle.

He was proving Parmenides correct by showing how Heraclitus was wrong. Space is not infinitely divisible because nothing is divisible at all, as per Eleatic monism