Is Planck length/time a valid solution to Zeno's paradox?

>>7708213
Only if the position something can occupy in space is quantized.

If it moves to some intermediate value during one of the universe's ticks, it just gets pushed to the closest open space. This would also explain why some quantum phenomena seems to have future actions affect the outcomes of prior events. If there's some sort of buffer to sort out conflicts and interactions.

It's obviously inspired by quantization error as we observe it, and probably not the case. But it doesn't reconcile Zeno's paradox.

>>7708219
does reconcile*

>>7708213
Well, a discrete space and time would sort it out, but there's no reason to assume they are described by the Planck units; they're just what we get by multiplying various fundamental constants involved in general relativity with fundamental constants involved in quantum field theory to get an idea of the scale where quantum gravity effects should be large enough to be relevant.

>>7708240
Anyway, though, continuous space also solves Zeno's paradox; hell, we solve it every time we take an integral, which also involves taking an infinite number of infinitesimal steps to reach a finite accumulated answer over a finite range.

>>7708213
You have shmutz in your beard

>>7708213
did babby watch a Vsauce video and think he's a scientist now

>>7708251
you clearly did too

>>7708253
yes but i don't pretend to be smart

>>7708258
Yes you do.

>>7708213
>Zeno's paradox
Which one?

>>7708253
i do to be able to spot faggots like you who ALWAYS make fucking threads like this after a new vsauce comes out

File: 1359062458029.jpg (41KB, 268x265px) Image search: [Google]

41KB, 268x265px

>>7708213
No, the point of Zeno's Paradox is that when you reach a boundary that will continually give you a grasp while you go further and further into smaller and smaller increments is just an analogy for the collection and application of knowledge

Bringing it to a point of classical mechanics of superposition: you have the symbiotic relationship of progression with less being what is being applied to as more as relativity sets in; which goes as far to say, the smaller you get the further your ability to be disrupted is; which eventually entails what can be called out as as slip streaming or the whole carrier/pilot wave structure

Little noticed point of Zeno's Paradox: Travel any smaller than the size of your matrixs allow and you start folding into yourself at such point, which is just a simple example of ZPE in cohesion with the fabric of space making the point even further reduced
I mean there's an argument against induction, but there's an equally valid one for it, as with all logic quandries

>>7708213
The infinite series 1+2+3+4+5+6+7... = -1/12

So no mater the distance gained relative to the tortoise he'd still always be behind by a factor =< 1/12.

>>7708545
>= 1/12

>>7708492
the banach tarski paradox video was quite entertaining.

https://www.youtube.com/watch?v=s86-Z-CbaHA

but who am i judging, i just have a small understanding of mathematics, since i have a bachelors in physics

>>7708213
>Zeno's paradox?
Which one?

>>7708213
The principle of the One is altogether ideal and belongs entirely to thought, even though we wish to say that atoms exist. The atom may be taken materially, but it is supersensuous, purely intellectual. In our times, too, more especially through the instrumentality of Gassendi, this conception of atoms has been renewed. The atoms of Leucippus are, however, not molecules, the small particles of Physics. In Leucippus, according to Aristotle, (De gen. et corr. I. 8) there is to be found the idea that “atoms are invisible because of the smallness of their body,” which is much like the way in which molecules are nowadays spoken of: but this is merely a way of speaking of them. The One can neither be seen nor shown with magnifying glasses or measures, because it is an abstraction of thought; what is shown is always matter that is put together.

It is just as futile when, as in modern times, men try by the microscope to investigate the inmost part of the organism, the soul, and think they can discover it by means of sight and feeling. Thus the principle of the One is altogether ideal, but not in the sense of being in thought or in the head alone, but in such a way that thought is made the true essence of things.

>>7708963
all of zeno's paradoxes basically deal with a reductio ad absurdum, the argument, 'there is a smallest elementary unit of existence' is shown, via a reductio, to be impossible, because any value that would be called 'elementary' could be divided, materialistically speaking, and the remaining unit would still be matter put together, that could be divided further still. therefore the only way to achieve an 'elementary' substance is via pure reason, and not experience

>>7708240
Space is quantized by planck volumes. Any movement within a planck volume is indiscernible so for all intents and purposes such movement does not exist. Thus, things can only move in discrete multiples of h. Granted, "movement" isn't occurring in the usual sense at this scale but still.

>>7709551
You do realize that's all unconfirmed don't you?

It may be true but we really don't know still.

>>7708249
diogenes famously simply got up and walked away from zeno to refute his argument

but in philosophy and science, arguments are resolved through the dialectic and not action

>>7709518
I thought it was about time/distance, not matter?

>In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

So like the problem zeno has is that the ground achilles has covered isn't a function of the lead of the tortoise, but a function of his speed and the time which has passed.

If it was a fraction of the tortoise's lead, he would be correct to say that achilles could never catch up, but this isn't the situation which is described.

>>7709826
>If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.

For this one to be correct, the last clause should read:
>the flying arrow is therefore motionless -at every moment-.

>>7709822
It was about matter too but now that we know about atoms we most focus on the arguments relating to space and time.

>>7709831
It's weird, I remember when I was in first year physics I found the concept of instantaneous velocity really strange and confusing by intuitively this same line of reasoning.

>>7708213
Proof that the universe is ayylien simulatio
Their computers can't run that fast after all and also suffer from floating point errors. Wake up \sci/

The problem is easy. Don't use division when you should be subtracting.

>>7711332
It's because instantaneous velocity isn't the displacement over a timeframe of zero, but is the limit of the displacement as the timeframe approaches zero. Key difference.

>>7708518
>superposition

>>7709500
>retarded drivel

no, it's an elementary problem solved by understanding the quantities involved and completely understood by formalizing convergent infinite sums. stop spewing bullshit everywhere.

>>7711496
>completely understood by formalizing convergent infinite sums.
Honestly it can be completely understood with algebra and functions, which, sadly for Zeno, were not around yet.

>>7708213
you don't need a "solution" to this. it's not a paradox and it hasn't been for centuries. stop taking old, obsolete shit and pushing it around, then mixing it with "WOAH SPACE! QUANTUM MECHANICS!"

fucking pop scientists

>>7711502
Most of it, sure. But the question will always be there of how to explain that the "infinite number of steps" don't actual take infinite time and you need to evaluate the sum somehow.

>>7711505
Could always just use taxicab geometry to get round the infinite number of steps
Faster guy goes two blocks per unit time, slower goes one block per unit time but has a 10 block headstart
Clearly after 10 units time the faster one catches up.

>>7711511
That's not the "hard" part. The reason that it was a paradox is that you can also see it as a sum of an infinite number of steps. How do you reconcile that without knowing how to manipulate that kind of thing? It was seemingly contradictory, and that's why you need to be able to sum infinite terms.

>>7711504
Why not? Because integrals? You've been memed by the popsci yourself, my man.

>>7711518
It's more paradoxical to me why he thought it was a paradox at all.
Just introduce the axiom that any moving object can cover an infinite number of zero-'length' lengths in any nonzero span of time.

>>7709551
That's not actually known, or even widely believed. In fact, of the potential extensions to QFT and GR, only one (doubly special relativity) accords any particular physical significance to the Planck length at all. Even loop quantum gravity, which actually has discrete quantized space and time, doesn't break them into even planck-length-sized uniform chunks.

>>7711523
>zero-length lengths
They aren't zero length, there's an infinite number of non-zero numbers that sum to a finite quantity. That's the "paradox" which obviously isn't once you know how to sum.

wouldn't it be more correct to say there is an infinite amount of moments that the turtle is ahead of achilles? as is there is an infinite amount of moments afterwards too?
not that achilles will never catch up?

im just a popsci pleb so i probably dont understand this at all

What class can I take that would teach me about philosophy and stuff like this?

>>7711579
>about philosophy
A philosophy class

>and stuff like this
Stay in your house and watch popsci vids all day long

>>7711552
sure. it was never accurate, it's old, outdated and useless. the paradox is of no use or relevance whatsoever in modern times

>>7711546
>there's an infinite number of non-zero numbers that sum to a finite quantity.
Well that is paradoxical. I would say that clearly at some point you are counting points, since x * infinity = infinity where x =/= 0.

>>7711592
>multiplying by infinity
I guess even after 5000 years, some people still haven't learned.

>>7711598
>multiplying by infinity is problematic, but taking an infinite sum is fine

>>7711592
>multiplying by infinity

top kek

>>7711603
Exactly right. 5000 years have passed, we shouldn't have to spoonfeed your dumbass.

Take the geometric series for instance. Sum of x^i where 0 < x < 1. For example 1/2. Well known sum, you'll learn about it in highschool although you should have already seen it if you bothered writing down Zeno's "paradox" as a sum.

Dumbass.

>>7711616
>Take the geometric series for instance. Sum of x^i where 0 < x < 1. For example 1/2. Well known sum, you'll learn about it in highschool although you should have already seen it if you bothered writing down Zeno's "paradox" as a sum.
>Dumbass.
And I'm positing that this sum starts counting points eventually, otherwise it wouldn't converge.

>>7711528
The principle is not in that the space is quantized into Plank-scale chunks, but that the space is quantized in principle.

>>7708545
I strongly wished you'd die

>>7708958
>bachelors in physics
>small understanding of mathematics