Zeno's paradoxes - The arrow

That's the wrong Zeno, bud.

>can't measure the area under a curve
>can't track rates of change

this is what every undergrad says

and it's WRONG

You aren't measuring anything. You are calculating.

Have you never taken calculus? If it's wrong, how do we have satellites? The theoretical cannot contradict the practical. To the extent that something is useful, it must be true.

lol undergrad gonna undergrad

You're defining movement as a change of position over time, and then asking people to measure movement without time. What's the sound of one hand clapping?

>am a graduate
>getting criticized by a high schooler
Why do I do this with my life?

why do you lie on the internet

or even worse, finished compsci/electrical engineering and had no classical education whatsoever

If the brain is one-dimensional can the left or right dimension ever become predominate?

Why the fuck are people arguing about calculus and not the topic at hand

Because it's relevant

because STEMlords are brainlets

Paradoxes only exist because models do not accurately depict phenomena. As models become refined, old paradoxes become irrelevant, and new ones eventually take their place. The theories of relativity and quantum physics will do this to Zeno's in time.

Let me rephrase that; why the fuck are people arguing whether someone is an undergraduate or graduate and don't directly apply their knowledge and interpretation of calculus since it seems relevant? And why is nobody addressing the main question, infinitely divisible versus finite chunks of space/time/space-time?

Calculus is a useful tool for describing (and predicting) what we perceive.
There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of science and math is to find out how nature is. It only concerns what we can say about nature.

Oh, because this is Veeky Forums

I don't mean to be rude but you sound like someone who's read too much pop-sci and believe people like Carl Sagan and Lawrence Krauss when they say that science is the only thing pushing us forward towards a better tomorrow.

I mean I'm a STEMfag myself but I've taken up philosophy on the side solely due to the reason that many scientific endeavors fail to conceptualize and prefer repeating calculations that have been done to death rather than try to explain nature.

Quantum physics is a very shitty field; it's at best an okay approximation of a theory that's yet to take its place with more interpretations than there are people trying to figure out which one is correct. And I have to admit that I see no way General Relativity can explain Zeno's paradoxes for they are not the "paradoxes" that theory is used to resolve (they are actually explainable just by Special Relativity but I guess you meant GR in your post, that's why I'm mentioning it).

>science is the only thing pushing us forward towards a better tomorrow.
That's... not at all what I'm saying? I have no idea where you got that from. Are you saying that Zeno's paradoxes expose a flaw in something beyond science models? Because it doesn't make much difference, regardless of where a paradox is being found, what I said is the case with them and how they eventually become irrelevant, just change "models" with "worldviews".

Solvitur ambulando

because /bantz/ is an indirect form of argumentation. The implication of a proper insult invalidates the argument, but a proper rebuttal reverses it. It's shorthand/ the body language of the internet.

My apologies for misunderstanding you. Still, saying that the paradoxes will be resolved by QM and GR is not resolving the paradoxes, don't you agree?

why is this board more interested in non-Veeky Forums and non-philosophy questions than anything even remotely tied to those two?

books are boring

Zeno was like the first brainlet to argue 0.999... =/= 1

His argument is mathematically wrong

I haven't stumbled upon that information, can you provide source for what you speak of?

Not that guy, but the arrow in flight paradox demonstrates that between points A and B, because you can point to an infinite number of decimal points in between them, motion shouldn't be possible and the arrow should never be able to reach point B from point A.

>Mathematical realism

That literally isn't equivalent to 0.999...=/=1

mathematically wrong is correct but chemically two hands clapping together do not actually touch, which is one analogy people use for zenos arrow.

bump

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You know the only point in learning this stuff is to accept the failings of words/reason and that sometimes you just gotta stop trying to rationalize everything.

What a brainlet post.

Yeah, why enjoy things?

It's pretty obvious that one must have a few unprovable axioms in his theory of nature, but Zeno's paradoxes show that two opposing worldviews (namely, dividing space and time into indivisible and infinitely many pieces) will both prove unsatisfactory and I don't believe that the situation is a false dychotomy either. How does one proceed from such a situation?

>How does one proceed from such a situation?

By accepting that processes with infinite steps can happen in a finite amount of time, just like a finite series can arise from adding together an infinite amount of quantities.

>a finite series can arise from adding together an infinite amount of quantities.
No, it can't. A finite series is by definition a sum of finite number of elements.

yeah, I didn't say what I meant to say, I meant a convergent series

but that doesn't mean what I said isn't true
if you add together an infinite amount of quantities, and their values converge, that gives you a finite quantity
you get a few of these finite quantities you get a finite series, ergo a finite series can arise from adding together an infinite amount of quantities.

>if you add together an infinite amount of quantities, and their values converge, that gives you a finite quantity
Wrong, 1+1/2+1/3+1/4+... converges.

diverges*, I'm autistic, sorry.

oh no mr semantics got me again

But it is what you said, is it not? Adding infinitely many quantities whose values converge, you get a finite quantity.

And I have no idea why everyone here is so sure that convergent infinite series resolve the paradoxes; they literally deal with the ambiguity and paradoxical nature of the fabric of space-time yet nobody addresses that?

Time is quantised, lads. And so is space.

en.wikipedia.org/wiki/Planck_time

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>But it is what you said, is it not?
no, I said "that gives you a finite quantity" which can happen when the series converges
I did not say that it always does, and I assume you know what I meant

Explain "the rows paradox" then.

you haven't even read that wiki article, brainlet

that's just a theoretical really short amount, beyond which our theories can't say much

The "rows paradox" is only a paradox if you buy the assumption that passing two Bs should take longer than passing one A. There's literally no reason to buy into this, because it doesn't make sense.

You're right, I haven't read the wiki article but I do have a degree in physics and I've studied quantum physics. It's all still up for debate, and obviously we can't (yet) know the exact Planck time.

However, for me, the discrete energy levels - proven beyond all reasonable doubt - in electron shells and the rest of it, down to quantum field theories, implies a fundamental discreteness of the very small.

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>implies a fundamental discreteness of the very small.
braindead statement

at the moment things imply that at very short distances spacetime is neither continuous nor discrete

>at the moment things imply that at very short distances spacetime is neither continuous nor discrete

What is it then? Because the only theory of physics that works at very short distances is quantum physics, and that gets shit done by "quantising" what classical physics assumed was purely continuous.

I'll even accept the answer "both" continuous and discrete but not "neither"

>a paradox isn't a paradox because it doesn't make sense to me

Btw, the exactness of the Planck scales, be they time or distance, is not important per se. I believe that everything is fundamentally quantized as well but you still run into problems if you describe nature in that way.

Imagine actually believing this

string theory suggests it

it seems your understanding of physics stopped at about 50 years ago

>Btw, the exactness of the Planck scales, be they time or distance, is not important per se
Yeah, fair enough.

>a paradox isn't a paradox because it doesn't make sense to me
Hey, Zeno wasn't some god who never made mistakes. He came up with some interesting and clever paradoxes that make you think. But the assumption Zeno makes in the rows paradox actually doesn't make sense.

See pic related. The Cs are moving faster relative to the Bs than the stationary As. How does Zeno's assumption that passing two Bs will take longer than passing one A seem like a reasonable thing to assume? It's a nonsensical assumption that's only made in order to set up the paradox.

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>string theory suggests it
Hoo boy, here we go.

String theory suggests what exactly?
What string theory are you talking about?
But it doesn't matter because no string theory is yet a proper scientific theory. Quantum physics, the quantised nature of the very small, has been proven in the lab. String theories have no experimental proof.

At this point it's just maths. Maths that could describe nature but also could be bullshit.

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tell me, what grand insight has Xeno's autism brought you? nothing

Reality is representation
Becoming is illusory
God isn't real

>Instants are part of time, and we can measure them with calculus.
Calculus is only articulation here, not refutation. It allows us to more clearly describe how we perceive something that doesn't make sense, but it is in no way negating Zeno's claims that it really doesn't make sense.

>if they seem not to budge, it's because you're pulling in the wrong direction.
basically what you're saying is "if Zeno's paradoxes seem not to budge, it's because you're not ignoring them properly!"

so Xeno is equivalent to taking a few doses of shrooms and fucking your brain up forever? got it

No because one comes from reason and the other doesn't. I never touched psychedelics in my life by the way.

how come you sound like your average stoner then

maybe it's just that all escapism leads down the same path

time is just a convenient concept used to measure motion. it doesn't exist

>time is just a convenient concept used to measure motion. it doesn't exist

If time doesn't exist why are you getting older?

motion is just a convenient concept to measure time, it doesn't exist

Did I trigger you in some way

it's almost as though the cells which make up my body interact with the environment

At any instant, in the thought experiment, all things are completely stopped but there is some vector which captures extra information and carries it to any next instant. As a result, space and time are worthless constructs of this simplified model.

>there is some vector which captures extra information and carries it to any next instant.

you are a worthless construct of your simplified brain

>it's almost as though the cells which make up my body interact with the environment
It's almost as if they interact with the environment over time, you mean

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time is defined by the interaction of matter, not the other way around, you blithering retard

go ahead and tell me how you would measure time in a vacuum, i'll wait

Gentlemen, this is temporality manifest. Te-ta and farewell.

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I'm so SO sorry but for me to explain how I'd do that would take time. That's something I don't have - according to you.

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glad you admitted you got owned and have no reply other than this mediocre attempt at wit

Nice attempt at a shit post.

So if nothing interacts, time doesn't flow, is what you're saying?

brainlet here. I think I got it.
What relativity presents to us that solves the Arrow, is Lorentz contraction.
This solves the Arrow because Zeno thinks, essentially, that there is nothing we can find IN the object that could determine whether or not it is in motion. He believes motion can only be determined with external references.
With Lorentz contraction, however, we can determine that an object at motion time is shorter along it's direction of motion.
> Anything occupying a place just its own size is at rest.
Objects in motion don't occupy a space their own size, if we define their size to be the space that they occupy at rest.

zeno's paradoxes are not meant to be solved by post Newtonian physics, or even Newtonian physics themselves

You can always shift to their frame of reference and they will always occupy the same space.

non-argument
If Zeno's god-observer can stop time, surely it can choose its frame of reference to be the most appropriate one for analysis.

Are you saying that different observers don't see the same physical phenomena? There is no such thing as a preferred frame of reference.

Idiot. All paradoxes are a misdirect. Consider Achilles and the Tortoise. We are given the speed of the tortoise in relationship to Achilles speed. When Achilles reaches the halfway point, the tortoise will have moved half that distance. This will happen again and again and again. But by highlighting this process, you have been tricked into looking at irrelevant points. Achilles does not slow down. He runs at a constant speed. Speed is measured by distance over time. That is what it is. When Zeno proposes that the tortoise has moved half the previous distance away from where Achilles now stands, he has tricked you by using a smaller section of time than he used in the "moment" before. A paradox is simply a chinese figner trap for the mind. You are pulling at the wrong pieces. If you take someone moving at a constant speed, and measure the distance traveled in increasingly shorter intervals, of course they will have traveled less than in the larger interval. Zeno's paradox does not reveal a flaw in our concept of either motion or time, but rather sets the mind to try and resolve a fractal equation.

The Achilles and Tortoise and The Dichotomy paradoxes can both be resolved by treating them as finite values obtained by infinite sums of ever decreasing values; The Arrow and The Rows lead to contradictory conclusions.

fuck off you sperg. What is touch if not the physical phenomenon we experience from our hands when they approach other material?

I've already resolved the arrow. He gives a definition for motion that requires the passage of time, and then asks you to consider an object, which he calls moving, without granting it a span of time. It is not a valid question. It is not that reality is unresolvable, but rather that illogical statements are illogical. The rows paradox is even more ridiculous. The bodies are granted a speed not in relationship to each other, but in relationship to the field. He then tries to say that the movement is impossible because their movement related to each other is not the same as their movement related to the field. Absolute absurdity.

What the fuck no.
>then asks you to consider an object, which he calls moving, without granting it a span of time
You do consider it in a span of time and you're left with the choice if that span of time is "now" (an infinitely small chunk of time) or a finite chunk; an interval if you will.

>The bodies are granted a speed not in relationship to each other, but in relationship to the field
What is this supposed to mean? They move at same velocities in opposite directions relative to an observer at rest.

You're calling them illogical and absurd yet you don't seem to understand them.

> Are you saying that different observers don't see the same physical phenomena?
clarify, please.
> There is no such thing as a preferred frame of reference.
the preferred, or most appropriate frame of reference to analyze a human arrow is rest with respect to the surface of the earth

Stop believing in time.

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Crash course in Relativity. Two postulates:
1) The laws of physics are the same in all inertial frames of reference.
2) The speed of light in vacuum has the same value in all inertial frames of reference.

In layman's terms, all observers must agree on what happens, whether they are stationary or riding a rocket going at near light speed. Hence, there is no preferred or "most appropriate" frame of reference to analyze the arrow - you specified the surface of the Earth. Why not the surface of the Moon? The center of the Milky Way?

because you can't measure the arrow and determine if it is Lorentz contracted if your measuring stick is also contracted by the same amount. is that right?

in either case, do you agree that, in this way, relativity solves Zeno's Arrow?

Why would the measuring stick be contracted?

imagine a universe in which all matter is perfectly static. how do you measure the passage of time? does such a concept even make sense in that scenario?