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File: zeno.png (88 KB, 1050x1050)
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Even today, is there really a satisfactory answer to Zeno's paradoxes?
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planck length is finite
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>>10376366
inb4 muh limits
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>>10376366
yes rtard math =\= reality
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>>10376366
There is no paradox. Even if a number has infinite digits past the decimal it has a finite upper bound. This is patently obvious if you actually watch a race between a runner and a tortoise.
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>>10376366
https://en.wikipedia.org/wiki/Convergent_series
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the infinite series converges to a point in time at which achilles is at the same position as the tortoise, at any time after this achilles is past the tortoise. The calculus is the resolution. The notion that infinite series may converge to finite values.
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>>10376366
https://en.wikipedia.org/wiki/Geometric_series
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>>10376366
Time and space are continua, so no.
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>>10376368
>t. physicslet
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>>10376366
limits
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>>10376368
doesn't help, Achilles would catch up
and then they would run at equal speed after that
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>>10376366
Watch any animation that shows a race, say on a video game. We know exactly why one object passes the other: the display is composed of finite units, and each object only moves a certain number of finite units each second. We know that these animations operate discretely, so the universe can also operate discretely. Why assume infinity exists and the world is continuous?
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If the turtle always move first and has space to keep moving, then the gladiator will never catch the turtle. But the turtle and the gladiator have to get smaller every time they move, if they don't get smaller every time they move, at some they will get in touch.....
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At some they will get in touch.....*
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At some point they will get in touch.....*X2
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>>10376366
>question of space and time itself, not about it
>>>/lit/
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>>10376375
Obviously. Are Zeno's paradoxes entirely mathematical in your view?
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>>10376366
The thing that's traveling faster is always covering more distance in the same timeframe as the slower thing.
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>>10376366
No because the idea of the closest real number to a given number doesn't make sense in the real number line.
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>>10376366
It shows that special relativity is not a physical construct, but a mathematical prerequisite for motion.

maybe.
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Easy. To go where you want, you just need to aim twice as far. On the first step you reach the halfway of that distance. Conveniently that just happened to be the place where you initially wanted. Thus, you can always cover any distance in one step.
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>>10377024
But the original dichotomy paradox was that you wouldn't be able to cover any distance because, to reach the halfway of that distance, you would first need to reach the halfway of that halfway, and to reach the halfway of that halfway, you would need to reach the halfway of the halfway of that halfway, and so on...
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>>10376366
Infinitely many values do not necessarily lead to infinite lengths. This has been proven several times. And in the real world, certain lengths do not make sense, such as any below the planck length.
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>>10377037
Well, in that case you have to start going backwards, taking the steps in opposite order. Formally you can do this, because a finite length divided into infinite segments stays the same, no matter the order of their summation.
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>>10376366
Try it in real life and see what happens
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>>10376366
It seems pretty obvious that they are both shrinking, explaining why every new step is less
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>>10376366
It's not a paradox to anyone who graduated middle school.
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>>10376454
>movies are discrete therefore the universe is
Your logic might be flawed
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>>10376481
get the fuck out /lit/ard
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If runner and turtle is a points, they'll met after infinite amount of time. If they are real, they'll touch at some definite moment, because one time when length between turtle and runner will be less than one runner step. For example, we have 1 step between turtle and runner, and next moment 1/10 of step between them, and runner easily reach the turtle.
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>>10377037
I don't get it. These distances are infinitely small so I can cover them in the single step. What's the point of this paradox? it's just so seperated from reality. is math retarded?
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>>10377558
The original point of zeno is that what ever makes things work the way they are it cant be motion. He just wanted to illustrate that motion as described doesnt fit what was observed. Tl dr zeno not a fan of physics
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>>10376366
All the questions that don't have answers aren't questions at all and just meaningless jumbo jumbo
t. Early Wittgenstein
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>>10377616
What an idiot.
Why would anyone quote a person like that?
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>>10377632
I'm not quoting you absolute total retard.
God, why is /sci/ so much dumber and oblivious than /lit/?
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I actually have a good argument why calculus and convergent series are not an explanation to zeros paradox but I'm on my phone so I cba
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>>10376366
Because some still talk about the infinite series's sum:

> However, none of the original ancient sources has Zeno discussing the sum of any infinite series. Simplicius has Zeno saying "it is impossible to traverse an infinite number of things in a finite time". This presents Zeno's problem not with finding the sum, but rather with finishing a task with an infinite number of steps: how can one ever get from A to B, if an infinite number of (non-instantaneous) events can be identified that need to precede the arrival at B, and one cannot reach even the beginning of a "last event"?[7][8][9][39]
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>>10376373
>inb4 muh solution
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Yes
[math]\sum_{n=1}^{\inf}\frac{1}{2^n}=1[/math]
This equal sign is *exact*
Naysayers are trolls or uneducated. Then again, this is a troll thread
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zenos paradox is about time, its not about length. the fact that the sum of the increments will never exceed the specified bounds is obvious and not at all a solution to the paradox
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>>10376419
Are you dense? The distance would get down to one planck length. Then Achillies continues to advance on the Tortoises position, due to his relative velocity. He cannot get any closer, so he is then 0 planck lengths behind the Tortoise, then 1 planck length ahead.
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>>10379278
Reminder there is no physical principle preventing the runner from being half a planck unit away
The answer is here
>>10379209
>>10379202
>>10376387
>>10376391
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>>10376366
Does this satisfy you?
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>>10376366
i dont really understand the problem. from how i see it achilles runs lets say 100m meters in 10 seconds. then the turtle runs 10m. by the time achilles got there the turtle ran 1m so achilles has to run 1m but that didnt take him the same amount of time as before. this is just time slowing down exponentially. it is every single point before achilles passes the turtle
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>>10379186
>Simplicius has Zeno saying "it is impossible to traverse an infinite number of things in a finite time".
This is false, as shown by the infinite sum.

>This presents Zeno's problem not with finding the sum, but rather with finishing a task with an infinite number of steps: how can one ever get from A to B, if an infinite number of (non-instantaneous) events can be identified that need to precede the arrival at B
Because infinite intervals doesn't mean infinite time.

Fucking retard.
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>>10379390
infinite sums are limits dipshit. it has nothing to do with an object occupying an infinite amount of unique locations, and therefore unique momments between a change in location. please kill yourself
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>>10379390
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>>10376366
yes the greek guy will never catch the turtle
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>>10379482
>infinite sums are limits dipshit.
And your point is?

>it has nothing to do with an object occupying an infinite amount of unique locations
Where did I say it did? The intervals between the points are what get summed, not the points themselves.

Fucking retard.
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In my grade 12 math textbook years ago, when they introduced this concept, someone had written in pencil 'fuck off'.

So I guess that's the best answer you're gonna get
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>>10376366
>>10376373
Explain how 1+1=2
Inb4 addition
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>>10379583
You have one carrot
Now I give you another (one) carrot
You now have two carrots.

we covered this in pre-school anon, how could you forget :(
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>>10379603
another = addition
fail
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>>10376366
Time is a constant
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>>10376366
Yes, we are completing a supertask
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>>10379607
This is just common sense, if we can't agree on the most basic and intuitive things, how can we agree on the complex and strange?
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>>10376366
yes. you can look at the time it takes him to run halfway to the tortoise.
you will see that it will take him half as long as it took him previously each time.
use existing limit evaluation techniques or invent them yourself to see that the limit for the time it takes him to reach the tortoise is finite, then ask the question "what if he runs for longer than this finite time?" and you will see that he does indeed pass the tortoise

>>10379619
pop-sci retard
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>>10379732
yes it's common sense.
as is OP's question solved with limits.
I think you misunderstood my post.
he says to solve the "paradox" without limits, and I say solve 1+1 without addition.
it's the same.
it's impossible.
and retarded.
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>>10379782
I did misunderstand, sorry senpai
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Zeno's paradox implies you can't complete an infinite number of tasks in a finite amount of time.
Time isn't discrete, so there's no reason why you can't.
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>>10380037
>time isn't discrete
Lol
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>>10376366
> the absolute brainlets IT saying "just watch a race dude!"
God having done a philosophy degree and a medicine one i hate STEM student retardation more than anything.
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>>10380217
Shouldn't you be finishing your application to McDonalds instead of shitposting on the internet?



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