/sci/ - Science & Math » Thread #12916753

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Anonymous Fri 02 Apr 18:21:58 2021 No.12916753 View Reply Original Report

Quoted By: >>12916758 >>12916805 >>12916806 >>12916962 >>12917143 >>12917171 >>12917359 >>12917654 >>12918036 >>12918516 >>12918722 >>12918814 >>12918907 >>12919537

What is the solution to Zeno's Paradox?
>Muh limits
This just opens up the question that is what is the difference between a single point and a continuum

Anonymous

Anonymous Fri 02 Apr 2021 18:22:54 No.12916755 Report

Quoted By: >>12916761

the solution is "infinite sums converge to finite values sometimes"

Anonymous

Anonymous Fri 02 Apr 2021 18:23:44 No.12916758 Report

Quoted By:

>>12916753
To silently stand, and walk.

Anonymous

Anonymous Fri 02 Apr 2021 18:24:03 No.12916761 Report

Quoted By: >>12916773 >>12916799 >>12916811

>>12916755
>infinite sums converge to finite values sometimes
This is a premise of the problem, not the solution.

Anonymous

Anonymous Fri 02 Apr 2021 18:26:17 No.12916773 Report

Quoted By: >>12916782

>>12916761
then what's the problem? there is a rigorous definition for the convergence of sequences. ?(1/n^2) can be shown to converge.
>hurr but whyyyy
not math or science

Anonymous

Anonymous Fri 02 Apr 2021 18:28:19 No.12916782 Report

Quoted By:

>>12916773
***** ?(1/2^n)

Anonymous

Anonymous Fri 02 Apr 2021 18:32:09 No.12916799 Report

Quoted By:

>>12916761
Not him, but you need to start by stating what problem you're trying to solve, and what is preventing you from solving your problem. A simple, preliminary statement is fine.

Anonymous

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Anonymous Fri 02 Apr 2021 18:33:23 No.12916805 Report

Quoted By: >>12916967

>>12916753
What part of "incommensurable" do you not understand? To the sea we shall cast you into again?

Anonymous

Anonymous Fri 02 Apr 2021 18:33:30 No.12916806 Report

Quoted By: >>12916935

>>12916753
>This just opens up the question that is what is the difference between a single point and a continuum
There are no continuum (one thing) and no single points (many one things).

The problem keeps coming up in various interesting forms. For example the idea of "non dual" philosophy in Buddhism deals with this. We know about monism (continuum) and dualism (many one things) but there's also nondualism from buddhism (not one, not two, and not zero)

Anonymous

Anonymous Fri 02 Apr 2021 18:35:26 No.12916811 Report

Quoted By: >>12917790

>>12916761
>YEAH BUT WHY???????

El Cabrón

El Cabrón Fri 02 Apr 2021 19:18:45 No.12916935 Report

Quoted By: >>12917755

>>12916806
Buddhism in the west is entirely soÿboy cope for having zero culture and hating their parents. Go stick your yoni egg up your surgical created vagina and dial 8

Anonymous

Anonymous Fri 02 Apr 2021 19:25:56 No.12916962 Report

Quoted By:

>>12916753
>What is the solution to Zeno's Paradox?
Calculus

Anonymous

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Anonymous Fri 02 Apr 2021 19:26:18 No.12916965 Report

Quoted By:

Anonymous

Anonymous Fri 02 Apr 2021 19:26:59 No.12916967 Report

Quoted By: >>12917870

>>12916805
>What part of "incommensurable" do you not understand?
Ashamed to admit I had to google the definition

Anonymous

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Anonymous Fri 02 Apr 2021 20:00:20 No.12917115 Report

Quoted By: >>12917143

zeno's paradox, as it is presented, ignores the passage of time. remember that moving half the distance takes half the time, which is why it is deceptive.

if you keep moving at a constant rate
and one unit of time elapses
then you will have moved one unit of distance

Anonymous

Anonymous Fri 02 Apr 2021 20:05:08 No.12917143 Report

Quoted By:

>>12916753
It was used to demonstrate the impossibility of change. The atomists came up with their theories in response, Aristotle said this >>12917115 , and Epicureans similarly used an improved Atomist theory, one that placed emphasis on the existence of void (most people thought the existence of void in the air was ridiculous)

Anonymous

Anonymous Fri 02 Apr 2021 20:10:26 No.12917171 Report

Quoted By:

>>12916753
Well matter cannot be divided infinitely but numbers can. So that's all. It's a fun paradox.

Anonymous

Anonymous Fri 02 Apr 2021 20:51:53 No.12917359 Report

Quoted By:

>>12916753
Math is just an abstraction that doesn't necessarily correspond to anything in the real world

Anonymous

Anonymous Fri 02 Apr 2021 22:02:14 No.12917654 Report

Quoted By:

>>12916753
>What is the solution to Zeno's Paradox?
In math, limits
In reality, quantization

Anonymous

Anonymous Fri 02 Apr 2021 22:26:52 No.12917755 Report

Quoted By: >>12917870

>>12916935
This says more about you than it says about buddhism, retard.

Anonymous

Anonymous Fri 02 Apr 2021 22:35:08 No.12917790 Report

Quoted By: >>12918966

>>12916811
If you can’t answer why, you have dogma, not truth.

Anonymous

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Anonymous Fri 02 Apr 2021 22:56:00 No.12917870 Report

Quoted By: >>12917897

>>12917755
Buddhism is nihilism lite. Saying anything at all would be saying more than it does. That's why they tell you to "meditate(translation: Do fucking nothing)" so much. There is no original Buddhist doctrine that denies the existence of "soul".

>>12916967
At least you're not scared of it like a mathematician is.

Anonymous

Anonymous Fri 02 Apr 2021 23:06:53 No.12917897 Report

Quoted By: >>12917931 >>12918423

>>12917870
>Buddhism is nihilism lite.
No, nihilism has nothing to do with buddhism. Nihilism is the statement that nothing matters. Buddhism is the statement that everything matters. I’m neither, but how can you possibly confuse those two things?

Anonymous

Anonymous Fri 02 Apr 2021 23:18:47 No.12917931 Report

Quoted By: >>12917977 >>12918423

>>12917897
Buddhism is nihilistic. A Theravada monk told me that outright. Nihilistic in the sense of “nothing exists”. This world is an illusion of maya.

Anonymous

Anonymous Fri 02 Apr 2021 23:27:45 No.12917977 Report

Quoted By:

>>12917931
>Theravada
Which country were you in, and why would you confuse localism with globalism? It sounds like you were annoying and got trolled to leave.

Anonymous

Anonymous Fri 02 Apr 2021 23:39:40 No.12918036 Report

Quoted By:

>>12916753
Rejection of the paradox

Anonymous

Anonymous Sat 03 Apr 2021 01:11:33 No.12918423 Report

Quoted By: >>12918555

>>12917897
>No, nihilism has nothing to do with buddhism
I don't even know what buddhism has to do with anything since none of what they preach is actually in doctrine, namely the whole "there is no soul".

>Buddhism is the statement that everything matters
Lolno

>I’m neither, but how can you possibly confuse those two things?
>how can a religion rely so heavily on dualism.
Easy, that's what all "religion" relies on. Buddhism is nihilistic in that they do not believe in soul, yet they don't actually know what to believe in so they believe in nothing. Atheists who practice the gestures of a religion because surprisingly enough believing in nothing leaves you in complete privation. They fill their proverbial "holes" with Himalayan salt lamps and yoga mats and pretend like they're accomplishing something by role-playing a house plant.

>>12917931
>A Theravada monk
A beggar in an orange robe preaching doctrine that doesn't exist.

Anonymous

Anonymous Sat 03 Apr 2021 01:38:54 No.12918516 Report

Quoted By:

>>12916753
Infinite intervals doesn't mean infinite distance

Anonymous

Anonymous Sat 03 Apr 2021 01:40:12 No.12918519 Report

Quoted By:

It's a super task basically

Anonymous

Anonymous Sat 03 Apr 2021 01:53:22 No.12918555 Report

Quoted By: >>12918782

>>12918423
>Atheists who practice the gestures of a religion
Sounds like you’re describing atheists, not buddhists. Lol.

Anonymous

Anonymous Sat 03 Apr 2021 02:42:36 No.12918722 Report

Quoted By:

>>12916753
There is no paradox, infinite series can have finite sums. Also, infinite subdivision of space might not even make sense physically, depending on the fundamental nature of physics.

Anonymous

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Anonymous Sat 03 Apr 2021 03:11:13 No.12918782 Report

Quoted By: >>12918791

>>12918555
>Sounds like you’re describing atheists, not buddhists.
If what I described isn't a distinction without a difference, then differentiate the two.

Anonymous

Anonymous Sat 03 Apr 2021 03:13:38 No.12918788 Report

Quoted By: >>12918793 >>12918858

limits dont even solve this, I don't know why people keep bringing it up
limits are a patch job for mathematics, a 'close enough' they break down when you are not ignoring the close enough

Anonymous

Anonymous Sat 03 Apr 2021 03:14:53 No.12918791 Report

Quoted By: >>12918799

>>12918782
I’m not a buddhist, I wouldn’t know. Your description sounds like bullshit, though. I’d bet against it.

Anonymous

Anonymous Sat 03 Apr 2021 03:15:11 No.12918793 Report

Quoted By: >>12918868

>>12918788
The convergence of infinite series IS the solution to this however, and convergence is formally defined by a limiting process. You're wrong.

Anonymous

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Anonymous Sat 03 Apr 2021 03:17:54 No.12918799 Report

Quoted By: >>12918904

>>12918791
>Your description sounds like bullshit, though
I have described Atheism and Buddhism.
>I’d bet against it.
How about "explain the difference" like I suggested?

Anonymous

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Anonymous Sat 03 Apr 2021 03:23:25 No.12918814 Report

Quoted By: >>12918819 >>12918828

>>12916753
You need to specify what you mean by solution

>Assuming you want to know who gets there first
Since it's an iterative process they both get there at the same time, one sequence just converges faster than the other. This, however does not imply that one will get there before the other becuse the sum is bounded, please review your real analysis notes.
>Assuming you're asking if they'll even get to the end
That depends on what the relationship between the time each step takes and the indexing of your iterations, if the time it takes is inversely proportional to the index then the answer is yes, assuming you believe in the completed infinite axiom (I'm looking at you, finitists).

Anonymous

Anonymous Sat 03 Apr 2021 03:25:11 No.12918819 Report

Quoted By:

>>12918814
Even Norman believes in the geometric series though

Anonymous

Anonymous Sat 03 Apr 2021 03:26:16 No.12918828 Report

Quoted By: >>12918864

>>12918814
doubting the convergence of 1/2^n makes you look extremely dumb, just so you know

Anonymous

Anonymous Sat 03 Apr 2021 03:34:20 No.12918858 Report

Quoted By: >>12918861

>>12918788
Are infinite series infinite if you zoom out or zoom in enough? From a macro perspective some problems don't have a solution unless you look at them microscopically or extra-macroscopic ally? Can the same solution apply to limits? I get that natural numbers and what not are what get you where we are now, but surely there's someway to look at it that doesn't result in a seemingly endless answer.

Anonymous

Anonymous Sat 03 Apr 2021 03:35:48 No.12918861 Report

Quoted By:

>>12918858
You should take the time and study calculus. Not only does it answer all the questions you just asked and give a comprehensive solution to OP, but it isn't that hard.

Anonymous

Anonymous Sat 03 Apr 2021 03:36:26 No.12918864 Report

Quoted By: >>12918875 >>12918979

>>12918828
I don't doubt of it's convergence, I just point this out because even if it converges, not a single member of the sequence is 0 so there might be some debate on whether or not there is a step that takes you to the end of the line.

Anonymous

Anonymous Sat 03 Apr 2021 03:38:25 No.12918868 Report

Quoted By: >>12918873 >>12918875

>>12918793
I don't see how it could work in a universe with infinite divisibility. You would have an infinitely small remainder. I know the mathematics of p-series convergence, but I don't see how that could work outside of equating infinitely small with zero.

Anonymous

Anonymous Sat 03 Apr 2021 03:40:45 No.12918873 Report

Quoted By:

>>12918868
Any number that's greater than or equal to zero and that's smaller than any positive number is zero. Once again, you need to review your analisis notes if you have them.

Anonymous

Anonymous Sat 03 Apr 2021 03:41:44 No.12918875 Report

Quoted By: >>12918890

>>12918864
>not a single member of the sequence is 0 so there might be some debate on whether or not there is a step that takes you to the end of the line.
I don't follow
>>12918868
Math is math. It is about abstractions not the literal universe we live in. In real life, there are atoms and quantization of momentum and all that shit but it really isn't necessary to explain Zeno because basic calculus already does a fantastic job.

Anonymous

Anonymous Sat 03 Apr 2021 03:49:33 No.12918890 Report

Quoted By: >>12918915

>>12918875
>I don't follow
The sequence converges even though none of it's members is the one who take the final step, this doesn't affect the understanding of the convergent series but it doesn't imply that you actually get there because 0 isn't a member of 1/2^n, for that to be the case, you need to assume that you can take an infinite amount of steps and then stop.

Anonymous

Anonymous Sat 03 Apr 2021 03:54:19 No.12918904 Report

Quoted By:

>>12918799
Sounds like you did a pretty shitty job, because you described them as the same thing. I’m still betting against your description.

Anonymous

Anonymous Sat 03 Apr 2021 03:56:44 No.12918907 Report

Quoted By:

>>12916753
>What is the solution to Zeno's Paradox?
Unironically God

Anonymous

Anonymous Sat 03 Apr 2021 03:58:57 No.12918915 Report

Quoted By: >>12918923

>>12918890
>The sequence converges even though none of it's members is the one who take the final step
There is no final step. This is obvious and also the whole point of developing a rigorous notion of "convergence" in the first place. A series $S$ converges to a value $L$ if and only if for any small $\epsilon>0$ there is an associated natural number $<br />N$ such that the difference between $L$ and the n'th partial sum for any $n>N$ satisfy $|S_n-L|<\epsilon$ . This is the literal, unambiguous meaning of convergence for an infinite series. $\Sigma_{n=1}^{\infty} 2^{-n}=1$ definitively and absolutely. There's no debate whatsoever.

Anonymous

Anonymous Sat 03 Apr 2021 04:02:25 No.12918923 Report

Quoted By: >>12918930

>>12918915
I'm not debating about the convergence, Zeno's paradox asks about if the person will get there via steps, that's where the debate lies in because, just as you said, there isn't a final step

Anonymous

Anonymous Sat 03 Apr 2021 04:04:55 No.12918930 Report

Quoted By: >>12918937

>>12918923
Right, there's no final step, so person must take an infinite number of steps to get there. Fortunately it's possible that an infinite number of chunks of time can sum to a finite value. The paradox is solved.

Anonymous

Anonymous Sat 03 Apr 2021 04:07:23 No.12918937 Report

Quoted By: >>12918941

>>12918930
Only if time is infinite or continuous

Anonymous

Anonymous Sat 03 Apr 2021 04:08:45 No.12918941 Report

Quoted By: >>12918968

>>12918937
sure. and it is continuous in basically every physical theory as far as I know.

Anonymous

Anonymous Sat 03 Apr 2021 04:23:36 No.12918966 Report

Quoted By:

>>12917790
Why?

Anonymous

Anonymous Sat 03 Apr 2021 04:24:18 No.12918968 Report

Quoted By:

>>12918941
To be fair, time sufficiently small discrete chunks of time stacked together are almost indistinguishable from continuous time

Anonymous

Anonymous Sat 03 Apr 2021 04:30:41 No.12918979 Report

Quoted By: >>12919014

>>12918864
>there might be some debate on whether or not there is a step that takes you to the end of the line.
There is no debate, there is no last step. You teach the end of the line after infinite steps in finite time.

Anonymous

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Anonymous Sat 03 Apr 2021 04:47:47 No.12919014 Report

Quoted By:

>>12918979
You came late to the party anon, I am now vigorously beating my throbbing cock to Helen from The Incredibles pinups.

Anonymous

Anonymous Sat 03 Apr 2021 09:05:18 No.12919537 Report

Quoted By:

>>12916753
>What is the solution to Zeno's Paradox?
Philosophy is stupid and inapplicable to reality.

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