How has Xenon's paradox been solved?

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Anonymous Tue Jul 28 00:35:08 2020 No.15980393 [Reply] [Original]

How has Xenon's paradox been solved?

>>	Anonymous Tue Jul 28 00:35:38 2020 No.15980397 >>15980393 yes

>>	Anonymous Tue Jul 28 00:35:54 2020 No.15980400 which one?

>>	Anonymous Tue Jul 28 00:36:09 2020 No.15980404 >>15980393 Sorry about the name, it's zeno's paradox. Sorry for being a brainlet

>>	Anonymous Tue Jul 28 00:37:55 2020 No.15980414 >>15980400 I'm most curious about Achilles's. Arrow too.

>>	Anonymous Tue Jul 28 00:38:20 2020 No.15980420 >>15980393 yes its called the planck length

>>	Anonymous Tue Jul 28 00:38:58 2020 No.15980424 >>15980393 It's been "solved" notionally via mathematics. But not yet in the physical world since we don't even know if the world is ultimately discrete or continuous. It seems to be continuous, but until we have a complete ToE, we can't be certain.

>>	Anonymous Tue Jul 28 00:40:31 2020 No.15980436 >>15980420 The Planck length plays no special role in the structure of space or spacetime.

Anonymous Tue Jul 28 00:40:57 2020 No.15980438

>>15980393
>>15980424
>It's been "solved" notionally via mathematics. But not yet in the physical world since we don't even know if the world is ultimately discrete or continuous. It seems to be continuous, but until we have a complete ToE, we can't be certain.
So we can safely say it only mattered for Greeks who viewed being under such a projected and mythological way?

>>	Anonymous Tue Jul 28 00:41:17 2020 No.15980444 >>15980436 LOL

>>	Anonymous Tue Jul 28 00:41:41 2020 No.15980445 approaching something infinitely is the same as having arrived

>>	Anonymous Tue Jul 28 00:42:30 2020 No.15980454 >>15980393 Yes, they're called supertasks.

>>	Anonymous Tue Jul 28 00:43:12 2020 No.15980460 >>15980424 What if somebody proved world cannot be discrete? I'm saying about Hermann Weyl's tile argument. https://en.m.wikipedia.org/wiki/Weyl%27s_tile_argument

Anonymous Tue Jul 28 00:44:56 2020 No.15980473

>>15980436
It's the smallest possible length that (we know of) where physics (as we know) applies.

Even if the length itself is not exact- that is not what is relevant.

What IS relevant is that it suggests that the universe at some fundamental point is made up of a finite "unit" that we cannot divide any smaller.

Hence why you can walk 10 meters- and not just 9.9m , 9.99m 9.999m infinitely.

>>	Anonymous Tue Jul 28 00:49:06 2020 No.15980516 >>15980473 Just stop. You have no idea what you're talking about.

>>	Anonymous Tue Jul 28 00:50:50 2020 No.15980527 >>15980473 9.9999... = 10 though

Anonymous Tue Jul 28 00:53:12 2020 No.15980543

>>15980393
It's a retarded proposition to begin with
rhetoricfags are midwits. there's no reason for the negative acceleration to begin with. YOU make up a situation that is implausible to begin with and then YOU jack yourself off about how it's a "paradox." It isn't a paradox, you are just an attention whoring tard who doesn't have anything better to do.

Fuck you all.

>>	Anonymous Tue Jul 28 00:54:16 2020 No.15980552 >>15980473 >It's the smallest possible length that (we know of) where physics (as we know) applies. wrong

>>	Anonymous Tue Jul 28 00:56:23 2020 No.15980570 >>15980393 Yes. Achilles only needs to set his end point as beyond the tortoise. If he sets it as twice as far as where the tortoise is, he'll meet up with the tortoise about halfway there.

Anonymous Tue Jul 28 00:57:20 2020 No.15980579

the paradox is happens because you assume that space = space, but we talk about space as continuous, and space as made up of discontinuous zones, like the squares of a chessboard. the question is asking, when things move do they really move continuously or do they really move discontinuously?

the meat of the question "when will hercules overcome the tortoise" can be restated as
>when will an object moving continuously at a fixed speed be overtaken by an object moving in discontinuous "jumps," if the distance covered by each jump gets smaller and smaller (infinitesimal) as it approaches the continuously moving object?

it's similar to the problem of squaring the circle. keep increasing the number of sides that a polygon inside a circle possesses. when does it become the same as the circle?

it's also similar to asking, how many times can you divide a line? for a cartesian or mathematician a line is merely abstract, the whole point of a line is that it is infinitely divisible, there is ALWAYS another point between any two points you define, no matter how small. but for a physicist who believes in empirically real smallest possible lengths, the answer might be different.

calculus isn't a real solution to the problem, it's just avoiding it by applying a specific metaphysics to the situation. it's also not quite right to say that it's an empirical problem which we can answer better today (or will be able to answer someday) when we know whether space is REALLY discrete or continuous, whatever that might ultimately mean. that's obviously interesting too, but the point of zeno's paradox is primarily to contrast the CONCEPTUAL difference between continuous and discontinuous movement, and that ultimately we have to pick between the two. we have to say either "movement is really discontinuous, and continuous sliding movement is only an illusion, made up of very very tiny discontinuous movements" or "movement is really continuous, and discontinuous movement is only an illusion based on our limited ability to perceive the continuity of motion in some cases"

because we apply both discontinuous and continuous conceptions to the idea/visualizing of "space" by reflex, it trips us up. we reflexively want both to be true, but they clearly don't play nice with eachother in instances like this, where we're forced to see them both seemingly interacting at the same time.

zeno's motivation for doing this was to show that we can't conceive of movement without invoking paradox, therefore, movement (and by extension change) is illusory, and the true nature of reality is non-change, or permanence. he was an adherent of parmenides school. this seemed compelling for him and parmenides other students because they had a hard time separating thoughts about the world with thoughts about our thoughts about the world. they thought that our thinking was an accurate mirror of reality, so paradoxes in our thinking pointed to paradoxes in reality.

Anonymous Tue Jul 28 00:57:50 2020 No.15980584

>>15980393
Zeno's paradox's are built on exploiting the vagueness of "infinity" and are mainly built to point out that those who criticized the Monists were just as ridiculous as they claimed the Monists were.

In this example, Zeno says Achilles can never pass the turtle because he has to reach the turtle to pass it, but the turtle will have moved. He's conflating infinite approachability (i.e., a limit) with infinite magnitude. It's impossible to finitely approach an object without changing your state. If your velocity is faster than the object, you can approach it but you can only become infinitely closer, you cannot occupy its space. If your velocity is the same or slower, you simply cannot reach it ever, regardless. You can only reach an object in a finite sense (you reach a point where your distance is 0 and you can't approach any closer) if you occupy the same space, which is impossible if reality is composed of separate things. We know this is true, because reality IS composed of separate things, and you cannot occupy the space taken up by something else, though you can approach it almost infinitely and there's some wackiness involved at certain levels that's not worth getting into here.

But the problem with it is that in the sense that it's a race Achilles' goal isn't to infinitely approach the turtle, it is to come within a certain distance of the goal sooner than the turtle, so Achilles does not have to infinitely approach the turtle, he infinitely approaches the goal with a fixed point at which it rounds to a distance of 0. Since this can then be measured a function analogous to distance/rate = time-to-complete, Zeno is wrong, and Achilles can still win the race.

>>	Anonymous Tue Jul 28 01:00:24 2020 No.15980602 AH ok genius then please explain how an infinite cycle process is completed in finite time.

>>	Anonymous Tue Jul 28 01:01:55 2020 No.15980610 >>15980527 10 - 0.0...1

>>	Anonymous Tue Jul 28 01:04:05 2020 No.15980626 >>15980610 Its been proven that 10-.0...1 is equal to 10

>>	Anonymous Tue Jul 28 01:04:19 2020 No.15980627 >>15980527 In mathematics yes- In the real world no- thats the entire point of the paradox. You are completing an infinite sequence in a finite amount of time- this is the TRUE paradox.

>>	Anonymous Tue Jul 28 01:07:02 2020 No.15980640 >>15980627 In math and the real world. There is nothing between 0.999... and 1, they are the same thing. An infinite approach is the same as being there.

Anonymous Tue Jul 28 01:09:53 2020 No.15980661

>>15980393
Technically I think mathfags have "solved" it. He may still be correct in reality though, either way its fun to think about. All of Zeno's paradox are kind of the same idea once you filter them down. I have some notes I wrote myself when I was reading about the monists.

In order for something to change, there must be a halfway point, then another, and so on
For every infinite half step taken, there must be a thing(s) there to note it's change <-key idea
Thus the principle must be infinitely divisible and numerous
~~~Think of a fire turning wood to ash, at every infinite halfstep a change must be occurring, thus there must be infinite things as well to change into~~~~~~~~
~~~A helpful idea is thinking in terms of pixels or a flipbook
So say it is infinitely divisible
If when divided it has no magnitude, then neither does the whole object have magnitude. (0+0=0)
If it continues to have a magnitude, then the object will become infinitely large

>>	Anonymous Tue Jul 28 01:09:57 2020 No.15980662 File: 379 KB, 500x213, 1516346532213.gif [View same] [iqdb] [saucenao] [google] >>15980584 >at which it rounds to a distance of 0 oof

>>	Anonymous Tue Jul 28 01:10:07 2020 No.15980665 >>15980626 Just stated

>>	Anonymous Tue Jul 28 01:11:16 2020 No.15980675 >>15980640 >There is nothing between 0.999... and 1, they are the same thing. Within the ontology of calculus, sure. But that ontology was made up for practical reasons and it has its limitations. It's not metaphysically true.

>>	Anonymous Tue Jul 28 01:12:38 2020 No.15980683 >>15980640 >There is nothing between 0.999... and 1, they are the same thing. More like you can name them the same (especially if you use your theories in real world where both 0.999... and 1.000... are unnecessarily precise).

Anonymous Tue Jul 28 01:16:51 2020 No.15980707

>>15980640
No its not that's the entire point of the paradox.

In a mathematics sequence this is true: infinite sequence approaching 1 = 1.

The the problem is, in the real world, you start at 0 and then approach 1 infinitely getting closer. This, if time is not defined, logically takes an infinite amount of time.

If you define time to it- which you can do- it then takes a finite time to complete the infinite sequence. This is the entire paradox.

How can a real world person- move 1 meter in 2 seconds (or whatever) - if moving that 1 meter is an infinite sequence? How is a infinite sequence being completed in a finite amount of time?

Thats the part of the paradox that hasn't been fully worked out yet.

>>	Anonymous Tue Jul 28 01:24:53 2020 No.15980743 >Iron age retards didn't understand limits Why do you keep wasting time on the Greeks?

>>	Anonymous Tue Jul 28 01:25:04 2020 No.15980745 >>15980707 If space is continuous, there is no "sequence". If space is discrete, then it is not infinitely divisible. Either way, there is no "paradox".

>>	Anonymous Tue Jul 28 01:26:09 2020 No.15980752 >>15980640 >There is nothing between 0.999... and 1 what is there between 0.999...8 and 1?

>>	Anonymous Tue Jul 28 01:26:55 2020 No.15980758 >>15980743 >we'll try to sidestep the problem and then claim that we have solved it

>>	Anonymous Tue Jul 28 01:27:58 2020 No.15980765 >>15980752 0.999...9 of course.

>>	Anonymous Tue Jul 28 01:28:22 2020 No.15980767 >>15980473 Why don’t I just cut it in half with me plank knife lmao

>>	Anonymous Tue Jul 28 01:29:01 2020 No.15980772 >>15980745 >If space is continuous, there is no "sequence". Does not follow.

>>	Anonymous Tue Jul 28 01:30:21 2020 No.15980780 >>15980765 and what is there between 0.999...8 and 0.999...?

>>	Anonymous Tue Jul 28 01:30:41 2020 No.15980784 >>15980780 0.999...85

>>	Anonymous Tue Jul 28 01:33:51 2020 No.15980809 >>15980784 and what is there between 0.999...8999... and 0.999...?

>>	Anonymous Tue Jul 28 01:34:00 2020 No.15980810 >>15980772 Yes, it does. Continuous sets (like the Real numbers) cannot be put into one-to-one correspondence with the natural numbers. I.e., they are uncountable. https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

>>	Anonymous Tue Jul 28 01:35:16 2020 No.15980819 >>15980809 0.999...8999...8

>>	Anonymous Tue Jul 28 01:36:19 2020 No.15980825 >>15980810 A subset of them can be countable though.

>>	Anonymous Tue Jul 28 01:37:06 2020 No.15980828 >>15980745 For the record- I agree with you. The universe seems most likely to be not infinitely divisible. Thus units like Planck length arising. Its more of a mathematical curiosity than a real "physics paradox"

>>	Anonymous Tue Jul 28 01:37:11 2020 No.15980829 >>15980819 0.999...8999...8 is less than 0.999...8999... is it not?

Anonymous Tue Jul 28 01:44:47 2020 No.15980870

>>15980825
You can't have a sequence unless every object has a unique successor. The Natural numbers qualify, but real numbers do not. If, as is assumed in current physics, space is a Continuum (= having the cardinality of the Real numbers), then it cannot be a sequence.

>>	Anonymous Tue Jul 28 01:45:45 2020 No.15980880 >>15980829 What about 0.999...999...5?

>>	Anonymous Tue Jul 28 01:46:00 2020 No.15980883 >>15980828 >Thus units like Planck length arising. The role of the Planck length in physics implies nothing about the continuity or discreteness of space.

>>	Anonymous Tue Jul 28 01:46:55 2020 No.15980891 >>15980870 You can have a sequence of real numbers. 1/2, 3/4, 7/8 and so on.

>>	Anonymous Tue Jul 28 01:49:20 2020 No.15980912 >>15980891 Those are rational numbers, and no, 3/4 isn't the unique successor of 1/2.

>>	Anonymous Tue Jul 28 01:51:08 2020 No.15980926 >>15980912 Rational numbers are a subset of real numbers, and Zeno's paradox does not imply uniqueness.

>>	Anonymous Tue Jul 28 01:53:17 2020 No.15980942 >>15980926 {} is also a subset of real numbers. What does that have to do with anything? And Zeno's paradox does require a uniquely ordered sequence.

>>	Anonymous Tue Jul 28 01:54:15 2020 No.15980947 who would've thought /sci/'s inability to realize that the planck length is not a "fundamental discrete length" would bleed into /lit/

>>	Anonymous Tue Jul 28 01:54:45 2020 No.15980953 >>15980942 That "those are rational numbers" does not contradict "those are real numbers". >And Zeno's paradox does require a uniquely ordered sequence. Where does Achilles mention uniqueness?

>>	Anonymous Tue Jul 28 01:58:11 2020 No.15980969 >>15980947 What is better: planck-length cube or planck-length sphere?

>>	Anonymous Tue Jul 28 01:59:51 2020 No.15980976 >>15980969 we're living in a planck-honeycomb universe, baby!

>>	Anonymous Tue Jul 28 02:03:20 2020 No.15980997 >>15980953 Because for any two points in the race, there is no ambiguity about which is closer to the finish line.

>>	Anonymous Tue Jul 28 02:06:08 2020 No.15981014 >>15980997 Yes, Achilles runs half of the way to the tortoise, then 3/4, then 7/8 and so on. Every member is larger than the previous and they form a sequence.

>>	Anonymous Tue Jul 28 02:09:43 2020 No.15981035 >>15981014 There is no way to order the rationals in increasing or decreasing order. Hence they cannot form an increasing or decreasing sequence.

>>	Anonymous Tue Jul 28 02:11:25 2020 No.15981048 >>15981035 1/2, 3/4, 7/8, ... is clearly an increasing sequence.

Anonymous Tue Jul 28 02:13:27 2020 No.15981061

>>15980393
How is this a paradox? Assuming both creatures move at a constant velocity, the closer they approach the goal, the quicker each fractional distance is traversed. Thus, as the next distance approaches an infinitesimal value, so too will the time taken. It doesnt matter how many times you divide the distance, as it will take a proportionally less time to traverse.

>>	Anonymous Tue Jul 28 02:14:50 2020 No.15981076 Zeno died in the best way.

>>	Anonymous Tue Jul 28 02:16:41 2020 No.15981086 >>15981061 I suppose the problem is, even if the time it takes shortens relative to the distance, it’s still infinite distance so technically your journey should not end.

>>	Anonymous Tue Jul 28 02:21:28 2020 No.15981118 >>15981048 So is 1/2, 5/8, 3/4,... What's your point?

Anonymous Tue Jul 28 02:21:35 2020 No.15981120

>>15981086
Wouldn't adding all those fractional distances equal the length of the line (distance required to overtake the tortoise)? Even if you keep adding the infinite number of fractions they are getting progressively smaller so would never amount to infinity as a whole.

>>	Anonymous Tue Jul 28 02:23:28 2020 No.15981125 >>15981118 Yes, this is an increasing sequence too. But we were talking about Zeno's paradoxes, right? So what is your point?

>>	Anonymous Tue Jul 28 02:25:58 2020 No.15981135 >>15980393 Make a turtle and a man race. Assuming both follow the course, man will always win. The issue here is that of language and not of physics.

>>	Anonymous Tue Jul 28 02:27:44 2020 No.15981145 >>15980516 Add your own point then retard

Anonymous Tue Jul 28 02:27:56 2020 No.15981147

>>15981120
Yes if you add those fractions you get the line but I suppose the issue is that, according to the paradox, you can infinitely divide a finite distance. This creates a conceptual issue, not really a practical one, in that an infinite should have no end (even if they are increasingly smaller units, they’re still infinite) and yet you are able to get from point A to B in reality.

>>	Anonymous Tue Jul 28 02:29:25 2020 No.15981152 >>15981135 The man lost the moment he accepted the challenge because he degraded himself.

>>	Anonymous Tue Jul 28 02:30:07 2020 No.15981154 >>15981152 Maybe it was a big turtle.

>>	Anonymous Tue Jul 28 02:30:38 2020 No.15981158 >>15981135 Joke's on you, a turtle defeated me in a race, mocked me until I cried and then snatched my girlfriend.

>>	Anonymous Tue Jul 28 02:34:32 2020 No.15981170 >>15981125 Sorry, I'm lost. Can you explain where you're having trouble? Is it in the distinction between convergent and divergent series?

Anonymous Tue Jul 28 02:38:37 2020 No.15981185

>>15981170
In >>15980745 you wrote
>If space is continuous, there is no "sequence".
Zeno's paradox shows that Achilles way to the tortoise includes at least one infinite sequence. It doesn't matter that you can show a different sequence, or that space may be about rational, real or surreal numbers - they still will have sequences as a subset.

Anonymous Tue Jul 28 02:43:05 2020 No.15981221

>>15981147
Gotcha. Thanks for clarifying. I had to kinda look at it in reverse to understand it:

Suppose you can traverse 1m in 1s. As we know, as the number of fractions increases, the fractional distance and time taken will approach 0. Now suppose that you CAN split the 1m into infinite fractions.This would mean that each fraction would be 0m, and would take no time to traverse (0s). Does this mean that the 1m = 0m? Furthermore, does this mean that you can traverse the entire 1m distance instantly?

My conclusion is that you cannot divide a finite distance into an infinite number of fractions.

Anonymous Tue Jul 28 02:46:10 2020 No.15981236

>>15980473
Space is not physics, Physics takes place on spacetime, but space is ontologically infinitely divisible, even if you can't measure division beyond the Planck length, this doesn't prevent you from just saying a shorter length, it's not imaginary just inapplicable.

>>	Anonymous Tue Jul 28 02:47:15 2020 No.15981242 >>15980393 plank length

>>	Anonymous Tue Jul 28 02:49:04 2020 No.15981247 >>15981242 Planck length turtle?

>>	Anonymous Tue Jul 28 02:49:06 2020 No.15981248 didnt aristotle btfo him by just saying "thats not how it works bro"?

>>	Anonymous Tue Jul 28 02:50:05 2020 No.15981253 >>15980745 >If space is continuous, there is no "sequence". This is the whole point of Zeno's argument, to prove Parmenides' Monism. Most people keep forgetting that paradoxes are meant to fall apart to prove monism.

>>	Anonymous Tue Jul 28 02:50:11 2020 No.15981255 >>15981185 >they still will have sequences as a subset But they are arbitrary. There are infinitely many substeps between any two arbitrarily selected steps.

>>	Anonymous Tue Jul 28 02:52:40 2020 No.15981265 >>15981255 Yes, but how does their arbitrariness connect with Zeno's paradox? And how does their arbitrariness cancel the fact that they are still sequences (even when sequences of real numbers)?

Anonymous Tue Jul 28 02:56:06 2020 No.15981279

Doesn’t the paradox only work for 0-dimensional points, though? In the case of anything with physical size, the size of the object, no matter how small, will eventually compensate for any diminishing distance. Either that or Achilles and the tortoise will have to exponentially shrink as they move.

>>	Anonymous Tue Jul 28 02:59:18 2020 No.15981294 >>15981279 Imagine Achilles finishing the race and realizing that he is now an infinitesimal.

>>	Anonymous Tue Jul 28 03:01:24 2020 No.15981302 >>15981265 Do you disagree that if spacetime is indeed a continuum, Cauchy basically solved the puzzle?

Anonymous Tue Jul 28 03:14:49 2020 No.15981388

>>15981302
I was initially simply addressing some of the intermediate points of your arguments which did not follow from each other.
But answering your question: Cauchy, Dedekind and others constructions are of course important and good for making useful theories. But they are ultimately still a matter of convenience and you can use alternative systems to build nonstandard analysis theories. Even more, there is no evidence that universe is built in a Cauchy way and doubt that it will ever appear. So it's not in any way a (meta)physicl truth.

Anonymous Tue Jul 28 03:21:37 2020 No.15981420

>>15981388
>I was initially simply addressing some of the intermediate points of your arguments
My points were about the model of space being assumed. How you divide up a continuum into steps is arbitrary and irrelevant. What matters is that there is one (if there is). Given continuous spacetime, the paradox cannot arise because even a 1-D slice is never a sequence. Standard real analysis solves it but so does nonstandard analysis. Regardless of technique, the paradoxes provably don't apply to the continuum.

>>	Anonymous Tue Jul 28 03:22:57 2020 No.15981425 >>15980424 you have no idea what you're saying. All 3 paradoxes are completely resolved by simple mathematics.

>>	Anonymous Tue Jul 28 03:26:45 2020 No.15981446 Lmao its solved by real life you retarded nerds. Just walk somewhere lol

>>	Anonymous Tue Jul 28 03:28:12 2020 No.15981458 >>15981446 No tortoises around.

>>	Anonymous Tue Jul 28 03:29:57 2020 No.15981469 >>15981425 Nope, not unless you assume physical space and time fit a certain mathematical model.

>>	Anonymous Tue Jul 28 03:34:23 2020 No.15981492 >>15980473 A black hole increases it's area by one Planck length when it swallows one bit of information. This would be impossible if 1 Planck length was the smallest possible unit.

>>	Anonymous Tue Jul 28 03:39:57 2020 No.15981525 >>15981279 No because the smallest fractions of you still have to traverse the distance. Take for example the smallest fraction on the tip of your nose.

>>	Anonymous Tue Jul 28 03:41:52 2020 No.15981539 >>15981446 based thracian woman

>>	Anonymous Tue Jul 28 03:42:52 2020 No.15981547 >>15981236 this desu. all these fucking brainlets confusing science with ontology

>>	Anonymous Tue Jul 28 03:43:09 2020 No.15981549 >>15980393 I solve it every day on my way to work

>>	Anonymous Tue Jul 28 03:43:55 2020 No.15981551 >>15980602 if it accelerates infinitely fast, like a supertask

>>	Anonymous Tue Jul 28 03:44:06 2020 No.15981552 >>15981236 >>15981547 ^ retards

>>	Anonymous Tue Jul 28 03:44:57 2020 No.15981555 >>15981549 based empiricist

>>	Anonymous Tue Jul 28 04:07:40 2020 No.15981641 >>15981552 all particles are smaller than the planck lenght

>>	Anonymous Tue Jul 28 04:09:51 2020 No.15981646 >>15980393 He was just fuckin' around and pointing out some of the flaws of formal logic. Don't be a dork and try to "solve" it, you're just the kind of guy he's making fun of.

Anonymous Tue Jul 28 04:20:03 2020 No.15981684
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>>15981641
>>15981552
If you drop a pencil—or even an single atom of gold—the earth moves, in factual reality and hypothetically measurable, a distance far beyond the shortness of the planck length.

>>	Anonymous Tue Jul 28 04:27:10 2020 No.15981717 >>15981641 The mathematics of current physical theory breaks down below the Planck scale. That does not imply anything about the actual structure of spacetime.

>>	Anonymous Tue Jul 28 04:28:39 2020 No.15981720 File: 396 KB, 1275x1181, planck.jpg [View same] [iqdb] [saucenao] [google] >>15981717 that's the point http://rantonels.github.io/is-the-planck-length-the-minimum-possible-length/

>>	Anonymous Tue Jul 28 04:35:40 2020 No.15981758 >>15981720 Not sure what you mean.

>>	Anonymous Tue Jul 28 04:36:31 2020 No.15981761 h is a height of than plank

Anonymous Tue Jul 28 04:38:15 2020 No.15981774

>>15980393
Zeno's paradox is great to train yourself to analyze your thoughts and keep track of what is said about experienced reality, and what is said about mental models, and of the process of framing the world by your observation.

>>15981684
This, for example, is obviously said about ideal models, the big ball of Earth, the small ball of atom, and the complete nothingness around, and the All-Powerful Observer who can put the infinitely precise locations of those object into formulas and check that the experimental result is exactly that.

That situation can be described more correctly if we imagine the earth as a twirling and bubbling swamp, the atom as a twirling and bubbling swamp, and the space around them as a twirling and bubbling swamp. Their interactions won't really move the whole Earth swamp as a whole, the waves would be sent in all directions instead.

>>	Anonymous Tue Jul 28 04:39:42 2020 No.15981783 Why do we use the height of a dead white male Planck as a universal constant?

>>	Anonymous Tue Jul 28 04:47:56 2020 No.15981820 >>15981783 He was alive before he died, you know.

Anonymous Tue Jul 28 04:47:56 2020 No.15981821

Interesting. Midwits already got the answer but they keep rambling.
We can conclude that some discussions aren't about finding the answer (or truth) but are an end in itself - maybe some kind of dick waving or trying to impress the audience by a showing off a disregard to one's own ignorance?

>>	Anonymous Tue Jul 28 04:50:31 2020 No.15981836 >>15981758 planck length is where classical physics break down, quantum physics deals with concepts beyond distance

>>	Anonymous Tue Jul 28 05:02:04 2020 No.15981898 >>15981821 You do not understand that philosophy only discusses questions that have no answers.

>>	Anonymous Tue Jul 28 05:23:37 2020 No.15982012 >>15981821 It's why I just lurk

>>	Anonymous Tue Jul 28 05:26:36 2020 No.15982029 >>15981821 >Midwits already got the answer but they keep rambling. Did you just describe the philosophy in general?

>>	Anonymous Tue Jul 28 05:27:38 2020 No.15982035 >>15981836 Schrodinger's cat is a Platonic idea.

Anonymous Tue Jul 28 05:36:03 2020 No.15982073

>>15980393
Read le cimetière marin by Paul Valery

Zénon ! Cruel Zénon ! Zénon d’Élée !
M’as-tu percé de cette flèche ailée
Qui vibre, vole, et qui ne vole pas !
Le son m’enfante et la flèche me tue !
Ah ! le soleil… Quelle ombre de tortue
Pour l’âme, Achille immobile à grands pas !

Non, non !… Debout ! Dans l’ère successive !
Brisez, mon corps, cette forme pensive !
Buvez, mon sein, la naissance du vent !
Une fraîcheur, de la mer exhalée,
Me rend mon âme… Ô puissance salée !
Courons à l’onde en rejaillir vivant.

>>	Anonymous Tue Jul 28 05:39:33 2020 No.15982089 >>15980707 Tbh, 1 second can also be viewed as an infinite sequence of moments.

Anonymous Tue Jul 28 05:40:49 2020 No.15982094

>>15980626
how could you prove something contradicting self-evident. 9.999999.... there's a rest. there's always a rest. there's no rest in 10. is your 10 incomplete? there's no rest. there's no rest for the wicked. and there's no rest for numbers, man

>>	Anonymous Tue Jul 28 05:52:16 2020 No.15982136 >>15980473 Wow, after reading this post I've resolved to never try and talk about something I'm not absolutely certain I understand, because you clearly have no fucking clue what the hell you're talking about.

>>	Anonymous Tue Jul 28 05:59:22 2020 No.15982157 >>15980393 After hearing of Zeno's paradoxes, Diogenes started walking

>>	Anonymous Tue Jul 28 06:20:45 2020 No.15982245 >>15982157 So Zeno was the original Christ?

>>	Anonymous Tue Jul 28 06:24:37 2020 No.15982257 File: 7 KB, 512x512, Race between Achilles and the tortoise.gif [View same] [iqdb] [saucenao] [google] >>15980393 Yes

>>	Anonymous Tue Jul 28 06:28:07 2020 No.15982265 >>15982257 so who won the 200 metres run?

>>	Anonymous Tue Jul 28 06:29:09 2020 No.15982269 People on here really believe the universe consists of Planck length pixels like some kind of computer monitor

>>	Anonymous Tue Jul 28 06:29:38 2020 No.15982272 File: 250 KB, 3345x1679, achilles.png [View same] [iqdb] [saucenao] [google] >>15982257 Can be worse.

>>	Anonymous Tue Jul 28 06:30:43 2020 No.15982279 >>15982269 Spacetime is clearly 24-cell honeycomb.

Anonymous Tue Jul 28 06:32:28 2020 No.15982290
File: 77 KB, 1024x655, ho pepi.jpg [View same] [iqdb] [saucenao] [google]

>>15982035
yes
also an Egyptian and Assyrian idea

INVOKING THE SPIRIT AS OSIRIS 4 RECITATION. Ho, Pepi! You have gone that you may become akh and take control as a god, as Osiris’s replacement. You have your ba within you, your control about you, your crown atop you, your Pale Crown atop your shoulders.
Face forward, for praise of you is before you. The god’s followers are after you, the god’s privileged ones before you, making (the paean): “The god has come, the god has come! This Pepi has come on Osiris’s throne! The akh from Nedit has come, the controlling power from Great-Land!”
Isis will speak to you, Nephthys will call to you. The akhs will come to you in obeisance, kissing the earth at your feet, because of your ferocity, oh Pepi, in Perception’s towns.
So, you should go forth to where your mother Nut is, and she will take hold of your arm and give you the way to the Akhet, to the place where the Sun is.
The sky’s door has been opened to you, the Cool Waters’ door has been made to pull open to you, and you will find the Sun standing, waiting for you. He will take hold of your arm, lead you into the sky’s dual shrines, and put you on Osiris’s throne.
Ho, Pepi! Horus’s eye has come to you and will claim you. Your ba from the gods has come to you, your control of the akhs has come to you. The son has saved his father: Horus has saved Osiris, Horus has saved this Pepi from his opponents.
You shall take up your position, Pepi, on Thighs-Forward’s throne, saved, provided as a god, and equipped with Osiris’s form on Foremost of Westerners’s throne, and do what he used to do among the akhs and the Imperishable Stars.
Your son shall take up his position on your throne, equipped with your form, and do what you used to do before at the fore of the living, by command of the Sun, the great god. He shall farm barley, farm emmer, and endow you with them.
Ho, Pepi! What pertains to you has been given to you by the Sun. You shall claim your body, having received a god’s form, and become great through them with the gods at the lake’s fore.
Ho, Pepi! Your ba shall take up its position among the gods and among the akhs: it is your fearsomeness against their hearts.
Ho, Pepi! Take up your position, oh Pepi, on your throne at the fore of the living: it is your ferocity against their hearts. Your identity on earth shall live, your identity on earth shall endure. You shall not perish, you shall not come to an end, for the course of eternity.

TL;DR Pharaoh is unified with God in real distinction.

>>	Anonymous Tue Jul 28 06:34:13 2020 No.15982299 >>15982269 You could calculate the speed of the tortoise and Achilles, then you could plot it in a graph and see that at 20 seconds they are equal before that Achilles is behind and after that Achilles is ahead. Achilles wins.

>>	Anonymous Tue Jul 28 06:36:55 2020 No.15982313 >>15982157 am OP, definitely /thread here

>>	Anonymous Tue Jul 28 06:37:33 2020 No.15982318 >>15980393 Achilles should just do two circles at once.

>>	Anonymous Tue Jul 28 06:39:16 2020 No.15982329 >>15982157 In his barrel.

>>	Anonymous Tue Jul 28 06:46:52 2020 No.15982354 >>15980393 >if you keep taking steps that are not enough to overtake the tortoise, you'll never overtake it Where's the paradox?

>>	Anonymous Tue Jul 28 07:30:01 2020 No.15982499 >>15982269 Failed STEM crowd, God have mercy on them.

Anonymous Tue Jul 28 07:31:11 2020 No.15982502

Aristotle's answer to the paradox is that the question of whether the infinite series of runs is possible or not is ambiguous: the potentially infinite series of halves in a continuous run is possible, while an actual infinity of discontinuous half runs is not.

>>	Anonymous Tue Jul 28 07:34:00 2020 No.15982513 >>15982499 God is a coder.

>>	Anonymous Tue Jul 28 07:48:03 2020 No.15982580 >>15980393 Yes.

>>	Anonymous Tue Jul 28 08:02:39 2020 No.15982649 >>15982499 >/lit/ fails >blame it on "STEM"

Anonymous Tue Jul 28 08:35:06 2020 No.15982853

>>15980393
Aristotle made an argument against it in his Physics, which is probably the best you can do without modern mathematical notation or physics:
Something along the lines of - space and time can be either finite or infinite. However, they both have to be either finite or infinite since movement unites the two: i.e. you move a finite distance in finite space through finite time, and if you move at a constant speed over an infinite time, this will mean that you cover an infinite distance.
Now, since Zeno's paradox posits infinite movement (Achilles always moves) then it cannot achieve a finite distance (in this case the "infinite" distance would be like 0.99999...) which makes sense if you live 1000 years before limit notation. Then, if A makes finite movements over a finite time, well he will travel a finite distance (like 0.5 in one period). So there really is no paradox, Achilles cannot cover a finite distance if he uses infinite intervals, this does not mean movement isn't real, just that it is infinite.

Feel free to correct me but I interpreted the passage in the Physics as running something along these lines.

>>	Anonymous Tue Jul 28 09:02:00 2020 No.15982991 >>15980393 Retroactively refuted by Spengler. Greeks could only think of numbers as lengths or magnitudes which is why this was a "paradox" to them.

>>	Anonymous Tue Jul 28 09:13:14 2020 No.15983035 >>15982649 > /lit/ is one person > that person thinks that a “solution” to Zeno's paradox is an arbitrary limit in a convenient place of modern-day physics

Anonymous Tue Jul 28 09:24:21 2020 No.15983080
File: 3 KB, 415x75, sum.png [View same] [iqdb] [saucenao] [google]

>>15980393
Anybody who understands pic related now knows why the paradox is solved in modern times. Ancient Greeks did not have a strong concept of infinity, nor the infinitesimal. As a result, they believed that the distance between Achilles and the tortoise would always be significant.

You can also literally see in the real world that Achilles will run right past that tortoise. This is not a problem today.

Anonymous Tue Jul 28 10:40:42 2020 No.15983533

>>15982094
You are clearly retarded. .999999999... repeated to infinity is 1. Think about how 1/3 = .333... which would make 3/3 = .99999... but 3/3 = 1 meaning .9999... = 1 since 3/3 = 3/3

>>15980393
Xenon's paradox is actually a trick because the man is constantly slowing down as he chases the turtle. Think about it this way:

The man starts out 10 meters away from the turtle, going twice the turtle's speed. The man runs 20 meters, while the turtle runs 10. At this moment the man and the turtle are at the exact same point. From here the man continues on past the turtle

>>	Anonymous Tue Jul 28 11:37:18 2020 No.15983945 >>15980543 There isn’t any negative acceleration

>>	Anonymous Tue Jul 28 11:54:31 2020 No.15984062 >>15980579 I appreciate your response.

Anonymous Tue Jul 28 12:09:19 2020 No.15984163

>>15982269
For reductio, suppose that the Planck length is the minimum possible distance. It follows that every distance is some integer multiple of the Planck length. Now construct a square whose sides are each one Planck unit in length. What is the distance between two of the square's opposing vertices? By Pythagoras' theorem, it is certainly no integer multiple of the length of the square's sides. But this contradicts a consequence we earlier derived from our initial supposition, namely that every distance is some integer multiple of the Planck length. By reductio, then, our initial supposition that the minimal possible distance is equal to the Planck length was false. QED.

>>	Anonymous Tue Jul 28 12:13:50 2020 No.15984205 >>15984163 Lmao seethe retard

>>	Anonymous Tue Jul 28 12:28:14 2020 No.15984293 >>15983080 > This is not a problem today. How do you know that running past the tortoise wasn't a problem back then?

>>	Anonymous Tue Jul 28 12:34:15 2020 No.15984332 >>15981783 Other physicists mockingly called it that as a reference to plancks notoriously small penis

>>	Anonymous Tue Jul 28 12:38:30 2020 No.15984366 >>15980460 Doesn't seem very convincing in general. What if the fundamental tiles are so small we've never observed the pythagoras theorem to hold at their scale? Does it hold at Planck scale for instance?

Anonymous Tue Jul 28 12:41:49 2020 No.15984399

>>15980602
Each step of the process takes less and less time to complete, so that the sum of the completion times converges to a finite limit.
Which is exactly what happens with the sum 1/2 + 1/4 + 1/8.... that is involved in Zeno's paradox. It's not even particularly hard to prove with the tools fo analysis.

Anonymous Tue Jul 28 12:45:15 2020 No.15984424

>>15980675
Who knows what is metaphysically true? But when it comes to quantities the ontology of calculus is finer than common intuition, so it works for our purposes. And in practice nobody has ever doubted that an arrow can close a nonzero distance. Zeno's paradox is just about poking fun at our intuition of infinity. The "solution" provided by calculus is consistent, useful, reasonable and intuitively sound. There's no reason to doubt it outside the realm of metaphysics where nothing is ever really proved or agreed upon, so the point is a bit moot.

>>	Anonymous Tue Jul 28 12:47:05 2020 No.15984438 >>15980707 >In a mathematics sequence this is true: infinite sequence approaching 1 = 1. In the "real" world too, seeing as people who walk actually manage to move.

Anonymous Tue Jul 28 12:49:03 2020 No.15984455

>>15980752
> 0.999...8
This number is undefined. There is no last digit in an infinite sequence. Just try to express that number as a converging infinite sum of reals and you'll see.
0.9999 = 9*1/10 + 9*1/100 + 9*1/1000+...
What is the equivalent formulation for 0.99...98? Try it and you'll see there is none.

>>	Anonymous Tue Jul 28 12:49:10 2020 No.15984457 >>15983080 >they believed Don't attribute one person's autism in theorizing to the entire civilization.

>>	Anonymous Tue Jul 28 12:50:30 2020 No.15984468 >>15984455 >There is no last digit in an infinite sequence. There's no such thing as "an infinite sequence" in a real physical world.

Anonymous Tue Jul 28 12:51:16 2020 No.15984471

>>15980758
The point is there is nothing to solve. Zenon's paradox is only that, a paradox, that is something that defies common intuition, something that apears contradictory, not necessarily something that defies logic or is truly contradictory.
Calculus wasn't created to solve Zeno's paradox, it was created to provide a way to quantitatively describe movement. Nobody is ever truly bothered by Zeno's paradox, it's a fun thing to think about which bears no consequence.

>>	Anonymous Tue Jul 28 12:51:19 2020 No.15984472 >>15980393 space is not infinitely divisible

>>	Anonymous Tue Jul 28 12:52:08 2020 No.15984483 File: 37 KB, 398x376, 1572317651564.jpg [View same] [iqdb] [saucenao] [google] >>15980767

>>	Anonymous Tue Jul 28 12:53:08 2020 No.15984487 >>15980780 >>15980784 >>15980809 >>15980819 spergs

>>	Anonymous Tue Jul 28 12:53:22 2020 No.15984489 >>15984205 Really contributing to the board there bro

Anonymous Tue Jul 28 12:54:17 2020 No.15984501

>>15981086
> it’s still infinite distance
It's not. It's a sum of distance whose number of step increases towards infinity as the size of the step decreases towards zero. it's as paradoxical as being surprised that a great number of small things make a big pile.

>>	Anonymous Tue Jul 28 12:54:42 2020 No.15984502 >>15984472 See: >>15984163

>>	Anonymous Tue Jul 28 12:55:24 2020 No.15984506 >>15981135 >>15981152 >>15981154 The true king move would be to ride the turtle as a battle mount, and declare war on the race organizers.

>>	Anonymous Tue Jul 28 12:57:45 2020 No.15984518 >>15984205 Planck length dick confirmed

Anonymous Tue Jul 28 12:59:17 2020 No.15984529

>>15984163
Also, if materialism is true, then our thoughts are bound by the Planck length (assuming it's real reality, since out mind is subsection of matter), this means you can't even imagine a circle, any equation that implies a circle doesn't exist, which means math is wrong.

Anonymous Tue Jul 28 13:00:42 2020 No.15984538

>hurr durr big words hurr durr maths burr durr gurr murr lurr surr
Can you walk a distance of 1 atom?
2 atoms?
3 atoms?
.
.
.
Once you reach the smallest distance you can move that is the point when it is over taken. Wow just blew your retarded mental jerkoff session out of the water with 1 easy step.

>>	Anonymous Tue Jul 28 13:03:26 2020 No.15984552 >>15984538 this is still too complicated: https://en.wikipedia.org/wiki/Solvitur_ambulando >Diogenes of Sinope, also known as "Diogenes the Cynic", is said to have replied to Zeno's paradoxes on the unreality of motion by standing up and walking away.

>>	Anonymous Tue Jul 28 13:04:59 2020 No.15984558 >>15984552 The absolute mad featherless biped.

>>	Anonymous Tue Jul 28 13:05:28 2020 No.15984565 >>15984552 >Diogenes the brainlet

>>	Anonymous Tue Jul 28 13:05:34 2020 No.15984569 >>15982073 Based and Valérypilled. >Ah ! le soleil… Quelle ombre de tortue I had never paid attention to how cool this visual metaphor is before.

>>	Anonymous Tue Jul 28 13:05:44 2020 No.15984570 >>15984552 >Diogenes of Sinope, also known as "Diogenes the Cynic", is said to have replied to Zeno's paradoxes on the unreality of motion by standing up and walking away. Based Diogenes chad #rekt autistic nerd making up shit.

>>	Anonymous Tue Jul 28 13:08:37 2020 No.15984596 >>15980473 Planck length isn't an indivisible unit of space; it's the point at which energy required to observe anything smaller would create a singularity. Smaller things can exist, we just have no way to observe or interact with them.

>>	Anonymous Tue Jul 28 13:09:12 2020 No.15984600 >>15980579 >it's similar to the problem of squaring the circle. Squaring the circle is about how to build a square with the same area as a given circle given only a ruler and a compass.

>>	Anonymous Tue Jul 28 13:10:59 2020 No.15984614 >>15982265 Achilles, the tortoise only ran 100 meters.

Anonymous Tue Jul 28 13:14:21 2020 No.15984644

>>15984163
How would you construct a square whose side is one Planck unit long if a Planck unit is the smallest possible distance? Are you imagining that there are Planck lines lying around that you can just assemble?

You paradox doesn't work because you don't know if the microscopic (Planck-scale) structure of the universe is compatible with such an operation as constructing an elemental square. That's like saying "try constructing a square whose side is exactly one carbon atom long, we see that the carbon atom is not square, therefore atoms don't exist". No, it only means the assumption that you can make a exactly atom-sized square with carbon atoms is misguided.

You're making assumptions about things we can't observe (yet).

Anonymous Tue Jul 28 13:17:00 2020 No.15984660

>>15984468
There's no such thing as a real physical world. Doesn't matter what is real or not, if you're talking about numbers, be mathematically rigorous.
And mathematically speaking there is such a number as 0.99999... (it's actually 1), but there is no number such as 0.999...98. Unless you're using a different theory of analysis, in which case the numbers take different meanings.

Anonymous Tue Jul 28 13:20:00 2020 No.15984682

>>15984529
>this means you can't even imagine a circle
Not necessarily a problem unless you can prove human really picture an infinity of points when they picture a circle (protip: they don't, no mental image is infinitely accurate).

> any equation that implies a circle doesn't exist
Existence of an equation =! ability to picture the solution of that equation in your mind. Nobody can truly picture a brownian motion, yet it is a solution of some important partial (stochastic) differential equations.

>which means math is wrong
No, see: all of the above.

>>	Anonymous Tue Jul 28 13:24:06 2020 No.15984721 >>15984660 >There's no such thing as a real physical world Yes, there is. And in this world imaginary mathematical concepts lie infinity, perfect circle or even a point do not exist.

Anonymous Tue Jul 28 13:26:00 2020 No.15984745

>>15984721
To me you don't exist either. You're just words on a screen, that is to say visual cues produced by electron bouncing off a metal structure. And concepts like infinity are electrons and chemical circulating in the brain. You're not any more real than them, you are a derivative entity, at best.
So stop being so haughty and learn your math.

>>	Anonymous Tue Jul 28 13:38:57 2020 No.15984866 >>15984745 I don't give a shit about your philosophical mind experiments. >You're not any more real than them Me, brain and elections exist in the real physical world. Infinity does not.

Anonymous Tue Jul 28 13:46:29 2020 No.15984928

>>15984682
again, if MATERIALISM is true, then the picture in our head is material, thus it is bound by the planck length, therefore Phantasia can't even imagine a circle, this includes all curves, there are no real curves if planck length is physically real.

>>	Anonymous Tue Jul 28 14:08:12 2020 No.15985085 >>15984471 > made people wonder what “space”, “time”, “movement” are, and what we actually perceive when we talk about them > it's a fun thing to think about which bears no consequence

Anonymous Tue Jul 28 14:08:21 2020 No.15985088

>>15984644
The reductio doesn't require that the sides of the square be one Planck unit in length. I just presented it that way for simplicity.

If the Planck unit is the minimal distance, the length of anything in the universe will be an integer multiple of the Planck unit. So the length of the sides of any square will likewise be some integer multiple of the Planck unit. But, by Pythagoras' theorem, the distance between opposing vertices of the square will be equal to no such multiple. So we get a contradiction anyway.

>>	Anonymous Tue Jul 28 14:19:37 2020 No.15985177 Kant solved this pretty thoroughly in the first Critique with the whole unconditioned and infinite series section in the Antinomy.

>>	Anonymous Tue Jul 28 14:20:36 2020 No.15985182 >>15984163 >It follows that every distance is some integer multiple of the Planck length no it doesn't

>>	Anonymous Tue Jul 28 14:20:53 2020 No.15985185 >>15980393 calculas.

>>	Anonymous Tue Jul 28 14:23:09 2020 No.15985202 >>15980420 you are a stupid nigger that watches popsci on youtube and then spouts it off like you know shit, kys >>15980393 the rationalization is the idea that infinite sums can add to finite values

>>	Anonymous Tue Jul 28 14:28:24 2020 No.15985246 >>15984538 10/10 made me reply

>>	Anonymous Tue Jul 28 14:30:40 2020 No.15985262 >>15985182 It does on the reasonable assumption that there are indivisible distances larger than the absolute minimum distance.

>>	Anonymous Tue Jul 28 14:32:45 2020 No.15985284 >>15985182 It does on the reasonable assumption that there are no indivisible distances larger than the absolute minimum distance.

>>	Anonymous Tue Jul 28 15:01:42 2020 No.15985523 >>15985284 that isn't a reasonable assumption though

>>	Anonymous Tue Jul 28 15:03:51 2020 No.15985545 >>15980640 LOL the brainlets don't get this. So if 1/3 = .3333 etc. and 1/3*3=1 then .3333 = .9999 which equals 1

>>	Anonymous Tue Jul 28 15:05:17 2020 No.15985562 >>15985523 Yes it is. All lengths greater than the minimal length are divisible into smaller lengths.

>>	Anonymous Tue Jul 28 15:06:03 2020 No.15985569 >>15980404 Infinitesimals. >>15980424 The fuck? Don't you overtake cars on the freeway?

>>	Anonymous Tue Jul 28 15:06:22 2020 No.15985572 >>15984538 m8 there is no smallest distance man bro

>>	Anonymous Tue Jul 28 15:06:39 2020 No.15985575 >>15985545 edit .3333*3 =.9999 which equals 1

>>	Anonymous Tue Jul 28 15:08:19 2020 No.15985592 >>15980424 We can be certain, a priori, see: >>15984163

>>	Anonymous Tue Jul 28 15:12:03 2020 No.15985628 >>15985562 the minimal length does not dictate anything about lengths greater than it, you have the smallest possible penis, it doesn't mean someone cannot have a penis 1.5x the size of yours

>>	Anonymous Tue Jul 28 15:17:50 2020 No.15985680 >>15980445 So Zeno and the tortoise can only ever tie?

Anonymous Tue Jul 28 15:19:27 2020 No.15985695

>>15985628
So you think it is coherent for the smallest possible region of empty space to have Planck length 1, and for there to be another empty region of space that has Planck length 2 but which is not divisible into two regions of Planck length 1?

I mean, you do you, I guess, but it's glaringly obvious which one of us is making the more reasonable assumption.

>>	Anonymous Tue Jul 28 15:24:11 2020 No.15985739 >>15980393 yes, with calculus

Anonymous Tue Jul 28 15:39:44 2020 No.15985859

>>15985088
>The reductio doesn't require that the sides of the square be one Planck unit in length.
You still have to be close enough to Planck length than measures uncertainties will be under Planck length. Given what we know about physics currently it's a very unlikely scenario, but even putting that aside, the principle of my objection holds.

> So the length of the sides of any square will likewise be some integer multiple of the Planck unit.
It just means there won't be any exact square, ie, anything we think is a square is only approximately square. This is already the case in all practical situations. The point is Pythagoras can be applied perfectly only to abstract construction, material constructions are bound to be imperfectly geometrical.

Btw
> the Planck unit is the minimal distance
is not true, see http://rantonels.github.io/is-the-planck-length-the-minimum-possible-length/ already posted earlier in the thread. But that's tangential to your argument I guess.

>>15984866
> philosophical mind experiments
>light from computer screens are produced by electronic devices
>brain signals are encoded with chemical reaction and electrical currents
All I said was remind you of some basic scientific facts.

>Me, brain and elections exist in the real physical world.
Your brain exist physically. You don't, you're just a set of patterns in your brain. Get brain damage and what you think of as "you' would become unrecognizable or disappear entirely. This is not an abstract experiment, just go visit anyone with a severe case of Alzheimer's.

> Infinity
Exists as a set of pattern in many human brain. Not only is it as real as (you), but it is actually more undying.

>>15984928
>again, if MATERIALISM is true, then the picture in our head is material, thus it is bound by the planck length
Planck length doesn't follow from materialism alone, it is a particular quantity bound to a modern theory that might be overturned in the next 30 years. You can have materialism without Planck length. Also Planck length isn't defined as "that which nothing can be smaller", it's just at scale at which things get very weird and hard to approach with current theories.

>therefore Phantasia can't even imagine a circle
This is actually true for all continuous lines, so not only a circle but a straight line, etc. And this is already the case, no human brain ever imagined a circle with perfect accuracy, we don't have infinite resolution of picture, not even in our minds.

>there are no real curves
You have never met a real curve once in your life, only dotted lines made of atoms.

>>15985085
What are the consequence of the Zeno paradox other than "dude infinite space lmao"? It didn't change physics, geometry, mathematics, not to mention other humans endeavors, it didn't even really change philosophy. It's just an interesting thought experiment, like that fucking trolley problem. Even on a purely speculative standpoint it's not that important.

>>	Anonymous Tue Jul 28 16:14:21 2020 No.15986100 >>15984163 You are assuming space is Euclidean in order to prove space is Euclidean. Obvious petitio principii.

Anonymous Tue Jul 28 16:16:27 2020 No.15986112

>>15985859
>You still have to be close enough to Planck length than measures uncertainties will be under Planck length. Given what we know about physics currently it's a very unlikely scenario

What does this even mean? In a universe where a length L is the minimum possible distance, every distance is *guaranteed* to be an exact integer multiple of L. "measures uncertainties" have nothing to do with anything.

>It just means there won't be any exact square, ie, anything we think is a square is only approximately square. This is already the case in all practical situations. The point is Pythagoras can be applied perfectly only to abstract construction, material constructions are bound to be imperfectly geometrical.

This completely misunderstands the point. I'm not talking about building a perfect square out of any physical material, I'm talking about a square region of space. After all, we're discussing the topology of *space itself*, not of material objects. In a universe where space is discrete, square regions of space have contradictory properties. This is absurd, so space is not discrete.

>>	Anonymous Tue Jul 28 16:18:45 2020 No.15986126 >>15986100 I'm assuming there are square regions of space in order to prove that space is infinitely divisible. Infinitely divisible space needn't be Euclidean, so I have no idea what you're talking about.

>>	Anonymous Tue Jul 28 16:22:32 2020 No.15986142 >>15986126 >I'm assuming there are square regions of space Squares obviously can't exist without infinitely divisible space. They are notional objects that exist in Euclidean and other geometries, but not necessarily in the physical universe.

Anonymous Tue Jul 28 16:26:18 2020 No.15986166

>>15986112
> "measures uncertainties" have nothing to do with anything.
Measure uncertainties are the entire problem. Where do you think the idea of the Planck length comes? Straight from the incertainty orinciple which constraint the accuracy of measurement.

This is simple really. You're talking about constructing a square and measuring its length. You want to catch an impossibility by showing a length related to the square would violate Pythagoras theorem. However since this violation comes from the Planck length being elementary, that violation would be on the order of the Planck length. You would therefore need to measure length with a margin of error smaller than the Planck length, or the imprecision of your measuring would drown out the very error you're trying to catch.

>I'm not talking about building a perfect square out of any physical material, I'm talking about a square region of space.
Same problem, you have to measure it somehow, this supposes to use instruments that can grasp the small lengths involved. Again, it's all about measurement accuracy.

>After all, we're discussing the topology of *space itself*
Measuring distances implies measure methods, just like measuring objects.

>In a universe where space is discrete, square regions of space have contradictory properties.
Why should square region of space exist? You've never had a need for an absolutely perfect square in your life, we have never encountered one in physics, for what you know there might not be a single square in the entire universe.

>This is absurd
Only if you think space must contain square regions. Which is tantamount to assuming it must roughly look at small scale like it does at our scale. But maybe at elementary level space is made of a lattice of supersmall interlocked hexagons. You don't know.

Your argument boils down to "I want to do geometry in real space as I do on a piece of paper, if there is a minimal length, I cannot do, therefore there cannot be a minimal length". The correct deduction should be, "it's possible that real space isn't structured like a plane on a piece of paper".
Basically >>15986100 said it way more concisely and clearly that I did.

Anonymous Tue Jul 28 17:06:27 2020 No.15986494

>>15986166
I thought I already explained this in a previous post: >>15985088

Basically, nothing I said requires that space is a lattice of squares at the finest grain (how could it be in 3d space?). The square regions can be macroscopic and the same problem still arises.

All your talk about measurement is a red herring. Given that such square regions actually exist, space cannot be discrete on pain of contradiction.

Anonymous Tue Jul 28 17:11:42 2020 No.15986539

>>15986142
That's the whole point of the argument: there can be no square regions of space unless space is infinitely divisible. That's how valid deductions work. And no, contrary to your claim, not all logically valid arguments are question-begging in virtue of the truth of their premises requiring that their conclusion also be true.

In any case, the argument can be run using other geometric constructions in curved space too, so all of this is beside the point.

Anonymous Tue Jul 28 17:17:17 2020 No.15986582

>>15986539
>And no, contrary to your claim, not all logically valid arguments are question-begging in virtue of the truth of their premises requiring that their conclusion also be true.
What? You straightforwardly assumed the conclusion of the argument in your premises. If space is a discrete graph of some kind then obviously standard geometric objects like squares cannot be exactly instantiated in physical reality. You haven't proven anything about physical space. You are simply assuming physical space is a metric space.

Anonymous Tue Jul 28 17:22:53 2020 No.15986632

>>15986582
Why can't you just take two equal-length one-dimensional regions of space that are at right angles to one another, then take parallel regions of the same length that connect up with them so as to construct a square? It is absurd that you wouldn't be able to do this in discrete space. But equally, being able to do this leads to contradiction. Either way you have an absurdity, so discrete space is absurd.

Anonymous Tue Jul 28 17:28:11 2020 No.15986670
File: 218 KB, 960x960, tumblr_p99pp7WbNa1suuc8do1_1280.jpg [View same] [iqdb] [saucenao] [google]

>>15980579

Indeed. Note the obvious Jesus Christ vs. Yaldabaoth contrast in discontinuous vs. continuous space. The Subject exerted upon by a bottom-up and outside-in becoming through a medium he is subordinate to, eternal work, eternal recapitulation, impossible, etc. in the latter. The Subject destroys the medium through top-down and inside-out indwelling, being anew proper, eternal rest, permanent advent, inevitable, etc. in the former.

Anonymous Tue Jul 28 17:31:45 2020 No.15986696

>>15986632
Loop Quantum Gravity requires discrete space.

>Ordinary measurements of geometric quantities are macroscopic, and planckian discreteness is smoothed out. The fabric of a T-shirt is analogous: at a distance it is a smooth curved two-dimensional surface, but on closer inspection we see that it is actually composed of thousands of one-dimensional linked threads. The image of space given in LQG is similar.

https://en.wikipedia.org/wiki/Loop_quantum_gravity

Graphics programmers work with discrete geometry all the time. The familiar shapes from continuous geometry are only instantiated approximately.

https://en.wikipedia.org/wiki/Discrete_geometry

>>	Anonymous Tue Jul 28 17:39:22 2020 No.15986747 >>15980780 is 0.999...8 attainable?

Anonymous Tue Jul 28 17:43:27 2020 No.15986782

>>15980393
It’s solution is in mathematical limits. Sort of. It’s obviously a paradox where the math, the physics and the logic will never ever cooperate with one another.

However calculus has a neat description of it. Just search “calculus limits zenos paradox”

>>	Anonymous Tue Jul 28 17:46:21 2020 No.15986805 >>15984455 0.999...8 = 91/10 + 91/100 + 91/1000+...81/100ooo...

Anonymous Tue Jul 28 17:47:01 2020 No.15986810

>>15986494
>nothing I said requires that space is a lattice of squares at the finest grain
And I didn't assume it did. It seems you are working with an assumption of continuous space instead. The objection stands nonetheless.

>All your talk about measurement is a red herring.
No, again, it's the whole point. You don't seem to have understood the criticism. Or perhaps you believe we have access to magical objects that allow us to draw perfectly square boundaries in space with arbitrarily fine accuracy. If you have such an instrument please give one to me, I'll easily become a billionaire with it.

> The square regions can be macroscopic
Again, the question is whether a truly square region can exist and can be precisely identified. If it can't (for instance because your measure instruments are too precise to tell a true square for a not-exactly-square) you aren't going to be able to reliably find a fault in Pythagoras theorem.

Just replace Planck sized square by human sized squares and Planck length regions by atoms and you get the problem. We appear to be surrounded by square objects yet on atomistic scale they turn out to be much more irregular. Are you going to measure the diagonal of a square table in your house expecting it to fit Pythagoras theorem down to the nanometer?

>>15986632
How would you ensure the angle is absolutely right, and the line are absolutely straight? For the latter you could use laser beam, though even laser beam have width and wouldn't give you perfectly thin lines. Not sure how you'd get the former.

> then take parallel regions of the same length
How do you make sure they have exactly the same length? The answer is that you have to measure them, which brings in the very measurement problem we've been talking about.
I'm seriously starting to think you have no education on physics. Any physics student knows that any actual physical quantity is associated with a margin of error on its measure.

Anonymous Tue Jul 28 17:49:26 2020 No.15986823

>>15986747
It doesn't make sense in real analysis. For any integer n you can choose the nth digit of a number. But you cannot set the infinitieth digit, as there is no such thing. You can have 0.98 (and plenty of zeroes after that). You can have 0.999999.. or 0.998998998.. or any repeating pattern. You can't have 0.999....98 with an infinity of 9s in between.

Anonymous Tue Jul 28 17:51:13 2020 No.15986834
File: 2.22 MB, 413x240, plato.gif [View same] [iqdb] [saucenao] [google]

>>15985859
>Planck length doesn't follow from materialism alone
IF
IF MATERIALISM IS TRUE
IF
the point if materialism is true, then he planck length is true physically speaking, as in reality is granular, but if that's the case then our math is wrong.
My original post was just an extra dab on atheism. Math as we know it presupposes the platonic world of forms where perfect circles exist, this doesn't mean Plato was right it just means the "earth people" of Plato's Sophist are wrong.

>>	Anonymous Tue Jul 28 17:51:39 2020 No.15986838 >>15986805 That's 0.99999800000.... if I read you correctly. Or perhaps 0.99999899999.... or 0.9999988888... (the way you used the dots is a bit confusing) not 0.9999...9998 which implies an infinity of 9s somewhere before the 8.

>>	Anonymous Tue Jul 28 17:56:09 2020 No.15986877 >>15985695 Not him but the assumption doesn't hold. If Plank length 1 is the minimum distance, then there also exists Plank length 1.5, 2.5, 3.6, sqrt(2), etc. etc. Not just Plank length 2, 3, 4, etc. Why does it have to be an integer multiple?

Anonymous Tue Jul 28 17:57:24 2020 No.15986884

>>15986834
>IF
Yes, I understand what 'if' means. Nonetheless, assuming materialism doesn't ensure there is a Planck length. In 30 years we might have a new theory of quantum gravity where the Planck length isn't the smallest unit at which things make sense (one can dream at least). Yet that new physical theory wouldn't invalidate materialism.

>but if that's the case then our math is wrong
Not really. Is plane Euclidian geometry wrong because we don't live in a two-dimensional universe? Is 100-dimensional Euclidian geometry wrong because there aren't 100 dimensions of space? Yet both are regularly used in practical applications.

>My original post was just an extra dab on atheism.
This is all pretty unrelated to atheism t.b.h.

>Math as we know it presupposes the platonic world of forms where perfect circles exist
Not necessarily, it's merely convenient to think that way in the day to day job of a mathematician. Many mathematician are formalists or instrumentalists.

Anonymous Tue Jul 28 18:00:23 2020 No.15986916

>>15986877
Not either people but in the case of 1.5 Planck length, what the fuck is a 0.5 Planck that you're adding to 1 if the Planck length is indivisible, since it's the smallest thing possible? (I know Planck length isn't that, just using the term how it's being used in the discussion)

Anonymous Tue Jul 28 18:05:55 2020 No.15986958

>>15986916
You're thinking that everything is "made up" of Planck lengths. All the Planck length is is the minimum distance where physics still works or where it turns into a black hole or whatever. Think of it as the lower bound for distance, anything higher than it is possible. It doesn't assume divisibility.

>>	Anonymous Tue Jul 28 18:06:58 2020 No.15986970 >>15986916 >have a piece of wood >have a second piece of wood that is 1.5 times longer

>>	Anonymous Tue Jul 28 18:08:18 2020 No.15986981 >>15986916 Worth noting that Planck length isn't even an exact length, it's more like an order of magnitude or a scale, like the micrometric or the nanometric scale.

Anonymous Tue Jul 28 18:08:18 2020 No.15986982
File: 123 KB, 684x960, b42f79c08406dc217588358b77ce1894.jpg [View same] [iqdb] [saucenao] [google]

This is more a question for /sci/, but it's funny seeing all the brainlet humanities graduates fumble to answer this.

The paradox fails because they hadn't defined limits well. The amount of time to travel a smaller distance decreases with the distance. Zeno assumed that the sum of the infinite time steps would diverge, but it's actually finite. I'll give an example. Suppose it takes Achilles 1 second to catch up to where the tortoise was, then half a second, then a quarter, then an eighth, and so on...

We consider the sum S=1+1/2+1/4+1/8+1/16+...
if you can prove this sum converges, then you can do the following algebraic manipulation

2S= 2+1+1/2+1/4+...=2+S
so 2S=S+2, thus S=2 (subtract S from both sides)

to prove the limit exists (this is necessary if you want to maths), you just note that
Sn=1+1/2+...+1/(2^n) = 2-1/(2^n), and taking the limit as n goes to infinity gives you 2.

So taking the limit as n approaches infinity for Achilles to approach the tortoise is a finite time. n in this example represents the number of times Achilles catches up to where the tortoise used to be. In reality, we now know that we can treat spacetime as discreet (see: quantum physics) and so he doesnt actually do the process infinitely many times.

tl;dr: Zeno assumed the infinite sum would diverge to infinity.

pic for attention

Anonymous Tue Jul 28 18:09:33 2020 No.15986990

>>15986958
I know. But read the post chain, it said:

>People on here really believe the universe consists of Planck length pixels like some kind of computer monitor
followed by:
>For reductio, suppose that the Planck length is the minimum possible distance.

They're using "Planck length" to denote a smallest possible distance, not the actual meaning of the word, it's what I said there in the end

>>	Anonymous Tue Jul 28 18:12:25 2020 No.15987012 >>15986982 >missing the point this hard Hello /sci/ >Zeno assumed the infinite sum would diverge to infinity. No, he didn't.

Anonymous Tue Jul 28 18:15:28 2020 No.15987041

>>15986982
you're missing the entire point of the paradox. math doesn't solve anything here, you're just treating infinitisemals as a real thing. for example, you still have to admit that there are an infinite amount of steps he has to take to arrive at the point. what does this even mean? just saying "well as this *tends to infinity* (not even well defined, you would have to use epsilon delta to show the limit exists), it converges" will not work. You added nothing that wasn't already present in the thread.
Usually when this is introduced in a phil class, they go over the paradox, go over the mathematical answer, and show how that doesn't solve it in the real world, it just abstracts things like discreteness, infinity, etc.

Anonymous Tue Jul 28 18:15:48 2020 No.15987045

>>15986990
to understand plank length you need to understand how subatomic particles work. They dont move around continuously like a twnnis ball flying through the air, they kinda just appear then disappear, basically teleportation on a very small scale. Where they teleport to and from is modelled by a wave function. The function (after some mabipulation) gives the probability of seeing the particle at a given point. When a particle "moves", there's essentially 0 probability that it will move under a plank length of where it was. Nothing physical, afaik, is actually a plank length long. Think of it like the fabric of spacetime is woven with plank length holes in it.

>>	Anonymous Tue Jul 28 18:17:55 2020 No.15987066 >>15986990 Oh, I get it. I missed that. Something tells me that wouldn't be his answer because he would have said something like "I'm just assuming it for the sake of argument".

Anonymous Tue Jul 28 18:20:38 2020 No.15987095

>>15987041
>you would have to use epsilon delta to show the limit exists
If you're a first year, yeah.

It is resolved by the fact that infinite processes (if we assume the universe is continuous) happen in a finite time. Quantum physics alludes to the idea that the number of steps would probably be discreet (although very large) and thus the premise of thebparadox would be a nonphysical abstraction of the world.

>>	Anonymous Tue Jul 28 18:23:24 2020 No.15987120 >>15987045 The underlying reality of QM is still continuous. The apparent discreteness only arises at the level of observation.

>>	Anonymous Tue Jul 28 18:24:20 2020 No.15987128 What if it was Usain Bolt

>>	Anonymous Tue Jul 28 18:26:57 2020 No.15987151 >>15987095 The point of the 'paradox' is to elucidate our pre-theoretical equivocation between continuous and discrete models of physical reality. The paradox is resolved once you 'pick a side', so to speak. It's not a math problem.

>>	Anonymous Tue Jul 28 18:30:39 2020 No.15987188 >>15987151 The paradox resulted from Zeno treating it as a maths problem but lacking the correct mathematical tools to approach it because he was a Greek brainlet.

>>	Anonymous Tue Jul 28 18:34:30 2020 No.15987227 >>15987188 No.

>>	Anonymous Tue Jul 28 18:45:22 2020 No.15987307 File: 494 KB, 200x200, 1442410516824.gif [View same] [iqdb] [saucenao] [google] If nothing can be smaller than a plank then how will you hammer it and where are you going to find the nails for it?

>>	Anonymous Tue Jul 28 18:47:43 2020 No.15987326 iirc big gay catholics put cavalieri and torricelli in the shadows about indivisibles/infintesimals >>15986982 >not just expanding (1-1/2)S

>>	Anonymous Tue Jul 28 18:49:30 2020 No.15987339 >>15987307 wood glue is pretty strong these days m80

>>	Anonymous Tue Jul 28 20:11:34 2020 No.15987996 >>15980675 no one summed an infinite series ever, calculus is just speculation

>>	Anonymous Tue Jul 28 20:30:38 2020 No.15988119 >>15986838 100ooo... represents 1 followed by infinite zeros

Anonymous Tue Jul 28 20:45:51 2020 No.15988245

>>15980579
>it's similar to the problem of squaring the circle. keep increasing the number of sides that a polygon inside a circle possesses. when does it become the same as the circle?
That's not what squaring a circle refers to.

Squaring a circle was an old puzzle solved by Greek mathematicians like Pappus.

>>	Anonymous Tue Jul 28 20:46:30 2020 No.15988251 >>15980393 Scientifically, energy levels in atoms are discrete, therefore energy in chemical reactions (like taking a step) are also discrete, and not infinitely divisible.

>>	Anonymous Tue Jul 28 22:01:17 2020 No.15988848 >>15988245 wrong

Anonymous Tue Jul 28 22:09:55 2020 No.15988917

>>15988848
With no justification?

Sorry, but the problem of constructing a square with the same area of a circle is very old indeed.
https://en.wikipedia.org/wiki/Squaring_the_circle

What you are talking about is the way Archimedes proved pi. Very different.

Anonymous Tue Jul 28 22:12:11 2020 No.15988936

>>15980393
It's a retarded "paradox" that's not even a paradox. If you move at a constant speed of 10 feet per second then you will move 10 feet in one second. Zeno tried to make it confounding by having the distance shorten, but to do this you need to shorten the time. "OH HO HO you move 10 feet in one second but what about the next five feet? DURRR" yeah it takes half a second to move five feet, quarter of a second to move 2.5 feet. What's your point with this? Time does not slow down. It flows at a strict
consistent pace. This is another example of Redditors seriously overthinking something incredibly basic: movement from one point to another. It reminds me of LE HECKIN SCARY BASILISK AI DUDE WHAT IF

Just shut the fuck up

>>	Anonymous Tue Jul 28 22:20:11 2020 No.15989004 >>15980473 oh sweetie...

Anonymous Tue Jul 28 22:26:01 2020 No.15989050

Aristotles answer here is fine. Achilles can complete an infinite series of tasks, provided we understand that this infinitude comes from infinite divisiblity and not infinite extension. Achilles cannot mark his traversal of an infinite seires of decreasing distances, but he can travel an infinitely divisible distance.

>>	Anonymous Tue Jul 28 22:43:56 2020 No.15989188 >>15988917 your own source does not support your post here >>15988245

>>	Anonymous Tue Jul 28 23:07:27 2020 No.15989356 >>15989188 It sure does, sir. Just because Pappus is not mentioned within the Wikipedia article does not mean I am not correct. You think all available knowledge is on Wikipedia? You are incorrect, sir.

>>	Anonymous Tue Jul 28 23:12:27 2020 No.15989398 >>15982269 NOTHING PROVES THAT IT AINT BRUH JOKES ON YOU SCIENCE BITCH

>>	Anonymous Tue Jul 28 23:24:52 2020 No.15989506 >>15988936 Lmao. Get a load of this moron.

Anonymous Tue Jul 28 23:31:25 2020 No.15989550

Maybe I should go to /sci/ for this, but they're a bunch of faggots. This thread is making me realize how shaky my understanding of limits is. I mean, I understand the epsilon - delta proof of limits, BUTTTT isn't that still just arbitrarily choices, where things never ACTUALLY arrive at the limit?? How is that ultimately different than the paradox, and how does it get rid of the paradox?

You are arbitrarily close... but you still aren't AT the value, and that arbitrarily closeness could in theory still be an infinity away no matter how scaled down the arbitrary closeness is... It's like trying to take up all infinity with an infinite amount of objects, it's just another paradox???

>>	Anonymous Tue Jul 28 23:55:46 2020 No.15989720 >>15989550 What is the limit of the sequence 1,1,1,1,1,1,..? Or if you want to use a function what is the limit of the function f(x)=1 as x approaches infinity?

>>	Anonymous Wed Jul 29 00:06:06 2020 No.15989801 >>15989720 ... unless there is a trick here obviously 1, but how does this help me evaluate the limit of say (x^2-1)/x-1 as x -> 1? Or anything asymptotic where the function approaches a value but never actually arrives at it?

Anonymous Wed Jul 29 00:06:49 2020 No.15989811

>>15989506
No but how is it even a paradox? You're halving the time along with the distance, which is just arbitrary infinite division that does not actually make traversal from a to b have anything to do with mathematical limits. it would actually work for the sake of discussion if it was "in one second you move 10 feet, the next second five feet, the next second 2.5 feet and so on"

>>	Anonymous Wed Jul 29 00:19:05 2020 No.15989924 >>15989801 What is the function that never actually arrives at the value? Simple algebra will tell you when Achilles catches the turtle. You can sum the infinite series and it will give you the same answer

Anonymous Wed Jul 29 04:28:12 2020 No.15991117

>>15986884
Yes.
They're all wrong if thought itself is bound by granularity, it means we can't imagine non-granular things. Yet we can through mere impossibility in seeing the grains see everywhere perfect circles, but all of these are illusions. There's an infinite difference between a circle of Planck lines and a real circle.
It means all this math you mentioned have no existence, they're not even illusory they don't exist due to materialism. OUR THOUGHTS THEMSELVES HAVE Pixels this means just like we think there's a perfect circle over there we think our math have X properties because we can't find the pixels of our mindscape.

Anonymous Wed Jul 29 04:31:40 2020 No.15991134

>>15991117
It's like if infinity was mathematically impossible. Or it's exactly as if infinity was impossible. Materialism and Planck reality leads to the impossibility of quantitative infinity within any finite space. Mental or otherwise. Which makes circles physically and mentally impossible.

Anonymous Wed Jul 29 04:36:51 2020 No.15991156

>>15989811
The paradox is about how we intuitively think of space and time in both continuous and discrete terms, and that those conflicting models cannot both be implemented in our physical universe. Once you know the geometry of actual spacetime, the paradox doesn't arise since the model will be consistently continuous or discrete.

>>	Anonymous Wed Jul 29 04:56:58 2020 No.15991228 >>15984455 >There is no last digit in an infinite sequence. Depends on how you define that sequence.

Anonymous Wed Jul 29 05:02:49 2020 No.15991247

Physicist here, haven't had time (nor the will) to read through every single reply, but what the hell is this.. /lit/ is 'supposed' to be a sort of intellectual board, but instead there's people trying to use the freaking Planck length and Gnosticism (???) to explain the Paradoxes. I'm phone posting and only just woke up so I'll be brief, but can expand on my answers if someone wants.
First of all, not all paradoxes are unsolvable or circular or whatnot - some paradoxes simply mess with our 'naive' and everyday understanding of something. Zeno's paradoxes are like this. The "dividing distances in half" one and the "Achilles and tortoise one" both rely on the idea that to do an infinite amount of tasks, you certainly require an infinite amount of time. One's very first response to the paradox is common sense itself - obviously Zeno has a point when discussing movement, but you also obviously move, so the problem lies somewhere inbetween. And indeed, a formal solution to the problem would be infinitesimal calculus, where one easily proves that many infinite sums add up to a finite number - and Zeno's sum of 1/2+1/4+1/8+...1/2^n+... is one such case. The same is true for Achilles and the tortoise.
Regarding the arrow paradox, Zeno basically introduced the notion of vectors with his thought experiment and what he said is used in elementary physics all the time. In a sort of imagined instant of time - which is 'mathematically' super precise and without length so to speak - you can assign velocity and acceleration vectors to an object, which help in deducing the dynamics of said object. In other words, what Zeno and vectors posit are photographs - "instants" of time within a larger framework. No paradox there either, just counter intuitive to our daily life notions.

Anonymous Wed Jul 29 05:10:32 2020 No.15991278

After reading some additional posts, especially the ones dealing with '0.999...' and infinite sums, I have got to share with you people infinite sums that can be rearranged to give different answers, I just hope it doesn't completely break one of you. I'll do that a tad bit later, when I sit behind my pc, hopefully the thread survives till then.

>>	Anonymous Wed Jul 29 05:12:30 2020 No.15991283 >>15991278 That's the first year in the university, so not some obscure knowledge. But you can do it, it will not make the thread worse.

>>	Anonymous Wed Jul 29 05:15:11 2020 No.15991292 File: 112 KB, 1080x887, CAC369B2-C110-43AF-AA52-31D00C85D885.jpg [View same] [iqdb] [saucenao] [google] >>15980445 >0.999.... = 1

>>	Anonymous Wed Jul 29 05:16:31 2020 No.15991298 >>15980473 >humans can only observe down to x therefore x is all that exists, x - 1 doesn’t exist

>>	Anonymous Wed Jul 29 05:21:57 2020 No.15991318 >>15985545 >making calculations with infinite numbers Lmao

Anonymous Wed Jul 29 05:22:49 2020 No.15991323

This threadbis full of autism. It is purely a problem of descrription; the question is if you have a way to describe something in an infinite amount of steps it necessarily takes an infinite amount of time?
The answer is, obviously, no. Since we can easily place an upper bound on the necessary time in some cases. And, if you are willing to accept that 1/2 + 1/4 + 1/8 + ... converges to one, you can divide everything up in an infinite amount of steps.

>>	Anonymous Wed Jul 29 05:23:33 2020 No.15991327 >>15985545 That's a wonderful proof, I can prove Fermat's theorem in a couple of lines in a same way.

>>	Anonymous Wed Jul 29 05:26:02 2020 No.15991337 File: 27 KB, 600x418, 414381_spTyhrbhtZ_15540702252530.jpg [View same] [iqdb] [saucenao] [google] >math discussions on /lit/

>>	Anonymous Wed Jul 29 05:26:59 2020 No.15991342 >>15991337 Better than political or religious discussions.

>>	Anonymous Wed Jul 29 05:27:18 2020 No.15991344 >>15991342 That's also true

>>	Anonymous Wed Jul 29 05:27:37 2020 No.15991347 File: 13 KB, 480x412, BAE855A4-BC95-49BA-9FDF-8076CFE5A036.jpg [View same] [iqdb] [saucenao] [google] >>15991337 >philosophy discussions on /sci/ At least we acknowledge the use of mathematics instead of pretending it has none

>>	Anonymous Wed Jul 29 05:35:31 2020 No.15991379 >>15991337 It's a philosophical question, retard.

>>	Anonymous Wed Jul 29 05:40:27 2020 No.15991392 File: 15 KB, 1268x392, file.png [View same] [iqdb] [saucenao] [google] >>15980445 sure, but time still passes after taking over the tortoise, which means the event happened between any point of time during the approaching and any point of time after

>>	Anonymous Wed Jul 29 05:43:29 2020 No.15991403 >>15991392 oh, i thought that it was >approaching something infinitely is not the same as having arrived so here was my counterpoint to that

Anonymous Wed Jul 29 05:44:07 2020 No.15991407

First we'll look at the moment when Achilles did no progress.
Then at the moment when he finished half the distance.
Then again at the moment when he had no progress.
Then again at the half-distance moment and so on.

As you can see, such a sequence has no limit at all. Paradox?

Anonymous Wed Jul 29 06:14:59 2020 No.15991535

>infinite number of tasks
this also asserts that a task can be done in an infinitely short amount of time and that a task can be infinitely divided into smaller and smaller tasks
we can compare the finite number of actions in decreasing amounts of time in a manner that is consistent with the larger single task in the larger single time

>>	Anonymous Wed Jul 29 06:32:34 2020 No.15991580 There is no good definition of infinity. Of course you can define it as being not finite, but this isn't any better.

>>	Anonymous Wed Jul 29 06:34:54 2020 No.15991592 >>15991580 Having a subset that maps to the naturals.

Anonymous Wed Jul 29 06:48:09 2020 No.15991638

>>15986877
Because Planck length 1.5 would have to be an indivisible region of space, despite not being a maximally small region of space. It is incoherent for empty space to have this property.

Distance measures how much space there is in a region. A region that is 1.5 units long thus contains as much space as a 1 unit region and then some. If we subtracted the unit from the former region, the remainder would be 0.5 units long. But this length is impossible, per our supposition. So all distances must be integer multiples of the smallest possible distance, if indeed there is such a distance, lest we run into contradiction. Turns out we run into contradiction anyway, though, due to the Pythagorean theorem.

(I basically already made this point in the post you're replying to when I pointed out that is incoherent to think that a region of space that is 2 Planck units in length could somehow fail to contain two 1 Planck unit regions as proper parts.)

Anonymous Wed Jul 29 06:53:22 2020 No.15991657

>>15986810
Again, you're taking the construction metaphor too literally. The point is that these square regions exist in our space, regardless of whether we have the tools to measure them to arbitrary degrees of precision.

And, again, I'm not talking about square material objects, but about square regions of spacetime, that again exist whether or not they are demarcated as such by humans.

If you deny that such square regions must exist due to the possibility that space is curved or some such, the point can equally well be made using differently shaped regions of spacetime wherein the length of some edges are mathematically guaranteed to not be integer multiples of the units in which the other edges are measured. It's a very general argument.

Anonymous Wed Jul 29 06:56:11 2020 No.15991666

>>15986916
>>15987066
This guy gets it. Of course I don't think the Planck length is actually the minimum possible length. My whole point has been to show that it CANNOT be the minimum possible length!

The guy you're discussing things with is exactly right, but doesn't seem to realise that the three of us are actually all in agreement on this point.

>>	Anonymous Wed Jul 29 06:59:03 2020 No.15991678 >>15986970 Problem is, the second piece has both a 1 unit piece and a 0.5 unit piece as proper parts. The geniuses saying that the Planck unit can be the minimal length at the same time as there exist 1.5 Planck unit lengths fail to realise this.

Anonymous Wed Jul 29 07:00:34 2020 No.15991688

>>15980445
Incorrect. If the limit of a function f(x) as x approaches 1 is 1, it does not follow that f(1) = 1. For example, f(1) may be undefined. In any case, you’re still short an infinitesimal even in the situation you’re thinking of. There’s a reason why limits exist and why a limit is not equivalent to actual equality.

>>	Anonymous Wed Jul 29 07:38:51 2020 No.15991877 What if in the exact moment when Achilles gets equal with the tortoise, the universe is destroyed?

Anonymous Wed Jul 29 07:59:44 2020 No.15991958

>>15991688
There are two kinds of limits being talked about here the ones that apply to functions and the ones that apply to sequences. The paradox is talking about the sum of a infinite series and the sum of an infinite series is defined as the limit of that infinite series and the limit of an infinite series is defined as the limit of the associated sequence of partial sums.

A=Achilles speed T=Tortoise Speed S=Starting distance
Time of First Step:
(S/A)
Second Step:
(T/A)(S/A)
3rd:
(T^2/A^2)(S/A) and so on
This is a geometric series with ration of (T/A) and starting value of (S/A) so by the formula for the sum of a geometric series the limit is (S/A)/(1-(T/A)) rewritten as (S/(A-T)). Solved algebraically Ax = Tx + S x=(S/(A-T)) so the simple algebra and the infinite sum give the same answer

Anonymous Wed Jul 29 08:18:18 2020 No.15992022

I wanted to write a more extensive answer once I got to my computer, but having read almost every reply in the thread and seeing that the few answers (including my own) which were factually correct getting completely ignored while a couple of borderline idiots are still discussing Planck's length has made me decide to not write anything new at all.
All I know right now is that this thread (and probably this board) is filled with people who've never even took a course in University math, physics or philosophy, let alone graduated in one of those fields. And even if they did, they seem to be people who got bad grades but only "because the professor was really unfair and to be fair the subject matter wasn't all that interesting". Sad and pathetic.
Not to mention that, even ignoring the answers in the thread, one can easily today find an answer on YouTube, as there are countless videos by philosophers and mathematicians discussing it on that platform.
But the amount of replies attests to something else too - you only ever see this amount of replies on threads that either
>require no knowledge of the subject matter
>ask to write what's on one's mind
>posting recent/overall purchases
>or are involved with the latest meme spamming
Can't believe that at one point I thought this site to be a more interesting and dynamic option than stack exchange. At least there you have the slim opportunity to have your question answered by a leading figure in whatever field, here you'll get answers from 20 year old hotheads who read that one popsci book 3 years ago and if they recall correctly, the Planck length was like really tricky my dude...
Goodbye, everyone.

Anonymous Wed Jul 29 08:25:21 2020 No.15992064

>>15992022
>he thinks that that finishing the university course gave him the ultimate universal wisdom
>he thinks that philosophy goal is always to find the true answer and further discussion will be unnecessary
>he thinks that he is on the exam where there is right answer and fail the course answer
Maybe you should really stick to the youtube videos.

>>	Anonymous Wed Jul 29 08:32:08 2020 No.15992090 >>15992022 >people who've never even took a course in University math, physics or philosophy >who've never even took look out boys--le genius hath logged on!

>>	Anonymous Wed Jul 29 08:32:49 2020 No.15992092 >>15980424 QT says it discrete

>>	Anonymous Wed Jul 29 08:34:56 2020 No.15992098 >>15986877 lollllll dumb person: >the Planck length is the minimal distance, but some things are 1.5 x the Planck length smart person: >then how much longer are those things than the Planck length? dumb person: >uh uh ummmm uhhhh MOMMMYYYYYYYY

>>	Anonymous Wed Jul 29 08:36:42 2020 No.15992111 >>15992098 >then how much longer are those things than the Planck length? Planck length

>>	Anonymous Wed Jul 29 08:38:07 2020 No.15992116 >>15992090 typos that cannot be attributed to a slip of the fingers but instead must be due to a derangement of an exceptionally simple mind are my absolute favorite.

>>	Anonymous Wed Jul 29 08:39:29 2020 No.15992127 >>15992111 >0.5 = 1 very smart take brah

>>	Anonymous Wed Jul 29 08:43:45 2020 No.15992152 >>15992127 If two spaceships fly in opposite directions with 3/4 speed of light, what is their relative speed?

>>	Anonymous Wed Jul 29 08:44:56 2020 No.15992161 >>15992127 shutup he obviously has a very bright future ahead of him

Anonymous Wed Jul 29 08:46:21 2020 No.15992170

>>15980579
Bergson addresses this in Creative Evolution. Space cannot be continuous, because spatiality is by definition discreteness. Our attempts to apply a uniform grid or geometry to space are simply an intellectual extension of this larger, real-world trend for concrete duration to unravel into spatiality and geometry. So Xeno's paradox is founded on a misunderstanding of the nature of space.

Anonymous Wed Jul 29 08:48:15 2020 No.15992187

>>15985859
>you're just a set of patterns in your brain
So I do exist in physical world. Unlike infinity.
>Exists as a set of pattern in many human brain
No, that's an idea of infinity. Infinity itself does not exist in real world. You can imagine a unicorn all you want, the idea of a unicorn would be real as a set of electrical signal patterns in your brain, the animal itself would be not. You are not getting anywhere with this philosophical bullshit.

>>	Anonymous Wed Jul 29 08:53:18 2020 No.15992221 >>15992187 Large numbers don't exist too then. Have you ever seen the googol (not google)?

>>	Anonymous Wed Jul 29 09:01:36 2020 No.15992264 >>15992152 6/4 c. Speed of light is a limit of information transfer, moron. How do you think the universe is 93 billion light years wide while being only 13 billion light years old.

>>	Anonymous Wed Jul 29 09:02:48 2020 No.15992275 >>15992221 Imagine that, they don't.

>>	Anonymous Wed Jul 29 09:03:44 2020 No.15992286 >>15992264 Lols special relativity fail. Newtonian go BRRRR

>>	Anonymous Wed Jul 29 09:06:03 2020 No.15992291 >>15992275 Natural numbers actually don't exist too. These are not two apples, these are apple and apple and claiming that they form some set is an abstract speculation. Let's put aside the question of the reality of appleness.

>>	Anonymous Wed Jul 29 09:07:43 2020 No.15992298 >>15992264 >6/4 c. That's a Nobel-worthy discovery.

>>	Anonymous Wed Jul 29 09:09:22 2020 No.15992310 >>15992291 Nice try deflecting, but no. Go play with your infinitely small points elsewhere, real physical world is for real things.

>>	Anonymous Wed Jul 29 09:09:45 2020 No.15992315 >>15992264 >How do you think the universe is 93 billion light years wide while being only 13 billion light years old. No one have ever traveled it through.

>>	Anonymous Wed Jul 29 09:11:26 2020 No.15992323 >>15992310 >Nice try deflecting, but no. You can't escape the reality with such tricks.

>>	Anonymous Wed Jul 29 09:11:41 2020 No.15992326 >>15992264 I am reductio anon, and I do not endorse this message.

>>	Anonymous Wed Jul 29 09:13:03 2020 No.15992332 >>15992264 >6/4 c Wrong, you're using Galilean transformations instead of Lorentz ones. >How do you think the universe is 93 billion light years wide while being only 13 billion light years old. Inflation is the current leading theory.

Anonymous Wed Jul 29 09:13:22 2020 No.15992333

>>15992298
No, you are just a victim of common core education and wail to comprehend that the speed of light in reality is not defined by light, but is the limit at which the information can be exchanged. Two spaceships flying in opposite directions with 3/4 speed of light can not exchange any information between each other. The same would happen to every particle in the universe if the Big Rip theory is true.

>>	Anonymous Wed Jul 29 09:14:44 2020 No.15992340 >>15992333 >Two spaceships flying in opposite directions with 3/4 speed of light can not exchange any information between each other. They surely can, by radio. It isn't any different from exchanging it with Earth.

>>	Anonymous Wed Jul 29 09:17:34 2020 No.15992355 >>15992090 >start out sentence with 'who've never even taken' in mind >mid sentence change mind to "who never even took" >get a mix of both Not even him but that type of shit happens to everyone, everywhere.

>>	Anonymous Wed Jul 29 09:29:29 2020 No.15992409 >>15992355 but it's particularly satisfying when it happens to smug morons while they're in the middle of lecturing everyone else about their intellectual shortcomings

>>	Anonymous Wed Jul 29 09:29:35 2020 No.15992410 How can motion occur if there is no certain "next" point which you can transition to? This is why we have quantum mechanics and uncertainty.

>>	Anonymous Wed Jul 29 09:32:09 2020 No.15992422 >>15992410 Nothing to do with quantum mechanics just basic calculus. This board is full of pseuds

>>	Anonymous Wed Jul 29 09:35:40 2020 No.15992436 >>15992090 You should never use 'it's' twice in a sentence, next time (or first time) you have you use 'it is'.

>>	Anonymous Wed Jul 29 09:43:28 2020 No.15992487 >>15980393 Because you will eventually get to such a sub-atomically small unit of measurement or particle, a quark or string or whatever, that it is impossible to split the distance in half.

>>	Anonymous Wed Jul 29 09:47:28 2020 No.15992505 File: 362 KB, 717x508, many or one.png [View same] [iqdb] [saucenao] [google] The Solutions to all the Problems in this thread.

>>	Anonymous Wed Jul 29 10:00:35 2020 No.15992574 >/lit/ is full of popsci casuals I expected nothing more

>>	Anonymous Wed Jul 29 10:02:36 2020 No.15992587 >>15980393 >How has it been solved Achilles literally walks past the turtle

>>	Anonymous Wed Jul 29 11:14:21 2020 No.15992982 >>15992436 Did someone do this?

>>	Anonymous Wed Jul 29 11:29:55 2020 No.15993061 bump

>>	Anonymous Wed Jul 29 12:02:51 2020 No.15993224 >>15980393 You can never score if your goalpost keeps moving bruh

>>	Anonymous Wed Jul 29 12:05:58 2020 No.15993251 Trying to grab the turtle takes nonzero time.

>>	Anonymous Wed Jul 29 13:25:19 2020 No.15993752 >>15992982 all the time >>15992355

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/lit/ - Literature