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Old 9th September 2021, 08:45 AM   #41
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Originally Posted by Robin View Post
OK for anyone not convinced tell me this.

Why are convergent series inconsistent if you try to use them as a description of actual motion?
Because...

Case 1:. "Actual motion" is quantized. If that's the case, then there is a small, finite, distance over which motion occurs. Since that distance is not infinitely small, an infinite series is not needed to describe it.

Case 2:. "Actual motion" is continuous. Therefore, motion does not consist of discrete steps, such as 1/2, 1/4, etc. And once again infinite series are not necessary.

Either way, when racing against turtles, we don't run halfe the distance, then a fourth, etc. Infinite series can, in some cases, be a handy mathematical tool, but they don't model real motion.

Eta:. If "actual motion" is continuous, then the key descriptors of motion are rate and direction.
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Old 9th September 2021, 08:45 AM   #42
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
So basically you're just trolling with repeating the same nonsense over and over instead of even trying to understand what's being said? Well, I guess it's easier than actually engaging the brain.
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Old 9th September 2021, 08:46 AM   #43
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Originally Posted by HansMustermann View Post
No they're not. And if in all honesty that's what you're understanding, go see a neurologist.
If you were to search through an infinite set of values, none of which were 3, would you find 3?
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Old 9th September 2021, 08:46 AM   #44
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Oh dearie me, the attempted pile on backfired on them.
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Old 9th September 2021, 08:47 AM   #45
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Nobody is falling for this obvious of a linguistic trap question.

You're basically asking "What is outside of everything?" but trying to turn it into a math problem, a poor man's version of the Paradox of the Grand Hotel, in order to support a bit of philosophical gibberish that doesn't even relate to it.

You might as well go "If an unstoppable force meets an immovable object, then the ship is still the Ship of Theseus."
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Old 9th September 2021, 08:47 AM   #46
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
Well, this has got to be new on the Internet Troll repeats the same idiocy ad nauseam, when they don't actually have a point. Got it already, really. No need to keep repeating it like a broken parrot.
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Old 9th September 2021, 08:47 AM   #47
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If you were to search through an infinite set of values, none of which were 3, would you find 3?
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Old 9th September 2021, 08:48 AM   #48
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Originally Posted by HansMustermann View Post
Idiot troll repeats the same idiocy ad nauseam, when they don't actually have a point. Got it already, really. No need to keep repeating it like a broken parrot.
If you were to search through an infinite set of values, none of which were 3, would you find 3?

You do realise that it is very obvious that you are avoiding the question, don't you?
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Old 9th September 2021, 08:48 AM   #49
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
If A doesn't equal B, what happens when A equals B?
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Old 9th September 2021, 08:49 AM   #50
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Wasn't this covered on this forum elsewhere recently? I think I'll be repeating someone.
Originally Posted by JoeMorgue View Post
Quantum Mechanics solved all of this.
This problem isn't even in the domain of QM. If you think that space has been determined to be quantized that wouldn't be right but it's a common misconception. In particular, The Planck length, which is the usual source of this confusion, is not known to be some minimum distance that things can move. It would be better thought of as defining the minimum volume of space that can be measured.

Calculus "solves" the problem, if ever there was one. I always considered this paradox to be an example of reduction to absurdity and questioned the premises (in whatever form the argument is presented).
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Old 9th September 2021, 08:49 AM   #51
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Originally Posted by JoeMorgue View Post
If A doesn't equal B, what happens when A equals B?
If you were to search through an infinite set of values, none of which were 3, would you find 3?
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Old 9th September 2021, 08:50 AM   #52
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Stay glued to your seats

And for the record my seat is still pretty much frictionless as this point.
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Old 9th September 2021, 09:09 AM   #53
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
Probably not.
How does that stop a thrown rock hitting your head?
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Old 9th September 2021, 09:12 AM   #54
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Originally Posted by Captain_Swoop View Post
Probably not.
How does that stop a thrown rock hitting your head?
By excluding the point where it connects to their head from the model, obviously. Really, that's been the whole confusion in two different threads already: that if your model excludes some points, it somehow says something about the actual movement not reaching those points, as opposed to just saying that the model is wrong.
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Old 9th September 2021, 09:13 AM   #55
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Originally Posted by Robin View Post
In the set of all the partial sums of the series, would you find the algebraic sum of the infinite series?
No.

The limit of the sequence is not a member of the sequence.



What's your point?
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Old 9th September 2021, 09:14 AM   #56
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Originally Posted by Robin View Post
Wouldn't it be fun if someone actually answered that question.
The infinite series summing to 3 is just another way of describing the exact same mathematical concept of 3 that the real number "3" describes. Which is all very well for the artificial world of mathematics.

All you're really saying is that traversing a number line in conceptual space according to certain arbitrary axioms may not be exactly like traversing a distance in spacetime. Which is what everyone else has been saying to you all along. The map is not the territory.

Just because it suits mathematicians to define 3 as an infinite sum of infinitesimals in some artificial contexts, doesn't mean that's how spacetime defines 3. You need to drop that assumption and try again.
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Old 9th September 2021, 09:17 AM   #57
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
No.
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Old 9th September 2021, 09:23 AM   #58
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Originally Posted by HansMustermann View Post
And what I'm saying is that if your problem is determining movement from the 0 mile point to the 3 mile point, and you chose a model that excludes 3, it's just a case of YOU choosing the wrong model for the problem. It's not saying anything profound about the problem. It's just saying that you should pick a model that works instead of a nonsense one.

I mean, what the hell... the idea that you must choose a model that fits the problem you're trying to solve, was taught to me in physics class since middle school. Much as I like to be a snarky assh... err... hat about other people's education, I assume the same must apply to American schools, or really any schools in the world.
The mistake Robin is making is not understanding that the infinite set of values she's referring to *is* 3. It's defined that way as a direct result of the arbitrary axioms of mathematics in which the construct appears and has relevance.

It's (a very little) like asking, "how can you ever find a human body by examining each and every cell in a human body?" The truth is that if you do that, you'll have found an entire human body, down to the cellular level.

Zeno's paradox only makes sense if we assume that spacetime conforms to certain arbitrary mathematical axioms about the artificial concept of a number line. Something we have good reason not to assume, as Zeno so ably demonstrated.
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Old 9th September 2021, 09:23 AM   #59
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
Where's Doron Shadmi?
I want him here now to answer this question!

But absent Doron, I'll hazard what he would say.

Infinity can't be limited or completed. You can't complete the search and you can not exclude 3. The line between 1 and 3 is finite. Any finite quantities you parse can be summed to a finite quantity.

I hope this makes it worse.
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Old 9th September 2021, 09:24 AM   #60
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Originally Posted by Robin View Post
Because everybody here is actually saying to me that they could search through an infinite set of numbers, none of which is 3 and find 3.
The infinite series you're talking about is 3 by definition.
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Old 9th September 2021, 09:26 AM   #61
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
No, you wouldn't find 3. Fortunately, that's not what we're doing. We're iterating through an infinite series of values that comprise the value 3 under certain arbitrary and artificial axioms.

3 infinitely subdivided is still 3. Iterating over the infinite subdivisions of 3 is still 3.

And of course, an artificial number line and its defining axioms are still not spacetime as such.

Gosh this is fun!
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Old 9th September 2021, 09:28 AM   #62
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
Depends which series of values we're talking about. If I'm iterating over the infinite series of values that comprise 3 under certain arbitrary rules, then I'm pretty much guaranteed to find 3 every time.
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Old 9th September 2021, 09:29 AM   #63
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Originally Posted by Robin View Post
If you were to search through an infinite set of values, none of which were 3, would you find 3?
Of course I would, tautologically: I can't iterate over the infinite subdivisions of 3 without already having found 3 to subdivide it.
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Old 9th September 2021, 09:29 AM   #64
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Originally Posted by Robin View Post
A - bloody - stoning.

A bunch of people implying that an infinite set of values, none of which were 3, could be searched through and 3 could be found but they won't say it explicitly
You're doing math wrong.
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Old 9th September 2021, 09:32 AM   #65
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I think it was Cantor that made the argument that there was an equal amount of whole numbers and an equal amount of odd numbers.

You start counting 1, 2, 3, 4, 5, etc into "infinity."
You start counting 1, 3, 5, 7, 9, etc into "infinity."

You will never count more whole numbers than odd numbers.

To me the problem with this (in some contexts) is that just labeling the "sets" arbitrarily.

But this has as much to do with Zeno's Mistake of Motion (as I will now be calling it) as this inane "If I have everything where do you find something that isn't in it" question.
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Old 9th September 2021, 09:38 AM   #66
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Originally Posted by JoeMorgue View Post
But this has as much to do with Zeno's Mistake of Motion (as I will now be calling it) as this inane "If I have everything where do you find something that isn't in it" question.
The worst part is it isn't even the right question. The question of motion Robin is actually trying to ask is "where can I find a thing among all the parts of the thing?"

And the answer to that, obviously, is, "if you have found all the parts of the thing, you have found the thing."
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Old 9th September 2021, 09:40 AM   #67
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I think that never since the time of Galileo's trial has his famous aphorism been more apt, than in this thread.
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Old 9th September 2021, 09:50 AM   #68
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Originally Posted by Meadmaker View Post
Bad luck. First you have to save half the page. Then 3/4. You'll never save it all.
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Old 9th September 2021, 10:04 AM   #69
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Mod WarningRobin - a series of your posts have been moved to Abandon All Hope as a rule 6 breach.
Responding to this mod box in thread will be off topic Posted By:Darat
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Old 9th September 2021, 10:19 AM   #70
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Originally Posted by theprestige View Post
The mistake Robin is making is not understanding that the infinite set of values she's referring to *is* 3.
And I'm saying that even that doesn't really matter all that much. I gave an example earlier where fundamentally the series doesn't even converge to that value. Like, I'm running 2 miles, but I define the series so that it converges to 1.

Or here's a problem where another point than the final one is missing from the model: a train is going at 60 miles per hour between two points A and B on the tracks, which are a mile apart. So basically it'll take a minute to get from A to B. So now I do Zeno's dichotomy: it has to pass through the 1/2 miles point first, then through the 3/4 mile point, then through the 7/8 mile point. But I'm standing on the tracks some 1/4 of a mile from point A. That's not a point in that series. I have the point that's 1/4 miles from B in the series, but not the one that's 1/4 miles from A. It's not even a point the series converges to. It's just outside it. Well... can that series predict when is the train going to hit me? More importantly, does the fact that my point is missing from the series, actually mean that I'm safe to stand on the tracks there, because it's not one of the points in the model?

The more basic issue is: The model is supposed to contain everything that I need to solve the problem (and only that.) If the model missing the solution point entirely from the set of values it can produce, then it's a wrong model. If I chose a model that doesn't cover all the points I need for the problem, then it's just a case of me choosing the wrong model.

More importantly, a good model reflects reality (or rather the part of it that are relevant.) Not the other way around. Choosing the wrong model doesn't change reality. It's a model, not a voodoo doll. Choosing a model which makes it impossible to calculate when the train will hit me, doesn't mean the train never will.


TL;DR version: if Robin needs to find 3, and their chosen model is a series that never equals 3 (for whatever reason), then that's just a case of Robin choosing the wrong model for that problem. They should choose a better model, then. That's really all there is to it. There is no deeper insight there.
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Old 9th September 2021, 10:20 AM   #71
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Basically "Don't model the problem specifically so it won't work, then demand a solution."
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Old 9th September 2021, 10:22 AM   #72
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Thanks, Darat. Including for moving my answers to that, which weren't helping the discussion either.
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Old 9th September 2021, 10:23 AM   #73
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Originally Posted by JoeMorgue View Post
Basically "Don't model the problem specifically so it won't work, then demand a solution."
That. You just put it more clearly and concisely than I could.
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Old 9th September 2021, 10:31 AM   #74
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But even beyond that "modeling" pure math seems like... a less than pointfull exercise anyway.

The base concept is flawed. There is not an "infinite" number of recursive halfway points between Point A and Point B so there's no paradox to even account for.

Motion is demonstrably possible in real life so there's no reason to even be asking the question.

Trying to model is as some weird version of the Russell-Zermelo paradox both doesn't work and doesn't make sense.

It's fractally wronger than not even wrong.
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Old 9th September 2021, 10:55 AM   #75
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Originally Posted by Robin View Post
OK for anyone not convinced tell me this.

Why are convergent series inconsistent if you try to use them as a description of actual motion?
That is a damn fine question. However, the answer is probably not, "if a convergent series can't describe an observed phenomena, that phenomena doesn't exist."

You're mistaking the limitation of the tool for a limitation of reality. In the end, it doesn't matter if calculus can't accurately describe movement through spacetime. Eppur si muove.
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Old 9th September 2021, 10:56 AM   #76
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Well, it helps if you understand what Zeno's point actually was, since this thread was an exercise in strawmanning it. Just like it was the case in the other thread. Zeno's point wasn't "the actual series converges to X, but none of the members actually equal X." Whether or not the series itself includes the final point was NOT the point. The point was that Zeno thought that that an infinite number of finite times can't add up to anything else than infinite time. (Mis-understanding and mis-using infinity is THE common denominator for Zeno.)

Which makes the whole handwaving exercise in this thread a case of missing the point in more than one way:

1. Zeno's argument doesn't even work if you stop at any point short of literally summing it up to infinity. A finite sum of finite times, sure, that's obviously finite. Even Zeno could figure that one out. His argument needs an infinite number of terms to even seem like it works, even after ten pints and a lobotomy. So saying that yeah, but a given member in the series -- i.e., one after a finite number of steps -- isn't yet equaling the limit, is just no longer Zeno. It's something else entirely.

2. Even IF the series somehow failed to reach the limit, even after infinite steps, is not making a difference in Zeno's argument. Let's say the series actually falls short of reaching the destination. (Even if by a truly infinitesimal amount, like 1 planck unit.) That means that the time to actually reach the destination is actually (infinitesimally) higher than the time that the series sums up to. But Zeno says it sums up to infinity. He's wrong, of course, but that's what he says. So your end point being even higher, is still not a way out or anything.

It's basically like saying X=∞, BUT -- ah-ha! -- my actual result is X+1. Like, so what?


Also, it helps if you understand the general position of the Eleatic school of philosophy. It's basically a version of Plato's allegory of the cave. Basically I may think I see a rabbit, or at least its shadow on the cave wall, but in reality it's some guy holding his hands together with two fingers pointing up outside the cavern. Not actually Plato's words, but my attempt to illustrate the general concept without writing a whole philosophy paper. What you perceive (a rabbit) is not the actual thing that causes that perception (a guy doing shadow figures.) There's a hidden 'real' reality behind the reality you perceive.

Sure, the reality you perceive is that you shot an arrow and it moved all the way to the target, but that's basically an illusion. That's just your perception of it. In reality, there's an underlying immovable, unchanging, and indivisible... err... thing (well, ok, "being") behind that perception. You may see an arrow moving and hitting a target, but that's just your perception of it, while the 'real reality' behind it never moved.

That is basically what the Eleatics were going on about.


And if at this point you want to call it stupid and pointless... well... exactly. I mean, you know I'm not even against philosophy per se, but even I wouldn't call it good philosophy.
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Last edited by HansMustermann; 9th September 2021 at 11:22 AM.
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Old 9th September 2021, 10:59 AM   #77
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I'm reminded of how so few people got that Schrodinger's Cat Thought Experiment was Schrodinger basically going "See how amazingly absurd this is, this can't actually happen, the cat can't be alive and dead."
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Old 9th September 2021, 11:07 AM   #78
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It's kinda like that, indeed, except in Zeno's case it was more like "see how amazingly absurd it is that reality could be really real"
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Old 9th September 2021, 11:08 AM   #79
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Maybe we should shift gears a bit and ask Robin for practical applications. Obviously, assuming motion is real has a *lot* of useful results in the real world. (Assuming "usefulness" and "the real world" are also real.) What are the useful results to be derived from assuming motion is not real? If it doesn't lead to a new form of steel that will revolutionize the railroad industry, who cares?

This is like ghosts and fortune telling. If we stipulate the claim is true, the conclusion is that it is entirely useless and inconsequential. Assuming ghosts are real doesn't produce any practical applications that aren't produced by assuming ghosts aren't real.

Whether motion exists or not, it's pretty clear that the world works just fine and makes tons of sense if we assume it does exist. The world makes no sense at all if we assume it doesn't. Arriving at a nonsensical conclusion should be a big red flag to Robin that they're on the wrong track.

On the other hand, the lack of progress along that track does lend some credence to the premise that motion doesn't exist.
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Old 9th September 2021, 11:10 AM   #80
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Well that and Zeno lived in the 5th Century BCE and Schrodinger in the first half of the 19th century so I'm going to assume the person who lived after we learned the Earth revolved around the Sun and that maggots didn't magically form in rotting meat knew what his was talking about more.
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