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| Thread: The Real & the "mathematical world" are both DISCRETE |  This thread is pages long: 1 2 3 4 5 6 · «PREV / NEXT» |
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Gandalf196
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posted February 16, 2021 04:35 PM |
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JollyJoker said:
No, that's not true. The infinite dimension is already in play with the natural numbers which are discrete (and (countably) infinite), and the rational numbers are discrete as well (and still countably infinite).
In fact, if you follow the (mistaken) assumptions of the paradoxon, then Achilles reaches the turtle in the infinite (not never), mathematically spoken.
I believe you did not read my words correctly.
If the universe in finite (in both time and space), then, for all practical purposes, it can be seen as a chessboard with an enormous number of houses of the smallest size available (be it electron, quark, etc.).
So, if the turtle starts 1000 squares ahead, but runs at 100 squares per unit of time whereas Achilles runs at 1000 squares per unit of time, in 2 units of time, Achilles will be ahead.
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JollyJoker
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posted February 16, 2021 06:15 PM |
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That is true in an infinite universe as well (it's not a REAL paradox in the sense that there are a couple of "strange" assumptions made - evryone knows Achilles catches and overtakes the turtle eventually).
Also, it's a big IF - I don't think the universe is finite and space and time are changable variables and depend.
Then, that's physics, not mathematics. Mathematics isn't interested in theories whether the universe is this or that, but it can and does describe both.
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Gandalf196
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posted February 16, 2021 06:24 PM |
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JollyJoker said:
That is true in an infinite universe as well
[...]
Also, it's a big IF - I don't think the universe is finite and space and time are changable variables and depend.
Then, that's physics, not mathematics. Mathematics isn't interested in theories whether the universe is this or that, but it can and does describe both.
1) Why?
2) Did not understand
3) On what grounds does mathematics stand? I mean, Euclid was clearly talking about the physical world, about measuring things that exist... This idea that mathematics is some sort of glimpse into the mind of God came much much later and was not widespread as you may believe (check the works of C.K. Raju for reference)
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JollyJoker
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posted February 16, 2021 07:57 PM |
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The paradox assumes that Achilles must reach the position the Turtle is. "The turtle has a headstart. When Achilles reaches the position the turtle started at, the turtle has moved a fraction - ad infinitum.
Zenon says that Achilles won't even reach the turtle - but he does because you can describe what's happening mathematically as a series or sum with a limes or limit (for n=infinite) and that limit is that AChilles DOES reach the turtle.
Now, your square has something of a size. Which is the minimum size possible in your definition of the universe. Mathematics, though, allow me, with rational numbers to have NUMBERS that are smaller. The rational numbers are DISCRETE. STILL there is no "amalles unit".
Mathematics nowadays is axiomatic. Different parts or disciplines of mathematics are based on different axioms.
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Gandalf196
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posted July 18, 2021 12:09 AM |
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"The ideas discussed in this essay—randomness and lack of structure—are very close to ideas from physics, such as entropy and disorder in statistical mechanics. To physicists, these ideas seem familiar and comfortable. What the work discussed here really shows is that pure mathematics may not be identical to theoretical physics, but it is not that different. Pure mathematicians like to think that they have absolute truth, and that we physicists—I consider myself an honorary physicist—use proofs that are heuristic and non-rigorous. But even in pure mathematics there are wonderful non-rigorous heuristic proofs of the kind that mathematical physicists feel comfortable with. Leonhard Euler used them all the time!"
source: https://inference-review.com/article/doing-mathematics-differently
As Mando would say, this is the way
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NimoStar
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posted July 19, 2021 02:15 PM |
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Edited by NimoStar at 14:15, 19 Jul 2021.
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There is no proof the real world is discrete. For example, while quantum orbits are certainly not continous, space is continous and doesn't have a minimum "unit of lenght" - not even plank lenght. Movement across spacetime is continous so far we know, thus.
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Gandalf196
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posted July 19, 2021 03:19 PM |
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NimoStar said:
There is no proof the real world is discrete. .
What kinf of evidence would you accept?
NimoStar said:
For example, while quantum orbits are certainly not continous, space is continous
Where is the proof that space is continuous?
See, you put the burden of proof on my back while assuming that space is continuous.
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JollyJoker
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posted July 19, 2021 04:01 PM |
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1) No one knows what "space" actually IS. Einstein told us that mass is curving it by way of "gravitation", but it's unknown how this interaction takes place (a "graviton" hasn't been detected, yet).
2) If that of which we don't know what it actually is WAS discrete, it would be discrete "blobs" of what we don't know they were "within" or "on" something making it discrete - another "space" altogether.
In other words, there were "holes" in space if it was discrete, and those "holes" were different from space. Your discrete space blobs would be separated by something from each other.
The assumption it could be that way doesn't make sense because you now have an additional phenomenon (to explain) without any actual explanatory gain.
So you'd always assume a continuous space, until proven otherwise.
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Gandalf196
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posted July 19, 2021 04:30 PM |
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Gandalf196
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posted July 19, 2021 04:52 PM |
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“The (Euclidean) point is not the point, but rather, that beyond some point there is no point.”
- Jonathan Lenchner
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JollyJoker
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posted July 19, 2021 05:07 PM |
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*Sigh*
It's just a fallacy.
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Gandalf196
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posted July 19, 2021 05:11 PM |
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JollyJoker said:
*Sigh*
It's just a fallacy.
No, 'tis not. Read it carefully
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NimoStar
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posted July 19, 2021 05:56 PM |
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The "proof" that spacetime is continous is that no experiment has been able to find a minimum unit of space or time.
Zeno's paradox is not about the granularity of space.
And besides, infinitesimal calculus by newton and leibnitz already show that there is a continous solution to the problem.
But anyways, the set of real numbers is already mathematically constructed that there is an infinite division of numbers between 1 and 2. You claim we cannot count to two because there are infinitely many steps in between?
https://www.quora.com/What-are-calculus-solutions-to-Zenos-paradoxes
But also:
Quote:
This is the resolution of the classical "Zeno's paradox" as commonly stated: the reason objects can move from one location to another (i.e., travel a finite distance) in a finite amount of time is because their velocities are not only always finite, but because they do not change in time unless acted upon by an outside force. If you take a person like Atalanta moving at a constant speed, she will cover any distance in an amount of time put forth by the equation that relates distance to velocity.
This is basically Newton's first law (objects at rest remain at rest and objects in motion remain in constant motion unless acted on by an outside force), but applied to the special case of constant motion. If you halve the distance you're traveling, it takes you only half the time to traverse it. To travel (½ + ¼ + ⅛ + ...) the total distance you're trying to cover, it takes you (½ + ¼ + ⅛ + ...) the total amount of time to do so. And this works for any distance, no matter how arbitrarily tiny, you seek to cover.
For anyone interested in the physical world, this should be enough to resolve Zeno's paradox. It works whether space (and time) is continuous or discrete; it works at both a classical level and a quantum level; it doesn't rely on philosophical or logical assumptions. For objects that move in this Universe, physics solves Zeno's paradox.
https://www.forbes.com/sites/startswithabang/2020/05/05/this-is-how-physics-not-math-finally-resolves-zenos-famous-paradox/?sh=4c87317b33f8
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Gandalf196
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posted July 19, 2021 06:12 PM |
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NimoStar said:
The "proof" that spacetime is continous is that no experiment has been able to find a minimum unit of space or time.
That is no proof though. Absence of proof is not proof of absence.
Zeno's paradox is not about the granularity of space.
Care to trace the difference between granularity and discreteness?
And besides, infinitesimal calculus by newton and leibnitz already show that there is a continous solution to the problem.
A not very convincing one, as this dude Steve points out.
But anyways, the set of real numbers is already mathematically constructed that there is an infinite division of numbers between 1 and 2. You claim we cannot count to two because there are infinitely many steps in between?
The so called real numbers are a work of pure fiction. Mathematics should use just rational numbers, as your computer does (using rational numbers and floating point arithmetics)
https://www.quora.com/What-are-calculus-solutions-to-Zenos-paradoxes
But also:
Quote:
This is the resolution of the classical "Zeno's paradox" as commonly stated: the reason objects can move from one location to another (i.e., travel a finite distance) in a finite amount of time is because their velocities are not only always finite, but because they do not change in time unless acted upon by an outside force. If you take a person like Atalanta moving at a constant speed, she will cover any distance in an amount of time put forth by the equation that relates distance to velocity.
This is basically Newton's first law (objects at rest remain at rest and objects in motion remain in constant motion unless acted on by an outside force), but applied to the special case of constant motion. If you halve the distance you're traveling, it takes you only half the time to traverse it. To travel (½ + ¼ + ⅛ + ...) the total distance you're trying to cover, it takes you (½ + ¼ + ⅛ + ...) the total amount of time to do so. And this works for any distance, no matter how arbitrarily tiny, you seek to cover.
For anyone interested in the physical world, this should be enough to resolve Zeno's paradox. It works whether space (and time) is continuous or discrete; it works at both a classical level and a quantum level; it doesn't rely on philosophical or logical assumptions. For objects that move in this Universe, physics solves Zeno's paradox.
https://www.forbes.com/sites/startswithabang/2020/05/05/this-is-how-physics-not-math-finally-resolves-zenos-famous-paradox/?sh=4c87317b33f8
This article proves nada, in my opinion
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JollyJoker
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posted July 19, 2021 06:39 PM |
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Gandalf196 said:
The so called real numbers are a work of pure fiction. Mathematics should use just rational numbers, as your computer does (using rational numbers and floating point arithmetics)
That is just folly.
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Gandalf196
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posted July 19, 2021 09:25 PM |
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JollyJoker said:
Gandalf196 said:
The so called real numbers are a work of pure fiction. Mathematics should use just rational numbers, as your computer does (using rational numbers and floating point arithmetics)
That is just folly.
Why?
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JollyJoker
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posted July 19, 2021 10:18 PM |
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It's two sentences. The first is a wrong claim. The second is nonsensical because
a) there is no connection to the first claim,
b) "your computer" doesn't "use" anything. It's a machine like a refrigerator that is as good or bad as the technology and science behind it. The fact that current computers cannot work in "real number space" is a FLAW, not a virtue. Just as an example since it fits the forum, real RNGs are not possible with only rational numbers.
What you propagate is RELIGION, not science, because you want to limit science based on a belief.
I shudder imagining the mind-set of people who are prepared to sacrifice basic geometry, say the ability to compute the circumference of a circle, because Pi is supposedly a work of pure fiction. It's on the same level as book-burning.
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fred79
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posted July 19, 2021 10:45 PM |
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but pi is found everywhere in nature(the movie "pi" said so). and if god created nature, he used math to do it. thus, god is a mathematician; and math proves it exists.
fred =1
jj= 0
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Lith-Maethor
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posted July 19, 2021 11:11 PM |
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fred...
...never in my life have I wanted to smack someone on the nose with a rolled up newspaper so badly.
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artu
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My BS sensor is tingling again
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posted July 20, 2021 01:41 AM |
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Both real numbers AND rational numbers are fictional in the sense that numbers dont exist in the universe. Math is a language and new math is invented as we figure out new things. Nothing is in perfect order and math always uses approximation while modeling things.
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