But that animation isn't at all accurate. It splits the ball into distinct, separate points, and put each into categories, and then uses the concept of infinity to show that each of these categories must have the same amount of points as the ball that they split off from. Therefore duplicating it. It does not take huge, connected chunks of the sphere and multiply them.
@connorfrankston5548
Ай бұрын
I don’t think you understand what the theorem states. You can literally decompose the sphere into disjoint subsets, and then rearrange those subsets via affine transformations into two translated images of the original sphere.
@connorfrankston5548
Ай бұрын
It has almost nothing to do with the two sets having equal cardinality. You cannot do the same thing with a line segment, or a circle. The construction relies on the symmetry of the sphere, and on the axiom of choice.
@thomazk2507
9 жыл бұрын
If you look closely, it copies every piece of the sphere
@Urandomizer
8 жыл бұрын
Yes.
@KaitlynTice
8 жыл бұрын
Because there's an infinite amount of layers in the outer surface of the sphere. It separates the outer shell into layers and copies it, if you want to understand more about this you can watch v sauces video on this topic
@MarkChimes
8 жыл бұрын
Not quite what happens. But Vsauce's video is good.
@idkkkkk57986
7 жыл бұрын
There are no layers involved.Only points
@zulfika_
Жыл бұрын
@@KaitlynTice so, the ball made with pastry?
@MadDoktor88
5 жыл бұрын
Do it with a $100 bill....
@lapapar1174
4 жыл бұрын
edit: i made this comment 1 year ago apparently and it was stupid soooo…..
@derpedlerp1237
3 жыл бұрын
@@lapapar1174 it does
@danielanyie6359
2 жыл бұрын
200 billion HAHAHAHAHAHA
@someone-ja
28 күн бұрын
@@lapapar1174 you don't need to hide your dumb self
@LMB222
Жыл бұрын
Futurama has shaped genetations if future mathematicians.
@dylanlange3635
2 жыл бұрын
i still dont get it
@666gnarlsbad
2 жыл бұрын
This same principle is how the replicator was created.
@jareththegoblinking3191
Жыл бұрын
If only this worked on food All these apples made from one apple you break and rearrange the pieces But of course apples don’t last forever so every new apple is made there’s gonna be a little bit of rot and the more apples made the more rotten they’ll eventually become so you may want to get new apples to break and make more apples out of
@aguyontheinternet8436
Жыл бұрын
It might work on food. You just need to find a way to break up the food into infinitely many infinitesimally small points, and then combine and rotate groups of points to duplicate the food. Oh and also I'm not sure it works on objects that aren't geometrically perfect spheres, so you'd have to turn the food into a sphere, just to be safe
@jareththegoblinking3191
Жыл бұрын
Oranges might be better then
@romnickbuenaflor4703
2 жыл бұрын
No. You simply assumed Infinity does not obey rules applying to the other numbers. The paradox appears only because of that assumption. When a concept such as infinity assumes many “values”, then there is no real or physical equivalence for it. Only in the thought process… MATH has mislabeled infinity as a concept applied to numbers. What MATH actually requires, is a concept of undefined number, or unknown value, which can take on only one “value”. Then there will be no paradox…
@halbgefressen9768
Жыл бұрын
Of course there is no physical equivalent because our world is discrete in every way. Continuous space is a simplification that comes with its inaccuracies. In the real world, you can't do the thing in the video because all real world sets are measurable. Banach-Tarski requires immeasurable sets.
@pneujai
3 ай бұрын
No, such paradox is a truthful statement, which is built on the Axiom of Choice. We can have cardinals (many “values” of infinity from your words) without Axiom of Choice. This is not just a thought process, cardinals are defined accurately by the equivalence class induced by the relation of “has a bijection to”. Why the Banach Tarski Paradox seems false in real life is that we cannot take the points of a sphere point by point, in fact, we cannot take any point out from any object, we can only take a piece, which is a set of points, but not a singleton.
@brettselph7591
2 жыл бұрын
Acceptance of this paradox is required in the Mathematics community, because rejecting it means that a large portion of this edifice of "proofs" built upon prior "proofs", under construction since Cantor, would have to be torn down and cast into the waste bin. This is unthinkable to those who grew up thinking that the Axiom of Choice wasn't rotten timber, but that doesn't mean it's not the correct thing to do. And refusal to face the unthinkable, is a psychological barrier, not a mathematical one. Unthinkable, because it would mean your dissertation was was... worthless. Unthinkable because it would mean your whole career has been wasted mining iron pyrite (fool's gold). Unthinkable by those at the top of the pyramid of academic reputation. But again, these are all psychological barriers, NOT mathematical ones. Belief doesn't transmute iron sulfide into gold. Belief can certainly DELAY the collapse of a fiat currency, or a Ponzi scheme, but only temporarily. Properly understood, the Banach-Tarski Paradox isn't a paradox at all, it is a simple case of Reductio ad Absurdum, or proof by contradiction. In this view, it demonstrates that Cantor was WRONG. If you think that belief doesn't create a powerful fake reality that can vanish into thin air, when doubt begins to infect the community of believers, then you don't understand hyperinflation of fiat currency, you don't remember the "dot-com" bust, or the financial crisis of 2007-2008. Mathematicians, unlike physicists, don't have a Mother Nature to lay waste to their theories with "inconvenient" experimental results. Mathematicians, unlike theorists in physics, rely ENTIRELY on reputation and consensus. This consensus-only system, unique to Mathematics, works well MOST of the time ...until it fails. And then there is no mechanism to correct it. Unless, of course, we are visited by advanced aliens from space with crania so gigantic that even the most insufferable professor emeritus will stand down his ego. Two hypothetical news flashes from 2053: "Space Aliens Descend on Mathematics Departments Worldwide, then Mysteriously Depart. Major Reshuffling of Department Hierarchies, Some Eggheads Plummet from their Ivory Towers" Homeless Man Drawing Squiggles on Santa Monica Beach, is actually a former Maths Professor. 'The Aliens... They Overrode their own Prime Directive, not to INTERFERE. They said they JUST COULDN'T STAND IT ANYMORE'.
@halbgefressen9768
Жыл бұрын
lol nice shitpost
@praggapanchangma1351
3 жыл бұрын
Instructions unclear i ended up disliking the video
@justblue4427
8 жыл бұрын
25 second of video 25 likes and dislikes coincidents? I think not!
@ferlywahyu342
2 ай бұрын
This paradox exist in kuantum fishick is crazy 😂
@-_Nuke_-
9 жыл бұрын
Either misleading title or no info what so ever...
@-_Nuke_-
8 жыл бұрын
***** I'm only just saying this because the illustration didn't really help much... But I also don't get what is so awesome about the Banach Tarski Paradox? You have a non physical thing. An object that is made out of INFINITE points, it is no surprise for me that we can theoretically create 2 things out of 1, when that one thing is made out of infinite amount of points!
@tylergalligani1599
7 жыл бұрын
It's awesome because a "point" is an infinitely small location with no width or length. So technically, everything is made of an infinite number of points. This means that this paradox isn't just about a "theoretical object with an infinite number of points", because every object in the universe has an infinite number of points. So if we had the tools needed, this paradox could apply to every object in the universe.
@dabmasterian8089
5 жыл бұрын
@@tylergalligani1599 Except we got the Planck length to worry about. Nothing is infinite in our Universe.
@nagarmalsharma9992
5 жыл бұрын
@@dabmasterian8089 planck length is what it is because of our limitations, not because the space can't be divided further, you can still divide space further way beyond the Planck(infinitely), we cant measure it because we need some kind of electromagnetic wave to measure, and a wavelength of electromagnetic wave smaller than the planck length would collapse to a black hole. But that doesn't mean that space can't be divided further.
@dabmasterian8089
5 жыл бұрын
@@nagarmalsharma9992 But you can't cut something into an infinitely small new thing. There's always new stuff to cut off, no matter how long you do it, so you will never reach the end.
@Dyslexic-Artist-Theory-on-Time
2 жыл бұрын
This is possible mathematically because of Huygens principle that states: Every point on a wave front may be considered a source of secondary spherical wave, which spreads out in the forward direction at the speed of light. We can think of it as a process of spherical symmetry forming and breaking. The Axiom of Choice is formed by the wave particle duality of light and matter in the form of electrons acting like a blank canvas that we can interact with.
@michawolski2584
Жыл бұрын
🤓
@zzztriplezzz5264
Жыл бұрын
@@michawolski2584 😐
@halbgefressen9768
Жыл бұрын
No, this is possible mathematically because the ball is approximated to be continous and is thus able to be partitioned into immeasurable parts. In the real world, everything is discrete and thus we don't have immeasurable parts.
@methatis3013
Жыл бұрын
Using physics to define mathematics is so backwards lol
@Randomguy-rc1ei
Жыл бұрын
@@halbgefressen9768 your comment made the most sense.
@apurbadeb7618
3 жыл бұрын
The problem of Physics is that it relies too much on mathematics
@teleofunctionality9246
Жыл бұрын
So does everything else
@PravinDahal
Жыл бұрын
No, the problem is that any moron with a degree is a Mathematician.
@Panzbigniew1984
Жыл бұрын
Nie ma nieskończoności, nie ma paradoksu.
@yorusuyasoul69420
9 жыл бұрын
Lol
@carahiggs7157
6 жыл бұрын
What is the difference between this and a turd - shit doesn’t just theoretically stink.
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