# Have You Heard Of This Banach-Tarski Paradox?

Can you get your mind around THIS??

The concept is very bizarre and the ever inquisitive “VSauce” walks us through.  It is hard to get one’s mind around this one but he gets into depth in the details thoroughly and it involves thinking about 3 dimensional plains in a new way.  Once commenter even says:

I lost you after like 6 minutes

Some one else has a similar comment:

17 minutes in and i’m just here like, what is he talking about…

Here is a bit more information from wikipedia on the background of this theorem:

The Banach–Tarski paradox is a theorem in set-theoreticgeometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjointsubsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them, without changing their shape. However, the pieces themselves are not “solids” in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces.[1]

Let’s find out more about this amazing paradox in this video on page 2

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1. Erik Von Weishaar said:

Ya it’s pretty awesome and hard to follow… But to be able to duplicate without losing anything from the original. Just the opposite of making a photocopy never using the original, you lose data, and it gets fuzzy.

2. Peter Moomaw said:

I don’t think his definition of countable infinity holds up to scrutiny. Specifically the rational numbers are countable (they in fact have the same carnality as the natural numbers), but you can’t count all the rational numbers from 0 to 1 in a finite about of time, since there are an infinite number of rationals between 0 and 1.

3. Fabian Obeso said:

Did anyone notice that to fill the void pieces remaining, movement may it be (spin in this case since it is a circle) needs to be added to the factor. To me that means in still life you can have 1 circle. If you add spin or movement to the object you can in the theoretical sense they have broken down here have 2 circles. Where did the energy come from to spin or move to fill the void? From the original 1 point that is missing? I hope the mathematicians read this and see if there is any merit to my theory.

4. Tristan Bridges said:

In a theoretical sense yes just by adding the spin is the energy itself so it was already there, and I know that’s a contradiction but in common quantum fields you have to understand that the impossible is possible and not having a definition or a reason is ok, that happens so for this to happen that’s normal in this field!

5. Tristan Bridges said:

That’s why it’s displayed like that because it is possible, just because we can’t as humans rationally prove it or fathom it doesn’t make it less true or not, take quantum mechanics, even though it’s pretty much theoretical it can still be count as being feasible because in quantum anything, not having an exact deffiniton or reason is a ok!

6. Zack Isbill said:

If you apply other algorithms, fractal geometry, Julia sets. It goes much deeper. Parallel dimensions, dark matter is now more probable. There is more space inbetween the bilding blocks of atoms, than matter has atoms, but can a whole be less than its parts…

7. Nate Schoening said:

If space is infinite, is it even seemingly possible to apply this theory to it maybe for travel? Maybe im just simple minded and dont actually understand as much as i think XD

8. Anthony Edward Malcuit said:

What? Then how is quantum physics legit? The energy needs to have a source even if it’s from thin air, but it needs to be reliable. How can a whole scientific field have merit based on faith?!? This isn’t religion.

9. John Mare said:

If I had an infinite number of lifetimes to study this then I might understad…..yea…..I still wouldn’t get it……

10. Derrick Jowers said:

i think in the molecular picture…you will run out of places to make a point…kinda like the lack of mass, or the empty space in an atom…if there’s no place to make a point, the point cannot be made. kinda like zeno’s paradoxes…shows that the arrow will never hit the tree…but we all know that it does!

11. Trevor Rideout said:

Does this mean an inch and a centimeter are the same length since they both have an infinite number of points between them.

12. Matt Perkins said:

Why are people taking things from algebraic geometry and using it to talk about dark matter and multiple universes? It’s not that deep. This kind of stuff is useful for creating simulations and animations.

13. Gregg Forester said:

The quantum world is the merger of spirituality and science. Simply because they understand in a way what happens and have shown multiple scientific studies. But no they do not know where the energy comes from. Some say it is our concious that supplies the energy.

14. Michael Osborne said:

An “infinite scattering of points?” Then, theoretically, those two objects could be reassembled into anything, Correct? Wouldn’t that fall under quantum uncertainty and non determinism?

15. Adam Henshel said:

I understand this in the way that I understood a question I posed to my high school math teacher. I asked if you have a number line, and start from zero and go to infinity, and then have another that starts from 3 and goes to infinity, aren’t they both the same size? He said, no the one starting at 0 is technically longer, even though they both go to infinity. This paradox expands on that theory.

16. Adam Henshel said:

It’s the same principle as: let’s say you cut a piece of paper in half, then cut one of those half sheets in half, then one of those, etc. No matter how many times you can half something, you will still never end up with nothing. Just very very very very very tiny paper.

17. Jeff Beer said:

Go read 1,2,3… Infinity by George Gamow. You’re rehashing null and aleph-null. This “paradox” only works with theoretical numbers, not matter.

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