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