Banach-Tarski Paradox

[Royal]

The paradox (which is actually a proof) shows how it is possible to take a mathematical representation of a ball, break it into several pieces, and then reassemble those pieces to make two identical copies of a ball. Moreover, it shows how once can decompose a pea-sized ball...

and then...


















reassemble the pieces to make another ball the size of the moon.

This paradox, built on the early work of Felix Hausdorff, shows that the kinds of quantities that can be measured in our physical universe are not necessarily preserved when a ball, as defined by mathematicians, with an infinite set of points is chopped into pieces and reassembled in a different way using just translations and rotations. In BT paradox, the unmeasurable subsets (pieces) involved are very complicated and convoluted, lacking straightforward counterparts to boundaries and volume in the physical world.

[Pana]

I don't understand how the area of an object the size of a pea would be able to create an object with a larger area.

[Royal]

I don't quite get it either.


But what happens when you split an atom?

[Pana]

Energy released.

[Royal]

And it was all packed into something smaller than a pea. The paradox may be explaining the physical attributes to reality.

If we apply string theory to this- matter is made up of strings, the pea would be unwinded to the scale of a moon.

[Pana]

Yeah, I think you have it right there. I went and read up on it more and it has less to do with the 'volume' of properties...but more to do with subsets of points. I have to keep reading it to understand it more.

[Pigeon]

This might be another reason why as science senses what the universe is showing, the grand rules that are said to be the truth to reality may not really be true (or just unique).

What if these rules can be reassembled, much like BT does with solids, into another set of diferent rules that are just as true.

[Pana]

...and that is most exciting.

[Royal]

I think you have summed up the paradox pretty well.

[Royal]

(Bump)

Apply this concept to news hype.