[paulpauper]

I don't understand the paradox. Obviously if you dissaemble or scamble something u can reararange it?

[bobthechef]

When's the last time you came across something that you could disassemble and could then reassemble into two things identical to the first thing you disassembled?

It is natural to suspect that foundational axioms are somewhere flawed.

[x3n0ph3n3]

One thing worth pointing out is that our universe operates on the integers rather than the real numbers, and the Banach-Tarski requires operating on the reals.

[Smaug123]

Is that known? It's an appealing idea, but bearing in mind that general relativity is very resistant to quantisation, I'm not sure I'd be comfortable to declare it as fact.

[x3n0ph3n3]

It's implied by quantization. There is a minimum divisibility of space (plank lengths) and objects (fundamental particles).

[Smaug123]

I specifically said that the resistance of GR to quantisation is why I'm not very happy saying that it's fact.

[roywiggins]

It's like taking a bed apart and rearranging it into two beds, each identical to the original bed, without adding any more material.

[paulpauper]

Oh that is pretty cool. I wonder if it could be proved with differential geometry for the sphere, which has a simple paramertization

[Smaug123]

The ability to do it is equivalent to the axiom of choice, so my guess is going to be "not without considerable effort".