Mason  🏃‍♂️ ✂️

If you're familiar with the Banach Tarski Paradox of being able to take a sphere, cut it up into pieces, move the pieces, and get two spheres, that's a consequence of the Axiom of Choice.

Ah, re: P∨¬P, I was confused about whether an assertion was implied. You've brought up set theory a few times, but it's not something I'm familiar with. It'll be helpful to me if we can stick to mathematical concepts that someone without a math background can work with.

This gets to the heart of it. Mathematicians believe in wild, absurd things that not only have no bearing on the rules of the universe, but that it would be patently absurd to believe they did. Banach Tarski, if a real physical sphere in the universe behaved like that, 1 + 1 = 1

Aaron, I'm not familiar with this topic.

Hmm, I'm not sure how to express it then. There are mathematical theories which most mathematicians accept are true, whose result (if applied to the real world) are absurd, and whose results are necessary for some formulations of modern physics.

There is another bunch of mathematicians - a minority I think - that say that's bonkers, and have constructed *alternative* mathematical universes. And then there are even weirder, more obscure divisions. If anything, math is not approaching a consensus, it is diverging

Sure — even re: physics you can find yourself e.g. using units that are completely incomprehensible to do calculations that make predictions that are in fact borne out. Bc math is the realm of abstractions, I see the challenge in essentially not getting to "check your work."

But in this case the two groups can find contradictions. Things that are true in one mathematical universe and false in the other. And as I said, lately there's been a lot of interest in taking this bifurcation further and making more and more of these!