Assuming Pythagoras discovered irrational numbers, what are we to say about irrational numbers before Pythagoras discovered them? — tim wood
I guess the circumference of a circle was just as many times longer than the diameter before the discovery of irrational numbers as it was after the discovery. — litewave
If our space or at least some part of it is continuous — litewave
and flat — litewave
Is this the line of argument you are putting forward? If not, then what are you saying exactly? — fishfry
And of course, as I said, there may actually exist continuous Euclidean spaces, even though we don't live in one. — litewave
Do you suppose that the axiom of choice is true in such a space? — fishfry
Then the Banach-Tarski paradox is true as well. Then matter could be created, contrary to the laws of physics. — fishfry
Is it possible that you (like me, like Kant, like everybody) have a strong intuition of Euclidean space, yet that intuition is simply misleading? And that in fact mathematical Euclidean space is inconsistent with physical reality? — fishfry
I don't know. If the axiom of choice is consistent with Euclid's axioms — litewave
Our space is generally not Euclidean but in everyday life the curvature is usually negligible. — litewave
Well, according to physicist Max Tegmark, there's no difference between physical and mathematical structures. — litewave
If you don't understand the distinction between abstract mathematics and the actual, physical world that we live in, that's something you should try to understand. You've fatally weakened your own argument by admitting you don't know the difference between the two. — fishfry
Numbers can carry information that is both passive (like a newsreport) and active (like a software program). — TheMadFool
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