Ha, this from @swart is lovely.
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Ha, this from @swart is lovely.
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Paul Cantrellreplied to Paul Cantrell last edited by [email protected]
It reminds me of the classic:
THEOREM: Horses have an infinite number of legs.
PROOF: All horses have the two hind legs in the back, and the fore legs in the front. That’s a total of 6 legs. Now 6 is an even number, but 6 is certainly an odd number of legs for a horse. The only number that is both even and odd is infinity. QED
cc @swart
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Behind this ridiculous silliness is a serious point: proof is a rhetorical device, not a mechanical process; the purpose of proof is to •convince•. Language is slippery. Thought is slippery. There is always a gap between (language + assumptions + human thought) and Platonic mathematical abstraction. Attempts to mechanize proof do not actually close this gap; they just move some things to the other side of it. You can’t escape that gap — and that gap is the •heart• of mathematics.
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Paul Cantrellreplied to Paul Cantrell last edited by [email protected]
The way mathematics actually develops, the whole history of it, is a process of exploring that gap between human thought and mathematical abstractions: letting imaginary things surprise us, uncovering hidden assumptions, reworking proofs, sharpening definitions, finding new imaginary things to surprise us more.
And this is the point where I, like a broken record, tell you to read _Proofs and Refutations_, because it is profound and also delightful.
/end
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@inthehands @swart "Duck, Duck, Grey Duck" ?
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@michael_w_busch @swart
Yes, it is a very Minnesotan theorem!In Colorado, where I grew up, the theorem would be that all ducks are geese.