Cody

idk, I've wondered about what the endgame of proving cut elimination is. Like the Master Theorem.
Something like the analogue of the index theorem vs the fundamental theorem of calculus.
So to speak.

2024-10-03 22:34:40 UTC

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so how would I specify local soundness for *some connective*? Just "there exists a way to eliminate an intro followed by an elim"?
Or is the shape of the reduction somehow involved?

2024-10-03 22:14:54 UTC

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I'm now confused: what's the property called "local harmony" for, say implication, in proof theory/type theory terms?

2024-10-03 21:25:56 UTC

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I guess the property would be "beta and eta are type preserving"?

2024-10-03 21:01:05 UTC

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neat! I always forget what the mathy definition is, though. Some kind of local cut-elimination?

2024-09-26 18:02:29 UTC

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I need a diffeq refresher I think.
I always liked the topology bits.

2024-09-26 12:05:06 UTC

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oh wait a moments thought tells me that *is* true: the ball only reaches the top at the limit t = infinity.

2024-09-26 11:21:24 UTC

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uh oh, now I'm confused: time reversibility now suggests there's no way to roll a perfect ball up a half sphere so that it stops at the top.
Is *that* true?

2024-09-25 17:41:18 UTC

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is there a way to formalize this intuition, e.g. proving Kolmogorov's axioms in some sense?

2024-09-25 15:55:18 UTC

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ah nice, I was wondering whether that theorem (we called it Cauchy in France for some reason) applied.

2024-09-25 12:22:40 UTC

@npub1nf4…nqe4 I have a question with probaly no good answer: let's pretend the world is completely classical.
Is there a good way to explain why it "feels" like there's randomness at a macro scale, even though everything is deterministic? It feels like ignorance should be a part of this.
I guess I'm asking for a synthetic theory of probability without random variables that makes some kind of sense.
Maybe this is a well-known solved problem.

2024-09-25 01:58:42 UTC

You know you're old when you think things like "man, how good *is* hobbit metabolism?"

2024-09-24 20:44:56 UTC

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oh yeah.

2024-09-24 20:16:40 UTC

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is it an instance or...?

2024-09-12 18:09:31 UTC

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I'm sure ice-nine will get us first.

2024-09-10 14:21:56 UTC

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that's how they get you