Aw man, I can’t make this and I just moved to New York!

score 1 · canonical

The famed nlog(n) integer multiplication algorithm involves a 1729-dimensional Fourier transform!

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Yup, they do, didn’t read the OpenAI paper clearly enough!

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I was working off the assumption that 3-SAT is NP-Complete, so if there’s a subexponential algorithm for solving it then there are problems in EXPTIME harder than 3SAT. But this comment on the orange site points out that a polynomial time reduction of something to 3SAT can increase the problem size enough to recreate exponential time-bounds. That’s why the paper says this:

Note that runtime bounds of the form 2^o(n) do not transfer under general polynomial-time reductions (2ⁿo(1) would be needed for this), so our result does not imply that general NP problems admit subexponential time algorithms. However we do obtain subexponential time algorithms for counting graph colorings and perfect matchings.

Does this potentially mean that there are can be other shades of “hardness” inside NP-Complete?

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Anthropic has now published a proof that #3SAT is also subexponential

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It proves that one of {NP ≠ PSPACE, PSPACE ≠ EXPTIME} is true, which is a pretty big deal!

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I can’t decide which is more impressive, the fact that it survived this long, or the things that the ground team did to make it last so long.

Come to think of it, a lot of NASA probes last well beyond their lifetime. Spirit and Opportunity were supposed to be 90 day missions but were active for 6 and 18 years, and Curiosity is still going strong. I’d speculate it’s because they’re all engineered to last their full lifetimes in the absolute worst case, which for space problems is much, much worse than the average case.

score 7 · canonical

Try prompting it with some other answers and see if it justifies them all

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