sheafification

> Well, I interpreted it differently.

Congratulations, you have political opinions. Despite your claims elsewhere, you’re not “politically neutral.” Nor do you believe, in practice, that political opinions do not belong on HN.

Yeah, you could use it for that, but it’s got some caveats and is unsafe in some cases.

https://en.cppreference.com/cpp/language/reinterpret_cast

EDIT: If you’re able to use C++20 then clearly bit_cast is better.

If that’s your standard for what counts as prediction, Asimov beat him to it by seventy-ish years.

EDIT:

> Scott made comments on a specific emerging technology

He was speculating on what would happen if one gave GPT-2 “near-infinite training data and compute.” It’s a thought experiment, not a prediction. Near-infinite amounts of anything is a fantasy.

I acknowledge that he has predicted some things in a falsifiable way and turned out correct, but this isn’t one of them. You’re reading hindsight into the text.

The context shows he was simply whining about AGI skeptics back in 2018, and many of the “predictions” he makes in that paragraph (including the one you quoted) are trivially wrong because he phrased them so hyperbolically and categorically.

Anyway, there were plenty of normies who thought images generated by e.g. stable diffusion (c. 2022) was “real art” and equivalent to human artwork.

I don’t think it’s useful to glaze Scott (or any of the LW crowd for that matter) as if he was (or they were) some kind of prophet(s). They got a couple points right, sure, but most of it was them flinging armchair philosophy spaghetti against the wall and seeing who would fund MIRI to let them fling the next batch.

I’m not seeing anything like a falsifiable prediction that LLMs will write math proofs in that article.

I see a thought experiment about giving GPT-2 “near-infinite training data and [compute]” but that’s not falsifiable. That’s also not how we got to modern GPT models.

I’m inclined to agree. Sometimes when (perhaps other) people say this there’s an undertone of “and the field is full of not-real mathematicians” as if there’s a large contingent just hanging on for the money or prestige, and I personally haven’t seen that in the wild.

True, 2D Poisson is only approximately banded. Still, I don’t think I’d bother rolling my own sparse solver. It’s a well-trod problem.

I doubt outside of a few exceptional cases that one is going to do better on CPU-bound problems than a well-written LAPACK implementation built for the architecture you intend to run on.

Maybe pedagogy was the point? I didn’t really get that from the article, maybe some intention was lost by filtering it through AI.

Various algebras of dual numbers are used in most automatic derivative routines.

This is treated more rigorously and generically in the subject of synthetic differential geometry.

I remember learning about that from Stephenson’s Cryptonomicon, back in the day.

It’s not even a US-specific thing. Many countries recruit foreigners to their militaries.

https://en.wikipedia.org/wiki/List_of_militaries_that_recrui...

> Technically a large landmass, but essentially nothing happens in the western half.

Depends what you mean by "western half," I suppose, but China is definitely not a relatively small country. Shanghai to Chongqing is about the same distance as Chicago to Dallas; Beijing to Kunming is about the same as D.C. to Denver.

I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.

This is very sad, but I came to the same conclusion with my math blogging a couple years back. There’s little point to publishing any personal effort on the internet anymore. At best you get some spam comments and your work stolen by bot scrapers; at worst you get a doxxed and targeted by a harassment campaign.

My go-to is “It’s the only thing I was good at in school, I was hopeless at everything else,” which is only a slight exaggeration.

It’s highly nontrivial to verify that a 250k loc Lean program actually represents that which it claims.

I guess it could be AI turtles checking and summarizing all the way down, but is that any more credible than a single AI checking it? I doubt it.

> do you expect this to remain true? If so, for how long?

For the foreseeable future. Left to their own devices current LLMs kinda wander off into outsider art territory. They aren’t grounded in the real world and they need that feedback loop to stay within the category of relevant ideas. I haven’t seen anyone working on fixing that.

Regarding 1, the same is true of every other scientific field. Verifying some tidbit of knowledge for yourself as an individual isn’t optimally useful in all circumstances.

Regarding 2, if the proof isn’t understandable then it probably isn’t useful. Many people today work in the hypothetical world where the Riemann Hypothesis is true, and many work in the hypothetical world where it is false. If it takes decades to validate that some horrifically complex AI proof of either fork is true, people will probably continue working on the other fork just in case.