> It's amazing to me that the fact of them doing it isn't well-known (there is plenty of research and evidence) and assumed, but still a question even on HN. Bring it up to most people and they will ostracize/ridicule you - an odd response which I can't explain well, given the evidence, likelihood, and very serious consequences which those same people are unhappy with.
an explanation would be that these voices doing the ostracizing/ridiculing [anyone who tries to increase awareness of astroturf] are also astroturf. because astroturf is only effective while people are unaware of it. it also seems compatible with the shutdown of research you mention.
i'm no mathematician/physicist but i think this question is one of the reasons why the original question (possibility of singularities) is interesting. in these cases the equations most likely fail to accurately model reality, and then the next questions are what additional physical assumptions are needed to describe reality in this case, and what behavior do we actually see.
i always found it fascinating how existence and uniqueness of solutions for the basic types of PDEs (Laplace, wave, heat...) follows from boundary conditions of just the right type intuition tells us, i.e. either value or derivative for Laplace (corresponding to fixing voltage or charge on the conductors), both value and derivative for wave (corresponding to initial position and velocity of the parts of the string, as we'd expect from classical mechanics), and also something about the solutions for the heat equation being unstable for negative times (which totally makes sense when you think of "diffusion" -- can't unmix it).
> An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work.
the post you were replying to quotes Buckmaster specifically denying this: "It is not the direction one arrives at in a few days by giving a model the problem statement."
> And the article states "an insane amount of compute had been used," which implies OpenAI brute-forced their way to a solution. I.e. they searched for every paper published on Navier-Stokes and exhaustively attempted every approach. Such an approach would lead them to a solution.
"implies" is a surprising choice of word here. that's certainly one interpretation of "an insane amount of compute had been used". what came to my mind, considering Buckmaster's statement that the AI would not head down this specific path on its own, is, though, that they prompted it in this specific direction and then used an insane amount of compute. this seems consistent as well with these other statements:
> Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler (...)
i don't know if i understand what you're saying. but i'm no mathematician. here's the full statement in question once again:
> The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag.
so, you're saying that "the direction one arrives at in a few days" is (A) "the route through a smooth force, options c and d in Feffermann's statement of the problem", and no more specific than that, i.e. does not necessarily include (B) "the same path route as Luis and Diego" (quoted from the post i was replying to) (which, as i understand, is a subset of A -- directly from Buckmaster's quote: "the route A is is the route Luis and Diego opened")?
but the post i was replying to claims that "An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work", i.e. that the AI model could independently chose B. but choosing B implies choosing A, since B is a subset of A. and in this case it is irrelevant whether Buckmaster claimed that an AI could not independently choose A or B -- the point which you seem to be contesting.
EDIT: my understanding is that "solving the Navier-Stokes existence and smoothness problem" consists of proving at least 1 of 4 precise statements ("options (a) through (d) of Fefferman's statement of the problem"), and Luis and Diego's work were developments towards a proof of statements (c) and (d), which have been recently further expanded by Alpoge and Buckmaster
if you assume the choice of route is a uniformly distributed random variable, yes. but this assumption does not seem consistent with "Almost nobody else I know of was working on it", from Tristan's quote. nor with "It is not the direction one arrives at in a few days by giving a model the problem statement".
It doesn't really make sense what he said. Everyone expects N-S to have blow-up. If you are going to try to show blow-up, C and D are strictly easier than A and B. So Tristan was not clear about what detail of "route" he is talking about, because what he literally said can not be it.
yeah, it looks like i don't have enough knowledge of this subject to discuss this. but i'd be interested in reading what more knowledgeable people have to say about it -- Tristan's work, how different from others' it was (they claim no one else was following the same path), and how it compares with the AI's
Well, no one arrived in this direction, because no one was sitting and prompting a model. It was 10000 agents working 24/7 for several days, trying millions of different directions.
Buckmaster did also mention, for example, that a team of people was employed to solve the problem, which supports this claim. but that is another claim whose veracity could also be questioned. but at some point we must trust other people, unless we can be satisfied with only believing what we personally see.
(also, IMO, the coincidence of both discoveries in time is pretty suspicious. this one doesn't need you to trust many people i guess)
> And I agree that sort of proof is impossible to acquire. Like, there is no way to prove conclusively that anyone else is conscious. Like, there is no way to prove conclusively that anyone else is conscious. But that's why we instead treat it as an axiom instead. We basically say "We're not going to prove it, we're just going to accept it as true". And that's fine.
> Mostly because it not being true is an existential horror no one wants to truly confront.
we can't prove, in this mathematics sense, that other people are conscious just as we can't prove that the sun will rise again tomorrow, or that my food will nourish me instead of killing me, or that everything is still there when you're not looking. for questions of this type we normally content ourselves with empirical evidence instead. and the empirical evidence for the consciousness of other humans (and, taking it further, other animals) for me would be the facts (1) that i am conscious, and that (2) i am a human like other humans: same anatomy, same behaviors, same story. indeed, empirically, it'd be absurd to think that i'd be so profoundly different from other humans in this particular aspect.
i guess what i'm saying is for me the real existential horror is the problem of induction.
it looks from the article that some cancers are notably correlated with radiation exposure, and these were the ones they looked for. they also mention excluding lung cancer because it's also correlated with smoking.
from the point of view of the judge and society, i guess, what matters, ultimately, is whether the arguments presented for a case hold, not where did they come from -- so it shouldn't matter if ChatGPT was the one that came up with the argument if the argument is good.
though one could point out that if one particular method of generating arguments tends to generate arguments that take time to analyse but are often enough pointless, we'd save time by not using them.
so assuming that the report will be analysed on its own merits, really, it was 3M who got scammed here, because they paid $475/hr for a guy that was just prompting ChatGPT. i mean, i don't know much about the subject, but that screenshot of the gas detector with the "what am i looking at here"... wow, it looks like i already know enough to be an expert witness. no wonder these people are so drawn to stuff like positive affirmations, when they do make it by faking it.
re: "you either have strong currency or strong exports"
if i understood correctly, you are stating that the only way to have strong exports is by having cheaper labor ("... losing jobs and industries to those nations that are willing to have expensive consumer goods for their populations in order to export more and import less.")
well, that is one (easy) way to do it, but it's not the only one. for example, you could have more productive labor. i think the fact that underdeveloped countries are still net importers of complex goods such as cars and computers, despite having the cheapest labor, supports this.
also if you allow for some poetry, i guess we could say that trust is like a baloon in the sense that a tiny hole can destroy it completely and abruptly
where i come from, university admissions are determined exclusively by performance on an exam you take after high school. it's meritocratic, and the work it involves is much more sensible IMO: no leadership/well-roundedness/whatever theater, and in the ideal case, it only lasts 1 year.
also, this grind is barely meritocratic. all these extracurricular activities show is you had a solid family supporting you. it's literally impossible for a poor kid to participate in this. they can pick up a book, OTOH. yes, it'll be harder, it'll take longer, and they won't do as well as the rich kids with test prep, but they are given the opportunity to try.
an explanation would be that these voices doing the ostracizing/ridiculing [anyone who tries to increase awareness of astroturf] are also astroturf. because astroturf is only effective while people are unaware of it. it also seems compatible with the shutdown of research you mention.