> 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
No, you did not understand correctly if your eyes read "cheap currency" and your mind read "cheap labor". Something went wrong between the text processing unit and the meaning processing unit. Perhaps your meaning processing unit is overwhelmed with all sorts of preconceived notions and voices that are interfering with your text processing unit.
Look, this is not hard. You have two countries, one makes bad apples and the other makes fantastic, amazing, glorious apples. One was seeded by Johnny Appleseed and the other by Johnny Rottenseed. The only labor involved is picking the apples, which both countries do equally well. Does that mean that the GA (Glorious Apple) country will run a surplus against the BA (Bad Apple) country?
No, it will not.
Trade will still be balanced, because the exchange rate will adjust so that neither country is running a surplus or a deficit. Maybe one Glorious Apple is worth 10 Bad Apples. Then the Bad Apple country will import 100 glorious apples and export 1000 Bad Apples.
So the terms of trade, the ratio of GA/BA rises, so that total trade is balanced. It is balanced when one glorious apple dollar is worth 10 bad apple dollars.
The only way that this will not happen is when someone interferes with the exchange rate. Now, if someone interferes, say by making it illegal to sell more than 5 Bad Apples for 1 Glorious Apple, then Glorious Apples will look amazingly cheap to the Bad Apple people, but the Bad Apples will look awfully expensive to the Glorious Apple people, and so this artificial strengthening of the Bad Apple currency will create a huge trade deficit, as people rush to dispose themselves of their bad apples and obtain the superior and affordable glorious apples.
On the other hand, suppose that we see the Bad Apple country running a deficit against the Glorious Apple country. What can we surmise? That for some reason, the investment demand for Bad Apple currency is high, causing people to want to accumulate Bad Apple dollars, even though the Apples made there kinda suck. That investment demand is what creates the trade deficit, by inflating the value of the Bad Apple. And it is the only thing that can cause that deficit.
Nowhere anywhere here does the price of labor enter into the picture. That is a you story -- I would try to fix that meaning processing unit.
> you did not understand correctly if your eyes read "cheap currency" and your mind read "cheap labor".
i actually read "expensive consumer goods for their populations" and concluded "cheap labor", as i pointed out. suppose you ask citizens from nation A and nation B how many hours they'd have to work to be able to buy a certain good. if both answer the same number, then how can you say that the good is more expensive in any one of the nations? and if citizen from nation A answers a larger number than citizen from nation B, so that the good is more expensive in nation A, then how does A not have cheaper labor than B, as one unit of the same good literally buys your more labor from A than from B?
i'm still digesting your apple example.
i'd be interested if you could cite a real case of this happening, because it doesn't agree with everything that i have seen. for example, sometimes the apple business in BA will simply die. this is what i was getting at when i mentioned that "underdeveloped countries are still net importers of complex goods". if you take a mildly complex good like refrigerators or office chairs, chances are that a random not-so-developed country has some local manufacturers. but they're just struggling, not exporting proportionally larger quantities. indeed the only way they'd export K>1 refrigerators for every Samsung imported is if there were 0 exports and 0 imports (so the country is so poor no one has a good refrigerator).
also, suppose that BA produces a total of N apples per year per capita. if the people in GA work the same hours, then GA produces the same number, N, of apples per year per capita, because they are both equally good at picking apples. since trade is balanced, it does not affect the level of value/utility/wealth on each side, whatever the amount of trade. so in the end, for the same hours worked, BA has a total product of N bad apples per year per capita, which is 10 times less than GA, which has a total product of N good apples per year per capita. people in BA are poorer.
assuming people in this economy just buy/sell work and apples, the people in BA must work for less value, i.e. they are cheaper labor. if labor in BA is more or less than 10x cheaper than in GA, then apple orchards will simply close in BA and reopen in GA or vice-versa until it gets 10x cheaper, at which point there's no point in switching. this is moreover compatible with the real anecdotal examples i mentioned i have seen.
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.
interesting concept. you get a letter of recommendation of sorts from every professor.
this makes me think how education could be better if it were more individualized (smaller student/teacher ratio). maybe that'd be a good use of the oversupply of labor in academia.
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.
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