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On the Navier–Stokes Millennium Prize Problem

openai.com

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Re: On the Navier–Stokes Millennium Prize Problem

#721

Post by vemacs »

mucha wrote: post #685
tedsanders wrote: post #623

Earlier quoted context omitted.

If they opted out of training, then we definitely did not train on them. If they did not opt out, then I don't personally know if training signals came from their chats, and I don't think we'd be able to tell without their cooperation in identifying them. And even if signals were trained on in some manner, I highly doubt it made a difference to a problem as challenging as the NS proof. Reasons for my doubt: - I know…

That's not what your Chief Research Officer, Mark Chen, says on X: "Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company." https://x.com/markchen90/status/2097400166554993041

Does OpenAI think de-identified data is no longer user data? Wild take for OpenAI and certainly not industry standard.

Re: On the Navier–Stokes Millennium Prize Problem

#722

Post by root_axis »

hackinthebochs wrote: post #711
root_axis wrote: post #453

Earlier quoted context omitted.

It's incredible to me that every single time there's a new model people scream "singularity" from the rooftops and every time they are wrong. This is an impressive result, but there is absolutely zero evidence of "the singularity".

It is not reasonable to not believe anything unless there is "evidence" (narrowly construed as an observation incompatible with the negation of some state of affairs). Beliefs have a wide spectrum of characterizations, and not all belief must wait until publicly corroborated evidence is available. Some events defy evidence and we can and should use experience and reasoning to infer unobservable states of affairs.

This is olympic level mental gymnastics to justify believing things without evidence. The double negative with the word evidence in scare quotes is chef's kiss.

Re: On the Navier–Stokes Millennium Prize Problem

#723

Post by sobellian »

semi-extrinsic wrote: post #707
sobellian wrote: post #668

Earlier quoted context omitted.

Whether or not ways exist to work around the singularities, that they exist is surely of note. Before von Neumann formalized QM people were still doing QM, okay fine. But it's wrong to then say von Neumann was doing no physics of note.

"Does there exist a pathological combination of smooth body forces and initial conditions for this set of PDEs, where singularities appear, which by the way is completely impossible to actually create in the real world unless you are a literal God?" is a question of math, not physics. This is a hill I will die on.

AFAICT the unforced problem is still open. I don't think we've established that you need to be a literal God to create a finite-time blowup.

Re: On the Navier–Stokes Millennium Prize Problem

#724

Post by qlte »

reducesuffering wrote: post #321
armchairhacker wrote: post #216

Earlier quoted context omitted.

Let's wait until AI solves a longstanding practical problem before "dawn of the singularity" (which could be tomorrow, but still).

Practical?! The goalposts will keep moving until morale improves (narrator: it doesn't)

Uh I'm pretty sure the "singularity" always presupposed a lot of previously unthinkable technologies becoming part of daily life, and was not ever limited to just computer stuff or math problems.

"Moving the goalposts" as shallow dismissal doesn't work if e.g. someone points out AI hasn't even built a new type of spaceship yet in response to a claim that AI is on the verge of building a Dyson sphere.

Re: On the Navier–Stokes Millennium Prize Problem

#725

Post by NotSuspicious »

I really hope OpenAI doesn't take the bad press some people are giving them too seriously here. They should throw their whole weight behind the rest of the Millennium Prize Problems. To think – if everyone lets their egos calm down we could have the Riemann Hypothesis solved by the end of the year...

Re: On the Navier–Stokes Millennium Prize Problem

#726

Post by jdm2212 »

nozzlegear wrote: post #672
WarmWash wrote: post #209

Earlier quoted context omitted.

Everyone knows that they train on the discounted rate plans data. All the labs are upfront about this too. If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".

> If you need privacy, then you are going to have to pay full price for those tokens (API). At this point, how can we even trust that they aren't accidentally training on those tokens too?

It'd be corporate suicide for them to be caught violating zero-data-retention commitments. But also if you're really paranoid you can just use ChatGPT on Azure or AWS, where nothing is flowing back to OpenAI at all.

Re: On the Navier–Stokes Millennium Prize Problem

#727

Post by sp527 »

redox99 wrote: post #597
aeve890 wrote: post #565

Earlier quoted context omitted.

>If anyone has counterpoints to this I'd love to hear them! Sure. A proof without an unknown amount of human steering (and/or stolen research) would be an unquestionable achievement. To this day there's zero (0) evidence of any result by an LLM alone (maybe I'm wrong). If I just prompt ChatGPT right now with "give me a proof of the Riemann Hypothesis" and this thing delivers, I'm sold. But anything close to "yeah Cha…

The amount of goalpost moving is insane. "Yeah it can solve Millenium problems, but can it do it with nothing more than a one sentence prompt?" Also there are proofs where the only human steering was "keep going".

Well, in fairness, the OP asked for counterpoints. He didn't stipulate that they need to be reasonable.

Re: On the Navier–Stokes Millennium Prize Problem

#728

Post by hackinthebochs »

root_axis wrote: post #722
hackinthebochs wrote: post #711

Earlier quoted context omitted.

It is not reasonable to not believe anything unless there is "evidence" (narrowly construed as an observation incompatible with the negation of some state of affairs). Beliefs have a wide spectrum of characterizations, and not all belief must wait until publicly corroborated evidence is available. Some events defy evidence and we can and should use experience and reasoning to infer unobservable states of affairs.

This is olympic level mental gymnastics to justify believing things without evidence. The double negative with the word evidence in scare quotes is chef's kiss.

I believe the sun will rise tomorrow without "evidence" (again, narrowly construed). We all do. It's only those who abuse the idea of epistemic hygiene who claim otherwise, usually with ulterior motives.

Re: On the Navier–Stokes Millennium Prize Problem

#729

Post by Kotlopou »

HDThoreaun wrote: post #639
Kotlopou wrote: post #385

Earlier quoted context omitted.

Not all, see the cycle double cover conjecture proof: https://news.ycombinator.com/item?id=48863490 But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904 We will have to see whether any other millennium problems fall. I guess that in a year th…

Nuts that Tao literally predicted the exact strategy openAI seems to have used not even a week ago

Since he wrote this five days ago, when these efforts were already underway, if he was not Terence Tao I would suspect he had inside access. But since he said he did not and was speaking hypothetically, and he seems to be an honest person as far as I can judge, I guess some people are just on another level.
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