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The Navier–Stokes Millennium Prize Problem

simonwillison.net

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Re: The Navier–Stokes Millennium Prize Problem

#241

Post by zvolsky »

sodic wrote: post #146
bob1029 wrote: post #24

> ... we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors ... I've observed this exact effect last week. I made a discovery regarding a stepwise performance improvement in a codebase. I shared the benchmark results with a peer and within 12 hours they replicated the same. We had both been looking for this for years. I think giving someone hope that an answer exists might as…

I have a similar story, but perhaps even stranger. I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick. The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters. There are always a few competitive guys who spend the entire conference taking tu…

Climbers know this phenomenon as the "send train". A group of climbers has been working on a problem for a while. When the first person sends it, it often happens that multiple people are successful in the immediate attempts that follow. Part of it is watching the successful beta, but it happens even when everyone knows the moves. Once you've seen it's possible, you stop climbing tentatively and commit to the hard move instead of hedging for a fall.

Re: The Navier–Stokes Millennium Prize Problem

#244

Post by aswegs8 »

Mawr wrote: post #182
aswegs8 wrote: post #157

Earlier quoted context omitted.

Reminds me of amateur table tennis. There is a strange dynamic where you down regulate your performance unconsciously when the opponent is playing worse and vice versa. Could be described as some physical form of this effect: https://en.wikipedia.org/wiki/Asch_conformity_experiments The term would be conformity / normative social influence.

Surely this has nothing to do with specifically table tennis, nor that it's amateur. A better example would be mixed boys/girls sports classes in school, where the boys deliberately hold back as to not injure/scare the girls. It's a pretty obvious and human thing not to go out and completely destroy a much weaker opponent. We're social animals after all. There also may be an element of energy conservation, there's ob…

I am pretty sure if you play at pro level you train this out of yourself. But then, the marathon / running examples where certain milestones get broken by one person and then suddenly by a host of others, is a counterargument.

Re: The Navier–Stokes Millennium Prize Problem

#245

Post by inboulder »

LLMs are an excellent tool for discovering which problems mathematicians thought were interesting, actually aren't. If the LLM's haphazard jaunt (somewhat exhaustively) through the problem space can 'solve' it, the solution was never going to be particularly useful or illuminating.

Re: The Navier–Stokes Millennium Prize Problem

#246

Post by [deleted] »

zvolsky wrote: post #241
sodic wrote: post #146

Earlier quoted context omitted.

I have a similar story, but perhaps even stranger. I work for a startup. We often bring a wooden arcade with us to conferences as a marketing gimmick. The arcade runs a single side-scrolling video game. You're running from a monster and dodging obstacles. The goal is to survive as long as possible, and your result is measured in meters. There are always a few competitive guys who spend the entire conference taking tu…

Climbers know this phenomenon as the "send train". A group of climbers has been working on a problem for a while. When the first person sends it, it often happens that multiple people are successful in the immediate attempts that follow. Part of it is watching the successful beta, but it happens even when everyone knows the moves. Once you've seen it's possible, you stop climbing tentatively and commit to the hard mo…

[deleted]

Re: The Navier–Stokes Millennium Prize Problem

#247

Post by inboulder »

burrish wrote: post #43

>While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. What do you mean, as OpenAI employee, you cannot tell that his work has entered the training data ? But also correct me if I'm wrong, if the two mathematician were really close to finish this problem, and their conversation were used by OpenAI, shouldn't the Agent have succeeded way faster/e…

"shouldn't the Agent have succeeded way faster/efficiently instead of using "4.9 million messages and used about 300 billion output tokens."" No. Have you seen LLM output? The fact that it managed to converge at all in the problem space is amazing, an LLM is a 'book', the context window is the page number, the page has a token, that's it, that this huge book of weights already contains a method to search a problem space at all and actually go down a 'good' path eventually is remarkable, but it's going to be incredibly inefficient at doing so, a book doesn't have any kind of real-time model building like a brain.
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