If you'd like to explore what the Navier–Stokes blow-up construction looks like visually, I vibe-coded an interactive 3D visualization based on the published result for fun :)
Demo: https://minfx.ai/navier-stokes/
Source code: https://github.com/minfx-ai/navier-stokes-blowup
On the Navier–Stokes Millennium Prize Problem
971–980 of 1001 posts
Re: On the Navier–Stokes Millennium Prize Problem
#972Earlier quoted context omitted.
> 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.
Zero data retention commitments? Technically generating synthetic data off of user data on the fly, counts as zero retention of user data! And it technically means they didn't lie either, because they didn't keep user data, they kept their own, synthetic data. That is what they already do with reasoning when they provide summaries/sanitized versions of it to prevent "distillation attacks" even via the API. They generate synthetic data aka summaries of reasoning traces, and that is technically not user data, because the user did not enter it directly into the LLM! It still counts as zero data retention when they only keep original LLM created reasoning traces as well as all LLM outpit, because the user did not enter it, so it counts as synthetic data and is thus not user data.
Re: On the Navier–Stokes Millennium Prize Problem
#973Earlier quoted context omitted.
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.
They have no zero data retention commitments anymore though? In fact they have quite the opposite, a direct message of storing prompts since the release of sol (but we wont train on it trust us wink wink)
Not storing prompts but they absolutely can store reasoning traces, summarized or sanitized reasoning traces and the whole LLM output as well.
Re: On the Navier–Stokes Millennium Prize Problem
#974Earlier quoted context omitted.
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.
Not long ago it'd have been corporate suicide being caught massively torrenting pirated media. Yet here we are.
I think people actually expect it so they are not impressed when it happens
Re: On the Navier–Stokes Millennium Prize Problem
#975Earlier quoted context omitted.
Maybe. Maybe not. Look at AI drug design - it's not really speeding up the important part - drug trials. There isn't really a coherent plan to use AI for the most complex part of drug discovery at all.
I work in pharma and I've advocated for directly training models that predict drug trial outcomes. I don't think we have the necessary support (data + algorithms) to produce accurate models in this space. I suspect that predicting drug trial outcomes is roughly isomorphic to understanding human biology at a fundamental level (and accepting that our existing models of how drugs work are extremely limited).
Agree, it is effectively understanding human biology - which we suck at, have little data on, have few good models for.
So, it doesn't appear there is any way to avoid the clinical trial process. And it won't speed up, and it won't get cheaper.
Am I wrong?
Re: On the Navier–Stokes Millennium Prize Problem
#976Earlier quoted context omitted.
How can you possible say this sort of thing in context of what looks like a millenium prize being solved. I swear there's nobody blinder than those who won't see.
People will cling to views as long as they possibly can, despite evidence slapping them in the face. Eventually it won't matter. Arguments over whether LLMs are "truly" intelligent are going to be a matter of philosophy, and look a little silly.
It literally reminds me of climate denialism.
“Line go up! That is bad! Planet might become unsafe for human life.”
“Nuh uhh! Malankovich cycles and humans are a drop in the bucket! Krakatoa! See!”
“All of California is on fire!”
“Haha, stupid shrill liberals! Go rake your woke forests! Drill baby drill!”
“Are you kidding?! Look at this graph.”
“That’s just propaganda from the elites of the Build-a-bear group!”
“Do we even live in the same universe?”
“And 5g causes COVID!”
“Oh, I guess we’re don’t.”
Re: On the Navier–Stokes Millennium Prize Problem
#977Earlier quoted context omitted.
Why would Anthropic employee even use OpenAI's models? Cross-polination would have been avoided
They should have used a zero data retention agreement, user error
I doubt it would've made any difference, zero data retention is truly trivial to get around and I think it's highly likely OAI is already doing this. Just use another model to distill, summarize, and/or paraphrase the data and boom - you get to train on the ideas, while claiming zero data retention, which is true. You legitimately retained zero data.
Re: On the Navier–Stokes Millennium Prize Problem
#978Earlier quoted context omitted.
> Should I just say fuck it, and go hitchhiking across Europe with some friends? Yes. Assuming you are young and haven't had such experience. The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career persp…
Have you people gone insane?
There is a land war in Europe for the first time in generations. The only reason you can say that big things aren't happening is because you're lucky enough to live where they're happening.
Re: On the Navier–Stokes Millennium Prize Problem
#979Earlier quoted context omitted.
Just don't. If you read the story here carefully, you see that AI was used to work from theory built by others which showed that the Euler equations possesed finite-time blow-ups. But to make that step, actual good understanding for mathematics was needed. My experience with software has been the exact same.
I fear this is only temporary and due mostly to the complexity of the problem. Consider the recent counter-example to the Dinitz–Garg–Goemans conjecture: > https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de0... The prompts for the chat above are: > Construct a counterexample to general (non-planar) case of Dinitz Garg Goemans conjecture. You should do a breakthrough and find a structured counterexample. > [g…
You're probably correct. FWIW most people with math degrees haven't gone on to do math research regardless, so in that regard this isn't a big change.
Re: On the Navier–Stokes Millennium Prize Problem
#980Is this truly the beginning of the AGI era? Running agents and prompting excessively to produce 'slopcode' to solve mathematical problems and generate a solution. If this is what anyone calls 'slop' then slop has no meaning. I'm all for it on the use case of solving mathematical breakthroughs!
No AGI here, it's just extreme brute forcing. AI doesn't understand fluids dynamics, it just slops it's way to the solution.
If you don't need to 'understand' to do this, then maybe what you call 'understanding' is less important than you think. When people in the real world reach for a tool, what they care about is whether or not it'll produce results, not whether or not it has the capacity for interior phenomenological experience.