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Notes -
A Big Day in the Culture War
Apologies for any incoherency or grammatical errors; today's events led me to down more than my usual share of booze.
Earlier today, big things happened in math. No, not Claude providing a sub quadratic 3SUM. OpenAI released hundreds of notable math results, in a GitHub repo.
Fun results:
Hilbert's tenth problem over (\mathbb{Q}) is undecidable
The quasi-Riemann hypothesis
The rational Hodge conjecture holds for every CM abelian variety
Integer multiplication can be done in sub-log-linear time. Oh, there's also a sub-log linear DFT.
Thoughts and observations:
Mathematicians are big mad. View the relevant subreddit on our progenitor site. Most there are probably, at best, adjuncts at community colleges desperately coping with the downward trajectory of already marginal careers, but it's fair to say that the writing is on the wall for mathematicians. There's probably a double digit number of grad students staring into a glass of whiskey tonight and thinking of hanging themselves.
My immediate question was about whether this closer to the current peak of performance, or just a lazy demonstration of OpenAI's power. So, I took one of the particularly interesting preprints to me (memory and precision in Gaussian models) and tested whether it's at the edge of capabilities or not. 30 minutes of back and forth with Astra (itself behind OAI's internal model) resulted in a significantly stronger result, on multiple dimensions. While I finished my first bottle, I spent a fair amount of time convincing myself of the result; I was convinced the strengthened results were plausible. Write this off as AI psychosis if you want, but try it yourself; I'm genuinely curious for what you get. (The back and forth, here, was entirely me saying "you can do it!", "keep at it, I believe in you", and "you've got this, finish it!")
Probably the most important line in OAI's announcement post is "The average result used the equivalent compute of roughly three hours of ChatGPT Pro thinking." This isn't a case of OAI spending millions for a marketing bump. My bet is a kind of Pareto distribution: most took minutes, not hours, with a long tail around Riemann-level results pulling up the average significantly.
Notably, ML related results are nearly entirely absent from this batch of proofs; maybe a half dozen touch on it, distantly. Some problem indices are skipped in overview.md. Conspiratorially, my inclination was to think they filtered them out for competitive advantage. I can't find any evidence of that in the GitHub repo or any of the preprints (equally plausible: deduping), so maybe they judiciously decided not to point their mathematical ballista at ML. ML also doesn't have a meaningful bank of rigorous conjectures, so given the conjecture sources, maybe they're not yet digging into ML math. But color me skeptical.
Does math matter? Is it something to advance civilization and technology, or an artistic pasttime for humans to create logical beauty? Likely both, today, but this is an almost nuclear detonation against the latter.
I don’t see why mathematicians would be so upset. 99% of professional mathematicians have never contributed to the field of mathematics in any real way.
There are two arguments about AI and employment.
The first and primary one is about mass unemployment. This is a real issue but people obsessed by it also need to understand, as I think @self_made_human increasingly does, that basically all of the surge in white collar labor since 1970 consists of fake make-work very thinly disguised by the laws of classical economics. The invention of the computer literally automated almost all white collar labor as it existed in, say, 1920, and yet instead of an unemployment crisis we just gave ourselves fake titles and decided to spend all day having meetings and making PowerPoint slides. The format in engineering and medicine was very slightly different but vast amounts of both professions, their demand and their provision were and are make-work too. I go to the doctors office and a GP diagnoses the way AI can in 20 seconds or a competent and cheap nobody who could use a search engine could do in 5 minutes even 25 years ago. If society survives the AI X-risk, we will emerge into a world of such unfathomable abundance that it will be trivial to provide every human, certainly in the rich world but eventually the whole world, with a comfortable material life. Dying from an AI engineered virus or a drone war or something is far more likely than starving because AI replaced all jobs and the owners of capital are too tightfisted to share.
The second and more interesting one is about meaning. The mathematician, even though he never meaningfully contributes to the field, imagines that he might. This is why AI makes him depressed. It’s the lack of hope that kills you, but is it? I mean, is it really? Meaning is invented, we’ve spent thousands of years inventing rather arbitrary forms of meaning. We can invent more. We can have kids. We can touch grass. We can compete against each other, if we want to, in games and competitions. Academia is already one such game. If mathematicians still want to play it, all they have to do is change the rules.
I guess I’m more sanguine on this than most. I increasingly converge on one observation, which is that it’s extinction or utopia. Other scenarios (weird AI hell) are plausible but increasingly unlikely. Compute always wins, the bitter lesson is always true, so the only question is whether it destroys us entirely (or someone uses it to) - accidentally or deliberately are really irrelevant - or whether it liberates us from material want entirely.
I'm less sanguine than you. The utopia AI will offer us does have advantages, the biggest being significantly healthier throughout a (neverending?) lifespan. And I, personally, am very excited for the knowledge and discoveries it will have about the universe.
But beyond that, the utopia won't fundamentally change that much. Even today, no one (at least in the USA) is starving for lack of food. The deprivations most people feel are positional and status-related: most people can get a house somewhere, but when people complain about not having access to housing, what they mean is they can't afford a brownstone in Park Slope.
Before AI, society could, at least in part, use merit and economic contribution as a way to allocate those inherently exclusionary goods; that's going away in the utopia. I'm lucky enough to have a almost two-decade-long career during a time where I could convert my intellectual capabilities into something that lets me acquire those resources, but that path won't exist for people like me. I don't have faith that whatever way society decides to allocate status resources will allocate them in a way I like (though I expect I personally am positioned in a place to have the level of exclusionary goods I want; it's more what I'm imagining for future generations).
That's following the optimistic utopia branch. The extinction branch is also quite likely (though I'd guess on the order of decades, not months or years) and much worse.
One reason that matters, though, is because opportunity clusters. If you can't afford a brownstone in Park Slope (wherever that is), that's a problem because you then can't access the high-paying job/networking/cultural opportunities in Park Slope. There is a plausible downward spiral of
couldn't quite afford Park Slope -> moved to the boonies -> could only find low-paying local jobs -> could never even think of moving to Park Slope -> can't even afford the boonies any more
which doesn't quite hold in a utopian society.
Park Slope is a nice neighborhood in Brooklyn. A brownstone in Park Slope is roughly a Victorian in Noe Valley.
In the utopia, how does someone not in Park Slope get their brownstone in Park Slope?
I think the idea is that while some people value a brownstone in Park Slope for its own sake, some value it because it puts them near the job opportunities of NYC and otherwise wouldn't want one.
If the job opportunities of NYC don't matter anymore, that second group no longer wants to be in Park Slope, so while there probably still won't be enough brownstones to go around, there may be less of a gap than there currently is.
We're also seeing some significant declines in fertility rates, and I think more so in the demographics that want to be in Park Slope. So if that trend continues in utopia (which seems reasonable, material abundance if anything seems to get people less interested in children if we look at the modern era), over time there will be fewer people looking for them and the gap might shrink further.
If we get infinite life extension that might be a different matter, but I expect eternal youth will also lead to "eh, I'll get around to making kids later" for some very long definitions of later, and the city-seeking crowd also seems to have a problem with depression that might lead to disinterest in infinite lifespans.
Thanks @wraelk!
@ThenElection, this is what I was trying to say, but much better put. Currently, the area you live in affects the trajectory of your life: moving to... Idaho? (forgive the Brit please) doesn't just mean you have shelter in a less prestigious place, it means that your income and future life opportunities are going to shrink.
That means that the number of people who want a brownstone in Park Slope is currently
whereas in utopia it's just
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