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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.
We shouldn't have mocked the people from the "What's your job on the leftist commune?" Twitter thread. Seems like they might've been right after all. If we survive as a civilization and do not get made redundant via a BNW-like transition to a tiny humanity.
There's no "we" when you and all your children didn't make it through the cull.
I'm sorry, I don't get it.
Wrong reply, my mistake.
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I don’t think mass automation AI future proves communists correct. Not only because the timely invention of AI required capitalism (yes we don’t have the counterfactual, but I’d say it seems likely) but even more importantly because the only way any kind of ‘from each according to ability, to each according to need’ economy can work is if unlimited ‘ability’ is provided by AI and unlimited ‘need’ can be absorbed by it.
Well, communists did often say that capitalism would bring about its own destruction. Communists also often said that far from capitalism being useless, it is in fact the necessary precursor for communism.
It's hard to give them full props for these ideas given that originally these ideas did not envision something like AI being the mechanism.
However, communists did think that increases in production would play a major role in the transition, and they were aware that technology is key in increases in production.
Marx: "This “alienation” (to use a term which will be comprehensible to the philosophers) can, of course, only be abolished given two practical premises. For it to become an “intolerable” power, i.e. a power against which men make a revolution, it must necessarily have rendered the great mass of humanity “propertyless,” and produced, at the same time, the contradiction of an existing world of wealth and culture, both of which conditions presuppose a great increase in productive power, a high degree of its development. And, on the other hand, this development of productive forces (which itself implies the actual empirical existence of men in their world-historical, instead of local, being) is an absolutely necessary practical premise because without it want is merely made general, and with destitution the struggle for necessities and all the old filthy business would necessarily be reproduced;".
Engels: "Only the immense increase of the productive forces attained by modern industry has made it possible to distribute labour among all members of society without exception".
Right, they envisioned it being because of the tendency of the rate of profit to fall - ie capitalism being so maximally efficient that it turns in on itself - which is actually untrue (capitalism is more efficient than the alternatives but not maximally so; rates of profit ie margins are actually quite high in historical terms right now).
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I'm not saying it proves communists correct. I'm saying the jobs the kumbaya-adjacent leftists envisioned themselves having might be the only source of meaning left in a post-singularity utopia.
I don't think that any kind of work is necessary for meaning. There are other sources of meaning, such as curiosity, philosophical exploration, and social connection.
The supposed connection between work and meaning is, I think, largely just humanity making the best (meaning) of a bad thing (work).
'Work has meaning' is a coverup for simian greed. People who say they get meaning from their work really mean they enjoy the power it affords them as measured in wealth and status, and that it would sadden them to see their dreams torn to bits owing to a turning of Fortuna's wheel. That is at the heart of what I see in all these salarymen, men who boast about their portfolios and talk in big, drunken voices about their vaunted careers. The reddit normies. Underlying all their grown-up chatter is nothing more than the humblebragging of narcissists who thought they were winning the darwinian game.
If you have a device which allows you to read the minds of other men, by all means, share it with us so we can all use such a useful tool. But for my part at least, you are wrong. I derive meaning from my work because of the satisfaction of a job well done and making the world around me a tiny bit better, not because I'm a narcissist who secretly glories in being better than others.
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What do you draw meaning from that cannot be sneeringly explained away in unflattering terms?
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I suspect that the main sources of meaning will continue to be things like religion and family / childrearing / marriage that code as trad.
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