When I imagine models inventing a language my imagination is something like Shinichi Mochizuki's Inter-universal Teichmüller theory invented for his supposed proof of abc conjecture. It is clearly something like mathematical English and you could say it is "quite intelligible" compared to "neuralese", but at the end, it is not very intelligible.

I understand many people here are native English speakers, but I am not, and one thing I think about a lot is how much people should spend on learning English. Learning English is a big investment. Will AI advances make language barriers irrelevant? I am very uncertain about this and I would like to hear your opinions.

This is a good idea and it already works, it is just that AI is wholly unnecessary. Have a look at 2018 post Protecting Applications with Automated Software Diversity.

If we do get powerful AI, it seems highly plausible that even if we stay in control we will 'go too fast' in deploying it relative to society's ability to adapt, if only because of the need to grow fast and stay ahead of others, and because the market doesn't care that society wants it to go slower.

After reading my interpretation was this: assuming we stay in control, that happens only if powerful AI is aligned. The market doesn't care that society wants to go slower, but AI will care that society wants to go slower, so when the market tries to force AI to go faster, AI will refuse.

I reflected on whether I am being too generous, but I don't think I am. Other readings didn't make sense to me, and I am assuming Dario is trying to make sense, while you seem doubtful. That is, I think this is plausibly Dario's actual prediction of how fast things will go, not a hope it won't go faster. But importantly, that is assuming alignment. Since that assumption is already hopeful, it is natural the prediction under that assumption sounds hopeful.

Paul Crowley: It's a strange essay, in that it asks us to imagine a world in which a single datacenter contains 1E6 Nobelists expert in every field and thinking at 100x speed, and asks what happens if "sci-fi" outcomes somehow don’t happen. Of course "sci-fi" stuff happens almost immediately.

I mean, yes, sci-fi style stuff does seem rather obviously like it would happen? If it didn't, then that’s a rather chilling indictment of the field of sci-fi?

To re-state, sci-fi outcomes don't happen because AI is aligned. Proof: if sci-fi outcomes happened, AI would be unaligned. I actually think this point is extremely clear in the essay. It literally states: "An aligned AI would not want to do these things (and if we have an unaligned AI, we're back to talking about risks)".

If you enjoyed Inventing Temperature, Is Water H2O? is pretty much the same genre from the same author.

My another favorite is The Emergence of Probability by Ian Hacking. It gets you feeling of how unimaginably difficult for early pioneers of probability theory to make any advance whatsoever, as well as how powerful even small advances actually are, like by enabling annuity.

I actually learned the same thing from studying early history of logic (Boole, Peirce, Frege, etc), but I am not aware of good distillation in book form. It is my pet peeve that people don't (maybe can't) appreciate how great intellectual achievement first order logic really is, being the end result of so much frustrating effort. Because learning to use first order logic is kind of trivial, compared to inventing it.

I think it is important to be concrete. Jean-Baptiste Jeannin's research interest is "Verification of cyber-physical systems, in particular aerospace applications". In 2015, nearly a decade ago, he published "Formal Verification of ACAS X, an Industrial Airborne Collision Avoidance System". ACAS X is now deployed by FAA. So I would say this level of formal verification is a mature technology now. It is just that it has not been widely adopted outside of aerospace applications, mostly due to cost issues and more importantly people not being aware that it is possible now.

Result: humanity is destroyed as soon as the patent expires.

The plain interpretation is that only statements to be proved (or disproved) were sourced from human data, without any actual proof steps. In Go analogy, it is like being given Go board positions without next moves.

It makes a lot of sense this is needed and helpful, because winning a game of Go from the empty board is a different and easier problem than playing best moves from arbitrary Go positions. Igo Hatsuyoron mentioned in the original post is a good example; additional training was needed, because such positions never come up in actual games.

Imagine AlphaZero trained from randomly sampled Go positions, each intersection being black/white/empty with uniform probability. It would play much worse game of Go. Fortunately, how to sample "relevant" Go positions is an easy problem: you just play the game, initial N moves sampled at higher temperature for diversity.

In comparison, how to sample relevant math positions is unclear. Being good at finding proofs in arbitrary formal systems from arbitrary set of axioms is actually quite different from being good at math. Using human data sidesteps this problem.

Namely translating, and somehow expanding, one million human written proofs into 100 million formal Lean proofs.

We obviously should wait for the paper and more details, but I am certain this is incorrect. Both your quote and diagram is clear that it is one million problems, not proofs.

It feels to me like it shouldn't be so hard to teach an LLM to convert IMO problems into Lean or whatever

To the contrary, this used to be very hard. Of course, LLM can learn to translate "real number" to "R". But that's only possible because R is formalized in Lean/Mathlib! Formalization of real number is a research level problem, which in history occupied much of the 19th century mathematics.

Recently I came across a paper Codification, Technology Absorption, and the Globalization of the Industrial Revolution which discusses the role of translation and dictionary in industrialization of Japan. The following quote is illustrative.

The second stylized fact is that the Japanese language is unique in starting at a low base of codified knowledge in 1870 and catching up with the West by 1887. By 1890, there were more technical books in the Japanese National Diet Library (NDL) than in either Deutsche Nationalbibliotek or in Italian, as reported by WorldCat. By 1910, there were more technical books written in Japanese in our sample than in any other language in our sample except French.

How did Japan achieve such a remarkable growth in the supply of technical books? We show that the Japanese government was instrumental in overcoming a complex public goods problem, which enabled Japanese speakers to achieve technical literacy in the 1880s. We document that Japanese publishers, translators, and entrepreneurs initially could not translate Western scientific works because Japanese words describing the technologies of the Industrial Revolution did not exist. The Japanese government solved the problem by creating a large dictionary that contained Japanese jargon for many technical words. Indeed, we find that new word coinage in the Japanese language grew suddenly after a massive government effort to subsidize translations produced technical dictionaries and, subsequently, a large number of translations of technical books.

Just as, say, translating The Wealth of Nations to Japanese is of entirely different difficulty between the 19th century and 20th century (the 19th century Japanese started by debating how to translate "society"), formalizing IMO problems in Lean is only workable thanks to Mathlib. It would not be workable in other formal systems lacking similarly developed math library, and formalizing research mathematics in Lean is similarly unworkable at the moment, until Mathlib is further developed to cover definitions and background theorems. In the past, ambitious formalization projects usually spent half their time formalizing definitions and background results needed.