TiB 194: Automating mathematicians; Shaping the very long run; Immortal universities; and more...

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We discussed in TiB 72 and 114 the idea that one for the most important applications of AI might be to accelerate progress in science. There are many ways this might happen, from “reading” entire corpuses of research to searching for patterns in enormous datasets. This paper by Maithra Raghu and Eric Schmidt has more examples. DeepMind has a new publication in Nature (or see their blog post for a less technical write-up) that demonstrates a powerful use case for machine learning in mathematics, and perhaps beyond: guiding human intuition towards important results.

Broadly, if a mathematician believes there is a relationship between two mathematical objects, a machine learning model can generate a plausible function that relates the two by training on generated data. The mathematician can then use this as a starting point to iterate through conjectures until they find one that is viable. DeepMind demonstrates two real world examples that led to new results in combinatorics and in knot theory. It seems important to ask, though, how long will the AI need the human “in the loop”?

We’ve talked before about the brief period in which it seemed as though human plus computer (“centaurs”) could outcompete computers alone in chess… before AlphaZero came along and made the human contribution irrelevant. Could the same thing happen to mathematicians? Coincidentally, researchers at Google published a new paper this week (summary here) that suggests ML models do better on complex, iterative tasks (like mathematics) if they “show their work” - i.e output text to a scratchpad - between steps. It’s not hard to imagine future versions of this technique making the mathematician redundant. Enjoy the centaur era of science while it lasts.

A favourite TiB topic is the long-run impact of historical events. We’ve talked about the persistent effects of the Cultural Revolution, the Reformation, the teachings of the Catholic Church, and living at the frontier, among others. One way of thinking about this phenomenon is that if the consequences of major - particularly institutional - change today persist for many generations, perhaps we should put more effort into trying to shape the values of our descendants through this mechanism. That’s the starting point for Jaime Sevilla’s excellent study of seven papers that purport to show multi-generational effects (thanks Sam for the link). This link has a more informal write up.

Sevilla asks two questions. First, are the reported effects real or spurious? Second, if they are real, can we identify the causal mechanism? The answers are a mixed bag. Some papers fall apart under deeper investigation, but on balance Sevilla concludes that there is evidence for persistent, if relatively small, effects. He estimates that every unit that values shift by today might produce an effect 10% as strong in future generations. (It’s worth noting that Sevilla is a model of rigour and intellectual honesty; he flags up front that he started with a strong bias against finding evidence of long-run effect, but “reluctantly changed [his] mind")

The question of the causal mechanism is less clear. Sevilla finds that most of the papers he reviews fail to identify the mechanism of persistence. The best guess seems to be simply cultural transmission via parents teaching children down the generations, but there’s also the possibility that institutions “lock in” values in some way. As Sevilla says, there are many unanswered questions for those who would seek to shape the future in this way: how long do such effects last? do they weaken over time? can these kinds of effects be created deliberately? I hope we’ll see more research in this space.

This week’s podcast episode is a conversation with writer and venture capitalist Rohit Krishnan. Rohit is probably the most interesting writer I’ve discovered in 2021 - see TiB 176 and 187 for coverage of some of his ideas - so I was excited about this episode and wasn’t disappointed. 

If I had to summarise Rohit’s project at Strange Loop Canon, it’s something like: how to create and maintain the institutions needed for broad-based progress in the 21st century.

In this conversation, we talk through some of the building blocks that underpin this. Among other things, we discuss:

… and much more.

Rohit and I have a lot of interests in common, so if you like Thoughts in Between, I’m pretty sure you will enjoy this conversation.

BONUS: I was on Jim O'Shaughnessy’s Infinite Loops podcast this week and we discussed many fun, TiB-adjacent topics.

Thanks for reading. As always, shares / referrals / shouting from the rooftops are appreciated.

Next week will be the last “normal” TiB of the year, followed by the TiB Review of 2021 on 21st December and then a two week break.

Do feel free to reply if you have comments, questions or recommendations.

Until next week,

Matt Clifford