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In general, it’s hard to find ideal mathematical concepts and principles. Daniel Filan: But I think an intuition you might have is, well, super powerful AI that we care about understanding, maybe that’s going to be more like ideal AI than it’s going to be like E. coli. It seems like we should be able to turn that intuition into math. Your brain has to get the concepts from somewhere and get them all loaded into your head before you can actually figure out what the math is supposed to look like. The intuition is coming from somewhere. This is how most biologists are thinking about them, how most biologists are driving their intuition about how the system works. We go and figure these things out by having some intuition for how the thing is supposed to work, and then backing out what the math looks like from that. John Wentworth: Now, from that perspective, there’s the question of how do we get bits of information about what that ideal case is going to look like before we’ve worked out the math? John Wentworth: Some of your work has found something similar in neural networks.

John Wentworth: And so, it’s just like in other areas of math. John Wentworth: People do what now? John Wentworth: Yes. Probably if you had a sufficiently deep understanding of category theory and could take the probabilistic formulation of abstraction that I have and express it in category theory, then it would clearly generalize to all this other stuff in nice ways. John Wentworth: They are distinct phenomena, the way I think about them. Therefore, things are going to pop out with utility functions, or at least that’s the implicit claim here, right? I’ve got this chunk of the world - there’s this water bottle here, this is a chunk of the world. Davis retired from the event following this victory, having won the title at all 15 events from 1927 to 1946, making him, as of 2022, the only undefeated player in the history of the World Championship. Davis achieved his highest break ever in billiards of 2,501 on 27 April 1927 in this final.

The final ended on 20 April 1929, with the score 18,000-17,219 to Davis. Davis was sent to live with his grandparents in Newbold for several years. John Wentworth: So there’s these different concepts like intelligence, agency, optimization, world models, where we need to figure these things out more or less simultaneously and see the relationships between them, confirm that those relationships work the way we intuitively expect them to in order to know that we’ve gotten the models right. Daniel Filan: Or you might think, "Oh, I want to understand microeconomics" or something, how do I get a thing that achieves its goal in the real world by making trades with other intelligent agents or something? John Wentworth: That also means if you go look at real agents and see that they don’t match your current math for ideal agents, that’s a pretty strong hint that something is wrong with that math. John Wentworth: So I wouldn’t say that agency is the concept to understand so much as it’s the name for that whole cluster.

If you want to know what ideal agency is going to look like, if you want to get bits of information about that, the way you’re going to do that is go look at real agents. So it updates our understanding of what the right notion of ideal agency is. You expect both of these to be much closer to an ideal agent than a rock. We had these coherence theorems that we’re talking about - ideal agents, they should end up being expected utility maximizers. John Wentworth: So, first of all, from my perspective, the main reason you want to understand ideal agents is because it’s a limiting case which you expect real agents to approach. John Wentworth: We don’t go figuring these things out just by doing brute force search on theorem space. I don’t know if you consider yourself to be. Daniel Filan: I guess an obvious concern is that if we don’t have the right language for modularity, then presumably there’s no theorem in which that language appears. Daniel Filan: I think so. Daniel Filan: Okay. So independent measurements and each of them takes the same random distribution.

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