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He’s interested in like, "Okay, what’s a good rough algorithm we could use? So in that one, is it just saying like, yeah, here’s a region of the world that’s somehow linked with my house? So for instance, it should be able to look at Shannon’s theory of information and these measures of mutual information and channel capacity and say, "Ah, yes, these are very natural abstractions in mathematics." It should also be able to look at a water bottle and be like, "Yes, in this universe, the water bottle is a very natural abstraction", and this should robustly extend to all the different things we think of as abstractions. And so what would it look like to understand enough about abstraction that we could satisfy multiple of these divergent ways to start caring about abstraction? Alternatively, how to play billiards you can just look at the front page and I will probably have a post on the front page at any given time.

They don’t even have to be surfaces in our four dimensional space time. If we have a legible notion of what abstractions are, then it’s much more clear how to go looking for those things, what the criteria are for success, whether you’ve actually found the thing or not. Or how much of it have you knocked off? John Wentworth: So there’s a general challenge here in communicating why it’s important, which is you have to go a few layers down the game tree before you run into it. It also became favored in British colonies; the game's longest-running champion was an Australian, Walter Lindrum, who held the World Professional Billiards Championship from 1933 until his retirement in 1950. The game remains popular in the UK, although it has been eclipsed by snooker. How many levels will you pass in this game? Concentrate on the cue ball side that will strike the object ball, not the edge that will pass the object ball.

I think it’s just squarely on the clean side of things. Do you think there’s just a large zone of things that are squarely within the actual concept of abstraction, but our understanding of abstraction is something a low dimensional manifold, like a line on a piece of paper where the line takes up way less area than the paper? Daniel Filan: Yeah. I guess it seems like this is almost like… Daniel Filan: Yeah. Yeah. Daniel Filan: Yeah. Well, I don’t. Don’t Miss Out on the Latest Updates. And indeed the math bears that out. Because in some sense all you really need is the theory of abstraction, and then the rest is just math. You’re saying this part of the world is the agent, the rest of the world is not to the agent. So that’s a first reason you might run into it if you’re thinking specifically about agency. There’s things which are mathematical abstractions, like agency or information and there’s things that are physical abstractions like ‘water bottle’ or ‘sunglasses’. Like in physics, we have force and mass and density and pressure and stuff. Abstraction is mostly about the structure of the world, whereas the kinds of modularity I’m talking about in the context of selection theorems is mostly about the internal structure of these systems under selection pressure.

I don’t know. Sometimes people are really worried that even if I wanted to create the best theorem prover in the world, that just could walk around, prove some theorems and then solve all mathematics for me. John Wentworth: I mean, the best category theory textbooks I have seen are solidly decent. John Wentworth: Oh, there’s absolutely other paths to this. John Wentworth: You start to see it when you’re trying to formulate what an agent even is. John Wentworth: In part I expect this because I’ve now spent a while understanding abstraction better and I’m already seeing the returns on understanding agency better. John Wentworth: You can worry about macroscopic things. John Wentworth: If something is only optimizing a tiny little chunk of the world and a one centimeter cube around it, we mostly don’t care that much about that. It’s very much about interacting more with some chunk of stuff and not very much with the stuff elsewhere, right? The more difficult the level, the more balls you need to put in the hole. They could be more abstract things than that.