Daniel Filan: Cool. So before we get into what’s going on with abstraction, first I’d like to ask, why should we care about abstraction? Daniel Filan: So going there, if an agent is an abstraction, it doesn’t seem like it has to follow that we need to care a lot about abstractions, just because - the word agent is a word, but we don’t have to worry too much about the philosophy of language to understand agents just because of that, right? Or how much of it have you knocked off? I personally haven’t spent that much time looking into neuroscience, but it’s certainly an area where you can end up with similar intuitions. The jargon is that the time evolution is unitary, which means that two different initial states always turn into two different subsequent states. There are only two sizes approved for tournament play by the International Olympic Committee-recognized sport governing body of pool, the World Pool-Billiard Association (WPA), and its various regional and national affiliates; under the world standardized rules of pool, these are the 9 × 4.5 ft and 8 × 4 ft models. Abstraction is a useful building block to use for building those models.

I’m not quite sure if you think of abstraction as closely related to modularity or analogical, or just another thing out there. Thinking about how you think about agency, I get the sense that you’re interested in selection theorems. Daniel Filan: I think that makes sense. Daniel Filan: Okay, that makes sense. Daniel Filan: What’s wrong with that? Daniel Filan: Well, why are they important and maybe what’s the right name for them? A billiard table or billiards table is a bounded table on which cue sports are played. To see who will be the starting player, players perform a lag, where both simultaneously hit a cue ball up the table, bouncing it off the top cushion so that it returns to baulk (the first quarter-length of the table). Davis could not focus with his right eye so he played using a stance in which he rested the cue slightly to the left side of his chin, allowing him to sight along the cue with just his left eye.

Regardless of the initial direction, after passing through one focus, the billiard ball reflects off the ellipse and passes through the other focus. John Wentworth: Right. I mean, given the initial conditions, there’s only one way the universe could be. In an exhibition match at Chesterfield against Falkiner on 14 September 1916, he lost 232-400, after being given a 150-point head start. The BA&CC initially refused to recognise the break because it was not made under their version of the rules; the match had taken place under the rules used by professionals that included the "play again" rule under which the opponent can require a player who has made a foul shot to play the next shot as well. As a billiard hall manager, Davis noticed the increasing popularity of snooker and with the help of Birmingham-based billiards equipment manager Bill Camkin, he persuaded the BA&CC to recognise an official professional snooker championship in the 1926-27 season.

A challenge was issued to a championship title holder accompanied by stake money held by a third party. 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. There’s a technical component where you have to have the right technical results in order to support this kind of work. There’s the Cartesian boundary, is the key thing here, the boundary between the inside of the agent and the outside of the agent. There’s no physically fundamental barrier that’s the Cartesian boundary in the physical world, right? That’s how confused we are. That would be a sign that humans just are using a word that doesn’t have a corresponding natural abstraction. John Wentworth: I mean, the best category theory textbooks I have seen are solidly decent. So if you’re a biologist starting out trying to understand how E. coli are agents, or if you’re an AI person just working on interpretability of neural nets, or if you’re at MIRI trying to figure out principles of decision theory or embedded agents or whatever, it’s not immediately obvious that abstraction is going to be your big bottleneck.

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