You might be interested in some of my open drafts about optimization;

One distinction that I pretty strongly hold as carving nature at its joint is (what I call) optimization vs agents. Optimization has no concept of a utility function, and it just about the state going up an ordering. Agents are the thing that has a utility function, which they need for picking actions with probabilistic outcomes.

I feel very on-board with this research aesthetic.

Here are just some nit-picks/notational confusions I had while reading this;

  • The sequence , i.e., , is the computation seeded at  (or a “trajectory” in dynamical systems terminology).


  • A property  is achieved by a computation s if there exists some number of steps  such that ...

It took me a second to figure out what  referred to, partly because the first s was not rendered in LaTeX, partly because it was never shown as a function before, and partly because it looked kinda like , so I thought maybe the notation had changed.

the empty board 

I've seen  as "false" before, but I don't think it's super common, and you also previously said

a pattern is an infinite two-dimensional Boolean grid, or equivalently a function of type ℤxℤ→{true, false}

which made this feel like a switchup of notation. (Also, I think the type signature is off? The empty board  should be a function, but instead it's a set containing one symbol...)

This includes still lifes (), blinkers ()

I think if blinkers have period 2 then still lifes have to be considered to have period 1, and not 0.

Eater. An eater p is robust for  within any context  that contains  spaceships traveling in the direction of the eater (and nothing else on the board).

I think the true thing is a lot weaker than this; it's robust to gliders (not all spaceships) traveling along a specific diagonal with respect to the location of the eater (and possibly the glider has to have a certain phase, I'd have to check).


The basin of attraction for a pattern  and a property  is the largest context set  such that  is robust for  within .


  • Eater. Let  be an eater and  is the context set containing  spaceships moving in the direction of the eater and nothing else (in any other context, the contents of the board don't get consumed by the eater).

This is definitely not the largest context set , because there are tons of patterns that extinguish themselves.

I would especially especially love it if it popped out a .tex file that I could edit, since I'm very likely to be using different language on LW than I would in a fancy academic paper.