Field Note
Finite Moves, Infinite Space
Game theory, discrete choices, and the larger spaces those choices create.
A game begins by becoming finite
To study a game, we name the players, the available moves, the information each player can see, and the outcomes they care about. The world is continuous and unruly; the model becomes useful by drawing a boundary.
That boundary is not a defect. A finite representation lets us derive something precise. But the precision belongs to the model, not automatically to the world.
Between rational and real
I like the strange intimacy between discrete moves and infinite spaces. A sequence of rational choices may approach a point it never contains. A small rule can generate an enormous state space. An algebraic structure becomes most expressive through the operations it permits and forbids.
Engineering works the same way. Every interface declares a game. Every evaluation function chooses which outcomes become visible.
The unresolved edge
When a system optimizes perfectly inside the game we gave it, how do we remain attentive to the world the game left out?