Given a territory and a class of queries, construct a map which throws out as much information as possible while still allowing accurate prediction over the query class.
Can’t remember the specific reference but: Imperfect-information game theory has some research on abstractions. Naturally, an object of interest are “optimal” abstractions—i.e., ones that are as small as possible for given accuracy, or as accurate as possible for given size. However, there are typically some negative results, stating that getting (near-) optimal abstractions is at least as expensive as finding the (near-) optimal solution of the full game.
Intuitively, I would expect this to be a recurring theme for abstractions in general.
The implication of this is that all the goals should have the implicitly have the caveat that the maps have to be “not-too-expensive to construct”.
(This is intended to be a side-note, not an advocacy to change the formulation. The one you have there is accessible and memorable :-).)
A side-note:
Can’t remember the specific reference but: Imperfect-information game theory has some research on abstractions. Naturally, an object of interest are “optimal” abstractions—i.e., ones that are as small as possible for given accuracy, or as accurate as possible for given size. However, there are typically some negative results, stating that getting (near-) optimal abstractions is at least as expensive as finding the (near-) optimal solution of the full game. Intuitively, I would expect this to be a recurring theme for abstractions in general.
The implication of this is that all the goals should have the implicitly have the caveat that the maps have to be “not-too-expensive to construct”. (This is intended to be a side-note, not an advocacy to change the formulation. The one you have there is accessible and memorable :-).)
Thanks for the pointer, sounds both relevant and useful. I’ll definitely look into it.