No Abstraction Without a Goal

  • Abstractions are important.

  • Abstractions are functions that map a high-dimensional space to a low-dimensional space. They have more possible inputs than possible outputs, so abstractions have to shed some information.

  • Abstractions filter out useless information, while keeping useful information.

  • In order for there to be such a thing as “useful information”, there must be some goal(s) being pursued.

You might argue that “abstraction” only means preserving information used to predict faraway observations from a given system. However, coarse modeling of distant objects is often a convergent subgoal of the kind of organisms that Nature selects for.

The scout does not tell the general about the bluejays he saw. He reports the number of bombers in the enemy’s hangar. Condensation of information always selects for goal-relevant information. Any condensation of information implies that the omitted information is less goal-relevant than the reported information; there is no abstraction without a goal.