quinta-feira, 10 de maio de 2012

Let me now put aside biological questions and return to human adaptivity and its implications for the laws of psychology. A look at computer adaptivity may cast some light on the human kind. A computer, it is said, can only do what it is programmed to do (which may be quite different from what the programmer intended it to do). Generally, it is not instructed to do specific things at all (e.g. to solve a particular linear programming problem), but to adapt its behavior to the requirements of a given task chosen from a whole population of tasks (e.g. to solve any linear programming problem lying within given size limits). Then its behavior in response to each task is adapted to the requirements of the task, and it behaves differently, in appropriate ways, with each task it is given. In short, it is an adaptive system.

The adaptiveness of computers leads to a question that is the converse of the one raised above. Can a computer be programmed to do anything? Of course not. Upper limits are set by the famous theorems of Gödel, which prove that every symbol processing system must be, in a certain fundamental sense, incomplete. It is a truth of mathematics and logic that any program (including those stored in human heads) must be unable to solve certain problems.

Far more important than the Gödel limits are the limits imposed by the speed and organization of a system's computations and sizes of its memories. It is easy to pose problems that are far too large, require far too much computation, to be solved by present or prospective computers. Playing a perfect game of chess by using the game-theoretic minimaxing algorithm is one such infeasible computation, for it calls for the examination of more chess positions than there are molecules in the universe. If the game of chess, limited to its 64 squares and six kind of pieces, is beyond exact computation, then we may expect the same of almost any real-world problem, including almost any problem of everyday life.

From this simple fact, we derive one of the most important laws of qualitative structure applying to physical symbol systems, computers and the human brain included:
Because of the limits on their computing speeds and power, intelligent systems must use approximate methods to handle most tasks. Their rationality is bounded.

Herbert A. Simon: INVARIANTS OF HUMAN BEHAVIOR; Adaptivity, Computational Limits on Adaptivity; Annu. Rev. Psychol. 1990.41:1-20; 1990.