Mathematical definition of “ intelligence ” ( and consequences ) Warren

In §9 we propose an abstract mathematical definition of, and practical way to measure, “intelligence.” Before that is much motivating discussion and arguments why it is a good definition, and after it we deduce several important consequences – fundamental theorems about intelligence. The most important (theorem 5 of §12) is our construction of an algorithm that implements an “asymptotically uniformly competitive intelligence” (UACI). Although our definition of intelligence initially seems “multidimensional” – two entities would seem capable of being relatively more or less intelligent independently in each of an infinite number of “dimensions” of intelligence – the UACI is an intelligent entity that is simultaneously as intelligent as any other entity (asymptotically) in every dimension simultaneously. This in a considerable sense makes intelligence “one dimensional” again and presumably explains why “IQ” is a useful quantity. Unfortunately the obvious UACI implementations are useless for practical purposes because of enormous constants of inefficiency. There are many obvious and nonobvious ways to try to get more practicality and efficiency, and it is entirely unclear how far and fast that can be