Ultimate Intelligence Part I: Physical Completeness and Objectivity of Induction

We argue that Solomonoff induction is universal and complete in the physical sense via several strong physical arguments. We argue that Solomonoff induction is fully applicable to quantum mechanics. We show how to choose an objective reference machine for universal induction by defining a physical message complexity for the presently considered ultimate intelligence research program. We introduce physical measures and limits of intelligence that are rigorously objective. We propose volume and energy measures that are more appropriate for physical computations. We extend logical depth and conceptual jump size measures in AIT to stochastic domains and physical measures that involve volume and energy. We show the relations between energy, logical depth and volume of computation for AI. We also introduce a highly relaxed, general physical model of computation that we believe to be more appropriate for our universe than other low level automata models previously considered. We briefly apply our ideas to the physical limits of computation in our universe to show the relation to ultimate intelligence.