Ultimate Intelligence Part II: Physical Measure and Complexity of Intelligence

TL;DR

This paper extends measures of intelligence to stochastic problems, introduces a graphical complexity model, and explores physical limits of intelligent computation, culminating in a 'black-hole equation' linking energy, volume, and information.

Contribution

It introduces a new graphical model of computational complexity for intelligent systems and derives a novel 'black-hole equation' relating key physical and informational measures.

Findings

Derived asymptotic relations between energy, volume, and logical depth.

Introduced the 'black-hole equation' connecting physical and informational parameters.

Applied concepts to the physical limits of computation in the universe.

Abstract

We continue our analysis of volume and energy measures that are appropriate for quantifying inductive inference systems. We extend logical depth and conceptual jump size measures in AIT to stochastic problems, and physical measures that involve volume and energy. We introduce a graphical model of computational complexity that we believe to be appropriate for intelligent machines. We show several asymptotic relations between energy, logical depth and volume of computation for inductive inference. In particular, we arrive at a "black-hole equation" of inductive inference, which relates energy, volume, space, and algorithmic information for an optimal inductive inference solution. We introduce energy-bounded algorithmic entropy. We briefly apply our ideas to the physical limits of intelligent computation in our universe.