A Quantitative Definition of Intelligence

TL;DR

This paper introduces a universal, quantitative framework for defining intelligence across physical systems, emphasizing generalization, domain knowledge, and contextuality, challenging traditional syntax-semantics distinctions.

Contribution

It proposes a substrate-independent measure of intelligence based on description length and introduces a new perspective on semantics and contextuality.

Findings

Defines intelligence density as log of outputs over description length

Characterizes knowing as fixed description length with diverging outputs

Refutes Searle's premise by linking correctness and independence

Abstract

We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system memorizes if its description length grows with its output count; it knows if its description length remains fixed while its output count diverges. The criterion for knowing is generalization. A system knows its domain if a single finite mechanism can produce correct outputs across an unbounded range of inputs, rather than storing each answer individually. The definition places intelligence on a substrate-independent continuum from logic gates to brains. We then argue that meaning over a domain is a selection and ordering of functions that produces correct outputs where correctness is specifiable. We also define a measure of contextuality of an output as the inverse of its conditional Kolmogorov complexity given the context of prior outputs, which unifies correctness and independence into a single condition. Together, these refute Searle's third premise, that syntax is insufficient for semantics, over any domain where correctness is specifiable.