A Quantitative Definition of Intelligence

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. We argue that meaning over a domain is a selection and ordering of functions that produces correct outputs, and that a system whose intelligence density diverges necessarily captures this structure. The definition (1) places intelligence on a substrate-independent continuum from logic gates to brains, (2) blocks Putnam's pancomputationalist triviality argument via an independence condition on outputs, and (3) resolves Searle's Chinese Room Argument by showing that any finite rulebook handling an infinite domain must generalize.