Intelligence as high-dimensional coherence: The observable dimensionality bound and computational tractability.

Abstract

Intelligence arises from the maintenance of high-dimensional coherent dynamics. High-dimensional systems are effectively nonergodic on relevant timescales-the curse of dimensionality confines trajectories to vanishingly small regions relative to the full space. This confinement is not a limitation but the foundation of biological computation: a system's position in phase space functions as its memory, its constraints, its structured dynamics. Within these nonergodic regions, high entropy flow enables rich internal exploration; at the boundary, sparse outputs minimize free energy expenditure while defending the conditions for continued nonergodic existence. We formalize this through an Observable Dimensionality Bound: external observers cannot track systems whose effective dimensionality exceeds a critical threshold set by channel capacity and temporal resolution. This bound functions as protection-the opacity of high-dimensional dynamics shields internal structure from external disruption. Living systems exploit this by embodying the dynamics: the substrate is the high-dimensional field, information lives in geometric configuration, and irreversible commitments concentrate at sparse behavioral output events. The framework illuminates a thermodynamic pressure contributing to the efficiency gap between biological and artificial intelligence (brains concentrate irreversible commitments at behavioral boundaries rather than at every internal micro-update), provides a substrate-independent characterization of intelligence (capacity to maintain and defend coherent high-dimensional dynamics), and connects to the emergence of reusable codes through adaptive dynamics. Human cortex likely operates beyond this observable threshold, consistent with recent discussions of consciousness and dimensionality in the systems biology literature.