Intelligence as High-Dimensional Coherence: The Observable Dimensionality Bound and Computational Tractability

Intelligence emerges whenever a system maintains high-dimensional internal dynamics that collapse to coherent outputs — and this architectural principle, not clever algorithms, explains the million-fold efficiency gap between brains and computers.

Mathematical foundation: The Observable Dimensionality Bound claimed here is proven rigorously in the companion paper Curvature Amplification of Tracking Complexity, which shows that covering numbers on negatively curved statistical manifolds grow exponentially with geodesic radius.

The human cortex operates 100–1000× beyond what external observers can track. It doesn't compute by enumerating possibilities like a digital computer. Instead, it evolves through a high-dimensional landscape where incompatible solutions coexist peacefully until behaviour demands a choice. You can simultaneously consider "fight" and "flee" and "negotiate" as superposed possibilities — until the moment you must act.

This is thermodynamically necessary. Committing to discrete states costs energy (Landauer's principle). By deferring commitment and exploring reversibly, biological systems avoid paying that cost until the last possible moment. Digital computers pay for every bit at every clock cycle; brains pay only at the output.

The same principle applies at every scale: bacteria tracking chemical gradients, immune cells recognising pathogens, social groups coordinating behaviour. Intelligence isn't a human monopoly — it's what happens when high-dimensional dynamics meet low-dimensional constraints.