Substrate Dimensionality in Neural Systems: Limits on Capability, Interpretability, and Consciousness

AI may hit a hard capability ceiling because digital hardware has the wrong dimensionality — one global clock versus $10^{14}$–$10^{18}$ continuous degrees of freedom in a biological brain.

Modern AI achieves enormous algorithmic complexity, but it runs on substrates with essentially one degree of freedom: the global clock that synchronises all operations. Biological brains exploit vastly higher substrate dimensionality through asynchronous, continuous dynamics — every synapse, every dendritic branch, every ion channel is a semi-independent variable.

This dimensional mismatch may explain three stubborn problems. First, why AI plateaus: scaling parameters doesn't add substrate dimensions. Second, why AI resists interpretation: you can't reconstruct internal states when the system operates beyond your measurement capacity. The paper proves this "projection singularity" is a mathematical impossibility, not just a practical difficulty. Third, why AI may never achieve consciousness: subjective experience may require volumetric field coupling (continuous 3D dynamics), not just graph connectivity (discrete node-edge structures).

The implication is uncomfortable: we may already be approaching the ceiling of what digital hardware can achieve, regardless of how many parameters we add.