The Geometric Parity Hypothesis: High-Dimensional Addressability as a Substrate for Implicit Neural Connectivity

Comparisons between artificial and biological neural systems often focus on explicit connection counts—trillions of parameters versus hundreds of trillions of synapses. This framing presupposes that functional relationships must be stored as fixed synaptic weights. We propose an alternative: high-dimensional representational geometry itself can serve as the primary substrate for large-scale neural computation, with functional connectivity emerging implicitly through distance-based interactions rather than stored wiring. Drawing on high-dimensional geometry, we show that spaces on the order of ten thousand dimensions can embed neuron-scale populations with minimal interference. We support this hypothesis with mathematical analysis and a computational demonstration of geometric clustering in 16,000-dimensional space. Dimensionality alone enables representational capacity; intelligence must arise from the dynamics within this geometric space.