Can a Neuron Store Infinite Information? Continuous Morphology, Finite Biological Resolution, and Accessible Neural Memory

Abstract

This paper separates four questions that are often hidden inside claims about neural information capacity: how many distinctions an ideal continuous morphology admits, how many states a physical neuron can reliably occupy, how many of those states implement distinguishable functions, and how much of that information a downstream network can recover and use. It preserves a 2012 Self Aware Networks curve and morphology-as-program intuition while replacing a literal infinite-biological-storage reading with a testable, resolution-dependent framework. The analysis includes state packing, correlated noise limits, functional equivalence, output and receiver bottlenecks, and conservative decoder-linked bounds. A deterministic illustration shows that capacity can grow as resolution becomes finer while remaining finite under every realizable measurement protocol, and that accessible capacity can saturate below structural capacity. The numerical values are illustrative and are not estimates of neuronal storage.