Neuromorphic computing seeks to escape the von Neumann bottleneck by co-locating memory and computation, as biological neural networks appear to do. This paper investigates the topological properties of biological connectomes that enable this efficiency. We apply the capped alternative-path action metric to four complete biological connectomes spanning 600 million years of evolution: C. elegans (White et al. 1986; Cook et al. 2019), Platynereis dumerilii (Jékely lab 2024), and Drosophila melanogaster larva (Winding et al. 2023), computing the metric for 100% of synapses with no sampling. We introduce and prove the Von Neumann Obstruction Theorem, demonstrating that a pure von Neumann memory hierarchy contains no odd cycles and therefore no triangles, making triangulated local computation structurally impossible. Consequently, the specific topological friction value of 3 is established as the formal signature distinguishing in-memory from von Neumann computation. All four biological connectomes exhibit massive dominance of this signature (ranging from 77.3% to 95.2%). Furthermore, signal propagation is modeled as an absorbing Markov chain with transition probabilities reflecting topological impedance, providing a mechanism-agnostic latency model for synaptic networks. The results suggest a quantitative neuromorphic design target: over 85% of routing connections should meet this topological threshold, mirroring the biological optimum.
Andres Sebaatian Pirolo (Fri,) studied this question.