Dynamic Graphs as Unifying Primitive: From Kuramoto Oscillators to Transformer Attention via Higher-Order Functions

We propose message passing over dynamic graphs as a unifying primitive con-necting three domains: physical synchronization (Kuramoto model), neural computation(Transformers), and functional programming. The key distinction is whether graph topol-ogy is static (xed) or dynamic (generated from state).The Transformer's attention mechanism exhibits structural similarity to higher-orderfunctions: both generate computational patterns from data rather than apply xed transfor-mations. Attention uses probabilistic weighting via softmax, whereas higher-order functionsoperate deterministicallythis dierence constrains what attention can compute. Never-theless, the parallel illuminates why attention is powerful: like map and fold, it abstractsover structure.Since semantic computation runs on physical hardware, it inherits deterministic dynamicsat the substrate level. Programs execute exactly as written; neural networks follow theirlearned parameters exactly. Flexibility emerges from complexity, not from departure fromdeterminism.This paper employs autoethnography to document abductive reasoning, foreground-ing the context of discovery. We trace a decade-long development: reactive programming asgraph (2016), software architecture as graph pattern (2020), and the present synthesis withnonequilibrium physics (2026). Building on a companion paper connecting Newton to ac-tive matter, we sketch how synchronization, computation, and learning may share commonmathematical structure.Keywords: Message passing, Dynamic graphs, Attention mechanism, Higher-order func-tions, Kuramoto model, Autoethnography