Ex Chao Ordo: From Hesiod's Theogony to the Kuramoto Model

How does order arise from the unordered? This question, arguably the oldest in Westernthought, was first articulated in Hesiod's Theogony (c. 700 BCE), where Cosmos emerges fromChaos without an external designer. The same question was reformulated by Thales and thePresocratic natural philosophers, who replaced mythological language (mythos) withrational-naturalistic language (logos) while preserving the underlying structure of the inquiry. Inthe twentieth century, the Kuramoto model (1975) provided a precise mathematical answer:coupled oscillators with heterogeneous natural frequencies spontaneously synchronize whentheir coupling strength exceeds a critical threshold, producing macroscopic order frommicroscopic incoherence. This paper argues that these three formulations — Hesiodic,Presocratic, and mathematical — constitute a single intellectual trajectory spanning 2,700 years,expressed in three successive languages: mythos, logos, and mathesis. By demonstrating thestructural correspondence between Hesiod's cosmogonic narrative and the synchronizationphase transition described by the Kuramoto model, we extend Cornford's classical thesis on thecontinuity between myth and philosophy into the domain of mathematical physics. Thepersistence of this question across radical changes in explanatory frameworks suggests thatcertain fundamental problems are invariant under paradigm shifts.