Semantic Bifurcations: Applying Dynamical Systems Theory to the Detection of Meaning Transitions in Language

Abstract

This paper proposes and empirically tests a dynamical systems framework for understanding semantic change in natural language. We argue that word meanings do not drift continuously but instead occupy stable attractors in semantic space, destabilize near critical transitions, and bifurcate into new stable states — a process described mathematically by catastrophe theory. Using word embedding models and Google Books Ngram frequency data as independently measured control parameters, we construct semantic phase space trajectories for eight English words with documented meaning shifts: network, virus, cloud, artificial, gay, awful, broadcast, and computer. We demonstrate that (1) neighborhood variance in embedding space — a proxy for the critical slowing down signal predicted by bifurcation theory — peaks during or before semantic transitions, not after; (2) the speed of bifurcation correlates with the intensity of independently measured discourse pressure; and (3) bifurcations can fail or reverse when the control parameter declines before the transition completes, as demonstrated by the word virus during the COVID-19 pandemic. We identify artificial as a word currently under bifurcation pressure from competing AI and authenticity discourses. The framework generates falsifiable predictions about future semantic transitions and offers a mechanistic account of why some meaning changes are sudden rather than gradual — a question standard linguistic frameworks cannot answer.

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