Ricci curvature and the stream of thought

This study investigates the dynamics of semantic associations by exploring the interplay between continuity and direction in a geometric semantic space. While acknowledging the role of continuity in guiding associations, our work introduces Direction as a crucial factor influencing transitions. Conceptually, we define the stream of associations as movement along a sequence of objects, with attention amplifying dissimilarity and progressing in the direction of maximal resolution, conceptualized as the most "stretched" direction. The core of our methodological innovation lies in the introduction of a unique adaptation of discrete Ricci curvature to measure the direction of maximal resolution, tailored specifically to a hypergraph framework. By reinterpreting traditional curvature concepts within this context, we provide a novel quantitative approach to understanding semantic transitions. Empirically, our investigation involves a categorical fluency task where participants name animals, allowing us to construct a hypergraph for transition analysis. We evaluate two hypotheses: the relationship between edge "stretchiness" and transition probability, and the enhanced explanatory power of considering Similarity + Direction over similarity alone. Our model challenges the standard view by proposing that the stream of thought moves in the direction of maximal resolution. By introducing the concept of Ricci curvature in a hypernetwork, we offer a novel tool for quantifying resolution and demonstrate its practical application in the context of semantic space. (PsycInfo Database Record (c) 2026 APA, all rights reserved).