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. This study explores how people connect ideas by examining the role of direction in guiding these connections, within a space that represents meaning. Traditionally, it has been thought that our thoughts flow smoothly from one idea to the next based on how similar they are. Our research, however, suggests that the direction of movement between ideas—specifically, moving toward the most distinct or “stretched” ideas—also plays a key role. We introduce a new way to measure this direction using a concept from geometry called Ricci curvature, which we adapt to fit complex networks of ideas. We tested our ideas by asking people to name animals and analyzing how they transitioned from one animal to the next. Our findings challenge the conventional view, showing that considering both similarity and direction better explains how thoughts progress. This new approach offers a deeper understanding of how we navigate through ideas and associations.