Ricci curvature and the stream of thought

Area of Science:

• Cognitive Science
• Computational Linguistics
• Network Science

Background:

• Semantic associations are often modeled using continuity.
• The directionality of semantic transitions remains less understood.
• Existing models may not fully capture the dynamic flow of thought.

Purpose of the Study:

• To investigate the role of directionality in semantic associations.
• To introduce a novel quantitative method for measuring semantic transition dynamics.
• To challenge existing models by proposing direction of maximal resolution as a key factor.

Main Methods:

• Developed a hypergraph framework to model semantic transitions.
• Adapted discrete Ricci curvature to quantify the 'direction of maximal resolution' in semantic space.
• Utilized a categorical fluency task (animal naming) for empirical data collection.

Main Results:

• Found that 'edge stretchiness' (a measure of resolution) relates to transition probability.
• Demonstrated that incorporating Direction significantly enhances explanatory power over similarity alone.
• The proposed model suggests thought streams move towards maximal resolution.

Conclusions:

• Directionality is a critical, quantifiable factor in semantic associations.
• Discrete Ricci curvature offers a novel tool for analyzing semantic network dynamics.
• This approach provides new insights into the cognitive mechanisms underlying the stream of thought.