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First paragraph of this page, asserts that the theory of mathematical manifolds find application in psychology: They appear "[i]n psychology as spaces of sensations (for example, colours)". An inconclusive search led me to believe that the author confused manifolds with its dictionary definition: something having many different parts or features.

Can you inform me about any use of mathematical manifolds in psychology? One specific example per post.

Manifold. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Manifold&oldid=47752

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    An old acquaintance of mine worked with a company on a mathematical model of "word manifolds" (Riemannian manifolds with a metric describing distances between words) to predict and treat suicidal ideation. – Ninad Munshi Jun 26 '20 at 12:22

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I see that this question might not be of general interest for this community. I attach two resources I've found for the interested.

Two Kinds of Global Separability and Curvature by Townsend and Spencer-Smith. And the book:

Psychophysics Beyond Sensation: Laws and Invariants of Human Cognition by Kaernbach, Schröger, Müller

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Just a tourist here. I'm reading "The Long Journey Home" by A.H. Almaas and he refers to Riemannian Manifolds in the context of psychology as a core component.

Fascinating that there is crossover here describing reality, ego structures, and how they relate to soul identity. Check it out. I’m still puzzled but at least finding others with the same question. This will probably get deleted by moderators (hi folks!) because I’m not answering but pointing to a resource for your question that goes beyond it to some truly fascinating research.

311411
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Andrew Tannehill
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    You can improve your answer, I think, by telling us more about what Almaas specifically writes regarding the mathematical object. Welcome to Math Stack. – 311411 Feb 22 '24 at 16:24