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What areas of geometry are used in psychology/cognitive science/neuroscience? Are the applications of a sophisticated nature or superficial?

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Do you mean employed in the study of? If you could just make sense of that line ty and welcome :) – user3543 Dec 6 '13 at 2:40
Yes. 'Employed' in the study of. – Zeph Dec 6 '13 at 8:00
Do you consider general applications of linear algebra as geometry? Or must some specific geometric insights beyond that be used? – Artem Kaznatcheev Feb 6 '14 at 6:20
Do you count topics like the psychology of visual perception and gestalt psychology, or do you mean only areas where geometry is used to study a cognitive process which is not directly related to geometry itself? Because the first would be a very wide area, while the second interpretation will give you a more interesting list. – rumtscho Feb 10 '14 at 21:11

Here are a few off the top of my head from neuroscience:

  • neural activity may primarily exist on low dimensional attractors.
  • reconstructing PET signal origins from emitted gamma rays
  • It's widely believed our brains are gyrencephalic (wrinkly) to maximize surface area.
  • Various distance metrics (Euclidean, Mahalanobis) are common tools for clustering data, for example spike sorting.
  • Neuron morphology (shape) follows function.
  • Microgeometry of objects is important for tactile texture perception.
  • Bat echolocation and fish electrosensation are limited in range due to the inverse square law.
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Semantic foraging in memory is another nice example: concepts in memory can be represented spatially as locations in multidimensional space, and the route we travel in that 'space' has a lot in common with the optimal foraging movements animals adopt.

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I was reading Goldstone and Son's chapter on 'similarity' in the Cambridge Handbook of Thinking and Reasoning the other day, where they discuss the geometric multidimensional scaling approach to similarity. In a nutshell (the chapter describes it in detail), the theory holds that if you represent the values of relevant features of anything as independent dimensions, concepts can be located in high-dimensional space, and distances/relationships between them calculated geometrically. – Eoin Feb 7 '14 at 11:42

Though not a direct bridge between Linguistics and Cognitive Science, Semasiographic communication systems are a ripe territory for the studio of Mereology.

Off-hand, consider:

Dewalque, A. Brentano and the parts of the mental: a mereological approach to phenomenal intentionality. Phenomenology and the Cognitive Sciences, September 2013, Volume 12, Issue 3, pp 447-464

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Fascinating answers! I'd love to see a little elaboration here though, as I don't think the hyperlinked GRE-level vocab words are doing justice to your ideas, which come very unexpectedly and usefully from outside the proverbial box. – Nick Stauner Feb 8 '14 at 22:23

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