What areas of geometry are used in psychology/cognitive science/neuroscience? Are the applications of a sophisticated nature or superficial?
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$\begingroup$ Do you mean employed in the study of? If you could just make sense of that line ty and welcome :) $\endgroup$– user10932Commented Dec 6, 2013 at 2:40
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1$\begingroup$ Yes. 'Employed' in the study of. $\endgroup$– ZephCommented Dec 6, 2013 at 8:00
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1$\begingroup$ Do you consider general applications of linear algebra as geometry? Or must some specific geometric insights beyond that be used? $\endgroup$– Artem KaznatcheevCommented Feb 6, 2014 at 6:20
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$\begingroup$ 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. $\endgroup$– rumtschoCommented Feb 10, 2014 at 21:11
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4 Answers
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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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1$\begingroup$ 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. $\endgroup$– EoinCommented Feb 7, 2014 at 11:42
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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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$\begingroup$ 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. $\endgroup$ Commented Feb 8, 2014 at 22:23
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The book Theories of Meaningfulness of Louis Narens deals with Erlanger program, which is the connection between group theory and projective geometry.
