{"id":281,"date":"2013-08-14T12:14:31","date_gmt":"2013-08-14T17:14:31","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=281"},"modified":"2013-08-14T12:14:31","modified_gmt":"2013-08-14T17:14:31","slug":"this-is-your-brain-this-is-your-brain-on-category-theory","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2013\/08\/14\/this-is-your-brain-this-is-your-brain-on-category-theory\/","title":{"rendered":"This is your brain. This is your brain on category theory!"},"content":{"rendered":"

I often ponder whether mathematics is lying around waiting to be discovered or is non-existent until we invent it. \u00a0One of the most recent posts at Math Rising<\/a>\u00a0 led me to a similar question concerning the brain. \u00a0Has the physical structure of the brain led us to create certain mathematical structures or did a fundamental sort of mathematics govern the formation of the brain?<\/p>\n

Math Rising\u00a0blogger Joselle DiNunzio Kehoe combs through mathematical papers as well as popular media and blogs like n-Category Cafe looking for mathematical connections between different disciplines including art, physics, and biology. \u00a0To find these connections requires one to focus on structure, so category theory is recurring theme. \u00a0One of her latest posts focuses on how category theory might describe the means by which we mentally process and sort information.\u00a0 In particular, she discusses the 2003 article by Ronald Brown and Timothy Porter Category Theory and Higher Dimensional Algebra: potential descriptive tools in neuroscience<\/a>\u00a0 The two authors, both mathematicians, propose colimits as a way of describing processes of processes. \u00a0The paper also invites discussion with neuroscientists concerning how to use mathematics to connect the activities of a single neuron to formation of a \u201cconcept\u201d or \u201cemotion\u201d. \u00a0 One intuitive advantage to category theory is that regardless of the choices made along the way, the end product is preserved.<\/p>\n

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The Universal Property of a Co-limit shown by a diagram — Colimits can be thought of as a way to amalgamate many pieces of information into one.<\/p><\/div>\n

Ms. Kehoe, who teaches Mathematics at the University of Texas at Dallas also writes for Plus Magazine<\/a> \u00a0and Scientific American<\/a>\u00a0about mathematics and cognition.<\/p>\n

The idea that category theory is not “abstract nonsense” (as it is so fondly referred to by many a mathematician) was also discussed in Science News<\/a>\u00a0back in May by science writer Julie Rehmeyer. \u00a0In particular, she mentioned David Spivak’s recent book “Category Theory for Scientists”<\/a> which is available for free on arxiv. \u00a0This book is aimed at a broad scientific audience.<\/p>\n

Lastly, the Foundational Questions Institute<\/a> recently featured the work of John Baez and the quest for the categorification of quantum mechanics.<\/p>\n

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I often ponder whether mathematics is lying around waiting to be discovered or is non-existent until we invent it. \u00a0One of the most recent posts at Math Rising\u00a0 led me to a similar question concerning the brain. \u00a0Has the physical … Continue reading →<\/span><\/a><\/p>\n

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