*This gallery contains 6 photos.*

nerves of cell complexes

Yes! Video games are the best way to explain basic topology. You know those special levels in Super Mario Bros. where the screen doesn’t move with you — you’re just in a “room” and if you go off to the … Continue reading

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July 17, 2012
Tagged Mario, mathematics, Pac Man, Star Fox, topology, toroid, torsor, torus, Video Games
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Why bicontinuity is the right condition for topological equivalence (homeomorphism): if continuity of the inverse isn’t required, then a circle could be equivalent to a line (.99999 and 0 would be neighbours) — Minute 8 or so. Geometric construction (no … Continue reading

Calculus is topology. The reason is that the matrix of the exterior derivative is equivalent to the transpose of the matrix of the boundary operator. That fact has been known for some time, but its practical consequences have only been … Continue reading

I feel vindicated in several ways by the Netflix Engineering team’s recent blog post explaining what they did with the results of the Netflix Prize. What they wrote confirms what I’ve been saying about recommendations as well as my experience … Continue reading

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Tagged BellKor, business, collaborative filtering, computational homology, consulting, dimension reduction, domain knowledge, Doug Hinton, econometrics, ensemble methods, Gilbert Strang, John Wilder Tukey, Kaggle, linear algebra, machine learning, Netflix, neural networks, Pragmatic Chaos, RBM's, recommendation engines, regression, restricted Boltzann machines, statistics, SVD, topology, web startups
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Dmitri Tymoczko — author of The Geometry of Music how to make visual representations of music (in paintings, video games, sculpture) 5 constraints on a composition that are necessary (but not sufficient) for it to sound good global statistical properties of songs … Continue reading

If you don’t read Sketches of Low-Dimensional Topology already, your personal astrologer advises that you start doing so before the next ecliptic. Sample pics and text: ctctstr4, originally uploaded by epsilon_is_afraid_of_zeta. View this 3-manifold as an interval of concentric spheres where … Continue reading

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Tagged geometry, imagination, Ken Baker, mathematics, topology, visualisation
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William Thurston, geometrizer of manifolds Sometimes I like to spend an hour looking at something I barely understand. The inside of this guy’s mind has got to be so interesting, but it’s been shaped by geometry rather than words, so … Continue reading

Topology as a tool for Postmodern Philosophy

The existential quantifier ∃ of logic (the propositional calculus) and the image operation along a continuous function ƒ from topology turn out to be essentially the same operation: from a categorical point of view they are both adjoint functors. Steve … Continue reading