Tag Archives: topology

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

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Topology as a tool for Postmodern Philosophy

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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

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Tim Maudlin reformulates topology using open lines as the basis rather than open sets. He thinks this sheds some light on the “arrow of time” question (why does time only move forward, when physical equations can be used to postdict … Continue reading

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More drawings by Robert Ghrist. Point-set topology, differential topology, geometric topology, symplectic topology, algebraic topology illustrated. From his (free) notes on applied homology. GLOSSARY Topology = connections between things. Manifolds come in a wide variety of shapes, but they’re all tame. Vector fields = arrows on … Continue reading

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Polyhedra

Polygons (2), polyhedra (3), polychora (4-D), and polytopes (∀) can be represented as a graph — the same network-skeletal structure that models Facebook friends computer networks loop quantum gravity spin foams Ising magnetism molecules subway maps scientific collaboration artistic composition … Continue reading

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Blood Types

Blood types form a topological space (and a complete distributive lattice). There are three generators: A, B, and Rh+. Above the “zero element” is the universal donor O− and the “unit element” is the universal receiver AB+. A topological space contains … Continue reading

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