Tag Archives: manifolds

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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Again I say: STRING THEORY MOTHAF**KAAAAAAAAAAS (Source: http://www.clunkyrobot.com/2008/07/thinking-4th-dimensionally.html)

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Space

The word ‘space’ has acquired several meanings, which is what you would expect of such a sexy, primitive, metaphorically rich, eminently repurposeable concept. Outer space, of course, is where cosmonauts, Hubble telescopes, television satellites, and aliens reside. It’s ℝ³, or … Continue reading

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Manifolds, Star Fox, and Self-versus-Other

Branes, D-branes, M-theory, K-theory … news articles about theoretical physics often mention “manifolds”.  Manifolds are also good tools for theoretical psychology and economics. Thinking about manifolds is guaranteed to make you sexy and interesting. Fortunately, these fancy surfaces are already … Continue reading

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Pictures of the 3-sphere, or should I say the 4-ball? It’s a 4-dimensional circle. Even though these drawings of it look completely sweet, I have a hard time parsing them logically. They’re stereographic projections of the hypersphere. All they’re trying … Continue reading

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Complement

Here’s an inside-out thought: The air around us is a 3-manifold with 3-holes where solid objects are, and the 2-boundary is the ground. Or if you think of all the sky, it’s a spherical 3-shell (with one 3-hole, the Earth) floating … Continue reading

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In the loop quantum gravity approach, space-time is quantized by a procedure that encodes it in a discretized structure, consisting of spin networks and spin foams. A spin network consists of an oriented embedded graph in a 3-dimensional manifold with … Continue reading

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