Thursday, August 21, 2008

Cosmology and Complexity - almost understandable

This Aaronson lecture is surprisingly readable. Thank you scribe!
PHYS771 Lecture 20: Cosmology and Complexity

...But that's only one thing that's wrong with the simple "spherical/flat/hyperbolic" trichotomy. Another thing wrong with it is that the geometry of the universe and its topology are two separate questions. Just assuming the universe is flat doesn't imply that it's infinite. If the universe had a constant positive curvature, that would imply it was finite. Picture the Earth; on learning that it has a constant positive curvature, you would conclude it's round. I mean, yes, it could curve off to infinity where you can't see it, but assuming it's homogenous in curvature, mathematically it has to curve around in either a sphere or some other more complicated finite shape. If space is flat, however, that doesn't tell you whether it's is finite or infinite. It could be like one of the video games where when you go off one end of the screen, you reappear on the other end. That's perfectly compatible with geometric flatness, but would correspond to a closed topology. The answer, then, to whether the universe is finite or infinite, is unfortunately that we don't know....
Very fun topic. I finally have a personal story for the limits of information -- when bits become a black hole.

Curious relationship between computation and the cosmological constant.

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