by moonlord » Sat Jul 15, 2006 7:32 pm
Well, with certain deformations, one can represend H2 in E2. But I still fail to visualise hyperbolic spaces. I can't even figure out whether H1 exists, and if it does, what's its shape. Horocircle perhaps, but how does that look in euclidean?
For example, if the universe had the shape of S2, it can be embedded in E3 for visualisation purposes. However, even if the universe is 4D, some very complicated geometries exist. Not to mention the manifolds in these geometries...
"God does not play dice." -- Albert Einstein, early 1900's.
"Not only does God play dice, but... he sometimes throws them where we cannot see them." -- Stephen Hawking, late 1900's.