Wednesday, July 02, 2008

3-manifold

Because the three-dimensional "surface" of a four-dimensional hypersphere looks locally like Euclidian 3-space, give me a flight simulator or game that can fly around in the 3D surface of a 4D hypersphere.

Can a human form a mental map of such a space? Easier is probably the surface of a 4D torus, which is simply a cube with opposing faces attached.

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