Those pictures use 2-D images because
1. They're printed on 2-D paper
2. In order to picture curvature to our limited Euclidean imaginations, it helps to picture a non-Euclidean space imbedded in a higher dimensional Euclidean space. So that means you use 2-D images of things in 3-D space just to convey the ideas of how our 3-D (+time) space behaves.
The only directions that really exist are within the space. The other directions are just left over from trying to picture the curvature, whose definition is really internal to the space. Only the picture involves the other dimensions, just as a somewhat misleading visual aid.
Mike W.
(published on 10/19/2011)
