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I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle around a black hole and this showed the warping of space.

The instructor said that it is actually more like a table cloth because the ball would cause a warping as well.

The problem I have is transferring this image of 3d objects on a warped 2d plane to actual actual space.

Another way to look at my dilemma: There is space above the 3d object on the table, and on the sides of it. If we were on the 3d object and left if in any direct but down, we would be in space, but how is this space described? I can only picture the one "bottom" portion of space.

Help me understand the rest.

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You can't transfer that image to actual space because then you'd have to visualize curvature in 4 dimensions, which is impossible. The purpose of what the teacher did was to alleviate that problem. – Florin Andrei Jan 4 '12 at 23:48

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Unfortunately Human beings haven't evolved to deal with thinking outside 3 spatial dimensions and as such any attempt to do so will require analogy or reduction.

The rubber ball on a sheet is useful in a reduced dimension problem but is more of a lesson in how geometry relates to particle motion rather than 4D General Relativity. Think of it as a stepping stone towards the maths, and once you've got that sorted you can investigate as many dimensions as you want!

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By the way psychology research suggests that the humans' vision perception of the world (3 Dimensional vision) completely depends on external stimuli we were all exposed to during youth. So perhaps with appropriate training we humans just might be able to visualize 4D space! – namehere Feb 16 at 15:10
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Look at the world through the bottom of a wineglass with one eye. Then close that eye and open the other, seeing the world as normal. Switch back and forth a few times if necessary. It produces the same distortion as a gravitational lens, so you can visualize the warping of space a little better that way.

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