Can't add a map right now, but here are some "illustrations"
First, picture a normal 3d sphere:
Now, imagine an infinite row of normal 3d spheres:
Code:
[color=white]
...ooooooooooooooooooooooooo...
[/color]
Each 3d sphere is the cross-section of a higher dimension object -- in this case, a 4d hypercylinder.
Imagine being able to
turn in a certain way, and when you
turn that way, you step across spheres instead of stepping across points on a single sphere. Clearly, a point on sphere N is also touching that point on sphere N+1 and N-1, so if you're in a forrest, you're going to see forrest even when you
turn.
When you
turn in this simple 4d world, you perceive yourself to be on a normal 3d cylinder. The length of the cylinder
is the infinite row of 3d spheres. When you un-
turn, you will be on a normal 3d sphere.
Does this make sense so far? If so, I'll keep going to 5d
-- Nifft