If one can draw (or represent) a 3 dimentional figure on a 2 dimensional surface (ie-a cube on a blackboard), is it possible to "draw" (or represent) a 4 dimensional "figure" on a 3 dimensional "surface"?
Yes; however, just as in two-dimensional representations of three-dimensional objects, you can only see one view of the object. Also, because we have no experience with four-dimensional objects and because our eyes are limited to a planar visionscape, it would be much more difficult to intuitively grasp a four-dimensional object's representation than it is that of a three-dimensional one.
Just as a cube drawn on a blackboard introduces distortions [e.g., some 90-degree angles are not drawn as such, or true lengths are not drawn], a 4-D figure drawn on a 3-D surface will have distortions.
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