Reddit mentions of Flatland (Start Publishing)

To build on doc_daneeka's answer, I'll try to recollect an explanation I read about 4D objects in 3D space.

An object existing in n dimensions may be represented in n-1 dimensions. This representation may be called a shadow.

So, a 2D representation of an object existing in 3 dimensions is called a shadow (and is a shadow as we know it). Looking at a 2D representation alone, one might be able to reconstruct what the original object looks like in 3D.

Say, you see the shadow of a clear glass vase. If you know where the light source is placed, you might be able to ascertain what the vase looks like based solely on its shadow. Spin the vase, and the shadow will show some movement as well.

What we're looking at is a 3D representation of an object that exists in 4 dimensions. For a moving object in 3 dimensions, its shadow would also show movement albeit only in two axis. Similarly, objects in 4 dimensions would show movement along three axis.

From what I gather, we haven't yet developed a sophisticated way to think or even explain (to the layman at least) what an object might look like in 4D. Most of our brains aren't wired to think that way. Kinda like the characters in Flatland - really nice read, BTW.

You know...I may have come across this explanation while attempting (and failing miserably) to read and understand Lisa Randall's Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions.