Edwin Abbott's "Flatland, A Romance of Many Dimensions" www.amazon.com/Flatland-Romanc… is a story of two dimensional creatures dwelling in a planar universe. They can't conceive of a 3rd dimension, it's beyond their experience. The central character of Flatland is A. Square.
A. Square's perception of a sphere passing through his world is first a point, then a growing circle. As the Sphere's equator moves south of the plane, the circle shrinks and then vanishes. So the planar creature perceives the 3D object as a series of two dimensional sections. Here's my attempt to illustrate this notion: hop41.deviantart.com/art/4-Dim…
Abbott goes on to point out the possibility of 4 dimensional spaces (and higher). Euclidean 4 space is self consistent, adding a 4th dimension introduces no contradictions. A good mathematical look at higher dimensional spaces is Coxeter's "Regular Polytopes" www.amazon.com/Regular-Polytop… . There are physics theories that speculate our universe may have more than 3 spatial dimensions.
My interest in polychora and higher dimensional polytopes has led me to become a fan of Jonathan Bowers. He has been rendering sections of polytopes with POV-Ray for years. His shortened terms for polytopes have become widely used by those studying these objects.
So I am delighted Bowers (aka Hedron Dude) has started a gallery on Deviant Art. Please check him out: hedrondude.deviantart.com/…; Thumbnails don't do his images justice. To appreciate the intricacy and detail of his art, full view is definitely needed.
You may want to check out Flaterland, a modernization / unofficial sequel to Flatland, if you've not heard of it. It gives a solid discussion on an infinite number of dimensions, time travel, Klein (think that's right. The fourth dimensional one) bottles, and many other interesting tidbits I cannot recall. It is crammed with basic math ideals while staying at a layman's reading level, i.e. I understood it but super advanced math is over my head. Good stuff.
I has been years since read that story