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Here's one of my favorite explanations of just the sort you're looking for, again by way of my old hero Carl Sagan: . After seeing this as a boy on Carl's PBS series "Cosmos", I just had to know more, so I picked up a copy of Abott's "Flatland", and soon thereafter a copy of a book taking the next logical step, namely Dionys Burger's sequel "Sphereland", the lot of which gave me a nice intuitive feel for what might be the case, what might be possible, given additional spatial dimensions. Enjoy :-)