1. What sort of mathematical proofs exist to demonstrate the validity of the assumptions about the fourth dimension made through analogy? Is it possible that the relationship between the second and third dimension is not exactly analogous to the relationship between the third and fourth? Perhaps four is a unique quality (e.g. it's the first integer that's not prime...)?
2. What sort of surface is Flatland on? I would assume it's a plane curved in the third dimension, so as to produce the "downward attraction" in varying degrees. Was Abbott suggesting that forces in our own three-space are created by curvature in higher dimensions, as Einstein would postulate years later?
3. How common is the link between theology and theories of higher-dimensionality? While reading the book, I constanly was reminded of Dali's Christus Hypercubus. Also, I've heard some references to the theory that angels are higher-dimension creatures...