Life in three dimensions is familiar and there is a huge body of literature on the fourth dimension. But what would a universe of just two dimensions be like? The first and the most charming book on the subject is Edwin Abbott's Flatland: A Romance of Many Dimensions (1884).1 This was followed by Charles Hinton's lengthier An Episode of Flatland (1907) in which the 2-d world is not a plane, as in Abbott's yarn, but the rim of a large circular world called Astria. Hinton was the first to explore in some depth what science and technology might be like in two dimensions; in fact, an earlier pamphlet of his called "A Plane World," (reprinted in Scientific Romances in 1884) may have helped inspire Abbott's novel. Hinton's speculations were taken much further by Alexander Dewdney in Planiverse (1984).3
1. Abbott. Edwin A. Flatland: A Romance of Many Dimensions.
London: Seely and Co., 1884. Reprinted Mineola, NY: Dover Publications,
2. Rucker, R. (ed). Speculations on the Fourth Dimension: Selected Writings of C. H. Hinton. New York: Dover, 1980.
3. Dewdney, A. K. The Planiverse: Computer Contact with a Two-dimensional World. New York: Simon & Schuster, 1984.