In 1884, in Victorian England, a headmaster and Shakespearean scholar named Edwin Abbott Abbott wrote a classic of scientific popularisation called Flatland. Written under the pseudonym 'A. Square', it tells of a world of two dimensions, a flat Euclidean plane that came straight out of the geometry texts of that period. The inhabitants of Flatland are geometric figures—lines, triangles, squares, pentagons... The rather narrow Victorian attitudes of A.Square are shattered by rumours of the Third Dimension, confirmed by a visitor from that extra-dimensional realm: The Sphere.
        Flatland's appeal has survived all intervening scientific and social upheavals. It exists in numerous editions, and several writers have published sequels or derivative works, such as Dionys Burger's Sphereland and Kee Dewdney's The Planiverse.
          Flatterland is another.   
        Abbott's sights were focussed not on the Third Dimension, but the Fourth. Can space of more than three dimensions exist? Abbott softened up his readers' resistance to such an outlandish notion by making them imagine how a Flatlander would respond to the outrageous suggestion that a Third Dimension could exist.
          His second purpose was to satirise the rigid social structure of Victorian England, with its hierarchies of status and privilege—especially the lowly status accorded to women.
        At the start of the twenty-first century, mathematics and science have moved a long way from where they were at the end of the nineteenth. The Fourth Dimension is mild indeed compared to the mind-boggling inventions of geometers and physicists— spaces with infinitely many dimensions, spaces with none, spaces with fractional dimension, spaces with finitely many points, curved spaces, spaces that get mixed up with time, and spaces that aren't really there at all. There is ample scope to play Abbott's game again in lots of new contexts, and that's the scientific content of Flatterland. The social commentary is also brought up to date, though less obtrusively.
    The central character is A.Square's great-great-granddaughter Victoria Line. Flatland's male-dominated culture is coming to bits as its women break away from their traditional restraints. Vikki finds an old notebook, the original manuscript of Flatland, and is bitten by the 3D bug. Like her ancestor, she attempts to enter the Third Dimension. She succeeds beyond her wildest dreams. Guided by the Space Hopper, she encounters a series of bizarre characters—Moobius the cow, the Space Girls, Superpaws the quantum cat, the Hawk King... She learns about topology, finite geometries, relativity, quantum theory,time travel, and superstrings.
        If you think that serious science has to be solemn, look elsewhere. But if you want to have fun with the latest concepts of space, time, and geometry, Flatterland is the place to go.

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Also Available: The Annotated Flatland — the first ever annotated edition of Edwin A. Abbott's classic Flatland, with material on the history, science, mathematics, philosophy, and religion of the Fourth Dimension in Victorian times, together with biographical information on Adwin A. Abbott and Charles Howard Hinton.