# Two-dimensional characters

To follow the circles in this storyline, dig out your geometry textbook

One of the most astonishing and original works of utopian fiction was written in the 1880s by Edwin A. Abbott. (The A. improbably enough stands for "Abbott.") He was a Victorian headmaster and author of a number of volumes that have fallen into obscurity. But his "Flatland: A Romance of Many Dimensions by the Author, A SQUARE" has been in print continuously since 1884.

"Flatland" is one of those books that, once read, are never forgotten. The author, A Square, lives on a plane, a world where all the inhabitants are figures from Euclid's geometry. His two-dimensional existence is shattered one day when a Sphere enters his rooms and lifts him up into the previously unimagined third dimension.

"Flatland" is not just a math text; it is also a cutting satire of Victorian England. Social class is rigidly delineated - triangles are the lowest order, ranging up through polygons to the lofty and aristocratic circles. Women are at the bottom of the scale. They are just straight lines, required to buzz a warning continuously so as not to present a puncture danger to the males.

Since the 1880s, several authors have tried to emulate Abbott's simple metaphor, in works such as "Sphereland," by Dionys Burger (1965). "Flatterland," subtitled "Like flatland only more so," is a modern effort to try to extend the Euclidean geometry of the 19th-century volume into the complex realms of contemporary physics and cosmology.

The author, Ian Stewart, is a professor of mathematics in England and for several years has written a monthly column called "Mathematical Recreations" for Scientific American. He is also the author of a number of science-fiction works that depend on mathematical speculation.

Stewart's utopian protagonist is Victoria Line, a descendent of Albert Square. Her guide through the higher geometries is the Space Hopper, an inflatable beach toy. Victoria, a thoroughly modern, Internet-savvy line, has adventures in most of the current areas of mathematical speculation. She is led from fractals and projective geometry, through black holes and time travel, to the startlingly improbable worlds of quantum cosmology and 11-dimensional superstring theory. Along the way she meets a number of curious characters, including Moobius, the one-sided cow, and Superpaws, Schrodinger's famous cat.

The problem with all this is that one cannot really explain modern physics with the kind of simple images that Abbott used so successfully. If you already know a great deal about the topic, you'll understand the jokes (Moobius = Moebius strip, get it?).

The charm of the original, for the modern reader, is the combination of mathematical imagination with clever social satire. The modern version has a harder job, and succeeds less well.

Frederick Pratter is a freelance writer in Missoula, Mont.

(c) Copyright 2001. The Christian Science Monitor