A Square in Flatland

Edwin Abbott was born on this day in 1838. A theologian, a schoolmaster, and the author of dozens of books, Abbott’s fame today is based on Flatland, surely a candidate for the most offbeat contribution to the genre of fantasy literature. Described by some as a “mathematical satire,” Flatland is the story of daily life in a two-dimensional universe — the houses, customs, and beliefs enjoyed by a race of triangles, hexagons, lines, and other geometrics. The hero of the story is “A Square,” who is moved to document life among the Flatlanders by several world-shattering encounters, first with the one-dimensional inhabitants of Lineland, then with a cube and a handful of other 3-Ders in Spaceland. As the Linelanders find it hard to conceive of 2-D Flatland, so most Flatlanders, “even among the highest Polygonal or Circular society,” refuse to accept the idea of 3-D Spaceland. In short, A Square is imprisoned, where he serves a life sentence for uttering heretical beliefs — a “Flatland Prometheus” in chains, his news of depth falling on flat ears.

In order to help direct us through his satire of blinkered Victorian society, Abbot includes a handful of line drawings. Glancing at A Square’s house and household we see that his sons and grandsons — pentagons and hexagons, respectively — have ample, squarish bedrooms, because successive generations of male Flatlanders are able to grow a new side, so that even those “of the lowest type of the Isosceles may look forward to some improvement of his angle,” ultimately arriving at Circularity. A Square’s wife and daughters, on the other hand, live in cramped closets, because women are born as straight lines in all generations — as the Flatlanders like to say, “Once a Woman, always a Woman.” We see also that Mrs. Square, according to her status, is made to enter the home through a separate door, as all Flatland women must do. There is a practical reason attached to this custom: approached head-on, women are virtually invisible points, and when they rush into the house unannounced, they kill or maim too many of the men — unintentionally, of course. Similarly, when going out in public, women must constantly utter the “peace-cry,” enabling the men to hide behind the nearest hypotenuse.

Flatland: The Movie, a short animated film released in 2007, will soon be re-released in — you guessed it, an IMAX 3D version. The British mathematician-writer Ian Stewart has published an annotated edition of Abbott’s book and a sort of sequel, Flatterland.

Daybook is contributed by Steve King, who teaches in the English Department of Memorial University in St. John’s, Newfoundland. His literary daybook began as a radio series syndicated nationally in Canada. He can be found online at todayinliterature.com.