In 1884, the British theologian and educator Edwin A. Abbott published the science-fiction novella Flatland under the pseudonym “A. Square;” this slim volume is his primary claim to fame today. Abbott studied mathematics, classics and theology at Cambridge and became Headmaster of the City of London School in 1862. He was a stern critic of Victorian society and a staunch supporter of higher education for women, which placed him well outside the mainstream of 19th-century British thought.
Abbott incorporated his criticisms of Victorian society in Flatland, and introduced a number of new ideas as well, chief among them the concept of the fourth dimension. The novel is narrated by A. Square, who lives in a world of two dimensions (Flatland) but also describes his visits to worlds which are one-dimensional (Lineland) and three-dimensional (Spaceland).
Flatland is ruled by a strict social hierarchy dependent upon the geometric figure one assumes. More sides means higher rank, and equal sides rank higher than unequal. So women, automatically relegated to the bottom of the heap, are straight lines. Among men, soldiers and unskilled laborers are isosceles triangles (in part because their narrow angles make them resemble women), the middle class are equilateral triangles, and professionals are squares or pentagons. The several grades of nobility being with hexagons and increase up to those who have so many sides that they are simply referred to as “polygonal.” At the very top of the hierarchy are the priests, who are circles, on the principle that a polygon with an infinite number of sides eventually comes to resemble a circle.
Everyone in Flatland appears horizontal and end-on to everyone else, so you may wonder how, in two dimensions, they can distinguish each other’s rank. Fortunately, Flatland is as foggy as 19th-century London, and shapes can be distinguished according to how quickly their sides vanish in the fog.
The detailed creation of a world contrary to our assumptions, yet consistent within its own, explains why Flatland remains popular today. Another reason is Abbott’s casual yet informative presentation of current scientific and mathematical ideas: one of his goals was to get people to consider the possibility of a fourth dimension. Ian Stewart’s notes add considerable background about Abbott and Victorian society and go into much greater detail about the mathematical ideas. For readers who like to ruminate over ideas, be they mathematical, social, or historical, this annotated edition of Flatland will be a welcome addition to their library.
Ian Stewart is Professor of Mathematics at the University of Warwick. His previous books include The Science of Discworld (1999, with Terry Pratchett and J. Cohen), Flatterland (2001), What Does a Martian Look Like? (with J. Cohen, 2004), Letters to a Young Mathematician (2006) and Why Beauty is Truth (2007).
Sarah Boslaugh (email@example.com) is a Performance Review Analyst for BJC HealthCare and an Adjunct Instructor in the Washington University School of Medicine, both in St. Louis, MO. Her books include An Intermediate Guide to SPSS Programming: Using Syntax for Data Management (Sage, 2004), Secondary Data Sources for Public Health: A Practical Guide (Cambridge, 2007), and Statistics in a Nutshell (O'Reilly, forthcoming), and she served as Editor-in-Chief for The Encyclopedia of Epidemiology (Sage, 2008).