Finishing Flatland, a novella published by British mathematician and teacher Edwin Abbott a good 20 years before Einstein’s General Theory of Relativity and the growth of quantum mechanics, leaves the reader wondering what Abbott could possibly have known about these later figures and events. But the book’s very existence underscores just how fundamental those 20th century ideas are. The entire premise of Flatland, in fact, is about shaking our perceptions of what we believe to be our own – and only – physical world. Even the popularity of Flatland today is shaped by the changes in our worldly perceptions since 1884.
A Geometric Satire
Abbott wrote Flatland as a satirical novel, skewering what he believed were short-sighted traditions of Victorian England: strict divisions of social classes, which in Flatland are personified by geometric objects:
The lowest forms are points (with no dimensions), and in Flatland, a two-dimensional world inhabited by the author’s narrator, A. Square, women are the lowest life forms, consisting solely of simple straight lines. Soldiers and “lowest classes of workmen” are triangles with two equal sides, members of the middle class are equilateral triangles, professionals are squares or pentagons, and the highest aristocratic classes are polygons of nearly infinite numbers of sides. And since Flatland is in two dimensions, one cannot actually see these geometric shapes, but feel the sharp end of a soldier’s “point” or determine the multiple (yet flat) dimensions of an aristocrat. And true to Victorian values aimed at improving one’s social status, the offspring of certain classes can move up the social ladder by adding a side (a square’s sons can become pentagons, pentagon sons become hexagons, and so on).
The Case for Women
Women do not fare as well in this two-dimensional (or one dimensional) society. Consisting simply of a straight line, they are considered simultaneously untrustworthy and dangerous by Flatland society. Since a straight line, straight on, is simply a point, women are forbidden to walk in public without making noise, and required to enter houses through a special entrance, so to avoid spearing their neighbors and loved ones.
How Many Dimensions are Enough?
Trapped in this two-dimensional society, A. Square recounts his adventures as he discovers for the first time, an extra dimension. Guided by a three-dimensional cube, Square and his society cannot comprehend the idea that an extra dimension (providing height or space) can even exist. However, like theoretical physics, an algorithm of sorts provides the proof necessary that any dimension has an extra one. The comparisons among one-, two- and three-dimensional worlds bring to light our attempts to understand four, five or even six dimensions in our universe.
And much like our society, Flatland’s court system and social hierarchy firmly (and flatly!) reject Square’s accounts of a universe that appears differently from their perception. Trials take place, reminiscent of the consequences of Galileo Galilei’s daring new assertion of planetary motion.
While Abbott’s 19th century English can prove a little daunting, “Flatland” is a worthwhile read, if only to gain the perspective lacking amongst Flatlanders; that whatever world you inhabit, you’ll always have another dimension.
The book provides two important lessons for a scientific career, as well as one (mine) in marketing and communications:
1) Being flat in a round world: never assume that your perspective, whether in designing an experiment or observing results, is the only one or the “correct” one.
2) It’s more than algorithms: explaining difficult scientific concepts to somebody whose world view is not yours is very challenging, indeed!
Author: Edwin A. Abbott
Paperback: 96 pages
Publisher: Dover Publications; Unabridged edition (September 21, 1992)