Flatland: A Romance of Many Dimensions
Edwin A. Abbott
Originally published: 1884, UK
Rating: 3 (Worth A Try)
How often have you read mathematical fiction? Never before, eh? Well, Abbott’s novella, Flatland, can change all of that.
Flatland is a story told by a Square living in the two-dimensional world of Flatland inhabited by different geometric figures on a two-dimensional plane. The Square is an upstanding citizen of Flatland until he is visited by a Sphere who changes his perspective of reality by showing him Pointland (with no dimensions), Lineland (with one dimension), and Spaceland (with three dimensions). The Square’s information about any land outside of Flatland, however, has been deemed heretical, placing him in a difficult position since he feels he must tell others that the third dimension is real.
Much like Gulliver’s Travels, Flatland is a humorous fictional story written like a nonfiction travel document. The Square describes the existence of Flatland and the other lands in detail as if he were recording this information for future inhabitants to read. Although it is serious, this style still has humor in the way he practically speaks about what to the reader seem to be unthinkable things. For example, the women in Flatland are straight lines, and so can be dangerous to the men (geometric shapes) because the can impale them like a needle.
“For whenever the temper of the Women is thus exasperated by confinement at home or hampering regulations abroad, they are apt to vent their spleen upon their husbands and children; and in the less temperate climates the whole male population of a village has been sometimes destroyed in one or two hours of simultaneous female outbreak.” (Part I, Chapter 4)
In addition to the sometimes humorous tone, Flatland provides an interesting satire of British society at the time, which can also be (and has also been) connected to the present-day UK or even US (See Flatland, a movie from 2007). For example, because of the danger women present due to their shape (if viewed the right way, a line on a two-dimensional plane can be a difficult to detect point), they have their own door into their homes and often have to be escorted by the males of their family when they are out in public (sounds like Victorian women or even some present-day conservative religious groups, right?).
This book also has some geometry education. The first time I read this book was for geometry class my sophomore year of high school. I can’t remember exactly how we used it in class, but I bet it involved some of the geometric concepts and calculations in the book itself. This connection to education is very accessible and interesting.
Along with the education bent, Abbott includes diagrams that help the reader not only understand some of the geometry but also the perspective shifts that the Square goes through when he travels between lands. These diagrams are very useful and appear hand drawn.
Bumps in the Road:
Although the tone can be humorous, Flatland is written like an encyclopedia, and sometimes a travel narrative or dream journal, so it can get dull. I especially found the very Victorian sounding passages tedious. These happen when the Square is visited by the Sphere, so for some reason the Square has to address this third-dimensional being like he was addressing a superior in the Victorian era (I suppose he views the Sphere as his superior, or he’s just being polite). He goes from a more readable version of English to addressing the Sphere like this:
“But before your Lordship enters into further communications, would he deign to satisfy the curiosity of one who would gladly know whence his Visitor came?” (Part II, Chapter 16)
While this is more difficult to read than the rest of the novella, at least it only lasts while the Square is talking to the Sphere.
My last issue with Flatland is that it mentions but does not actually answer some of my more pressing questions about Flatland. For example, the Square discusses what the children of the Flatland citizens look like and that families gain sides as they procreate, but there is no discussion of how sex works in Flatland. While this may not seem like a big deal, after lengthy discussions about children and multiple examples about the dangers of the women’s shape, how are they able to have sex without the woman killing off the man? How are they children carried by the woman? How does she give birth? These are the types of questions the Square dances around but does not find important enough to explain; I guess they weren’t needed for the satire.
This book is worth reading for its unique style and for being mathematical fiction. It is a novella (a short novel), so I would recommend you try it out, mostly for the satire and the experience of thinking about the different spaces and perspectives of the different worlds.