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Flatland cover

One hundred and twenty-two years ago a modest little volume entitled Flatland appeared in London, written by the pseudononymous A. Square. Flatland purported to be a memoir by Mr. A. Square of his adventures and misadventures during a series of fantastical journeys—rather like those in Gulliver's Travels or the Alice books.  A cursory examination might have tempted Victorian readers to dismiss Flatland as a charming but far-fetched fantasy for Victorian children. 

Victorian readers would have been wrong.  And Victorian children would have been baffled.  Despite its brevity—less than one hundred pages—Flatland seamlessly melds social satire, pointed commentary on the vanity and hypocrisy of the upper classes, philosophical musings, higher mathematics, and a dash of what we would now call hard SF. It has inspired numerous successor books and quasi-sequels: most recently Flatterland, by mathematician Ian Stewart (originally published in 2001), and Spaceland, by mathematician and SF writer Rudy Rucker (originally published in 2002).  

A. Square, the author and narrator of the original Flatland, is a mild-mannered mathematician who likes nothing better than a quiet evening puzzling over geometry problems.  He lives in a society that seems very much like Victorian England.  The class structure is solidly in place: members of the lowest classes are considered to be scarcely better than animals; women are delicate, emotionally unbalanced, and need the controlling, stabilizing force of men; and there is an aristocracy, although of priests rather than peers. 

Flatland seems very much like Victorian England.  And very much not. 

Flatland is just that—flat. Everyone and everything in it is two-dimensional. Class is denoted by the number of one's sides; the more sides, the higher one's social standing, and, it is assumed, the more finely honed one's intellect and the greater one's moral rectitude.  Triangles are the lowest class, all the way up to the priestly class of Circles, who are not true circles but who have so many sides they might as well be.  A. Square himself is literally a square.  And women?  Women are straight lines, the poor dears, but they really can't help themselves.   

A. Square's life in Flatland is rather flat itself, but he's content.  He is kind enough to take the first part of his memoirs to introduce us to his society—which he does not question—until his world is rocked by the appearance of a sphere that takes him on a 3-D jaunt. Upon his return to Flatland, A. Square attempts to spread his multidimensional message and suffers the consequences. 

What in Heaven's name is this rubbish? a Victorian reader might ask.  And who is this A. Square chap? 

In reality, A. Square was Edwin Abbott Abbott, and surprisingly he was not a mathematician.  Abbott was a theologian, classicist, educator, and author of books and articles ranging from a Shakespearean grammar to a Frances Bacon biography to theological fiction—not to mention the article about the Gospels in the ninth edition of the Encyclopedia Britannica.  This thoughtful man of God lived in a time and culture of contradictions: where great scientific minds were matched by rank spiritualist frauds; where a willingness to believe in fairies was matched by a reverence for logic; where the upper classes congratulated themselves on being the epitome of human development while indulging in a visit to a freak show or an asylum.  

Abbott disagreed with some of the most ingrained views of his time (for example, he supported education for all—including women) and viewed Victorian self-satisfaction as an intellectual straightjacket.  He saw contemporaries who were willing to believe in illusions but dismissed the message of Christ because of the trappings of the miraculous that surrounded it.  The conclusion he drew from such an observation, however, was somewhat surprising; Abbott argued against both illusion and miracles as a basis for faith.  Illusion was false by definition, while miracles might someday be explained by a deeper understanding of natural law.   

Abbott returned to this theme again and again, usually in theological fiction.  However, at some point—probably through acquaintance with the mathematician Charles H. Hinton—he was exposed to the idea of the fourth dimension, and methods of visualizing it through the analogy of viewing the third dimension from the vantage point of the second dimension.  (Whew.  Caught that?)  What Abbott saw in this was not a geometry lesson, but a chance to illustrate his idea of a miracle simply being a manifestation of a greater reality.   

To A. Square, the appearance of the sphere in Flatland is at first miraculous.  But we, three-dimensional beings that we are, know that spheres aren't miracles.  A. Square comes to realize this as well, but still falls prey to the temptation to treat the sphere with a bit too much reverence, until he continues the analogy and questions the sphere concerning a fourth dimension he is sure must exist.  The sphere vehemently rejects the idea of yet more dimensions, proving itself not even A. Square's intellectual equal. 

This seemingly miraculous sphere is no god—it is as close-minded as the priests of Flatland.  Regardless, what the sphere has shown A. Square is the truth.  Our hapless square tries to share this revelation of higher dimensions with his fellow polygons, only to be arrested and summarily sentenced to life imprisonment.     

Ultimately, Flatland is a book that is a great deal more than the sum of its parts. How do its recent descendants stack up against the original's exquisite intermingling of issues? 

Flatterland cover

Of the two, Flatterland is the more obvious homage.  Stewart apparently has a great deal of respect for Flatland; he also provides the introduction and the annotations for The Annotated Flatland, the only such version.  In Flatterland, Stewart picks up where Abbott left off (and strikes a blow for women's equality while he's at it) by introducing us to Vikki Square, the young great-great-granddaughter of A. (now Albert) Square.  Vikki discovers Albert's memoirs (Flatland, of course) and manages to catch the attention of another transdimensional guide—though instead of a simple sphere, Vikki takes up with the Space Hopper, a being capable of traveling through more than just the third dimension.  The Space Hopper snatches up Vikki and they're off for the ride and the education of her life. 

Truth be told, I found Flatterland to indeed be flatter than Flatland, although it weighs in at almost 300 pages.  Stewart's focus is clearly the mathematics, where for Abbott the mathematics—rigorous though it was for the time—existed to serve his story.  Social commentary in Flatterland is restricted to a heavy-handed emphasis on gender equality, though Vikki is at times a rather annoying girl, occasionally making entries in her diary that show no relationship to how real girls think and talk.  Some of the humor also falls flat, especially the attempts at Alice in Wonderland-style puns—for example, the episode of the Running Turtle, which keeps a—ah—running total ... See what I mean?  The book, all three hundred or so pages of it, just stops when Vikki decides she's tired and wants to go home.  It is occasionally fascinating, but definitely not up to Abbott's example. 

Spaceland cover

What then of Rudy Rucker's Spaceland?  This I approached with more anticipation, since I already knew that that Rucker can write hard science and fiction, as amply demonstrated by his well-known 'Ware novels, and on the whole I wasn't disappointed.  

Spaceland introduces us to Joe Cube, a marketing weenie caught in the Silicon Valley rat race with only a cookie cutter condo and a discontented wife to show for it, who accidentally catches the attention of the fourth-dimensional being Momo.  This being Silicon Valley during the largest circumference of the tech stock bubble, Momo has a business proposition for Joe.  This being Silicon Valley, another culture ripe for satire, Rucker manages to take some savage swipes at one of the silliest economic fantasies the world has ever seen.  With technology from Momo, code and hardware from two uber-geeks, and the sales savvy of his (apparently) ex-wife, Joe sets up a cell phone company in the hopes he can sell it before everything falls apart. 

And given the Momo's nefarious plans, everything falling apart is just what Joe should worry about.  At least in the third dimension. 

I found Spaceland to be a worthier successor than Flatterland to Abbott's masterpiece.  The direct references to Flatland are low-key, and all the more successful because of it.  The action starts on New Year's Eve, as did A. Square's adventures; Joe makes a memorable visit to Pointland, Lineland, and Flatland in much the same fashion that A. Square visited Pointland and Lineland, and Rucker even has a character who is blinded to the possibility of a greater reality by religion.  Joe's trip though the dimensions is certainly thought-provoking, and Silicon Valley practically satirizes itself.  If anything is missing in Spaceland, it's the math.  It lacks the rigor of Abbott's analogies; I'm sure I learned a few things, but I'm not sure what.  

In short, of the three books, Flatland—that slim little volume—still reigns as having the greatest breadth and depth of ideas.  Chances are, it will continue to do so even after Hypercubeland, and Stringland, and ...

Lori Ann White is a writer from the San Francisco Bay Area who has decided to go back to school so she can put actual science in her science fiction, but she may just end up writing more stories about crazy people such as herself. Her work has been in Asimov's, Analog, and The Best of the Rest 3, and she is married to F&SF cover boy Gary W. Shockley.

Lori Ann White likes to write about mind-bending stuff, whether real or imaginary. Her fiction has appeared in Asimov's, Analog, Polyphony 3, and various other publications. Her current day job is as a science writer for the SLAC National Accelerator Laboratory, where "Unique Hazards May Exist." Obviously, she has died and gone to heaven.
One comment on “Flatland, Flatterland, Spaceland: An education in three books”

At the risk of looking like a total idiot for necro'ing an 11-year-old post that seems to have been dead for the better part of a decade, I have a question for the author (if she actually still reads these comments). What do you think of 1965's "Sphereland"? I've been familiar with Flatland for a while but have never actually gotten around to reading it, and I would like to know whether or not Sphereland is a worthy successor and if I should try reading it along with Flatland. I like the idea of a Flatland sequel that tackles the concept of non-Euclidian geometry, but I'm not sure how exactly it would work in practice.

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