Upward, Not Northward
A reader overhearing our conversation about FLATLAND asks: “What are you guys talking about? Is this some fantasy series I have overlooked?”
It is a rare pleasure to be able to introduce a literary treasure to one unaware of it! We are talking about the grandfather of all fantasy, or, at least, of mathematical fantasies. It is a classic, and I would urge every science fiction writer to add it once to his reading list.
FLATLAND A Romance of Many Dimensions by A Square is a very slim volume from 1884, the days before the readership was constrained by the categories of fantasy and mainstream, and so it is hard to categorize. Some call it a satire, but I would call it fantastical, both in its speculations and in its flights of fancy.
“A Square” is the nom de geometrie of Edwin Abbot Abbot, a schoolmaster. The first of his many jokes is in the name: he abbreviated his last two initials AA or A^2 hence A Squared.
The Tale concerns the life and adventure of a Square occupying a two dimensional plane which is visited by the intersection of a Sphere from solid Space. The author makes wry commentary about the nature of an overly stratified or complaisant society, and about the limitations of the inhabitants of two-dimensional space to understand worlds higher than their own. The parallel to Victorian England and to modern skepticism about higher matters is pointed.
The plot, such as it is, consists of the Sphere taking the Square, like Virgil leading Dante, on an Odyssey to examine the nearby dimensions of Lineland, which is a one-dimensional realm, and Pointland, which has no dimensions.
The satiric humor here is that the sole inhabitant of Pointland is its king, and, being unable to imagine anything outside itself, adores itself as a godlike Unmoved Mover and All-in-All. Even the interruption of the Square’s truthful words describing its humble nigh-nonexistent condition into its limited existence it attributes to itself, glorifying itself for its ability to make its glory greater by pretending to doubt it.
Later, when A Square waxes rhapsodic upon the possibility of a Fourth or Fifth or Sixth dimensions, the Sphere is displeased and rebukes him that such things, being unimaginable, are impossible. Upon his return to the flatness of his own realm, A Square finds himself disbelieved in his doctrine of a Third Dimension by his peers, and he attempts to teach it to his wife and grandson with bitter result.
In his book THE INCREDIBLE UMBRELLA by Marvin Kaye, one of the multiple worlds visited by the protagonist is Abbott’s Flatland – and Sherlock Holmes (from yet another world) disguises himself as a line segment there. Robert Heinlein also makes a passing reference to Flatland in the scene in STRANGER IN A STRANGE LAND where Mike the Martian throws a solid object into nonexistence. Other sequels or homages include SPACELAND by Rudy Rucker; SPHERELAND by Dionys Burger; FLATTERLAND by Ian Stewart.
Yours truly made extensive use of the metaphor of Flatland in my own CHRONICLES OF CHAOS trilogy, in the attempts of my heroine to explain the Fourth Dimension and higher.
To give you something of the flavor of this tale, allow me to quote the opening:
I CALL our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.
Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows – only hard and with luminous edges – and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said “my universe”: but now my mind has been opened to higher views of things.
And perhaps the dedication will also show something of the author’s humor and point:
To
The Inhabitants of SPACE IN GENERAL
And H. C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE Dimensions
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE OR EVEN SIX Dimensions
Thereby contributing
To the Enlargement of THE IMAGINATION
And the possible Development
Of that most rare and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
The book is published before 1924, and so in the United States is in the public domain. Thanks to the miracle of modern electronic technology, you may read it now and free of cost, except for the expense of an hour, which, I promise, the reading will amply reward:
http://www.geom.uiuc.edu/~banchoff/Flatland/
About John C Wright
John C. Wright is a practicing philosopher, a retired attorney, newspaperman, and newspaper editor, and a published author of science fiction. Once a Houyhnhnm, he was expelled from the august ranks of purely rational beings when he fell in love; but retains an honorary title.
