Flatland, A Romance of Many Dimensions
Square is a lawyer living in Flatland, a two-dimensional world that has height and width, but not length. In Edwin Abbott’s book Flatland, Square serves as our tour guide, describing both the physical and social characteristics of living in a world without depth. Flatland works on two levels: as an effective portrayal of an alien civilization living in two dimensions and as an elegant, subtle social commentary on our own society.
The number of angles and regularity of shape a Flatland inhabitant has determines their social status. Servant classes are isoceles triangles, the middle class are equilateral triangles, gentlemen are squares and pentagons, nobility are polygonals, and the priestly class are circles. Women are straight lines, and in a world where every angle a person has increases their intelligence, this makes women the lowliest of Flatland’s inhabitants.
Is this sexist? It’s hard to say. We are talking about alien beings here. Is it sexist for the male angler fish to become a parasitic attachment on the female of the species? The narrator acknowledges the deplorable state of existence for women in Flatland, but then he also acknowledges the deplorable state of existence for all of Flatland in comparison with the fantastic Spaceland.
In Square’s community triangular houses are forbidden because of their pointy angles, which are hazardous to Flatlanders, as are all sharp points. With their pointy single angle, the isoceles worker classmembers are dangerous to the blunt circles. Women are the most dangerous of all, having the sharpest point of all flatlanders.
Isoceles of less than 10 degrees are used for experimentation in schools, and Square defends this Flatlander eugenics policy toward the lowest classes. He applies double standards to different shapes in his law practice. An isoceles criminal cannot help being a criminal because of their irregularity. Therefore their irregularity must be punished and the isoceles executed for the betterment of society. However, when a polygonal commits a crime, and blames it on temorary irregularity, Square cannot bring himself “logically to reject, nor practically to accept, his conclusions (Abbot, 41).”
Square is a bigot. He believes irregular figures are naturally born burdens on society, rejecting the idea that societal expectations make their lives difficult. Square is anti-democracy, and rejects the idea of freewill, believing instead that people are born with certain proclivities for behaviors. Square believes in the class heirarchy because he was born into it and it is the natural state of things for him.
Square’s bigotry, anti-democratic beliefs, and chauvanism are made all the more infuriating by his intelligent and often logical defense of his opinions. Abbott’s narrator is not a dunce, he is a lawyer, and as such he aptly defends positions we know are wrong with our Spaceland view of things, but encounter difficulty refuting within the context of Flatland’s alien dynamics.
Square’s narrowmindedness and the narrowmindedness of his society reflect the narrow perspective of their world. When he meets the Sphere, who takes him to Spaceland, a reality with three dimensions.
Spoiler Warnings! Abandon Ye All Hope Who Read on From Here!
I kept looking for Edwin Abbot to give the reader some little knowing wink to show that he recognizes Square’s profound ignorance, something to show us that he disavows Square’s racist and anti-democratic stances, but there was none forethcoming. At least, nothing obvious.
Instead we are left to our own enlightened perspective on Flatland’s social ills. At one point, Square tells the story of the “Color Revolution,” a time in Flatland history when the inhabitants painted themselves different colors. The majority of Flatlanders identify the shapes of others by feeling them, but the upper classes are educated in the art of identifying shapes using sight (How they do this, Abott explains in detail). By painting themselves with identifying colors, sight-derived knowledge became available to all citizens.
This threatened the social heirarchy dominated by the Circles, who’s priesthood formerly held a monopoly on knowing the world by sight. It reminds the reader of how literacy stripped Church leaders of their power, as people could read and interpret the Bible for themselves.
In Flatland, as in our own world, the solution was for the political power to stir up infighting among members of the lower class. Circles play the isoceles against one another, instilling them to fight and cull their populations to prevent them from organizing to overthrow the higher classes with their dangerously sharp angles.
[Priests] “doing nothing themselves, they are the Causes of everything worth doing that is done by others,” Square tells us. There are too many obvious correlations to some of our own histories of the relationships between classes in our own world to think the Flatlanders’ ignorance irrelevant to our own experiences.
Square experiences an iconoclasm when a being known as the Sphere visits him. Sphere pulls Square out of Flatland and into Spaceland, from two dimensions to three. Sphere takes Square to see Lineland, a world consisting of two points, whose inhabitants rely entirely on their hearing to interact with their world and can only see the citizens immediately neighboring them. Square challenges the Linelanders, tries to broaden their horizons, but they dismiss him, unable to see what he sees.
Then Sphere takes Square to see the Point, living in Pointland. Sphere describes the miserable existence this being, a misery of which the Point is incapable of being aware:
Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.
When Square wonders what dimensions exists beyond Spaceland, Sphere laughs at the idea. How could there be dimensions beyond three?
What about different combinations of dimensions? Flatlanders experience a pull towards the South in their world because one of their two dimensions is oriented along a verticle axis (height), giving them a sense of direction. This implies their world exists within our own and is subject to our gravity (there are all sorts of logical problems with this (Does Flatland orbit the Sun with our Earth? How far into our sky does Flatland go?);yet, their world could just as easily only have length and width. How would that orient their world differently, but with the same number of dimensions?
From Spaceland, Square is able to look down at Flatland and see inside every house and the internal organs of every citizen. A human pulled into four dimensions would have the same viewpoint, seeing inside everything we don’t see in our three-dimensional space, impossible to imagine.
Square cannot communicate his experiences in Spaceland when he returns to Flatland, because he has returned to a reality that lacks the dimension of depth. His experience is one of personal revelation, and he has no means to prove what he has seen, which amounts to heresy, to a skeptical audience. The reader believes Square only because we are Spacelanders ourselves.
Flatland is an imperfect book, but its imperfections endear it to me over the attempts of many other authors to replicate and improve upon it. There are hard-SF problems with the dynamics of Flatland, such as the Flatlanders being able to see, even though their perspective, lacking a third dimension, would not even be a line. Despite his incredible experiences in Spaceland, Square remains unapologetically and profoundly ignorant in all respects that offend the reader.
It’s the exersize of picking apart these logical and moral issues that give make this book a classic. Solving these problems from our enlightened perspective here in Spaceland make reading the book a joy, and make us question our own reality and what dimensions might we be missing in it.
Imagining the Tenth Dimension (Check out the awesome flash demo at this site)