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 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.
In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines.
It's an ingenious set-up: a first-person account of a two-dimensional world. Flatland (1884), by Edwin A Abbott (1838-1926), is a slim, fascinating little fable: part social satire, part musing on the limitations of human perception, and all inventiveness.
The book is couched as a description of the ways of Flatland, for the benefit of an audience in another world, glimpsed briefly and with the force of revelation by our narrator: Spaceland, where three dimensional shapes are the norm (i.e., our own world). The narrator is a Square, which - in a society where an individual's status rises with the number of their sides - makes him (self-consciously... it is a Victorian novel, after all) lower middle class. Herein lies one of the book's pleasant surprises: for the lead figure in an allegorical tale, whose role it is to channel the themes, our Square is an unusually complex and interesting character.
Much of the time, he presents a conservative, rather priggish image of himself - as when he explains, for example, the hierarchical structure of his society in terms of the essential qualities of its inhabitants. One's disposition depends upon, and can be readily predicted by, the acuteness of the angles one presents to the world: thus, for example, triangles are reckless and violent (all the more so if they are of the isosceles variety...), and are fit only to be soldiers or the lowest of labourers.
By extension, he is firmly convinced that the number-of-sides hierarchy is fundamentally a Good Thing, although he does condemn the hazardous, rather cruel ways that ambitious upper-class parents seek to improve their children's standing - by fracturing their young sides repeatedly to increase said sides' number. (As if hothousing them at some horrific boarding school wasn't bad enough...)
Nonetheless, he considers efforts to offset/undermine the hierarchy, by the introduction of colour into Flatland, to be "diabolical", since "the road would then lie open for a total destruction of all Aristocratic Legislature and for the subversion of our Privileged Classes". People whose sides are of irregular lengths, moreover, are a threat to the fabric of everything, because - the horror - one cannot easily judge who they are and where they fit into the hierarchy simply by examining their angles:
[I]t does not need much reflection to see that the whole of the social life in Flatland rests upon the fundamental fact that Nature wills all Figures to have their sides equal. [...] if no one could calculate the Regularity of a single figure in the company, all would be chaos and confusion, and the slightest panic would cause serious injuries, or - if there happened to be any Women or Soldiers present - perhaps considerable loss of life.
He considers irregularity to be a condition (analogous to physical or mental disability, or perhaps more broadly to simple non-conformity) that must be remedied by "the art of healing" with "compressions, extensions, trepannings, colligations, and other surgical or diaetetic operations"; or, if absolutely necessary (!), euthanasia.
The reference to women's violence in the passage above stems from the fact that women, in Flatland, are not shapes but straight lines, and thus the pointiest of all:
If our highly pointed Triangles of the Soldier class are formidable, it may be readily inferred that far more formidable are our Women. For, if a Soldier is a wedge, a Woman is a needle; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a Female, in Flatland, is a creature by no means to be trifled with.
It is the familiar rhetoric of misogyny: women, by their very nature, are dangerous to men (not to mention devious); since it is their nature they cannot be trusted to do any better, and must be confined to special quarters and follow certain social rituals to minimise the harm they might cause to men. If there is a social hierarchy, women are always at the bottom of it. He is splendidly deadpan about the more extreme consequences of the arrangement:
On the whole we got on pretty smoothly in our domestic relations, except in the lower strata of the Military Classes. There the want of tact and discretion on the part of the husbands produces at times indescribable disasters. [...] The result is massacre; not, however, without its advantages, as it eliminates the more brutal and troublesome of the Isosceles; and by many of our Circles the destructiveness of the Thinner Sex is regarded as one among many providential arrangements for suppressing redundant population, and nipping Revolution in the bud.
(I especially like the combination of the dry, detached tone with near-hysterical words like "massacre" and "Revolution", here, and "the Thinner Sex" also made me chuckle; in places, Flatland is very funny indeed.)
But women are one topic on which our Square clearly entertains doubts about the wisdom and justice of the status quo; he anticipates, and agrees with, his audience's belief that the condition of women in Flatland is "truly deplorable". But what he deplores must surely have carried a ring of familiarity for the book's Victorian readers (as indeed it still does today):
About three hundred years ago, it was decreed by the Chief Circle that, since women are deficient in Reason but abundant in Emotion, they ought no longer to be treated as rational, nor receive any mental education. The consequence was that they were no longer taught to read, nor even to master Arithmetic enough to enable them to count the angles of their husband or children; and hence they sensibly declined during each generation in intellectual power. And this system of female non-education or quietism still prevails.
He goes on to note how many of the assumptions about differences between men and women are essentially in the eye of the beholder, and that ideas and actions which are considered irrational and silly in women become perfectly correct and admirable when they are done or felt by men ("'Love' then becomes 'the anticipation of benefits'; 'duty' becomes 'necessity' or 'fitness'; and other words are correspondingly transmuted.") He also notes how the language of chivalry - special regard for, and protection of, women - hides contempt:
Moreover, among Women, we use language implying the utmost deference for their Sex; and they fully believe that the Chief Circle Himself is not more devoutly adored by us than they are: but behind their backs they are both regarded and spoken of - by all but the very young - as being little better than 'mindless organisms'.
This particular passage ends with a restrained but heartfelt plea for the education of women that seems very clearly aimed as much at Spaceland as it is at Flatland.
Whether or not he always had such doubts about the inherent rightness of his world, as he narrates this account Square has undergone something like a religious conversion or a conceptual breakthrough. Towards the end of the book, the Square describes how he was, for a brief time, exposed to the world of three-dimensionality. He recounts his encounter with a Sphere, who urges him to "proclaim the Gospel of Three Dimensions to your blind benighted countrymen in Flatland" - something that lands him in prison, assumed to be insane, once he is back home.
But while Square is awestruck at the sight of solid shapes in Spaceland, he is inevitably led to wonder whether there are not further dimensions beyond the ordinary perception and comprehension of Spaceland, just as Spaceland is beyond his own; the Sphere, predictably, scoffs at the very notion:
I. And even as we, who are now in Space, look down on Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me - O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend - some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed.
Sphere. Pooh! Stuff! Enough of this trifling!
Abbott - a theologian, philosopher, and mathematician - was undoubtedly interested in the realms of imagination and thought that lie beyond our experience, and the ways in which such realms might call into question the things in our social order that we take for granted as 'natural' and 'correct'. For all the fun of the scenario, this is a book that punches above its weight; nineteenth-century postmodernism, anyone?
Still, the end result for our visionary Square is not a cheerful one; whether or not he is ultimately correct, being right in a cosmic sense isn't necessarily much help when faced with the daily realities of social expectations, which don't take kindly to either reformers or holy fools:
It is part of the martyrdom which I endure for the cause of Truth that there are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarce-possible existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream.