Flatland: A Romance of Many Dimensions

Colour. Colour is the book’s image of the life of the senses and the Circles’ enemy, and the age of Chromatistes, when “living implied seeing” (§ 8), gave Flatland its finest poetry and the Square, for once, a subject he writes of with longing. But colour also lies, for it lets a low Isosceles pass for a Dodecagon and ruin a girl, and it lets the lower classes do without the long training in sight on which the rule of the Circles depends. Its abolition is the victory of a class that governs by reasoning over a people who had begun to see for themselves, and its secret now passes from one Chief Circle to the next on his death-bed. In § 19 colour returns as the sensation for which a Spacelander might mistake a fourth dimension, just as Flatlanders take their own unrecognised height for mere brightness, so that in this book any sensation may be a dimension in disguise.

The Circle. The Circle is Flatland’s idea of perfection, and a courtesy. The priests are polygons who boast of having no sides but a single perimeter, the Chief Circle is assumed by courtesy to have ten thousand sides, and the infants of the highest classes are fractured to make them rounder. The first true circle in the book is the Stranger, in whom the Wife and then the Square, feeling him, find no trace of an angle. He is “a more perfect Circle than any in Flatland” (§ 15) because he is not a Circle at all, but the passing section of a body the plane cannot contain. Perfection is real. But it belongs to a higher order, and below it appears only in slices that grow, shrink and vanish.

The Point. The Point stands at both ends of the book’s mathematics. Every generation of figures begins from it, since a moving point makes a line in the Grandson’s lesson and again in the Sphere’s. Every descent ends in it, as the Sphere dwindles to a point when he rises out of the plane, and a Woman shrinks to one when she turns end-on. Pointland makes it a world. Its King is everything he can conceive and nothing else, and he takes all speech for his own thought. The Point is thus both the origin of every figure and the image of a mind with no room for another, which is why the Sphere can call it a God and pity it in the same breath.

The Cube. The Cube is the book’s emblem of knowledge that has been seen and cannot be held. In the story it first appears as the Grandson’s unnamed “Something else” (§ 15), receives its name by Analogy in § 16, is built and felt in § 19, and fathers the Extra-Solids of the dream. The Square calls himself its Progenitor, since a Square moving upward would generate it, so that the highest thing he has touched is also his own offspring. By the end it is “the once-seen, oft-regretted Cube” (§ 22), whose exact shape he cannot swear to; he can count its faces and corners, but he cannot be sure that he sees it truly.

Prison. Walls run through the book, and its last image is “this hard wall that bars me from my freedom” (§ 22). The wall is literal, but by then the reader has learned to see every dimension as a confinement, with prisoners who do not know that they are inside. The Preface draws the moral itself when it observes that Spacelanders would lock up a Cube for preaching the Fourth Dimension as readily as Flatlanders lock up a Square for preaching the Third. No world is exempt.

Dreams. The book’s one waking revelation is framed by two dreams, for Lineland comes in sleep and so does Pointland, and between them, the Square insists, “From dreams I proceed to facts” (§ 15). Yet the facts behave like dreams. He follows the Sphere through Spaceland as if in a dream, the clue that seemed plain when he woke is fading before the morning is out, and the Sphere reports that most people put apparitions down to the seer’s brain. By the last paragraph the waking world itself, wall and tablets and all, may be no more than a dream, and Abbott leaves the frontier between vision and fact unguarded on purpose. The reader can no more prove that the Square saw Spaceland than the Council could, and must decide, as the brother did, what to make of a witness.

The Metaphysical Layer

What follows is this edition’s reflection, offered to readers who come to Flatland from Plato and from Scripture, and since Abbott names neither Plato nor Aristotle anywhere in the book, each parallel is weighed as it comes. His own reading, that of a Broad Church clergyman who had come to doubt the Gospel miracles, survives in two later books, and it is given below in his own words.