Flatland: A Romance of Many Dimensions

§ 18. How I came to Spaceland and what I saw there. After a darkness and a sickening sight that is not like seeing, the Square beholds the surface of the Sphere and worships him. He sees his house from above, with his Wife roving the Hall and the Page at his cabinet, then his city and the mines, and claims to be like a god. The Sphere rebukes him, and while declining to rank the faculties himself, reports that many of the wisest in Spaceland prize the despised Straight Lines above the Circles. In the Assembly Hall, in the first hour of the year 2000, the Council renews its millennial resolution against revelations, and the Sphere appears in its midst and escapes six policemen. The President, who knows from secret archives of the earlier visits, silences every witness. It closes on the brother’s sentence to perpetual imprisonment.

§ 19. How, though the Sphere showed me other mysteries of Spaceland, I still desired more; and what came of it. The Sphere builds a Cube from square cards and lets the Square feel it, and the Sphere himself, and the Square calls this the Paradise of his history, before the Fall. He asks to see the Sphere’s interior and to be taken into a land of Four Dimensions, and the Sphere denies that any such land exists. The Square then argues for it, in a passage partly added for the second edition, and by Analogy deduces a figure of sixteen points bounded by eight cubes. When pressed, the Sphere admits only that apparitions in closed rooms are reported and usually put down to the seer’s brain, but the Square soars on towards an Eighth Dimension until a crash returns him to his Study as his Wife approaches.

§ 20. How the Sphere encouraged me in a Vision. The Square tells his Wife that he fell through the cellar trap-door, and she sends him to rest. Repeating the formula “Upward, yet not Northward” like a charm, he falls asleep and dreams that the reconciled Sphere shows him Pointland, the Abyss of No Dimensions. Its King is a single Point that thinks itself the All and takes the Square’s furious harangue as one more happy thought of its own. The Sphere draws the moral that to aspire is better than to be blindly content, owns that his anger at his pupil’s ambition was a mistake, and teaches him to build Extra-Solids. Both the confession and the lesson come only in a dream.

§ 21. How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success. The Square wakes resolved to evangelise all Flatland, Women and Soldiers included, but a herald is crying the Council’s resolution in the street. He decides to proceed by demonstration rather than revelation, finds the clue less obvious than it had seemed, fears that his Sons might hand him over to the Prefect, and puts off his Wife with an untrue account. He locks himself in with the Grandson whose remark about three cubed the Sphere had approved. At the herald’s second cry the boy weeps and disowns his question, and when the Square waves a moveable Square about to show it rising, he laughs and runs out. So ends the first attempt to make a disciple.

§ 22. How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result. The Square writes Through Flatland to Thoughtland, hampered by a world in which every diagram is a line, neglects his clients, and about eleven months after his return fails to see a Cube with his eye closed. Indiscretions follow, until at the Local Speculative Society he tells everything and is arrested. Before the Council he cannot answer the President’s two questions, and he is sentenced to perpetual imprisonment, while the officials who heard him are, he infers, to die. Seven years later he writes in prison, visited weekly by a brother who saw the Sphere and does not believe in it, and the book ends on a hope of rebels to come and a fear that all of it was a dream.