Flatland: A Romance of Many Dimensions

§ 12. Of the Doctrine of our Priests. The Circles’ one maxim, “Attend to your Configuration”, makes conduct a matter of shape, so that praise and blame are idle; yet the Circles scold their own children, and the Square’s Grandson pleads his Configuration to win sweetmeats. Men are taught to honour their grandsons rather than their parents. The weak point of the system is the Women. Circles marry for a low voice or a little extra lustre and risk Irregular heirs, and three hundred years of keeping Women uneducated have forced men to live in two languages, one for the Women’s rooms and one for the books. Part I ends with the Square’s humble appeal to reconsider the rules on Female Education, made on the ground that the double life weakens the male mind.

Part II. Other Worlds

§ 13. How I had a Vision of Lineland. On the last day but one of the year 1999, the first day of the Long Vacation, the Square falls asleep over an unsolved problem and dreams of a world that is a single straight line. Its people, Lines for men and Points for women, can see only points and can never pass one another. Neighbours stay neighbours for life. The King, who takes his line for all Space, had heard the Square’s voice as if it came from his own insides. He explains that every man has two voices and two wives, whom he marries by song across great distances, and that each marriage yields one boy and two girls. The section ends on the long wooing of three voices.

§ 14. How I vainly tried to explain the nature of Flatland. The Square tries to teach the King that there is a second direction, and the King, who knows every shape by sound, will not have it. Words fail. So the Square tries deeds, stepping out of the line and counting the King’s neighbours from outside, and the King calls it a magic art of vanishing and takes his visitor for a Woman. Losing his temper, the Square calls himself the completion of the King’s incomplete self, a Line of Lines. The King advances to pierce him through the diagonal, his subjects raise a war-cry, and the Square wakes to the breakfast-bell, in a scene that rehearses, one dimension lower, everything he is about to suffer and to do.

§ 15. Concerning a Stranger from Spaceland. On the last evening of 1999, after a lesson in squaring numbers, the Square’s youngest Grandson reasons that three cubed must describe some figure beyond the Square, and is sent to bed. Sitting up with his Wife to see the Millennium out, the Square turns the half-hour glass for the last time and declares the boy a fool. A Presence chills the room, a Voice defends the boy, and a Figure appears that seems to change its size, which the Wife, who trusts touch over sight, feels and takes for a perfect Circle before she withdraws. The last sands fall. The new Millennium begins, under a numeral that the Textual Notes discuss.

§ 16. How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland. In a dry season and a room without Fog, the Square has to feel the Stranger, and finds him perfectly round. The Stranger says that he comes from Space, names a Third Dimension that lies up above and down below, and describes the household; in a passage added for the second edition he argues that a visible line must already have height. He is a Sphere. Flatland can show only his section, he explains, and he rises, vanishes and returns to prove it. Then he tries Analogy, leading the Square from the point to the line and the square, and so to a Cube of eight points and six sides. Enraged, the Square hurls himself at his visitor.

§ 17. How the Sphere, having in vain tried words, resorted to deeds. The Sphere slips out of the Square’s grip and out of the plane, laments that he has found no fit apostle for the Gospel of Three Dimensions, which he may preach only once in a thousand years, and turns to deeds. He takes a tablet of accounts from a cupboard the Square had locked half an hour before, describes a neighbour’s household and a theatre ten doors off, and touches the Square inside his stomach. The Square, persuaded only that he faces a magician, tries to pin him against the wall and shouts for help, and as the Wife approaches, the Sphere warns that no stranger may witness what has passed and carries him out of his Plane.