Flatland: A Romance of Many Dimensions

Afterword

The Story Told Straight

Part I is a treatise. The only story it tells is the story of a society. The Square, a lawyer by profession and a mathematician by taste, describes a world of plane figures who see one another only as lines and rank one another by their sides. Women are Straight Lines and soldiers are sharp Isosceles triangles, and above them the classes rise through Equilaterals, Squares and Pentagons to the noble Polygons and the priestly Circles, each regular son having one side more than his father. Irregular figures are treated as criminals, and the Women live under a Code that makes them sound a Peace-cry in public on pain of death.

History supplies the one drama. In remote ages a Pentagon called Chromatistes found out how to make colours, and soon all Flatland was painted except the Women and the Priests. A Universal Colour Bill, devised by an Irregular Circle, proposed to paint these too, so that a Woman might pass for a Priest. After three years of agitation a low Isosceles, painted as a Dodecagon, tricked a noble orphan into marriage, and when she killed herself the Women turned against the Bill. At an extraordinary Assembly the Chief Circle, Pantocyclus, feigned surrender, spoke for nearly a day and gave a signal, and at once Convicts transfixed Chromatistes, the Women charged the soldiers unseen, and the Isosceles killed one another to the last man. Colour was abolished. Part I closes on the Circles’ failing fertility and on the Square’s humble appeal to reconsider the denial of education to Women.

Part II keeps a calendar. On the last day but one of the year 1999 the Square dreams of Lineland, a single line whose King takes it for the whole of Space. The King decides that his one-voiced visitor must be a Woman, and when the Square steps out of the line to show him another direction, calls it magic. As the King advances to pierce him, the breakfast-bell wakes him.

That evening his youngest Grandson, a bright Hexagon, reasons that if three squared is a square, three cubed must be something else, and is sent to bed. Late at night, sitting up with his Wife to see the old Millennium out, the Square turns the half-hour glass for the last time and exclaims, “The boy is a fool.” A Voice contradicts him. A Figure appears that seems to change its size, and the Wife, feeling it, takes it for a perfect Circle and retires. When the Square next looks at the glass, the last sands have fallen.

The visitor is a Sphere, and he explains that Flatland can show only a slice of him, a Circle that grows and shrinks as he passes through the plane, but the Square will not believe him. Then the Sphere leads him by Analogy from point to line to square, and on to a figure with eight corners and six sides that he calls a Cube. The Square attacks him. The Sphere takes a tablet from a locked cupboard without opening it, touches the Square inside his stomach, and at last, as the Wife approaches, lifts him bodily out of Flatland.

From Space the Square looks down into his own house, then over his city and into the depths of the mines. He claims to have become like a god, and the Sphere asks whether such sight has made him any more just or more loving. In the first hour of the year 2000 they look down on the Council of Circles, which meets at every millennium to renew a resolution against anyone who claims revelations from another World; the Square’s brother, its Chief Clerk, reads it out. The Sphere drops into the Council and proclaims a land of Three Dimensions. Six policemen seize him, and he is gone. The President, unsurprised, cites secret archives recording a similar occurrence at the last two millennia, has the policemen gagged, and sentences the brother to perpetual imprisonment.

The Sphere then builds a Cube from square cards and lets the Square feel it, the climax of his history, but the Square asks to see the Sphere’s insides and then to be taken on into a land of Four Dimensions. The Sphere denies that any such land exists. The Square argues for it by the Sphere’s own Analogy, and when he soars on past a Fifth towards an Eighth, deaf to the Sphere’s commands of silence, a crash hurls him home. He wakes in his Study, “a common creeping Square”.

He tells his Wife that he fell through the cellar trap-door. In a dream that night the reconciled Sphere shows him Pointland, where a single Point sings of its own perfection and takes every insult as one more happy thought of its own, and on the way back the Sphere owns his error. Next morning a herald cries the Council’s resolution. The Square locks himself in with his Grandson, but at the herald’s second cry the boy bursts into tears, swears that his question was only fun, and runs off laughing.