Flatland: A Romance of Many Dimensions

Regular In geometry, having all sides and angles equal; in § 3 an official status as well. An Equilateral child born of Isosceles parents is examined by the Sanitary and Social Board and, “if certified as Regular”, is admitted with ceremony into the class of Equilaterals and taken from his parents. The capital marks a rank and not merely a shape.

Sight Recognition The art of telling another figure’s shape by sight, practised only among the higher classes and in the more temperate regions (§ 6). Because Fog dims the farther parts of a line, a trained eye can read the shading of what it sees and infer the angles behind it, and the art is taught, at length and at great cost, at the University of Wentbridge. Only the rich can afford to master it.

Spaceland The narrator’s name for the readers’ world of three dimensions, the Space in which they are “privileged to live” (§ 1), formed like Flatland, a name he gives his own country only to make its nature clear to his readers. From its first use in the story, also in § 1, he speaks of Spaceland as a place where he has been.

Straight Line In § 1 the simplest figure of Flatland, and also the only thing a Flatlander ever sees, since every figure viewed edgewise from within the plane looks like one. In § 3 a paragraph of one sentence gives the term its social sense, “Our Women are Straight Lines.” Thereafter the capitalised plural can stand for Women as a class.

Third Dimension The Dedication’s writer says that he was initiated into the mysteries of three dimensions after knowing only two. In the story the readers’ own world is called “the happy region of Three Dimensions” (§ 5), where height is added to the length and breadth of the plane, and where an angle can be seen and not merely inferred.

Thoughtland A coinage that first appears in § 19, formed like Flatland, Lineland and Spaceland as the name of a world, for a region of thought rather than of matter (see the note there).

Universal Colour Bill The measure that gives § 9 its title, brought before “a general and extraordinary Assembly of all the States of Flatland”. It requires Women and Priests to be painted, red on the half that holds the eye and mouth and green on the other, so that in certain positions a Woman would look like a Priest. It is the furthest point of the demand that all classes be treated as equal.

“Upward, not Northward” Flatland’s slight pull to the South makes North the nearest thing it has to up (§ 2), so when the narrator is asked in § 16 to imagine a Square moving upward, he supposes that Northward is meant. The answer draws the distinction, “No, not Northward; upward; out of Flatland altogether.” Motion Northward slides within the plane, while motion upward leaves it, and later sections shorten the distinction into this phrase.

Characters

The figures of the book are given here as the reader first meets them, grouped by their part in it, with the section in which each first appears. Nothing is said of what becomes of any of them.

Voices at the threshold. H. C. is the friend to whom, “in Particular”, the Dedication is addressed; he is generally identified as Howard Candler, a mathematics master and Abbott’s friend from their schooldays (see the note there). The Editor is the voice of the Preface, a Spacelander who answers the reviewers of the first edition on the narrator’s behalf, and A Square himself, the narrator, names himself on the title page and speaks from § 1 onward.

The narrator. The Square, of the professional class (§ 3), is a Lawyer by trade (§ 7) and an amateur geometer, “a Mathematician of no mean standing” (§ 6), who writes of his country with a historian’s care and a loyal citizen’s pride. His house, like almost every house in his country, is pentagonal (§ 2). His Father, a Triangle, appears in § 6.

The household. His Sons, first mentioned in § 6, are Pentagons, as the law of § 3 requires, and § 15 shows that there are four of them. His two Grandsons are Hexagons (§ 6), and the younger, “a most promising young Hexagon”, is described in § 15. His Wife first appears there too.

Rulers and inventors of the past. The Chief Circle is the head of the Priests, named in § 3 as the ruler who keeps a small force of Isosceles “in pay for emergencies”. The title passes from holder to holder. Chromatistes is the legendary discoverer of colour, “a Pentagon whose name is variously reported” (§ 8), and Pantocyclus appears in § 10 as “the Chief Circle of those days”.

Monarchs and visitors. The King of Lineland is the monarch of a world of one dimension, met in § 13, and the Stranger from Spaceland gives § 15 its title; from § 17 onward the headings call him the Sphere.

Places

Flatland. The narrator’s country is a vast plane with the four points of the compass and a slight but constant pull towards the South. Rain falls from the North at stated times, and light comes equally from everywhere, by day and by night, so that nothing casts a shadow and the houses need no windows (§ 1–§ 2). By law and custom nearly all of them are five-sided, with the roof on the North, a large door on the West for the Men and “a small door for the Women” on the East (§ 2). Square and triangular houses are not allowed.