Flatland: A Romance of Many Dimensions

Seeing and inferring. Flatlanders see nothing but straight lines, and they know one another by the voice, by touch and by the faint shading of a line in fog, so that nearly all their knowledge of one another is inference. The book keeps returning to the difference between what is seen and what is only inferred. The reader, who sees Abbott’s figures from above in the drawings, enjoys a view that no Flatlander has ever had, and the narrator keeps reminding his readers of their advantage. Ask now and then whether your own view is as partial as theirs.

Analogy. The book’s method is announced in § 1, when the reader is asked to put a penny on a table and lower an eye to the table’s edge until the coin becomes a line. That small experiment carries the reader down into the plane, and the Dedication hopes that the same reasoning will carry him higher, from three dimensions to four and beyond. Reasoning from a lower world to a higher one is the hinge of the whole romance, and the reader should notice where such reasoning persuades and where it meets resistance.

Shape as destiny. Flatland’s rulers hold that a figure’s shape decides its worth, its conduct and its fate, and nearly every institution of Part I follows from that belief, from the certification of children to the surgery of the State physicians and the laws against the Irregular. The doctrine is comic, and it is also chilling, because its Victorian originals in the sciences of heredity and the skull lie so close beneath the surface. Ask, as the narrator rarely does, who gains from it.

Mysteries and shadows. The Dedication speaks of initiation, mysteries and secrets, a vocabulary that does not stay on the first page, and a reader who knows Plato will notice, too, that the narrator’s countrymen live “very much like shadows” (§ 1). They take their plane for the whole of reality, like the prisoners in the Republic who see only the shadows on the wall of their cave (VII, 514a–517a). Abbott was a Senior Classic as well as a clergyman, and his religious and Platonic language is never idle. The notes mark it where it occurs.

Comedy. The book is funny, and its humour is a schoolmaster’s. It gives exact figures for absurd things and solemn laws for small dangers, and its footnotes correct the reader with mock patience. A treatise that bans square and triangular houses because their corners might hurt an absent-minded traveller (§ 2) is teaching its reader, with a straight face, to look at the reasons a society gives for its rules.

The two virtues. The Dedication supplied the measure by which every figure in the book can be judged, the narrator and his readers included, and it is worth keeping in mind from the first page to the last. Imagination asks whether a mind can reach beyond what it has seen, and modesty asks whether it can admit that what it has seen is not everything. Put both questions to each figure who appears, and then to yourself. The book is built so that you cannot escape them.