Flatland: A Romance of Many Dimensions

The rest is quickly told. The Square spends months writing a treatise, Through Flatland to Thoughtland, and about eleven months after his return tries to see a Cube with his eye closed, and fails. At last, at a meeting of the Local Speculative Society, he tells the whole story and is arrested, and when he cannot point out the direction he means or show a Cube, the President sentences him to perpetual imprisonment. Seven years later he is still in prison. His brother, who saw the Sphere, visits him every week and still does not believe in it. Without a single convert, the Square hopes that his book may stir up rebels in some Dimension, and in darker hours fears that all of it is “the baseless fabric of a dream”. The Preface adds that he is now old and forgetful, and that once a year the Chief Circle visits his cell to ask whether he is any better.

Themes

Dimension and the Limits of Perception

Every creature in the book takes its own world for the whole, from the Point of Pointland, which knows nothing beyond itself, to the King of Lineland, who, corrected on a word, snaps back that “Space is Length”. The Square, in his turn, assures his Grandson that “Geometry has only Two Dimensions” (§ 15), and the Sphere, pressed for a fourth, will not hear of it. What turns this ladder from a mathematical toy into a moral fable is that each rung repeats the same speech. Each sees the limit below, never his own.

Abbott is careful to make the limit itself innocent, for a Flatlander cannot see an angle, and the Square says so plainly, “though we cannot see angles, we can infer them” (§ 5). The whole art of Sight Recognition, taught at the University of Wentbridge and practised in the Fog, is a science of inference from dimness, a guessing at shapes that no Flatlander has ever beheld. In Spaceland, looking down into his own house, the Square learns “how poor and shadowy was the inferred conjecture” (§ 18) beside the thing seen, yet there is no fault in the inference, since a creature of two dimensions can only reason from appearances. The Square, a good reasoner, reasons well.

The fault lies in what the reasoner will allow. The Square’s first response to the Sphere is not curiosity but disbelief, and his attack on the visitor follows from the same refusal to entertain what he cannot see. In the second edition Abbott added a passage to § 19 that sharpens the point, for there the Square argues that when he saw a Line in Flatland he was already seeing a dimension he did not recognise. Now, in Spaceland, when he sees a Plane and infers a Solid, he must likewise be seeing an unrecognised fourth. The limit of sight is the same in every world. The limit set on belief is chosen.

The Preface sums up the Square’s later state in a single phrase, for having once understood height he says that now he “can but apprehend it by faith”, and that is where the book comes to rest. Perception fails at every border, and the honest response is to hold what cannot be seen as one holds a thing once shown and since lost, without saying either that it can never be or that it is already fully known. The two sayings that the Preface’s modest readers decline to utter cover the whole range of the book’s dogmatists, from the King who knows that Space is a line to the President who knows from his archives that nothing need be done. Both are forms of pride.

Hierarchy, Shape and Destiny

Flatland reads a citizen’s worth off his body, and the comedy of Part I lies in the calm with which the Square accepts the reading. Rank is the number of one’s sides, virtue is regularity, and Irregularity of figure means, he explains, what moral obliquity and crime mean in Spaceland (§ 7). From this premise everything follows with dreadful logic. A criminal of low angle becomes a Specimen, fettered in an infant school to teach the feel of angles (§ 5), and a student who fails his final examination may, some statesmen think, be imprisoned or put to death (§ 6). The chain ends in the Square’s own modest suggestion that an incurable Irregular infant be “painlessly and mercifully consumed” (§ 7), offered as a via media, or middle way, between harsher views. The voice is that of a reasonable reformer. That is the horror of it.

Pantocyclus, the victor of the Colour Revolt, turned the premise into a creed, teaching that “Configuration makes the man” (§ 12). If shape decides conduct there is nothing to praise or blame, and the example is drily exact, for why praise a lawyer’s honesty when one ought to admire the precision of his right angles? The Introduction has described the science of heredity and the politics of reform that the satire touches, but the satire needs neither as its key. Its target is older and larger. It is the habit of every ruling class of calling its own advantages Nature.