Flatland: A Romance of Many Dimensions

Schools were Abbott’s own trade, and Flatland is full of them. The Elementary Education Act of 1870 had set up elected School Boards to fill the gaps in the schooling of the poor. Flatland has its Elementary and Infant Schools, its Board of Education and its partisans of “the cheap system” (§ 5), and above them the University of Wentbridge, which has Cambridge’s degrees, examinations and punishments under the name of another river. Abbott’s own footnote to § 4 points to a country rector who required the teacher of the village Board School to come to his house by the back way, and so ties the treatment of Flatland’s Women to the manners of an English parish.

Taste has its turn too. The age of colour in § 8 was written for a public that had seen the chemist William Perkin’s mauve, the first synthetic dye on the market, become a fashion in the late 1850s. It had also laughed at the aesthetes in the comic opera Patience (1881).

The Church is the satire’s last and gravest target. Flatland’s Circles are its priests and also its rulers, the directors of its trade, its science and its morals, and the narrator speaks of them with a reverence that does not quite conceal what they do. A Broad Churchman who distrusted priestly claims to govern thought could hardly have drawn a sharper picture.

The other conversation concerned space itself, and by 1884 its fourth dimension led two lives, one in mathematics and one in the séance room. In mathematics it was respectable, for the German mathematician Bernhard Riemann’s lecture of 1854, published in 1868 and translated in Nature in 1873, had made the number of dimensions of space a question of fact rather than of logic. The physicist Hermann von Helmholtz, in a lecture of 1870 later printed in English in Mind, asked his hearers to imagine reasoning beings of two dimensions living on a surface. The mathematician Arthur Cayley, addressing the British Association in 1883, spoke of beings in a line or a plane to whom one more dimension would be unthinkable.

In the séance room the fourth dimension was notorious. In 1878 the Leipzig scientist J. C. F. Zöllner explained knots that had appeared in a sealed cord at his sittings with the American medium Henry Slade, in December 1877, as the work of beings who could move through a fourth dimension. Slade had been convicted in London under the Vagrant Act in 1876, though the conviction was quashed on appeal, and Zöllner’s book came out in English in 1880. Between the two camps stood the English writer Charles Howard Hinton, whose essay of 1880, What is the Fourth Dimension?, was reissued in 1884 under the subtitle Ghosts Explained.

None of these writers can be shown to be Abbott’s source, though he had certainly read Hinton by 1886, and an educated reader of 1884 could have known them all. What Abbott added is plain. Helmholtz’s beings had no history, no laws and no church; Abbott gave the plane a constitution, a class system and a priesthood, and so turned a thought-experiment into a mirror held up to his readers. The mathematicians had asked whether a flat creature could conceive of a third dimension, and Abbott asked as well what such a creature would think of its neighbours, its wife and its priests, and left his readers to put the same questions to themselves.

What to Look For

The narrator. The Square is the book’s instrument and also its first target. He is a professional man, a lawyer by trade (§ 7) and a geometer by taste, proud of his right angles, deferential to those above him and complacent about those below. He reports the cruelties of his country in the level voice of a historian, and much of the satire works through that voice. When he admires “this Law of Compensation”, which disarms the poor as they grow cleverer (§ 3), or offers the killing of irregular children as a moderate middle way (§ 7), the reader is meant to hear what he does not. Watch the distance between what he reports and what he approves.

Women. The pages on Women in § 4 and § 12 are the hardest in the book, and they have divided its readers from the first reviews to the present day. Look closely at how the narrator argues. Almost every claim he makes about women’s nature describes, on a second reading, the effects of law, custom and schooling, which he then calls a decree of Nature, as in the saying “Once a Woman, always a Woman” (§ 4). How far the satire reaches, and against whom, is for each reader to judge; the Afterword sets out the critics’ views, and the account of Abbott’s life above records his own work for the education of women.