Flatland: A Romance of Many Dimensions

Critical Reception

On First Publication

Flatland appeared in the last days of October 1884, and the notices came quickly and were mostly kind. The Academy, the London weekly of literature and learning, found it “very cleverly worked out, with many happy satiric touches” and promised readers something “much more entertaining than this account of it will lead the reader to suppose”. The Literary World of London was warmer still, calling the book “a magnificent protest against self-sufficiency and dogmatism”, though the geometry was set out so formally that the reader felt he was “going through an educational course rather than reading a story”. The Architect, a trade weekly, was among the first to distrust the narrator, and did so on the subject of women, observing that “Mr. Square is not so impartial as he professes to be”. It went on to praise a book “written in good English instead of debased German”.

The Athenaeum, the leading literary weekly, was puzzled. Its reviewer, whom William Lindgren and Thomas Banchoff, the editors of the Cambridge edition, identify as Arthur J. Butler, a scholar of Dante, began by saying that the book “seems to have a purpose, but what that may be it is hard to discover”. It read in turn like a primer of geometry, a defence of the higher mathematics, a tract for spiritualism and a covert satire on social theories. His real objection was mathematical. If the Square and his relations could see each other edgewise, “they must have had some thickness”, and so need not have been distressed by a third dimension. Abbott replied in the Square’s own voice, and what came of the exchange is told under Things You May Not Know.

The scientific weeklies took the book as a mathematician’s game. Robert Tucker, mathematical master at University College School and Honorary Secretary of the London Mathematical Society, reviewed it for Nature and praised its ingenuity, and, like The Architect before him, he separated the author from his narrator on the question of women. The Square’s account of them, he wrote, was “an ex parte description by a Square”, meaning one side’s evidence only, and he would be glad “if some female will favour us with her view” of Flatland. He also caught a slip in the note to § 15, which the second edition corrected. The astronomer Richard Proctor’s weekly Knowledge called the book a jeu d’esprit, a playful trifle, by “a follower of Lobatschewsky and Riemann”, the founders of the new geometries.

The Spectator gave it one of the longest and most balanced of the London reviews. “The assumption of the author is worked out with wonderful consistency,” it judged, and his mathematics were sound, though marred by two or three slips of terminology. Its chief complaint was “a want of proportion”, above all in the heavy dissertation on sight recognition in § 6, and it recommended the book “to any mathematician fond of paradox”, allowing that others might read it as satire or as pure nonsense.

The American edition of 1885 met a harder press. The New York Times opened with “This is a delirious book.” It called the work “a very puzzling book and a very distressing one”, and granted only that “Some little sense is apparent in an appeal for a better education for women”.

Science was kinder, crediting Abbott with a new idea, “to make the conceptions of transcendental geometry the basis for an amusing story”. A later notice in the same journal read the book chiefly as a satire on the social theories of the day, while the Boston Literary World foresaw the spiritualist reading and headed it off. “Our friends, the Spiritists, will be sure to hail it as a strong argument,” it wrote, when in truth the book “annihilates the third dimension, instead of adding to it”.

Others were less sure. The Critic of New York found that “For the non-mathematical reader the satire is too nebulous to be effective”, and Lippincott’s Magazine granted that “There is undeniable wit in Flatland, but it is a mathematical fantasy”. The first response from a fellow worker came from Charles Hinton. In “A Plane World” he acknowledged “that ingenious work, ‘Flatland’”, but set it aside as a model, since Abbott had used his plane “as a setting wherein to place his satire and his lessons”. That distinction, between the plane as a stage for satire and the plane as a physical world to be worked out, has divided the book’s readers ever since.

Since

For a generation the book was half forgotten. It was revived by the physicist William Garnett, who wrote to Nature in February 1920, after the eclipse expedition of 1919 had confirmed Einstein’s theory, and recalled the Sphere passing through the plane. The Flatlanders, he argued, “will attribute to growth in time” what an observer outside their plane would see as motion in a third dimension, and the flow of time may likewise be motion through a fourth. The reading took hold. His introduction to Basil Blackwell’s reissue of 1926 judged that the book had not at first received the attention it deserved, and that Abbott’s sphere pointed “the way to the clearest imagery of the fourth dimension”. Not everyone was persuaded that Abbott had been a prophet of relativity. Reviewing the reissue in the Saturday Review of Literature, the publisher Frank Morley held that the book “is in the kingdom of literature, and not in the kingdom of science”.