Flatland: A Romance of Many Dimensions

Plato’s Republic. The Republic stands behind Part I as well as Part II. Its myth of the metals (III, 414b–415d), in which rulers teach that the god mixed gold into some citizens and iron into others, is the classical type of every order that calls its classes natural. Two borrowings are probable. The double language of Flatland’s Circles is that myth, Plato’s noble lie, made into a system, and the Colour Revolt carries into politics the tenth book’s quarrel between measurement and the illusions of colour and painting (602c–603a). But the Square mourns the age of colour as Plato never would. The book’s sympathy is not wholly with the guardians.

Hinton and the scientific romance. The closest contemporary is Charles Howard Hinton. His essay “What is the Fourth Dimension?”, first printed in 1880 and reissued in 1884 among his Scientific Romances, already has a being confined to a line and a plane being lifted out of a closed square. It even shows a sphere of four dimensions as a solid that grows and shrinks. Who influenced whom is unsettled. Hinton nodded to Abbott’s book in an essay on a plane world of his own (1886), and went on to build the physics that Abbott had left aside, at greatest length in An Episode of Flatland (1907). Abbott, for his part, praised Hinton’s work in 1886 as very able and original. From these two the line runs to the computer scientist A. K. Dewdney’s The Planiverse (1984), which designs a two-dimensional world that would actually work, and to the sequels by other hands.

The sequels. The Dutch physics teacher Dionys Burger’s Sphereland (Dutch 1957, English 1965) is narrated by the Square’s grandson, a Hexagon, who carries the analogy into curved space and an expanding universe. The mathematician Ian Stewart’s Flatterland (2001) sends the Square’s great-great-granddaughter, Vikki Line, through fractals and modern physics, and the mathematician Rudy Rucker’s novel Spaceland (2002) brings a visitor from the fourth dimension to a man in Silicon Valley.

Abbott’s own books. The Introduction sets Flatland beside Abbott’s two anonymous memoirs of disciples, Philochristus and Onesimus, and the ending sharpens the likeness into irony, for the Square’s memoir is that of an apostle who made no disciple at all. Abbott’s Through Nature to Christ (1877) is subtitled the Ascent of Worship through Illusion to the Truth, which is the Square’s story told in the language of a sermon. The title of the Square’s treatise in § 22 is cut to its pattern. His Philomythus (1891), an attack on Newman’s defence of the miracles of the Church, shows the same cool mind that lets the Sphere answer reports of apparitions with a shrug.

Film and television. A short animated Flatland was made at Harvard in 1965, directed by Eric Martin from an idea by John Hubley, with voices from the company of the revue Beyond the Fringe. The astronomer Carl Sagan played out its central demonstration in the tenth episode of Cosmos (1980), to show how a higher dimension would look from inside.

Later films. Two films appeared in 2007. Ladd Ehlinger’s feature makes the Sphere the head of a corporation called Messiah, Inc. The shorter animated film by Dano Johnson and Jeffrey Travis names the Square Arthur and gives him a granddaughter, Hex, and its sequel of 2012 follows Burger into Sphereland. That a modern film gives the Square a granddaughter where Abbott gave him only grandsons is a small answer, after more than a century, to the reviewer who asked for a female view of Flatland. It came late, but it came.

The Dedication again. The last relation is to the book’s own first page. The Dedication bowed to the inhabitants of Space, the superior races of solid humanity, and wished them two virtues, a larger imagination and the rare gift of modesty. A first-time reader takes the bow as a compliment. The reader who has finished the book knows better. The one being of solid humanity who ever spoke with the Square, the Sphere, answered his pupil’s question about a Fourth Dimension with indignation, “There is no such land.” Below them both lay the Monarch of Pointland, perfect self-satisfaction with no Dimension at all. The modesty the Dedication wishes its readers is exactly what the Sphere lacked, and the reader of three dimensions now stands where the Sphere stood, at the edge of his own world, with a smaller creature’s question in front of him. The Sphere had one good moment. Asked in § 18 whether omnividence, the power of seeing all things, belonged to others besides Gods, he said, “I do not know.” The book leaves its reader to keep that answer and to give up the other, and so to be the solid being who, faced with a question about a world beyond his own, does not reply that it cannot exist.