The sphere speaks to A Square as a disembodied voice while not within the plane of Flatland. The sphere plunges his three-dimensional body through the plane of Flatland, resulting in the appearance of a point that grows into a circle and then shrinks away again into a point before disappearing. The individual he encounters is a sphere, who proves his existence to A Square by a variety of means. After this mind-expanding dream, he receives a visitation from an inhabitant of a higher, three-dimensional realm-Spaceland or Space.
A Square then describes his own experiences, beginning with a dream he had of a lower, one-dimensional realm known as Lineland. In the course of his account, many ideas, mores, and customs of Victorian England are satirized (in particular, attitudes regarding women, the upper class, and the lower class). All its inhabitants are figures that could be drawn on a two-dimensional surface-line segments, triangles, squares, circles, et cetera.įor the benefit of the three-dimensional reader, the narrator explains the nature of life in Flatland and Flatland’s history. He introduces us to Flatland, a world with width and length but no height (technically, with an imperceptible amount of height).
More recently, string theory has proposed the existence in our universe of a number of physical dimensions, but these are thought to operate primarily on the subatomic level, leaving us to consciously experience only the conventional three.)Ībbott’s novel is an autobiographical tale told by the character A Square, whose is named after his geometrical shape. (After Abbott, Einsteinian physics proposed time as a dimension paralleling height, width, and length, but we experience it in a different manner than the other three, and so it may be classified as a temporal rather than a physical dimension. This keeps the main story within the realm of the comprehendible (our minds being structured to work comfortably with a maximum of three physical dimensions) while allowing the reader to wonder about possible encounters with higher-dimensional beings. In particular, it is intended to help him imagine the relationship between our own universe-which we experience in the three physical dimensions of height, width, and length-and realms with more physical dimensions.Ībbott induces his readers to think about the possibilities of interacting with higher physical dimensions through his story of an encounter between a two-dimensional being and a three-dimensional being. It is a mathematical allegory that is still in print and also widely available on the Internet.įlatland is an imaginative exercise to help the reader explore the idea of multi-dimensional geometries. Though Abbott was a scholar of several disciplines-including mathematics, theology, and Shakespeare- Flatland is his most popular work. Abbott (1838–1926) produced a short book titled Flatland: A Romance of Many Dimensions.
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