Flatland: A Romance of Many Dimensions, Edwin Abbott
Flatland: A Romance of Many Dimensions Edwin Abbott
(Full name Edwin A. Abbott; also published under the pseudonym A. Square) English novelist, essayist, and nonfiction writer.
The following entry presents criticism on Abbott's novel Flatland: A Romance of Many Dimensions (1884).
As a cleric, biblical and literary scholar, and author, Abbott established a place in Victorian literature and inspired many twentieth-century writers and thinkers to explore the scientific issues of space and time with his novel Flatland: A Romance of Many Dimensions (1884).
Plot and Major Characters
In Flatland, Abbott created a fictional world, called Flatland, of only two dimensions inhabited by two-dimensional beings. The narrator, A. Square, begins by introducing readers to his two-dimensional world, including its different types of life and its social order. A male's position in this social order is determined by angles and sides; the square narrator, a lawyer, is higher in the social hierarchy than triangles (who tend to be laborers, soldiers, and merchants) but lower than more complex regular figures. The highest figures in Flatland are those with so many sides and angles that they are close to being circles. Parents aspire to have children who possess more sides and angles than themselves. In addition, figures with irregular angles are considered outcasts and criminals. Females in Flatland possess no angles or complexity of form whatsoever; rather, they are simply line segments, representing, for Abbott, the second-class status of women in Victorian society. Women in Flatland are, however, powerful figures, since their sharp forms can puncture and deflate the males. Given this fact and their emotionally volatile natures, females in Flatland are governed by sets of rules that limit their full participation in society. The second part of the novel concerns the narrator's vision of a one-dimensional world called Lineland. More fantastic and less satiric than the first part of Flatland, this section describes what life might be like in such a world. This dream of Lineland is both highly imaginative and mathematically intriguing. The tables are turned on the narrator in the last third of the novel, in which the two-dimensional being encounters a being from Spaceland—in other words, a being from a three-dimensional world. The Spacelander, Lord Sphere, tries valiantly to explain the concept of three dimensions to someone who knows only two, but A. Square cannot understand and feels threatened by the Spacelander's seemingly supernatural view of events in Flatland granted by his three-dimensional perspective. As the Flatlander was attacked by the Linelanders, so the Flatlander here attacks the Spacelander—a sharp commentary on how people tend to respond to things beyond their understanding. The Spacelander then lifts A. Square to three-dimensional space, from which he can see Flatland from above. The narrator finally accepts the notion of space and ascribes divinity to its inhabitants, which the Spacelander appropriately denies. Any notions of more than two dimensions are considered heretical in Flatland, so the narrator's experiences with the sphere cause him trouble with the Flatland Council. Still, despite persecution and imprisonment, he continues to insist on the reality of a three-dimensional world, worlds of more than three dimensions, and a world revealed by the sphere called Pointland, inhabited by a single being satisfied with its own existence and unaware of the existence of others.
Primary among Abbott's themes in Flatland is his satire of Victorian social structure and mores. Abbott's portrayal of women is sharply critical of traditional women's roles in his society. Additionally, since Flatland is a two-dimensional world, its inhabitants see each other as line segments or, if facing a female directly, a point. Thus, distinctions between people, though they exist, are difficult to perceive. Significantly, the ability to judge another's shape, and with that another's status, comes mainly with education. Given Abbott's position as a cleric and his deep interest in spiritual issues, religion is also a topic of concern in Flatland. Some readers have seen A. Square's encounter with Lord Sphere as a metaphor for humanity's limited understanding of its encounters with the divine. Though Abbott never clarified these issues in subsequent editions of Flatland, he defined his religious views in his many theological works, especially in his late entry into the Tractarian controversy. In his religious writings Abbott also distinguished between the miraculous, which he dismissed as untrue, and the supernatural, which he thought was different from the miraculous in being both above nature yet linked to nature. In light of this, one might see a connection between Abbott's fanciful novel and his theological beliefs.
Reviewers at the time of its publication were mixed in their opinions of Flatland. Some appreciated its imagination and satire, while others found the book tedious and didactic. Many readers were puzzled by what they took to be the metaphorical intent of the novel, unsure whether Abbott was suggesting that God occupies a higher dimension and can become partially manifest on the human plane just as Lord Sphere can appear in Flatland as a cross-section, or whether the divine is more vaguely related to the natural world, as a three-dimensional world would be related to one of two dimensions. Nevertheless, Flatland acquired an eccentric but loyal following in the twentieth century. Later critics noted that Abbott explored issues of scientific relativity a half-century before Albert Einstein would develop his world-changing theory. Flatland's champions include scientists, mathematicians, and fantasy and science-fiction fans, and the novel has inspired several tributes and sequels by twentieth-century authors. A 2002 edition annotated by noted mathematician Ian Stewart has once again renewed interest in the novel.
A Shakespearean Grammar: An Attempt to Illustrate Some of the Differences between Elizabethan and Modern English (nonfiction) 1869
How to Write Clearly: Rules and Exercises on English Composition (nonfiction) 1875
Through Nature to Christ: The Ascent of Worship through Illusion to the Truth (nonfiction) 1877
Philochristus: Memoirs of a Disciple of the Lord (nonfiction) 1878
How to Parse: An Attempt to Apply the Principles of Scholarship to English Grammar (nonfiction) 1880
The Common Tradition of the Synoptic Gospels: In the Text of the Revised Version [with W. G. Rushbrooke] (nonfiction) 1884
Flatland: A Romance of Many Dimensions [as A. Square] (novel) 1884
The Kernal and the Husk (nonfiction) 1886
Philomythus, an Antidote against Credulity: A Discussion of Cardinal Newman's Essay on Ecclesiastical Miracles (nonfiction) 1891
The Anglican Career of Cardinal Newman. 2 vols. (nonfiction) 1892
English Lessons for English People [with J. R. Seeley] (nonfiction) 1893
The Spirit on the Waters: The Evolution of the Divine from the Human (nonfiction) 1897
Clue: A Guide through Greek to Hebrew Scripture (nonfiction) 1900
From Letter to...
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SOURCE: Review of Flatland, by Edwin Abbott. Spectator 57, no. 2944 (29 November 1884): 1583-84.
[In the following review, the critic finds Flatland amusing and occasionally overly technical.]
Strange are the tales of travellers, decisive the effect of experience upon previous speculations, and marvellously appropriate the morals brought home from outlandish quarters. Such are the reflections suggested by the attractive little book now before us [Flatland: A Romance of Many Dimensions]. It tells of a region more unfamiliar than that of giants or pigmies, of anthropophagi, or men whose heads do grow beneath their shoulders. It throws a light on the question of the nature of space, which will be eagerly welcomed by seekers after a Fourth Dimension; and it proves that the institutions and failings of the race which inhabits the strangest countries bear a curiously perverted resemblance to those of our own.
Mathematicians have long speculated on the nature of space, and some have even questioned its universality. While rejoicing in the fact that their hands were free to move upwards as well as sideways, they have speculated on the possibility of worlds whose inhabitants should not be limited in their movements to the three prosaic directions of forwards, sideways, and upwards. They have lamented over the absence of the invaluable sense which would enable a man to get...
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SOURCE: Morley, Frank V. “An Engaging Fable.” Saturday Review of Literature 3, no. 14 (30 October 1926): 354.
[In the following review, Morley finds the 1926 reissue of Flatland to be a pleasant read but not “in the stream of serious thought.”]
Dr. Abbott was out for fun when he wrote his friendly little geometrical romance, and it is good to see that the old wine is no worse for its new bottle. It is still a pleasant tonic, and an excellent stimulant for boys. Hitherto, only a few have enjoyed Flatland. It is now a pleasure in store for many.
Yet there is oddity in its reappearance at this time. The obvious reason for republishing is that in recent years we have waked up to the importance of what is loosely called “the” fourth dimension. An ingenious and easy narrative, introducing a fourth dimension by simple geometrical analogy, putting its eye-straining argument in words of one syllable, is therefore sure of a sale. Tanquam ex ungue leonem. I suspect Basil Blackwell of this cool logic. He must be at the bottom of it. It is a shrewd notion, so far as publication is concerned. By all means let us buy the book, in this time of scientific quickening. But let us not be confused in reading it. The introduction suggests that Dr. Abbott was a prophet paving the way for the revelation of the theory of relativity; this is a gallant claim which ought to be...
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SOURCE: Garnett, William. Introduction to Flatland: A Romance of Many Dimensions, pp. vii-x. New York: Barnes and Noble, Inc.: 1963.
[In the following introduction to the 1963 edition of Flatland, Garnett discusses thoughts on the fourth dimension illuminated by Abbott's novel.]
In an address to the Committee of the Cayley Portrait Fund in 1874 Clerk Maxwell, after referring in humorous terms to the work of Arthur Cayley in higher algebra and algebraical geometry, concluded his eulogium with the lines—
March on, symbolic host! with step sublime, Up to the flaming bounds of Space and Time! There pause, until by Dickenson depicted, In two dimensions, we the form may trace Of him whose soul, too large for vulgar space In n dimensions flourished unrestricted.
In those days any conception of “dimensions” beyond length, breadth and height was confined to advanced mathematicians; and even among them, with very few exceptions, the fourth and higher dimensions afforded only a field for the practice of algebraical analysis with four or more variables instead of the three which sufficiently describe the space to which our foot-rules are applicable. Any geometrical conclusions reached were regarded only as analogies to the corresponding results in geometry of three dimensions and not as having any bearing on the system of Nature. As an illustration, reference may be made...
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SOURCE: Kanigel, Robert. “ReReading.” Los Angeles Times Book Review (9 May 1982): 3.
[In the following review, Kanigel praises Abbott's commentary on mathematical theory and social issues in Flatland.]
You and I live in three dimensions. The would-be author of Flatland, identified in the original edition only as “A square,” lives in two. His tale—a provocative, always lively blend of science fiction, pure mathematics and social satire—recounts his discovery of the third dimension, and his fate at the hands of his fellow Flatlanders for daring to tell about it.
Flatland could so easily have been just another clever idea amateurishly executed, like a sophomore's strained efforts at “creative” writing; instead, it's a virtuoso performance. What makes it so satisfying a century later is not the idea itself so much as how well it's realized. Imagined details of its world are worked out with great clarity and precision. The range of human social experience upon which it comments is astounding.
The basics: In Flatland, the universe is a thin disc of limitless extent. We, in “Spaceland,” can look down upon the otherwise quite human triangles, squares, hexagons who inhabit it. But confined to their pancake of a world, Flatlanders themselves can't directly see one another, though they can infer presences.
In Flatland's pecking...
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SOURCE: Peterson, Ivars. “Shadows from a Higher Dimension.” Science News 126, no. 18 (3 November 1984): 284-85.
[In the following essay, Peterson surveys the themes of Flatland and its influence on modern students of both mathematics and literature.]
Flatland is a thin book—about 100 pages of Victorian prose that now seems somewhat quaint and old-fashioned. Yet, for a century, the book's central figure and narrator, “A Square,” has enticed innumerable readers into a two-dimensional world where a race of rigid geometric forms live and love, work and play.
Edwin A. Abbott's narrative begins: “Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard and with luminous edges—and you will then have a pretty correct notion of my country and countrymen.”
Over the years, this imaginary world has inspired students to take up geometry, mathematicians to conceive of higher dimensions, writers to build on Abbott's themes and artists to explore the nature of space and time. Last month, to celebrate the original publication of Flatland in October 1884, mathematician Thomas F. Banchoff of Brown University in...
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SOURCE: Jann, Rosemary. “Abbott's Flatland: Scientific Imagination and Natural Christianity.” Victorian Studies 28, no. 3 (spring 1985): 473-90.
[In the following essay, Jann argues that Abbott addresses in Flatland the Victorian conflict between spirit and intellect and therefore the contemporary debate over the role of hypothesis in scientific study.]
Edwin Abbott's Flatland (1884), published under a pseudonym and scarcely acknowledged by his biographers, has become the best-known work of this late Victorian clergyman and headmaster.1 As one of the first and surely the most entertaining speculations on the nature of the fourth dimension, Abbott's “Romance of Many Dimensions” has earned its place among science fiction classics. I will argue, however, that although its appeal to the imagination and to the possibilities of a “more Spacious Space” are timeless, Flatland also reveals strategies central to the brinksmanship of a late Victorian society divided between the needs of the spirit and the demands of the intellect. As part of Abbott's wider commentary on the role of imagination in cognition, Flatland alludes to contemporary debate over the role of hypothesis in scientific discovery and the relationship between material proof and religious faith. In his Broad Church reconciliation of science, Christianity, and Higher Criticism, Abbott...
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SOURCE: Banchoff, Thomas. Introduction to Flatland: A Romance of Many Dimensions, pp. xv-xxxi. Princeton, N.J.: Princeton University Press, 1991.
[In the following introduction to the 1991 edition of Flatland, Banchoff provides an overview of the novel and discusses its relevance for a contemporary reading audience.]
Flatland first appeared over one hundred years ago and a dozen different editions have been published since then. Why now put out a new edition of this book in the Princeton Science Library? For each generation of readers, Edwin Abbott Abbott's classic story of encounter between beings from different dimensions has had different significance. In 1884, the social satire on the limited perspective of Victorian England was as important as the comments on the use of analogy in treating higher dimensions, and both of these elements were clarified by the introduction to the second edition, purportedly written by an editor but actually written by Abbott himself. When the book was reissued in 1926, the main stimulus for considering higher dimensions was relativity theory, and a new introduction was written by William Garnett, a physicist student of Abbott's. In 1952, when the first modern edition appeared, it was again a physicist, Banesh Hoffmann, who wrote the introduction, referring to the connection between the dimensional analogy and the curvature of space. Other recent...
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SOURCE: Smith, Jonathan. Review of Flatland, by Edwin Abbott. Victorian Studies 36, no. 1 (fall 1992): 94-5.
[In the following review, Smith discusses the long-lived appeal of Flatland and Thomas Banchoff's introduction to the novel.]
Edwin Abbott was one of Victorian Britain's most fascinating and wide-ranging figures. Appointed headmaster of the City of London School in 1865 at the age of twenty-six, he quickly developed a reputation as a leading educational reformer, championing the introduction throughout the curriculum of such subjects as natural science and English literature. During his quarter-century at the CLS, Abbott published, in addition to Flatland (1884), textbooks on writing, Latin, and Shakespeare; scholarly works on Bacon and theology; and several Christian historical novels. When he retired in 1889, it was to devote the remainder of his life to the development of his theological system, the multi-volume Diatessarica. Yet it is Flatland, the clever little mathematical “Romance in Many Dimensions,” that survives.
That survival has been due in large part to the interest of scientists and mathematicians (who use the book to introduce students to concepts of dimensionality and space-curvature) and science-fiction lovers (who see it as an early example of that genre). Neither of these groups, however, has shown much concern for Abbott...
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SOURCE: Gilbert, Elliot L. “‘Upward, Not Northward’: Flatland and the Quest for the New.” English Literature in Transition (1880-1920) 34, no. 4 (1994): 391-404.
[In the following essay, Gilbert examines the themes of novelty and progress in Flatland.]
When perceptible amounts of new phenomenal being come to birth, must we hold them to be in all points predetermined and necessary outgrowths of the being already there, or shall we rather admit the possibility that originality may thus instill itself into reality?
William James, Some Problems of Philosophy1
“Your country of two dimensions is not spacious enough to represent me, a [Sphere] of three, but can only exhibit a slice or section of me, which is what you call a Circle. … You cannot indeed see more than one of my sections, or Circles, at a time, for you have no power to raise your eye out of the plane of Flatland; but you can at least see that as I rise in space my sections become smaller. See now, I will rise; and the effect upon your eye will be that my Circle will become smaller and smaller till it dwindles to a point and finally vanishes.”
Edwin A. Abbott, Flatland
Kaluza showed that electromagnetism is actually a form of gravity, but not...
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SOURCE: Smith, Jonathan, Lawrence I. Berkove, and Gerald Baker. “A Grammar of Dissent: Flatland, Newman, and the Theology of Probability.” Victorian Studies 39, no. 2 (winter 1996): 129-50.
[In the following essay, Smith, Berkove, and Baker explore Abbott's interest in the writings of John Henry Newman and Bishop Joseph Butler and their theories of analogical and probabilistic reasoning.]
In Philomythus (1891), his belated attack on John Henry Newman's Essay on Ecclesiastical Miracles (1843), Edwin Abbott rejects Newman's claim that accounts of miracles do not require legal proofs: “here faith has no place,” writes Abbott, “and ‘legal proof’ is the best possible proof; and if you cannot get it, you ought to try at least to get something as much like it as possible” (90). In place of Newman's principle of “antecedent probability”—that ecclesiastical miracles should be presumed true on the basis of their Biblical predecessors—Abbott offers a diametrically opposite principle:
[P]eople practically deny, and are quite right in practically denying, the existence of everything of which they have no evidence, direct or indirect. There may be regions of four, five, or fifty dimensions. … But we are so constituted as not to act on any “may be” that is not at least suggested by some evidence. … The right rule is,...
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Hoffmann, Banesh. “Introduction.” In Flatland: A Romance of Many Dimensions. New York: Dover Publications, Inc., 1952.
Discusses the relevance of Flatland to a 1950s reading audience.
Renz, Peter. “‘The World Is Broad and Wide’: A Modern Mathematician Annotates a Classic and Gives It Yet Another Dimension.” Scientific American 286, no. 4 (April 2002): 89-90.
Praises mathematician Ian Stewart's annotated edition of Flatland and includes a list of works, both fiction and nonfiction, inspired by the novel.
Stewart, Ian. “Tales of the Unexpected: How Media Hype Led the Victorians Back to the Future.” New Scientist 17, nos. 2322-2323 (22-29 December 2001): 68-9.
Explains the Victorian fascination with time travel and multiple dimensions.
Additional coverage of Abbott's life and career is contained in the following sources published by the Gale Group: Dictionary of Literary Biography, Vol. 178; and Literature Resource Center.
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