Flatland Analysis

  • Flatland is Edwin A. Abbott's satire of Victorian England. Flatland itself is a two-dimensional world where men are many-sided figures and women (represented as line segments) are second-class citizens. Abbott uses these geometric dimensions to explore the differences between the genders.
  • In many ways, Flatland is a thought experiment imagining what society would be like in two-dimensional and one-dimensional worlds. A. Square describes the social stratification in Flatland, which resembles our world in its attitude toward gender.
  • A. Square's violent reaction to meeting the Great Sphere, a three-dimensional figure, illustrates man's tendency to lash out at the unknown and resist change. A. Square doesn't understand the three-dimensional world and reacts poorly when faced with someone different from himself. 


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.

Major Themes

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.

Critical Reception

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.

Principal Works

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 Spirit: An Attempt to Reach through Varying Voices the Abiding Word (nonfiction) 1903

Silanus, the Christian 1906

Apologia: An Explanation and Defence (nonfiction) 1907

Notes on New Testament Criticism (nonfiction) 1907

Light on the Gospel from an Ancient Poet (nonfiction) 1912

The Fourfold Gospel. 5 vols. (nonfiction) 1913-17

Spectator (review date 29 November 1884)

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...

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Frank V. Morley (review date 30 October 1926)

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...

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William Garnett (essay date 1963)

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...

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Robert Kanigel (review date 9 May 1982)

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...

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Ivars Peterson (essay date 3 November 1984)

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...

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Rosemary Jann (essay date spring 1985)

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...

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Thomas Banchoff (essay date 1991)

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....

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Jonathan Smith (review date fall 1992)

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...

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Elliot L. Gilbert (essay date 1994)

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


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Jonathan Smith, Lawrence I. Berkove, and Gerald A. Baker (essay date winter 1996)

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...

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Further Reading


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...

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(Critical Survey of Science Fiction and Fantasy)

Flatland functions as a geometry lesson, a satire of Victorian England, and an attempt to mediate the nineteenth century debate between science and religion. As a geometry lesson, the novel illustrates basic concepts of dimensionality in a manner appealing to young readers. Abbott, who was the headmaster of the City of London School, recognized the value of entertainment in instruction and advocated a broad, liberal education for his students.

His novel is also a satire of Victorian England, specifically its class consciousness, its penchant for conformity, and its disenfranchisement of women. The Color Revolt, in particular, ridicules conformity in art and the societal forces that stifle creativity and individuality.

Finally, in its suggestion of higher dimensionality, Flatland offers a plausible, though not scientifically provable, explanation for the spiritual world, including God and heaven. Using induction to demystify supernatural phenomena, Abbott effectively bridges the chasm between observable fact and blind faith and shows that science and religion are not necessarily incompatible.

The structure of the novel complements its theme. Divided into two parts, Flatland has twenty-two chapters. The chapters often pair off, treating first a general topic and then a subtopic. For example, chapter 5 discusses Flatlanders methods of recognizing one another, and chapter 6 focuses on the art of sight recognition. The number...

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