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Flatland | Study Guide

Edwin Abbott Abbott

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Flatland | Context

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Satire

Satire is a genre of literature in which an author uses a variety of literary techniques to criticize a contemporary person, event, or issue. Such literary techniques include the following: parody, or imitation of another well-known source; hyperbole, or exaggeration; euphemism, or mild language used to describe a harsh reality; understatement, or the presentation of information as less important than it actually is; and sarcasm, irony, or mockery.

Often a satire presents a fictional scenario where the issues the author wishes to criticize are portrayed to an extreme degree. Other times they are presented in a context where analogous logic is applied to situations that show how ridiculous that logic is. In some cases authors invent an entire new world based on the faulty logic they wish to criticize. One classic example of a fictional world created for satire is Anglo-Irish author and clergyman Jonathan Swift's (1667–1745) novel Gulliver's Travels (1726), which features fantastic kingdoms of tiny people, giants, floating scholars, and civilized horse people on an island where humans are beasts. During each one of these visits, Gulliver attempts to explain English society to a strange civilization and is met with ridicule, forcing the English reader to confront idiosyncrasies of their own lives that they might otherwise take for granted.

Another well-known example is French satirist Voltaire's (1694–1778) 1759 novel Candide, which criticizes the logical optimism of the 17th- and 18th-century Enlightenment and the idea that all things exist for a purpose. An optimistic Candide tries to maintain his Enlightenment ideals while traveling through a world of cruelty and idiocy, ultimately coming to the conclusion that excessive idealism causes more misery than it is capable of solving.

Like these two works, Abbott creates a fantastic world in which systems and philosophies the reader might take for granted are presented in strange ways that highlight their hypocrisy. In this invented society, the number of sides of two-dimensional figures acts as a parody of the rigid Victorian class system. Victorian society had strict class, race, and gender hierarchies. Nobles and monarchs maintained historical privileges based on traditional birthrights. Meanwhile, workers, many of them children, labored for low wages 12 hours a day, six days a week, in dangerous factory conditions. Much of Britain's wealth came from conquered territories around the world and enslaved plantation workers. Supporters of colonialism and conquest asserted the inherent superiority of white Europeans and argued that so-called lesser races were better off under their administration. In Flatland, the more sides a shape has, the higher its class. This system is enforced through hyperbolic ( exaggerated) violence, censorship, and eugenics, and it is bolstered by philosophical and religious doctrines that the ruling class of circles has invented for its own benefit. The first half of the book displays both verbal and dramatic irony as Abbot's protagonist, A Square, speaks favorably of the very system Abbott criticizes, supporting all its horrors as right and necessary. However, by the end of the book, much like Gulliver and Candide, A Square comes to understand the inherent folly of his own system, and he speaks out against it.

Victorian Ideas about Biology and Natural Order

The period in British history from roughly 1820 to the start of World War I (1914–18) is referred to as the Victorian era, as it loosely corresponds to the reign of Queen Victoria (1819–1901; reigned, 1837–1901). Rapid advances in science and the imperial aspirations of Europe during this period raised a number of moral and social questions for thinkers of the day. Popular pseudosciences (false scientific premises) such as phrenology (study of inherent character traits based on skull shape) already used biology to justify strict Victorian social hierarchies. Then British biologist Charles Darwin (1809–82) published On the Origin of Species (1859), laying out the theory that biological fitness passed from parent to child, evolving over generations. Many Victorian thinkers extrapolated this idea to mean that the current social order was the natural, inevitable result of the strong overcoming the weak, a theory called social Darwinism. Darwin's theories also led to the development of the eugenics movement, which encouraged reproduction among the so-called best members of society and discouraged it among the so-called least fit, such as the poor, criminals, or the unhealthy.

In addition to hierarchies of class and race, Victorians also maintained strict gender hierarchies, with men considered biologically and intellectually superior to women, though women were considered morally superior. This belief was incorporated into their understanding of science and medicine. Women, especially of the higher classes, were considered delicate and prone to psychological complications brought on by the malevolent effects of their uteruses. Even Queen Victoria, who held the throne in her own right, often deferred to her husband in matters of government, saying, "We women are not made for governing."

Flatland heavily satirizes Victorian ideas about natural order with its intense hierarchy of shapes, its laws restricting women for their own good, its narrator's disregard for the intelligence of the lowest classes, and its fear and brutal destruction of irregular figures.

Abbott was not the only educator and writer of the Victorian era prone to combining social commentary with mathematics, The more well-known British author Lewis Carroll (Charles Lutwidge Dodgson, 1832–98) speculates tangentially on alternate dimensions and space in his Through the Looking-Glass (1871). Carroll also had an interest in how geometry was taught in the English educational system of the time, noting that as mathematics and science curricula had been newly introduced into the schools (attended by boys, as girls were educated only at home), a great many inaccurate and complicated methods for teaching geometry had surfaced. His response to this murky condition was a play called Euclid and His Modern Rivals (1879), designed to be read and studied as parlor entertainment in the home, from which both boys and girls could learn. Although no geometric figures appear as characters in Carroll's play on geometry (which is a series of dry discussions to debunk faulty methods of geometry), it is interesting to note that both Carroll and Abbott satirize Victorian beliefs regarding the superiority of intellect held by men over women.

Interest in Flatland as a Mathematical Text

Though Abbott advocated for scientific education, his own training was not in science or mathematics but in classics and theology. During his lifetime he was respected principally for his teaching career and religious writings. Flatland, at the time of its writing, used dimensions as a metaphor (comparison) for its characters' abilities to comprehend the universe both scientifically and spiritually.

However, most modern interest in Flatland is concerned with the way it presents the subjective experience of moving from two to three dimensions and what this movement implies about a fourth dimension. Mathematical thought experiments regarding the possibility of other dimensions were not unheard of even in Abbott's time. The idea of geometry that did not comply with Euclidean principles reached a height of popularity in the mid-19th century. Greek mathematician Euclid (fl. c. 300 BCE) is known for a text on geometry entitled Elements. Italian mathematician Eugenio Beltrami (1835–1900), for example, described solely with equations a shape called a pseudosphere, which had a constant negative curvature and did not conform to Euclidean principles. Beltrami's work provided an important foundation throughout the 20th century for the development of hyperbolic geometry (rejects Euclid's fifth postulate regarding one parallel line through a point not present on a given line; hyperbolic geometry supposes that there are at least two such parallel lines).

The greatest popular resurgence of Flatland came after German American physicist Albert Einstein (1879–1955) proposed his theory of general relativity in 1915 and especially after his Nobel Prize in 1921. General relativity relies on non-Euclidean geometry to explain the curvature of space and time. A 1920 letter published in the prestigious scientific magazine Nature, entitled "Euclid, Newton, and Einstein" and possibly written by Abbott's friend and student William Garnett (1850–1932), mentions Flatland as a work dealing with multiple dimensions. Though Abbott's fictional work differs significantly from Einstein's theoretical ideas about space and dimension, many readers find it a useful and suggestive thought experiment concerning difficult-to-explain concepts in mathematics.

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