Flatland (Barnes & Noble Library of Essential Reading): A Romance of Many Dimensions

By Edwin A. Abbott and Lori M. Campbell

Since its first appearance in 1884, Edwin Abbott Abbotts Flatland: A Romance of Many Dimensions has charmed and intrigued readers and scholars alike with its inventive mix of fantasy and reality. What on the surface amounts to a clever means of teaching principles of mathematics and science, upon deeper inspection emerges as an entertaining yet thought-provoking literary experiment. Through the eyes of its narrator A. Square, the novel implicitly satirizes a Victorian society in the grips of extraordinarily rapid change.

Already having delighted and inspired for more than a century, Flatland continues to enjoy a rightful place in literary, scientific, and philosophical history, inviting its readers to be transported without roaming too far from home.

• Language: English
• Publisher: Barnes & Noble
• Release date: Sep 1, 2009
• ISBN: 9781411428287

Book preview

INTRODUCTION

SINCE ITS FIRST APPEARANCE IN 1884, EDWIN ABBOTT ABBOTT’S Flatland: A Romance of Many Dimensions has charmed and intrigued readers and scholars alike with its inventive mix of fantasy and reality. What on the surface amounts to a clever means of teaching principles of mathematics and science, upon deeper inspection emerges as an entertaining yet thought-provoking literary experiment. Through the eyes of its narrator A. Square, the novel implicitly satirizes a Victorian society in the grips of extraordinarily rapid change. Abbott divides A. Square’s story into two main parts: the character’s descriptions of his own culture, followed by his travels to three Other Worlds. A. Square’s experiences impact him in meaningful ways, making him first a spokesman for and finally a victim of the culture he describes. In the spirit of Wonderland, Neverland, and Oz, Flatland shares inescapable, politically charged parallels to the world outside the text. Exaggerating the restrictions governing gender relations, social status, religion, and politics in nineteenth-century Britain, Abbott, through A. Square, creates Flatland as a parody of empire and human nature. Already having delighted and inspired for more than a century, Flatland: A Romance of Many Dimensions continues to enjoy a rightful place in literary, scientific, and philosophical history, inviting its readers to be transported without roaming too far from home.

Widely published as a scholar, educator, and theologian, Edwin Abbott Abbott (1838-1926) remains best known for Flatland: A Romance of Many Dimensions. He was born in Britain’s capital and at age twelve entered the City of London School where he quickly excelled, particularly in mathematics. A scholarship took Abbott to St. John’s College at Cambridge University in 1857, where he focused on Classics. Graduating from Cambridge in 1861, Abbott later resigned a fellowship at the college to take orders as a deacon in the Anglican Church. He became a priest in 1863, yet earned his living and gained a considerable reputation as an educator. As headmaster at his alma mater, the City of London School, from 1865 until his retirement in 1889, Abbott was known for his tireless work ethic. He split his time between administrative duties, curriculum development, and teaching courses in English Literature, Classics, and Comparative Philology. Throughout his life Abbott interacted with some of the most noteworthy, influential thinkers and writers of his day, including Prime Minister Herbert Asquith among his former pupils, and novelist George Eliot among his friends. Abbott passed away in 1926 following a seven-year illness and is buried near his family in Hampstead Cemetery, not far from his home at Wellside.

Perhaps most appreciated for his remarkable contributions as an academic and religious reformer, Abbott found what may have been his true calling when he started publishing his ideas in 1871. He authored numerous theological treatises, many of which argued his vehement rejection of miracles as a basis for Christian belief. Abbott’s article Illusion in Religion, published in the Contemporary Review in 1890, marked his first public comments on what became an ongoing obsession in challenging the philosophies of John Henry Newman. More than a dozen years after his first foray into publishing, Abbott temporarily turned from scholarship to fiction with Flatland: A Romance of Many Dimensions, but his spiritual philosophy clearly resonates in the novel, particularly in the latter half. A. Square’s experiences culminate in his epiphany that if a world of three dimensions has existed heretofore without his knowledge, then surely lands of four, five, or more dimensions lie further beyond. Yet Abbott emphasizes that A. Square reaches his conclusion empirically, through hypothesis and experimentation, rather than as a result of an encounter with the miraculous. The portrayal extends from what Frank Turner calls Abbott’s scientific naturalism, which coincides with a Victorian movement to reconcile the seeming opposition between faith and science. Devoting his retirement years almost entirely to writing, Abbott produced numerous books on theology and literature, never revisiting Flatland, yet posterity, perhaps ironically, has placed A. Square’s adventure far above any of his alter ego’s more serious works.

On the surface, of course, Flatland: A Romance of Many Dimensions appears as a primer of sorts on principles of geometry and scientific analogy. Ian Stewart makes a good point in suggesting Abbott may have been influenced by the work of Charles Howard Hinton (1853-1907), whose article What is the Fourth Dimension? (published in Dublin University Magazine in 1881 and as a pamphlet in 1884) has several echoes in Flatland. Although the concept of other dimensions had already captured the Victorian scientific and literary imagination by the time Hinton’s article appeared, his use of geometrical shapes moving within confined space obviously finds a place in Abbott’s mathematical fantasy, particularly through his choice of characters: lines, circles, squares, polygons, and the like. Still, if an influence exists, Abbott moves far beyond it, devising a world inspired by his own experience as educator and scholar. He peppers the story with diagrams rather than illustrations, and many of A. Square’s explanations about life in Flatland easily read as lessons. For example, in relating how one Flatlander identifies another, A. Square says, Suppose I see two individuals approaching whose rank I wish to ascertain? They are, we will suppose, a Merchant and a Physician, or in other words, an Equilateral Triangle and a Pentagon. The lines read like a word problem that A. Square goes on to solve by applying the principles of bisecting angles and lines diminishing to show how Recognition by Sight operates in Flatland. In fact A. Square is a Mathematician of no mean standing, and his subsequent experiences in Spaceland and Pointland proceed in similar fashion, propelled by explanations relying almost solely on mathematical theory. To argue his proof that worlds of multiple dimensions exist to his Spaceland guide the Sphere, for instance, A. Square applies the Argument from Analogy of figures and later adopts a similar approach in his effort to diffuse the Theory of Three Dimensions in his own world, an activity which, incidentally, turns out to spell his doom.

Interestingly Hinton was among the first to extend Abbott’s portrayal, publishing An Episode of Flatland: How a Plane Folk Discovered the Third Dimension in 1907. Several sequels have since appeared, including Dutch physicist Dionys Burger’s Sphereland (1965), Jeffrey R. Weeks’ The Shape of Space (1985), and more recently, Ian Stewart’s Flatterland (2001). Each of these works follows Abbott’s example in different ways to apply the ideas and confirm the satirical slant of Flatland, ultimately paying tribute to his original accomplishment. To this day Flatland remains a standard text for teaching concepts of mathematics and physics, as well as an entertaining fantasy and an illuminating view of British history. Although the novel remains explicitly concerned with teaching some basic aspects of math and science, Abbott’s creation of Flatland is fueled by social and political interest of which the geometrical shapes populating that world represent the unimaginative and restrictive quality of Victorian life.

At a time when challenging the establishment carried the possibility of being ostracized or worse, fantasy allowed many Victorian writers, as it had for their predecessors from Homer to Shakespeare, the opportunity to disseminate volatile statements to the reading public while working out in their own minds opinions about the most troubling societal conditions. Displaying undeniable connections to early fantasies inspired by Thomas More’s Utopia (1516), such as Jonathan Swift’s Gulliver’s Travels, H. G. Wells’ The Time Machine, and George Orwell’s 1984, to name a few, Flatland most notably compares as a close precursor to William Morris’ News from Nowhere (1891). Like Morris (1834-96) in terms of outspokenness, social consciousness, and literary accomplishment, Abbott was something of an intellectual radical and, above all, as Thomas F. Banchoff describes, the headmaster was a social reformer who criticized a great many aspects of the limitations of Victorian society. Both Abbott and Morris responded in their fiction and nonfiction to influences of the major thinkers of their day and of the past, including Thomas Carlyle, Matthew Arnold, and John Ruskin, as well as to their own persistent beliefs about their nation’s future. In News from Nowhere Morris portrays a time traveler’s encounters in a futuristic world approximating what Britain might become were it to transform into an egalitarian community. Similarly Abbott imagines in Flatland at least three realms meant to expose what was lacking in his own time and place.

Abbott’s work more accurately reflects a dystopian rather than utopian approach, yet Flatland and News from Nowhere similarly treat the uneasiness felt by their respective writers and indeed by many Victorians. Abbott’s A. Square reports information, but unlike Morris’ Guest, who explains Victorian Britain by contrasting it to Nowhereian society, Abbott’s narrator essentially does the opposite, spending most of his time specifically characterizing life in his own world. Morris more closely follows More’s example by creating a utopia to show in a positive light how things might be and, through Guest’s repeated comparisons, to reflect the misery of his own present. For example, Guest learns from his host that the building formerly housing Parliament now provides a subsidiary market and a storage place for manure. Both works emerge out of the mixture of fear and optimism defining an approaching millennial moment, as Abbott makes especially clear by pinpointing the shift in A. Square’s thinking at the turn of the twenty-first century. To show Victorian readers the folly of their ways, Abbott makes A. Square’s descriptions intensely troubling yet clearly comprehensible as an exaggeration of their own experience. Flatland, Abbott implies, is the world capable of being born if present conditions are allowed to continue. For example, when the Victorian reader reaches A. Square’s discussion Of the Universal Colour Bill, he or she would easily recognize the controversy still lingering from the passage of The Great Reform Bill of 1832, which altered virtually the entire Victorian social and political system by granting the vote to larger numbers than ever before, thus furnishing power to the emerging middle class. A. Square, however, carefully and pointedly characterizes The Suppression of Chromatic Sedition as a violent overthrow resulting in the balance of the classes [being] again restored. Such a situation, while literally presented as positive, plainly illustrates an opposing view and reflects a darker reality. Great Britain had avoided the massive, violent revolutions that tore apart much of Europe in the eighteenth and nineteenth centuries, but the anxiety about such upheaval striking at any time remained embedded in the Victorian consciousness. Here Abbott plays with the possibility, making revolution appear to be a necessary return to order but unmistakably defining such condition as a backward move. The complexity of A. Square’s argument continues to unravel, especially when, in the manner of a Browning dramatic monologuist, he describes a society in which Colour is now non-existent. The Victorian reader would recognize the negative implication, receiving Abbott’s underlying meaning that a world defined by stagnant, rigid conformity stands in greater danger — or perhaps in even greater need — of a revolution than one defined by freedom and equality.

As the above example indicates, among many themes Abbott explores in Flatland, class constitutes one of the most prominent. Arguably, though, the novel treats the matter of gender in an even more vivid