Flatland: A Romance of Many Dimensions

  Edwin A. Abbott (1838–1926), a Victorian of great intellect and wit, enjoyed success not only as a writer, but as a scholar, educator, and theologian. Educated at St. John’s College, Cambridge, he was Headmaster of the City of London School from 1865 to 1889. During that time, his progressive belief in the importance of the study of English for every student, even before the traditional classic curriculum, led him to write A Shakespearian Grammar (1869) “to help solve most of the difficulties that will present themselves to boys.” It ran to three editions within its first year of publication alone and continues to be a touchstone for Shakespearean scholars. In 1884, he wrote Flatland. First considered by many as merely “a pleasant tonic, and an excellent stimulant for boys,” it was later recognized as a magnificent work of science fiction, as prophetic as those of Jules Verne and H. G. Wells. Retiring to a scholarly life in 1889, he produced numerous other works, including Silanus the Christian (1907), Apologia: An Explanation and Defense (1907), Message of the Son of Man (1909), and Light on the Gospel from an Ancient Poet (Odes of Solomon) (1913).

  Valerie M. Smith earned her PhD from the University of Connecticut. An associate professor of English at Quinnipiac University in Hamden, Connecticut, she is currently at work on a manuscript entitled Crossroads: Cultural Autobiography and Imperial Discourse.

  John Allen Paulos is a Professor of Mathematics at Temple University and the bestselling author of eight books including Innumeracy, A Mathematician Reads the Newspaper, and Once upon a Number. He has been a columnist for ABCNews.com, Scientific American, and the Guardian, as well as the author of numerous reviews, articles, and op-ed pieces for a variety of publications. Among his many honors are the 2003 American Association for the Advancement of Science Award for Promoting Public Understanding of Science and the 2013 Mathematics Communication Award from the Joint Policy Board for Mathematics.

  FLATLAND

  A Romance of Many Dimensions

  With Illustrations by the Author, A. Square

  Edwin A. Abbott

  With an Introduction by Valerie Smith

  and a New Afterword by John Allen Paulos

  SIGNET CLASSICS

  SIGNET CLASSICS

  Published by the Penguin Group

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  Published by Signet Classics, an imprint of New American Library,

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  Introduction copyright ©Valerie Smith, 2005

  Afterword copyright © John Allen Paulos, 2013

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  REGISTERED TRADEMARK—MARCA REGISTRADA

  ISBN 978-1-101-63778-4

  If you purchased this book without a cover you should be aware that this book is stolen property. It was reported as “unsold and destroyed” to the publisher and neither the author nor the publisher has received any payment for this “stripped book.”

  CONTENTS

  About the Authors

  Title page

  Copyright page

  Introduction

  Preface

  PART I: THIS WORLD

  1 Of the Nature of Flatland

  2 Of the Climate and Houses in Flatland

  3 Concerning the Inhabitants of Flatland

  4 Concerning the Women

  5 Of our Methods of Recognizing one another

  6 Of Recognition by Sight

  7 Concerning Irregular Figures

  8 Of the Ancient Practice of Painting

  9 Of the Universal Colour Bill

  10 Of the Suppression of Chromatic Sedition

  11 Concerning our Priests

  12 Of the Doctrine of our Priests

  PART II: OTHER WORLDS

  13 How I had a Vision of Lineland

  14 How I vainly tried to explain the nature of Flatland

  15 Concerning a Stranger from Spaceland

  16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland

  17 How the Sphere, having in vain tried words, resorted to deeds

  18 How I came to Spaceland, and what I saw there

  19 How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it

  20 How the Sphere encouraged me in a Vision

  21 How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success

  22 How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result

  Afterword

  INTRODUCTION

  MEN SOUGHT TRUTH IN THEIR OWN LITTLE WORLDS, AND NOT IN THE GREAT AND COMMON WORLD.

  Another error is an impatience of doubt and haste to assertion without due and mature suspension of judgment. For the two ways of contemplation are not unlike the two ways of action commonly spoken of by the ancients; the one plain and smooth in the beginning, and in the end impassable; the other rough and troublesome in the entrance, but after a while fair and even. So it is in contemplation; if a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.

  —Sir Francis Bacon

  Advancement of Learning

  Edwin Abbott (1838–1926), progressive educator, scholar, theologian, and prolific author, was born in London, England. After earning a degree in divinity from St. John’s College, Cambridge, he was appointed assistant master at King Edward School in Birmingham. Following his two years in Birmingham, Abbott returned to London as headmaster of the City of London School, where he remained from 1865 to 1889.

  As a progressive educator with a commitment to social reform, Abbott was concerned with advancing the study of English, mathematics, and the natural sciences, and was active in promoting educational opportunities for women and members of the middle class. Many of Abbott’s works, including How to Write Clearly: Rules and Exercise on English Composition (1875) and Hints for Home Teaching (1886), reveal his dedication to educational reform. Abbott’s first publication, A Shakespearian Grammar: An Attempt to Illustrate Some of the Differences Between Elizabethan and Modern English (1869), reflects his (at the time radical) interest in the study of English when Latin and Greek dominated the curriculum. Abbott’s firm belief in the close and careful reading of literature, as evidenced in his ideas about educational reform and his literary scholarship, is palpable in his most well-known work, Flatland: A Romance of Many Dimensions (1884), which richly rewards the careful reader.

  Following his 1875 appointment as a Cambridge lecturer, Abbott was freer to pursue his wide-ranging scholarly interests as attested to in his numerous publications. Philomythus, an Antidote Against Credulity: A Discussion of Cardinal Newman’s Essay on Ecclesiastical Miracles (1891) is Edwin Abbott’s second most well-known work. Philomythus was his entry into the Tractarian controversy surrounding Anglican priest John Henry Newman’s stance on traditionalism within the Church of England. Cultural anxieties concerning the relationship between religion and science during the Victorian era provoked this debate in which Abbott, unlike Newman, perceived value in reconciling re
ligious views with contemporary scientific thought. Many readers of Flatland have suggested that it was Abbott’s commitment to religious questions that inspired and formed the metaphorical basis for the novel, but as Rosemary Jann has noted, there is ‘‘no evidence that contemporary reviewers detected the relevance of Abbott’s arguments to specifically religious questions.’’1 Victorian reviewers’ neglect of Abbott’s status as a theologian in their considerations of Flatland may help to point us toward some potentially useful dimensions when considering the novel. That Abbott’s novel continues to provoke a wide variety of readings vouchsafes the necessity of the type of close and careful reading Abbott himself practiced and obviously playfully anticipated from his own readers.

  Abbott’s other works have been fairly easy to classify, but Flatland has been referred to variously as a mathematical or scientific novel, a social satire, a work of science fiction and fantasy, a philosophical treatise, a mystical adventure, an artistic inspiration, a fictional work of travel, and ‘‘a very puzzling book.’’2 Flatland continues to inspire tributes and sequels, ranging from logician C. H. Hinton’s An Episode of Flatland (1907) to Dionys Berger’s Sphereland (1983) to Allen Moore’s Tales of the Uncanny comic book miniseries entitled 1963 (1993). Flatland also continues to inspire attention across a wide spectrum of disciplines, from physics to English literature to (more recently) computer graphics. Some scholars have suggested that Flatland ‘‘celebrates the powers of the imagination’’ while others argue that it ‘‘is a cautionary tale about the dangers of the imagination.’’3 Scientists and mathematicians tend to focus on the text’s use of geometry and dimensionality, while literary critics and historians have often been most concerned with the text’s reflection of and on Victorians’ relationships to class, gender, religion, and science.

  However one chooses to categorize it, Flatland persists in raising important epistemological questions for its numerous readers, as early reviewers remarked.4 Abbott’s interest in epistemology is not surprising, given his attention to the work of Sir Francis Bacon. Indeed, Abbott edited two volumes of Bacon’s essays (1876) and produced a biography of Bacon (1885). Bacon’s Advancement of Learning (1605) also explores questions of epistemology, although the term itself was not coined until 1856 by James Frederick Ferrier, a mid–nineteenth century Scottish philosopher, in his Institutes of Metaphysic. Abbott’s fascination with the study of knowledge, or how we know what we know, is evident both in the details of A. Square’s expeditions and in Abbott’s artful use of discourse.

  Victorian Britains were a traveling people, with Queen Victoria herself often promoting travel under the banner of the ‘‘Civilizing Mission.’’ It is no wonder, then, that an early review of Flatland in The Spectator would remark:

  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. 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.5

  It is important to consider Flatland from the aspect provided by this anonymous nineteenth-century reviewer because he indicates sympathy toward an emerging Victorian concern about the ethics and consequences of colonial expansion. As Mary Louise Pratt explains in her discussion of Paul Du Chaillu’s 1861 Explorations and Adventures in Equatorial Africa, questions concerning the propagation of certain imperial views were just beginning to be more widely considered during the second half of the nineteenth century.6 But a contemplation of Abbott’s Flatland from this point suffices as only one angle from which to regard the text, which deliberately complicates what its audience thinks it knows about its own and others’ cultures.

  Just as Jonathan Swift’s Gulliver’s Travels created fictional worlds through which the author could satirize his own culture, so does Edwin Abbott’s Flatland create ‘‘worlds’’ through which its author’s culture could be effectively satirized. But Flatland is not a straightforward fictional travel narrative, because its narrator, A. Square, is a Flatlander himself. He is not a citizen of the metropolis reporting back from a journey to strange lands; he is a citizen of the periphery, acting as tour guide. A. Square produces a powerful work of transculturation, which asks its readers to reconsider the basis and legitimacy of their own systems of truth and knowledge through his very careful use of the materials provided to him by Lord Sphere of the Third Dimension, or Sphereland. It is Lord Sphere, a citizen of the metropolis, who introduces A. Square to the system of logic that allows Square to perceive ‘‘Pointland, The Abyss of No Dimensions,’’ ‘‘Lineland,’’ a world of one dimension, Sphereland, and the limits of Square’s own two-dimensional world, Flatland. In an exquisite moment of transculturation, A. Square then hypothesizes, using Lord Sphere’s metropolitan system of logic or reason, on the existence of a fourth dimension, a hypothesis Lord Sphere rejects with as much certainty as A. Square (and the Monarchs of Pointland and Lineland) had previously rejected the idea of other dimensions. Each of the dimensions we encounter, both literally and figuratively, contributes another dimension to Abbott’s epistemological exploration. Each dimension reflects both backward and forward in a prismlike revisioning of what we thought we knew up until that point, as our understanding of how we know what we know refracts seemingly endlessly, like A. Square’s reference to the possibility of endless dimensions.

  Abbott begins his epistemological exploration by making clear the position of its central ‘‘informant,’’ to use the language of ethnography. ‘‘I call our world Flatland,’’ A. Square begins his explanation, ‘‘not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space’’ (p. 15). Abbott’s familiarity with the discourse of Victorian ethnography (defined in the eighth edition of the Encyclopaedia Britannica (1878) as ‘‘embrac[ing] the descriptive details . . . of the human aggregates and organizations’’7) is evident in Janet Burnstein’s ‘‘Victorian Mythography and the Progress of the Intellect.’’8 In part, Abbott’s text operates as an epistemological exploration through its reproduction of charmingly mischievous ethnographic discourse. Abbott’s informant immediately raises his readers’ awareness of the difficulty of cross-cultural translation in the realm of concepts in Square’s first sentence, in which Square also establishes himself as a nonthreatening foreigner. Square clearly acknowledges his subservient position as a citizen of a two-dimensional reality in relation to his more ‘‘privileged’’ Space-dwelling readers. A. Square also makes it clear that the information proffered, and the understanding produced, will merely be ‘‘pretty correct.’’ He views the perspective he provides of ‘‘my country and countrymen’’ as limited, as it does not encompass the whole ‘‘universe,’’ but only one part of the known universe since, as he notes, ‘‘now my mind has been opened to higher views of things.’’ Square’s reference to the potential for ‘‘higher views’’ opens up the possibility of limitations on knowledge, dependant upon one’s angle of approach, in a manner reminiscent of that suggested in Bacon’s epigraph on the fruitfulness of beginning with doubts rather than certainties in the quest for knowledge.

  A. Square’s ethnographic description of Flatland precisely accentuates physical differences between the two worlds while simultaneously revealing cultural similarities. It is thus that Abbott’s seemingly hapless informant manages to reveal the foibles of both his own universe and the three-dimensional universe of his audience, while appearing completely unaware of the ridicule toward himself, his world, and the three-dimensional world of Victorian Britain his commentary invites. For exam
ple, Flatland’s ‘‘Laws of Nature’’ concerning women, members of the lower classes, and the disabled, as the narrative appears to inadvertently reveal, do not hold up any more ubiquitously than did those of Victorian Britain, but must instead be upheld by a legal and political system whose arrangement proves to be based upon unreasoned and unreasonable claims. That our informant appears sublimely (or perhaps stubbornly) unaware of this paradox reveals the foolishness of his judgments, which in turn reflects back upon his initial subserviency toward his audience. If he is incorrect about his own world due to his obviously limited perception, perhaps he is also incorrect in his assessment of his audience’s superiority.

  But, once again, Abbott’s critical mirror does not rest there. His reading of ‘‘The Law of Compensation,’’ which guarantees (although not always) upward class mobility, reveals that ‘‘Laws of Nature’’ can be carefully manipulated by members of the upper classes to ensure that any revolutionary impulses aimed at ensuring social equity for the largest numbers of people are stifled. The carrot of upward class mobility allows those of the highest classes (Polygons and Circles) to take ‘‘advantage of the irrepressible and boundless hopefulness of the human mind,’’ while, at the same time fomenting class distrust through the propagation of ‘‘jealousies and suspicions’’ among competing members of the lower classes. While Isosceles Triangles (considered ignorant barbarians because of their dearth of sides) may ‘‘know’’ that their chances of advancement are limited, as is evidenced by the numerous revolts they have fomented, they nevertheless continue to believe what the upper classes promise them, thereby neatly refracting Abbott’s argument in yet another direction.