COMMENTARY in His Essay, “The Fourth Dimension,” E. T. Bell Urges

æ COMMENTARY

In his essay, “The Fourth Dimension,” E. T. Bell urges that Flatland be read “merely as a work of the creative fantasy without reading nonsense into the white spaces between the print.” [The Search for the Truth, 1934, p. 233] While Bell’s remarks were directed toward those who found spirits in the fourth dimension, they might also be taken as a warning against encumbering a very charming story with critical explanations and analysis. Nonetheless, Flatland was written for a British audience of more than a century ago, and a modern-day reader, especially an American reader, will need to have a great many things explained in order to understand this ingeniously contrived book fully. In the foreword to his book, Lectures on Literature, Vladimir Nabokov makes some suggestions on how to be a good reader: “In reading, one should notice and fondle details. ... Curiously enough, one cannot read a book: one can only reread it. A good reader, a major reader, an active and creative reader is a rereader.” It is especially to the rereaders that we address the following annotations.

Cover.

Romance. This ‘romance’ is a fictitious prose narrative with scenes and incidents that seem to be remote from those of ordinary life. In English Lessons for English People,Abbott and Seeley define a romance to be a form of imaginative narrative in which character and manners are subordinate to adventure. The reviewer in The Critic (April 18, 1885) attributes to Hawthorne the statement that the aim of a novel is to present to humanity “the illusion of a lofty reality.” He notes that A Square has inverted this statement in presenting “the reality of a lofty illusion.” Dimension. Flatland is more than a novel introduction to the geometry of higher dimensions; here ‘dimension’ is not restricted to the notion of measurement of spatial extent. Abbott intends that the dimensions of an entity include any component aspect or attribute as well as any way in which it may be regarded or in which it presents itself to the mind. A Square. Edwin Abbott Abbott’s name reflects the surname of both of his parents, Edwin Abbott and Jane Abbott, who were first cousins. ‘A Square’ is a pun on his initials, EAA = EA2; this pun accounts for the absence of a period after the A in author’s name, A Square. Abbott published two other books anonymously (Philochristus and Onesimus), but let it be known in each case that he was the author. In a letter to his publisher, Macmillan and Co. (January 6, 1874), he explained that he did not wish “to be abused by name in the religious papers.” He made A Square the author of Flatland not to avoid controversy, but rather to emphasize that it was a first-person story of a two-dimensional being. 1 The first public indication that Abbott was the author of Flatland appeared in the Literary Gossip column of The Athenaeum, No. 2978 (22 Nov 1884), p.660: “That curious little book Flatland, which we noticed last week is said to be the production of the head master of a well-know school. This was followed by an (unsigned) review of Flatland in The City of London School Magazine 8 (December 1885), 217–221 in which the author concluded: We have strong reasons for believing that the author of the above is not unknown to most of our readers: that this is not the first or the most philosophical production of his pen: and, what is more to the point, that the name of A Square will be found in the Mathematical Tripos list for the year 186- by any one who will consult the Cambridge Calendar for that purpose. (The Tripos is the final honors examination for the B. A. degree. In 1861, Abbott finished first in the Classical Tripos and was seventh ‘Senior Optime’ in the Mathematical Tripos.) Abbott confirmed his authorship of Flatland in a footnote on page 29 of The Spirit on the Waters (1897). Epigraph. The epigraph is from Hamlet, Act 1, Scene 5. Horatio: O day and night, but this is wondrous strange! Hamlet: And therefore as a stranger give it welcome. There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy. Horatio has seen the ghost of Hamlet’s father appear and disappear. There is an allusion to the miraculous, and to the way we confront phenomena we recognize as being beyond our ordinary experience. In his reply, Hamlet urges Horatio not to shrink from the wondrous, but rather to welcome it and learn from it. It was natural for Abbott to use a quotation from Shakespeare. His first published work, Shakespearian Grammar (1869), was a pioneering study of Shakespeare’s language The book is subtitled, An attempt to illustrate some of the differences between Elizabethan and modern English for the use of schools. At the time he wrote the grammar, the City of London School was one of a few where English was systematically taught. (The classics, Greek and Latin, were emphasized instead.) Abbott felt strongly that the study of English should be a part of the curriculum, and he knew from his own experience that school boys had great difficulty in understanding Shakespeare’s language. [3] Seeley & Co. Seeley & Co. was owned by Robert B. Seeley, the father of Abbott’s friend, John R. Seeley. Earlier, Seeley, Jackson, and Hallilday had published Abbott and Seeley’s highly successful English Lessons for English People. In all, Abbott published eleven books with Seeley & Co. 2 Half-a-crown. A half-crown is (was) 1/8 of a pound. The present value of 1/8 of a pound of silver in 1884 is $38.63. In 1881, the average annual income of a teacher was 120 pounds. Title page. “Fie, fie, how franticly I square my talk,” is a punning reference from Titus Andronicus, Act 3, Scene 2. Dedication.

H.C.InApologia(1907), p. xiii, Abbott explicitly identiﬁed his life-long friend Howard Candler as “the ‘H. C.’ to whom Flatland was dedicated many years ago.” When he inscribed the title page of a prepublication copy of Flatland for his best friend, Abbott wrote,

To H. C. in particular from the Square. Oct. 1884 That volume was given to the Wren Library of Trinity College in 1969, by Christopher Candler, a grandson of Howard Candler. Abbott’s weekly letters to Candler were a primary source for A. E. Doulas-Smith in writing his history, The City of London School (1937). Unfortunately, it appears that these letters no longer exist; they probably were destroyed by Abbott’s two children, Edwin and Mary, when they disposed of their books and personal papers late in their lives. Mysteries. This may be a reference to mystery religions, where anyone who attempts to reveal the cult’s secrets is punished. One such cult was the Pythagorean brotherhood, founded by the Greek mathematician, Pythagoras, in southern Italy in the 6th century BC. Imagination. Rosemary Jann notes: “The idea of imagination working through appearances to higher truth is for Abbott the fundamental mechanism of both scientific and religious thought.” [1, p. 294] In The Kernel and the Husk, Abbott writes: “Our knowledge of the external world as well as ourselves comes not from sensations as interpreted by reason, but (at least to a large extent) from sensations as interpreted by imagination.” “The role of imagination in science was a subject that had been in the air at least since the forties, when it was raised by William Whewell’s controversies with J. S. Mill over the nature of scientific induction. Both Whewell and Mill wished to correct the naive Baconianism that limited scientific endeavor to mere observation.” [1, p. 295] In the title essay of his book Possible Worlds (pp. 292–293), the legendary British geneticist J. B. S. Haldane (1892–1964) wrote Our only hope of understanding the universe is to look at it front as many different points of view as possible. This is one of the reasons why the data of the mystical 3 consciousness can usefully supplement those of the mind in its normal state. Now my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. I have read and heard many attempts at a systematic account of it, from materialism and theosophy to the Christian system or that of Kant, and I have always felt that they were much too simple. I suspect that there are more things in heaven and earth than are dreamed of, or can be dreamed of, in any philosophy. That is the reason why I have no philosophy myself, and must be my excuse for dreaming.

Modesty.InThe Spirit and the Waters (p. 32), Abbott explained that he hoped that the reader of Flatland might be led to contemplate wider views of possible circumstances and existences and thereby develop modesty, respect for facts, a deeper reverence for order and harmony, and a mind more open to new observations and to fresh inferences from old truths. In Apologia, p. 83, he reiterates the importance of (intellectual) modesty. The remedy ... is to liberate our thoughts from the yoke of materialism, and to take a more ample view of the Universe. Not — as I have said before — that we must ever mix Thoughtland and Factland. But we must make ourselves modest by trying to conceive that there may be a Thoughtland, as much more real than Factland as the land of three dimensions seems to us more real than the land of two. Apologia, pp. 11 – 12: “We really know nothing whatever about what is ‘real.’ We have only faith and feeling about it — that kind of faith which bursts out in the words ‘The things that are seen are temporal, but the things that are not seen are eternal.’ ” (II Corinthians 4:18)

Solid Humanity. The use of ‘solid’ is a play on words. A solid (geometric) object has three dimensions; a solid person has a substantial nature.

Preface to the Second and Revised Edition, 1884. The first edition of Flatland appeared in November, 1884; about a thousand copies were quickly sold. A second, revised edition, with a preface by ‘the editor’ (the author) and several emendations of the illustrations and the text was printed in December, 1885. Except for new introductions nearly every subsequent English ‘edition’ of Flatland has been merely a reprinting of the second edition. Abbott was blessed with an enlightened American publisher, Roberts Brothers of Boston which printed the first American edition in 1885. This American edition was based on a copy of the first edition, and various American publishers have continued to reproduce its errors — for example, the ‘Collector’s Edition’ published by The Easton Press in 1995 and the ‘Pocket Classic’ published by Shambhala in 1999. 4 In several letters (now cataloged in the British Museum) Abbott discusses business affairs with Roberts Brothers of Boston, whom he calls ‘my American publishers.’ During the late nineteenth century, Roberts Brothers ranked among the choicest publishing houses in the United States, and its list was accorded distinction by American booksellers and publishers. Roberts Brothers was one of the first and remained one of the most steadfast in recognizing the rights of foreign authors by paying the equivalent of a copyright. In 1898, Roberts Brothers was acquired by Little, Brown and Co, which continued publishing Flatland.[2] Since the United States did not recognize international copyright law until 1891, English authors (and their American publishers) of popular books were often victimized by firms that published their books without paying any royalties. (Congress passed a law for the protection of literary property of U.S. Authors in 1790.) Without any international agreement, American publishers had a strong incentive to prefer works by English authors over those by Americans. [5] Writers on both sides of the Atlantic formed associations to press for an international agreement. Abbott wrote a considered letter to The (London) Times concerning the issue. He decried “the mischief that would accrue to both nations from the literary traditions of a conflict between them.” The book was out of print in England in 1926, when Basil Blackwell republished the second edition with an introduction by ‘W.G.’ — William Garnett, a former student of Abbott at City of London School. Much of the popularity of Flatland in the US is due to Hayward Cirker, founder of Dover Publications. In 1952, he chose Flatland as one of his first titles in mathematics.

The Editor. Since it is unlikely that Flatlanders speak English, the text must be the editor’s translation of A Square’s words. There is implied a continuing conversation between the imprisoned Square and his editor, even though he does not seem to have further contact with the Sphere or other Spacelanders. He states explicitly that he is deprived of all human contact except for occasional visits from his brother.

The first objection.InThe Athenaeum 2977 (November 15, 1884), p. 622, a reviewer of Flatland argues that if A Square and his polygonal relatives could see each other edgewise, then they must have some thickness, and so should not have been so distressed by the doctrine of a third dimension. In response to this review, A Square wrote a letter from ‘Flatland State Prison’ to The Athenaeum which begins with a phrase from Hamlet, Act 1, Scene 2. “I write from a world that has been truly and literally described as ‘weary, stale, flat, and unprofitable,’ — from the land of Two Dimensions, some of the characteristics of which I have recently endeavored to describe in a little treatise entitled Flatland.” This preface is an expanded version of the letter from ‘the State Prison’ explaining the 5 (meta-)physics of Flatland. While Abbott was not primarily interested in the physical as- pects of existence in a plane world, his letter to The Athenaeum shows that he recognized a need to be more explicit. — even I cannot now comprehend it, nor realize it by the sense of sight or by any process of reason; I can but apprehend it by faith. This key statement is much more explicit than any profession of faith in the text. Faith is a way of apprehending not only the unseeable but also that which transcends our reason. The words are well chosen — he cannot comprehend it (height), but he can apprehend it. This use of language is similar to the that of the Victorian debate whether a person could conceive of higher dimensions even if he could not reason about them. In The Kernel and the Husk, Abbott writes: “Absolute reality cannot be comprehended by men, and can only be apprehended as God, or in God by a combination of desire and imagination, to which we give the name of faith.” high-ness. In old English, highness meant the condition of being high. Of course, this condition is now described as height, and ‘highness’ has become a title of honor given to royalty — part of our geometrization of hierarchical relations. true dimension. A Square understands that color and brightness may be regarded as dimensions, but here he intends a ‘true dimension,’ a measure of spatial extent. Would not you have him locked up?. This is not in agreement with actual scenario. In Flatland, the disciple is locked up rather than the visitor. The challenge formulation is reminiscent of the debates over the existence of the soul, which extends, if it extends (exists) at all, in a direction we do not recognize even when we see it. family likeness. The inhabitants of spaces of every dimension all have their respective ‘dimensional prejudice’ — their belief that what is perceived defines the limits of all that exists. In this respect they are like the prisoners in Plato’s cave, which represents the limited world of sense perception. One touch. The quotation, which the Square included in his letter from Flatland State Prison, is from Shakespeare’s Troilus and Cressida, Act 3, Scene 3. The phrase means that in one respect all mankind is alike. In Shakespeare’s play, the common trait was the tendency to “praise new-born gawds.” As we noted above, the common trait of humanity in all dimensions is their dimensional prejudice. In a review of Abbott’s Shakespearian Grammar (The Nation, 16 Feb 1871), the phrase, ‘one touch of nature’ was cited as an example of the change in English pronunciation from Shakespeare’s English to that of the Victorians. In three hundred years, every syllable has changed its sound: In Shakespeare’s time, ‘One’ sounded very much like ‘own’; ou in touch 6 had the same sound as in ‘you’ or ‘youth’; ‘of’ had the Yankee short sound of o in ‘bone’ or ‘coat’; while ‘nature’ was pronounced as in French except with the accent on the second syllable. The footnote to the quotation refers to an additional dialogue between the Square and the Sphere that was inserted into sections 16 and 19. The American editions did not include this new dialogue, nor did they correct several miscellaneous errors in the first edition. The position of the author, as expressed in the words of the Sphere in section 18, is unmistakable, and this introduction only reinforces it. The qualities associated with women in Flatland are to be prized more than the (extrapolated) rational stance of the circles. No such justification is given for his revision of his opinion of the isosceles or lower classes, except a general enlightenment and perhaps a realization that he has more in common with them than with any being from a higher dimension.

second (or moral) objection. Most contemporary reviewers understood that Flatland was a satire. Two notable exceptions were the reviewers for the New York Times (“Some little sense is apparent in an appeal for a better education for women, but beyond that all the rest of Flatland is incomprehensible.”) and The Athenaeum (“The whimsical book Flatland by A Square, seems to have a purpose, but what that may be it is hard to discover.”) Since the social commentary was a too subtle for some readers, the editor uses the preface to distance himself a bit from the narrator. women-hater. It isn’t clear who ‘objected that he is a woman-hater.’ We have found no reviewer who made such an allegation, although one did say that a woman acquaintance can’t ﬁgure out what the book is about. the opinion of the Sphere. The Sphere doesn’t say that the Straight Lines are superior to Circles. In fact, he says, “It is not for me to classify human faculties according to merit.” However, he does say that the best and wisest people in Spaceland think more of the Straight Lines than of the Circles.

Historians in whose pages. Virginia Woolf observes that histories, which are typically written in terms of (male) heroes and villains, ignore contributions of women. “It is to be found in the lives of the obscure — in those almost unlit corridors of history where the figures of generations of women are so dimly, so fitfully perceived. For very little is known about women. The history of England is the history of the male line, not of the female. Of our mothers, our grandmothers, our great-grandmothers we know nothing except their names and the dates of their marriages and the number of children they bore.” [Virginia Woolf, Collected Essays, vol. II, p. 141] aristocratic. Although Abbott was a graduate of Cambridge, he was by no means aristo- 7 cratic; indeed, he was the headmaster of an independent day school. infecundity. Jann notes, “The self-defeating sterility of the circles’ imaginations is mirrored in their infecundity as a class and spells their defeat in the age to come.” [1, p. 303] Law of all worlds. The Square’s great law of all worlds is based on a statement of Francis Bacon: “... so is the wisdom of God more admirable, when nature intendeth one thing, and Providence draweth forth another, than if He communicated to particular creatures and motions the characters and impressions of His Providence.” (The Second Book of Francis Bacon of the Proficience and Advancement of Learning, Divine and Human, 1605) that which is of the highest importance but lies beyond experience.InApologia, p. 14, Abbott emphasizes that he “never intended to suggest that alleged historical facts belong to the province that ‘lies beyond experience.’ The phrase referred to the ultimate cause of things.” He hopes that Flatland will bring us closer to God by opening our minds to new possibilities and to fresh inferences from old truths. At the same time he disassociates himself from those who taught that God and other spirits exist in the fourth dimension. The English philosopher, Henry More (1614–1687) was one of the first to write that spirits have four dimensions. [4, pp. 52–53]

References.

1] Rosemary Jann. “Abbott’s Flatland: Scientiﬁc Imagination and ‘Natural Christianity.’ ” Victorian Studies 28(1985), 473 – 490. 2] Raymond L. Kilgour. Messrs. Roberts Brothers. University of Michigan Press, 1952. 3] Barbara A. Mowat. “Edwin Abbott Abbott and Shakespeare.” Unpublished manuscript. 4] Rudy Rucker. The Fourth Dimension. Houghton Miﬄin, 1984. 5] “The Struggle for an International Copyright Law.” The Cambridge History of English andAmericanLiterature. [http://www.bartleby.com/228/0615.html]