A Sphere’s Progress: Flatland as a Social-Ethical Space

 

Several editions of Edwin Abbott’s short satire Flatland: A Romance of Many Dimensions have appeared in the nearly 120 years since its original publication. Through introductions, forwards and occasional annotations, these editions are helpful to varying degrees in illuminating the full measure of Abbott’s humorous and also very philosophical book.[2] There are now a number of sequels in print “updating” the lineage of the self-described “Flatland Prometheus,” or using A Square’s prison notebook as a stepping-off point for further space-time adventures.[3] As many of the commentaries, analyses and follow-ups to Abbott’s text have observed, the original indeed moves within “Many Dimensions,” containing both an intellectually stimulating and provocative challenge to the reader’s mathematical and spatial assumptions, as well as a stinging satirical criticism of Victorian social attitudes and practices.

And yet, most commentaries and analyses of the novel gloss over the importance of its social and ethical dimensions. The novel is usually presented to readers as having mathematics and the conceptualization of the physical dimensions of space as its chief concerns.[4] But, this “mathematical fantasy,” typically introduced as inviting its readers “to consider the outrageous possibility of four dimensions and more,” at least equally presents a powerful satirical challenge to the broader intellectual pretensions and social conventions of its day, and ours.[5] Abbott’s sharp critique of Victorian arrogance and the scientism that supported it is often noted as an afterthought in editions of and commentaries on the novel.

While I think the claim that the social-ethical space of Flatland is often not clearly perceived would be hard to refute on its own merits, I think a stronger claim is warranted—that the social and ethical dimensions which define Flatland figuratively as a kind of social-ethical space are really the primary concerns of the novel, and reflect its central and enduring message to the reader. Flatland is an imaginative story focused on the complexities of conceptualizing spatial dimension. But its most controversial and difficult messages appear here as satire, and these are messages to a privileged audience in 1884 about the pervasiveness of sexism, racism and elitism and the intellectual laziness, complacency, arrogance and pseudo-scientific dogmatism that supported them. The choice to convey all this satirically, (and anonymously in the first edition), may mark Abbott’s own reticence and sense of Victorian and clerical propriety.[6] It may also suggest that he regarded a more direct approach to such subjects as likely to be deflected, dismissed or denied by the readers he wanted to reach. Whichever of these, or other, explanation may best account for the novel’s satire, it is nonetheless true that there are several dimensions of enduring philosophical interest packed into it.

No one, I think, should conclude that the mathematical and spatial dimensions of Flatland are unimportant. The centerpiece of the novel is A Square’s journey of discovery as the result of which he overcomes some of the epistemic limitations suffered as a Flatlander, liberating him to conceptualize reality in previously inconceivable ways. But I think A Square has made only a first, although terribly important step in coming to realize that things in general—and even space itself, will not always be what they seem, and may be extremely different from what they appear to be. In making such progress it is hoped that the Victorian reader, and the “Inhabitants of Space in General” to whom the narrator dedicates his manuscript, “may aspire yet higher and higher,” furthering our intellectual and moral betterment.

As noted above, recognition that the novel operates on both mathematico-physical and social levels is widespread, but how these levels are related, and how they relate to the story are typically glossed over if not ignored entirely. Interpretations of the novel that integrate these two levels without losing sight of the importance of its social and ethical concerns would advance understanding and appreciation of this philosophically and critically rich text. In what follows, I share some observations on the novel toward such a project of interpretation.

 

ii. Difference and Danger

 

The author of fifty books, Abbott was a classicist, an Anglican minister and theological writer, and a scholarly expert on Shakespeare.[7] To all accounts, he was an enthusiastic teacher and Headmaster at the City of London School during the years 1865-1889.[8] Research by Charles Howard Hinton on four dimensional space had caught Abbott’s attention in the 1880’s, at which time, “[t]he fourth dimension was very much ‘in the air.’” As Ian Stewart notes, “interest began among scientists and mathematicians, but their excitement transmitted itself to the general public.”[9] Hinton’s work to assist this transmission clearly reached Abbott. A mathematician and effective popularizer, Hinton also happened to be a colleague of Abbott’s good friend Howard Candler—the infamous “H.C.” mentioned in the Dedication of Flatland, at a nearby school.

Hinton’s work and the general air of interest in the topic of four dimensional space undoubtedly were important in framing the context for Abbott’s novel. But that the directly mathematical and physical issues they raised for the author represent the most important part of his central message in the book is a separate conclusion it would be wrong to draw. In fact, the larger philosophical dimensions of the novel, whose central conceit is a two-dimensional universe existing entirely within a plane, are immediately suggested in the map illustrated by Abbott for the frontispiece complete with Shakespearean epigrams.

The first two of these involve a famous exchange between Horatio and Hamlet from the beginning of Hamlet. Horatio expresses the shock and fear of encountering the voice of the King’s ghost seeming to come from nowhere, off-stage, out of bounds: “O day and night, but this is wondrous strange.”[10] Hamlet’s reply makes ready to take on the challenge of the unknown: “And therefore as a stranger give it welcome.”[11] The unusual and strange, the voice from the margins, Hamlet suggests to the stunned and terrified Horatio, makes a legitimate demand of us. But Horatio’s fear of the unknown and different stems from the narrowness and certainty of his prior convictions about what ‘reality’ and ‘truth’ mean. Our fear of the unknown and of ‘the world beyond’ reflects an irrational reaction that has practical and ethical consequences for our actions and choices.[12]

Hamlet’s next lines, which Abbott is certainly thinking of but does not quote, are among the best-known lines from the play. In alluding to them, Abbott allows Shakespeare to introduce the major philosophical motif of the novel in Hamlet’s famous words: “There are more things in heaven and earth Horatio, than are dreamt of in your philosophy.”[13] What we can know of the world is hemmed in and limited by our worldliness. The limits of perception do not exhaust the limits of reality. In this sense, our collected assumptions are as contingent as any set of historical and temporal facts—merely “such stuff as dreams are made on.”[14]

These quotations clue us to Abbott’s intentions in framing the novel, and alert the reader to the importance of its philosophical and figurative dimensions. This helps explain the otherwise enigmatic quotation from Titus Andronicus that also appears on the title page. As the title character is forced to observe the difficulty of making his own words match his changed reality, he utters in frustration, “Fie, fie, how franticly I square my talk!”[15]

Even without the play’s context provided, the sense of working hard to make one’s words “square” with, or correspond to the world of perception draws attention to an assumption that is deeply embedded in experience, but is also certainly wrong—that the world really somehow is made up of only the kinds of things we have names or labels for. We naturally are puzzled and confused by claims that something is real or exists for which we haven’t got a name; we tend to approach things for which we do not have well-established categories with suspicion and confusion; we tend to be fearful of what is strange and different. This is true for the most obvious matters of physical fact, but is especially true for social and ethical ‘truths,’ which have a more patently subjective and conventional dimensions but which characteristically also can take on the aura of self-evidence, common sense, and “natural law,” as they notoriously do for the Flatlanders.[16] These are the central philosophical issues that frame the novel.

A Square’s Dedication bears out the notion that Abbott is writing in a philosophical vein of broad intellectual and social import. He hopes that sharing his story will contribute to “the Enlargement of the Imagination,” and the development of “Modesty” among Spaceland readers.(xxi) He thus guides attention away from the reform of Flatland, toward the expansion of the reader’s imagination and the diminution of our hubris. These are clearly our moral tasks and challenges, not his, although in sharing his story of overcoming the difficulty of conceptualizing the third spatial dimension, he provides us with encouragement and preparation. It is the reader’s intellectual and moral prospects to which the work is dedicated.

If the central contribution of A Square is a parable about how the pursuit of truth is conditioned by the limits of perception, this supports the idea that imagination and modesty are required if we ever approach truth of any kind. It isn’t surprising then that Abbott would choose to express this message through satire to people he regarded as most needing to hear it. As the great majority of Abbott’s writing seems to have been explicitly didactic, one wonders if it had occurred to him that a frontal attack on Victorian morality would be just that much easier for the reader to deflect or dismiss.[17] This would tend to be true to exactly the extent they were characterized by the hubris and dogmatism the Dedication focuses the reader’s attention on in giving the highest status to the virtues of imagination and modesty.

Additional support for the thesis that the novel’s social and ethical dimensions are paramount comes from the Preface Abbott added to the second edition of the book. Speaking as editor of A Square’s manuscript, Abbott responds to two “objections” on behalf of his author. The first of these relates to the difficulty involved in conceptualizing dimensions ‘downward.’ As persons for whom three-dimensions are natural, to move from three to two, we seem to have to imagine that a line in Flatland takes up no space, or else that it takes up three-dimensional space. In other words, since we conceptualize space as three-dimensional, it is hard for us to ‘look’ mentally at a plane without ‘seeing’ what we ‘know’ to be “height.” In ‘seeing’ Flatland as a Flatlander would, however, we are asked to bracket or block this out, just as a visitor from a fourth dimension, upon entering our world, would have to negate his or her knowledge of the fourth crypto-dimension in recognizing our inability to perceive or understand what he or she takes for granted without strenuously exercising our imaginations. Within the plane of Flatland, beings take up the entire range of what would constitute the up-down axis in Spaceland. For the Flatlander, “up” and “down” are just not places one can go to, or directions one can move.

Abbott thus reinforces the challenge of moving imaginatively in both directions, both of which are very hard, and one of which seems to be easy. Either way, the perceptual field we take for granted will not work. This is what A Square will encounter in attempting to grasp, in his major challenge in the book, a third dimension he has never had to conceptualize before.[18] But here, as the novel begins, Abbott stresses that the reader who doesn’t appreciate the severity of the essential philosophical predicament at its center threatens to miss the point of the book:

Suppose a person of the Fourth Dimension, condescending to visit you, were to say, “Whenever you open your eyes, you see a Plane (which is of two dimensions) and you infer a Solid (which is of Three); but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true dimension, although I cannot point out to you its direction, nor can you possibly measure it.” What would you say to such a visitor? Would you not have him locked up? (3)[19]

But bad physics is not generally regarded in itself as worthy of much more than poor grades or tenure problems. It is a crime in Flatland, but not because it is physically dangerous for Flatlanders to imagine or infer the existence of a third dimension, or for anything at all that has to do with its physics, but because of Flatland’s social and political reality.[20]

That challenging reality-as-we-are-used-to-perceiving-it can be a crime presupposes a society that is fundamentally oppressive and whose rule are dependent on deception. This is why in Flatland and similar places the new and different has to be suppressed as socially and politically dangerous. Abbott is looking in the face of his reader as he poses to us at the outset of the book the two deeply moral questions quoted above, concerning our response to the strange and the Stranger—“What would you say to such a visitor? Would you not have him locked up?” The Preface remains effective for the reader of today in part because we typically nod in agreement as we read it, just as many Victorian readers did, confirming the extent of our shared comfort with the notion that those whose ideas differ from our own should be imprisoned.

This observation draws attention to a further question taken up by Abbott’s Preface, which also sheds light on Flatland’s social and ethical dimensions. This is, why A Square should not have been more generally enlightened as the result of the journey of discovery recounted in the narrative itself. As he begins his memoir, A Square has seen the truth of three dimensions, and has painfully had to enlarge his view of reality in order to conceptualize what he can no longer doubt or repress.[21] He has seen the truth, and it has set him free—which of course means he must now be imprisoned by the ‘well-adjusted’ members of Flatland society to whom the truth of a third dimension can only appear wrong-headed and socially dangerous.[22]

Although A Square knows himself to be wrongfully imprisoned by leaders who are liars and frauds, nonetheless, his manuscript recounts Flatland social and political history and class structure as if he remains a true believer in the legitimacy of its authorities and basic doctrines. But why, if A Square’s story of challenge and resolution is really the heart of the novel, shouldn’t Abbott want to show that enlarging his imagination about reality and space carries over somehow in other essentially positive, if more vague intellectual and moral ways, as well? A Square’s challenge to overcome perceptual prejudices with regard to the structure of space and reality is resolved for the reader by the second paragraph of the novel. Unresolved is the more difficult and important challenge with which A Square doesn’t directly engage, which has to do with a type of progress he doesn’t seem to make, concerning problems toward which he remains at the end of the novel as more-or-less blind as any other Flatlander.[23] I think this may indicate that the less direct set of challenges and concerns are the ones Abbott wishes most to draw our attention to: He holds up enough of a mirror to make us consider the real possibility that our own very obvious and common-sensical world of necessary, normal and natural truths is also perhaps just as narrow and perspectival, limited and restrictive, barbarous and oppressive as he one we see in Flatland.

But it is probably true that the Victorian reader was more likely to sympathize with A Square as we see him here, rather than were he to directly call the values, attitudes and practices of patriarchy and imperialism into question. The every-day reader of Abbott’s time—not to say of ours as well, would be more likely to relate to the well-meaning, well-adjusted, resistant to change, unremarkable solid citizen who has had something remarkable thrust upon him that we see in the novel than to a rebel who has perhaps followed out all of the logical implications of what he has seen, and drawn social and political conclusions  from it. That Abbott does not have A Square end his prison narrative by denouncing British rule in India and calling for universal suffrage perhaps made it more likely that the Victorian reader would not feel attacked and defensive, and would maybe come away more willing to think about alternatives that might otherwise have just remained “inconceivable.”

In support of this reading we can further consider the implausibility of the main alternative: that the elaborate moral landscape of Flatland is simply background scenery, providing comic relief or a stable element against which A Square’s epistemological growth can be measured. This would seem odd, however, coming from Abbott, uncontroversially depicted as a tireless educator, theological writer and supporter of social reform, in giving an uncharacteristically cynical cast to his labors.[24] It seems unlikely that Abbott should want to say to his reader that the ways we might conceive of physical space may be “broader and wider” than anything we may have previously imagined, but that sexist, classist, racist social space simply is and must remain as the most complacent and “immodest” among us have always suggested, an irremediable human blind-spot.[25]

As it is, the Preface draws the reader’s attention directly to the social dimensions of the story, and switches the focus away from the question of its author’s moral progress to the reader’s ability and willingness to think effectively about his or her own world and history:

While doing justice to the intellectual power with which a few Circles have for many generations maintained their supremacy over immense multitudes of their countrymen, [A Square now] believes that the facts of Flatland, speaking for themselves without comment on his part, declare that Revolutions cannot always be suppressed by slaughter….For the rest, …he hopes that, taken as a whole, his work may prove suggestive as well as amusing, to those Spacelanders of moderate and modest minds who—speaking of that which is of the highest importance, but lies beyond experience—decline to say on the one hand, ‘This can never be,’ and on the other hand, ‘It must needs be thus, and we know all about it.’ (4)

 

 

iii. A Sphere’s Progress

 

The mental visualization of ever higher spatial dimensions, although the central conceit of the novel as fantasy, is only the central conceit of the novel as satirical critique and social exhortation. I think there are many aspects and events of the novel that could be mentioned which only become clearer, richer, and more poignant in connection with this thesis. For purposes of brevity and focus here, I turn to the chapters of climax where I think the thesis is strongly borne out.

On the most obvious level, the novel’s central feature is the epistemic epiphany recounted by its narrator. But in stepping aside from that narrative and looking at its movement from an angle slightly oblique, something else emerges as the locus in the central chapters of his transition. Tracking what occurs to the Sphere here suggests that his progress can be considered the crux or even the climax of the novel in terms of its broader philosophical import.

In the dream-vision of Chapters 13-14 with which Part II begins, A Square stands in place of the reader. We have in Part I been imagining a lower-dimensional world with the assistance of his narrative vision. In doing so, it has been necessary to become comfortable with the awkwardness of a kind of reverse-epiphany. As Spacelanders, we believe ourselves to already be well-informed about lesser-dimensional matters, and in thinking about Flatland, we naturally tend to think we see it with greater clarity than its inhabitants do, since any n-dimensional reality must already contain a reality of n — 1 dimensions.

But, we tend to forget that we do not cease being three-dimensional creatures when imaginatively or otherwise intervening in a universe of 3 — 1 dimensions. The ease with which we seem to move ‘downward’ is thus extremely deceptive, and our confidence in thinking we can know what things would really be like in such a space is badly misplaced. In fact, we can never understand a two-dimensional universe as a two-dimensional-universer would, so long as we are three-dimensional-universers. In reading Part I, our task has been to imagine two-dimensions independent of the context of three. Our difficulty in doing this is that of imagining a two-dimensional universe as itself complete, and not merely as deficient in relation to us.

Remembering this helps clarify the importance of what happens as Part II of the novel begins, and how it is related to Part I. A Square is recounting an event in which it is made clear to us that he has not mastered this difficulty. Dreaming a visit to a one-dimensional world, he interprets its differences as deficiencies in relation to himself and his world. His attempts to convince the King of Lineland of this verbally fail, and he then resorts to actions.(71-4) But, his movements flanking the line of Lineland are interpreted by the King merely as annoying magical deceptions. From the King’s standpoint, rational explanations take for granted the assumptions of one-dimensional space and experience. A Square is a provocative magician throwing his voice in order to make fun of the King and his subjects.

The King responds to all this in the same way we saw the Flatlanders respond to Color, which briefly added a dimension to their experience, as recounted in Chapters 8-10, but which ended horribly. Although the disaster of misunderstanding in Chapter 14 looms only in a dream, it links those earlier events to what it foreshadows that is soon to occur, and gives us insight into what the author principally wants us to recognize as the story develops. The best A Square can do intellectually at this juncture is to insist upon his own epistemic and moral superiority:

‘Besotted Being! [A Square finally exclaims to the King of Lineland] You think yourself the perfection of existence, while you are in reality the most imperfect and imbecile. You profess to see, whereas you can see nothing but a Point!…Why waste more words? Suffice it that I am the completion of your incomplete self. You are a Line, but I am a Line of Lines, called in my country a Square: and even I, infinitely superior though I am to you, am of little account among the great nobles of Flatland, whence I have come to visit you, in the hope of enlightening your ignorance.’ (76)

This utterly hypocritical diatribe exposes the assumptions A Square makes as a member of a perceptual universe in which two-dimensionality is taken for granted and, imagining anything else is regarded as a crime.[26] He also belongs, as the first part of the novel made indelibly clear, to a rigidly class-organized social universe in which women, workers, and “Irregulars” are regarded as naturally inferior, incomplete and deficient persons. The speech tightens the connection between these aspects of A Square’s intellectual life in a concentrated indictment of the social and political attitudes and practices of patriarchy and imperialism.

A Square is still very much a well-adjusted “square” Flatlander who regards the most basic and obvious truths of the physical world as inseparable from the beliefs that organize his social existence. His outburst here, just as he assumes the standpoint of the reader, highlights his unwillingness to question, bracket, screen or reconsider his assumptions about space and society even in the face of something “wondrous strange” and different. Abbott thus subtly asks his reader to check that we are not reading ‘downward’ to Flatland in the same way A Square ‘reads’ the lower-dimensional reality of Lineland, as a confirmation of our own arrogant and uncritical assumptions about physics and social life according to which the different is merely an earlier stage in a larger progressive development toward Ourselves and Ourways. If we look at Flatland as merely an incomplete version of our own physical and social space, populated with persons who, in contrast with ourselves, are simply ignorant about what space and social life are really like, (which of course we have since figured out and gotten right), then we should go back and re-read Part I before going any further.

But the dream of Chapters 13-14 plays a further important role in advancing the story. A Square is visited by what will turn out to be a Sphere from the Third Dimension, and is as puzzled and fearful at its manifestations as the King of Lineland had been at A Square’s sudden appearance in the dream. The Sphere refers to this parallel directly, in attempting to convince A Square of the reality of three dimensions:

[D]o you not remember, I say, how, when you entered the realm of Lineland, you were compelled to manifest yourself to the King, not as a Square, but as a Line, because that Linear Realm had not Dimensions enough to represent the whole of you, but only a slice or section of you? In precisely the same way, your country of Two Dimensions is not spacious enough to represent me, a being of Three, but only can exhibit a slice or section of me, which is what you call a Circle.(85-6)

But A Square is not compelled by these, or by any other words of the Sphere, who nonetheless patiently tries to help him infer the possibility of a three-dimensional sphereness that would explain the strange apparitions he sees.[27] At length, he is not convinced until he travels to Spaceland with the Sphere, where the sight of objects in three dimensions overwhelms him.(95) 

No sooner does A Square come to recognize the truth of the third dimension, however, then he sets upon the Sphere to show him the mysteries of four, five, six and further dimensions. He demands to continue the “divine” pursuit of knowledge to the “higher, purer region,…some yet more spacious Space, some more dimensionable Dimensionality,” he is sure must exist beyond the highest frontiers.(101-2) A Square believes he has in some sense broken through to a level of divinity.

The Sphere’s reaction to this equation of divinity with knowledge tells us something of the depth of Abbott’s views, and of their connection to the broader intellectual and social sensibilities of the novel.[28] The Sphere—standing in for humans as the representative three-dimensional figure of the book, distances himself from A Square’s identification of knowledge with divinity on ethical and humanistic grounds. If “divinity” were to be equated with knowledge in the way A Square has suggested, then “the pick-pocket or cut-throat” of Spaceland, for whom three-dimensionality is simple, “should be accepted by you as a God.” But, the Sphere asks, does greater, higher, broader, better knowledge in itself “make you more just, more merciful, less selfish, more loving? Not in the least. Then how does it make you more divine?”(95-6) Abbott here draws attention to the Sphere as a moral agent and stand-in for the reader in a way A Square cannot be, and isn’t.

Yet, the Sphere at this point has not been affected by his interaction with the visitor from Flatland. When A Square earnestly suggests that higher dimensionalities exist beyond the third, the Sphere arrogantly dismisses the suggestion as silly and impertinent, unintelligible nonsense—a reaction such as we would expect from a Flatlander, but also, what we would expect from any human when at first confronted with the outlandish and unusual or strange.(101-2) A Square turns up the heat, using the methods of rational argument and mathematical demonstration that the Sphere had earlier used in trying to give proof of a third dimension:

How long I should have continued I know not. In vain did the Sphere, in his voice of thunder, reiterate his command of silence, and threaten me with the direst of penalties if I persisted…[I]ndeed I was intoxicated with the recent draughts of Truth to which he had himself introduced me. However, the end was not long in coming. My words were cut short by a crash outside, and a simultaneous crash inside me, which impelled me through space with a velocity that precluded speech. Down! down! down!…return to Flatland was my doom.(105-6)

And at the end of Chapter 19, it appears as if these methods have failed with the Sphere as well.

        Returned to Flatland, A Square faces the immediate task of trying to explain to his wife where he has been, and figuring out what to do next with the dangerous knowledge of the third dimension he has gained. At length, in a dream, he is visited by the Sphere.[29] He notices that the Sphere has visibly changed, and is no longer angry. He brings A Square a parting message. Taking him on a trip, he shows A Square an almost Dickensian portent of the danger posed to humanity by itself: “I conduct thee downward to the lowest depth of existence, even to the realm of Pointland, the Abyss of No dimensions. Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf.”(108)[30]

In the scene that follows, Abbott completes the panorama of dimensional ‘levels’ or ‘lands,’ each of which has its own physical, intellectual, and moral dimensions. The image of Pointland is pathetic and disturbing in a way the other ‘lands’ could not be. Here, it is as if Abbott instructs the principal character of his own book as to the moral stakes should its message go unheeded. The description of its sole inhabitant metaphorically suits the patriarchal Victorian world in a way that rings true with the sharpest twentieth-century social and political criticisms of the era, without losing focus on what stands out for Abbott as its main epistemic and ethical failing, to appreciate the importance of difference. In the King of Pointland, Abbott confronts the pathology with which he has been concerned here, as in much of his other writing: "He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing." (108) The King or “God” of Pointland understands himself to be and is the extent of Being in that miserable place. He is completely trapped in his own “self-satisfaction” conceiving everything solely through the one and only experience of himself, unable to overcome his own complacency.

In A Square’s dream, running parallel to Abbott’s “dream” or vision of the novel,  the Sphere has grown and changed as a result of the journey, and he offers encouragement to A Square, “stimulating me to aspire, and to teach others to aspire...He had been angered at first—he confessed—by my ambition to soar to Dimensions above the Third; but, since then, he had received fresh insight, and he was not too proud to acknowledge his error to a Pupil. Then he proceeded to initiate me into mysteries yet higher than those I had witnessed…." (110) The Sphere seems central to what Abbott asks of the reader, who may also be liberated by the knowledge that what had seemed inevitable and obvious may turn out to have been false; and what seemed inconceivable and even dangerous on first examination can also advance our understanding of the world and our ability to live in it in human ways. His progress is, in this sense, the moral center of a morally interesting novel, forming a link between the relatively narrow epistemic growth of its main character and the kind of change in his readers that Abbott wanted to stimulate. Abbott urges us to see that a ‘fuller-dimensional,’ more human social and ethical existence requires opposition to the arrogance that says reality is and must be as we have conceived it, and the insistence instead that the work of reason is both necessary for a humane world, and impossible without assistance and challenge from imagination.

            A Square, finally, is an odd tragic hero who never really escapes from or returns to a normalcy he nonetheless can no longer accept, but which could never accept him anyway, for reasons he doesn’t quite understand. His awareness of the truth about space, his “mental vision,” makes him a dangerous stranger who can never be welcome in a social world where difference and imagination are simply not tolerated.(113) At length, he blurts out his whole story at a meeting of the “Local Speculative Society,” an organization dedicated to promoting ‘Civic Correctness’ in the spirit of the Stalinist Young Pioneers, or George Orwell’s “Two Minutes Hate.”[31] A Square is “at once arrested and taken before the Council.”(116) He doesn’t understand the moral and political stakes involved, nevertheless, he has enough of a concern and reverence for the Truth that he is able to realize that something is wrong about its suppression, and that this should be resisted. "Seven years have elapsed and I am still a prisoner,…[I—poor Flatland Prometheus—lie here in prison for bringing down][32] nothing to my countrymen. Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality."[33]

This is a draft of an article currently under review for publication. © Peter Amato, 2002-3.

Notes.