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by Robert K. J. Killheffer

The Annotated Flatland by Edwin A. Abbott, introduction and notes by Ian Stewart, Perseus Publishing, 2002, 240 pages, $30.00

Schild's Ladder by Greg Egan, Eos, 2002, 342 pages, $25.95

"He who still sees the stars as 'up' does not perceive with the eye of truth."
—Friedrich Nietzsche

Now and then it pays to wonder what "science" signifies in the term science fiction. If it were called carpentry fiction, we'd expect to read about the work of carpenters, but science fiction clearly isn't restricted to recounting the labors of scientists. Most sf pays no attention to what actual scientists do, today or in their imagined futures. Some sf takes its inspiration from scientific concepts, or indulges in informative lectures on scientific topics, but this is not what gives the genre its name. We all recognize works with little or no explicit scientific content nonetheless as sf think of Philip K. Dick, R. A. Lafferty, Joanna Russ.

If the science in sf's name means anything and I think it does it's something more figurative, something that connects it to science on a less literal level. Science fiction is fiction that behaves like science it adopts the same viewpoint, and produces a similar emotional effect. Science (done right) questions received wisdom and re-examines common assumptions. It subjects opinions to testing against observed facts, and in the process it makes the familiar seem strange.

From the scientific perspective, little that we know is as it seems. The stars are not mere points of light, they are huge balls of fiery gas, unimaginably distant Olympian campfires around which other worlds might huddle. The ground beneath our feet is not firm, but constantly in motion, though we do not feel it. The tabletop is not solid, but composed of the tiniest particles, which are themselves mostly space: what seems solid is really hole-riddled, more empty than full. Science and science fiction both believe that this process of estrangement offers a path to enlightenment that the altered reality it offers comes closer to the truth, and from that truth we might take a greater wisdom.

This view of sf emerges clearly in Edwin A. Abbott's beloved Flatland, originally published in 1884 and since reissued in a variety of editions and several other languages. Mathematician and popular science writer Ian Stewart has now produced the first annotated version, on the heels of his own sequel to Abbott, Flatterland (2001).1

Stewart's notes bring a welcome new level to Abbott's classic. They help us to know the author and to understand the gestation of the book. They flesh out the mathematical concepts in the text, as they existed before and during Abbott's time, and as they have evolved in the years since. Perhaps most valuably, they place Abbott and his book solidly in their social and cultural context. Stewart reveals connections to notable figures and events of the time, from the mathematician George Boole to Karl Marx, and traces ideas about extra dimensions especially the fourth as they may have influenced or been influenced by Abbott's book.

Abbott himself was no sf writer, not as a vocation. He was an Anglican priest and spent most of his professional career as headmaster of the City of London School. He wrote several dozen other books, but none like Flatland: mostly theology and devotional literature, and English and Latin grammar. Only Flatland continues to attract readers.

And it deserves them. It's a charming bit of Victorian whimsy with undercurrents of a more serious nature, a literary curiosity that leaves a surprisingly firm impression on the mind. The diction of the schoolmaster is perfectly suited to its mixture of studious exactitude and playful fancy: "Windows there are none in our houses: for the light comes to us alike in our houses and out of them, by day and by night, equally at all times and in all places, whence we know not."

Flatland is a mathematical fantasy, set in a world of two dimensions, a plane, upon (or, more correctly, in) which exists a civilization of polygons triangles, squares, pentagons, etc. not accidentally reminiscent of British Victorian society in its basic structures and attitudes. We learn of this world through the writings of one of its citizens, A. Square2, who receives a glimpse of our own world "Spaceland" through the intercession of a visitor, the Sphere.

The first part of Flatland "This World" introduces the place and its inhabitants. A. Square explains how things appear to two-dimensional sight (everything is straight lines), and how the Flatlanders nevertheless manage to recognize each other and their different shapes. He describes the environment (a slight "gravitational" attraction exists in one direction, which they term South, and so allows them to orient themselves), the layout of Flatland houses, family life, and class divisions based on shape (or, more properly, on number and sharpness of angles). We learn little of Flatland history, but A. Square does recount a period when Flatlanders experimented with the use of color painted on their sides to assist in recognition, and how this innovation produced social upheaval and was banned.

Abbott was a progressive thinker, and this section of Flatland is thick with social satire. Abbott advocated improved education for women (which was sorely limited in his time, particularly in the realm of mathematics), and the place of women in Flatland forms the center of his ironic critique. (In his introduction and notes, Stewart tells us that many of Abbott's readers, though sympathetic to his views, missed the irony in his tone, and complained about the portrait of women in the first edition. The second edition, on which Stewart's text is based, includes a preface in which Abbott tries to clear this up.)

In Flatland, women are lines or, rather, polygons of only two sides. Since social status grows in proportion to the number of a citizen's sides, and estimations of intelligence and moral fortitude vary likewise, Flatland's women are consigned to the lowest level on all scales, below even the "Soldiers and Lowest Classes of Workmen," who are isoceles triangles. Abbott's satire, like that of Swift and others before him, trades on outrageous exaggeration. Women are "wholly devoid of brain-power, and have neither reflection, judgment nor forethought, and hardly any memory." It says something unflattering about the actual opinions of women in Abbott's time that anyone could have misunderstood his intent.

Abbott isn't content simply to spoof Victorian chauvinism, he also slyly suggests its psychological underpinnings. Sharp angles are what make the isoceles triangles suitable as soldiers, and "if a Soldier is a wedge, a Woman is a needle." Her two points make her deadly: "what can it be to run against a Woman, except absolute and immediate destruction?" And so in Flatland women are subject to heavy restrictions in order to minimize their danger to the men they have their own doors into buildings, and they are required to emit a "Peace-cry" at all times to announce their locations. In Flatland, discrimination against women stems directly from men's fear of them. Abbott even introduces a little pre-Freudian analysis into the equation. On one end women have an eye and mouth; it's the other, the "nether end," that is most likely to wound a man accidentally, and so women's nether end is the focus of men's fears, possessed of "a death-dealing but inaudible sting."

Flatland remains interesting so many years after its original publication in part because many of the social concerns of Abbott's period remain issues today. The society of Flatland raises questions of nature versus nurture in criminal behavior, the clash of high and low culture in the arts, class hierarchy and elitism, even domestic violence. "I have actually known a case," A. Square mentions, "where a Woman has exterminated her whole household, and half an hour afterwards, when her rage was over and the fragments swept away, has asked what has become of her husband and her children." Flatland's social relevance is hardly confined to its historical period.

The second part of Flatland "Other Worlds" concerns A. Square's encounters with higher and lower dimensions. First he visits a world of one dimension, "Lineland," in a dream. He tries to explain to one of its inhabitants the limited nature of his world, and the higher truth of Flatland. But the Linelander will have none of it, considering A. Square's ideas nonsense. "Besotted Being!" A. Square says finally in exasperation. "You think yourself the perfection of existence . . . . You profess to see, whereas you can see nothing but a Point!"

Abbott was a teacher and is not overly subtle. The Lineland episode serves to prepare the reader for A. Square's own reaction when the Sphere visits him in turn from the land of three dimensions. His objections mimic the Linelander's almost exactly. Words having failed, the Sphere resorts to show and tell: he tears A. Square out of his plane and moves him into Spaceland itself.

The first section made the familiar strange by showing us Victorian society reproduced in a two-dimensional world of sentient geometrical shapes. Now A. Square himself experiences the cognitive dislocation of a new perspective most literally and his response is characteristic of reactions to scientific revelation: "Either this is madness," he says, "or it is Hell." But quickly he changes his mind and embraces the Sphere's gift of transcendent knowledge. When he returns to Flatland, his preaching on the existence and significance of higher dimensions gets him thrown into prison.

Abbott was a churchman, an academic, and a mathematician, and in A. Square's story the strands of religion and science become entwined inextricably. In his dedication, Abbott describes A. Square's experience in unmistakeably religious terms he is "Initiated into the Mysteries," and the world of three dimensions is "that Celestial Region." But it's a spiritual achievement founded on scientific insight, clearly intended to suggest a similar process for his readers. Flatland perfectly encapsulates one of the common themes of sf, the ennobling possibilities of the scientific perspective, the power of science to free us from "our respective Dimensional prejudices" to lift us, as the Sphere lifted A. Square, into a position of greater wisdom.

* * *

Greg Egan's latest novel, Schild's Ladder, shares Abbott's perspective-altering agenda, and it ventures into areas much more challenging to twenty-first-century sensibilities. Egan's novels tend to be so full of ideas that they defy simple summary, and I doubt I can convey the intellectual richness of the book here. I can only hope that, if my description inspires any curiosity, you'll go and read the book for yourself.

More than twenty thousand years from now, humanity has spread itself to thousands of other worlds, and through a variety of means has extended life spans so that they are practically unlimited. Light speed has not been beaten, however, so travel between planets leaves the traveller hopelessly out of chronological synch with the planet she left. Most people never leave their home planets, and those who do form an entirely different sort of community, running across each other here and there around the cosmos, leaping past whole eras of planetary history with each trip. Their journeys take place at light speed, with the traveller in the form of an encoded transmission. Upon arrival, a body may be created not always like the one left behind but many people now live entirely bodiless in the infosphere.

Egan introduces us to his imaginary world in time-honored manner of sf, with an immersion in strangeness punctuated by just enough comprehensibility for us to hang our grappling hooks on while we get oriented. Egan's especially good at this sort of thing, and he packs a lot into sentences like this: "From the moment she'd arrived, as a stream of ultraviolet pulses with a header requesting embodiment on almost any terms, the Mimosans had been polite and accommodating."

In the opening section of Schild's Ladder something of a long prologue the physicist Cass has travelled to Mimosa Station in hope that the station's resident scientists will agree to run an experiment she has proposed. Cass wants to create a tiny bubble of spacetime with different rules from our own. Her calculations indicate that it should last for only six trillionths of a second, but something goes wrong. The bubble grows uncontrollably, expanding at half the speed of light, and devouring converting normal spacetime and everything in it as it goes.

The novel proper opens six hundred years later, after the Mimosan novo-vacuum has obliterated two thousand populated star systems. A research ship, the Rindler, has been positioned near the expanding border, moving away from it as fast as it grows, and here interested parties have gathered to study the bubble.

Egan doesn't adopt a typical race-to-save-the-universe scenario. The Rindler plays host to a variety of factions, principally divided into the Yielders and the Preservationists. The Yielders believe that the new spacetime has an equal right to exist, and that the only ethical approach would be (at most) to stabilize the border and prevent further expansion. The Preservationists think the survival of the old universe is the most important thing, and the only way to ensure it is to destroy the bubble. Since no one knows how to accomplish either goal, the debate remains theoretical, and both sides work together most of the time in studying the novo-vacuum, though tensions have grown by the time a new Yielder, Tchicaya, arrives on the Rindler. The issue reaches a crisis when the researchers detect a signal which implies that living creatures of some kind exist in the novo-vacuum.

Egan is as interested as Abbott in challenging the comfortable assumptions with which we surround ourselves. No one here has a gender or even a permanent set of sex organs (though Egan uses gendered pronouns, perhaps to let the narrative flow smoothly we don't have a good neutral alternative, so deeply engrained is the gender assumption). Under some conditions, when the emotional resonance is right, two people may spontaneously develop sex organs uniquely suited to each other different every time and if the bond fades, so do the organs. What's most striking about Egan's scheme is how offhandedly he treats the idea; it's not the center of the story, but it does mean that a whole category of interpersonal issues we take for granted doesn't exist in Egan's world.

He handles most of the cultural differences of this future with a similar casualness that tends to heighten their strangeness. One character, normally acorporeal, describes his childhood this way: "'My earliest memories are of CP4 that's a Kahler manifold that looks locally like a vector space with four complex dimensions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible.'" Courtship in his society involves giving creative intellectual presents, such as mathematical theorems. "'When I was ten years old, all I gave my sweetheart was a pair of projections that turned the group of rotations in four dimensions into principal bundles over the three-sphere. Ancient constructions, though I did rediscover them for myself.'" There's a bit of inescapable humor in moments like this, but that's not how Egan plays them. He presents them as normal making our more limited ideas appear the oddity.

Schild's Ladder is a brief book, and we only get brief glimpses of what must be complex social and cultural patterns in this world. We see some of Mimosa, and some of the Rindler, and some of life on one of the settled worlds, but just enough to sense of the general shape of things. Out of these hints, Egan constructs a society that looks very strange, but feels recognizably human. As in Flatland, human nature remains the same at some level, no matter how different the setting. The debate between the Yielders and the Preservationists contains echoes of issues that divide our world tensions between development and conservation, and between intercultural respect and universal values.

One of Egan's great achievements here is his portrayal of human beings much saner and stabler than we know them, without losing their individuality and interest, or their passion. The co-existence of such radically opposed viewpoints on the Rindler, in the midst of a disaster of cosmic scale, can scarcely be imagined in our world. Egan's characters display a wholly unfamiliar level of rationality under the most trying circumstances. "The fate of the vacuum had to be decided on its merits, not treated as a surrogate through which its creators could be condemned or absolved," thinks Tchicaya, summing up the majority opinion.

And Egan presents a credible sense of optimism, that the future of humanity might hold more happiness and less conflict than our history thus far has known and that it might achieve that state through the application of scientific knowledge. Encountering this attitude in Schild's Ladder reminds one just how scarce it has become, in sf or out.

At one point, a Preservationist attacks Tchicaya for his interest in saving and even exploring the novo-vacuum. "What do you think you're going to find in there?" she asks scornfully. "Some great shining light of transcendence?"

Tchicaya calmly dismisses the suggestion, and Egan launches a brief tirade on the subject. Transcendence, he says, "was a content-free word left over from religion . . . . It was probably an appealing notion if you were so lazy that you'd never actually learned anything about the universe you inhabited, and couldn't quite conceive of putting in the effort to do so . . . ."

But I think Egan protests a little too strongly. Transcendence is exactly what Schild's Ladder offers, in the same manner as Flatland: the transcendence of our own constraints, our familiar boundaries, the limits and viewpoints that entrap us, our "Dimensional prejudices." It's good to see that the notion still lives, a century and more after poor A. Square landed in prison, a prophet, like them all, unloved in his own land.


1 There seems to be a mini-revival of Flatland in effect. Just as this column was going to press, we received Spaceland, a novel by Rudy Rucker that attempts to do for the fourth dimension what Flatland did for the third.

2 Stewart doesn't mention the possibility, but the name of Abbott's protagonist seems to contain an echo of his own. Through a peculiarity of family history, Abbott's middle name was Abbott also; he was Edwin Abbott Abbott, or (in the mathematical terminology he enjoyed) Edwin Abbott-squared. His initials were E. A. A., or E. A-squared.

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