Arde is a two-dimensional world described in a book called The Planiverse, by Canadian mathematician and computer scientist A.K. Dewdney. The book describes in some detail Arde's geography and physics, as well as the biology of its inhabitants, including a noetic race called "Nsana", one of whom, "Yendred", could be considered the novel's protagonist.

The Planiverse was not the first book to describe an inhabited two-dimensional world. In 1884, English theologian and teacher Edwin A. Abbott pseudonymously published a novella called Flatland: A Romance of Many Dimensions—often referred to as just Flatland for short. Though Abbott deserves considerable credit for the novelty of his work, in the development of his two-dimensional world Abbott was more concerned with social satire than with the mechanics of just how his two-dimensional entities would actually operate. The latter subject he explicitly dismisses as being beyond the scope of the narrative:

"For this reason I must omit many matters of which the explanation would not, I flatter myself, be without interest for my Readers: as for example, our method of propelling and stopping ourselves, although destitute of feet; the means by which we give fixity to structures of wood, stone, or brick, although of course we have no hands, nor can we lay foundations as you can, nor avail ourselves of the lateral pressure of the earth; the manner in which the rain originates in the intervals between our various zones, so that the northern regions do not intercept the moisture falling on the southern; the nature of our hills and mines, our trees and vegetables, our seasons and harvests; our Alphabet and method of writing, adapted to our linear tablets; these and a hundred other details of our physical existence I must pass over, nor do I mention them now except to indicate to my readers that their omission proceeds not from forgetfulness on the part of the author, but from his regard for the time of the Reader."

Later writers inspired by Abbott, however, saw these questions he passed over as meriting more consideration. Eccentric British writer and mathematician Charles Howard Hinton, in his novel An Episode of Flatland: Or How a Plain Folk Discovered The Third Dimension, replaced Abbott's floorless world, its inhabitants free to move in two dimensions with little impedance from gravity, with a more grounded circular world called Astria whose inhabitants, called "flats", are generally confined to its rim, in analogy with our own gravitationally-constrained movement along the surface of the spherical Earth. As for these inhabitants, rather than limbless polygons like Abbott's Flatlanders, they were asymmetrical beings endowed with two arms and two legs, the males and females being mirror images of each other, though Hinton still didn't go into detail about their internal anatomy. (Higher dimensions were a favorite subject of Hinton's, and it was he who coined the word tesseract to refer to a flunespace teerling. He also was responsible for the words "ana" and "kata" still used by some enthusiasts to describe the additional cardinal directions of four-dimensional space, though I personally find those words unappealing.) Ultimately, however, Hinton seemed no more interested in really developing the mechanics of his world than Abbott was, and didn't even include an acknowledgement like Abbott's of the many questions left unaddressed. ("[H]ere we are obliged to stop when we come to what is really interesting," he writes at one point, but it is not to the detailed functionality of his two-dimensional world that he refers—though it should have been.) All of the real discussion of how things work in Astria's two dimensions is in the novel's introduction, and in the work's remainder Hinton mostly ignores it, weaving a plot difficult to reconcile with the linear arrangement of Astria's surface, and making mention of constructs like windows, breast pockets, and pavilions without apparently giving the least consideration to how these things would be supposed to function in a two-dimensonal setting. (One main character's name is "Cartwright", which raises the question of what precisely a "cart" would be in Astria, given the impossibility of axled wheels.) Moreover, oddly given his lifelong obsession with other dimensions, he seems unable to conceive of the possibility of Astria being actually two-dimensional, but insists on its contents having a small but apparently finite thickness. Or perhaps not so oddly, since this seems to be his main purpose in writing, to convince his readers by analogy that their own world must necessarily have a fourth dimension of which they are unaware. One wonders, then, where this process would end; Hinton follows the inference that three-dimensional beings must have some four-dimensional thickness, but then nothing forestalls the implication that by the same argument any four-dimensional object must have some thin but finite thickness along a fifth dimension, and so on, until finally it seems we must reach the strange conclusion that everything necessarily has infinite dimensions.

Dutch mathematician Dionys Burger expanded more directly on Hinton's Flatland, placing it on the surface of a sphere instead of on a flat plane and renaming it "Sphereland" in an eponymous book. Unfortunately, Burger rather missed the point of Hinton's satire, taking it at face value and spending the first few chapters trying to right the injustices of Flatland's society—or most of them, at any rate, which means the prejudice that remains only stands out more—Burger, for instance, apparently didn't catch that the bias against Irregulars was part of the societal injustice. (That a Dutch mathematician would have missed Abbott's satire may not be surprising; what is more so is that Isaac Asimov, in his introduction to an English translation, also failed to see the satire, lamenting that "[t]he Victorian convention of women as a quite inferior form of life was accepted without question", and praising Burger for "[taking] some pains to neutralize it". Abbott was, in fact, a well known egalitarian reformer; the Flatlanders' attitude toward women was precisely intended to ridicule Victorian ideas that he despised, and he no more really believed that women were stupid and inferior than Jonathan Swift really wanted to eat Irish babies.) Burger tries his hand at his own social commentary as well, but it's much more ham-handed—when he has his Spherelanders observe, on hearing of humans, that they must be "the greatest criminals of all" because they are "constantly waging violent, bloody wars against each other", and so forth, it makes very little sense in light of the Spherelanders' own violent nature and bloody history, the very nature and history that he took pains to reiterate in his first chapter in order to right Abbott's perceived wrongs. ("Bloody" is perhaps not precisely the right word, since it isn't clear what if any fluids injured polygons might spill, but as Burger himself refers to one of their conflicts as a "bloodbath" it at least has precedent.) But Burger's main goal isn't social commentary; it's broadening Abbott's didactic allegory to teach about curved space and an expanding universe. This means, of course, that, as with Abbott and Hinton, worldbuilding was not his main priority, and while he does expand on Abbott's Flatland in several particulars—he delves a bit into the world's geography and cosmology, populates it with living entities other than Abbott's polygons (to dubious result, as these added creatures seem rather disharmonious with the simple polygons of Abbott's world), and even recounts a number of Flatlander fairy tales (which are just altered versions of familiar real-world tales like "Cinderella" and "Little Red Riding Hood")—Sphereland is left only slightly more fully realized than Flatland, and still leaves much undetailed and unexplored.

There were other successors to Flatland besides Hinton's Astria and Burger's Sphereland, but Dewdney's Arde is a far more thorough and rigorous depiction of a two-dimensional world than any produced before it. Drawing not only on his own conclusions and speculations but on correspondence with physicists, biologists, and other experts who communicated with him privately or as part of a symposium, Dewdney develops not only the life of Arde, but its physics and, to a very limited degree, its chemistry. Even just in terms of Arde's biology, Dewdney goes into much more detail than any of his predecessors. He describes a dozen organisms aside from the Nsana, both fauna—from the tiny Zar Hyet to the formidable Bes Sallur—and flora—from the aquatic Ilma Kabosh to the terrestrial Jirri Basla. He also delves where Abbott, Hinton, and Burger did not into the anatomy of his two-dimensional beings, discussing, for instance, the "zipper organs" that make it possible for fluid to circulate through their bodies without their separating into discrete parts. Dewdney does not neglect to discuss the culture of the nsana, either, going so far as to develop their musical instruments and even a board game of sorts, "Alak", that they play on a one-dimensional board.

Like that of the original Flatland, the plot of The Planiverse is rather thin, and, like Hinton's opus, it descends in the end into unfortunate mysticism—but then, as with these earlier works, the plot isn't really the raison d'être of the book, but rather the elaboration of its two-dimensional setting, and on that regard the book is a triumph. If it has an imaginative deficiency, it is that the physics of Flatland are little more than an extrapolation into two dimensions of the physics of our own universe (or would that be an intrapolation?)—but then, this is probably more aptly regarded as a feature than a bug. Dewdney didn't set out to create a two-dimensional universe as alien as possible; rather, he probably intended to make his world as close to ours as was feasible in the lower dimensions. Therefore, while there are plenty of possibilities left to be explored for two-dimensional worlds, Arde deserves a lot of regard for being (as far as I know) the first such world to be developed in such a level of detail.