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Conceptual Fiction: Flatland by Edwin A. Abbott

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Mathematicians get little credit in the literary world. Go figure! But when the history of conceptual fiction is finally written, they may turn out to be the visionaries and pioneers.

The use of storytelling as a means of experimenting with our conceptions of reality—in essence the cult of the perversely anti-realistic novel—didn’t become an important force in literature until the twentieth century. Most of the agent provocateurs who made this happen came out of the blatantly commercial world of pulp fiction. Yet, in a strange turnabout, the innovations of the sci-fi writers eventually managed to influence “serious” fiction, and even a Philip K. Dick could posthumously be rehabilitated enough to join The Library of America.

But the mathematicians were there even earlier—especially Charles Lutwidge Dodgson (1832-1898), who you will know better as Lewis Carroll, and Edwin A. Abbott (1838-1926), author of the quirky cult classic Flatland. The term science fiction did not exist when these authors were active, and their attempts to invent and explore alternative universes built from their own vivid imagination were, to a great degree, an extension of their theoretical work with numbers.

Fast forward to the modern era, and you find that—once again—some of the most conceptually advanced writers of the contemporary era reveal an affinity with conceptual thinking of a non-literary nature. Recall, Thomas Pynchon applied to do graduate work in mathematics at Berkeley in 1964—and was turned down. David Foster Wallace’s senior thesis at Amherst was on the modal logic.

Most people today would struggle to see the connection between numbers and storytelling, yet from an anthropological point of view, the linkage is far from arbitrary. Calculations and stories both possess functional value as means of grappling with our surroundings, and securing our knowledge in a way that can be passed on to others. Before tales were recognized for their aesthetic dimensions, they had “survival value”—to use a Darwinian term—not dissimilar in this regard from quantitative skills.

If Flatland demands recognition as one of the first major works of conceptual fiction, it must rank even today as one of the most ambitious. Abbott, writing under the pen name of A Square aims at nothing less than depicting life within a two-dimensional universe. Our narrator lives on a geometrical plane, where he can perceive only length and width, but not height. Here he and his family lead flat Euclidean lives, in a rigidly hierarchical society, with circles at the top of the heap, and women (who are straight lines) and the lower classes (isosceles triangles and other irregular shapes) at the bottom.

But the book is not flat, even if the setting is. Abbott is a fascinating individual (in a surviving photo he looks like he was destined to be cast in the role of Harry Potter headmaster Albus Dumbledore). His "geometry novel" presents a pointed critique of Victorian attitudes and proves that, even at this early point in the evolution of conceptual fiction, these kinds of stories need not be limited by the formulas of escapist literature. In fact, the author may have found here a perfect platform for exposing the narrow-mindedness and prejudices of his day—after all what could be a better stick figure to represent a narrow view than a two-dimensional sentient square?

Flatland, it turns out, is a society built on questionable dogmas. Women are believed incapable of advanced thinking, and are thus prevented from gaining an education, or even learning how to read and write. Triangles who fall short of the equilateral ideal, are treated as akin to an untouchable class—almost literally so, since their sharp angles are potentially dangerous. Parents are so caught up in the geometrical symmetries of their offspring, that they will resort to dangerous medical procedures with the hopes of straightening out the angles of their progeny.

Our narrator tells about his own dealings with one-dimensional (Lineland) and no-dimensional (Pointland) societies. He is amazed at the inability of those in these settings to comprehend his own, much richer universe. Yet he is similarly limited in imagination when a visitor from our three-dimensional world (Spaceland in Abbott’s terminology) tries to open up the Square’s mind to the possibilities of spheres, cubes and other solid figures. Yet A Square's epiphany takes place when he is rudely dragged out of Flatland and allowed a brief glimpse into our world. Our hero concludes, however, that even three-dimensional space is itself a limited perspective on the nature of things, and he hungers for the wonders of the fourth, fifth and sixth dimensions, and so on until infinity.

But this advanced knowledge does not come without a cost. In Flatland—as perhaps in our own more elaborate world—those who see more deeply into the things around them are often branded as a threat by those whose positions of power are built on complacency and dogma. In short, even a square can be a revolutionary in two-dimensional space, contrary to what you might have heard from various hipsters and beatniks.

Yes, Abbott manages to deal with everything from politics to theology in his story, and finds time to pause and reflect on the nature of painting in a two-dimensional society, the history of rebellions and uprisings among the lower geometrical classes, the construction of houses, and various other matters of import small and large. Yet this tale has enough mathematical and conceptual content to justify its cult status among the slide rule and pocket protector folks. In other words, like any good book, Flatland is one with many dimensions—certainly more than the two that its inhabitants recognize.

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About Ted Gioia

  • doug m

    Good article. I have always wanted to read this. I must remember it my next trip to the library