Flatland by Edwin Abbott: Satire, Math, and Victorian Society

Introduction: A Work of Many Dimensions

Though written largely as a satirical response to the institutions and beliefs of the Victorian England society to which its author belonged, Edwin Abbott's Flatland: A Romance in Many Dimensions also serves — and has for over a century — as an enjoyable introduction to many different fields of human knowledge. Practically since its first publication, scholars have noted the skill with which Abbott describes complex topics in such diverse fields as philosophy, mathematics, and even cultural anthropology, though he rarely mentions these fields explicitly (Beidleman, 1973).

Instead, through the main character of the Square and his interactions with other humanized characters in the two-dimensional world of Flatland, these concepts are illuminated as logical necessities of the world we live in. Some of the subjects and concepts outlined in the book may have led to unintentional interpretations; though the author certainly had specific sociological views in mind, he probably did not have any particular anthropological conclusions he was trying to lead his readers toward. Still, the fact that these conclusions can be drawn from the work is a testament to its writing and broad appeal.

The Limits of Education Through Fiction

This broad appeal is also the book's downfall in many ways. Because it illustrates so many concepts — and does so indirectly — it does not fully or accurately describe any of them. For instance, when the Square is ruminating on the appearance of the three-dimensional Sphere from Spaceland in two-dimensional Flatland, he describes the way the appearance seems to shift: "At the first glance it appeared to be a Woman [who appear as lines in Flatland], seen sideways; but a moment's observation shewed me that the extremities passed into dimness too rapidly…and I should have thought it a Circle, only that it seemed to change its size in a manner impossible for a Circle or for any regular Figure of which I had had experience" (Abbott, 1884).

This description is confusing and, though perhaps accurate for the way a two-dimensional being might perceive a three-dimensional creature, it is difficult for Abbott's three- (or four-) dimensional readers to understand. What Abbott gains in interest by humanizing all aspects of the story, he loses in the clarity of his mathematical discussions. If the purpose of the novel is to educate — and from the depth and breadth of information contained within it, education can reasonably be assumed to be at least one of its purposes — then it falls somewhat short of that goal due to the book's attempt to maintain a cohesive story. As one critic notes, "packing such diverse information into a small space inevitably makes the various sections of the introduction tantalizingly cursory" (Smith, 1992).

Unfortunately for Abbott (and, to a degree, his readers), this same principle works the other way round as well. That is, the book loses much of its potential entertainment value due to the technical nature of many of its discussions.

Satire as the Novel's Primary Purpose

Overall, the book is much heavier in satire and entertainment value than it is in philosophical and mathematical information, leading one to believe that education was not its primary purpose. Rather, through reliance on logic, "satire is here always integrated with a more or less serious depiction of an alternative historical locus" (Suvin, 1983). The satire is made more poignant by the fact that the injustices and absurd institutions being satirized occur in a world of seemingly supreme logic. Logic itself, along with other mathematical concepts that can be rationally verified, is not satirized. Rather, Flatland satirizes the misuse, misunderstanding, and misapplication of logic, and calls for a reexamination of certain so-called "logical" principles.

The various social principles discussed in the book go a long way in determining Flatland's purpose and the audience Edwin Abbott had in mind when he wrote it.

Conclusion: Flatland's Enduring Relevance

Though this book is almost one hundred and thirty years old, it remains very useful today. It can be read as an introductory text to certain mathematical and philosophical concepts, as a historical document illuminating the opinions and mores of an incredibly restrictive society and the response that restrictiveness inspired in certain individuals, and as a manifesto for social justice. It is still meaningful in all of these ways, and the popularity the book has enjoyed over the past century is a strong indicator that it will remain relevant for centuries to come.