Upward, not Northward

The Annotated Flatland: A Romance of Many Dimensions
by Edwin A. Abbott, notes by Ian Stewart

“I find science more subtle, more intricate and more awesome than much of science fiction.”

–Carl Sagan, “Science Fiction–A Personal View” (1979). Published in “Broca’s Brain: Reflections on the Romance of Science” (1993)

“…the whole tale is much too imaginative to have been invented–certainly not in the intellectual climate of the previous century.”

–Victoria Line, speaking of Flatland”, in Ian Stewart’s “Flatterland: like flatland, only more so” (2001)

The conflict between fantasy and perceived reality is at the heart of Flatland, a small book published in 1884 by Edwin A. Abbott, who was a headmaster, a mathematician, and a clergyman. While Mr. Abbott was not the first to publish a story about a two-dimensional world (and hardly the first to propound the possibilities of higher dimensions), Flatland is today the favorite work to introduce the analogies of higher dimensions. Thanks in no small part to the clever critiques of stodgy thinking and hidebound attitudes towards class and a woman’s place in Victorian society, protagonist A. Square’s tale has resonated with an entire generation of forward-thinking mathematicians, feminists, and social reconstructionists.

This book, however, is not merely Flatland, it is Ian Stewart’s take on the work. Through circuitous notes, Mr. Stewart makes his opinions quite clear: Flatland was intended by the esteemed Mr. Abbott to not only open up geometers’ minds, but to advance Abbot’s crusade of furthering female education. This point is made abundantly in Mr. Stewart’s work Flatterland, where the heroine journeys into worlds beyond ken of even the Sphere that so entranced A. Square–and later ruined his life. (A. Square wrote Flatland from prison.)

However, with his goal of portraying Mr. Abbott favorably, there seems to be much that Mr. Stewart is ignoring. There are numerous paragraphs of digressions that give the original volume perhaps too much credit for inspiring multidimensional studies that came later. The notes speaking of color and shade as “virtual” dimensions perhaps go too far in this regard. While these are important to conceptualizations of string theory, I would suspect that the original volume was simply setting up plot points and allegories.

On the other hand, Mr. Stewart is correct to point out the limitations of Flatland and its inconsistencies. Further literature is also cited, including, irritatingly, the author’s own Flatterland–citations that appear with increasing frequency as the volume progresses.

For the most part, this volume is a lively and rewarding read. Mr. Stewart brings areas into play as diverse as physics, color theory, Victorian education, calendar theory, biology and religion. Of course, this is in addition to discussions on geometry and other maths.

The mutability of individual perception is a major theme in Flatland. Mr. Abbot did an excellent job of portraying varying viewpoints, with the aim of producing a popular and educational work. (Ironically, Carl Sagan wrote of most science fiction as being difficult to swallow with its often-suspect science. Not long after that, he used Flatland (which certainly contains science of dubious accuracy) as the core of his introduction to higher dimensions in the television series “Cosmos”. It’s debatable if this shows him to be more accepting of science-fiction than he claimed or if it proves his point.)

Flatland is an excellent work, and one worthy of being annotated. I wish, however, that someone other than a writer with an unofficial sequel to the work would write an annotated version.


This review was originally published at my old blog on 12 December 2004. This version has been significantly edited and rewritten.

Neil Fein is a freelance editor. On the side, he’s the guitarist in the band Baroque & Hungry, he rides a mean bicycle, and he paints with oils when the mood strikes him.

Baroque & Hungry will be playing in Webster Hall in New York City on Sunday, 4 Dec 2011.

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