Neil Fein's Blog

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

"I find that science fiction has led me to science. 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)

"A real tesseract in four spatial dimensions cannot exist in out three-dimensional world."

Isaac Asimov, commenting on the story "--And He Built a Crooked House--" (1941) by Robert A. Heinlein, in the anthology Where Do We Go from Here" (1971)

"But then she seemed to hear a voice, or if not a voice, at least words, words flattened out like printed words on paper: 'Oh, no! We can't stop here! This is a two-dimensional planet and the children can't manage here!' "

Madeline L'Engle, A Wrinkle in Time, (1962)

"My evidence is that the whole tale is much too imaginative to have been invented -- certainly not in the intellectual climate of the previous century."

Victoria Line, 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 Headmaster, Mathematician, and Clergyman Edwin A. Abbott. 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, the tale of A. Square 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 elucidated A. Square.

However, there seems to be much that Mr. Stewart is ignoring, in the aims of portraying Mr. Abbott favorably. There are numerous paragraphs of digressions into topics that give the original volume perhaps too much credit for multidimensional studies that came later. The notes speaking of color and shade as "virtual" dimensions perhaps go too far in this regard, where I would suspect that the original volume was simply setting up plot points.

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 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. Much of the book is interesting, and some of it is fascinating.

The mutability of perception is of course a major theme in Flatland. Mr. Abbot did an excellent job of portraying varying viewpoints, in the end of producing an educational work. (After Carl Sagan wrote of most science fiction as being difficult to swallow, as the science is often suspect, he then proceeded to use Flatland, which certainly contains science of dubious accuracy, as the basis for his introduction to higher dimensions in the television series "Cosmos" one year later.)

Flatland is an excellent work, and one well worthy of being annotated. I wish, however, that someone other than a writer who has already contributed to the genre of work which Flatland has spawned would write an annotated version. Recommended, but with reservations.