Flatland [Paperback]

In order to understand this twenty-two chapter book (first published in the mid-1880s) by Edwin A. Abbot (1838 to 1926), you have to understand what is meant by the word "dimension," a word in the book's subtitle "A Romance of Many Dimensions." A dimension is any measureable distance such as length or width. So something that has one dimension has only one measurable distance, something that has two dimensions has two measurable distances, and so on. You also have to realize that there are geometrical forms that can be drawn in these dimensions. Thus a line is such a form that only has one dimension, a triangle is such a form that has two dimensions that appears flat and non-solid, and a sphere is such a form in three dimensions that appears solid. (Another name for three dimensions is space.)

Part one (twelve chapters) of this book gives us a glimpse of the two-dimensional land where the narrator, Mr. "A. Square," comes from. This place, called "Flatland," is inhabitated by two-dimensional beings of which Square is one. These beings no nothing of "up" and "down." Square tells us details of Flatland society such as its resident's domestic life and its political turmoil. It is a place dominated by such things as a rigid social hierarchy, sexism, and closed-mindedness.

Abbot was a Victorian and his description of Flatland is meant to be a parody (using wry humor and biting satire) of English Victorian society. Abbot seems to have fun mocking the upper classes of the 1880s in his book. I found that much of what Abbot says can be applied to modern society.

As an example, Square tells us of the social hierarchy that exists: "Our women are straight lines. Our soldiers and lowest classes of workmen are Triangles with two equal sides [called an Isosceles triangle]...Our middle class consists of Equilateral or equal sided triangles...Our professional men...are Squares...and five-sided figures, or Hexagons, and thence rising in the number of their sides till they receive the honorable title of Polygonal, or many-sided...Finally when the number of sides becomes so numerous...that the figure cannot be distinguished from a Circle, he is included in the Circular or Priestly order; and this is the highest class of all."

Part two (ten chapters) of this book is very interesting since Square tells us of his visits to "Lineland" (a land of one dimension), "Spaceland" (a land of three dimensions, a land Earthlings are used too), and "Pointland" (a land of no dimensions). Readers will find that they will have to adjust their thinking every time the two-dimensional Square visits a world of different dimensions. For example, when Square meets "Sphere" (of Spaceland), the reader will have to "see" Sphere as Square does--in two dimensions. The end of this part has Square realizing that three (and perhaps more) dimensions exist and trying to tell his fellow close-minded Flatlanders this.

My favorite sentence in part two occurs when Sphere makes an unexpected visit to Square's home (and Square doesn't know who Sphere is, fearing that he is a burglar). Square says, "The thought flashed across me that I might have before me a burglar or cut-throat, some monstrous irregular Isoceles, who by feigning the voice of a Circle, had obtained admission somehow into the house, and was now preparing to stab me with his acute angle."

Abbot, besides being a writer and educator, was also a theologian. So are their any spiritual or metaphysical aspects to this book? The answer is yes but this is not always obvious. For example, when Sphere makes his first unexpected visit to Square's home, he slowly seems to materialize in front of Square. Thus Sphere seems to be a supernatural, supreme being and Square refers to him as "your Lordship." Another example is Sphere sees Square as "a fit apostle for the Gospel of the Three Dimensions."

This book is written in Victorian English that may be difficult (for some) to comprehend at first. But I found that as I progressed further into the book and got used to this type of English, it becomes much easier to comprehend. The sketches found throughout the book also help immensely in getting across what Abbot was attempting to convey.

This book raises a number of questions, some of which are as follows:

(1) Why does our universe have three dimensions and not two or four?
(2) In what ways does our three-dimensional universe affect its physical, chemical, and biological properties?
(3) Do universes that have two, four, five, or more dimensions exist?
(4) If other universes of different dimensions do exist, then are there beings in these other dimensions?

Finally, for those who want a good non-fiction account of possible other dimensions, I recommend Dr. Michio Kaku's book "Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 10TH Dimension" (1994).

In conclusion, this is a unique book that sparks your imagination and raises certain questions. Be warned though! By reading this book, you may become one in "a race of rebels who...refuse to be confined to [a] limited dimensionality."

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Abbott meant his book as a treatise on theoretical physics-- if at all-- in only a minor way. According to Abbott himself, his main goal in the writing of Flatland was to produce a kind of "satire of manners" on Victorian England. And, given what little I know of the ways of life in Victorian England, he seems to be right on the money. But what do I know? Abbott's assertion is backed up by the structure of the novel, certainly; the first hundred pages of this small (hundred fifty page) tome are devoted to the customs and mores of Flatland. How stinging a criticism they are of the values and mores of Victorian England is not for me to say. Thus, those of us who are not historians are left with the final fifty pages, and the impact of the first hundred pages upon them (which, aside form the knowledge gained therein, is minimal); and, at least as far as the physicists go, the book has metamorphosed into a trestise on theoretical physics.

I'm not a theoretical physicist, either, but I've always been interested in mathematics in a sort of hobbylike way, and the math presented in Flatland is good, solid theory that also happens to be thought-provoking. Seeing how A. Square's realization of how the third dimension works dawns on him, and seeing how Lord Sphere explains the mechanics of the third dimension to A. Square, it is easy to take those arguments and make them to postulate a theoretical fourth dimension (albeit one that is impossible to visualize, at least within the narrow scope of my mathematical knowledge) and its supercubes with sixteen points and eight faces, and the like.

The point is, however, we seem to have taken a minor part of the book's appeal to its original audience and made that its full appeal today. We still think it's good (or it wouldn't still be in print a hundred sixteen years after its release, no?), but we think different aspects of it are good. The opinions of the artist have passed on, and the work itself remains in a different perspective.