Flatland

My first foray into the wonderful world of Penguin Classics: Flatland, A Romance of Many Dimensions, by A. Square (Edwin A. Abbott), first published in 1884.

This was an odd little . . . volume. I can't really call it a novel, although it's certainly novel. It takes place in a world where -- well, A. Square describes it better than I can:

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows -- only hard and with luminous edges -- and you will then have a pretty correct notion of my country and countrymen.

That is, it's a world with only two dimensions. The first half of the book (60 pages) consists of the description of this world. It's written like a treatise. No dialogue, all exposition. It covers everything from the floor plans of their houses to the details of their sexist, classist society. Abbott intended this to be a satire of Victorian society, and it is so extremely scathing that it's actually painful to read. The Flatland class hierarchy is based on the number of sides a person has -- the more the better, with Circles at the very top (infinite sides). The wider your angles, the more intelligent you are. Bottom of the heap are Isosceles Triangles, who suffer the added indignity of not having all their sides the same length. They make up the very lowest class, and are considered to be disposable, expendable -- the red-shirts, if you will. And women? They're Straight Lines. No angles at all! Which of course makes them lower than the lowest Isosceles. 'Nuff said!

The second, more interesting, half of the book (58 pages) is also treatise-like, but now the subjects are math and philosophy. A. Square discovers Lineland, a world of only one dimension, and then a three-dimensional entity -- a sphere -- discovers him. There are some funny moments here, such as this bit of dialogue:

"Pardon me," said I, "O Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg thee to vouchsafe thy servant a sight of thine interior.

SPHERE. My what?

I. Thine interior: thy stomach, thy intestines.

SPHERE. Whence this ill-timed impertinent request?

A. Square initially considers the sphere to be the Perfection, etc., because a sphere comprises an infinite number of circles, and Circles are the pinnacle of Flatland society. But it occurs to him that if there are worlds of one, two and three dimensions, couldn't there also be worlds of four, five, or six? And wouldn't a four-dimensional being comprising an infinite number of spheres be even more perfectly beautiful than a mere three-dimensional sphere? Ad infinitum? And the most interesting part of the whole book is the Sphere's reaction to this idea: even though the Sphere is well aware that there are worlds of one and two dimensions, he is so angered by A. Square's assertion that he evicts him out of Spaceland forever. Is this a wry comment on the way we humans cannot see ourselves as anything less than the crown of creation?

One of the strangest things about this book is its half-and-half structure. Stories are supposed to be divided in thirds, not halves. Beginning, middle, end. Just two feels unstable, unfinished. I liked the math, though. I actually found myself awake in the middle of the night after I finished it, pondering geometry. I tried to remember the formula for calculating the measurements of the angles of regular polygons. I came up with this: if n is the number of angles (or sides), the measurement of each angle is (n-2) times 180, all divided by n. Then I attempted some calculations in my head . . . and soon drifted off to sleep.

This reminds me, too, that I have another anecdote about Cousin Ward. (Please click on the link to refresh your memory about Cousin Ward; he's well worth the effort.) Anyway, I'm sitting next to him at Easter dinner. Conversation with him is awkward because he's a mathematician, but I do my best. I ask him how his grandkids in Pittsburgh are doing. They are well. The older one is, what? 8? 9? Neither of us can remember.

"It's hard to tell them apart at that age," says Ward.

"Very true," I agree, going off into a little reverie about kids getting older. When they're babies, a difference of three months seems insurmountable, but the older they get the less it matters. My train of thought is heading toward Maudlin.

"Because, you know," he continues, "one is two to the power of three and the other is three to the power of two."

I love this guy. Betcha he's read Flatland.