101 Classic Novels, I have them. They were free. They take up no shelf space. I love this age. Right, I was noodling around the iPod App Store and there it was, English language reading to keep me busy… possibly forever. Being arranged alphabetically by author, my first selection would be “Flatland: A Romance of Many Dimensions” by Edwin Abbott Abbott (his parents were first cousins, but they did that more in the late 19th century).
Evidently, as e-books give away nothing of their length before one begins, Flatland is really a novelette, a sporadically popular little treatise on dimensional geometry. While it could be a quick read, I took my time to chew it thoroughly, to apprehend and digest the world Abbott presents. Our protagonist, Arthur Square, lives in a two-dimensional world, the only one he or his fellow geometrical figures know. In the classist system of Flatland, one’s number of angles is everything… and all one can ever be. Hope for the family’s future lies in progeny, each generation bearing one more angle than its antecedent. So, from lowly manual laborer triangles society rises to polyhedrons of such advancement as to be considered circles.
Our story of Arthur Square begins with his dreams of a place so strange he cannot even articulate it. His solid understanding of Flatland geometric science does nothing but set smoldering his curiosity. If a point moves three units away from itself, it completes a line of three units, 3 to the 1st power. If the line moves three units parallel to itself, it completes a square of three by three units, 3 to the 2nd power. Should not then that square be able to move in some unfathomable direction to complete a figure which would be 3 to the 3rd power? Foolishness. But a stranger, ostensibly a circle, appears suddenly inside Arthur’s home. But the circle will not be recognized as any of Flatland’s political priests, calling himself a sphere, an infinite number of circles in one three dimensional figure. Unable to comprehend the stranger, Arthur is plucked out of his plane existence and brought into the world of his dreams, a world of three dimensions. But first they visit a point, a silly creature who has no understanding of anything beyond his own existence. He cannot be conversed with at all. They next visit the King of Lineland, also unaware of the world beyond his own one dimension, but when Arthur drops into Lineland, the King is flummoxed, yet able to see and converse with him as he appeared out of nowhere. Then the sphere escorts Arthur through Spaceland, the world of the third dimension. His suspicions were right; the math worked after all, even if he could have never imagined how until he’d seen it.
But then Arthur Square, and myself as well, began to wonder. Shouldn’t there be some direction, however mysterious and peculiar, in which that 3 to the 3rd power cube could move to complete a new figure, 3 to the 4th power? A fourth dimension from which one could see all of our third dimension without being in it, as Arthur had looked down on Flatland, into homes and buildings and even his neighbors’ insides? Beings in this fourth dimension might intersect our own, as the sphere intersected Flatland as a recognizable circle, then step out of it again. We know what the rest of the sphere looked like on either side of Flatland’s plane, but his visible presence was just a circle like circles Arthur knew. Not to put too fine a point on it, creatures from the fourth dimension, call it Spiritland, could very well look just like us and yet be so much more at the same time where we cannot see.
Drawing theology out of this little booklet of geometric speculation really began to tickle me. I’ve been praying for some time for God to show me, just a little bit, what heaven is like. We pray, “Thy will be done on earth as it is in heaven.” So, how is it done in heaven? What am I praying for? Being so pleased with myself for finding spiritual allegory in such a secular text, I googled up Edwin Abbott Abbott. Oh for crying out loud! The man was a theologian. Well, he can take satisfaction, from his current possible position in Spiritland, in that he made his point. Good on ya, Edwin.
[For those interested, I do highly recommend the book, however oddly sexist it may be. But after that, if you are so taken, find the 30 minute animation released in 2007. It can be purchased for download from the producer’s site. It corrects the sexism and inherent implausibilities therein while illuminating the theories exquisitely.]