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God as the infinitely-dimensional
on April 28, 2000
Flatland is one of those pseudo-scientific novels that has since become a piece of the scientific canon in the same way that Alice's Adventures in Wonderland has; when attempting to explain theoretical physics to a class, and at a dead-end, a professor is most liekly to turn to an analogy from Flatland. Which makes sense. Flatland is the story of A. Square, a resident of the two-dimensional Flatland, and how he comes to understand that there are universes in every dimension. Previous to this, the idea of any universe but his own two-dimensional universe was unthinkable; by the end of the novel, he is positing the existence of a great, infinitely-dimensional being-- god. This is not surprising; Edwin Abbott was a theologist first and foremost. What is surprising is how modern eyes have seen this tale, and it gives us a perspective on the endless debate as to whether the author's belief about his story is the final and "right" one.
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.