The Females were Lines

As something that probably interests me more than anyone else, I’ve been debating whether or not this subject is worth getting into, but “Timeaus” brought it to my mind again, so…
Specifically, my interest was piqued by comments like this: “Now this we hypothesize to the origin of fire and the other bodies, making our way according to the likely account accompanied by necessity, but the origins that are loftier still than these triangles only god knows and whoever among me then gods hold dear.” (Timeaus 86, emphasis mine). These passages, as well as passages on the sublime that we’ve studied, point to the high priority geometry was assigned in classical theology and in later conceptions of art and proportion. Nowadays, we’d probably concede fire is not made of triangles, and and there may be a case that calculus has superseded geometry as the “godlike” branch of mathematics (and computer-based programming may have surpassed them both), but there is one work I’ve come across recently that uses geometry as a means of getting at both the sublime and concepts of space (if not exactly chora).
Yes, I’m talking about Flatland: A Romance of Many Dimensions, an 1884 novella by Edwin Abbott Abbott. Often credited as one of the pioneering stories of science fiction, Flatland is about a society of 2-dimensional shapes. The story is narrated by a square, a member of the gentry class. Triangles comprise the lower classes, and of the higher classes, the more perfectly proportioned and sided your are, the higher your rank. The square is a fairly normal shape, until one day he finds himself venturing to dimensions he never considered: Lineland, Pointland, and Spaceland. He tries to spread these teachings, and is thrown in a two-dimensional rendition of a prison for blasphemy.
Ok, so the work is clearly moving more towards social satire than anything else. But I think it has at least movements towards the sublime, such as when the square meets a sphere: “I began to approach the Stranger with the intention of taking a nearer view and of bidding him be seated: but his appearance struck me dumb and motionless with astonishment. Without the slightest symptoms of angularity he nevertheless varied every instant with gradations of size and brightness scarcely possible for any Figure within the scope of my experience.” And the implications for space should be obvious: the most significant accomplishment of the novella is its demonstration on how space and surroundings must be radically reconsidered when they are so narrowly constricted, a theme brought up again and again in chapters concerning how the shapes recognize each other, how they fashion buildings, and how their society was nearly destroyed before “the Supression of Chromatic Sedition.”
Flatland is not going to radically change our conceptions of space, or chora, or anything of that nature. Rather, I think that what we’ve covered so far gives us new tools for obtaining a fresh perspective on a work like Flatland. At least, that’s what it’s given me. I guess we’ll see what else comes up as we go along.
–Michael Hancock

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