Topology

Topology is the branch of mathematics that deals with surfaces. It attempts to describe whether or not an ant at point A could crawl to point B without crossing any boundaries, sidestepping any holes, or getting totally lost in a sea of white space. (Full disclosure: not every topologist would recognize this as a description of his day job.) From the root concepts of "Near" and "Far", the topologist builds dazzling theories of geodesics, fundamental groups, genus numbers, and cohomology, but the casual reader should take these theories with a grain of salt: for all their splendor, they are all just comments on the nature of distance and proximity.

Although it would be a mistake to take Topology as a paradigm of the soul, the field (like most fields in mathematics or the physical sciences) is packed with metaphoric potential, and has been much on my mind lately as I contemplate why exactly Pittsburgh feels Far Away, au sense moins mathematique du terme. From what, precisely? The mathematician in me cringes as I admit I don't know (define your problem! rages a vision of my old advisor.) Sunlight, perhaps? Family? The smell of the sea? Some core vision loosely coalesces, but comes apart when I turn to look it in the face: a serious voice droning on, the ghost of my old dog, ten screaming piglets, the ball-shrivelling cold of the Sierra lake water, a particular sadness to the afternoon sun as it sets across low hills of wild barley and dusty oaks. Like everything that penetrates the threshold of our perception, these images entered my imagination alone and without fanfare, but, unlike all the other one-night insights that streak into our lives and high-tail it out by dawn, these images stayed. They threw down roots, cross-pollinated, and now form a Landscape, never known and perhaps never to be known except as a gnawing discontent with the present.

There are many measures of distance. In mathematics, you can consider distances imposed by an arbitrary topologies, but in life, distances are imposed by experience: memories, relations, hopes, ambitions. In spiritual terms, we might say that each consciousness endows the earth with its own topology, its own set of geodesics and distances and genii and components, and from these concepts it derives others: Here, There, Close, Far, Native, Natural, Us--all the basic units with which we define Home. Perhaps this Landscape I'm dreaming of seems far away not because I'm in Pittsburgh, but because the suite of daily impressions to which, e.g. my job, social circle, and general lifestyle expose me are so far removed from those that first gave structure to my psychological world. In this conception, my Heimweh is not so much a response to this particular place and time, but a yearning for one in which opportunities dropped like ripe mangoes, and were gathered by the hatful into the structure of our daydreams.

Make no mistake: topologists are a weird lot, and in general I don't trust them. They avoid eye contact and spend a lot of time looking at the ceiling out of the corner of their eyes (seriously: their heads are usually pointed to the back of the room, their eyes are pointed to the left. I have never seen a right-looking topologist.) They ruminate on matters like how many intrinsic dimensions characterize a given material object, or what p-forms such and such a manifold might support; their shirt fronts tend to sport crumbs. But let us take the charitable view: perhaps the reason that topologists are so messed up is that the nature of their subject parallels the great movements of the human heart. Perhaps it is the attempt to formalize something that lies so close to the essence of Life that thwarts the usual mathematicians' game of Stonecold Technoblizzard, and leads to gimpy, quivering men and woman, spinning half-baked theories about impossible worlds. In a formal Gimp-off, it's not clear to me who would win, the topologist or the sociologist.

Be that as it may, somewhere on a Klein bottle sits an Ant, stewing in his own juices. He is sitting at the point of self-intersection, a place called A. A, for Another rusting city, A, for a town Ass-savaged by industrialism, A, for can Anyone remind me of why I took this job. He grinds his mandibles, wrinkles his antennae, takes stock: curvature, slope, texture, temperature. It all pisses him off. Somewhere, he suspects, maybe West of the Ohio river, there is an imaginary, impossible, chimeric Landscape in the Sky, a place of surpassing beauty, where cottontails dance in chorus-lines and cats smoke hookahs. In his dreamvision that place is called B, but he couldn't swear to that, he's never been there. He growls (as much as an ant can growl.) Discontent is his metric, his probe: he uses it like a riverman uses a leadline, heaving it here and there, plotting a course according to the rags and weeds that get dredged from the bottom. Somewhere in Fine Hall a group of ceiling-starers has proved beyond all reasonable doubt that if he just follows the right geodesic, he'll get there, but it remains to pick one, the right one, and to follow it bravely: to trust that he won't get snared in the boundaries, and that he won't disappear down a hole, and that the churning sea of white space will leave him as it found him, heading West under full steam.