How to Not be at Home in the World

Marianne Janack

1. What we think of as analytic geometry began with Descartes. A mathematician and philosopher, Descartes’s geometry relies on his ideas about space, about how to describe shapes, about the extension of bodies. Cartesian co-ordinates are points on a graph, measured in the distance from the point where the two axes of the graph intersect (designated as the point of origin: (0,0). What Descartes’s analytic geometry made possible was the description of a shape by means of algebraic formulae, and it is essential to modern engineering.

1.1When I was 16, in July of 1980, I went to France. This sounds, I imagine, like the usual story about a young person going to France. I read essays about “my summer trip to France, in which I learned so much about how people are different/the same” when I worked as a college admission dean in my mid-20s, and I felt a bit ashamed, since I’d written a similar essay for my college applications. But my trip to France was, as clichéd as this may sound, transformative and eye-opening.

2. I don’t come from a family that takes trips to Europe—in fact, we rarely even went to Canada, which was just about 100 miles from our home in Central New York (the state, not the city). My father worked in a factory; my mother stayed home with my siblings and me. She left her job as a secretary in a shoe factory in 1963, just before I was born.  From that point on, we rarely left that point of origination, that (0,0): 112 Bury Drive, Syracuse, NY 13209.

2.1. We went to our camp on Oneida Lake on weekends in the summer,  which was half an hour away; visited relatives who lived close by. We went to visit my grandmother in Star Lake in the Adirondacks; we went to Baltimore, MD several summers in a row to visit our relatives (a very big deal for us, riding in the car for 6 hours, going through a mountain via the Lehigh tunnel).

3. But then, we went to the Bahamas (without our father, who had no interest in going) in February 1980, five months before I went to France. It was the first time any of us had flown on a plane.

3.1. We loved the breakfast we were served: little link sausages and scrambled eggs.

3.2When I think about it now, I wonder why I’ve come to hate flying so much—is it that the seats were bigger then? That I had lower standards for comfort? That what was an adventure then is now mostly a burden? Maybe all of those. But I still love looking out the window, as people and cars become small, as clouds become eye-level scenery, as I see the topography of the earth.

 4. I was sitting by the window on the flight from Syracuse to Atlanta on that February day in 1980, and I looked down at the Finger Lakes, the snow-covered fields of Pennsylvania, the tiny lines of roads and rivers that covered the states of Maryland, Virginia, Georgia.

4.1 We landed in the Atlanta airport—a behemoth—and figured out how to get from the terminal in which we’d landed to another that seemed to be in a different town.

4.11 Our flight to Nassau was scheduled to leave from this distant place.

4.111 We stood and waited for the bus-like rail-bound transportation boxes, into which all four of us—my mother, sister, brother, and me— filed. We stuck close together like a small herd of wary deer, squeezing ourselves into the quiet white space.

4.12 It was a different world.

4.121 We were whisked off—with a space-age sounding sigh from the doors of the train— to the international departures terminal.

5. All points in Cartesian space are essentially the same—a body placed in the middle of the graph would be able to measure the distance between it and another point in space in terms of Cartesian co-ordinates, which are divided up equally in the flatness of the graph.

5.1 If you were to squash your body down to a two-dimensional, flat spot, that spot could be related to all the other spots on the graph, and the spot that is your body would be no different from all the other possible co-ordinates, occupied by other spots. 

5.2And thus is the spatial world born.

6. Descartes thought that space was always filled with matter—that to be a body was to be extended in space, and that space was nothing more than this extension.

6.1 Space does not exist prior to or independent of bodies: it’s not sitting there, waiting to be filled up with stuff, according to Descartes.

6.11 Space is an effect of the relationship between bodies.

7. But bodies are, of course, three-dimensional—they have height, length, and width.

7.1  Cartesian co-ordinates can handle that third dimension, too—the plane that extends horizontally and the plane that extends vertically can be supplemented with another plane that makes of the two dimensional graph a three dimensional shape, an upside down T extended toward the viewer and away from her.

7.11 Beyond that lawn, beyond that road, beyond those hills is more space, more points on the graph that have as their origin point this body.

8. The second time I flew on a plane was in the summer of 1980, when I flew to France to stay with a family that had volunteered to participate in the North American Cultural Exchange program.

8.1 My French teacher encouraged me to enter a contest at my high school—the prize was placement in the NACEL program, and the school paid for that: for the fee, for my transportation costs.

8. 11 I was mostly focused on winning; I hadn’t really thought much about the prize.

8.111 To be honest, I was ambivalent about the prize.

8.1111 I was a little anxious about living in a different country, with a different family. I wasn’t afraid to fly, though.

8.1112 It turned out to be harder than I thought to be away from my parents, my house, and even my siblings for a month. And I missed my friends, and speaking in English.

9. My host family took me to visit some other parts of France—they were very generous. And one day, we drove through the town of Descartes.

9.1 “Do you know the famous philosopher and mathematician, René Descartes?” the father of my host family asked me.

9.11 I didn’t.

9.111 “He invented the analytic geometry” my host father said. “You know this?”

9.1111 I knew about analytic geometry. I’d taken a class in analytic geometry that year in school.

9.11111 To be honest, I hated analytic geometry: still, do, really. I like the puzzle-solving of algebra, but I don’t like the messiness of adding bodies to the mix.

When I went off to college, two years later, I ended up in a philosophy class, much to my dismay. I wanted to be an English major—I had no interest in philosophy—but I’d mistakenly signed up for a philosophy class (it was deceptively titled “Genre of the Self”). and I read Descartes’s Meditations. No analytic geometry in that, thank heavens. But he did include a detailed analysis of bodies, and how they differ from minds—they are infinitely divisible; they take up space. The meditation begins with Descartes’s own story of travel—he has just come home from the Thirty Years’ War, and is thinking about all the things he has accepted on the basis of the authority of his teachers. He is a scientist, he thinks, rebelling against the Medieval and Scholastic traditions he has been immersed in during his schooling.

But if space is always an effect of bodies, as Descartes thought, how does one make sense of motion? Motion would seem to require that there be some empty space into which a body could move. But this Descartes denied. Motion, he said, was “the transfer of one piece of matter or of one body, from the neighborhood of those bodies immediately contiguous to it and considered at rest, into the neighborhood of others” (Principles of Philosophy, II 25).

Bodies at rest: my family, sitting in their little house in our neighborhood in Syracuse? I had moved on, to another “neighborhood”, our little herd of deer no longer together.

To not be at home is to be in motion, or to want to be in motion, straddling the ‘there’, the ‘here’, the “someplace else”. It resists the form of the geometric proof, the logical syllogism: to not be at home is not necessarily to be homeless.

As I look out the window of my house, I realize that to write about geometry and the metaphysics of motion can be to write a confession.