The Love of Geometry

When Sister Martin began her lessons in elementary geometry by drawing parallel lines on the blackboard using a chalk-holder with a wooden handle, magic entered the classroom. We had seen that curious instrument before, of course. Fitted with three pieces of chalk it had marked the lines between which we made our capital and lower case letters; fitted with five, it could make a musical staff. But my brothers and I received no musical instruction at St. Joseph’s School, and my class was writing cursive now. Still, when Sister Martin taught us about parallel lines, and how once they were parallel they would always be parallel, never crossing even if extended out to the most distant stars, it was as if something miraculous had entered the world.

I knew that the chalk-holder was only a tool, and that the lines drawn on the board were not perfect; I even understood that by turning the device as you drew, the lines could be made to converge and divide, but, in a revelation like that of Plato’s cave dweller climbing into the light of the sun, I understood that those lines were only drawings, representations of parallel lines, and that the real parallel lines were perfect, and ever the same distance apart, as my four younger brothers and I were all two years apart and always would be. I learned this not simply by accepting what I was taught, as I had accepted so much before, but by testing and failing.

I questioned Sister Martin, tried to show with my hands how I thought that two lines that weren’t parallel could still never cross—because another part of the teaching about parallel lines was that just as they would never cross, all non-parallel lines would cross eventually, if you followed them far enough back or forward. She indulged me, patiently allowed me to go to the board myself, where I struggled with chalk to show what I meant, saying, “see, here they pass, but they don’t cross, I can’t draw it on the board, but I can see it in my head.”

“The lines you are seeing in your head,” she said kindly, “are in different planes. That’s why you can’t draw them on the blackboard, because the blackboard is a plane. In a way you have proven the point. Do you see now?”

And I did see, and I felt not embarrassed or ashamed, but proud of myself, as the world seemed suddenly a wild geometry of planes, some parallel, like the opposite walls of the classroom, some intersecting at right angles, like the walls and the floor or ceiling, and some slicing through all the others, like the angled plane of my desktop, which I could adjust to be parallel to the floor or the front and back walls by tilting it into the right position. I walked home that afternoon through a beautiful Euclidean world, the pure, smooth forms of things aglow in, around, and along the ordinary surfaces of clapboard and stucco, concrete and macadam, glass and steel.

As if the miracle of geometry weren’t enough, the new math also came along around that time, bringing with it set theory and the concept of zero, an integer with remarkable power. I understood multiplication as much as anyone my age understood it. I had memorized the times tables up to 12 times 12, although I was too lazy to learn them in both directions—thus I knew by rote that six 8s were 48, seven 8s were 56, and eight 8s were 64, but I would have to reverse the numbers in my head to tell you what eight 6s or eight 7s were. Multiplication was a kind of shorthand for a lot of addition, as I saw it, and it made sense. Except for multiplying something by zero. How could a number be so powerful as to make what ever it touched disappear? It was like the power of death rays in The War of the Worlds—they shone on tanks, and, poof, the tanks evaporated, dematerialized, were gone.

At home, I threatened my brothers with multiplication by zero, which none of them understood, but which I made sound menacing enough to bring forth tears from the middle one. My closest brother ignored me as usual, irritated with my showy intelligence and already having made the decision that he would do whatever he could to avoid being compared to me, no matter how often the nuns asked him why he couldn’t be more like his bookish older brother. For years we would move not in parallel lines but in separate planes, and it would take the non-Euclidean reality of life and the space-bending gravity of loss to bring us close again.

John Van Kirk has received the O. Henry Award (1993) and The Iowa Review Fiction Prize (2011). His work has been published in various journals and several anthologies. His novel, Song for Chance, was published in August of 2013 by Red Hen Press. He teaches literature and writing at Marshall University in West Virginia.