I drop a pen on the floor and say, “This pen has not hit the floor.” Obviously it has, and my students glare at me like I am trying and failing to hypnotize them. I would have an easier time peddling a bottle of miracle-cure-for-acne to these skeptical high school and college students. But I push on: I lift the pen theatrically, letting it hover mid-air, and ask, “The pen crossed the halfway point between my hand and the floor, right?” I wait till I see a few reluctant nods and then kneel. “And halfway of the remaining distance? And halfway of that halfway? And halfway of that?” I look around as I slice the air with my pen, and I know I’ve got a few of them. I have learned to reserve the most revealing line until the end: “What happens when you keep dividing a number in half?”
That is my dramatic interpretation of Zeno of Elea’s dichotomy paradox, dating back to approximately 450 BC. I’m sure I am one in a long series of lecturers who have knelt to illustrate this paradox of motion. The seconds you took in reading this paragraph so far is about how long I wait to answer the above question, for dramatic effect, and in consideration for the slower few: “That’s right. The answer approaches zero, infinitely, but never arrives at zero. The pen never hits the floor!”
So what? That is the sobering question, usually from a bright skeptic I almost always find in every “Paradox and Infinity” workshop, thankfully. This time it is Andrew, the clever ice hockey player in Grade 11. Now he is my target, and my objective is to convince him of the mindboggling implications of the paradox. Here is my repertoire developed after about a dozen deliveries: I start with the physical, noting how I can never leave the room because I would infinitely approach the door but never arrive. Likewise, I can never eat, drink, speak, or move at all. No one can. I cannot hear because sound waves never arrive; nor do light waves, and I cannot see. I am bound in a philosophical prison, and I can only think. Or can I? Synapses never finish firing, and neurons never arrive, and I exist alone, senseless and thoughtless.
There is nothing like solipsism to depress teenagers, besides perhaps nihilism or absurdism (another workshop, another story). I would be an evil man to leave them there, so I switch the discussion to infinity. I tell them that if a thing never arrives but approaches infinitely, then it is moving infinitely, like the pen toward the floor. This can be a beautiful concept: everything is moving and happening infinitely. I am still being born, never stopped being born; still taking my first walk; still, paradoxically, learning my first English word; and falling in love, infinitely, eternally, for the first time. And, in a sense, I will never finish this sentence, and you will never finish reading it. But obviously you have, and that is the paradox.
I teach for money (let us get that out of the way.). I have been teaching for money because my family has been in debt, and a son does not stand and watch his father declare bankruptcy. His business failed in my junior year in college, and the final two years’ tuition was the log that broke his back. Those were tough times. I shelved my plan of attending law school and stopped fiddling with the idea of a Ph.D. in philosophy. Instead, I took a teaching job in ABC, where I could look after my parents and help pay off the debt.
Things improved gradually, and I moved back home to DEFG. Since then, I have been as busy as should be a man with debts and dreams. At first, the dreams were obstacles in getting things done; as hard as I worked, I could not stop myself from reserving time for my interests in philosophy, photography, poetry, and languages. In time, I have found that the act of teaching is not so different from the sharing of interests, and students respond better when I forget that I am teaching, as I often do when I roll a marked frisbee around the desk to illustrate Aristotle’s Wheel Paradox, or break a Starbucks stir stick repeatedly to imitate Zhuangzi’s infinite spear-breaking.
Now I teach mostly what I want to teach (is this what seniority and tenure must feel like?). For three years, I taught reading and writing and test preparatory courses that students asked for, but now I share with my students my readings of Jorge Luis Borges, Ted Hughes, J. M. Coetzee, Billy Collins, Thoreau, Beckett, Bukowski, and of other giants who happen to be trampling on my mind at the time. Though he has passed away before I had a chance to hear his lectures, Borges has been living with a foot on my head for a while. Many of my students share my love for his love for labyrinths, dreams, and infinity.
I try to do what I wish someone had done for me during high school, when I struggled to learn philosophy and poetry on my own. I know most students like Andrew the Hockey Player move on to study something more practical, like chemistry, economics, business, or dentistry, but I sometimes do get e-mails from former students saying they have decided to take a philosophy course (and earn a sadistic chuckle from me).
This essay signals the end of my six-year teaching career. As of late last year, I have been debt-free and started saving for school. I began this essay with my paradox workshop because I did not want to seem ungrateful by beginning with misfortune. That is not how I feel. Had I the choice to attend law school six years ago, you would have read an idealistic essay by a philosophy student eager to learn of the Truth of things for his own sake. This is and is not that essay.