It first struck me somewhere in eastern Oklahoma, I think, careening down a hill in my 5-ton, 14ft. U-Haul rental truck. In the past 16 hours, I'd driven through hundreds of towns, each with its own infinite set of possibilities, every sign an invitation and every face a reminder that I could be anywhere. Anywhere at all. And there I was, driving 2100 miles to a giant city in the middle of the desert. And here I am.
To be fair, I've never lived in the plains states and I never really intend to: Oklahoma, at least, is by no means without it's own personality, and it has its fair share of hills to break up the monotony (how else could I have been careening?). But the westward drive on I-40 left me with a vast sense of dislocation. The swollen greens of Missouri blended through Oklahoma into the patched openness of northern Texas, which subtly and suddenly became New Mexico desert all the same – and there I was in the middle, my ability to see out the window forever impeded only by the sloping curvature of the earth. The space itself was an open invitation to everything and nothing all at once, potential and entropy crashing together where the last green-brown blur met the sky.
Maybe it was the week at Math Camp, but I couldn't help thinking of Zeno in that moment that he first considered his paradox. Imagine: the man stands at one end of a room staring across the infinite expanse of infinitesimal spaces set before him, unable to register the wall before him so bewildered is he by the inch and half inch and millionth of and inch and a millionth of that millionth right before his toes. He cannot help but quail at the task before him: the infinitude of motion closes in on him, the expanse ever approaching him in these millionths of millionths, some kind of inexorable localized eschaton trumpeting the banality of every possible step. He is paralyzed by the task. Which millionth of a millionth of a millionth might he dare to cross?
In an instant, the world spins away in that green-brown blur – the walls and floor, his hands, those feet. And Zeno, a man who has never heard of canvas, finds himself twisting through some kind of monster scene, the bastard child of Van Gogh and Dadaism. His mind a swirling, darkening, stationary monument to the rigor of Greek logic, he has beaten Descartes and Sartre to the punch. He cannot know the impossible distances his blood has traveled, the countless electrons shivering with anticipation in his own fading body. How could he eat a peach?
And in one further cosmologically shattering motion, his right foot comes into perspective, swinging confidently across such infinite space, the room bursts back into existence, and first half, then all of his body crosses this immense mass of space. As step follows step, he does what he cannot, and his mind is restored to an order that his logic could not define. Reaching the opposite side of the room, he begins to write.
And, strangely, here I still am – me and my new city in the middle of the desert, walls and roads and sand beyond. I have taken Zeno's step inductively and crossed that room, marked the blur and walked into it. I have crossed these 2100 million millionths, and the horizon has become a solid thing – faces here and signs as well.
There's good news, too: the blur is ever returning and the curvature of possibilities themselves ineluctable. I do believe I will enjoy taking more steps, making these infinite millionths of anywheres into somewheres to behold.
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