What can actually be divided by zero?

As soon as I saw the question on a University of Chicago application, it wrapped its iron fingers around my neck and wouldn’t let me go; ephemeral bruises appeared on my neck and brain, as I went into overdrive wondering what could possibly defy the laws of mathematics and be divided into an infinite number of pieces, but in a way that’s within human grasp.

 Zero is the apostate of integers: first thought of as alien, even unholy, Greeks and Christians alike refused to touch it centuries after it was first used as a place-holder in Babylonian calendar calculations (the Indians and Arabs had less aversion to the void, seeing it as a natural counterpoint to the infinite). Zero might seem simple — it’s just nothing, the empty integer. But, strange things, twisted things happen when we start to use it in our math, let alone think about the implications of the void. Adding and subtracting zero leaves us right back where we started; multiplication by zero sucks any number into the bottomless maw of the void. Division by zero, though, is the worst offender, the greatest sin of the bunch. To divide a number by another number is to see how many times the first number fits into the second: 3 goes into 6 a total of 2 times, and 2 fits into 25 exactly 12.5 times. How many times, though, does the void fit into an unassuming integer like 17 or 168? The question warps the mind, with one coming to the conclusion that nothing fits into something for as many times as nothing can be nothing. It goes in an infinite number of times — and that’s no help, since infinity’s its own mathematical and philosophical beast slathering at the mouth. 

Can we put zero into infinity? Could two unruly monsters form a comfortingly mundane union? Nope. Asking us to divide infinity by zero is like asking a physicist to figure out what happens when the entirety of the universe gets sucked into a black hole: no one knows, and it’s best not to consider the implications. Could we, in our vain search, put zero over itself? We can try, but we’ll only come up with something ambiguous and unbelievably annoying in its amorphousness. 0/0 could mean (4 * 0)/0, or (14 * 0)/0, or (144444 * 0)/0; zero sucks everything back into itself, and this comes back to bite us when we tackle something as pesky as an indeterminate form of a number. If we had to solve a problem asking us to figure out a function value where a certain curve hits 0/0, we could brute force our way through with calculus and L’Hospital’s Rule. But as a philosophical concept, divorced from any practical or physical applications? 0/0 is as unattainable as the rest, and just as mind-numbingly frustrating. 

What, in short, could possibly be divided by something that at the end of the day makes so little logical sense it disrupts nature itself and was cast out of classical and Christian mathematics for centuries? Plain integers won’t do it, infinity is a poor candidate, and zero itself is hopelessly inept. Could we possibly divide something into uncountable pieces, and still have more left over — infinitely many more? 

It’s a daunting question, but perhaps it’s not entirely unanswerable. We just have to leave the realm of mathematics, and look across the way to where the poets dwell.

Do I contradict myself?

Very well then I contradict myself.

(I am large, I contain multitudes.)

— Walt Whitman, “Song of Myself, 51”

Mathematicians and philosophers don’t like things that can’t be explained with logic, things that can be clearly argued and articulated, even if they don’t have clear answers. Poets, by contrast, deal with the inarguable, the incomprehensible, every day; each time a poet sets pen to paper, they wrestle with the untamable fiend of the human condition, striving to use the art of language to grasp just a singular thread of what makes us humans — petty, selfish, power-hungry, ambitious humans, loving, gentle, caring, empathetic humans. 

Philosophers make their morning toast by pulling out their p’s and q’s to discuss human logic and emotion, but poets have made their peace with the multitudes of the human condition. It’s impossible to be a poet, to take single slices of living life on this earth — a red wheel-barrow, a prize-winning sow, a Jazz June day — and be willing to hold them close as representatives of the infinite human condition. No one can ever truly know thyself; even Walt Whitman, in his song of multitudes, spoke of a being beyond humanity, one that Whitman the poet could shape and structure to his liking. 

The vastness of the human condition is comforting to the poet, though. There’s warmth in something so large it seems a freezing tundra, shelter in something so deep it could be an ocean trench. There’s no use in trying to conquer the condition of billions of walking, talking, thinking, eating, loving meatsacks, so why try? They’re unknowable in their entirety, tangible, but incalculably infinite. 

You, me, my mother, my sister, my best friend: we’re all integers and infinities at once, knowable and here and having a place on the number line, while also an endless spiral of terms starting on the ground and ending high up in heaven, perhaps. For once, zero might be intimidated by an unassuming pile of flesh, blood, bone and muscle, that just so happens to have had the ingenuity to invent it and use it and even come somewhere near taming it. Challenge us, zero, divide us up until there’s nothing left. You’ll keep finding more, and for once, we’re comfortable with that. The void has nothing on my meat body and sunstorm mind — and I, for one, quite like things that way.