At some point in my schooling, they introduced the number Pi. They throw this number out there to you as a way to measure things about circles. But they don’t spend very much time on how downright odd it is. How the hell can you multiply anything by a number that is infinite? My kid, who’s 11, asked me this just yesterday. I stopped, thought about it, realized I’ve been thinking about it for 35 years, then said: “I dunno. Good question.”
Math class went on without me as I stayed stymied by Pi. Here’s a number that is absolutely precise, infinite, and unknown. Holy moly. That’s odd and beautiful and a pedagogy unto itself. In many ways, this is all I’ve thought about for decades.
Since I was a little boy — like most kids, I think — I’d been interested in infinity. I used to lie in bed at night, clothed in darkness and tightie whities, and conjure infinite space until my whole, skinny, little body would shake in a kind of pre-sexual orgasm. It was sublime.
But what was giving me this exquisite sensation of vertigo was infinity in general. And what was so strange about Pi was that it wasn’t the infinity of space. It was, in a way, small. It’s not even four!
Infinity, then, need not be a generality. In fact, there are infinite infinities — the numbers between one and two, between three and four, between one and 1.27869, between 17 and 64,943,999,329.07. All these different shapes — and I was going to say sizes — of infinity!
Infinity is not necessarily a sprawl in all directions — which was what turned my eight-year self on — but can be this tight, precise trajectory: 3.14159265358979323846264338327950…. What I’d come to learn from the calculus (although not from my dumb-as-a-doorknob calculus teacher) is that infinity is not just particular, it’s bound. It has a limit — a limit that’s never reached, sure, but a limit that it infinitely approaches. Limits and infinity are not opposed.
That may seem counterintuitive but that’s only because we tend to think in terms of geometry, shapes in three dimensions — squares and circles and such. We tend not to think of things in terms of four dimensions which, alas, is the way of things. Things move, always and necessarily. Time and change are not added to things after the fact. Time and change are of things, immanent to them. Everything is always and already in motion, in time, being stretched along a spatial and temporal trajectory. (This is what drives the philosophy of Henri Bergson — how to think in, and with, time.)
From geometry to calculus, from shapes to shapes in motion, from being to becoming, from Pi to you and me. Just as Pi is infinite yet bound and particular, so is a human being. We are these shapes in motion, these trajectories of becoming.
Step back for a moment and just picture yourself from inception — or even before — to now. See yourself as this thing stretching, morphing, continuously both physically and metaphysically. You are that shape in motion, bound by things such as bone and weight but also thinking and concepts. I’m a skinny ass dude; I will never be The Rock. Such is one of my limits.
And yet I am not pre-known. This is what’s incredible about Pi and human beings: we are precise, bound, and yet we have no idea what’s coming next. There are supercomputers around the world dedicated to figuring out the next step of Pi precisely because we don’t know. And yet it has to be that next number! It is precise. It can’t all of a sudden jump to four.
This is the same with human beings. Nietzsche uses the example of rolling the dice: you don’t know what’s going to come but whatever’s going to come is, indeed, going to come. It’s a matter of chance, yes, and it’s a matter of necessity. Fate and chance are not opposed; on the contrary, they are one and the same. You are a continual rolling of the dice, at once absolutely necessary and absolutely unpredictable.
You are a differential equation. You are a bound infinity. Or, better, you are this bound infinity.