It’s interesting to think about a world where the concept of zero doesn’t exist. It’s not that farfetched. Zero seems to have been invented long after other numbers, and doesn’t really arise from any desire to signify existential absence, only mathematical absence. It looks like zero was invented as a placeholder in mathematical operations. If you have a number in the tens column but nothing in the ones column, you put a little circle there so the rows stay straight. Someone thought that up in about 900 CE, apparently. The Arabic word for it, صف, signifies “sifre,” or “empty,” like “cypher,” or “chiffre,” meaning “figure,” also the name of the James Bond villain from Casino Royale, which is now my favorite movie character name—“Le Chiffre?” as in “The Figure?” or “The Empty?” I mean… that’s brilliant character naming, especially in a movie that involves lots of poker chips.
My point, though, is that zero came to exist because of specific mathematical operations within the decimal system.
I wonder, though, if zero tricks us in certain aspects of our understanding of the physical world. Here’s what I mean: we live somewhat comfortably with the idea of infinity in the universe. “Expanding into infinity” is something we can somewhat conceptually grasp (although there are tricky parts of it, like trying to imagine the universe expanding without some kind of voided area into which the universe is steadily creeping—there's no area, because it's not there yet) because it’s infinitely large. I'm saying that we are comfortable imagining infinity in a forward or external way. Infinity extends away from us to bigger and further sizes and distances—we’ve somewhat got that.
But when we think of smaller and smaller things, we think of them approaching zero. For a long time, the atom was the smallest particle, we thought. There were atoms, and then below that there was nothing, zilch, bupkis. But then we broke open atoms and found leptons and quarks and all that other stuff. Now those are the smallest. And although I think people have begun to recognize that there could be smaller and smaller things—smaller particles, smaller units--I think there’s a ground floor to our speculations about smallness, where there really isn’t a ceiling to our speculations about largeness. We don’t think, “things can get larger and larger until they reach 100, and that’s the largest.” But we do sort of think that zero places a bottom limit on how small things can get.
Of course, that’s not necessarily true. There’s an infinity of small numbers before zero. Another way of thinking about it: if zero were something you had to approach to arrive at, you could never arrive at it. If you had to start from one and then count backwards until you arrived, you would never arrive, because there could always be another fraction (or decimal place) between you and it. You'd get closer, but even closer starts to seem a little dubious when there's no possibility of ever arriving.
It’s Zeno’s Paradox in reverse. It’s a limiting function—the infinitely approachable border of a parabolic graph. It’s kind of easy to think of mathematically, but harder physically: could there be an infinite regress of small distances and sizes just as there is an infinite regress of large distances and sizes outward to the infinity of the expanding universe? What would that mean? I think it would mean that we are perforated, in a way—that every particle of everything somehow goes down, down, down into the rabbit hole at every point. Or the wormhole, maybe. I think it's the physical manifestation of the mathematical idea of infinity that Georg Cantor was encountering with his theory of the aleph--infinity at every point in the system. The idea drove him crazy, and might drive me crazy too, if I were as good at thinking as Georg Cantor was.
Yeah... it’s a hard idea to conceptualize. And there’s really no point in trying. N0ne whats0ever.