Alright I pulled myself together and am actually going to write this now.

Every so often, I think about that paradox where if you move half of the distance between your location and your destination an infinite number of times, you’ll technically never make it to your destination. According to Google, it’s called “Zeno’s Paradox,” and it was created by some dude named Zeno who wanted to prove that motion is a complete and utter sham.

At first, it kind of trips you out because it makes sense, *almost*. But the truth of the matter is that when you test it out in real life, and you really put your mind to it, or even if you don’t, you can probably overcome the paradox and get to the other side of the room.

I refuse to diss math, so I’ve gotta tell you the truth first. The truth is that all infinite converging series eventually sum to a finite number; that is, ½ + ¼ +1/8 + 1/16 … = 1. For some people, that is enough. The jury is still out on whether or not it’s enough for me, but that may just be because it’s been over two years since I’ve touched a series.

Math never hurts, but for me, Zeno’s paradox will always be disproven by a simple act of magic – The Final Step.

Zeno’s paradox is visualized in many different ways, including the original Zeno’s impossible tortoise race, Daniel Tammet’s lamp posts, and Hazel Grace Lancaster’s some-infinities-are-bigger-that-other-infinities. Personally, I’ve always imagined a race – specifically, one of those big-league races where the winner gets to break the ribbon at the end. The runner gets closer and closer and closer to the finish line until suddenly, the ribbon is broken and he’s won the race. And before math and the Internet explained to me why this worked, I justified this convergence through the magic of The Final Step

It is an explanation full of logical fallacies, but I think I’m okay with it. The way I imagine it, the runner can get fractions of millimeters away from the finish line through pure physics, and he makes up the rest of the distance through some combination of determination, grit, and agency that allows him to break through that threshold. Imagine a literal breakthrough, complete with shattering glass.

I’m well aware that this explanation makes even less sense than this blog has so far, but the reason I’m telling you this is that The Final Step is a purely human contribution of *agency*. If distance between A and B were a variable, and I programmed a robot with an infinite loop to move according to Zeno’s paradox, it would just get closer and closer and closer until the software crashed, as is typical of programs written with poor programming style. And the reason this would happen is that the robot doesn’t know how to decide for itself when to take The Final Step and reach the destination.

As a human, on the other hand, I can choose to take The Final Step when I’m 1/32 away, or 1/164 away, or 1/656 away, or… The number is arbitrary, and it makes virtually no difference on my finishing time because it takes fractions of seconds to travel those distances, but I have to choose one of them. Only then do I break the glass, and only then do I win the race.

But the funny thing is, it’s not that decision that allows me to beat all of the other runners. The outcome of that was decided long ago, and it was based upon an entirely different variable – how long it takes me to move a certain amount of distance.

It’s a sad thing to think about, to have beat all of the other runners, and yet still be stuck in the limbo of infinity.

I love that you connected math to agency. Like, why couldn’t we have talked about this in AP Calc instead of having to actually learn about series? Dude, that would’ve been great. I love that you brought STEM and existentialism together, though, because while math is great as a concrete means of explaining why things are the way they are, concrete explanations lead to contradictions. And the idea that we get to choose when to break away, just for a moment, from these concrete rules to unite infinity with our existence is a really, really fascinating one. We have agency, but also we don’t; we choose when to finish, but not how fast to run. Ugh I miss you & this post was so you and so beautiful.