The word "asymptote" comes from the Greek "asymptotos", meaning "not falling together". It was coined by Apollonius of Perga in around 200 BC to describe lines that do not intersect. Over time, of all the ways two lines can fail to meet, "asymptote" became attached to the one where they almost do, where the distance between them shrinks forever yet never reaches zero. Not parallel, not divergent, but almost.
I don't think the fact that this "almost" case was the one worthy of that naming is a mathematical preference. I think it is an emotional one. No one single person had to feel anything for this to be true. The narrowing happened gradually, perhaps imperceptibly so, across centuries of people deciding, without necessarily knowing they were deciding, as they returned again and again to this particular kind of separation, until it became the meaning of the word.
This is what the project begins with. The observation that even the most apparently technical and objective act of description, in this case the naming of a geometric relationship, is not free of the people doing the describing. That language, even mathematical language, carries the residue of whoever shaped it. That whoever shaped this word, at whatever point in its long history, found something in perpetual nearness-without-contact significant enough to isolate and preserve. I feel a deep and unignorable sadness in this perpetual nearness-without-contact, nested within the idea of "almost": two things that spend their entire existence oriented towards each other, narrowing the gap, and yet...
The asymptote describes a specific kind of closeness that the rules of the system will not allow to complete. Defiant of the rules of the system, "symptote" removes the negation, the word itself existing outside of language. A convergence without permission. "Symptoma", the root of "symptom", originally did not mean anything medical. It meant an occurrence, something that happens, befalls. But beneath it is the verb "sympiptein": to fall together. Only later did the meaning of "symptoma" also narrow, coming to denote a sign that coincides with illness, and "falling together" become associated with what happens when something goes wrong inside the body.
Symptote is the "falling together" that is neither an asymptote nor a symptom. Neither the endless almost, nor the body's malfunction. It is the convergence that mathematics says is impossible, happening anyway.
The piece maps two people moving through time. Each begins far from the other, as far as possible, neither knowing of even the existence of the other. Then, each tends, in its averaged direction of movement, towards a dividing line, the asymptote that separates their worlds. Mathematically, they should never cross it. And then they do.
The piece contains 50 simulations. In 49 of them, the people don't meet. In one simulation, they do. The 49 are not failures. They are not control cases. They are the honest truth of how often the phenomenon of meeting does not happen, visibly haunting the same space as the one case in which it does. Without them, the meeting would just be a single point. With them, that point carries the weight of everything it had to not be first.
There is an episode of Black Mirror called Hang the DJ in which a system runs a thousand simulations of two people meeting. In 998 of them, the two choose each other, so the system concludes they are a 99.8% match. It is my favourite episode of the show, but I never liked the implicit argument the episode makes, that the value of their connection is proportional to its likelihood, that what makes two people right for each other is discoverable, that this discovery itself is the meaning of their connection. That this connection is validated by evidence.
The framing means that, if 998 out of a thousand versions of both people choose each other, then the choice was never quite theirs. It was the choice of a pattern, a statistical regularity that the particular version of the two people we see in the episode happened to instantiate. It is probability dressed up as fate.
Symptote is not interested in confidence intervals. The 1 in 50 is not the likelihood of two people meeting. It is rather an acknowledgment that most paths through time do not converge, that most lives that could have touched don't, that the mathematics is not being pessimistic, but simply true. And it is precisely because the piece holds that truth without flinching that the one simulation where they meet means what it means. Not: look how many times this was true, therefore trust it. But: look how many times this wasn't, therefore understand what it means that it was.
In life there is no system running a thousand versions of you. There is only the one timeline you actually lived, surrounded by the invisible ghosts of all the ways it could have gone differently. You don't get the 998. The ghost curves in the piece give you the knowledge that the meeting almost didn't happen at all. They are the weight the meeting carries.
Once two people have met, they can no longer un-meet. Their worlds have mixed into a shared one, it cannot go on to separate. The piece says nothing of how their lives will proceed relative to each other's. It only insists on the possibility of convergence. It insists that mathematics is not the final word. That the phenomenon of two people meeting cannot be validated by the system. That something beyond the system - choice, circumstance, call it whatever you need to - can do what the rules said couldn't be done.