Death, Stars, and Mathematics
by Tyler Jagt
Image: “Untitled” by Josiane Kouagheu
Think slowly, and in one motion, about why human beings count.
The shortest answer is that we die. We rarely learn this early on in life, but understand it later through accumulation. Someone was here, then they were not. The shape of their absence had a length to it that could be tracked, and out of that tracking came counting, then out of counting came the calendar, and out of the calendar came the other instruments we have crafted for holding time. The order matters. We did not invent measurement to understand the cosmos at first, but we may have invented it to understand that we are leaving.
There are two operations bundled together in what I have just called counting, and this lecture hinges on keeping them apart, at least at the start. There is counting in the discrete sense of heartbeats, days, birthdays, the integer increments by which we mark recurrence, and there is measuring in the continuous sense of an hour cut into minutes, minutes into seconds, and so on and so on, into intervals so fine that no human gesture can occupy one. Both are responses to the same human difficulty: both are ways of holding what is leaving us. However, they hold it differently. Counting names returns, measuring names a flow; the calendar counts, the clock measures. We need both because we are creatures who experience time as continuous, and who also remember it as discrete and recurring.
Consider, before going further, the week. Weeks have no astronomical referent. The day is a rotation, the month is a moon, the year is an orbit, but the week is nothing. Instead it’s a unit we invented so that returns would arrive more often than the moon could provide them; and so the week is evidence, if any were needed, that measurement is not pure observation of nature but is partly imposed. We have laid a grid over time, and some of the grid’s lines are drawn from the sky while some of them are drawn from us, and after a while it appears we forget which is which.
So: measurement makes time legible. This is my first claim, and I suppose it is uncontroversial. Whether measurement makes time comprehensible is a different question, and it is the question I want to keep open for the rest of this inquiry.
Move to the clock, which maintains the calendar’s rationale but at much finer resolution. Hour, minute, second. And with each refinement a smaller mesh thrown over the same river of time. There is something worth noticing in the history of the second—for most of its life as a unit, the second was defined astronomically as a specific fraction of a day, the day being a rotation of the Earth. Then in the twentieth century, the second was redefined in terms of atomic oscillations, a specific number of transitions in a cesium atom, because the Earth’s rotation turned out to be slightly irregular and the atom did not. Literally, the unit became more precise as it became less human. We can now measure time with an accuracy that exceeds any practical need a human body has for it, and yet we feel time no more clearly than we did when the unit was a heartbeat. In this way, the precision of the measurement and the comprehension of the user have begun to come apart.
This is the crack in the wall I keep returning to. Mathematics gives us the shape of time, but it does not yet give us its weight.
The clearest example of this gap comes from calculus, with the idea of limits, or a function approaching a value. By any measure of closeness you like, the function gets closer to that value, but it does not necessarily reach it; the value is what the function is tending toward, and so it is defined by approach and not entirely by arrival. I find this idea strange every time I encounter it, that something can have a destination it does not reach. Or perhaps that something can be characterized by where it is going rather than by where it ever is. And yet the moment one accepts the definition, one realizes it describes a great deal of what we already know about the world. The horizon is a limit, but only depending on where you stand; the asymptote is a limit; and—this is the move I want to make carefully and not metaphorically—a life is a limit, in the technical sense.
Death is the value a life approaches in that we tend toward it. We do not, from the inside, arrive, but the moment of arrival is precisely the moment at which there is no longer an arriver, so there is no one to register that the value has been reached. Subjectively, a life is all approach and the limit is unreachable. Epicurus said this, more or less, roughly two millennia before calculus gave it some academic architecture: when death is, I am not; when I am, death is not. The mathematical formulation does not improve the consolation because it only makes the structure of the consolation visible. So, the limit was always there, and calculus gave us a way to write it down. I notice that this should be a comfort and it is not quite. Or it is, in a thinner way. I would argue the reason it is thin is that we do not actually live at the limit, we live in the approach, and of course, the approach is where the count is running. The clock above my desk is not measuring the limit, it is measuring the function, or the slow tending of a particular life toward a value that life will never quite touch but is unmistakably travelling toward. In short, the shape is consoling but the motion is not at all, once realized.
Let me turn now to the sky, which puts a different lens up to the idea, and the two thoughts now must be held together in this argument simultaneously. If the calendar measures time and the clock also measures time, the night sky displays it. This is not a metaphor, although it has often been used like one. In reality it is a consequence of a measurement, because the speed of light is finite. Light travels fast, fast enough that on human scales it appears instantaneous, but it does not travel infinitely fast, and the result of this is that all seeing is delayed seeing. Every photon that arrives at an eye is older than the moment of its arrival, so we never see anything as it is; we see it as it was when the light left. On a human scale the lag is small enough to ignore, because the face across a table is a few nanoseconds old when you see it, just like a voice on a phone is milliseconds delayed. We treat these lags as essentially zero, and for practical purposes they are. But the night sky gives the lag a scale that is a lot harder to dismiss, and I will anchor this in perspective: the sun we see is eight minutes old. The next nearest star is four years old when its light reaches us. The bright stars of a winter sky are sending photons that left their sources during recorded human history, some during the Middle Ages, some during antiquity, some even further before, and so on. Think of the faint smudge of the Andromeda galaxy, visible to the naked eye in a dark place, which is two and a half million years old to our vision. When that light began its journey, no human being existed in any form we would recognize.
And here is the consequence of all of this: the night sky is a calendar that runs backward. If the wall calendar marks our future in empty squares to be filled, the sky returns our past in points of light that have already arrived. In this sense, both are ways of keeping finite time that face opposite directions.
But there is a second lesson in the sky, and it is harder. Stars are not eternal. They have lifespans, durations measured in millions of years for the largest, billions for stars like our sun, trillions for the smallest. And in their cycle, they are born, they burn, they exhaust their fuel, and they end, so the same finitude that organizes a human life organizes a star. However, under this comparison the scale for the word life begins to strain. And because stellar lifetimes can be shorter than the time their light takes to reach us, a particular implication follows: some of the stars we see no longer exist. The light is real; their source is no longer real, because they are dead. We are receiving signals from senders who have, in transit, ceased. Yet all of this is what astronomy adds to our clock, by making time legible through flattening it, with every second equal to every other second and creating something portable. I’d argue the sky restores the strangeness the clock removes, because it shows time at a scale where a human lifetime is what it actually is, which is very small, and that what is ‘permanent’ here may have already ended elsewhere.
Now I want to turn the same sky to a different use, but this time look towards us. The stars in a constellation are not at all near each other. Orion’s belt is one of the more recognizable constellations, with three bright stars in a row, but is in fact three stars at radically different distances from the Earth, accidentally aligned along a particular line of sight from our particular planet. From any other vantage in the galaxy the belt would not exist: the hunter is a projection, made by us, only here on Earth. We have flattened a three-dimensional scatter of stars onto a two-dimensional inner dome and drawn a figure on it. We did this very well for many, many centuries, and considered it god-like. I do not say this to debunk anything, because the hunter is not less real for being drawn, but he is real in a different register from the mathematics underneath him. And the difference between those two registers is, I think, the useful distinction we can begin to chip away at and separate the debris from. There are, on the one hand, the patterns the universe truly makes, such as orbits, gravitational relations, the structure of matter, or again the lifecycles of stars. These patterns are real in the strong sense because they do not require an observer, and they were operating before any eye looked up to witness them. They will also continue when no eye remains. We would be right to call these the mathematical patterns. And on the other hand, there are patterns we lay over the first kind. Constellations, calendars, the names of months, or the decades of a human life. These are real in a weaker sense because they depend on observers, but they are constructed and meaningful, while still being observer-dependent and quite fragile. Different cultures draw different hunters, but they all draw, and they all exhibit narrative patterns and place them on top of other structures.
Considering all of this, it’s clear that while the mathematical patterns will outlast us, the narrative patterns will not. And yet the narrative patterns are what make the mathematical ones usable to the human mind. Without the hunter, the sky is just a scatter. In the same way, without the calendar, the year is undifferentiated duration; so on and so forth, without the named decades, a life is a continuous function with no marked points; and how sad that would be, to us. The narrative pattern is what allows the mathematical pattern to be inhabited by humanity, who needs not only to live in a world, but to make one, too; and to make it meaningful in some sense. And our whole existence is about making something meaningful, though history is, in part, the record of our deep disagreements about what meaning is and where it may be found.
Reduced to its simplest terms, here is the claim we now arrive at: a human life is a constellation laid over a mathematics, similar to the ones described earlier. The mathematics is the indifferent fact of finite duration with the limit and the approach as an unreachable value. The constellation, then, is the meaning we draw on top of that fact through birthdays, anniversaries, the named year, or the history of a life when it ends. The mathematics do not require the constellation, but importantly, the constellation cannot exist without the mathematics. We need both because humanity can perceive the mathematics but cannot fully live inside it.
Now step back. I want to consolidate, because this lecture has now placed three things in the same field and restrung them in a way that imposes meaning on them to belong together. Pattern-making is the single human response to endings, expressed in many different ways. But we do not have a separate strategy for the future, the present, and the past; we have one strategy, and we apply it in three directions. When we hold these things next to one another in our minds, we do arrive at something: mathematics is the version of pattern with the observer subtracted, story is the version of pattern with the observer central, and most human meaning lives between them. To look up at a star is to perform, in a single act, every gesture this lecture has tried to describe. You are counting, in principle, photons, arriving at a retina at a measurable rate, and you are encountering a limit with the finite speed of light, or the finite life of the source, all while receiving the past as light, since the light is old, maybe even dead. And you are, almost involuntarily, beginning to draw a hunter, because that is what a mind does when it sees points arranged on a dome; it tries to make meaning. To look up in the night is to do all of it at once, knowingly or not.
Tyler Jagt is from Ontario, Canada and presently lives in Georgia. He has previously taught literature, poetry, and critical writing at James Madison University, Mercer University, and several other institutions. Aside from writing, his artwork is featured across Atlanta’s contemporary art centers.
Josiane Kouagheu is a journalist, writer, photographer, painter and poet from Cameroon. Her works have appeared or are forthcoming in Brittle Paper, African Writer Magazine, Kalahari Review, Frontier Poetry, Prairie Schooner, The Nomad Review, Apricity Magazine, Al Dente Journal, Double Dutch Magazine, Barzakh Magazine, New Ohio Review and elsewhere.