December 31, 2025
My favorite professional cyclist, Alberto Contador, retired in 2017. For the last couple years of his career, as with so many athletes, being a fan became more and more about cheering for an underdog navigating his inevitable decline. Watching the final race of his career, I remember feeling an odd sense of relief. Soon he would retire, and would belong to the past, and the current (weakened) version would stop being the “real” Alberto Contador. The real version would become that of memory: dueling with Rasmussen in 2007, stopping Lance’s comeback in 2009, defeating Rodriguez at the eleventh hour in 2012. When constructing a mental model of something fully of the past, I’m free to pick and choose those elements that are most important and meaningful, because I’m not bound by any notion of the present.
I argue that this mental shift isn’t just more comforting—it’s more true, and it was more true even before Contador’s retirement. His career is just one instance of a ubiquitous pattern. What is the data structure of time? We intuit a mutable canvas, erased and rewritten moment by moment, the past destroyed. I argue that it’s a time series, a stream of immutable states accumulating over time, like those children’s books where you flip the pages to animate some moving thing. Old pages may be inaccessible, at least as we navigate this timebound world, but in some mysterious way they are real. (Indeed, they may be more real than the infinitesimal present or the contingent future. In a world where anything can happen, they—specific and concrete—actually happened.)
Time as a stream of successive states: isn’t this sort of trivial? Don’t we already think that the past exists (we treasure memories) and the future exists (we prepare for what’s to come)? Perhaps, but the psychological shift I describe around Contador’s retirement was material; something happened there. And, again, I argue that the time-series mindset isn’t just more comforting, but more true, and more true even before the time series has elapsed.
As we’ll see, looking at the world this way has some intriguing properties. In mathematical terms, we’ll go from caring about the present value (a single point on a graph) to summing up the entire area under the curve.
If the past (and even future) are as real as the present, what does that imply? For one thing, it implies that something in the future is just as valuable as that thing in the present. Our future selves are just as important as our present self; we should make decisions assuming all selves have an equal vote. In a straightforward way, this is a nudge toward all sorts of future-oriented behaviors: eating well, exercising, saving and investing money, anything that’s painful now but rewarding in the long term. (I sometimes wonder whether my fondness for all these behaviors might be less about fondness for the thing, and more about fondness for this philosophical notion of time.)
It goes farther, though. This perspective implies that the past is also as valuable as the present. A dollar spent yesterday is still just as valuable as one today; a great experience yesterday is still as valuable as one today or tomorrow. Parfit shares the thought experiment of a patient awakening from anesthesia and being told that either they had just completed a very painful surgery, or they were about to undergo a moderately painful one; somehow the doctor is not sure. In that moment, which would the patient hope to be true? Most of us would prefer the more painful surgery, the one in the past—but in the “area under the curve” model, this is plainly illogical, since it nets out to more overall pain.
Returning to the future, this mindset would have us think less and less about current values, and more and more about expected values. Future things are worth something today; expected values (and their accounting cousin, Net Present Values) let us express that value in the present. A promising but uncertainty opportunity is worth something today because it has positive expected value: if I roll the dice on it 1,000 times, I come out ahead. In the real world, I can’t actually do the thing 1,000 times, but knowing that it has positive EV lets me think of it as good even before knowing the outcome—or even knowing, after the fact, that it turned out bad. There can be real comfort here: if I don’t yet have a thing, but I’m working hard toward it and rationally expect to have it, I can rationally see myself as having it in expectation. My house doesn’t have much of a view, but I value beauty a great deal, and fully intend to prioritize a view the next time we move. So I already live in a house with a view in expectation, because that future beauty is worth something to me today; I would rather have it in expectation than not. As I start a workout program, I may be weak in the present, but I’m strong in expectation. As I start a new job, I am cautious and unsure, but I am skilled and confident in expectation. Expected value is real, and it lets us “pull forward” value and even identity from the future, experiencing it today.
This quickly runs in trouble: in expectation, aren’t we infirm, or fact dead? Well, yes. My answer would be to focus on the area under the curve: hopefully there’s a lot of other expected value first. Or here’s one that hits close to home: I all too easily fall into the trap of feeling like “all I have to do is tweak X or Y, and then everything will be good and I can really enjoy it and life can really begin.” (All I have to do is move into that house with a view, and then I’ll really enjoy that ambient connection with nature!) This failure mode has us living forever in the future, always a step or two away from life kicking in in its full realness. I would respond that the time-series model treats the future as real, but not as more real. It’s a mistake to overlook expected value and treat future goods as worth nothing today. But it’s also a mistake to think of only expected value, ignoring the present and the past.
There are implications for virtue (or any positive behavior). You don’t need to try to keep the plate spinning forever, behaving rightly at every turn, fearing that any lapse will tip you immediately into an unvirtuous state. What matters is maximizing the aggregation of virtue over your lifetime. If you stumble today, simply double down tomorrow. This model of time encourages the growth mindset.
Beyond virtue, this perspective changes how we think about personal identity. In Horizon, Barry Lopez writes:
A species is not so much a permanent thing as a point on the developmental line of that thing through time.
The thing-ness isn’t in the point; it’s in the line. So it is with people. The path something takes through space and time is called a “world line”: mine starts in Oregon, in 1988, and winds its way through to the here and now. What’s interesting is to think of the four-dimensional self—the world line—as the location of thing-ness, more real than the three-dimensional present.
A three-dimensional cube, projected onto a two-dimensional plane, casts a two-dimensional square as its shadow. You can think of your present life as the three-dimensional projection of your four-dimensional self. It’s not who you are: it’s just what you’re experiencing in the timebound now. Who you are is in the world line: the sum of the area under the curve.
Seeing yourself this way can color everyday experience. Many activities and relationships appear mundane in their local context, but remarkable in the context of a lifetime. My kids are about one year old; I play with them often; from the perspective of the present, it’s often a little boring. But when I locate myself in the world line, I think of all the years and decades to come in which I’ll know these people, and how our relationship will change, and what a vanishingly rare and remarkable thing it is for them to be babies like this. And then it’s not boring anymore.
This mindset also has implications for loss and grief. In the mutable model, loss is a binary event, a switch thrown from 1 to 0. In the immutable time-series model, it’s not a switch but a slider: time as incremental loss.
Loss has nothing to do with the past and everything to do with the future. You can’t lose what has already happened; the past is immutable. But loss feels like it has nothing to do with the future and everything to do with the past. When you lose something, it’s natural to think back on its presence in your life. The day you (say) move away from a beloved city, you look back on all the good times you’ve enjoyed there. But you already lost all those experiences: you lost them the moment they finished happening—the moment they became past—and they’re no more gone now than they were right then.
You can’t lose what’s already in the past; you’ve already lost it. If time is continuous, why do we feel loss all at once? Shouldn’t we “price it in,” the way markets move in advance of well-known events?
Or consider the way that a death’s sadness seems to vary with temporal proximity. The obituary of a stranger who died yesterday is inherently sad; it’s hard not to consider the circumstances, the grief of those who remain. Now consider a death from, say, 100 years ago. It’s still sad, but it’s also… unsurprising? Natural? (Of course this person died; they were born in 1840!) Now consider a death from thousands of years ago—say, in the time of the Greeks. The death of such a person is just one chapter among many; they are characterized by all the decades of their life, with older events no less important. The farther we zoom out, the more we adopt Nagel’s “view from nowhere,” the more we foreshorten time and see a person as the area under the curve. What is noteworthy is not the endpoint of their death but the whole of their life. It’s reassuring, as we contemplate the inevitable deaths of our own loved ones, to remember that they and we are no different than the Greeks.
The time-series model asks us to hold contradictory attitudes toward the past. First, to notice and mourn loss in the moment, and to grieve in advance those losses we see coming—over a lifetime, smoothing loss itself into something closer to a smooth line, not a jagged and discontinuous set of switches. Second, paradoxically, to grieve a little less, because the past is no less meaningful than the present. Far from being destroyed, it is a peer of the present and of the future.
Unifying these two, the impossible ideal would be to greet even a terrible loss with equanimity: “The area under the curve, which once was growing, has stopped. Though we cannot access it, the area remains.”
Similar to loss is decline. What a strange curse it is to enjoy something very good very early in life, and then to experience each passing year as a little less good. (What a blessing it would be if we aged in reverse, our strength and vitality growing alongside our wisdom, humility, and and gratitude, until our final years were crowned by the full bloom of youth!) Yet this is the cost of having good things: we must eventually give them up.
In these unavoidable circumstances, it is plainly advantageous to think in absolutes, not relatives: “I am a little less fit and strong than I was five years ago, but I am healthy and active, and I can do the things I love.” Or: “I am no longer healthy, but I am surrounded by loved ones, my mind is sharp, and I may still contemplate beauty.” In so many circumstances, there is something that continues to accumulate under the curve.
(A twist: you can imagine circumstances where thinking in relatives is advantageous. Maybe someone is terribly injured and learning to walk again—they may take heart not in their absolute circumstances, but in their relative improvement day over day. Perhaps what we want isn’t a wholesale commitment to absolutes, but a sort of cognitive flexibility to pick the perspective that serves us best.)
Even in the absence of decline, we take so much for granted. Part of this, I think, is because we’re so inclined to think in relative terms. The things we have year after year, always there—good health, a happy marriage, a favorite meal—are all too easy to underappreciate until they’re gone. The very consistency and durability that makes them so good is what makes us take them for granted. From the timeless perspective, it’s more obvious that some relatively constant good thing is good indeed, predictably accumulating value year after year.
You’ll note that we’re no longer talking only about time. Moving from a perspective of “now” toward a broad, time-series view is just one case of moving from a subjective perspective toward an objective one. Much of the arc of human learning and wisdom fits that pattern. Copernicus: “the earth is not more special than the universe.” Darwin: “humans are not more special than our fellow species.” Virtually every wisdom tradition, from the Bible to Buddha: “we are not more special than the others; I am not more special than you.” It follows: now is not more special than other moments. The present is not a different thing than the past and future; it’s one page among many, about to become past itself. (A note of humility: just as we judge the past full of moral error, we can be sure our own time will be judged in error too.)
In some ways, this perspective seems very different from that encouraged by Eastern mindfulness traditions: rather than embracing the present, living in the moment, we seek this extremely cerebral, disembodied notion of the whole of time. Yet I think it’s deeply aligned. Like mindfulness, it seeks to pull us away from our deep identification with self, which goes hand in hand with the present.
“The past and future exist”: I’m not even sure I believe the strong form of this claim. But it feels so helpful to think this way that I write this in part to convince myself.