Why Time Flies
I settle into a seat on the Paris Métro and rub the sleep from my eyes. I feel unmoored. The calendar says late winter but outside my window the day is warm and fair, the leaf buds gleam, the city is resplendent. I arrived from New York yesterday and stayed out past midnight with friends; today my head is still in the dark, glued in a season and a time zone several hours behind me. I glance at my watch: 9:44 a.m. As usual, I am late.

The watch is a recent gift from my father-in-law, Jerry, who wore it himself for many years. When Susan and I became engaged, her parents offered to buy me a new watch. I declined, but for a long time afterward I couldn’t shake the worry that I’d made a poor impression. What sort of son-in-law ignores the time? So when Jerry subsequently offered me his old wristwatch I said yes right away. It has a golden dial set on a wide silver wristband; a black face bearing the brand name (Concord) and the word quartz in bold letters; and the hours denoted by unnumbered lines. I liked the new weight on my wrist, which made me feel important. I thanked him and remarked, more accurately than I could understand at that moment, that it would be a helpful addition to my research on time.

On the evidence of my senses, I had come to believe that the time “out there” in clocks, watches, and train schedules is quantifiably distinct from the time coursing through my cells, body, and mind. But the fact was that I knew as little about the former as I did about the latter. I could not say how a particular clock or watch worked nor how it managed to agree so closely with the other watches and clocks that I occasionally noticed. If there was a real difference between external and internal time—as real as the difference between physics and biology—I had no idea what it was.

So my new, used watch would be a kind of experiment. What better way to plumb my relationship to time than to physically attach it to me for a while? Almost immediately I saw results. For the first few hours of wearing the watch I could think about nothing else. It made my wrist sweat and tugged at my whole arm. Time dragged literally and, because my mind dwelt on the dragging, figuratively. Soon enough I forgot about the watch. But on the evening of the second day I suddenly remembered it again when, while bathing one of our infant sons in the tub, I noticed it on my wrist, underwater.

Secretly I hoped that the watch might confer some degree of punctuality. For instance, it seemed to me that if I looked at the watch often enough I might yet arrive on time for my ten o’clock appointment in Sèvres, just outside Paris, at the Bureau International des Poids et Mesures—the International Bureau of Weights and Measures. The Bureau is an organization of scientists devoted to perfecting, calibrating, and standardizing the basic units of measurement used around the world. As our economies globalize, it becomes ever more imperative that we all be on precisely the same metrological page: that one kilogram in Stockholm equals exactly one kilogram in Jakarta, that one meter in Bamako equals exactly one meter in Shanghai, that one second in New York equals exactly one second in Paris. The Bureau is the United Nations of units, the world standardizer of standards.

The organization was formed in 1875 through the Convention of the Metre, a treaty meant to ensure that the basic units of measurement are uniform and equivalent across national borders. (The first act of the Convention was for the Bureau to hand out rulers: thirty precisely measured bars made of platinum and iridium, which would settle international disagreements over the correct length of a meter.) Seventeen nation members joined the original Bureau; fifty-eight now belong, including all the major industrialized nations. The suite of standard units it oversees has grown to seven: the meter (length), the kilogram (mass), the ampere (electrical current), the kelvin (temperature), the mole (volume), the candela (luminosity), and the second.

Among its many duties, the Bureau maintains a single, official worldwide time for all of Earth, called Coordinated Universal Time, or U.T.C. (When U.T.C. was first devised, in 1970, the organizing parties could not agree on whether to use the English acronym, C.U.T., or the French acronym, T.U.C., so they compromised on U.T.C.) Every timepiece in the world, from the hyperaccurate clocks in orbiting global-positioning satellites to the cog-bound wristwatch, is synchronized directly or eventually to U.T.C. Wherever you live or go, whenever you ask what time it is, the answer ultimately is mediated by the timekeepers at the Bureau.

“Time is what everybody agrees the time is,” a time researcher explained to me at one point. To be late, then, is to be late according to the agreed-on time. By definition, the Bureau’s time is not merely the most correct time in the world, it is precisely the correct time. This meant, as I glanced at my watch yet again, that I was not merely late: I was as late as I have ever been and as late as it is possible to be. Soon enough I would learn just how far behind the time I truly was.

• • •

A clock does two things: it ticks and it counts the ticks. The clepsydra, or water clock, ticks to the steady drip of water, which, in more advanced devices, drives a set of gears that nudges a pointer along a series of numbers or hash marks, thereby indicating time’s passage. The clepsydra was in use at least three thousand years ago, and Roman senators used them to keep their colleagues from talking for too long. (According to Cicero, to “seek the clock” was to request the floor and to “give the clock” was to yield it.) Water ticked and added up to time.

For most of history, though, in most clocks, what ticked was Earth. As the planet rotates on its axis, the sun crosses the sky and casts a moving shadow; cast on a sundial, the shadow indicates where you are in the day. The pendulum clock, invented in 1656 by Christiaan Huygens, relies on gravity (affected by Earth’s rotation) to swing a weight back and forth, which drives a pair of hands around the face of the clock. A tick is simply an oscillation, a steady beat; Earth’s turning provided the rhythm.

In practice, what ticked was the day, the rotational interval from one sunrise to the next. Everything in between—the hours and minutes—was contrived, a man-made way to break up the day into manageable units for us to enjoy, employ, and trade. Increasingly our days are governed by seconds. They are the currency of modern life, the pennies of our time: ubiquitous and critical in a pinch (for instance, when you just manage to make a train connection) yet sufficiently marginal to be frittered away or dropped by the handful without thought. For centuries, the second existed only in the abstract. It was a mathematical subdivision, defined by relation: one-sixtieth of a minute, one thirty-six-hundredth of an hour, one eighty-six-thousand-four-hundredth of a day. Seconds pendulums appeared on some German clocks in the fifteenth century. But it wasn’t until 1670, when the British clockmaker William Clement added a seconds pendulum, with its familiar tick-tock, to Huygens’s pendulum clock, that the second acquired a reliably physical, or at least audible, form.

The second fully arrived in the twentieth century, with the rise of the quartz clock. Scientists had found that a crystal of quartz resonates like a tuning fork, vibrating at tens of thousands of times per second when placed in an oscillating electrical field; the exact frequency depends on the size and shape of the crystal. A 1930 paper titled “The Crystal Clock” noted that this property could drive a clock; its time, derived from an electrical field instead of gravity, would prove reliable in earthquake zones and on moving trains and submarines. Modern quartz clocks and wristwatches typically use a crystal that has been laser-engineered to vibrate at exactly 32,768 (or 215) times per second, or 32,768 Hz. This provided a handy definition of the second: 32,768 vibrations of a quartz crystal.

By the nineteen-sixties, when scientists managed to measure an atom of cesium naturally undergoing 9,192,631,770 quantum vibrations per second, the second had been officially redefined to several more decimal places of accuracy. The atomic second was born, and time was upended. The old temporal scheme, known as Universal Time, was top-down: the second was counted as a fraction of the day, which took its shape from Earth’s motion in the heavens. Now, instead, the day would be measured from the ground up, as an accumulation of seconds. Philosophers debated whether this new atomic time was as “natural” as the old time. But there was a bigger problem: the two times don’t quite agree. The increasing accuracy of atomic clocks revealed that Earth’s rotation is gradually slowing, adding very slightly to the length of each day. Every couple of years this slight difference adds up to a second; since 1972, nearly half a minute’s worth of “leap seconds” have been added to International Atomic Time to bring it into sync with the planet.

In the old days, anyone could make his or her own seconds through simple division. Now the seconds are delivered to us by professionals; the official term is “dissemination,” suggesting an activity akin to gardening or the distribution of propaganda. Around the world, mainly in national timekeeping laboratories, some three hundred and twenty cesium clocks, each the size of a small suitcase, and more than a hundred large, maser-driven devices generate, or “realize,” highly accurate seconds on a near-continuous basis. (The cesium clocks, in turn, are checked against a frequency standard generated by a device called a cesium fountain—a dozen or so exist—which uses a laser to toss cesium atoms around in a vacuum.) These realizations are then added up to reveal the time of day. As Tom Parker, a former group leader at the National Institute of Standards and Technology, told me, “The second is the thing that ticks; time is the thing that counts the ticks.”

N.I.S.T. is a federal agency that helps produce the official, civil time for the United States. Experts at its two laboratories, in Gaithersburg, Maryland, and Boulder, Colorado, keep a dozen or more cesium clocks running at any given time. As precise as these clocks are, they disagree with one another on a scale of nanoseconds, so every twelve minutes they are compared to one another tick by tick to see which are running fast and which are running slow and by exactly how much. The data from the clock ensemble is then numerically mashed into what Parker calls “a fancy average,” and this becomes the basis for the official time.

How this time reaches you depends on your timekeeping device and where you happen to be at the moment. The clock in your laptop or computer regularly checks in with other clocks across the Internet and calibrates itself to them; some or all of these clocks eventually pass through a server run by N.I.S.T. or another official clock and are thereby set even more accurately. Every day, N.I.S.T.’s many servers register 13 billion pings from computers around the world inquiring about the correct time. If you are in Tokyo, you might be linked to a time server in Tsukuba that is run by the National Metrology Institute of Japan; in Germany, the source is the Physikalisch-Technische Bundensanstalt.

Wherever you are, if you’re checking the clock on your cell phone, it’s probably receiving its time from the Global Positioning System, an array of navigation satellites synchronized to the U.S. Naval Observatory, near Washington, D.C., which realizes its seconds with an ensemble of seventy-odd cesium clocks. Many other clocks—wall clocks, desk clocks, wristwatches, travel alarms, car-dashboard clocks—contain a tiny radio receiver that, in the United States, is permanently tuned to pick up a signal from N.I.S.T. Radio Station WWVB, in Fort Collins, Colorado, which broadcasts the correct time as a code. (The signal is very low frequency—60 Hz—and the bandwidth so narrow that a good minute is needed for the complete time code to come through.) These clocks can generate the time on their own, but for the most part they act as middlemen, serving you the time that is disseminated by more refined clocks somewhere higher up in the temporal chain of command.

My wristwatch, in contrast, has no radio receiver or any way of talking to satellites; it’s all but off the grid. To synchronize with the wider world I need to look at an accurate clock and then turn the stem of my watch and set the time accordingly. To achieve even greater accuracy I could regularly take my watch to a shop and have its mechanism calibrated to a device called a quartz oscillator, which gains its precision from a frequency standard monitored by N.I.S.T. Otherwise, my watch will keep its realizations to itself and will soon fall out of step with everyone else’s. I had assumed that putting on a watch meant strapping established time to my wrist. But, in fact, unless I take the measure of the clocks around me, I am still a rogue. “You’re free-running,” Parker said.

• • •

From the late seventeenth century to the early twentieth century, the most accurate clock in the world resided at the Royal Observatory in Greenwich, England; it was regularly reset by the Astronomer Royal according to the movement of the heavens. This situation was good for the world but quickly became a problem for the Astronomer Royal. Beginning around 1830, he increasingly found himself interrupted from his work by a knock on the door from a townsperson. Pardon me, he was asked. Would you tell me the time?

So many people came knocking that eventually the town petitioned the astronomer for a proper time service; in 1836 he assigned his assistant, John Henry Belville, to the task. Every Monday morning, Belville calibrated his timepiece, a pocket chronometer originally made for the duke of Sussex by the esteemed clockmaker John Arnold & Son, to the observatory time. Then he set off for London to visit his clients—clockmakers, watch repairers, banks, and private citizens who paid a fee to synchronize their time to his and, by extension, the observatory’s. (Belville eventually replaced the chronometer’s gold case with a silver one in order to draw less attention in “the less desirable quarters of the town.”) When Belville died, in 1856, his widow took over; when she retired, in 1892, the service passed to their daughter Ruth, who became known as “the Greenwich time lady.” Using the same chronometer, which she called “Arnold 345,” Miss Belville made the same tour, disseminating what by then was known as Greenwich Mean Time, the official time of Britain. The invention of the telegraph, which enabled remote clocks to synchronize with Greenwich time almost immediately and at lower cost, eventually rendered Miss Belville almost but not quite obsolete. When she retired around 1940, in her mideighties, she still served some fifty clients.

I had come to Paris to meet with the Greenwich time lady of the modern era, the Miss Belville for all of Earth: Dr. Elisa Felicitas Arias, the director of the B.I.P.M.’s Time Department. Arias is slender, with long brown hair and the air of a kindly aristocrat. An astronomer by training, Arias worked for twenty-five years at observatories in Argentina, her native country, the last ten of them with the Naval Observatory; her specialty is astrometry, the correct measuring of distances in outer space. Most recently she worked with the International Earth Rotation and Reference Systems Service, which monitors the ever-so-slight variations in our planet’s motions and consequently determines when the next leap second should be added to the temporal mix. I met her in her office, and she offered me a cup of coffee. “We have one common objective,” she said of her department. “To provide a timescale suitable to be an international reference.” The aim, she added, is “ultimate traceability.”

Of the hundreds of clocks and clock ensembles run by the Bureau’s fifty-eight member-nations, only about fifty—the “master clocks,” one per country—are up and running and providing official time; everywhere, at all hours, they realize seconds. But their realizations don’t agree with one another. It’s a matter of nanoseconds, or billionths of a second. That’s not enough to trouble electrical-power companies (which need accuracies only in the milliseconds) or disrupt telecommunications (which traffic in microseconds). But the clocks on different navigation systems—such as G.P.S., which is run by the U.S. Department of Defense, and the European Union’s new Galileo network—need to agree within a few nanoseconds in order to provide consistent service. The world’s clocks should agree, or should at least be well aimed toward the same point of synchrony, and Universal Coordinated Time is the designated goal.

Universal Coordinated Time is derived by comparing all the member clocks as they tick their seconds simultaneously, and noting the discrepancies. It is a tremendous technical challenge. For one thing, the clocks are hundreds or thousands of miles apart. Given the time it takes for an electronic signal to traverse such distances—a signal that says, in effect, “Start ticking now”—it is difficult to know precisely what “at the same time” means. To get around this problem, Arias’s section uses G.P.S. satellites to transfer data. The satellites all have known positions and carry clocks synchronized to the U.S. Naval Observatory; with this information, the B.I.P.M. can calculate the precise moments when time signals are being sent to them from clocks around the world.

Even then, uncertainties loom. The position of a satellite can’t be known exactly; bad weather and Earth’s atmosphere can slow or alter a signal’s path and obscure its true travel time. And the equipment harbors electronic noise that can obscure precise measurement. Offering an analogy, Arias motioned to the door of her office. “If I ask you what time it is, you’ll tell me the time and I’ll compare it to mine,” she said. “We are face-to-face. If I say, ‘Go out, close the door, and tell me what time it is,’ I will ask you and say, ‘No no no, say it again, there is some noise’?”—she made a funny buzzing sound with her lips, Brrrrrrrrip!—“?‘between us.’?” A great deal of care and effort goes into correcting for this noise, to ensure that the message heard by the B.I.P.M. accurately reflects the relative behavior of the world’s clocks.

“We have eighty laboratories around the world,” Arias said; some nations have more than one. “We need to organize all those times.” She sounded gentle and encouraging, like Julia Child describing the essence of a good vichyssoise. First, Arias’s team in Paris gathers all the necessary ingredients: the nanosecond-scale differences between each member clock and every other one, plus a strong dash of local data about the historical behavior of each clock. The information is then run through what Arias called “the algorithm,” which takes into account the number of clocks in service (on any given day some clocks may be down for repair or recalibration), gives slight statistical favor to the more accurate of these clocks, and whisks the whole to a uniform texture.

The process is not purely computational. A human is needed to consider small yet critical factors: that not all labs calculate their clock data exactly the same way; that a particular clock has been behaving oddly of late and its contribution needs to be reweighted; that, owing to software errors, some of the minus signs in the spreadsheet were accidentally changed to plus signs and need to be changed back. Wielding the algorithm also involves a certain amount of individual, mathematical artistry. “There is some personal flair involved,” Arias said.

The final result is what Arias calls “an average clock,” in the best sense: its time is more robust than any single clock or national ensemble could hope to provide. By definition and by universal agreement, or at least by agreement of the fifty-eight signatory countries, its time is perfect.

• • •

It takes time to make Coordinated Universal Time. Simply ironing out the uncertainty and noise from all the G.P.S. receivers takes two or three days. The task of calculating U.T.C. would be logistically overwhelming if it were done continuously, so each member clock takes a reading of local time every five days at exactly zero hour U.T.C. On the fourth or fifth day of the following month, each lab sends its accumulated data to the B.I.P.M. for Arias and her team to analyze, average, check, and publish.

“We try to do it as soon as possible, without neglecting any checking,” she said. “That process takes more or less five days. We receive on the fourth or fifth of the month, start calculating on the seventh, publish on the eighth or ninth or tenth.” Technically, what is being assembled is International Atomic Time; creating U.T.C. is a simple matter of adding on the correct number of leap seconds. “Of course there is no clock providing U.T.C. exactly,” Arias said. “You only have local realizations of U.T.C.”

I suddenly understood: the world clock exists only on paper and only in retrospect. Arias smiled. “When people say, ‘Can I see the best clock in the world?’ I say, ‘Okay, here you are, this is the best clock in the world.’?” She handed me a sheaf of papers stapled in one corner. It was a monthly report, or circular, that is distributed to all the member time laboratories. The report, called Circular T, is the main purpose and product of the B.I.P.M. Time Department. “It is published once every month, and it is giving information on time in the past, which is the month before.”

The world’s best clock is a newsletter. I flipped through its pages and saw column after column of numbers. Listed down the left were the names of the member clocks: IGMA (Buenos Aires), INPL (Jerusalem), IT (Torino), and the rest. The columns across the top were dated every five days through the previous month—Nov. 30, Dec. 5, Dec. 10, and so on. The number in each cell represented the difference between Coordinated Universal Time and the local realization of U.T.C. as measured by a particular laboratory on a particular day. On December 20th, for instance, the figure for the national clock of Hong Kong was 98.4, indicating that, as of that moment of measurement, the national clock of Hong Kong was 98.4 nanoseconds behind Coordinated Universal Time. In contrast, the figure for Bucharest’s clock that day was minus 1118.5, indicating that it was 1118.5 nanoseconds—a sizable step—ahead of the universal average.

The purpose of Circular T, Arias said, is to help member laboratories monitor and refine their accuracy relative to U.T.C., a procedure known as “steering.” By learning how far their clocks deviated from the U.T.C. average during the previous month, member labs can tweak and correct their equipment to perhaps aim a little closer next month. No clock ever achieves perfect accuracy; consistency is sufficient. “It is useful because laboratories pilot their U.T.C.s,” Arias said; she made time sound like a ship in a channel. “They need to know how the U.T.C. locally behaves. So they check if they have correctly steered to Circular T. That’s why they’re all checking their email and the Internet, to know where they were last month with respect to U.T.C.”

For the most accurate clocks, steering is essential. “Sometimes you have a very good clock, and then it takes a time step—a jump in time,” Arias said. On her copy of the latest Circular T, she pointed to the row of numbers representing the U.S. Naval Observatory. Its figures were all admirably small, in the range of double-digit nanoseconds. “This is an excellent realization of U.T.C.,” Arias said. That’s no surprise, she added, since the U.S. Naval Observatory, which has the largest number of clocks in the international pool, represents roughly twenty-five percent of the total weight of U.T.C. The U.S. Naval Observatory is responsible for steering the time utilized by the G.P.S. satellite system, so it has a global responsibility to follow U.T.C. very strictly.

But steering isn’t for everyone. Piloting one’s clock requires expensive equipment, and not all laboratories can afford to bother. “They let their clocks live their life,” Arias said. She noted a row of numbers from a laboratory in Belarus, which seemed to be living a life of leisure, well off the standard. I asked whether the B.I.P.M. ever rejects a laboratory’s contribution as too inaccurate. “Never,” Arias replied. “We always want their time.” As long as a national time lab is equipped with a decent clock and receiver, its contributions are averaged in to U.T.C. “When you build time,” she said, one of the goals is “the broad dissemination of time”—U.T.C. can’t be considered universal unless it includes everyone, no matter how out of step they might be.

I was still wrapping my head around what, and when, Coordinated Universal Time is. (“It took me a couple of years,” Tom Parker later told me.) To the extent that a paper clock can be said to exist, it does so only in the past tense, derived as it is from data gathered the previous month; Arias calls U.T.C. “a post-real time process,” a dynamic preterit. Then again, the numbers in the columns of her paper clock serve much like course corrections or channel markers for the real clocks out there, to help them steer in the right direction—as if U.T.C. were a future noun, like a harbor just over the horizon. When you look to your watch, clock, or cell phone for a reading of the official time, as derived from Boulder or Tokyo or Berlin, what you receive is only a very near estimate of the correct time, which won’t be known for another month or so. Perfectly synchronized time evidently does exist—just not anymore and not quite yet; it is in a perpetual state of becoming.

• • •

I had come to Paris under the assumption that the world’s most exact time emanates from some tangible, ultrasophisticated device: a fancy clock with a face and hands, a bank of computers, a tiny, shimmering rubidium fountain. The reality was far more human: the world’s best time—Coordinated Universal Time—is produced by a committee. The committee relies on advanced computers and algorithms and the input of atomic clocks, but the metacalculations, the slight favoring of one clock’s input over another’s, is ultimately filtered through the conversation of thoughtful scientists. Time is a group of people talking.

Arias noted that her Time Department operates within a still-larger ensemble of consultative committees, advisory teams, ad hoc study groups, and monitoring panels. It hosts regular visits from international experts, holds occasional meetings, issues reports, and analyzes the feedback. It is checked, supervised, calibrated. Occasionally the overarching Consultative Committee for Time and Frequency, or C.C.T.F., weighs in. “We don’t operate alone in the world,” she said. “For minor things we can make decisions ourselves. For major things we have to submit proposals to the C.C.T.F., and the experts from the best laboratories will say, ‘We agree’ or ‘We don’t agree.’?”

All this redundancy is designed to counterbalance one ineluctable fact: no single clock, no single committee, no individual alone keeps perfect time. That’s the nature of time everywhere, it turns out. As I began talking with scientists who study how time works in the body and mind, they all described its operation as some version of a congress. Clocks are distributed throughout our organs and cells, working to communicate and keep in step with one another. Our sense of time’s passage is rooted not in one region of the brain but results from the combined working of memory, attention, emotion, and other cerebral activities that can’t be singularly localized. Time in the brain, like time outside it, is a collective activity. Still, we’re accustomed to imagining an ultimate collective somewhere in there—a core group of sifters and sorters, like an internal Bureau International des Poids et Mesures, perhaps run by a brown-haired Argentine astronomer. Where is the Dr. Arias in us?

At one point I asked Arias to describe her personal relationship to time.

“Very bad,” she replied. There was a small digital clock on her desk; she picked it up and aimed its readout at me. “What time is it?”

I read the numbers. “One-fifteen,” I said.

She motioned for me to look at my wristwatch: “What time is it?”

The hands read 12:55 p.m. Arias’s clock was twenty minutes fast.

“At home, I don’t have two clocks giving the same time,” she said. “I am very often late for appointments. My alarm clock is fifteen minutes in advance.”

I was relieved to hear this but I was troubled on behalf of the world. “Maybe that’s what happens when you think about time all the time,” I offered. If it’s your job to coordinate the world’s clocks, to create from Earth’s gradients of light and dark a uniform and unified time, maybe you look to home as your refuge, the one place where you can ignore your watch, kick off your shoes, and enjoy some truly private time.

“I don’t know,” Arias said, with a Parisian shrug. “I have never missed a flight or missed a train. But when I know I can take this little degree of freedom, I do.”

We commonly talk about time as an opponent: thief, oppressor, master. In a 1987 book called Time Wars, written at the start of the digital age, the social activist Jeremy Rifkin lamented that humanity had embraced “an artificial time environment” ruled by “mechanical contrivances and electronic impulses: a time plane that is quantitative, fast-paced, efficient, and predictable.” Rifkin was particularly troubled by computers because they traffic in nanoseconds, “a speed beyond the realm of consciousness.” This new “computime,” as he called it, “represents the final abstraction of time and its complete separation from human experience and the rhythms of nature.” In contrast he praised the efforts of “time rebels”—a broad category that included advocates of alternative education, sustainable agriculture, animal rights, women’s rights, and disarmament—who “argue that the artificial time worlds we have created only increase our separation from the rhythms of nature.” Time, in this telling, is a tool of the establishment and an enemy of both nature and self.

The rhetoric is excessive but thirty years later Rifkin’s complaint does strike a common chord. Why else are we obsessed with productivity and time management if not to discover some saner way of navigating our lives? It’s not “computime” that haunts us as much as our slavish attachment to handheld computers and corporate-branded smartphones, which allow the workday and workweek to never end. Not wearing a watch was my way of shrugging off The Man, even if I’d never laid eyes on him.

Still, to cast blame on “artificial” time is to give nature too much credit. Maybe there was a time when time was a strictly personal affair, but it’s hard to imagine how long ago that would have been. Medieval serfs toiled to the distant sound of village bells; centuries earlier, monks rose, chanted, and prostrated themselves to the rhythm of chimes. In the second century B.C.E., the Roman playwright Plautus rued the popularity of sundials, which “cut and hack my days so wretchedly into small pieces.” The ancient Incas used a complex calendar to calculate when to sow and harvest and to identify the most auspicious times for a human sacrifice. (The calendar included a recurring “Vague Year” with eighteen months of twenty days each plus, at the end, five “nameless days” of ill omen.) Even early humans must have taken note of the daylight on the cave wall, in order to hunt effectively and return safely before dark. Even if any one of these customs were closer than today’s to “the rhythms of nature,” it would be hard to embrace as a model that Earth’s several billion residents should follow.

I looked again at the sheaf of papers Arias had handed me, then at her clock, then at my watch: it was time to go. For months I’d been reading the works of sociologists and anthropologists arguing that time is a “social construct.” I’d interpreted the phrase to mean something like “artificially flavored,” but now I understood: time is a social phenomenon. This property is not incidental to time; it is its essence. Time, equally in single cells as in their human conglomerates, is the engine of interaction. A single clock works only as long as it refers, sooner or later, obviously or not, to the other clocks around it. One can rage about it, and we do. But without a clock and the dais of time, we each rage in silence, alone.