What is time?

What then is time?

Around the year 400, in the Roman port of Hippo, now Annaba in Algeria, a bishop in his forties wrote down a sentence that philosophers have quoted ever since. Augustine, bishop of Hippo since 396, composed his Confessions there between about 397 and 400. In Book 11 he asks: “What, then, is time? If no one ask of me, I know; if I wish to explain to him who asks, I know not” (J. G. Pilkington’s translation; the Latin is quid est ergo tempus?, 11.14). Everyone understands the word, until asked.

He was not the first to be stuck. Around 330 BC Aristotle opened his discussion in the Physics with the same unease: one part of time has been and is not, the other is going to be and is not yet, and the “now” between them is not a part of time. His definition: time is the “number of motion in respect of before and after” (Hardie and Gaye’s translation). Augustine’s answer belongs to the next lesson. This one asks whether the word hides two different things.

This course proposes that it does. “Time” names two kinds of experience, and much confusion comes from mixing them. The first is timing: the right moment for something to happen. Spring is the time to sow; “you came at just the right time.” Chinese has a word for it, 时机 (shíjī). The second is flow: the inner sense that the present is slipping into the past while the future arrives, like a river nobody can stop. In this reading, timing faces outward, toward the world, and grows into the objective time of calendars, clocks, and physics; flow faces inward and stays what it is for each of us, lived time.

Timing becomes objective in two steps. First it turns into order: “tomorrow” and “yesterday” become positions in a sequence of before and after that does not depend on who is counting (Socrates died before Plato, whatever clock you use). Then the order is given a scale. Once the occasion is replaced by a mark anyone can read, the sun’s height, a shadow’s length, a tick, time has become a measure, and, this course argues, the person has dropped out: a number on a dial does not care whether the moment is right.

Flow has images of its own. Marcus Aurelius, Roman emperor from AD 161 to 180, called time a river made of events, “a violent stream” (Meditations 4.43, George Long’s translation). More than six centuries earlier Confucius stood by a river in China and said 逝者如斯夫，不舍昼夜: it passes on like this, never stopping day or night (Analects 9.17). Course 15 puts this line beside Heraclitus’s river. This course adds a thesis: the sense of flow is rooted in our awareness that we will die. If nothing lay ahead, the future would not press on the present. That is a philosophical claim, not a finding; Another view weighs it.

Philosophers have a pair of their own. In 1908 the Cambridge philosopher J. M. E. McTaggart, in “The Unreality of Time,” separated the A-series, events ordered as past, present, and future, from the B-series, events ordered as earlier and later. The B-series never changes; the A-series does, as a future event becomes present, then past. McTaggart argued that time needs the A-series and that the A-series is contradictory, so time is unreal; most philosophers reject that conclusion but keep his terms. In this course’s split, the B-series is what timing becomes when made objective, and the A-series is what flow looks like from outside. It is one framework, not the only one.

The sun was the first clock

Before there were clocks there was the sunrise, and a farmer could read it. The sun makes two motions. The daily one carries it from east to west. The yearly one is slower: against the stars the sun drifts eastward along a great circle, the ecliptic, about a degree a day, and completes the cycle of the seasons in 365.2422 days, a little less than the schoolbook’s “365 and a quarter.” As it climbs and sinks, the point where it rises slides along the horizon. At 40° north, about the latitude of both Beijing and New York, the sun rises roughly 32° north of due east at the June solstice and roughly 30° south of it at the December solstice, and due east only at the equinoxes (anywhere short of the poles). A village could read the date from where the sun came up over a hill.

In China this attention produced the 节气 (jiéqì), the 24 solar terms, with names like a farmer’s notes: “Awakening of Insects” (惊蛰, early March), “Grain Rain” (谷雨, about 20 April), “White Dew” (白露, early September). The four turning points came first, the solstices 夏至 (xiàzhì) and 冬至 (dōngzhì) and the equinoxes 春分 (chūnfēn) and 秋分 (qiūfēn); the complete list of 24 first appears in the Huainanzi, presented to the Han court in 139 BC, and the Taichu calendar of 104 BC wrote all 24 into the official calendar. A term is defined by the sun’s longitude along the ecliptic, which grows 15° from one term to the next (0° is the March equinox, 90° the June solstice). UNESCO listed the terms as intangible cultural heritage in 2016.

For centuries the calendar cut the year into 24 equal slices of time; only in 1645, in a new Qing calendar, did it switch to the sun’s true position. The terms are then unequal in days: the Earth is nearest the sun around 3 January (147.1 million kilometers) and farthest around 4 July (152.1 million), so the sun seems to move faster in winter, and a winter term lasts about 14.7 days against 15.7 in summer.

The simplest instrument is a stick. A vertical stick, a gnomon, casts its shortest noon shadow at the June solstice and its longest at the December solstice; the time between two longest shadows is a year. A painted pole from Taosi in Shanxi, perhaps 2300 BC, is probably the oldest gnomon known in China. In 1276 Guo Shoujing built a stone tower at Dengfeng, in Henan, with a stone scale about 31 meters long for the noon shadow. His year of 365.2425 days, the average the Gregorian calendar adopted in 1582, went into the Shoushi calendar of 1281, which ran for 363 years.

The moon is the second clock. Its phases repeat every 29.53 days, and English month comes from moon; Chinese uses one character, 月 (yuè), for both. In the traditional Chinese calendar a month begins on the day of the new moon, so the date tells you the phase: the full moon comes on the 15th or 16th. “The third of the month” once meant a thin crescent low in the evening sky. Day, month, and year each began as a sign for an occasion.

For anything shorter than a day people built machines, each with a weakness. A sundial needs sun. A water clock, the Greek klepsydra (“water thief”) or the Chinese 漏刻 (lòukè), reads time from water draining through a hole. The oldest document naming one is the tomb inscription of an Egyptian official, Amenemhet, of the sixteenth century BC. China’s Rites of Zhou (compiled perhaps in the third century BC) has an official who hangs a vessel to mark the watches and, in winter, boils water to pour in, presumably so the clock does not freeze. The hourglass is later than most people think: its earliest evidence in Europe is a painting, Lorenzetti’s Siena fresco Allegory of Good Government, about 1338.

Here, in this reading, is the loss. Each improvement made time more like a number and less like an occasion. A farmer once read the time to plant from the sunrise point and the insects; today a watch says 3:42 and a phone, guided by satellites, says where we are, and a date is a position on a scale. This course does not call the old way better. A measure can be read by anyone, anywhere, with no knowledge of the world around, and that is both what made it powerful and what let the occasion drop out.

A word that meant inquiry

The earliest Greek history that survives complete opens by announcing a historiē. In G. C. Macaulay’s 1890 translation the first sentence begins, “This is the Showing forth of the Inquiry of Herodotus of Halicarnassos,” so that “the deeds of men” may not “be forgotten by lapse of time.” Historia meant research, a finding-out by asking. The root survives in Aristotle’s Historia animalium, “Inquiries on Animals,” and in the old phrase natural history, the study of particular things, as against natural philosophy, the search for general principles. This course reads the word as a sign of a habit: for the Greeks, it argues, the point of inquiry was to find out what is so, and the pastness of the past mattered less than it does to us.

It would be wrong to say the Greeks wrote only about what their own generation had lived through. Herodotus (born about 484 BC) wrote about the Persian Wars of 490–479 BC but went back to Croesus of Lydia and the rise of Cyrus in the sixth century BC, and into Egypt’s past, partly as its priests told it to him. Thucydides, who lived through the Peloponnesian War (431–404 BC), gave his first nineteen or so chapters to earlier Greece and admitted that remote events “could not from lapse of time be clearly ascertained” (Richard Crawley’s translation). He wrote for those who want “an exact knowledge of the past as an aid to the interpretation of the future,” because the future “must resemble if it does not reflect” the past: “a possession for all time.” That is not a man uninterested in the past. It is a man who expects it to repeat its patterns, which this course reads as the cyclical habit of mind at work.

Calendars tell a similar story. The Greek world had no common calendar: each city kept its own, with its own month names and start of the year (in Boeotia, next door to Athens, it began in midwinter). Athens ran a lunar calendar for festivals, a ten-part one for the council, and a seasonal one of star-risings for the farm, and its officials added a leap month when they judged the months had slipped, with little system. In 423 BC Aristophanes put the grievance on stage: in the Clouds the chorus brings a message from the Moon, scolding the Athenians for tampering with the calendar so that the days no longer match her. What the cities shared was the games at Olympia, and historians counted in Olympiads, four-year spans reckoned from 776 BC, the first recorded games (early dates were worked out afterward and are shaky).

Yet the Greeks did keep chronologies. A marble slab from the island of Paros, the Parian Chronicle, cut in 264 or 263 BC, lists events from 1582 BC, naming the king or archon of Athens for each and counting years back from its own present. Its main fragment is in the Ashmolean Museum, Oxford. What Greece lacked, in this course’s reading, was one authority behind one calendar.

China was the opposite: the calendar belonged to the state. It was a symbol of the dynasty, new ruling houses often prepared a fresh one, and the official histories record about a hundred. This course reads that care as care for time as a line of records.

India, the usual third example of cyclical time, shows how careful one must be. Indian texts count in vast cycles: four ages, or yugas, make a mahayuga of 4.32 million years, and a thousand of those a kalpa, 4.32 billion years, a “day of Brahma.” Yet India did write chronicles: Kalhana’s Rajatarangini, a Sanskrit verse history of Kashmir from the twelfth century (usually dated 1148–49), has legendary early books, with one king reigning three hundred years, but it is a chronicle, and so is the Sri Lankan Mahavamsa. This course’s thesis is that where time comes round again, records matter less, because the past is also the future. It is a tendency, not a rule; Another view tests it.

The great return

Thales of Miletus, about 600 BC, is called the first Greek philosopher because, according to Aristotle, he asked what everything is made of and answered: water. Aristotle (Metaphysics A.3) describes the first principle, the arche, as that from which all things first come to be and into which they are finally resolved. Thales wrote nothing that survives, so that “return” may be Aristotle’s. This course sees a circle all the same: everything comes from a source and goes back to it, and the changes between are, in a Chinese idiom, “ten thousand changes that never leave the root” (万变不离其宗, wànbiàn bù lí qí zōng).

Pythagoras, born on Samos about 570 BC and later settled at Croton in southern Italy, taught that the soul is immortal and passes from body to body. His contemporary Xenophanes mocked him: Pythagoras once saw a puppy being beaten and told the man to stop, because he recognized a dear friend’s voice in its yelping.

The clearest Greek statement of a circular world comes from the Stoics, a school founded in Athens about 300 BC. The orthodox view, rejected by Panaetius in the second century BC, was that the cosmos periodically burns up in a conflagration, the ekpyrosis, and begins again from fire. Whether the next world is the same as this one is where our sources differ. According to Alexander of Aphrodisias, Chrysippus (died about 206 BC) held that the same things come about again, down to the same individuals; Origen, around AD 248, reports that the Stoics said not Socrates but someone indistinguishable from him will marry someone indistinguishable from Xanthippe and be accused by men indistinguishable from Anytus and Meletus. Marcus Aurelius made the doctrine a consolation: “all things from eternity are of like forms and come round in a circle” (Meditations 2.14), so the longest life and the shortest lose the same. In circular time, this course argues, past and future are mirror images, and a record of what will happen again is worth less.

The war on change

Not every early Greek wanted a still point. Heraclitus of Ephesus, active about 500 BC, wrote that the sun is new each day (so Aristotle reports in the Meteorology) and, in the river saying that scholars trust most, that ever different waters flow on those who step into the same rivers: the river stays a river while its water changes. The better-known “you cannot step twice into the same river” is a paraphrase, in Plato’s Cratylus, and “everything flows” (panta rhei) was put in his mouth centuries later. In this course’s reading, Heraclitus was soon outvoted.

The opposition came from Elea, a Greek town in southern Italy. Parmenides, in a poem of the early fifth century BC, argued that what is, is, and what is not cannot be thought; so nothing can come from nothing or pass into it, and change is an illusion of the senses. His follower Zeno of Elea, born about 490 BC, wrote a book that, according to Plato’s Parmenides, defended his teacher against ridicule. We know its arguments against motion through Aristotle (Physics VI.9), because the book is lost. In the Dichotomy, to reach a goal you must first reach the halfway point, then half of what remains, without end. In Achilles and the Tortoise, the fast runner must first reach where the slow one was, by which time it has moved on. In the Arrow, at every instant a flying arrow occupies a space exactly its own size, so it is at rest. Textbooks often group the first two (space and time divide without end) against the Arrow and a fourth argument, the Stadium (time is made of indivisible instants), though not every historian accepts that.

The Achilles argument yields to arithmetic, and you can try it below. Give the tortoise a 100-meter head start and let Achilles run ten times as fast. When he reaches the tortoise’s starting point it has crawled 10 meters; when he covers those, 1 meter more; and so on. There are infinitely many steps, but they take 10 seconds, 1 second, a tenth of a second, and so on, and the sum 10 + 1 + 0.1 + … is 11.11… seconds, or 100 ÷ 9: the head start divided by the difference of the speeds. Making such sums rigorous took the nineteenth century, notably Augustin-Louis Cauchy’s Cours d’analyse (1821). Aristotle had already given part of the answer: as the distances shrink, so do the times.

For most mathematicians that settles it. Philosophers still ask whether anyone could actually complete infinitely many tasks, a “supertask”: in 1954 James Thomson imagined a lamp switched on and off at intervals of one minute, then half a minute, then a quarter, and asked whether it is on or off after two minutes; Paul Benacerraf answered in 1962 that the story does not settle it. The Stanford Encyclopedia of Philosophy concludes that mathematics alone does not answer questions about real time and space.

This course draws a larger lesson from Zeno: in the Eleatic pattern, change is understood by showing that underneath nothing changes. Plato’s Timaeus (about 360 BC) puts the instinct in a sentence: the maker wanted “a moving image of eternity,” made it move “according to number,” while eternity itself “rests in unity”; this image we call time. Greek-style science, this course argues, is therefore a project for eliminating time: a search for the unchanging principle behind change, whose modern heirs seek a “final theory,” the last equation, the fundamental particle. It is a bold claim, and not one most physicists would sign.