Measuring time: calendars and clocks of the world

An old printed page in Latin, with a large title, ornamented letters and a coat of arms. — First page of the bull Inter gravissimas, the decision of Pope Gregory XIII that announced the Gregorian calendar in 1582. Gregorius XIII, Public domain, source

A year lasts three hundred and sixty-five days. Except when it lasts three hundred and sixty-six.

This oddity is not a mistake, but the trace of a problem that every society in the world has encountered, and that none has completely solved.

Three clocks that do not agree

Nature offers us three ways of counting time.

The day: the Earth turns on its axis. The lunation: the Moon goes from one crescent to the next, in a little over twenty-nine days. The year: the Earth goes round the Sun, and the seasons return.

Yet these three durations do not divide into one another exactly. The year does not contain a whole number of days: almost six hours are left over. Nor does it contain a whole number of lunations.

Every calendar in the world is a solution to this problem. Every solution involves giving something up.

Following the Moon

The Hijri calendar, used in the Muslim world, follows the Moon. Twelve lunations make about three hundred and fifty-four days, eleven fewer than a solar year.¹

The consequence: the months move. The month of Ramadan falls in summer for a few years, then in spring, then in winter. It goes round the seasons in about thirty years.

This is not a flaw, but a choice. This calendar gives priority to the Moon, which can be observed at a single glance, rather than to the seasons.

Catching up with an extra month

Other societies wanted to keep both: the lunar months, and the seasons in the right place.

Their solution: add a whole month from time to time. These calendars are called lunisolar. The Hebrew calendar works this way. So does the Chinese calendar, which explains why Chinese New Year does not fall on the same date each year in our calendar.²

It is a clever solution, but it requires knowing precisely when to add the extra month. So it takes observations, calculations, and people whose job this is.

Two counts at once

In Mesoamerica, the region’s peoples — among them the Maya — adopted another solution: using two calendars at once.

One counts two hundred and sixty days. The other counts three hundred and sixty-five. The two turn at the same time, like two gearwheels. A given combination of the two only comes round again after fifty-two years. This two-hundred-and-sixty-day count is, moreover, still used today, every day, by many Maya in Guatemala.³

That leaves the question of how these numbers were chosen. Why twenty and thirteen, rather than other numbers? Researchers put forward three explanations, and none is proven:

Pregnancy: about two hundred and sixty-six days separate conception from birth. (Counted from the last menstrual period, as obstetric medicine does, a pregnancy lasts about two hundred and eighty days.) An ethnologist observed that K’iche’ midwives do indeed use this count to follow a pregnancy.
The sky: at the latitude of certain very ancient sites, about fifteen degrees north, the Sun passes exactly overhead twice a year, and two hundred and sixty days separate these two passages. Other specialists find this explanation unconvincing.
Maize growing: its agricultural cycle is said to be very close to this length.

What we do know, on the other hand, is what the carved dates tell us — and we have understood this only very recently. For a long time, specialists believed that the figures sculpted on the stelae were gods. In 1960, Tatiana Proskouriakoff showed that they were kings and queens: the dates mark their births, their accessions to power, their deaths. She thus reconstructed a sequence of seven rulers over two hundred years.⁴

How she got there

She was not an archaeologist. She was an architect, and she left for Guatemala in 1936 with a museum team for which she drew as a volunteer, unpaid.⁵

Her task: to draw the ruins. Then she produced reconstructions of the city — drawings showing the buildings as they must have stood. These drawings were noticed by a specialist, who hired her and sent her to draw other Maya cities.⁶

But the essential part is what she did next, and it is always left out of the story.

Before her 1960 discovery, she undertook a substantial piece of work: analysing around four hundred monuments to establish a dating method based on the style of the sculpture — the shape of the features, the way the figures are handled. Her method makes it possible to date a monument with no inscribed date to within twenty or thirty years.⁷

This is not an artist’s eye at work. It is a systematic comparison of four hundred objects.

It was by spending so many years looking at these stones one by one that she finally saw the pattern: the same signs, in the same places, in the same order, from one stela to the next.

One Mayanist summed up the effect of her article in a single sentence: at one blow, this short paper freed the study of Maya writing from a lengthy stagnation.⁸

Ten days erased

The calendar used in the Roman Empire, introduced by Julius Caesar in 46 BCE, counted a year of three hundred and sixty-five and a quarter days. It was almost right. Almost: it drifted by about one day every hundred and twenty-eight years.

After sixteen centuries, the drift had become visible. In 1582, a reform decided to correct it in one go: ten days were removed from the calendar. People went to bed one evening and woke up ten days later.⁹

But not everyone followed at the same time. Great Britain and its colonies waited until 1752. Japan changed in 1873, China in 1912, Russia in 1918. Greece did not switch until 1923.¹⁰

A curious detail: the longer a country waited, the greater the lag, and so the more days had to be removed. Ten in 1582. Eleven in 1752. Thirteen in 1918.

For more than three centuries, two neighbouring countries could be on different dates on the same day.

From shadow to atom

To measure time within a day, other tools were needed.

The simplest is a stick planted in the ground. Its shadow turns and shortens: this is a gnomon. Then came water clocks, used in Egypt, in China, in the Greek and then the Arabic-speaking world. Water flows out at a steady rate, and its level indicates the hour.

For a clock to run regularly, it needs a mechanism that releases energy little by little, in regular jolts, instead of letting it run out all at once. This mechanism is called an escapement. It was developed in China in the eighth century, by a monk named Yi Xing and Liang Lingzan.¹¹

Around 1090, still in China, the engineer Su Song completed a water-driven clock tower in Kaifeng, as tall as a building, which also displayed the positions of the heavenly bodies. It was dismantled by an army in 1127, and no one has ever managed to reassemble it.¹²

In Europe, more than five centuries after the Chinese escapement, weight-driven clocks were built in the thirteenth century (the years 1200 to 1299) and installed on town towers. Then, in 1656, Huygens applied the pendulum to the clock: precision took a leap forward.¹³

Today, the reference is the atomic clock. It uses the regular vibration of atoms and drifts by less than one second in several million years.

Who decides the time?

One last question: why does the time change when you travel?

For a long time, each town had its own time, set by the Sun. This posed no problem as long as people travelled slowly.

The railway changed everything. With trains crossing a country in a day, common timetables were needed, otherwise collisions would become inevitable. The railway companies of North America did not wait for governments: meeting in Chicago in 1883, they divided the continent into five time zones and applied them.

The following year, in 1884, an international conference met in Washington. It adopted the meridian passing through Greenwich, near London, as the starting point for longitudes. This choice was by no means obligatory: it prevailed because most navigation charts already used it.¹⁴

The conference did not, however, divide the world into time zones. This is often claimed, and it is wrong. One delegate proposed it; others replied that this was not the subject of the meeting, and the proposal was not even put to a vote. Time zones came afterwards, country by country, each choosing its own moment.¹⁵

Not everyone agreed. France abstained in the vote. It continued to print its maps with the Paris meridian until 1911. Its law eventually accepted Greenwich time without ever writing the word: it defined it as “Paris time retarded by nine minutes and twenty-one seconds”.¹⁶

Our calendars and our hours do not come from the sky. They are human decisions, taken on specific dates, by people who had their reasons.

Three families of calendars

Family	What it is set by	What it loses	Examples
Observational lunar	The observed Moon	The seasons drift	Hijri
Lunisolar	The Moon, brought back into line with the Sun	Months have to be added	Hebrew, Chinese
Solar	The Sun alone	The months no longer follow the Moon	Julian, Gregorian, Ethiopian

Note 1

Douze mois lunaires comportent 354 ou 355 jours, l'année solaire comporte 365 ou 366 jours, les calendriers lunaires se décalent donc en moyenne de 11 jours par rapport à un calendrier solaire.

Twelve lunar months comprise 354 or 355 days, the solar year comprises 365 or 366 days, so lunar calendars drift on average by 11 days relative to a solar calendar.

Rocher, Patrick, “Les calendriers”, Institut de mécanique céleste et de calcul des éphémérides, Observatoire de Paris, cours, s. d., open access