Calendars exhibit

When did ancient months start?

In the eighth century B.C.E., civilizations all over the world either discarded or modified their old 360 day calendars. The 360 day calendars had been in use for the greater part of a millennium. In many places, month lengths immediately after that change were not fixed, but were based instead upon observation of the sky.

Priest-astronomers were assigned the duty of declaring when a new month began – it was usually said to have started at the first sighting of a new moon. Month length at that time was simply the number of days that passed from one new lunar crescent to the next.

During those years in Rome, for example, a Pontifex (priest) observed the sky and announced a new moon and therefore the new month to the king. For centuries afterward Romans referred to the first day of each new month as Kalends or Kalends from their word calare (to announce solemnly, to call out). The word calendar derived from this custom.

This practice of starting a month at the first sighting of a new moon was observed not only by Romans but by Celts and Germans in Europe and by Babylonians and Hebrews in the Lavant. All of these peoples began their month when a young crescent was first seen in the sky. This is still done for the Islamic Calendar, but a new moon’s date is calculated for traditional lunar calendars that are currently used in China and India.

During the period when month lengths were not fixed, new moons were usually sighted after either 29 or 30 days. If clouds obscured vision on the thirtieth day, a new month was declared to have begun.

When month lengths were identical with lunations, only those that lasted 30 days were considered to be normal. This was probably because all months had previously been 30 days for such a long period of time.

During this period in Greece, for example, months that consisted of 30 days were considered to be "full;" those that lasted only 29 days were said to be "hollow." Months containing 30 days were also called "full" in Babylon, but those containing 29 were deemed to be "defective."

After month lengths in the Celtic Calendar became fixed, those that had been given 30 days were termed "matos" (lucky) and those given 29 days "anmatos" (unlucky). This notion still exists today, months of 30 days in the Hebrew Calendar are called "full" and those with 29 are deemed to be "deficient."

When was the ancient new year?

In addition to their declaring the beginning of each month based upon a sighting of the new moon, priest-astronomers were also charged with pinpointing the start of a year.

By observing the movement of Sirius, Egyptians came to grips with the fact that the year was more than five days longer than their venerable 360-day calendar. This resulted in a change to their method of approximating year length that had been in use for nearly a millennium. But it also caused them to wonder where the additional days came from. In order to account for these additional days, Egyptians created a myth about their sky-god, Nut.

During the reign of the Babylonian king Nabonasser (traditionally dated between 747 and 734 B.C.E.) priest/ astronomers in that country discontinued their practice of looking for the new moon in order to name the beginning of a month. Instead, they returned to a fixed-length calendar that had 12 months of 30 days each, but with five days added at the end. 10

Usually at a date later than the mid-eighth century B.C.E., many other peoples who had previously considered the year to be 360 days in length reluctantly returned to a calendar of twelve 30-day months, but added five days to the end of their year. These additional days were considered to be very unlucky or unpropitious.

Two eastern Mediterranean peoples who did not embrace Islam were early Christians in upper Egypt, whom we now call Copts, and their neighbors to the south, the Ethiopians. Probably because they were surrounded by Islamic peoples, Coptic and Ethiopian churches never adopted the Western calendar. Instead, these two isolated pockets of Christianity continued to use the old 360-day calendar.

These two calendars are identical except for year number. Copts date their calendar from C.E. 284 but Ethiopians date theirs from C.E. 7. Both of them observe three 365 day years followed by one 366 day year. Their years are divided into 12 months of 30 days each, and the extra five or six days are added after the twelfth month.

Zoroastrians, who began their calendar in 389 B.C.E. with the birth of their founder, the prophet Zoroaster, use a calendar of 365 days. It consists of twelve 30-day months with five "gatha days" added at the end of the year. Each of the thirty days as well as each of the gatha days has its own name. They are referred to by that name just as we speak of a day by its number in the month. Beginning in 1906 of the Common Era, some modern Zoroastrians adopted the practice of adding an additional day every four years.

One of Alexander the Great’s generals, Seleucus Nicator, founded (late 4th Century BCE and early 3rd century BCE) an empire that stretched from Asia Minor to India. He established a new calendar that was essentially the same as one that had been used for some time in Syria. It contained twelve months of 30 days each and an extra five days at the year’s end. Every fourth year an additional day for a total of six days were added at the end of the year.

In Persia under the Sassanids, and in Armenia and Cappadocia the official system of time-reckoning was twelve months of 30 days followed by five more days at the end of the year. However, Arabian astronomers said the Sassanian year of twelve 30-day months was adjusted to the seasons by intercalating a month every 120 years.

Following are details about several ancient calendars...

The Hanging Gardens of Babylon

East bank of the River Euphrates, about 50 km south of Baghdad, Iraq Palace with legendary gardens built on the banks of the Euphrates river by King Nebuchadnezzar II (which might have never existed except in the minds of Greek poets and historians, although recent archaeological excavations uncovered the foundation of the palace). Greek historian Diodorus Siculus wrote: "The approach to the Garden sloped like a hillside and the several parts of the structure rose from one another tier on tier... On all this, the earth had been piled... and was thickly planted with trees of every kind that, by their great size and other charm, gave pleasure to the beholder... The water machines (raised) the water in great abundance from the river, although no one outside could see it." (Painting by Mario Larrinaga)

Babylonian calendar

Overview

The ancient Babylonians used a calendar with alternating 29- and 30-day months. This system required the addition of an extra month three times every eight years, and as a further adjustment the king would periodically order the insertion of an additional extra month into the calendar.

The Babylonians, who lived in what is now Iraq, added an extra month to their years at irregular intervals. Their calendar, composed of alternate 29-day and 30-day months, kept roughly in step with the lunar year. To balance the calendar with the solar year, the early Babylonians calculated that they needed to add an extra month three times every eight years. But this system still did not accurately make up for the accumulated differences between the solar year and the lunar year. Whenever the king felt that the calendar had slipped too far out of step with the seasons, he ordered another extra month. However, the Babylonian calendar was quite confused until the 300’s B.C.E., when the Babylonians began to use a more reliable system.

Details

Babylonia was the ancient cultural region occupying southeastern Mesopotamia between the Tigris and Euphrates rivers (modern southern Iraq from around Baghdad to the Persian Gulf). Because the city of Babylon was the capital of this area for so many centuries, the term Babylonia has come to refer to the entire culture that developed in the area from the time it was first settled, about 4000 B.C.E. Before Babylon’s rise to political prominence (c. 1850 B.C.E.), however, the area was divided into two countries: Sumer in the southeast and Akkad in the northwest. The Babylonian kingdom flourished under the rule of the famous King, Hammurabi (1792-1750 BC). It was not until the reign of Naboplashar (625-605 BC) of the Neo-Babylonian dynasty that the Mesopotamian civilization reached its ultimate glory. His son, Nebuchadnezzar II (604-562 BC) is credited for building the legendary Hanging Gardens. It is said that the Gardens were built by Nebuchadnezzar to please his wife or concubine who had been "brought up in Media and had a passion for mountain surroundings."

Five thousand years ago, Sumerians had a calendar that divided the year into 30-day months, divided the day into 12 periods (each corresponding to 2 of our hours), and divided these periods into 30 parts (each like 4 of our minutes).

In Mesopotamia, the solar year was divided into two seasons, the "summer," which included the barley harvest in the second half of May or in the beginning of June, and the "winter," which roughly corresponded to today’s fall-winter. Three seasons (Assyria) and four seasons (Anatolia) were counted in northerly countries, but in Mesopotamia the bipartition of the year seemed natural. As late as c. 1800 B.C.E. the prognoses for the welfare of the city of Mari, on the middle Euphrates, were taken for six months.

The months began at the first visibility of the New Moon, and in the 8th century B.C.E. court astronomers still reported this important observation to the Assyrian kings. The names of the months differed from city to city, and within the same Sumerian city of Babylonia a month could have several names, derived from festivals, from tasks (e.g. sheepshearing) usually performed in the given month, and so on, according to local needs. On the other hand, as early as the 27th century B.C.E., the Sumerians had used artificial time units in referring to the tenure of some high official – e.g., on N-day of the turn of office of PN, governor. The Sumerian administration also needed a time unit comprising the whole agricultural cycle; for example, from the delivery of new barley and the settling of pertinent accounts to the next crop. This financial year began about two months after barley cutting. For other purposes, a year began before or with the harvest. This fluctuating and discontinuous year was not precise enough for the meticulous accounting of Sumerian scribes, who by 2400 B.C.E. already used the schematic year of 30 x 12 = 360 days.

At about the same time, the idea of a royal year took precise shape, beginning probably at the time of barley harvest, when the king celebrated the new (agricultural) year by offering first fruits to gods in expectation of their blessings for the year. When, in the course of this year, some royal exploit (conquest, temple building, and so on) demonstrated that the fates had been fixed favorably by the celestial powers, the year was named accordingly; for example, as the year in which "the temple of Ningirsu was built." Until the naming, a year was described as that "following the year named (after such and such event)." The use of the date formulas was supplanted in Babylonia by the counting of regnal years in the 17th century B.C.E.

The use of lunar reckoning began to prevail in the 21st century B.C.E. The lunar year probably owed its success to economic progress. A barley loan could be measured out to the lender at the next year’s threshing floor. The wider use of silver as the standard of value demanded more flexible payment terms. A man hiring a servant in the lunar month of Kislimu for a year knew that the engagement would end at the return of the same month, without counting days or periods of office between two dates. At the city of Mari in about 1800 B.C.E., the allocations were already reckoned on the basis of 29- and 30-day lunar months. In the 18th century B.C.E., the Babylonian Empire standardized the year by adopting the lunar calendar of the Sumerian sacred city of Nippur. The power and the cultural prestige of Babylon assured the success of the lunar year, which began on Nisanu 1, in the spring. When, in the 17th century B.C.E., the dating by regnal years became usual, the period between the accession day and the next Nisanu 1 was described as "the beginning of the kingship of PN," and the regnal years were counted from this Nisanu 1.

It was necessary for the lunar year of about 354 days to be brought into line with the solar (agricultural) year of approximately 365 days. This was accomplished by the use of an intercalated month. Thus, in the 21st century B.C.E., a special name for the intercalated month iti dirig appears in the sources. The intercalation was operated haphazardly, according to real or imagined needs, and each Sumerian city inserted months at will; e.g., 11 months in 18 years or two months in the same year. Later, the empires centralized the intercalation, and as late as 541 B.C.E. it was proclaimed by royal fiat. Improvements in astronomical knowledge eventually made possible the regularization of intercalation; and, under the Persian kings (c. 380 B.C.E.), Babylonian calendar calculators succeeded in computing an almost perfect equivalence in a lunisolar cycle of 19 years and 235 months with intercalations in the years 3, 6, 8, 11, 14, 17, and 19 of the cycle. The new year’s day (Nisanu 1) now oscillated around the spring equinox within a period of 27 days.

The Babylonian month names were Nisanu, Ayaru, Simanu, Du'uzu, Abu, Ululu, Tashritu, Arakhsamna, Kislimu, Tebetu, Shabatu, Adaru. The month Adaru II was intercalated six times within the 19-year cycle but never in the year that was 17th of the cycle, when Ululu II was inserted. Thus, the Babylonian calendar until the end preserved a vestige of the original bipartition of the natural year into two seasons, just as the Babylonian months to the end remained truly lunar and began when the New Moon was first visible in the evening. The day began at sunset. Sundials and water clocks served to count hours.

The influence of the Babylonian calendar was seen in many continued customs and usages of its neighbor and vassal states long after the Babylonian Empire had been succeeded by others. In particular, the Jewish calendar in use at relatively late dates employed similar systems of intercalation of months, month names, and other details (see below The Jewish calendar). The Jewish adoption of Babylonian calendar customs dates from the period of the Babylonian Exile in the 6th century B.C.E.

The Egyptian calendar

Overview

The earliest Egyptian calendar was based on the moon’s cycles, but the lunar calendar failed to predict a critical event in their lives: the annual flooding of the Nile river. The Egyptians soon noticed that the first day the "Dog Star," which we call Sirius, in Canis Major was visible right before sunrise was special. The Egyptians were probably the first to adopt a mainly solar calendar. This so-called ‘heliacal rising’ always preceded the flood by a few days. Based on this knowledge, they devised a 365-day calendar that seems to have begun in 4236 B.C.E., the earliest recorded year in history.

They eventually had a system of 36 stars to mark out the year and in the end had three different calendars working concurrently for over 2000 years: a stellar calendar for agriculture, a solar year of 365 days (12 months x 30 + 5 extra) and a quasi-lunar calendar for festivals. The later Egyptian calendars developed sophisticated Zodiac systems, as in the stone calendar at right. According to the famed Egyptologist J. H. Breasted, the earliest date known in the Egyptian calendar corresponds to 4236 B.C.E. in terms of the Gregorian calendar.

Details

The ancient Egyptians originally employed a calendar based upon the Moon, and, like many peoples throughout the world, they regulated their lunar calendar by means of the guidance of a sidereal calendar. They used the seasonal appearance of the star Sirius (Sothis); this corresponded closely to the true solar year, being only 12 minutes shorter. Certain difficulties arose, however, because of the inherent incompatibility of lunar and solar years. To solve this problem the Egyptians invented a schematized civil year of 365 days divided into three seasons, each of which consisted of four months of 30 days each. To complete the year, five intercalary days were added at its end, so that the 12 months were equal to 360 days plus five extra days. This civil calendar was derived from the lunar calendar (using months) and the agricultural, or Nile, fluctuations (using seasons); it was, however, no longer directly connected to either and thus was not controlled by them. The civil calendar served government and administration, while the lunar calendar continued to regulate religious affairs and everyday life.

In time, the discrepancy between the civil calendar and the older lunar structure became obvious. Because the lunar calendar was controlled by the rising of Sirius, its months would correspond to the same season each year, while the civil calendar would move through the seasons because the civil year was about one-fourth day shorter than the solar year. Hence, every four years it would fall behind the solar year by one day, and after 1,460 years it would again agree with the lunisolar calendar. Such a period of time is called a Sothic cycle.

Because of the discrepancy between these two calendars, the Egyptians established a second lunar calendar based upon the civil year and not, as the older one had been, upon the sighting of Sirius. It was schematic and artificial, and its purpose was to determine religious celebrations and duties. In order to keep it in general agreement with the civil year, a month was intercalated every time the first day of the lunar year came before the first day of the civil year; later, a 25-year cycle of intercalation was introduced. The original lunar calendar, however, was not abandoned but was retained primarily for agriculture because of its agreement with the seasons. Thus, the ancient Egyptians operated with three calendars, each for a different purpose.

The only unit of time that was larger than a year was the reign of a king. The usual custom of dating by reign was: "year 1, 2, 3 . . . , etc., of King So-and-So," and with each new king the counting reverted back to year One. King lists recorded consecutive rulers and the total years of their respective reigns.

The civil year was divided into three seasons, commonly translated: Inundation, when the Nile overflowed the agricultural land; Going Forth, the time of planting when the Nile returned to its bed; and Deficiency, the time of low water and harvest.

The months of the civil calendar were numbered according to their respective seasons and were not listed by any particular name–e.g. third month of Inundation–but for religious purposes the months had names. How early these names were employed in the later lunar calendar is obscure.

The days in the civil calendar were also indicated by number and listed according to their respective months. Thus a full civil date would be: "Regnal year 1, fourth month of Inundation, day 5, under the majesty of King So-and-So." In the lunar calendar, however, each day had a specific name, and from some of these names it can be seen that the four quarters or chief phases of the Moon were recognized, although the Egyptians did not use these quarters to divide the month into smaller segments, such as weeks. Unlike most people who used a lunar calendar, the Egyptians began their day with sunrise instead of sunset because they began their month, and consequently their day, by the disappearance of the old Moon just before dawn.

As was customary in early civilizations, the hours were unequal, daylight being divided into 12 parts, and the night likewise; the duration of these parts varied with the seasons. Both water clocks and sundials were constructed with notations to indicate the hours for the different months and seasons of the year. The standard hour of constant length was never employed in ancient Egypt.

Sirius: the 'Dog Star’

Early Egyptians depended on the Nile’s annual rising and flooding. Each year as that great river flooded it brought down mountain soil to the Egyptian plain. This enriched the fields and enabled creation of an agricultural system that supported a large civilization.

In the eighth century B.C.E., the Egyptian Pharoh’s primary advisor, the Vizier, was charged with reporting the first appearance of the bright star we call Sirius after it had been missing from the sky for (depending upon the observer’s latitude) approximately two weeks. This first appearance of Sirius in the pre-dawn sky was used to start the so-called Egyptian "lunar" calendar year, which was used for purposes of regulating religious affairs and everyday life.

Shortly after Sirius first reappeared in the east, the Nile would have its annual life-giving flood. Because of the Nile’s flooding at this time, the fixing of the new year could well be said to have been based on a geophysical as well as an astronomical event. Although many other stars may be used to fix the beginning of a sidereal year, the Egyptians made an excellent choice for this purpose. Sirius – Egyptians called it Sothis – not only signaled the approaching Nile flood, but is the brightest "fixed" star in the heavens.

In Egypt at the present time, Sirius rises just before the sun late in July, but usually can’t be seen until early August. This is because as sunrise approaches, stars fade from view and the light of dawn obliterates starlight. At the time Sirius is about to reappear, the constellation Orion is fully visible in the lower eastern sky. With the bright star Betelguese on his shoulder, anyone familiar with constellations would find Orion hard to miss. Sirius can be seen in the next constellation to rise (Canis Major). Because of this close relationship, Sirius was sometimes referred to as the "dog star" by early Greeks who thought of Canis Major as one of Orion’s hunting hounds.

The rainy season

The Himba people in Ekambu, Namibia, are some of the last peoples in the world living in relative isolation from modernity. "When the thunderstorms start and the leaves grow from the ground, that’s how we know it’s the new year," said Maverihepisa Koruhama, one of the villagers in Ekambu. They measure time by the shifting sun and mark the coming of the new year with the arrival of seasonal rains that transform the parched red soil into a carpet of green. In their Herero language, the word for "day" is the same as the word for "sun," and the word for "year" means "rain." (Above left, children watch as a Himba woman, senior wife of Waitavira Tjambiru, anoints her arm with butter fat mixed with red ochre outside her hut in Etengwa, Namibia.)

A dappled, brown horse and a lunar calendar

Lascaux caves, France (about 15,000 years old)

Half the cycle: 13 dots and an empty square

The Pleiades star cluster sits above the bull’s shoulder

Cro-magnon man (Lascaux caves in France)

What could be the oldest lunar calendar ever created was been identified on the walls of the famous, prehistoric caves at Lascaux in France. The interpretation that symbolic paintings, dating back 15,000 years, show the Moon going through its different phases comes from Dr. Michael Rappenglueck, of the University of Munich. The German researcher has previously associated patterns left in the caves with familiar stars and constellations. He now says groups of dots and squares painted among representations of bulls, antelope and horses depict the 29-day cycle of the Earth’s satellite.

Works of art

Visiting the Lascaux caves is an opportunity most people would never get– to protect the historic site from unnecessary wear and tear, all visitors now tour a mock-up of the caves, the so-called Lascaux II. Visiting the caves, once one’s eyes adjust to the half-light, visitors are struck with amazement. Anyone who has seen the paintings on the walls can be left in no doubt that they represent some of the greatest works of art every created.

"The secret of understanding these caves," Dr Rappenglueck says, "is to understand the people who painted these walls. They painted the sky, but not all of it. Just the parts that were specially important to them."

Cro-magnon man

The animals were painted on to the walls of the chamber by Cro-magnon man, one of our close relations, 15,000 years ago. He thrived in a temperate valley in the Dordogne while the rest of Europe was held in the grip of an ice age.

Dr. Rappenglueck gave a tour to David Whitehouse of the BBC. "Here it is," he said, as he headed down a passage. He was pointing to a line of dots painted half way up the wall. "Count them. Count them." Below a stunning painting of a deer was a row of 13 dots, ending in a square. "Why 13?"

"It’s half of the Moon’s monthly cycle," Dr. Rappenglueck said. "One dot for each day the Moon is in the sky. At the new Moon, when it vanishes from the sky, we see an empty square, perhaps symbolically representing the absent Moon. "But there’s more, further along." The Munich researcher gestured to me to move along the passageway. Beneath a dappled, brown horse with a dark mane was another row of dots. This time there were more of them.

"There are 29 of them - one for each day of the Moon’s 29-day cycle when it runs through its phases in the sky. It was a rhythm of nature that was important to these people." Dr. Rappenglueck looked around at the bulls, antelope and horses painted on the walls with such obvious admiration. "They were aware of all the rhythms of nature. Their survival depended on them, they were a part of them."

But there is another puzzle. The series of dots that curve away from the main row. "Why do they do that?"

"I think that indicates the time of the new Moon, when it disappears from the sky for several days," said Dr. Rappenglueck.

There is definitely astronomy on the walls of Lascaux. Earlier this year, Dr Rappenglueck identified a series of constellations painted on the wall of a shaft off the main chamber at Lascaux. The tiny pattern of the Pleiades star cluster can also be seen hanging above the shoulder of a bull near the entrance to the main passageway.

We will probably never understand completely what Cro-magnon man had in mind when he painted the Lascaux caves. The images of the animals seem obvious but what are we to make of the geometrical shapes and patterns scattered in between these creatures?

Calendars in Iceland (before literacy)

Viking origins

Traditionally, the Vikings originating in Scandinavia in the early Middle Ages are associated with violence and brutal force. However, the views of modern scholars paint a less mono-chromatic picture. Many of the activities of the Vikings required and produced knowledge of time-reckoning and of what we would nowadays classify as astronomy. For example, their extensive travelling and trade must have involved some knowledge of astronomy. The necessity of such knowledge is generally recognized in the case of coastal navigation, but also holds for inland travel through previously unknown areas, such as the vast lands of Eastern Europe.

Inland travel and coastal navigation is one thing, but regular trans-oceanic traffic is quite another. Yet such traffic was required to support the Scandinavian settlement of Iceland and Greenland, around the years 900 and 1000 respectively, at a time when the people of Europe knew nothing of the compass or the sextant. Even with good luck the oceanic voyage would take about a week, and without it land might not be sighted for several weeks. The navigational methods used included both terrestrial and celestial observations. There is hardly any doubt that the knowledge written down on vellum in Iceland in the twelfth and thirteenth centuries derives to a high degree from these observations and this experience.

Why did they need a calendar?

In 930, the Icelanders decided to establish the Althingi, a kind of parliament where an important part of the population gathered once a year for purposes of legislation and justice. Those who went there would spend two to five weeks away from home at a precious time of the year. The farms were scattered at long distances and the landscape often barely passable. Therefore the traditional Scandinavian method of summoning meetings by message was not viable – they needed a simple and reliable calendar to help people know when to start from home so as to arrive at the same time as the others. Moreover, since the Icelandic summer is short, it was a matter of primary concern to utilize summer time as well as possible, and date the parliament at the time of summer when the loss of domestic labor was least harmful.

To understand the need for a calendar we may also look at the agriculture itself and its annual cycle. Certainly, the caprices of Icelandic weather and nature are such that the calendar may often be a bad guide for action. In deciding when to let cattle and sheep out on grass or when to start hay-making it is better to observe the actual signs of nature than the calendar. But there are certain kinds of annual operation where the calendar proves superior: for example, in determining when to sow the grain, something which people had tried with little success in the first centuries of settlement in Iceland. Another good example is that of deciding when to let the ram to the ewes. It is important to do this at the right time in the winter so that the lambs have the best possible prospect of growing in the short summer, without too much risk of interludes of bad weather in the spring just after they are born. When the individual farmer makes his decision on this at some point around Christmas time, he has no clear natural signs of a terrestrial nature to go by.

How similar was it to the Julian calendar?

In the brief history of Iceland called Íslendingabók (The Book of the Icelanders, Libellum Islandorum), written by Ari the Learned in the period 1122-33, we have a report on a calendar reform around 955:

This was when the wisest men of the country had counted in two semesters 364 days or 52 weeks-then they observed from the motion of the sun that the summer moved back towards the spring; but there was nobody to tell them that there is one day more in two semesters than you can measure by whole weeks, and that was the reason.

There was a man called Thorsteinn the black, a very wise man. When they came to the Althing he sought the remedy that they should add a week to every seventh summer and try how that would work.

By a correct count there are 365 days in a year if it is not a leap year, but then one more; but by our count there are 364. But when in our count a week is added to every seventh year, seven years together will be equally long on both counts. But if there are 2 leap years between the ones to be augmented, you need to add to the sixth.

How did Thorsteinn the Black determine his intercalation? His farm was favorably located in the country to utilize the so-called mountain circle method, that is, to follow the annual motion of sunrise and sunset near the horizon where he would have suitably distant mountains and other reference points in the landscape to make fairly exact observations possible. At high latitudes the points of sunrise and sunset move so fast that this method could easily be used to determine the length of the year to within a day.

According to this, people started by counting 52 weeks or 364 days in the year. When they realized the insufficiency of this they tried the remedy of intercalating one week every seventh year (sumarauki), thus making the average year 365 days. The method chosen may seem strange to us but it is a natural consequence of the important role of the week in the original calendar.

So far the interpretation of the text seems straightforward. However, the text continues to describe the relation and adaptation of the Icelandic calendar to the Julian one, which must have been gradually introduced in Iceland in the eleventh and twelfth centuries, following formal Christianisation of the country in the year 1000. The text says that if there are two leap years between the years to be increased by a week, then the sixth year (instead of the seventh) should be increased. This is plainly wrong and would yield a worse approximation than the more simple rule of intercalating a week every sixth year. Scholars find this confusing, except by assuming the Latin meaning of the numerals. Thus ‘septimo quoque anno’ actually means ‘every sixth year’ by our count. In this way Ari’s text can be interpreted so as to coincide with practice in his time, as seen from almost contemporary Easter tables. Also, he would escape Occam’s razor, since his formula would otherwise be more complicated than necessary for its accuracy.