The Calendar

by David Ewing Duncan

  The problem comes in the time it takes for the moon to pass through its phases as it orbits the earth, which is not a tidy number for dividing into a year of approximately 365 1/4 days. In fact a true lunar month is a cumbersome 29.5306 days long as measured by modern instruments, equal to a precise 12-month lunar year of 354.3672 days. Stack that up against the true solar year of some 365.242199 days and one can appreciate the intense frustrations of astronomers over the centuries trying to link up the sun and moon.

  As ancient cultures matured, frustration with the lunar drift stimulated their scientists and priests to ponder a solution--a line of inquiry that continues to this day as we try to fine-tune our days, weeks and months to fit into the true solar year. But for the ancients, lacking modern tools and concepts, even approximating this year using the moon proved immensely difficult. A number of solutions were tried, but all failed.

  The ancient Babylonians, for one, stuck with the moon despite their highly advanced knowledge of astronomy. But their infatuation was tempered by a compromise with the sun in what is now called a ‘lunisolar’ year. Sometime around 432 BC Babylonian mathematicians figured out that seven years of thirteen lunar months followed by twelve years of twelve lunar months would equal almost exactly nineteen solar years. This later became known as the Metonic cycle, after the Greek astronomer Meton (c. fifth century BC). It works by inserting or ‘intercalating’ extra months into the standard 12-month lunar year. But even this 19-year system is not completely exact, running several hours fast. It also proved unwieldy and impractical for everyday use, since few people were willing to keep track of such a complicated system over so long a time.

  Other ancient cultures unwilling to give up the moon devised other systems of intercalations. The Greeks added an extra 90 days every eight years to compensate for their standard lunar calendar of 354 days, though the months were not always added on schedule and were often inserted haphazardly. The Jewish calendar intercalates a month every three years, inserted just before the month of Nisan, though this system still leads to a gradual drift that requires a second extra month to be added now and then by Jewish elders. According to legend, Chinese mathematicians, under orders from the Emperor Yao (c. twenty-fourth century BC), began experimenting with a calendar in 2357 BC that eventually became Metonic, adding seven months to the lunar calendar every 19 years.

  The Sumerians by the twenty-first century BC had developed a slightly different system founded on a calendar year of 360 days. This came from rounding off the lunar month to 30 days, which fitted neatly into the Sumerians’ mathematic and astronomic system. This system is based on the numbers 6 and 60, which equal 360 when multiplied--the number we still use to divide the sky and every circular plane. No one knows why the Sumerians and later the Babylonians chose these numbers, though four thousand years later they remain the numeric basis for everything from determining one’s position at sea to the location in the sky of a distant galaxy vis-a-vis the earth.

  The Babylonians inherited and refined the older Sumerian numerology to divide the day up into 24 hours, which is divisible by six and also divides evenly into 360. Again, the reason for using 24 has been obscured by time, though it’s likely that it had something to do with the zodiac, which the astrology-crazed Babylonians used with great fervour to guide their lives. Possibly they divided first the day and then the night into 12 hours each to correspond to the signs of the zodiac, and then added them together in order to reach the 24-hour day we still follow.

  In the fifth century BC the Greek historian Herodotus told a story that points up the complications with these less-than-perfect luni-solar calendars. In The Histories Herodotus tells how the Greek law-giver Solon once answered a question put to him by the rich and haughty Croesus of Sardis: Who was the happiest man he had ever seen? In answering, Solon refused to name Croesus, explaining that fate could still render him unhappy. He used the Greek calendar to emphasize his point. ‘Take seventy years as the span of a man’s life,’ says Solon. ‘Those seventy years contain 25,200 days, without counting intercalary months. Add a month every other year, to make the seasons come round with proper regularity, and you will have thirty-five additional months, which will make 1,050 additional days. Thus the total of days for your seventy years is 26,250, and not a single one of them is like the next in what it brings. You can see from that, Croesus, what a chancy thing life is. You are very rich, and you rule a numerous people; but the question you asked me I will not answer, until I know that you have died happily.’

  Egypt was the first ancient civilization to correct the error of the moon and embrace the sun. Remarkably, they did it quite early--almost six thousand years ago, when people living along the Nile figured out the solar year was very close to 365 days. This led to a calendar with 12 months of 30 days each and an additional 5 days that Egyptian mythology says were added to the year by the god Thoth. These became the birthdays of Osiris, Isis, Horus, Nephthys and Set.

  How these Neolithic Egyptians figured out so close an approximation to the true year remains a mystery. Egyptian science was advanced very early, but they were never renowned for their astronomy, like the Babylonians, or for a keen interest in mathematics, like the Greeks.

  The most plausible explanation is the Nile. Herodotus called Egypt ‘the gift of the Nile’, and anyone who has visited understands instantly the division between the green along the river and the brown of the desert, between life and death. The Nile was responsible for the crops, the commerce, and the continuity of Egypt. The ancient Egyptians called it simply ‘the sea’. Flooding from late June till late October, each year the Nile brought down rich silt for crops to be grown from October to February, and harvested from February until the end of June. These were the three seasons of life in Egypt: flooding, growth and harvest. The regularity of this cycle and the availability of the great river as a natural timepiece provided an easy and dramatic alternative to the moon.

  North-east Africa was not always dependent on the Nile. Until the final retreat of the glaciers 10,000 years ago the Sahara was covered not with sand but with savannah. Then 7,000 or 8,000 years ago the savannah died as the earth waned and the people of the north-eastern Sahara were forced into the valley of the Nile. There they abandoned their Palaeolithic life of hunting and gathering and adapted to the cycles of the river. This provided a deep-set regularity to the Egyptian culture, which began farming and building settlements by about 7000 BC. Three millennia later Egyptians established what may be the first known date in human history, which chronographers have calculated to be as early as 4241 BC. A thousand years later the kingdoms of the Nile united politically, launching a complex and homogeneous civilization with a central authority and religion that persisted with few breaks for three thousand years, until the death of Cleopatra, all the while depending on the rhythms of the great river.

  The Nile is a gift of life; but it also is an enormous clock and calendar stretching over four thousand miles, the second-longest river in the world. Fed by rainfall and melting snow in the Ethiopian highlands and to a lesser extent by watersheds as far south as Uganda, the Nile floods with a predictability that Egyptians understood long before stone temples and pyramids began to rise on the river’s shoreline--or before anyone thought about a formal calendar. All an early Egyptian farmer needed to do was plant a tall reed in the mud along the river bank, cut a notch to measure the high point of the floods, and then count the days until the next high-water mark, which would occur almost exactly one year later. This simple device, called a Nilometer, was then the most accurate calendar in the world, based on the seasons as regulated by the earth’s orbit and the tilt of its axis rather than on the phases of the moon.

  Egyptian astronomers supplemented the Nilometer with another discovery that made their solar year even more accurate: that Sirius, the Dog Star and the brightest star in the sky, ascends in the dawn sky once a year in a direct line with the rising sun. Sirius’s appearance happened to coincide with the Nile’s annual f
lood; it also became the first day of the month of Thoth, the Egyptian New Year’s Day, commemorated annually with elaborate ceremonies that began when Sirius appeared on top of obelisks precisely aligned with observation points on the ground below. By timing Sirius’s appearance exactly from year to year, Egyptian astronomers eventually realized that the solar year was one fourth of a day longer than 365 days. Egyptians also used pyramids to measure shadows to determine the coming of the equinoxes.

  Adding a quarter of a day to the Egyptian year was a revolutionary discovery. It brought the Egyptian year within 11 minutes and 24 seconds (give or take a few seconds) of the true solar year at least two thousand years before Julius Caesar embraced the 365 1/4 day calendar for Rome, and over three millennia before Roger Bacon’s appeal to Pope Clement. Still, in a move Bacon would have ruefully understood, the priests who controlled Egypt’s calendar refused to alter their year to make the correction from 365 to 365 1/4 days. As orthodox and unbending as the Catholic Church in Bacon’s era, the white-kilted Egyptian priests with their shaved heads and painted faces considered their calendar too sacred to alter, leaving it to shift by six hours (a quarter of a day) each year. This launched the Egyptian calendar on a slow drift across the seasons in a cycle that repeated itself every 1,460 years. Called the Sothic cycle, this flaw was not corrected until the Ptolemaic era in Egypt. In 238 BC Ptolemy III* ordered a leap-year system by adding an extra day every four years. But even then the priests resisted the edict until 30 BC, when Rome conquered Egypt and Augustus forced the people of the Nile to add the extra quarter of a day to their calendar to bring it into line with the Julian calendar. This stabilized the Egyptian calendar so that the first of Thoth always fell on 29 August.

  *The royal dynasty of the Ptolemies should not be confused with the second century Alexandrian astronomer Claudius Ptolemy.

  Egyptians were not alone in their early turning to the sun. Far beyond the great Nile valley and even the Mediterranean, on the distant edge of the Eurasian continent, a little-understood people also figured out a close approximation of the solar year a few centuries after the Egyptians. We know this only because they left behind what appears to be an enormous calendar constructed out of immense slabs of bluestone, standing upright to form megaliths, some of them topped by lintels called henges. Standing on the barren Salisbury plain, this structure, Stonehenge, was used for over two thousand years by ancient Britons, who aligned the stones so that at the precise moment of the summer solstice a ray of sun shines down the main avenue and into its centre. But what was this for? Is Stonehenge truly an enormous calendar? Or is it an observatory, a fortress, a temple, a Bronze Age place of assembly--or all of the above?

  No one knows for sure, though the layout leaves no doubt that the people who built it were astronomically sophisticated enough to build a device to accurately measure the solar year. Further evidence comes from stones erected in patterns around Stonehenge that align with the sun at both solstices and at the equinoxes, and with the moon as it runs through its orbit around the earth. This giant calendar would have allowed an ancient Briton to anticipate astronomic cycles and events as accurately as the Egyptians watching Sirius--or, for that matter, a modem astronomer using solar and star charts. Some have claimed that Stonehenge can also foretell eclipses of the moon, which occur regularly after those months when the full moon rises precisely down the main avenue.

  The other ancient culture that invented sun time early on, the Maya, was far more isolated than the people of Wessex. Raising great cities filled with temples and palaces deep in the interior of Central America, the Maya also invented a calendric system so accurate that when the Spaniards conquered them in the sixteenth century, the Julian calendar the conquistadors brought with them was less precise.

  The Maya developed three calendar systems. The first was 365 days long, with 18 months of 20 days, to which they added 5 more days. This was called the haab. As for the Egyptians, these five extra days were considered special, though the Maya believed them to be unlucky and shunned all activity as they anxiously waited for them to pass. Apparently the Maya knew that the year was really closer to 365 1/4 days but ignored it in this calendar, which drifted, like the Egyptian version, about six hours a year. Concurrently with this 365-day calendar the Maya used a 260-day cycle called a tzolkin, or ‘sacred round’, which served a similar purpose as Hesiod’s ‘Days’, listing omens and associations for each day to guide the Maya and other Mesoamericans in planting, waging war and offering sacrifices to the gods. The 260-day cycle was developed early in the first millennium BC by the Zapotecs of Mexico, for reasons that remain obscure. Common to all sophisticated Mesoamerican peoples by the time of the Maya, who first appear in about 1000 BC, the tzolkin was joined to the 365-day calendar in a complex cycle of 52 years called the Calendar Round. This is the time it takes for both calendars to start again on the same day. Spanish conquistadors in the sixteenth century reported that the end of a 52-year cycle was commemorated by all advanced cultures in the region. It was universally greeted with great despondency, the people fearing that the sun might not return.

  The third Maya calendar was the Long Count, used to calculate long periods of time. It was based on 360-day unit called a tun and a number system based on 20 (Mesoamericans counted with their fingers and their toes). The Long Count cycles are as follows:

  20 kins = 1 uinal = 20 days

  18 uinals = 1 tun = 360 days

  20 tuns = 1 katun =7200 days

  20 katuns = 1 baktun = 144,000 days

  The Mayas multiplied the baktun by 13 to get what they termed a Great Cycle, equal to 5,130 years.

  At the same end of a great cycle, the Maya, Aztecs, and other Mesoamerican peoples believed all things would cease to exist and an entirely new world would be ushered in to start the next great cycle. The current great cycle probably began in 3114 BC and will end on 23 December 2012.

  Presumably the Maya discovered the true solar year using natural cues and careful astronomic observations, though exactly how they did it remains a puzzle. Until recently scholars believed their motivation was a literal worship of time, though new interpretations since the breaking of the Maya language code reveal that the Maya actually used their calendars to legitimize the acts of kings and other key events by recording with great accuracy the day, hour, and even minute when they occurred. This is shown in countless hieroglyphics, steles and paintings depicting the exact date when specific kings and queens waged battle, ceremonially mutilated themselves, married and performed important sacrifices.

  Maya and other Mesoamerican gods also seem to have demanded that their priests perform ceremonies precisely on time. Nowhere was this taken more seriously--and to such a bizarre extreme--than among the Aztecs. Obsessed with the belief that they must keep time on its proper course, the Aztecs offered a numbing progression of human sacrifices to appease their sun god, Tonatiuh, to assure that he would rise each day and cross the sky.

  The Aztecs believed that the sun required for ‘fuel’ rivers of blood from victims who ranged from priests and criminals to the deformed, though most were prisoners captured in warfare. If Spanish chroniclers can be believed, the Aztecs sacrificed 20,000 to 50,000 people a year in their capital, Tenochtitlan, with each month requiring a prescribed tally of victims: male and female, child and adult. For instance, in the months when the rains were supposed to come, children were drowned or walled up in caves. The more they wept and cried, the better the omen for rain. Others were flayed to help crops grow and burned to death during harvest time. To feed the need for such huge numbers of victims, the Aztecs arranged a peculiar agreement with their neighbours to fight regular ceremonial battles not for conquest, but to allow each side to capture large quantities of sacrificial victims. Apparently most of the victims seized in what was called the War of Flowers considered sacrifice an honour or an unquestionable act of fate. Most were anaesthetized first with narcotic plants, though all were left conscious enough to scream and exhibit pain
, which was part of this bloodiest of time rituals.

  Despite the remarkable achievements in time reckoning by Mesoamericans and the people of Wessex, out of all those who early embraced the sun, it is the Egyptians who lie in the direct path of our story. It is their affair with Sol which brought us our calendar, making the solar year victorious over the moon first along the Nile and then in Europe and, much later, around the world. But this triumph of the Egyptian year was hardly inevitable. Nor was it even likely given the circumstances that led to the fusing of the ancient solar calendar of the Nile with a brash, upstart empire ruled by a people living on another river, the Tiber, and led by a conqueror whose adoption of a new calendar had more to do with his love for a legendary woman than with a passion for accurately measuring time.

  3 Caesar Embraces Time

  Caesar . . . reorganized the Calendar which the College of Priests had allowed to fall into such disorder, by inserting days or months as it suited them, that the harvest and vintage festivals no longer corresponded with the appropriate seasons.--Suetonius, AD 96

  As night fell, a small ship slipped under the sea chain defending Alexandria’s harbour, raised by guards bribed to let it pass. The boat on this balmy October evening in 48 BC stole quietly through the black waters, past quays and warehouses full of grain and treasure. Skirting the fleets of Egyptian and Roman warships, the boat carried a cargo that would not only transform two great empires, but lead to a revolution in measuring time that is directly responsible for calendars hanging on walls from present-day St Louis to Singapore.

  After the boat landed unnoticed on a stone wharf, a Sicilian named Apollodorus leapt ashore, carefully lifting onto his back a rolled-up coverlet tied at each end. Apollodorus carried his load past Roman sentinels, explaining by the light of torches that he bore a gift for the recently arrived Julius Caesar, dictator of Rome. Led to the general’s apartment in Alexandria’s royal palace, Apollodorus greeted Caesar by unfurling the coverlet, which concealed a woman.