Some news from the Babylonian firmament

5 March 2016

Many newspapers reported M. Ossendrijver’s discovery which, based on the inscriptions found on some cuneiform tablets dating from the end of the first millennium BCE, revealed that the scholars of Hellenistic Babylon (323-63 BCE) had developed an algorithm that employs the trapezoidal rule to calculate the distance travelled by Jupiter along the ecliptic as a function of the development of its daily velocity over the course of 60 days subsequent to its reappearance in the heavens.[1]

How does this discovery fit in with developments in Mesopotamian astrology, and subsequently with its astronomy? The people of Mesopotamia very early on observed the heavens in order to establish their calendar and, starting from the second millennium BCE, to make prophecies of future events. The Babylonian calendar is composed of a solar year and of lunar months. In Babylon, the New Year was celebrated on the day of the spring equinox. The month begins on the evening when the new (crescent) Moon reappears in the sky. With twelve lunar months composed of 29 or 30 days, the year consists of 354 days; therefore it is eleven days short of a solar year consisting of 365 days. To make up for this deficit, the calendar was intercalated (i.e. evened out) by adding a thirteenth month. At the beginning of the second millennium, the addition of an extra month was decided on by the king and became an arbitrary process. Towards the year 400 BCE, scholars in the service of the temples of Babylon and Uruk established some rules for the addition of intercalary months according to a mathematical pattern: seven months were added in a 19-year cycle.

The heavens were also closely observed in order to make predictions. Starting in the second millennium BCE, celestial phenomena were interpreted as harbingers through which the gods communicated with mortals; they delivered both good and bad omens. To interpret them, the astrologers possessed some collected texts, the most important among them being the Enuma Anu Enil (‘the day when [gods] Anu, Enil…’), which assembles on 70 tablets close to 7,000 portents relating to the king or to the country. Tablet 63 provides a list of the visible risings and settings of Venus in a 21-year cycle recorded in the middle of the seventeenth century BCE at Babylon. Another text, ‘The Plough Constellation (or Great Bear)’ (fourteenth century BCE, inscribed on two tablets), provides a list of more than 70 stars and constellations divided up according to three paths running parallel with the equator (Anu, Ea, and Enil) and the helical rising of some of them. It also describes the procedures employed to predict the Sun’s movements, those of the Moon and of the planets, and the length of the shadow cast on a sundial at different junctures over the course of a day. One tablet lists separately 18 constellations which are found within the orbit of the Moon, the Sun and the planets: this, then, is the first ever description of the belt of the zodiac (the zodiac composed of twelve constellations dates to 419 BCE). The ‘twelve times three’, dating from the end of the second millennium, indicates for each month the three stars that rise just before the Sun in the three celestial zones. Here, then, one notes a knowledge of the main cyclical phenomena, the variation in the length of a day and a night over the course of a year, and the movements of the constellations, the Moon and the planets.

Astrology underwent some important developments in the first millennium BCE. The astrologers contributed to the surveillance of Assyria. Deployed at all the astronomical stations distributed throughout the kingdom, they sent reports of their observations to the king; particular attention was paid to eclipses (i.e. date, beginning, end, position in the sky, extent). Eclipse tables were drawn up that reach back to the year 747 BCE. The scholars attached to the temple of Marduk at Babylon observed the heavens every day, produced astronomical journals and wrote reports on their observations over six-month periods. These observations noted the moment the Moon first became visible, all the days that it was visible, the rising of the Moon and of the planets, the paths they took across the sky, solstices and equinoxes, meteorological conditions, the price of foodstuffs, and the level of the Euphrates, etc.

In the second half of the first millennium BCE, the progress made by astronomers exerted a profound effect on astrology. As soon as it was possible to calculate in advance certain celestial phenomena, it was believed that these could exert an influence on humans: the first Babylonian horoscopes date to 410 BCE. Babylonian astronomical almanacs first appeared in 220 BCE. Towards the middle of the third century BCE, Babylonian astronomers knew the periodicity of the permanent celestial bodies. A hundred or so tablets indicate the methods to employ for the calculation of periodical celestial phenomena, and more than 300 ephemerides list the consequences with which they were associated. Two systems based on arithmetical calculation techniques were employed. In one case the Sun moves along the ecliptic in a succession of two constant speeds (known as a ‘staircase’); in the other, its speed increases and decreases in a regular way (zigzag style).

The calculation of the distance travelled by Jupiter along the ecliptic over a period of 60 days can therefore be included among the remarkable achievements of Babylonian astronomers — the fruit of several centuries of celestial observations. The discoveries made by Babylonian astronomers were passed on by the Greek authors, and today it is widely agreed that the astronomy which subsequently developed in India, in the Arab world and in Europe can be regarded a legacy of the Babylonians’ discoveries.

‘The Babylonian astronomers, mathematicians ahead of their time’, Pour la Science, 21 February 2016.

[1] Ossendriver, Mathieu (2016): ‘Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph’, Science, 351, Issue 6272, 482-484.