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Kidinnu, the Chaldaeans, and Babylonian astronomy


Tablet with a list of eclipses between 518 and 465, mentioning the death of king Xerxes. British Museum, London (Britain).
Tablet with a list of eclipses between 518 and 465, mentioning the death of king Xerxes (British Museum)
Kidinnu or Cidenas: famous Babylonian astronomer (fourth century BCE?), one of the most important persons in the history of science.

The Greek geographer Strabo of Amasia (64 BCE-c.23 CE) gives a description of the life of the Babylonian astronomers, which he calls Chaldaeans.

In Babylon a settlement is set apart for the local philosophers, the Chaldaeans, as they are called, who are concerned mostly with astronomy; but some of these, who are not approved of by the others, profess to be writers of horoscopes. (There is also a tribe of the Chaldaeans, and a territory inhabited by them, in the neighborhood of the Arabs and of the Persian Gulf, as it is called.) There are also several tribes of the Chaldaean astronomers. For example, some are called Orcheni [those from Uruk], others Borsippeni [those from Borsippa], and several others by different names, as though divided into different sects which hold to various different dogmas about the same subjects. And the mathematicians make mention of some of these men; as, for example, Cidenas [Kidinnu], Naburianus [NabŻ-rÓmannu] and Sudines.
[Strabo, Geography 16.1-6]
The Babylonian temple astronomers, who were in fact called  tupšar EnŻma Anu Enlil, had been observing the skies for centuries and had recorded their observations in Astronomical diaries, astronomical almanacs, catalogues of stars and other texts. We possess observations of Venus written down under king Ammisaduqa (1646-1626 according to the Middle Chronology), detailed stellar catalogues from the eighth century -our Zodiac was invented in Babylon-, and astronomical diaries from the seventh century until the first century BCE.

Because there were many data available to Babylonian astronomers, their results could be pretty accurate. An example is the length of the synodic month, i.e., the period between two full moons, which they were able to establish with an error of only a couple of minutes. The same can be said for the length of the year.

Using these data, Babylonian astronomers were able to predict lunar eclipses and - later - solar eclipses with a fair accuracy. Their tool was the Saros-cycle: this is the period of 223 synodic months (or 18 years and 11.3 days) after which lunar and solar eclipses repeat themselves. E.g., when you know that there has been a solar eclipse on 18 May 603 BCE at dawn, you can be confident that there is an almost similar eclipse on 28 May 585 at sunset.

The importance of these predictions can not be exaggerated. The Assyrians and Babylonians regarded lunar eclipses as evil omens, directed against their kings. Now that they were predictable, it was possible to appoint substitute kings who would bear the brunt of the gods' wrath. The real king would remain unharmed and the continuity of the state's policy was guaranteed. (The poor man who was appointed as substitute king was killed. In this way, the omen was always right.)

Another result of the observations was a nearly perfect calendar. In the reign of king NabŻ-Nasir, the astronomers of Babylon recognized that 235 lunar months are almost identical to 19 solar years. (The difference is only two hours.) They concluded that seven out of nineteen years ought to be leap years with an extra month.

At first, intercalary months were announced by the king (who had an astronomical adviser), but after Babylon had been captured by the Persian king Cyrus in 539, priestly officials took over. They started to look for a standard procedure for the intercalation of months. It was introduced in 503 BCE by Darius I the Great (if not earlier).
 
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As this table shows, there are six years when a second month Addaru is added, and one year with an extra Ululu. The result is that the first day of the month Nisanu (New year's day) was never far from the vernal equinox (the first day of spring), so that the civil calendar and the seasons were never out of step. This system is often called the cycle of Meton, to commemorate the Greek astronomer who introduced it in the West. It is still used in the Jewish calendar.

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A Babylonian almanac, mentioning future positions of the planets. British Museum, London (Britain). Photo Marco Prins.
A Babylonian almanac, mentioning future positions of the planets (British Museum)

At an unknown moment in the fourth century, a second procedure for the intercalation of months was invented. This time, a cycle of 76 years was used, and the limits of variability in the start of the year were further narrowed. The new system must already have been known in 331, because in that year the Macedonian conqueror Alexander the Great captured Babylon and his scientific adviser Callisthenes of Olynthus ordered the astronomical diaries to be translated into Greek. The new knowledge was immediately applied in Greece: the astronomer Callippus of Cyzicus, a pupil of the philosopher Aristotle of Stagira, recalculated the length of the lunar month and proposed a new calendar, in which he used the longer cycle. His new era, which was used by all later Greek astronomers, started at 28 June 330, eight months after the capture of Babylon.
Callisthenes' translations are known from a very late Greek source, Simplicius; the truth of
his words, however, is
established, because he 
correctly translates the
Babylonian title, massartu, with tÍrÍseis, which is illogical in Greek but keeps the double meaning of 'guarding' and 'observing'.  A similar story is told by Ibn Khaldun.
Astronomical diary mentioning the comet of Halley. British Museum, London (Britain). Photo Marco Prins.
Astronomical text mentioning the comet of Halley (British Museum)

This calendar reform may have been the work of Kidinnu. We have already seen that he reached accurate estimates of the length of the solar year and the synodic month. Consequently, he had all the necessary knowledge to establish this cycle. There is, however, no hard proof  for this. On the other hand, it is unlikely that someone who has discovered the length of the year and month refrains from thinking about the calendar.

Another discovery is mentioned in a scholion (commentary) on the Handy tables by Ptolemy of Alexandria (second century CE). According to the scholiast, Kidinnu discovered that 251 synodic months are identical to 269 anomalistic months. (An anomalistic month is the period between two moments when the moon is closest to the earth, 27.55 days.) This discovery shows considerable skill in observation, because it is very difficult to see with the naked eye that the moon is sometimes closer than on other times. The distance varies between 356,000 and 407,000 kilometers and the diameter of the moon varies only 11%.

The Roman author Pliny the Elder (23-79) knows another discovery of Kidinnu.

The star next to Venus is Mercury, by some called Apollo. It has a similar orbit, but is by no means similar in magnitude or power. It travels in a lower circle, with a revolution nine days quicker, shining sometimes before sunrise and sometimes after sunset, but according to Cidenas [Kidinnu] and Sosigenes never more than 22 degrees away from the sun.
[Pliny the Elder, Natural history 2.39]
Kidinnu's greatest discovery, however, may have been the system to predict the motion of the moon. Modern scholars call it System-B. In the last years of the fifth century, the Babylonian astronomers discovered that the moon does not always move at the same speed. Sometimes, it seems as if the moon accelerates, at other times it seems to go slower. The explanation is the elliptic shape of the moon's orbit: when it is near the earth, it moves faster because of the earth's gravity.

Several astronomers have tried to describe this phenomenon. (As far as we know, no Babylonian, Greek or Roman has ever suggested an explanation.) The first system, called System-A, assumes that the moon has two constant speeds, and this idea makes predictions more accurate than when we assume a constant motion. Unfortunately, we do not know who invented this improvement.

The second system, which may have been invented by Kidinnu, was a further refinement. The moon's velocity changes as a function of time: first, it increases in steps (of a day each) from minimum to maximum speed, later the velocity decreases again. This system was very accurate. From now on, the Babylonian astronomers were able to predict the lunar phases and positions. A similar system was used for the movements of the sun and the five planets (which the Babylonians called NabŻ, Ištar, Nergal, Marduk and Ninurta). This is essentially an arithmetical system, and it is probably no coincidence that in our first quotation, Strabo connects Kidinnu with mathematics.

It has been argued in the 1930's that Kidinnu also discovered the precession, that is the slow reorientation of the earth's axis. He was certainly in the position to discover this phenomenon. In our age, the stars seem to rotate around the Pole Star, but in Kidinnu's age, the north pole of heaven was somewhere halfway the Little Bear and the Dragon. Kidinnu must have known that in the days of the legendary king Hammurabi (1792-1750), the earth's axis was directed to a point inside the Dragon and he must have been able to conclude that the axis of the earth was slowly changing its direction. However, there are no indications that he really reached this conclusion, and the theory that Kidinnu discovered the precession has now been abandoned. The Greek astronomer Hipparchus of Nicaea (second century BCE) was the first to understand the nature of the precession - using, as a matter of fact, Greek translations of age-old observations made in Babylonia.

If Kidinnu is indeed the inventor of System-B, he must have lived in the fourth century, because one tablet is dated to c.375 BCE. A cuneiform Chronicle (the Alexander Chronicle), which has recently dated to the reign of king Darius III Codomannus, mentions that a man named Kidinnu was put to the sword by the Macedonian king Alexander the Great on 14 August 329. This Kidinnu must have been someone well-known to the author, because he is mentioned without any familial or professional designation. As the Babylonian chronicles were written by the same scribes as the Astronomical diaries and other astronomical texts, it is tempting to think that the astronomer fell victim to Alexander's enlightened science policy. If this identification is correct, the inventor of System-B must have been an old man when he was executed.

It has been argued that the 'Sudines' mentioned by Strabo is responsible for the translation of Kidinnu's work into Greek. It is tempting to connect this hypothesis with the fact that Alexander the Great had the Babylonian astronomical diaries translated, but it is probably better to resist this temptation. However this may be, it is certain that the Greek translation was used by the Greek astrologer Critodemus (c.260 BCE), by Hipparchus of Nicaea and Ptolemy of Alexandria, who all knew System-B and accepted Kidinnu's values for the length of the year and the synodic month and his equation of 251 synodic months with 269 anomalistic months.

To honor the great Babylonian astronomer, a crater on the far side of the moon has been called Kidinnu (35.9N 122.9E). It is a small crater, however, with a diameter of only 56 kilometer.



 

Literature

A brief introduction to Babylonian astronomy, written by Asger Aaboe, can be found in volume 3, part 2 of Cambridge ancient history (2nd edition, 1991), chapter 28b, "Babylonian mathematics, astrology and astronomy". Hermann Hunger's and David Pingree's Astral sciences in Mesopotamia (1999 Leiden) is less accessible but offers a wealth of information.




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