Kidinnu
Encyclopedia
Kidinnu (fl.
4th century BC? possibly died 14 August 330 BC) was a Chaldean astronomer and mathematician
. Strabo
of Amaseia called him Kidenas, Pliny the Elder
Cidenas, and Vettius Valens
Kidynas.
Some cuneiform
and classical Greek and Latin texts mention an astronomer with this name, but it is not clear if they all refer to the same individual:
The following information is an excerpt of the overview of a century of scholarship in the sources referenced below.
The meaning of tersitu is not known definitively. Already Franz Xaver Kugler
proposed that the word can be interpreted here as "table"; in another context it seems to mean something like "tool", but in yet another it refers to a blue enamel paste. P. Schnabel, in a series of papers (1923–27), interpreted the phrase as an assignment of authorship. He argued that Naburimannu
developed the Babylonian System A of calculating solar system
ephemerides, and that later Kidinnu developed the Babylonian System B. A Greco-Roman tradition, mentioned above, attributes to Kidinnu the discovery that 251 synodic months equals 269 anomalistic months. This relationship is implicit in System B, and is therefore another reason to believe that Kidinnu was involved in developing the lunar theory
of System B. However, the conclusion that Kidinnu is the main creator of System B is uncertain. Babylonian astronomers before Kidinnu's time apparently already knew the Saros cycle
(old eclipse observations were collected in tables organised according to the Saros cycle since the late 5th century BC) and the Metonic cycle
(the dates of the lunar calendar in the Saros tables follow a regular 19-year pattern of embolismic months at least since 498 BC); both cycles are also used in System B. Schnabel computed specific years (first 314 BC and later 379 BC) for the origin of the System B lunar theory, but Franz Xaver Kugler
and Otto E. Neugebauer
later disproved Schnabel's calculations. Schnabel also asserted that Kidinnu discovered precession
when distinguishing between sidereal
and tropical year
s; Neugebauer contested this and current scholarship considers this conclusion to be unfounded.
The lunation length used in System B has also been attributed to Kidinnu. It is 29 days + 191 time degrees + 1/72 of a time degree ("barley corn") = 29d 31:50:8:20 (sexagesimal) = 29d + 12h + 793/1080h (Hebrew chelek) = 29.53059414...d, but being a rounded value in the archaic unit of "barley corns" it may be even more ancient. In any case, it is very accurate, with only ⅓ of a second in error in the 4th century BC. Hipparchus
confirmed this value for the lunation length. Ptolemy
accepted and used it, as mentioned above. Hillel
first used it in the Hebrew calendar
, and it has been used for that purpose ever since.
The existing evidence makes it difficult to put Kidinnu at a time and place. Schnabel placed Kidinnu in Sippar, but Otto E. Neugebauer
showed that Schnabel based this conclusion on a misreading of the cuneiform tablet. Classical sources like Strabo mention different "schools" and "doctrines" followed in different places (Babylon, Borsippa, Sippar, Uruk). System A and B have been used contemporaneously, and tablets for both systems have been found in both Babylon and Uruk. Tablets based on System B, associated with Kidinnu, have been found mostly in Uruk, but the earlier tablets came predominantly from Babylon. The oldest preserved tablet using System B comes from Babylon and dates from 258-257 BC. This is in the Seleucid era
, but it is plausible that the traditional Chaldean astronomical systems had been developed before the Hellenistic period. The Alexander chronicle mentioned above suggests that the famous astronomer Kidinnu died in Babylon in 330 BC, if it refers to the same Kidinnu who was mentioned on the ephemeris tablets centuries later.
Floruit
Floruit , abbreviated fl. , is a Latin verb meaning "flourished", denoting the period of time during which something was active...
4th century BC? possibly died 14 August 330 BC) was a Chaldean astronomer and mathematician
Babylonian mathematics
Babylonian mathematics refers to any mathematics of the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited...
. Strabo
Strabo
Strabo, also written Strabon was a Greek historian, geographer and philosopher.-Life:Strabo was born to an affluent family from Amaseia in Pontus , a city which he said was situated the approximate equivalent of 75 km from the Black Sea...
of Amaseia called him Kidenas, Pliny the Elder
Pliny the Elder
Gaius Plinius Secundus , better known as Pliny the Elder, was a Roman author, naturalist, and natural philosopher, as well as naval and army commander of the early Roman Empire, and personal friend of the emperor Vespasian...
Cidenas, and Vettius Valens
Vettius Valens
Vettius Valens was a 2nd-century Hellenistic astrologer, a somewhat younger contemporary of Claudius Ptolemy.Valens' major work is the Anthology, ten volumes in Greek written roughly within the period 150 to 175. The Anthology is the longest and most detailed treatise on astrology which has...
Kidynas.
Some cuneiform
Cuneiform
Cuneiform can refer to:*Cuneiform script, an ancient writing system originating in Mesopotamia in the 4th millennium BC*Cuneiform , three bones in the human foot*Cuneiform Records, a music record label...
and classical Greek and Latin texts mention an astronomer with this name, but it is not clear if they all refer to the same individual:
- The Greek geographer StraboStraboStrabo, also written Strabon was a Greek historian, geographer and philosopher.-Life:Strabo was born to an affluent family from Amaseia in Pontus , a city which he said was situated the approximate equivalent of 75 km from the Black Sea...
of Amaseia, in Geography 16.1–.6, writes: "In BabylonBabylonBabylon was an Akkadian city-state of ancient Mesopotamia, the remains of which are found in present-day Al Hillah, Babil Province, Iraq, about 85 kilometers south of Baghdad...
a settlement is set apart for the local philosophers, the Chaldaeans, as they are called, who are concerned mostly with astronomyAstronomyAstronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
; but some of these, who are not approved of by the others, profess to be writers of horoscopeHoroscopeIn astrology, a horoscope is a chart or diagram representing the positions of the Sun, Moon, planets, the astrological aspects, and sensitive angles at the time of an event, such as the moment of a person's birth. The word horoscope is derived from Greek words meaning "a look at the hours" In...
s. (There is also a tribe of the Chaldaeans, and a territory inhabited by them, in the neighborhood of the Arabs and of the Persian GulfPersian GulfThe Persian Gulf, in Southwest Asia, is an extension of the Indian Ocean located between Iran and the Arabian Peninsula.The Persian Gulf was the focus of the 1980–1988 Iran-Iraq War, in which each side attacked the other's oil tankers...
, as it is called.) There are also several tribes of the Chaldaean astronomers. For example, some are called Orcheni [those from UrukUrukUruk was an ancient city of Sumer and later Babylonia, situated east of the present bed of the Euphrates river, on the ancient dry former channel of the Euphrates River, some 30 km east of modern As-Samawah, Al-Muthannā, Iraq.Uruk gave its name to the Uruk...
], others Borsippeni [those from BorsippaBorsippaBorsippa was an important ancient city of Sumer, built on both sides of a lake about southwest of Babylon on the east bank of the Euphrates. The site of Borsippa is in Babil Governorate, Iraq and now called Birs Nimrud, identifying the site with Nimrod...
], and several others by different names, as though divided into different sects which hold to various dogmas about the same subjects. And the mathematicians make mention of some of these men; as, for example, Kidenas, Nabourianos and Soudines".
- The Roman encyclopaedist Pliny the ElderPliny the ElderGaius Plinius Secundus , better known as Pliny the Elder, was a Roman author, naturalist, and natural philosopher, as well as naval and army commander of the early Roman Empire, and personal friend of the emperor Vespasian...
, in Natural History II.vi.39, writes that the planetPlanetA planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...
MercuryMercury (planet)Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
can be viewed "sometimes before sunrise and sometimes after sunset, but according to Cidenas and SosigenesSosigenes of AlexandriaSosigenes of Alexandria was named by Pliny the Elder as the astronomer consulted by Julius Caesar for the design of the Julian calendar. Little is known about him apart from Pliny's Natural History...
never more than 22 degrees away from the sunSunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
".
- The Roman astrologer Vettius ValensVettius ValensVettius Valens was a 2nd-century Hellenistic astrologer, a somewhat younger contemporary of Claudius Ptolemy.Valens' major work is the Anthology, ten volumes in Greek written roughly within the period 150 to 175. The Anthology is the longest and most detailed treatise on astrology which has...
, in Anthology, says that he used HipparchusHipparchusHipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...
for the Sun, SudinesSudinesSudines : Babylonian sage. He is mentioned as one of the famous Chaldean mathematicians and astronomer-astrologers by later Roman writers like Strabo ....
and Kidynas and ApolloniusApollonius of PergaApollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
for the MoonMoonThe Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
, and again Apollonius for both types (of eclipseEclipseAn eclipse is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer...
s, i.e. solar and lunar).
- The Hellenistic astronomer PtolemyPtolemyClaudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
, in AlmagestAlmagestThe Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...
IV 2, discusses the duration and ratios of several periods related to the Moon, as known to "ancient astronomers" and "the Chaldeans" and improved by Hipparchus. He mentions the equality of 251 (synodic) months to 269 returns in anomaly. In a preserved classical manuscript of the excerpt known as Handy Tables, an anonymous reader in the third century wrote the comment (a scholiumScholiumScholia , are grammatical, critical, or explanatory comments, either original or extracted from pre-existing commentaries, which are inserted on the margin of the manuscript of an ancient author, as glosses. One who writes scholia is a scholiast...
) that Kidenas discovered this relation.
- The colophonColophon (publishing)In publishing, a colophon is either:* A brief description of publication or production notes relevant to the edition, in modern books usually located at the reverse of the title page, but can also sometimes be located at the end of the book, or...
of two Babylonian System B lunarMoonThe Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
ephemeridesEphemerisAn ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...
from Babylon (see ACT 122 for 104–101 BC, and ACT 123a for an unknown year) say that they are the tersitu of Kidinnu.
- A damaged cuneiform astronomical diary tablet from Babylon (Babylonian Chronicle 8Babylonian ChroniclesThe Babylonian Chronicles are many series of tablets recording major events in Babylonian history. They are thus one of the first steps in the development of ancient historiography...
: the Alexander Chronicle, BM 36304) mentions that "ki-di-nu was killed by the sword" on day 15 of probably the 5th month of that year, which has been dated as 14 August 330 BC, less than a year after Alexander the Great conquered Babylon.
The following information is an excerpt of the overview of a century of scholarship in the sources referenced below.
The meaning of tersitu is not known definitively. Already Franz Xaver Kugler
Franz Xaver Kugler
Franz Xaver Kugler was a German chemist, mathematician, Assyriologist, and Jesuit priest.Kugler was born in Königsbach, Palatinate, then part of the Kingdom of Bavaria. He earned a Ph.D. in chemistry in 1885, and the following year he entered the Jesuits. By 1893 he had been ordained as a priest...
proposed that the word can be interpreted here as "table"; in another context it seems to mean something like "tool", but in yet another it refers to a blue enamel paste. P. Schnabel, in a series of papers (1923–27), interpreted the phrase as an assignment of authorship. He argued that Naburimannu
Naburimannu
Nabu-ri-man-nu was a Chaldean astronomer and mathematician.Classical and ancient cuneiform sources mention an astronomer with this name:...
developed the Babylonian System A of calculating solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
ephemerides, and that later Kidinnu developed the Babylonian System B. A Greco-Roman tradition, mentioned above, attributes to Kidinnu the discovery that 251 synodic months equals 269 anomalistic months. This relationship is implicit in System B, and is therefore another reason to believe that Kidinnu was involved in developing the lunar theory
Lunar theory
Lunar theory attempts to account for the motions of the Moon. There are many irregularities in the Moon's motion, and many attempts have been made over a long history to account for them. After centuries of being heavily problematic, the lunar motions are nowadays modelled to a very high degree...
of System B. However, the conclusion that Kidinnu is the main creator of System B is uncertain. Babylonian astronomers before Kidinnu's time apparently already knew the Saros cycle
Saros cycle
The saros is a period of 223 synodic months , that can be used to predict eclipses of the Sun and Moon. One saros after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle...
(old eclipse observations were collected in tables organised according to the Saros cycle since the late 5th century BC) and the Metonic cycle
Metonic cycle
In astronomy and calendar studies, the Metonic cycle or Enneadecaeteris is a period of very close to 19 years which is remarkable for being very nearly a common multiple of the solar year and the synodic month...
(the dates of the lunar calendar in the Saros tables follow a regular 19-year pattern of embolismic months at least since 498 BC); both cycles are also used in System B. Schnabel computed specific years (first 314 BC and later 379 BC) for the origin of the System B lunar theory, but Franz Xaver Kugler
Franz Xaver Kugler
Franz Xaver Kugler was a German chemist, mathematician, Assyriologist, and Jesuit priest.Kugler was born in Königsbach, Palatinate, then part of the Kingdom of Bavaria. He earned a Ph.D. in chemistry in 1885, and the following year he entered the Jesuits. By 1893 he had been ordained as a priest...
and Otto E. Neugebauer
Otto E. Neugebauer
Otto Eduard Neugebauer was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages...
later disproved Schnabel's calculations. Schnabel also asserted that Kidinnu discovered precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
when distinguishing between sidereal
Sidereal year
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to at noon 1 January...
and tropical year
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
s; Neugebauer contested this and current scholarship considers this conclusion to be unfounded.
The lunation length used in System B has also been attributed to Kidinnu. It is 29 days + 191 time degrees + 1/72 of a time degree ("barley corn") = 29d 31:50:8:20 (sexagesimal) = 29d + 12h + 793/1080h (Hebrew chelek) = 29.53059414...d, but being a rounded value in the archaic unit of "barley corns" it may be even more ancient. In any case, it is very accurate, with only ⅓ of a second in error in the 4th century BC. Hipparchus
Hipparchus
Hipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...
confirmed this value for the lunation length. Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
accepted and used it, as mentioned above. Hillel
Hillel II
Hillel II, also known simply as Hillel held the office of Nasi of the ancient Jewish Sanhedrin between 320 and 385 CE. He was the son and successor of Judah III. He was a Jewish communal and religious authority, circa 330 - 365 CE...
first used it in the Hebrew calendar
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
, and it has been used for that purpose ever since.
The existing evidence makes it difficult to put Kidinnu at a time and place. Schnabel placed Kidinnu in Sippar, but Otto E. Neugebauer
Otto E. Neugebauer
Otto Eduard Neugebauer was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages...
showed that Schnabel based this conclusion on a misreading of the cuneiform tablet. Classical sources like Strabo mention different "schools" and "doctrines" followed in different places (Babylon, Borsippa, Sippar, Uruk). System A and B have been used contemporaneously, and tablets for both systems have been found in both Babylon and Uruk. Tablets based on System B, associated with Kidinnu, have been found mostly in Uruk, but the earlier tablets came predominantly from Babylon. The oldest preserved tablet using System B comes from Babylon and dates from 258-257 BC. This is in the Seleucid era
Seleucid era
The Seleucid era was a system of numbering years in use by the Seleucid Empire and other countries among the ancient Hellenistic civilizations. The era dates from the return of Seleucus I Nicator to Babylon in 311 BC after his exile in Ptolemaic Egypt, considered by Seleucus and his court to mark...
, but it is plausible that the traditional Chaldean astronomical systems had been developed before the Hellenistic period. The Alexander chronicle mentioned above suggests that the famous astronomer Kidinnu died in Babylon in 330 BC, if it refers to the same Kidinnu who was mentioned on the ephemeris tablets centuries later.