Naburimannu
Encyclopedia
Nabu-ri-man-nu (fl.
c. 6th–3rd century BC) was a Chaldean astronomer and mathematician
.
Classical and ancient cuneiform
sources mention an astronomer with this name:
The following is an excerpt of a century of scholarship discussed in the sources referenced below.
The meaning of tersitu is not known definitively. Already Franz Xaver Kugler
proposed that tersitu can be interpreted as "table" here; in another context it seems to mean something like "tool", but in yet another the word refers to a blue enamel paste. P. Schnabel, in a series of papers (1923–27), interpreted the phrase as an assignment of authorship. Based on this, he argued that Naburimannu developed the Babylonian System A of calculating solar system
ephemerides, and that Kidinnu later developed Babylonian System B. Otto E. Neugebauer
has remained reserved to this conclusion and disputed Schnabel's further inferences about Naburimannu's life and work. The mathematician B.L. van der Waerden
later (1963, 1968, 1974) concluded that System A was developed during the reign of Darius I (521–485 BC). System A, which uses step function
s, appears to be somewhat more primitive than System B, which uses zigzag
linear function
s, although System A is more consistent than System B. While it thus appears that System A preceded System B, both systems remained in use at least until the 1st century BC.
The earliest preserved System A clay tablets (BM 36651, 36719, 37032, 37053) calculate an ephemeris for the planet
Mercury
from 424–401 BC. The oldest preserved lunar tablets date from 306 BC
in the Hellenistic period. If Naburimannu was the originator of System A, then we can on that basis place him in Babylonia sometime between the Persian and Macedonian conquests.
Floruit
Floruit , abbreviated fl. , is a Latin verb meaning "flourished", denoting the period of time during which something was active...
c. 6th–3rd century 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...
.
Classical and ancient 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...
sources mention an astronomer with this name:
- 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, KidenasKidinnuKidinnu was a Chaldean astronomer and mathematician. Strabo of Amaseia called him Kidenas, Pliny the Elder Cidenas, and Vettius Valens Kidynas....
, Nabourianos and Soudines".
- The damaged 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 a cuneiform clay tablet (VAT 209; see ACT 18) with a Babylonian System A 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...
ephemerisEphemerisAn 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...
for the years 49–48 BC states that it is the [tersit]u of Nabu-[ri]-man-nu. This is similar to the colophons of two System B clay tablets that say that they are the tersitu of KidinnuKidinnuKidinnu was a Chaldean astronomer and mathematician. Strabo of Amaseia called him Kidenas, Pliny the Elder Cidenas, and Vettius Valens Kidynas....
.
The following is an excerpt of a century of scholarship discussed 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 tersitu can be interpreted as "table" here; in another context it seems to mean something like "tool", but in yet another the word refers to a blue enamel paste. P. Schnabel, in a series of papers (1923–27), interpreted the phrase as an assignment of authorship. Based on this, he argued that Naburimannu 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 Kidinnu later developed Babylonian System B. 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...
has remained reserved to this conclusion and disputed Schnabel's further inferences about Naburimannu's life and work. The mathematician B.L. van der Waerden
Bartel Leendert van der Waerden
Bartel Leendert van der Waerden was a Dutch mathematician and historian of mathematics....
later (1963, 1968, 1974) concluded that System A was developed during the reign of Darius I (521–485 BC). System A, which uses step function
Step function
In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals...
s, appears to be somewhat more primitive than System B, which uses zigzag
Zigzag
A zigzag is a pattern made up of small corners at variable angles, though constant within the zigzag, tracing a path between two parallel lines; it can be described as both jagged and fairly regular....
linear function
Linear function
In mathematics, the term linear function can refer to either of two different but related concepts:* a first-degree polynomial function of one variable;* a map between two vector spaces that preserves vector addition and scalar multiplication....
s, although System A is more consistent than System B. While it thus appears that System A preceded System B, both systems remained in use at least until the 1st century BC.
The earliest preserved System A clay tablets (BM 36651, 36719, 37032, 37053) calculate an ephemeris for the planet
Planet
A 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,...
Mercury
Mercury (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...
from 424–401 BC. The oldest preserved lunar tablets date from 306 BC
306 BC
Year 306 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Year of the Consulship of Tremulus and Arvina...
in the Hellenistic period. If Naburimannu was the originator of System A, then we can on that basis place him in Babylonia sometime between the Persian and Macedonian conquests.
External links
- A. Braeken, V. Nikov, and S. Nikova, "Zigzag Functions and Related Objects in New Metric"
- Luboš Motl's Reference Frame: Maldacena in the Lineland (defines and discusses zig-zag functions)