Nabu-rimanni

Babylonian astronomer and mathematician

• Born: Early first century b.c.e.
• Birthplace: Probably Babylonia (now in Iraq)
• Died: Late first century b.c.e.
• Place of death: Probably Babylonia (now in Iraq)

Nabu-rimanni copied and preserved astronomical tables for the computation of lunar, solar, and planetary phenomena. These accurate numerical parameters for the prediction of astronomical phenomena furthered the development and success of Greek spherical astronomy, developed to its fullest in the Ptolemaic system.

Life’s Work

The Hellenistic authors Strabo (64 or 63 b.c.e.-c. 25 c.e.) and Pliny the Elder (23-79 c.e.), who traveled and produced encyclopedic compendia of the knowledge and customs of the day, mention Babylonian astronomical “schools” and a few of the Babylonian astronomers by name. Thus, one finds in book 16 of Strabo’s Geōgraphia (c. 7 b.c.e.; Geography, 1917-1933) the name Naburianos (Nabu-rimmani), and also Kidenas, Sudines, and Seleucus, all associated with Babylonian cities such as Babylon, Uruk, and possibly Borsippa. Nabu-rimanni’s particular or distinguishing role in the history of Babylonian astronomy, however, cannot be determined either from the Greek account or from Babylonian cuneiform sources.

Early Life

Because the nature of Babylonian sources is such that authors and authorship remain obscure, it is not possible to reconstruct for Nabu-rimanni (nah-BEW rih-MAHN-nee) a biography in the strict sense. The historical period with which he is associated, however, may be sketched. While Nabu-rimanni flourished in the mid-first century b.c.e., one may also define this period more broadly, that is, from roughly 300 b.c.e. to the beginning of the common era, as the Hellenistic period.

Cuneiform texts yield information about the scribes only in the colophons at the ends of the inscriptions. These colophons, when complete, note the names of the owner of the document and the scribe who copied it as well as the date the tablet was written and who was king at the time. Nabu-rimanni’s name is preserved on the colophon of an astronomical tablet from Babylon. The only fact, therefore, that can be established about him from Babylonian sources is that he was a scribe who copied, or possibly computed, a table of dates and positions in the sky of new and full moons for the year 49-48 b.c.e.

This particular colophon is the source for the claim that Nabu-rimanni was the inventor of the method of astronomical computation represented in his tablet. Far from showing this scribe as an innovator of Babylonian astronomy, however, Nabu-rimanni’s tablet is one of the youngest of Babylonian lunar ephemerides; the oldest such tablets stem from the third century. Nabu-rimanni can therefore be credited only with preserving the tradition of Babylonian astronomy, not inventing it.

Because Nabu-rimanni is associated with a particular method of astronomical computation, but his individual contribution cannot be determined from the sources, the focus of any examination of his life’s work must be Babylonian astronomy itself. Babylonian mathematical astronomy of the last three centuries b.c.e. is known from only two identifiable archives, one found in Babylon and the other in Uruk. The bulk of the texts are lunar or planetary ephemerides, which are supplemented by a smaller group of procedure texts outlining the steps necessary to generate ephemeris tables. The ephemeris tables contain parallel columns of numbers in specific sequences that represent occurrences of characteristic lunar and planetary phenomena. Each column represents a different periodic phenomenon—for example, new moons, eclipses, first visibilities, stationary points. The consecutive entries in each column correspond to dates, usually months. In the case of the ephemeris for the moon, the objective is to predict the evening of the first visibility of the lunar crescent. The appearance of the new moon defines the beginning of the month in a strictly lunar calendar. Indeed, the control of the calendar seems to have provided a major motivation for the development of mathematical methods for predicting astronomical phenomena.

For calculations, the Babylonians used a number system of base 60; that is, numbers are represented with special digits from 1 to 59, while 60, or any power of 60, is represented by 1. These “sexagesimal” numbers were written using a place-value notation system similar to decimal notation, so that for each place a digit is moved to the left, the value is multiplied by 60. The positional system was extended for fractions, which were expressed by moving digits to the right of the “ones” place, thereby dividing each time by 60. The Babylonian sexagesimal system is still preserved in the counting of time by hours, minutes (1 hour equals 60 minutes), and seconds (1 minute equals 60 seconds).

Babylonian lunar and planetary theory comprised two separate but coexistent systems, designated A and B, which are defined according to two different arithmetical methods of describing the distance covered each month by the sun. In this way, the velocity of the sun could be measured in terms of the progress of the sun in longitude, or degrees along its apparent path through the stars, the ecliptic. In system A, the progress of the sun along the ecliptic is described as being 30° per (mean synodic) month for one part of the zodiac (from Virgo 13° to Pisces 27°) and 28° 7′30′′ for the other part (from Pisces 27° to Virgo 13°). A mathematical model is thereby created whereby the sun moves with two separate constant velocities on two arcs of the ecliptic. If the sun’s velocity, reckoned in terms of progress in longitude (degrees along the ecliptic), is plotted against time, the resulting graph represents a “step function.” System A also implies a certain length of the solar year, namely 1 year equals 12;22,8 months, expressed sexagesimally. (Sexagesimal numbers are represented in modern notation with a semicolon separating integers from fractions.) This method and its complementary system B were both used during the period from c. 250 b.c.e. to c. 50 b.c.e.

System B assumes the motion of the sun to increase and decrease its speed steadily from month to month. The variation in velocity is bounded by a minimum and a maximum value, and within this range of velocities, the monthly change is always by a constant amount. Plotting the progress of the sun by this model produces a graph representing a “linear zig-zag function.” The name Kidenas, mentioned by Strabo, Pliny, and Vettius Valens (second century c.e.), may be associated with System B, as a scribe by the name of Ki-di-nu (Kidinnu) is known from colophons of system B-type ephemerides for the years 104-101 b.c.e. The Greeks credited him with derivation of the relation that 251 synodic months equals 269 anomalistic months. This numerical relation is in fact seen in system B computations.

Systems A and B constitute theoretical mathematical models of the motion of the sun that account for the varying lengths of the seasons of the year. By analogy with solar motion, the methods of systems A and B were applied to many celestial phenomena of a cyclic character. A Babylonian lunar table deals with the determination of conjunctions and oppositions of sun and moon, first and last visibilities, and eclipses, all of which are cyclic phenomena. Planetary tables for the planets Jupiter, Venus, Saturn, Mercury, and Mars predict the dates and positions in the zodiac of the cyclic appearances of planets, such as first visibilities, oppositions, stationary points, and last visibilities. The fact that each phenomenon had its own period enabled the Babylonians to compute them independently. No general theory of planetary and lunar motion was needed, as the strictly arithmetical methods of the two systems were sufficient to predict the individual appearances of the heavenly bodies.

The goal of Babylonian astronomy was, therefore, to predict when the moon or planets would be visible. In contrast, the Greeks’ goal was to develop a single model that would serve to describe and account for the motion of celestial bodies in a general sense, and from which the individual appearances of celestial bodies would follow as a consequence. The achievement of this goal was found in geometrical methods and kinematic models (explaining motion), developed by Apollonius of Perga (third century b.c.e.) and perfected by Ptolemy in Mathēmatikē suntaxis (c. 150 c.e.; Almagest, 1948). Such geometrical concepts are not found in Babylonian astronomy.

The question of the identity of the Babylonian astronomers is not answered by the cuneiform astronomical texts. One scribe is hardly distinguished from another when the extent of one’s information is the appearance of the scribe’s name in a text colophon. Nevertheless, the question as to the significance of the scribes Nabu-rimanni and Kidinnu, whose names are remembered by later Greek and Roman authors, remains. The belief that they were the inventors of the systems A and B gains no support from the cuneiform texts. Indeed, the establishment of dates for the invention of systems A and B has proved difficult; thus, statements concerning the origins of Babylonian mathematical astronomy, in regard to both chronology and the role of individual scribes, must for the time being remain inconclusive.

Significance

Babylonian lunar and planetary theory became the foundation for the development and further refinement of astronomy by the Greek astronomers Apollonius, Hipparchus, and Ptolemy. In very general terms, one can enumerate the various Babylonian contributions to Greek astronomy and thereby to the development of science in general as follows.

About 300 to 200 b.c.e., the Greek astronomers adopted the Babylonian sexagesimal number system for their computations and for measuring time and angles (360 degrees in a circle with degrees divisible by minutes and seconds). The use of arithmetical methods characteristic of Babylonian astronomical tables continued, particularly in the procedures used by Hellenistic astrologers. While Greek astronomical theory depended on geometrical and kinematic models, neither of which was used in Babylonian astronomy, the parameters used in constructing those models were Babylonian. Indeed, the success of Greek astronomical theory rests on the accuracy of the parameters established by Babylonian astronomers (such as the length of the solar year given above).

The concepts related to the parameters must also have been transmitted. Such concepts were, for example, the following components of lunar motion: longitude, latitude (angular distance of the moon from the ecliptic), anomaly (irregularity in motion), and the motion from east to west of the line of nodes (the two diametrically opposed points where the moon’s orbital plane intersects the plane of the ecliptic) in a nineteen-year cycle.

Also of use for Greek planetary theory were the period relations essential to the determination of successive occurrences of a periodic phenomenon in Babylonian astronomy. Through the wide acceptance of the Ptolemaic tradition, as evidenced by Indian and Islamic astronomy, the direct influence of Babylonian astronomy on the Greek world had even greater impact as the ultimate impetus for the quantitative approach to celestial phenomena.

Bibliography

Aaboe, Asger. “Observation and Theory in Babylonian Astronomy.” Centaurus 24 (1980): 14-35. Suggests a reconstruction of the process by which the Babylonian systems of computing astronomical phenomena were developed.

Aaboe, Asger. “Scientific Astronomy in Antiquity.” In The Place of Astronomy in the Ancient World, edited by F. R. Hodson. London: Oxford University Press, 1974. Summary and explanation of the mathematical content of the Babylonian astronomical ephemerides and discussion of what constitutes a “scientific” astronomy.

Hunger, Hermann, and David Pingree. Astral Sciences in Mesopotamia. New York: Brill, 1999. This account of the beginnings of astronomy and astrology in the ancient Near East discusses the place a given tablet has in the development of astronomy both within Mesopotamian culture and outside it.

Neugebauer, Otto, ed. Astronomical Cuneiform Texts. New York: Springer Verlag, 1983. A transliteration and translation of the cuneiform astronomical texts, accompanied by an analysis.

Neugebauer, Otto, ed. The Exact Sciences in Antiquity. 2d ed. New York: Dover, 1969. Concise history of mathematics and astronomy in Babylonia, Egypt, and Greece.

Van der Waerden, B. L. The Birth of Astronomy. Vol. 2 in Science Awakening. 4th ed. Princeton, N.J.: Scholar’s Bookshelf, 1988. More accessible and less technical but also less reliable than Neugebauer. Gives an overall account of the phenomena of interest in Babylonian mathematical as well as pre-mathematical astronomy.