Babylonian Lunar Theory
Babylonian lunar theory, an astronomical table in Greek, manuscript on papyrus [Egypt, 1st century CE].
Papyrus Colker is the missing link between Babylonian and Greek astronomy. 'By this single papyrus fragment we learn that one of the two Babylonian systems of lunar theory had spread by the Roman period to Greek-speaking Egypt' (Jones, 1997). 'Our fragment demonstrates the existence of persons, not known to us from contemporary treatises, who were studying Babylonian astronomy (e.g., intelligent professional astrologers), from ephemerides written in Greek, thus without the need to consult cuneiform tablets. Needless to say, this opens an entirely new aspect on the transmission of Babylonian astronomy to the Greeks and on the spread of scientific knowledge in late antiquity' (Neugebauer, 1988).

c.174 x 51mm. A fragment, likely from a roll, the astronomical table written in three columns within a black tabular framework in a sloping late Ptolemaic or mid-1st-century hand, with letters written without ligatures representing numerals, the abbreviation signifying 'subtractive' in col. ii written with a ligature and cursive form of phi, sideways 'V's touching the vertical rulings between cols. ii and iii indicate where the numbers in col. iii change over from increasing to decreasing and vice versa, some horizontal rulings; the reverse, along the fibres, with parts of 13 lines of a heavily abbreviated register in a 1st-century cursive hand (darkened and somewhat tattered along the left edge, one small area at the top with remnants of another sheet, tabbed together very discreetly in a number of points, a few small holes). Between archival glass sheets.

(1) Erik von Scherling, Rotulus V, 1949, p.36, no 2193.
(2) Maggs Bros. cat. 892, 1964, p.109, no 790.
(3) Colker MS O2; acquired from Maggs in 1964.

The papyrus was first described as a writing exercise in the 1949 von Scherling catalogue, and later again when it appeared in the 1964 Maggs catalogue. Colker showed it to David Jordan at UCLA, who instantly identified the mathematical nature of the text, and in turn enlisted the assistance of Otto Neugebauer. In 1988 Neugebauer published an article containing photographs of both sides, a partial transliteration of the astronomical table, and a discussion demonstrating the relation of the numerical table to Babylonian lunar tables (O. Neugebauer, 'A Babylonian Lunar Ephemeris from Roman Egypt’, A Scientific Humanist: Studies in Memory of Abraham Sachs, Philadelphia, 1988, pp. 301-4). The papyrus is comprehensively described and transliterated by Alexander Jones, first in his 1997 article 'A Greek Papyrus containing Babylonian Lunar Theory', Zeitschrift für Papyrologie und Epigraphik 119 (1997), pp.167-172, and later, more analytically and with some clarifications, in 2016, 'More Babylonian Lunar Theory in the Astronomical Papyrus P.Colker', Zeitschrift für Papyrologie und Epigraphik, 199 (2016), pp.137-143. Jones has further identified a potential sister fragment, now Cairo, P.Cair.Mus. S.R. 3059 (part) that could have come from the same roll as Papyrus Colker.

The papyrus contains the first known example in Greek of a so-called System B lunar syzygy table, 'one of the most complex among the varieties of astronomical tables known from Late Babylonian cuneiform tablets from Babylon and Uruk' (Jones, 2016, p.137). System B describes the speed of the Moon’s motion around the zodiac as increasing gradually and then decreasing gradually in the course of a month, following a regular sawtooth pattern. The three columns of the table represent different computational components of System B, namely Columns J and G, where column J (col.i, with col.ii providing additive and subtractive abbreviations) ‘tabulates a time interval to be added to or subtracted from Column G in order to obtain the excess of time over 29 whole days of the interval from one opposition (or conjunction) to the next’ (Jones, 1997, p.172). Col.iii is the component of System B known as Column G, a ‘linear zigzag function’, that is, ‘a sequence that alternately increases and decreases by a constant increment δ; between fixed limits m and M. In Column G the numbers represent so-called “time-degrees,” such that 360 time-degrees equal one day and δ; = 22;30 time-degrees, m = 1,52;34,35 time-degrees (= 112;34,35 time-degrees), M = 4,29;37,5 time-degrees (=269;27,5 time-degrees) (Jones, 1997, pp.171-2)'. When complete, the papyrus must have contained the series of columns leading to the date and time of opposition or conjunction, as well as those determining the Sun’s and the Moon’s zodiacal position.

In a letter to Colker of 12 October 1989, Jordan wrote: 'The papyrus is amazingly important for the history of astronomy and would, I'm sure, have had a chapter devoted to it in Neugebauer's monumental History of Mathematical Astronomy if it had reached him in time [...] the big question was what link there was between Babylonian and Greek astronomy - what was the point of transmission? Your papyrus is that very missing link, the first example in Greek of such a Babylonian function'.

According to Jones: 'The presumption up to 1988 was that Babylonian mathematical astronomy, and especially the lunar theory, was much too complex and foreign to the Greek way of visualizing astronomical phenomena for it ever to have become accessible wholesale to Greek astronomers, especially since we only knew of it from tablets originating in a restricted milieu of scribes working in a dead language and in a script that by the Hellenistic period scarcely anyone was trained to read. This state of affairs was overturned by Prof. Colker’s papyrus.' (Jones, 1997, p.168).

We are heavily indebted to Alexander Jones' analyses in the cataloguing of this lot.
O. Neugebauer, ‘A Babylonian Lunar Ephemeris from Roman Egypt’ A Scientific Humanist: Studies in Memory of Abraham Sachs, Philadelphia, 1988, pp. 301-4

A. Jones, ‘A Greek Papyrus Concerning Babylonian Lunar Theory’, Zeitschrift für Papyrologie und Epigraphik 119 (1997) pp.167-172

A. Aboe, Episodes from the Early History of Astronomy, New York, 2001, pp.24-66, fig.6

T. Boiy, Late Achaemenid and Hellenistic Babylon, 2004, p.312

I.L. Finkel and M.J. Seymour, eds., Babylon: Myth and Reality, 2008, p.193, fig.180

A. Jones, 'More Babylonian Lunar Theory in the Astronomical Papyrus P.Colker', Zeitschrift für Papyrologie und Epigraphik, 199 (2016), pp.137-143

F. Rochberg, 'The Near-Eastern Heritage in Greco-Roman astronomy', Studying the Near and Middle East, 2018, p.18
British Museum, Babylon: Myth and Reality, 2008-2009
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