The Babylonian Theory of the Planets

by J. M. Steele
The Babylonian Theory of the Planets
J. M. Steele
Journal of the American Oriental Society
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Reviewed work(s): The Babylonian Theory of the Planets by N. M. Swerdlow

The Babylonian Theory of the Planets. By N. M. SWERDLOW. Princeton: PRINCETON UNIVERSITY PRESS, 1998. Pp. xv 246. $39.50.
It has been almost one hundred years since J. Epping, J. N. Strassmaier, and F. X. Kugler made the discovery that the Babylonians not only watched the skies, but also computed a whole host of celestial events, ranging from the first visibility of the lunar crescent, to the dates of the appearances and disappearances of the five planets. Through the extensive labors of these and later scholars most aspects of the operation of the Babylonian mathematical astronomy are now well understood. However, the question of how the various Babylonian theories were formulated has only recently begun to be addressed.
In The Babylonian Theory of the Planets, Noel Swerdlow has attempted to show how the fundamental parameters of the Babylonian planetary theory could have been derived from the observations that were available to the Babylonian astronomers, as represented by the records in the astronomical diaries. Swerdlow claims that his method, based upon manipulating observations of the length of time between two successive rising or setting phenomena--known as synodic time--"was the way the Babylonians derived the parameters of their mathematical astronomy," or that he "at any rate, can see no plausible alternative" (p. xiii).
Swerdlow begins his book with a discussion of the background to the various cuneiform astronomical texts. He is of the opinion that divination provided the primary motivation for astronomy in Babylon, although he does suggest that eventually the study of astronomy may have come to take on a life of its own through a purely scientific interest on the part of the Babylonian astronomers, writing that "the complexity and diversity of the ephemerides goes far beyond what is necessary to predict ominous phenomena ... and suggests nothing less than a rigorously scientific interest in the mathematical description of periodic phenomena" (p. 174). On the whole, this is a highly interesting and informative discussion, although at times slightly over-simplified in its interpretation of the omen literature and containing a few inaccurate statements in the description of the technical framework of Babylonian astronomy. For example, Swerdlow writes that, "the US of time is principally a unit of computation, although indirectly it can also be measured" (p. 36). However, the US, which corresponds to four of our minutes, is used extensively as the unit when quoting measured times of observations from at least the eighth century B.C. It is also equal to a thirtieth of a beru, which itself seems to have been originally defined as the time it takes to walk a fixed distance of about seven miles.
After this gentle introduction, Swerdlow leads us into a technical discussion of the methods he believes were used to derive the parameters of the various theories for calculating what have become known as the "Greek-letter phenomena"--the dates of the appearances, disappearances, and stationary points--of the five planets. The analysis itself is not for the faint-hearted. It is based upon a clever manipulation of observed synodic times, or, where there are no observations preserved, modern data used to mimic the observations that it is assumed were available to the ancient astronomers. These times are taken to be an excess number of days over an integer number of years. Since the Babylonian calendar was governed by the visibility of the moon, the month could contain either twenty-nine or thirty days, and so for convenience the Babylonian astronomers used a unit defined as being exactly one thirtieth of a lunar month in their mathematical astronomy. This unit has become known as a "tithi," after the corresponding unit used in Indian astronomy. Swerdlow therefore converts his synodic times into tithis and compares them with the approximate position in the zodiac at which the synodic event took place. From this he is able to determine the maximum and minimum synodic times and therefore, using previously established period relations--and sometimes a little force--the final parameters for the various theories.
In formulating the method outlined above, Swerdlow has come up with an ingenious way in which the parameters might have been derived for some of the planetary theories. However, whether Swerdlow is correct in his belief that he has found the one and only method by which the Babylonian astronomers derived these parameters still remains an open question. In an appendix he outlines his reasons for rejecting two other possible methods, one based upon counting the number of phenomena within zones of the zodiac, and the other by direct measurement of longitudes. Swerdlow's reasons for dismissing these methods, at least as detailed here, do not seem to be fully convincing. For instance, we do know that the Babylonian astronomers were capable of measuring longitudes if they wished; the existence of a fragmentary star catalogue proves this. Furthermore, he notes that the preserved diaries do not contain as many reports of the distance of a rising or setting planet to a normal star (from which the longitude could be obtained using something like the star catalogue mentioned above) as one would need to derive the planetary parameters. However, this does not necessarily imply that such measurements were not available, or could not have been made, by the astronomers who formulated the planetary theories. In truth neither Swerdlow's method nor either of the methods he dismisses works perfectly for every planet, and it seems much more likely that the Babylonian astronomers chose whichever worked best, or rather whichever was the most convenient, for each individual case.
Given the highly technical nature of the book, it is unfortunate that the exposition of the main arguments is somewhat hampered by the layout. Since the tables and figures are collected at the end of the book, rather than in the main body of the text, the reader is often trying to look at three pages at once when following Swerdlow's arguments. Furthermore, the quality of the reproduction of the figures is poor, and when, for example, one is invited to look at figure 2.3 which shows different sets of data as open circles, filled circles, and open squares, it is not always easy to distinguish among them.
The Babylonian Theory of the Planets is an interesting and provocative book. The inclusion of the introductory chapter on the place of astronomy in Babylonian society is particularly welcome since this is an aspect all too often neglected in technical works on the history of science. Although some of the analysis requires more than one reading to fully understand, it is certainly worth the effort, even if some readers will not agree with all of the author's conclusions.
COPYRIGHT 1999 American Oriental Society


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