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Brown, David R. 1998. Review Article of N. M. Swerdlow. 1998. The Babylonian
Theory of the Planets. Princeton: Princeton University Press. 1998, 246 + xvii pp,
$39.50, Cosmos and Culture 2:1: 61-66.
This book is concerned with the theoretical and empirical foundations of Babylonian
planetary theory. Some of the original ideas were presented in May, 1994 to a collo-
quium at the Dibner Institute for the History of Science and Technology. The work’s
premise and most important contribution to the history of the exact sciences is that the
parameters that underlie the cuneiform astronomical texts concerned with the five
planets visible to the naked eye owe much more to the records of the dates of the
various planetary phenomena than was hitherto imagined. Swerdlow argues his case
fluently and energetically, and his affection for the ancient scribes is clear. Aside from
the introduction, the non-specialist may find some of the more technical discussions
demanding, though these only reflect the complexity and sophistication of the source
material. Indeed, as the author writes (p181):
“I believe it is due precisely to the scientific and technical character of Babylonian astronomy
that most historians and philosophers remain without comprehension of it, still preferring to
dote upon childish fables and Delphic fragments of Pre-Socratics, requiring no knowledge of
mathematics and less taxing to the intellect.”
The so-called Mathematical Astronomical Texts (MATs), or ‘ephemerides’, are clay
documents that tabulate the times and locations of various lunar, solar and planetary
phenomena. They predict the intervals, both temporal and spatial, between successive
phenomena of the same type (synodic intervals) based on values for the mean synodic
intervals and linear approximations to the variations around the means. They are
attested from the last few centuries BCE. While the mathematical techniques that
underpin the MATs and the internal mechanisms whereby the final columns of
numbers are attained have been understood, in large part, for some decades, the
empirical basis of the texts and their relationship to the so-called Non-Mathematical
Astronomical Texts (NMATs) has still to be fully comprehended. The NMATs
include mainly empirical, and ominously significant, data. The role of calculation in
them is small, although they might sometimes reveal a high level of astronomical
knowledge. One particular group, known as the Astronomical Diaries, is attested from
the mid-seventh century BCE. It, and related collections, include records of the dates
(by day of the lunar month) of the heliacal phenomena of the planets (heliacal rising,
stationary points, acronychal rising, and so forth), the constellations or signs in which
they occur, and the distances of the planets from particular ecliptic stars known as
Normal Stars.
Swerdlow’s work asserts that the accurate measurement of planetary positions
“had no role whatever in the planetary theory of the ephemerides” (pxi). Instead,
based on a “well-known relation found in the ephemerides of every planet except
Venus, that synodic arc and synodic time differ by a constant…which is specific to
each planet” (pxii), he argues that the dates of the heliacal phenomena sufficed to
determine the parameters of the ephemerides “without a single measurement of
position more precise than location by zodiacal sign” (pxii). Consequently, this book
offers a means whereby the Diaries and the MATs may be connected in so far as the
particular records found in the former texts determine (at least in part) both the
parameters underlying, and the limitations of, the latter texts. In this reviewer’s
opinion this constitutes an important contribution to the field of Assyriology.1
It is no

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coincidence that a similar connection between Diary-like data and the lunar MATs
has plausibly been proposed by Lis Brack-Bernsen in recent years.2
In the introduction, Swerdlow discusses the relationship of the celestial omen
series to the data recorded in the Diaries. While this work is not original, nor does it
claim to be, it is nevertheless an extremely useful summary for those unfamiliar with
the background to cuneiform astronomy. The close similarity between the phenomena
considered ominous by the diviners and the data recorded in the Diaries is stressed,
and the crucial part that Mesopotamian divination played in the formation and inten-
tion of cuneiform mathematical astronomy is revealed.
In Part 1 the author concentrates on the derivation of the period relations in the
MATs from the dates of certain heliacal phenomena. This includes a method whereby
the deviation from a precise return in longitude can be computed from the dates of
successive phenomena of the same type, in order to derive longer periods of greater
accuracy.
Part 2 deals with the derivation, from the variations in synodic times about the
mean values, of the MAT parameters for the variations in the synodic arcs. As J. P.
Britton has indicated in his review for the Journal for the History of Astronomy (to be
published), the derivation of some of these MAT parameters would have been far
simpler using records of the longitudes of the phenomena rather than records of their
dates. His work does not need to be repeated here.
Part 3 concerns how the synodic arcs were aligned to the zodiac. The central thrust
is that records giving only a very imprecise location of the phenomena were sufficient
for this purpose.
The book concludes with a summary and an appendix describing two alternative
methods for deriving the MAT parameters - one from the records of the number of
phenomena in each zodiacal sign, and the other from the direct measurement of
longitude. Some 50 tables, some 25 figures, a useful table of abbreviations and
notations, a reasonably comprehensive bibliography, an index of names, and an index
of subjects accompany the text of the book.
Swerdlow makes the following claims as to his central thesis:
‘Considering the difficulty, if not impossibility, of precise measurement of position, computing
synodic arc from synodic time was probably more accurate than any measurement that could
be made’ (p175);
‘the methods…for deriving parameters from the measurement of time were motivated above all
by avoiding the requirement of precise measurement of longitude for the obvious reason that
they knew perfectly well that they could do no such thing.’ (p190).
Despite this, it is apparent that the book does not attempt to be the last word on Babyl-
onian planetary theory (cf. pxiii), but provides the case for incorporating in that final
model the derivation of parameters from dates. In light of the above two quotations, I
propose that a theme alluded to in the book’s introduction (e.g. p23), and which I have
considered in my own work, better explains why records of the dates of phenomena,
as opposed to their locations, provided some, if not the bulk, of the empirical
information utilised in the formation of the MATs. This explanation is that for the
diviners the dates of the phenomena were either directly ominous or constituted
important information in their daily analyses of the prognostications of the phenom-
ena of the universe. As to the location of the celestial phenomena, only the constell-
ation (or possibly part of the constellation) in which they took place was of signif-
icance. The conjunction or near conjunction of the planets (not their phenomena) with
each other, or with stars, was ominously important, and it was no doubt for this reason

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that their distances from the Normal stars were regularly recorded in the Diaries. This
does not mean that celestial longitudes were not measured, far from it, but it does
suggest that given that for ominous reasons the longitudes of the planetary phenomena
were not recorded in the Diaries and similar texts, the creators of the MATs, which
were after all designed to predict these same phenomena, were constrained to use the
data that were recorded - namely the dates and the zodiacal signs.
It is also probable, in this reviewer’s opinion, that some observations of celestial
positions were used in the derivation of some of the MAT parameters, even if only to
modify those first derived from the record of dates. Swerdlow’s book should be seen,
in a sense, as an exercise in how close one can get to the parameters in the MATs
using dates alone. This effort is extremely instructive, and the author must be congrat-
ulated for his pains. It is noteworthy that it has taken someone not directly in the field
to tackle afresh the question of the empirical background to the planetary MATs.3
While this reviewer opts for a multivariate, dates and longitude, solution to the
empirical origins of the MAT parameters, we must thank Swerdlow for alerting us to
the importance of the first variable, particularly in the case of Mercury.
Further to this, Swerdlow proposes (p173f) that the ephemerides may have first
been computed to supplement observations of the sort recorded in the Diaries when
this was made impossible due to bad weather (also p18) or whatever, secondly so as
to offer a guide to the most promising dates upon which to observe the heavens, and
thirdly as a result of interest in ‘applied mathematical science for its own sake’. While
it is laudable to emphasise the sophistication of the MATs, it is not clear that the
scribes shared the same intellectual interests as contemporary scientists. Certainly, the
specific circumstances which surround the existence of these texts in this form need to
be explained by more than ‘interest for its own sake’. Why were they written in
cuneiform when the vernacular language was quite different and most of the other
cuneiform material from this period was made up of copies of old ‘canonical’ texts?
As it happens, and as I have argued elsewhere, the mathematical methods and
systems of units that underlie the MATs closely mirror those of greater antiquity. Due
to this, and, as Swerdlow’s and Brack-Bernsen’s (see note 2) work suggests, since a
great many of their parameters were derived from precisely the type of data which
were recorded in the Diaries as a result of the constraints imposed by what was
ominous, so far as the diviners were concerned, the MATs were closer in form than is
often assumed to the other cuneiform material of the period. No doubt this helped
legitimate any conclusions drawn from them. This is not the place to elaborate this
line of argument, but suffice it to say that both the limitations and the successes of the
MATs can be accounted for satisfactorily on the basis of their fulfilment of the
requirements of the divination industry, and need not be seen as manifestations of
‘science for its own sake’.
1
Stated as fact by the author on p17: ‘it is the Diaries…that provide the observations that were later
used as the empirical foundation of the mathematical astronomy of the ephemerides’. In reality, his
work establishes it as more probably true, for it helps eliminate the main reservation expressed by F.
Rochberg in “Between Observation Theory in Babylonian Astronomical Texts” Journal of Near
Eastern Studies 50 (Chicago, 1991) 107-120 – namely the differing positional reference systems. See
in particular p112.
2
L. Brack-Bernsen Zur Entstehung der babylonischen Mondtheorie: Beobachtung und theoretische
Berechnung von Mondphasen (1997, Franz-Steiner, Stuttgart) with references to her earlier
publications.
3
Noel Swerdlow is Professor at the Department of Astronomy and Astrophysics at the University of
Chicago, and his background is in Renaissance History of Astronomy.