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Research Article
The place of theory in Babylonian astral science
Abstract
Babylonian astral science of the 1st millennium BC was a multi-faceted practice including detailed and systematic astronomical observation, the development and use of various computational methods for predicting the positions and phenomena of the sun, moon, and planets, descriptions using simple numerical schemes of regular changes in the celestial realm, and various forms of astrology. Despite the detailed study of these practices over the past 150 years or so, historians of science remain divided as to whether Babylonian astronomy should be classified as a ‘science’. Specialists of Babylonian astronomy and astrology uniformly agree that it is science, whereas some non-specialists argue that science is a uniquely Greek invention. Much of this disagreement comes down to the question of whether Babylonian astral science is ‘theoretical’ or (merely) the fitting of numbers to empirical data. In this paper, I explore whether we can identify ‘theories’ within Babylonian astral science and if so where these are to be found.
Keywords
astral scienceBabylonian astronomyBabylonian astrologysciencetheoriesIntroduction
Definitions of the term ‘science’ abound. According to the Concise Oxford English Dictionary, science is ‘the intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experience’, ‘a systematically organized body of knowledge on any subject’, or, archaically, ‘knowledge’. On the whole, historians of science have tended towards stricter definitions which take as markers of whether a practice counts as science that its goal be to provide an ‘explanation’ and/or to develop a ‘theory’ of observed phenomena or, more generally, of ‘nature’ or the world around us, based upon empirical evidence. For example, Clagett (1955: 15) defines science as ‘first, the orderly and systematic comprehension, description and/or explanation of natural phenomena and, secondly, the tools necessary for that undertaking’. Pingree (1992: 559) casts the net wider, writing that ‘science is a systematic explanation of perceived or imaginary phenomena, or else is based upon such an explanation’, thereby allowing him to include practices such as astrology and at least some parts of ancient magic within the umbrella of science. Gregory (2007: 2) states that, at a minimum, science ‘deals with the natural world’, which requires ‘an awareness of a distinction between the natural and the supernatural’, is ‘expressed in terms of theories’, and is ‘characterised by the use of mathematics, experiment and observation’. Graham (2013: 256) is somewhat more precise, writing that ‘science is (a) a systematic study of the natural world, (b) using an accepted theory and methodology, (c) allowing for open inquiry within (b), (d) permitting elaboration and revision of (b), (e) based upon empirical evidence’. None of these authors, however, define what they mean by ‘explanation’, ‘theory’, ‘nature’, etc.,1 and ultimately, as Cunningham (1988) notes, in practice most historians default to simply assuming that they know science when they see it.
The importance given to explanation and/or theory in many definitions of science, however, leads to problems when we encounter scientific traditions which do not look like either modern science or ancient Greek science (both of which are indubitably concerned with the development of explanations and theories, although not exclusively nor in the same way). In particular, going back centuries and still today we find authors, especially non-specialist authors, who dismiss Babylonian, Chinese, Indian, and other traditions as not being science—or at best being not quite science—in comparison to Greek science, which is taken to be science by default. Thus, in the middle of the 20th century the historian of science A.C. Crombie could write:
it was the Greeks who invented science as we know it, by their assumption of a permanent, uniform, abstract order and laws by means of which the regular changes observed in the world could be explained by deduction, and by their brilliant idea of the generalized use of scientific theory tailored according to the principles of non-contradiction and the empirical test. (Crombie 1959: 81)
More recently, Gregory (2007: 1) makes the ‘bold claim, that the ancient Greeks were the originators of science’, because, according to him, science has to start somewhere and it was the Greeks who first separated science from technology and theories from myths. Gregory argues that only the Greeks had a concept of a well-ordered cosmos and tried to explain the cosmos in terms of theories. By contrast, ‘previous societies’—he surely means the Babylonian here—‘sought only observation and prediction of the heavens’, whereas ‘the Greeks now began to frame natural theories about the nature of the heavens, and began to try to explain astronomical phenomena in terms of those theories’ (Gregory 2007: 4). For both Crombie and Gregory, what is important are theories and explanations.2
By the time Crombie was writing in the 1950s, cuneiform tablets containing astronomical and astrological texts had been known and extensively studied for more than seventy years.3 These studies had revealed an astronomy which included both the precise and systematic observation of celestial phenomena and the computation of many of those same astronomical phenomena using complex mathematical schemes which modelled, for example, the variable velocities of the sun and moon and the moon’s motion in latitude in order to determine the first appearance of the new moon crescent and lunar and solar eclipses. However, as discussed in detail by Rochberg (2002), up to at least the middle of the 20th century, the discoveries made by historians of Babylonian astronomy were rarely taken into account by the broader community of historians and philosophers of science. Indeed, even in recent years some scholars have dismissed the possibility that Babylonian astronomy, for example, rose to the level of science. For example, the Classicist and historian of Greek philosophy Daniel Graham wrote in 2006:
In Babylonia temple priests kept detailed observations of the skies in order to report—and, wherever possible, anticipate—ominous phenomena. … The Babylonians developed a powerful if complex system based on the number sixty, which they eventually (in Hellenistic times) used to track the motions of the sun and moon. The most important element of their calendar was the lunar month, which being of variable length, caused them to make minute observations. … The Greeks learned highly developed crafts and skills from their neighbors, but could have found no real sciences to borrow. (Graham 2006: 2)
Graham’s word choices are instructive: The Babylonians scholars were ‘priests’, which is factually true if we take anyone employed in the Babylonian temple to be a priest, but by that same reckoning we should note that Copernicus was canon of Frauenberg Cathedral and I doubt if Graham would have felt the need to describe him as such. The Babylonians ‘anticipate’ phenomena, which is an odd way of saying that they made astronomical predictions. Their interest was in astronomical phenomena which were ominous, and although it is true that many of the phenomena observed and predicted by the Babylonians could be interpreted as omens, the same could be said of the astronomical phenomena which were computed by Greek astronomers such as Ptolemy (who, lest we forget, also wrote a book on astrology). The Babylonians developed a ‘powerful if complex’ number system based upon the unit sixty which they used to ‘track’ the motions of the sun and moon ‘in Hellenistic times’. It is not apparent to me that any number system is more complex than any other, nor how a number system ‘tracks’ the motion of celestial bodies. Indeed, the word ‘track’ here seems to be used deliberately to avoid a word like the more scientific-sounding ‘model’. And the gloss ‘in Hellenistic times’, which perhaps implies some connection between the development of this system with Babylonia coming under Greek rule, is factually wrong—Babylonian interest in the development of models for lunar and solar motion are attested well before Alexander’s conquest of Babylonia. Finally, it is said that Babylonian interest in the varying length of the lunar month led to them making ‘minute observations’, whatever they might be. But, in truth, the problem of the variable length of the month led not to the Babylonians making more precise observations but rather to the development of complex systems of astronomical computation which relied upon mathematically modelling the effects of lunar and solar velocity.
Graham, Crombie, and others can perhaps be forgiven for misrepresenting the nature of Babylonian astronomy, given that their fields of expertise lie elsewhere. But similar statements have been made by specialists of ancient astronomy, including those who have worked extensively with the Babylonian material. For example, the Dutch astronomer and historian of astronomy Anton Pannekoek had this to say on the matter in his otherwise reliable and widely-read textbook A History of Astronomy published in 1961:
The Babylonians had no such spatial picture [like that of the Greeks]; to them the heavenly phenomena did not take place along circular orbits in three-dimensional space but on a two-dimensional vault where the luminaries followed their mysterious course. They did not develop new geometrical world structures; they were not philosophical thinkers but priests, confined to traditional religious rites, and therefore disinclined to adopt new cosmic ideas which did not conform to the holy doctrines. The planets to them were not world bodies in space; they remained luminous deities moving along the heavens as living men move on earth. … Being a priestly science, Chaldean astronomy could not pass beyond the inherited world system; but all the same the refined knowledge and the huge store of observations demanded a theoretical summary. Thus these astronomers faced the task of representing the irregularity of a planet’s motion by purely arithmetical methods. (Pannekoek 1961: 65)
Although he does not directly comment on whether Babylonian astronomy rises to the level of science or not, Pannekoek contrasts Babylonian ‘priests’, who are constrained by their religious beliefs and could not have a three-dimensional spatial picture of the heavens and therefore could only use ‘purely arithmetical methods’ to model their motion with free-thinking Greek ‘philosophical thinkers’ who could imagine the sun, moon, and planets as bodies in space moving along circular orbits within a three dimensional cosmos.
Running through all these discussions are a series of contrasts that are made between Babylonian and Greek astronomy: Babylonian astronomy is empirical, purely mathematical, uses arithmetical sequences to represent celestial phenomena, calculational, and is undertaken by priests, whereas Greek astronomy is theoretical, physical, geometrical, explanatory, and is practised by philosophers/scientists. And the conclusion drawn from them is that Babylonian astronomy falls into the not-quite science category, whereas Greek astronomy is (almost by definition) science.
More positive characterisations of Babylonian astronomy are found in the work of specialists such as Otto Neugebauer, Asger Aaboe, John Britton, and Francesca Rochberg. For Neugebauer, Aaboe, Britton, and others, that Babylonian astronomy was a science was self-evident.4 Furthermore, for many of these authors, Babylonian astronomy is not just a science but the first science in history. Writing about the development of Babylonian mathematical astronomy, for example, Neugebauer (1989: 392) states that ‘No more drastic discontinuity in the history of ancient astronomy can be imagined than the creation of mathematical astronomy’ and ‘the men who created this new science were fully aware of the revolutionary character of their approach’ and Britton (1999: 187) writes that its development, and more specifically models for treating lunar anomaly in the so-called lunar System A, ‘invites the question of whether its invention was not a transforming event in the creation of science as we know it’. Beginning with Neugebauer, historians of Babylonian astronomy—followed by most historians of science in general—routinely describe the various systems of mathematical astronomy developed by the Babylonians as lunar and planetary ‘theories’.
A significantly more nuanced discussion of science in the Babylonian context is found in the work of Francesca Rochberg. In her 2016 book Before Nature: Cuneiform Knowledge and the History of Science, Rochberg considers a range of Babylonian scholarly practices through the lens of recent work in the philosophy of science. She shows both how we can understand various aspects of Babylonian astronomy, divination, and other areas of scholarship as embodying approaches such as model-based reasoning, analogical reasoning, and empiricism which are found in many other scientific traditions, including modern science, and how the specific context of Babylonian scholarship and the Babylonian worldview mean that the way that these approaches operated differs from how they operate in other scientific traditions.
Despite Rochberg’s careful study there remains, I suggest, a problem with how scholars talk about theory within Babylonian astral sciences. This problem arises from the conflation of two separate questions: (1) can we identify theoretical knowledge or reasoning within the Babylonian material, and (2) did the Babylonians themselves have something that they considered to be a theory of celestial phenomena. Thus, when Neugebauer, Britton, Rochberg, and others talk of the Babylonian ‘System A lunar theory’, did the Babylonians themselves consider this thing to be a ‘theory’ or was it (just?) a computational system intended to calculate certain lunar phenomena. My aim in this paper is to try to disentangle these two questions—the external question of if and where we can identify theoretical approaches or knowledge in the Babylonian astral sciences from the internal question of whether the Babylonian themselves had what they considered to be theories within the astral sciences.
A brief summary of Babylonian astral science
More than five thousand cuneiform tablets from Babylonia that are inscribed with texts dealing with the astral sciences are currently known.5 The majority of these tablets come from the ancient city of Babylon and date to the Late Babylonian period which stretched from the middle of the 8th century BC to the latter part of the 1st century AD (with a high concentration of the preserved tablets coming from the 4th to the 1st century BC).6 A few hundred tablets dating between the 6th and the 2nd century BC are known from the city of Uruk in southern Babylonia and a handful have been recovered from other Babylonian cities such as Nippur, Sippar, and Ur. These preserved sources reveal that Babylonian astral science was a complex and multi-faceted activity that included the careful and systematic observation of celestial phenomena, the development of methods for predicting many of those same astronomical phenomena in advance, and the interpretation of observed and computed phenomena through various systems of astrology.
Observational astronomy
At the centre of Late Babylonian astronomy was a practice of detailed and regular observation and the systemic recording of those observations. The earliest known examples of this practice are reports of observations of lunar eclipses dating to the middle of the 8th century BC and of conjunctions of planets with each other, their passages past bright stars, and their synodic phenomena dating from the early to the middle of the 7th century BC (Steele 2019). By the early 6th century BC, the repertoire of astronomical phenomena that were regularly observed had stabilised and a genre of text dubbed by modern scholars ‘Astronomical Diaries’, in which systematic reports of these observations were recorded, had been created.7 An Astronomical Diary typically covers half a year and is divided into monthly sections. Each section begins with daily reports of observations made during the month followed by summaries of the value of six staple commodities in Babylon, the depth of the river Euphrates as it flows through the city, selected historical events, and the positions of the visible planets in the zodiac and the dates of their synodic phenomena if any occurred that month.
The observed phenomena systematically recorded in the Astronomical Diaries are:
The length of the preceding month and whether the new moon was seen on the first evening of the new month.
The interval between the moon and sun crossing the horizon on six specified occasions during the month. These intervals are known collectively to modern scholars as the ‘lunar six’.8 The first interval (NA) is the time between sunset and moonset on the first day of the month (taken to be the evening of first visibility of the new moon crescent). Four intervals are observed in the middle of the month on the days around full moon: moonset to sunrise (ŠÚ), sunrise to moonset (NA), moonrise to sunset (ME), and sunset to moonrise (GE6). Towards the end of the month on the morning of last visibility of the moon, the final interval is that between moonrise and sunrise (KUR).
Eclipses of the sun and moon.
Passages of the moon past the planets and past a group of reference stars spread unevenly through the zodiacal band known to modern scholars as ‘Normal Stars’.
Passages of the planets past each other and past the Normal Stars.
The synodic phenomena of the planets. For the outer planets (Mars, Jupiter, and Saturn), these phenomena are the first appearance, first station, acronychal rising, second station, and last appearance. For the inner planets (Mercury and Venus), these phenomena are for the first and last appearance as a morning star in the east and the first and last appearance as an evening star in the west. Observations of first and last appearances typically report the date on which the phenomena occurred and the constellation or zodiacal sign in which the planet was located at that time. Observations of stations record the date and either the zodiacal sign in which the planet was located or the distance of the planet in front of or behind (and sometimes also above or below) a reference star. Observations of acronychal risings usually give only the date on which the phenomenon was observed.
The dates of solstices and equinoxes.
The dates of the first appearances, acronychal risings, and last appearances of Sirius.
These phenomena are all cyclical phenomena which occur regularly over times ranging from a month to less than a couple of years. Irregular astronomical phenomena, including comets, meteors, and aurora are only occasionally recorded in the Astronomical Diaries; lunar and solar haloes, which are also irregular phenomena, are recorded somewhat more often but still not systematically (Steele & Ganguli 2022).
The reports in the Astronomical Diaries were used to produce various types of compilation texts which gather subsets of reports for several, or in some cases many, years (Hunger 1999; Gray & Steele 2008). With very few exceptions, compilation texts deal only with cyclical astronomical phenomena; most concern a single heavenly body and type of phenomena. For example, we have compilations of lunar eclipses, of the synodic phenomena of Jupiter, and of lunar six data.9 Compilation texts are known in two formats: simple chronological lists of observations presented as normal prose text and tables arranged according to known planetary periods, which highlight the repetitive nature of these phenomena (Steele forthcoming a). In addition, a special type of compilation text, the Goal-Year Text, was regularly created during the last three centuries BC.10 These texts gather observations for the planets, lunar and solar eclipses, and the lunar six to be used in making predictions for a target (‘goal’) year (see next subsection).
Three points particularly relevant to the present discussion are worth noting here. First, for the most part the observations recorded in the Astronomical Diaries and copied into the compilations and Goal-Year Texts are what I term ‘guided observations’. By this I mean that the observers had predicted most of the astronomical phenomena that they were observing before they made their observations. They were not simply watching the sky and recording what they happened to see, but actively looking for specific phenomena which they expected to occur on or around a given date. Consequently, the observers were able to make observations of things like very small partial solar eclipses (Huber & De Meis 2004). Such eclipses would not be noticed by a casual observer; they can only be observed by someone actively and very carefully looking for the eclipse at the right time. But more significantly for our discussion, for some astronomical phenomena it seems that the Babylonian observers’ aim was to check and refine the predicted circumstances of a phenomenon rather than to observe it in its own right. This seems to be the case, for example, with reports of the observations of planetary stations. These reports contain both the date of the station and the planet’s position at that time. In most cases, it seems that the date recorded in the Astronomical Diary is the date when the station had been predicted to occur and what has been observed is the precise position of the planet when it is at its station (Steele & Meszaros 2021). Only when the predicted date was obviously inaccurate did they apparently attempt to determine the actual date of the station by observation.
Second, and this is related to my first point, some of the records in the Diaries and related texts do not reflect observations of phenomena but rather predicted data. Sometimes this fact is explicitly noted using terms such as ‘not seen’ (NU IGI), often, but not always, accompanied by a statement about bad weather which, it must be assumed, prevented the observation being made. On other occasions phenomena are recorded which had been predicted to occur but to not be visible, such as an eclipse of the moon which was predicted to occur during the hours of daylight when the moon is below the horizon. These phenomena are indicated by terms such as it ‘passed by’ (DIB). During the last few centuries BC, equinoxes, solstices, and phenomena of Sirius, were simply not observed and the predicted date given without any comment.11
Thirdly, beginning in about 400 BC, the recorded dates of the first and last appearances of the planets were corrected to estimate when the phenomenon should have been observed had the conditions been optimal. Initially, the corrections seem to have been made when the planet was observed to be too high in the sky at its first or last appearance; beginning in the middle of the 4th century BC, the duration of visibility of the planet at its first or last appearance was measured and the date corrected depending upon the length of this time interval (Steele forthcoming b). Interestingly, it seems that the corrected date took priority over the actually observed date of the phenomenon. It is the corrected date which was recorded in the end-of-month summary of planetary positions and phenomena and which was used in making predictions within goal-year astronomy (Gray & Steele 2008).
Babylonian observational astronomy, therefore, can be seen to be a precise and systematic practice informed by prior prediction and which sought to determine the true phenomena underlying what can be seen.
Goal-year predictive astronomy
Goal-year astronomy refers to a type of predictive astronomy in which astronomical phenomena are calculated by manipulating earlier observations of the same phenomenon. Goal-year methods were developed for predicting lunar and solar eclipses (Steele 2000a), the lunar six (Brack-Bernsen 1999), and planetary synodic phenomena and passages past Normal Stars (Steele 2011). In their simplest form, goal-year methods exploit known planetary periods by simply assuming that phenomena repeat on the same day in the Babylonian calendar (subject to small corrections of a couple of days) after these periods. For example, the Babylonians identified that after eight years the synodic phenomena of Venus recur about four days earlier in the Babylonian calendar. Thus, to predict these phenomena, one must simply go back eight years and change the date by four days. This rule is set out in the goal-year procedure text BM 45728 as follows:
[¶ Appearances of] Venus: go back 8 years to your rear (and) [4 days you subtract.] 4 days you subtract and see it.12
The same eight-year period also works for predicting passages of Venus past Normal Stars, with both the date and the distance of the planet above or below the star repeating quite precisely (Gray & Steele 2008). Similar, though longer, periods were identified for all of the planets: 46 years for Mercury, 47 and 79 years for Mars, 71 and 83 years for Jupiter, and 59 years for Saturn. Comparison of observations recorded in the Astronomical Diaries, compilations texts, and Goal-Year Texts with predicted planetary phenomena recorded in Almanacs and Normal Star Almanacs reveals that these periods were indeed used in practice along with small corrections to the date (such as the four-day correction for Venus) and, when necessary, one-month corrections to take into account intercalation within the Babylonian calendar (Gray & Steele 2008, 2009).
Goal-year methods for predicting lunar phenomena were somewhat more complicated. Eclipses were predicted by exploiting the so-called Saros cycle of 223 synodic (lunar) months, which corresponds to 18 years or 18 years plus one month in the Babylonian calendar. Eclipse possibilities at five- and six-month intervals were arranged in a fixed pattern within the Saros cycle, which then could be repeated for many years. This distribution of eclipse possibilities within the cycle could then be matched with the record of observed eclipses and used to predict future eclipses (Steele 2000a). The time of the eclipse could then be predicted by adding on a value for the excess length of the Saros over a whole number of days (which varies between about six and eleven hours) to the time of the eclipse one Saros earlier (Brack-Bernsen & Steele 2005).
The lunar six intervals were predicted by combining data from one Saros and one Saros plus six months earlier. Instructions for making these predictions are also found in procedure texts. For example, consider the following procedure for predicting the new moon NA interval:
In order for you to calculate (whether the month is) full or hollow, you hold in your hand your year, you return 18 years behind you, and in the 18th year … you return 6 months behind you, and you take ŠÚ and NA of Month VII and add (them) together, and [you take one third of it, and] you subtract it from the NA of the 1st day of Month I of the 18th year.13
Here we are instructed to subtract one third of the sum of the full moon intervals ŠÚ and NA from 229 months earlier from the new moon NA interval from 223 months earlier. Similar rules are found for the other lunar six intervals.
The goal-year methods of prediction allow most of the phenomena which were observed by the Babylonians to be predicted by simply applying the relevant rule to observed or, if observations were not available, predicted data from the relevant number of years earlier. All the requisite data for making predictions for a given year were gathered together in texts known today as Goal-Year Texts, and the resulting predictions were recorded in the so-called Almanacs and Normal Star Almanacs (Hunger 1999; Gray & Steele 2008).14
Mathematical astronomy
A second type of predictive astronomy was developed and used by the Babylonians in the last four centuries BC. This astronomy, dubbed ‘mathematical astronomy’ by modern scholars, uses arithmetical methods to compute lunar and planetary phenomena without the need for ongoing empirical input (Neugebauer 1955; Ossendrijver 2012). Various systems of mathematical astronomy are known for the moon and the planets. The primary aims of the lunar and planetary systems are to predict most of the same phenomena as in goal-year astronomy: the length of the month, the lunar six, eclipses of the sun and moon, and the synodic phenomena of the planets. Secondarily, these systems compute things like the daily positions of the sun, moon, and planets and the latitude of the moon and the planets.
Babylonian mathematical astronomy is phenomena based, by which I mean that, rather than calculating the position of the moon or a planet at a time of the user’s choosing, it operates by computing a series of dates and positions of a phenomenon from the immediately precedingly computed occurrence of that same phenomenon. For example, the date and position of a planet at its first visibility are obtained by adding specific amounts (the synodic time and the synodic arc, respectively) onto the date and position of the preceding first visibility of that planet. Two basic systems of computation for the planets are found: System A-type schemes, in which the synodic time and the synodic arc are determined by the position in the zodiac of the planet at its preceding occurrence of the phenomena according to a piece-wise constant step function, and System B-type schemes, in which the synodic time and the synodic arc are determined by a linear zigzag function.
The lunar systems are considerably more ambitious and complex than the planetary systems. Once more, two systems are known: System A, in which the synodic arc between two successive positions of the moon at conjunction or opposition is given by a step function, and System B, in which it is given by a linear zigzag function. In both systems, the computation of the length of the lunar month (and hence of the time of conjunction or opposition) is achieved by separating the effects of the changing velocities of the sun and the moon (the so-called solar and lunar anomaly), modelling them independently, and then recombining them to find their total effect. An important consideration for our purposes is to note that the effects of solar and lunar anomaly on the length of the month cannot be observed independently of one another (Brack-Bernsen 1980). Thus, the functions which model their effects cannot be derived by simply fitting a mathematical function to observed data. Instead, these functions must be constructed through a careful consideration of the underlying astronomy (Britton 2009). The steps for computing the lunar six and the visibility of the new moon crescent also separate out the contributions from lunar anomaly, lunar latitude, and the inclination of the horizon to the ecliptic, which similarly show a detailed understanding of the underlying astronomy.
The corpus of mathematical astronomy comprises many computed tables—most numerous being tables of computed synodic phenomena of the planets and tables of computed conjunctions or opposition of the moon and sun—as well as procedure texts setting out instructions for producing these tables. It is worth noting that the procedure texts are written in the form of second-person instructions, just like those of goal-year astronomy discussed above. It is also worth noting that several systems for computing the phenomena of a given planet or of the moon coexisted and were used by the same scholars. Indeed, several procedure texts present different systems on the same tablet. Each system produces slightly different dates and positions of the computed phenomena. This fact is never commented upon in the procedure texts and there does not seem to have been a hierarchy of different systems—there were simply taken to be alternative approaches all of which had merit.
Schematic astronomy
I use the term ‘schematic astronomy’ to refer to a type of astronomy that provides descriptions of cyclical astronomical phenomena, such as the dates of the successive first appearances of selected stars and constellations, the change in the length of day and night across the year, and the variation in the duration of visibility of the moon over the course of the month. These descriptions can take the form of prose texts, lists of the dates of phenomena, or simple numerical schemes. All operate with the so-called ‘schematic calendar’ of twelve 30-day months rather than the civil calendar in which months have either 29 or 30 days depending upon when the new moon crescent is seen and the year is made up of either twelve or thirteen months depending upon whether an intercalary month was added to keep the calendar in line with the seasons.
Central to the schematic astronomical tradition is a text known from its incipit as MUL.APIN.15 This text was composed sometime in either the late 2nd or early 1st millennium BC and was widely copied, read, and used across Babylonia and Assyria down to the end of the 1st millennium BC (Steele 2021a). It contains several ordered lists of stars, including a list of the dates of their successive first appearances, a list of simultaneous risings and settings of stars or constellations, a list of successively culminating stars (known as ‘ziqpu stars’), and a list of stars in the path of the moon (that is, the constellations within the zodiacal band through which the sun, moon, and planets move), as well as numerical schemes for the change in visibility of the moon over the course of a month, the change in the length of night, and the length of the shadow cast by a gnomon at different times of day and in different months, lists of the periods of visibility and invisibility of the planets, and rules for determining when to intercalate. A few procedures are given, but these either explain how the numerical schemes can be expanded to, for example, other months of the year, or else provide mathematical justifications for the schemes. None of the procedures tell the reader how to make predictions using the schemes.
Five basic principles underlie much of the astronomy of MUL.APIN:
1.
The schematic calendar of twelve 30-day months with the solstices and equinoxes placed on the 15th day of Months I, IV, VII, and X.
2.
Periodic phenomena are modelled by simple linear zigzag functions with integer periods of either one month (30 days) or one year (360 days).
3.
The lengths of day and night vary according to a linear zigzag function with a period of one year and with extremes which are in the ratio 2:1.
4.
The duration of visibility/invisibility of the moon at night varies according to a linear zigzag function with a period of one month with a minimum of zero and a maximum equal to the length of night on the 15th of the month. The daily change in the duration of visibility/invisibility is equal to one-fifteenth of the length of night on the 15th of the month.
5.
The length of the shadow cast by a gnomon multiplied by the time after sunrise or before sunset is equal to a constant whose value varies according to a linear zigzag function with a period of one year and whose maximum is in the ratio 3:2.
These principles also form the basis of Late Babylonian schematic astronomical texts, many of which draw directly upon—and sometimes quote—MUL.APIN (Steele 2021a). These late-period texts include reworkings of parts of MUL.APIN (Steele 2021a), expansions of the MUL.APIN shadow-length scheme (Steele 2013, 2021b), and a scheme for the durations of rising of the signs of the zodiac (Steele 2017a).
Two points of importance can be noted for the present discussion. First, schematic astronomical texts are always written in the third person.16 The texts provide descriptions—usually numerical descriptions—of features of the celestial realm. Second, the corpus of schematic astronomy is fully self-consistent. There are no alternative schemes to model the same phenomenon or astronomical regularity, and all the schemes for different phenomena are founded on the same principles and assumptions and mesh together harmoniously. Schematic astronomy presents a simple, internally consistent, description of astronomical facts.
Celestial divination
Many thousands of texts attest to the importance of divination in Assyria and Babylonia (Koch 2015). Texts containing lists of celestial omens, written in the form of conditional protasis–apodosis statements, are well represented in this tradition with texts known from the early 2nd millennium down to the end of the 1st millennium BC. Central to the tradition of celestial omens is the omen series Enūma Anu Enlil, a large compilation of omens relating to topics including the visibility and appearance of the moon and sun, lunar and solar eclipses, stellar and planetary phenomena, and weather. Enūma Anu Enlil was widely copied in the 1st millennium BC along with numerous commentaries which purport to provide explanations of omen protasis. In addition, new omen texts were composed in the Late Babylonian period, some of which integrate newly developed astronomical concepts such as the signs of the zodiac (Rochberg-Halton 1984).
Late Babylonian astrology
Several new forms of astrology were developed in the Late Babylonian period. These include the casting of horoscopes from the date of birth (and possibly also the date of the conception) of individuals, various forms of astral medicine in which diseases, parts of the human body, and the ingredients for medical remedies, are associated with the signs of the zodiac, and methods for predicting the rise and fall in the value of commodities in the market and good and bad weather. Many of these new forms of astrology utilised the concept of the zodiacal signs—equal divisions of the path of the sun, moon, and planets into twelve equal parts—which was developed in the late 5th century BC (Britton 2010; Steele 2018).
Many of the new forms of astrology developed in the Late Babylonian period draw directly upon contemporary astronomical practices. For example, the Horoscopes contain planetary and lunar positions and other astronomical data from the date of birth of an individual.17 The sources of this data include observational material taken from the Astronomical Diaries as well as predicted data computed using both the goal-year methods and mathematical astronomy (Rochberg-Halton 1989, Steele 2000b, forthcoming b). The methods for predicting weather and increases and decreases in market value exploit the goal-year periods of the planets (Ossendrijver 2019, 2021). And the so-called kalendertext scheme, which associates signs of the zodiac with days of the year through a mathematical scheme and was used (among other things) to determine the ingredients used to make medical remedies, is constructed directly out of the methods and principles of schematic astronomy (Brack-Bernsen & Steele 2004; Steele 2017b).
Two developments within Late Babylonian astrology are particularly important for the present discussion. First, there was the creation of texts which present lists of astrological associations between items in the celestial realm, in particular the zodiacal signs, constellations, and the planets, and things in the terrestrial realm such as parts of the human body (Wee 2015; Schreiber 2020), cities (Steele 2015), and illnesses (Geller 2014). Second was the composition of texts which present astrologically significant geometrical relationships between signs of the zodiac and other astrological concepts such as the bīt niṣirti (‘place of protection’) where the planets have special significance and the so-called ‘terms’ where parts of each sign of the zodiac and each month of the year are assigned to the different planets (Rochberg 2004; Jones & Steele 2011; Brack-Bernsen 2021; Rumor 2021).
The place of theory in Babylonian astral science
Before exploring theory in Babylonian astronomy and astrology, it is necessary to give some consideration to the question of what we mean by ‘theory’ in this context. Like the term ‘science’, many competing definitions of a ‘scientific theory’ have been put forward by philosophers of science (Losee 2001). In practice, however, most historians have simply assumed that the meaning of ‘theory’ is self-evident. Thus, in his influential The Structure of Scientific Revolutions (1962), Thomas Kuhn frequently refers to scientific theories—indeed the process by which one theory is rejected and replaced by another is a key part of his discussion—without ever defining what a theory is.18 For Kuhn and others, theories tend to be implicitly understood as providing explanations of phenomena, as binding together a series of scientific laws, and as something that is capable of making predictions that are testable. It is in this way that the term has been understood and used by many of the authors of the definitions of science that I quoted at the beginning of the article.
Historians of ancient astronomy, however, have sometimes taken a broader view of what constitutes a theory. Goldstein (1972: 40), for example, refers to theories ‘whose goal has been the predictions of the positions of heavenly bodies as well as the times of certain phenomena such as eclipses’. Aaboe (1974: 23) defines a scientific theory in astronomy ‘a mathematical description of celestial phenomena capable of yielding numerical predictions that can be tested against observations’. For Goldstein and Aaboe, therefore, a theory can be understood simply as a system of computation. It may, for Aaboe, provide a ‘mathematical description’, but it need not explain phenomena. According to Aaboe’s definition, therefore, a theory must be able to compute an eclipse of the moon, for example, but need not explain that the eclipse is due to the moon moving into the Earth’s shadow.
A more detailed definition of ‘theory’ for the Babylonian context has been given by Francesca Rochberg:
Following Aaboe, ‘theory’ here denotes specifically the application of mathematical methods, not ‘explanation,’ either of the nomothetic sort, in which observed occurrences are fitted into a pattern of regularity called a ‘law,’ or of the sort that required explanation in terms of the causal agencies of the natural phenomena with which the theory is connected. (Rochberg-Halton 1991: 117)
Rochberg specifically excludes both ‘explanation’ and ‘laws’ from the requirements of a ‘theory’, in direct contrast to how the term is used by Kuhn and others. Indeed, she goes further, stating that ‘the use of the term “theory” in the context of Babylonian astronomy refers to the application of general models to compute particular phenomena characteristic of the planets, sun, and moon’ (Rochberg-Halton 1991: 117). Rochberg highlights computation and the use of common approaches as defining characteristics of an astronomical ‘theory’. In later works (Rochberg 2016, 2018), she considers broader themes drawn from the philosophy of science such as analogical reasoning and modelling and model-based reasoning as evidence for what I—these are not her words—would call theoretical methods for generating knowledge. Rochberg argues that these types of reasoning were widely employed by the Babylonians.
As I discussed in the introduction, discussions of theory in Babylonian astral science have tended to elide two questions: whether we can identify things in the Babylonian material which we call theories or which employ theoretical reasoning, and whether the Babylonians had things that they considered to be something like a theory, even if they did not call it as such. In what follows, I want to keep these two questions separate and address them in turn.
Looking for theory from the outside
Many of the definitions that I have discussed above refer to things like predictive power, the use of generalised models, forms of theoretical reasoning such as the use of analogies, an astronomical and/or physical understanding of phenomena or the circumstances that produce them, the testing of computation against observation, and provision of explanations as markers of a scientific theory. Let us examine whether these markers can be identified in the Babylonian material. For reasons of space, I will consider only four topics: (1) the use of analogical reasoning; (2) the application of generalised models to different phenomena and celestial bodies; (3) whether the Babylonians tested their systems of computation against empirical evidence to prove their correctness and/or to identify how to improve them, and (4) whether there is evidence for an understanding of the underlying astronomy or whether the systems of prediction simply fit numbers to previous occurrences and extrapolate from there.
Analogical reasoning: the moon as an archetype
As discussed by Rochberg (2016, 2018), the use of analogical reasoning is widespread throughout cuneiform scholarship. Omens were created through the similarity between Akkadian words, cuneiform signs, the visual appearance of objects or phenomena, and more (Brown 2000; Rochberg 2016), medical texts make frequent use of analogies (Johnson 2017; Panayotov 2017), and commentaries often draw on analogies to explain the meaning of words, phrases, or phenomena (Frahm 2011; Crisostomo 2018).
Within Babylonian astronomy, the clearest evidence for analogical reasoning is in the use of the moon as an archetype for other celestial bodies. A clear statement of the moon providing the model for the motion of the sun and the planets is found in MUL.APIN. Lines I iv 31–37 describe the constellations through which the moon moves each month:
The gods (variant: stars) who stand in the path of the moon, through whose region the moon during a month passes repeatedly and keeps touching them:The Stars, the Bull of Heaven, the True Shepherd of Anu, the Old Man, the Crook, the Great Twins, the Crab, the Lion, the Furrow, the Scales, the Scorpion, Pabilsag, the Goat-fish, the Great One, the Tails of the Swallow, Anunitu, and the Hired Man.19
The text continues:
¶ The sun travels the (same) path the moon travels.
¶ Jupiter travels the (same) path the moon travels.
¶ Venus travels the (same) path the moon travels.
¶ Mars travels the (same) path the moon travels.
¶ Mercury whose name is Ninurta travels the (same) path the moon travels.
¶ Saturn travels the (same) path the moon travels.20
In modern terms, this section of MUL.APIN is listing the zodiacal constellations through which the sun, moon, and planets move. But notice that this is not what the text presents. Instead, it presents the list of zodiacal constellations as those that the moon passes through. The sun and the planets are not said to also move through those constellations. Rather, they travel the same path as the moon. What do the sun and the planets do? They do what the moon does.
The idea that the sun and planets do what the moon does is not stated explicitly in other texts. But it is implicit in many of the systems of computation and understanding of phenomena across Babylonian astronomy (Chopra 2023, Steele 2024, forthcoming b). Consider the following example. The Babylonian scholars developed a method for predicting lunar eclipses by combining the concept of eclipse possibilities (months when an eclipse might occur as opposed to ones where it definitely would not) with the Saros eclipse period of 223 lunar months (Steele 2000a). This system was derived from the analysis of several decades (at least) of observations of lunar eclipses. It predicted eclipse possibilities at six- or occasionally five-month intervals from one another. But at less than half of these eclipse possibilities will an eclipse be visible. The lack of a visible eclipse may be because the moon was below the horizon when the eclipse would take place (that is, a lunar eclipse during the day) or else because the moon was too far from a node of intersection of the moon’s orbit with the path of the sun along the ecliptic. The Babylonians were aware that these eclipses would be invisible and marked them as eclipses which ‘pass by’ (DIB). This system for predicting lunar eclipses was then applied by analogy to the prediction of solar eclipses (Steele 2000a).21
We may not be surprised that methods developed for lunar eclipses were applied to solar eclipses; after all, the two phenomena are clearly similar. More interesting, therefore, is to note that the concept (and terminology) of events which ‘pass by’ was transferred to the phenomena of Mercury. In its regular cycle, Mercury has two phases of visibility: one in the evening, when it is in the west, and one in the morning, when it is in the east. These phases of visibility alternate: the planet will be visible as an evening star, then invisible for some time, then visible as a morning star, and then invisible for some time, and then this pattern keeps repeating. However, because Mercury is always close to the sun, at certain times of the year, when the ecliptic lies flat to the horizon, Mercury will skip a visibility phase. In other words, instead of the regular pattern of evening visibility–invisibility–morning visibility–invisibility–evening visibility, and so on, we will get a sequence like evening visibility–invisibility–morning visibility–invisibility–morning visibility. Here the second evening visibility phase has been skipped. The Babylonians were aware that this missing of Mercury’s visibility phase occurred every now and then. In such cases, in the Astronomical Diaries they note an estimated or predicted date when the planets would have normally been visible but write that it ‘passed by’, using exactly the same terminology as when an eclipse ‘passed by’. Thus, we have the transfer of a concept and its terminology from the moon to another celestial body, Mercury. What does Mercury do? It does what the moon does.
Generalised models
Rochberg-Halton (1991: 117) points to the use of generalised models for predicting lunar, solar, and planetary phenomena as a mark of theory within Babylonian astronomy. By ‘model’ here, Rochberg-Halton simply means the mathematical techniques used in the computation of celestial phenomena.22 In particular, she points out that there are several basic features found in all the systems of computation of mathematical astronomy. For example, computations of position always use either step functions (in so-called System A schemes) or linear zigzag functions (in so-called System B schemes). This holds true across almost all the planets and the moon.23 Similarly, in both System A and System B planetary schemes, it is assumed that the difference in time between two successive phenomenon of the same kind (the synodic time), and the difference in position between those same two successive phenomenon of the same kind (the synodic arc) differ by a constant value that can be derived from the period relation which underlies the system and the assumed value for the difference between twelve lunar months and the solar year (that is, synodic time = synodic arc + a constant).24 Rochberg-Halton (1991: 117) concludes: ‘The inherent character of the ACT schemes as general models within which particular natural phenomena could be individually computed justifies our modern designation of them as scientific and theoretical.’25
Testing
Aaboe (1974: 23) suggests that a scientific theory must be able to make predictions which can be tested by comparing them with observations. Both Babylonian goal-year astronomy and mathematical astronomy yield predictions of specific astronomical phenomena. The predicted data could include the date and sometimes the time at which the phenomenon will take place, the position of the celestial body at that time, and, in some cases, other aspects of the phenomenon (for example, the magnitude when predicting a lunar eclipse). These predicted data could easily be checked against what was observed and recorded in texts like the Astronomical Diaries. Indeed, we have a small number of texts which provide direct evidence for the testing of computed data by the Babylonians. For example, we have preserved three fragments of a text dating to the 4th century BC which contains about sixty years’ worth of the dates and positions of the synodic phenomena of Saturn calculated by a System A type scheme of mathematical astronomy.26 Accompanying the computed dates and positions of the first and last appearances of the planet are numbers which seem to represent the number of days between the date computed by the System A type scheme and the date on which the same phenomenon was observed. The computed dates and positions of the first and second stations are accompanied by quotations of observations of the position of Saturn at the station. It seems apparent that the author of the text wrote it to test the accuracy of his computational system by comparing the data it produces with observation (Steele & de Jong 2023). As it happens, we have no examples of this particular computational system for Saturn being used elsewhere, although that may just be due to the vagaries of survival. But perhaps we might speculate that the system of computation was not sufficiently accurate when it was tested and so it was abandoned in favour of other systems with slightly different parameters. Similarly, we have two copies of a text containing various computed functions relating to the position and anomalistic motion of the moon for a series of 38 solar eclipse possibilities between 475 and 457 BC.27 Alongside the computed details of the eclipses are remarks about those eclipse possibilities which are almost certainly taken from the Astronomical Diaries. Once more, at least parts of the system of computation in this tablet differ from those known elsewhere, which again raises the possibility that the system was rejected because the agreement with the observational record was not good enough.
Although these two cases provide the only extant examples of testing of methods of computation through comparison with observation, we can assume that similar testing must have been undertaken during the development of all methods of computation, both those of mathematical astronomy and those of goal-year astronomy.
Astronomical and physical understanding
The argument for Babylonian astronomy being a theoretical science made most often—even if frequently only implicitly—is simply that there is clearly an understanding of what is going on astronomically underlying it. Thus, Rochberg-Halton (1991: 117) writes: ‘To schematize and quantify such aspects of celestial motion as the movement in latitude of the moon and the regression of the lunar nodes, which are not directly observable per se, surely points to what can only be called a theoretical approach to these and other astronomical problems.’
Examples of an understanding of the underlying astronomy can be found throughout the various genres of Babylonian astronomy. Within the observational tradition, for instance, one could point to the idea of the true dates of the first and last appearances of the planets as being distinct from those that can be observed, which can differ because of the atmospheric conditions (most often, simple bad weather) and the schemes for correcting an observed date to give the true date by measuring the duration of visibility of the planet. Or to the idea of missing visibility phases of Mercury which are said to ‘pass by’, but which are still assumed to occur at dates that can be predicted.
Even clearer evidence for astronomical understanding can be found within the tradition of mathematical astronomy. For example, consider the concept and process of creating mathematical functions to model non-observable astronomical variations, such as column 𝛷 of lunar System A, which represents the variation in the length of the Saros (223 synodic months) due only to lunar anomaly. However, the variation due to lunar anomaly is swamped by that due to solar anomaly, so the variation modelled by column 𝛷 cannot be directly observed. Or the idea of separating out the effect of the variations due to lunar and solar anomaly on the length of the month, so that they can be modelled independently by relatively simple functions and then recombined to determine the actual length of the month. Or the calculation of the duration of lunar visibility which takes into account the contributions made by lunar and solar anomaly, lunar latitude, and the angle of the ecliptic to the horizon. One could make a similar list of examples of the astronomical understanding underlying the planetary systems.
Although an understanding of the astronomy by the Babylonians is granted—and celebrated—by many authors, it is also usually pointed out that Babylonian astronomy was purely arithmetical. For example, Aaboe (1992: 285) notes ‘the total absence of any underlying geometrical models or “orbits”’ in Babylonian mathematical astronomy. For Aaboe, this is a trivial point and does not change the status, only the character, of Babylonian astronomy. Similarly, Derek de Solla Price (1975: 17) contrasts Babylonian and early Greek astronomy, writing that:
The Greeks had a fine pictorial concept of the celestial motions, but only a rough-and-ready agreement with anything that might be measured quantitatively rather than noted qualitatively. The Babylonians had all the constants and the means of tying theory to detailed numerical observations, but they had no pictorial concept that would make their system more than a string of numbers.
Neither is better than the other: Price (1975: 17) dubs the Babylonians ‘arithmetical geniuses who were geometrical dullards’, whilst the Greeks were ‘precisely opposite’ in character. But for other authors, as I have discussed in the introduction, the absence of a geometrical or physical model marks Babylonian astronomy as deficient.
Let me state that I agree with Aaboe and Price: the presence or absence of geometry or of physical models merely reflects a different approach to astronomy and says nothing about that astronomy’s status as a science. But is it indeed true that the Babylonians had no ‘pictorial concept’ or physical understanding of astronomy? This opinion has been widely stated and until recently I would have probably stated it too (though not without some underlying unease).28 But a few years ago I discovered a tablet in the British Museum which changes this picture.29 The tablet concerns lunar and solar eclipses and includes references to the shadow which causes the eclipse. For example, lines 4′–5′ read:
(At) 1 UŠ it (i.e., the moon) goes out to the day, (and at) 1 [bēru of night] the shadow comes near to it, and it makes an eclipse.
This passage is part of a longer presentation of a scheme which states that, if the moon rises x UŠ of time before sunset then an eclipse will occur x bēru of time after sunset. UŠ and bēru are units of time with an UŠ corresponding to 4 minutes and a bēru to two hours. This scheme is a reasonable approximation to reality. But what is significant for the present discussion is the mention of the shadow. This is the first reference to an eclipse (or any other astronomical phenomenon) being caused by something physical in a Babylonian text. It implies that the Babylonian scribes were not simply fitting mathematical functions to phenomena—something Price (1975: 11) compares to Fourier analysis of wave motions—but also understood (some) of the physical causes of astronomical phenomena. And an understanding that eclipses are caused by shadows implies, for example, that the Babylonians had a three-dimensional image of the universe, where celestial objects are at different distances. Once we accept such things, it brings into question our characterisation of Babylonian astronomy in general as being purely numerical. And when we do, it becomes tempting to ask whether, for example, the Babylonians had some type of geometrical model in mind when they were thinking about the different contributions to problems like lunar visibility. Have we been so keen to avoid imposing Greek ideas of a spherical earth and cosmos on the Babylonian material that we have ignored the significance of basic facts such as that in Babylonian mathematical astronomy eclipses are predicted when the moon and sun are in opposite positions in the zodiac and the moon is close to the middle of its band of motion? These are important questions that are too big to address here, but I want to raise the possibility that there might be more geometrical and physical understanding hidden within Babylonian astronomy that we have been willing to assume.
Looking for theories within Babylonian astral science
I now turn to the question of whether there were theories within the Babylonian astral sciences. This question poses an immediate problem: what do we mean by a theory in this context? There is no Akkadian word meaning ‘theory’, just as there is no word meaning ‘science’ (Rochberg 2021), but that does not mean that there are not concepts within Babylonia that share sufficient similarities with these modern English terms to allow us to use them productively in discussing Babylonian scholarship. To do so, I think it is most useful to adopt a fairly broad understanding of ‘theory’ and propose to take it to mean a system of knowledge which is assumed by its creators and/or users to be a (fairly) comprehensive and self-consistent representation of the world around us (or at least that aspect of the world that is of interest to the users of that theory), and which provides a foundation that can be expanded upon following established rules or methods to provide additional information about the world. According to this definition, a theory need not be explanatory; it may simply be descriptive. Thus, a theory need not, for example, explain why the length of daylight changes over the course of the year; it may simply describe how it changes, whether that be in general terms or through a precise numerical scheme.
We can now ask the question: did the Babylonians have theories in the astral sciences? Many previous scholars have assumed that they did and have argued—or, more often, have simply stated—that we find these theories in the various systems of mathematical astronomy. The clearest statement of this position is given by John Britton & Christopher Walker (1996: 60):
It is convenient to speak of the assemblage of functions which describe the behaviour of a particular celestial body as a ‘theory’, even when our knowledge of the underlying assumptions is limited and indirect. So defined, Babylonian astronomical theories divide into two broad categories—lunar and planetary—which are distinguished both by their objectives and their procedures. … The theories are expressed in three classes of texts: ephemerides, which tabulate the functions necessary to compute the phenomenon in question for successive phenomena; procedure texts, which describe in compressed fashion the procedures for calculating each function; and auxiliary texts, which tabulate functions which relate to but do not figure directly in the computations of ephemerides. Generally, it is the ephemerides which comprise the clearest expression of each theory.
In the background to Britton and Walker’s use of the term is almost certainly an analogy with the lunar and planetary theories of ancient Greek astronomers, particularly those presented by the 2nd century AD author Claudius Ptolemy in his Almagest. In this work, Ptolemy presented quantitative geometrical models for the sun, moon, and planets ostensibly derived from empirical data, which can be used both to explain planetary phenomena such as eclipses or a planet’s retrograde motion and to calculate the positions of the heavenly bodies and their associated phenomena (Pedersen 1974, Neugebauer 1975: 21–343). Ptolemy also provided tables derived from his theories that can be used to compute solar, lunar, and planetary positions. As noted by Britton and Walker, the Babylonian material does not present the underlying assumptions, but it does allow calculation and, in their view, the calculated tables provide an ‘expression of each theory’.
The designation of the systems of mathematical astronomy as ‘theories’ can be traced back to publications by Otto Neugebauer in the 1930s. Before Neugebauer, scholars such as Franz Xaver Kugler referred to these systems in German as rechnung ‘calculation’, always referring to ‘die Mondrechnung’ and ‘die Planetenrechnung’ but never ‘die Mondtheorie’ or ‘die Planetenrechnung’.30 Writing in English, Pannekoek (1917) simply referred to the ‘tables’. By contrast, beginning with his earliest publications on Babylonian astronomy, Neugebauer consistently referred to these as ‘die Mondtheorie’ or ‘die Planetentheorie’ in German and ‘lunar theory’ and ‘planetary theory’ in English.31 Neugebauer’s use of the term ‘theory’ has been followed by most scholars including Aaboe, Britton, Brack-Bernsen, Hunger and Pingree, de Jong, Rochberg, Swerdlow, van der Waerden, and, on occasions, myself.32
But were the systems of mathematical astronomy ‘theories’ for the Babylonians, according to the broad definition I gave above? I suggest that they are not. The aim of these systems is—as Kugler recognised—to calculate astronomical phenomena. As such, the procedure texts present second-person instructions for making these calculations, the results of which are dated astronomical phenomena recorded in the tables. The process of making the predictions may be complex and embedded within these procedures may be a considerable amount of astronomical understanding, but the essential processes and aims of this type of astronomy are no different to those of goal-year astronomy. Within goal-year astronomy we similarly find procedure texts containing second-person instructions for how to make the predictions and tablets (the Almanacs and Normal Star Almanacs) where those predictions were recorded. Neugebauer, Aaboe, and others reject that this type of astronomy is a ‘theory’, however. More significantly, the various systems of mathematical astronomy (just like those of goal-year astronomy) are not consistent with one another, nor can they be expanded to provide information about other astronomical phenomena, both of which go against the definition of a theory as I have formulated it. Complex and as impressive in its modelling of astronomical variabilities as it is, for the Babylonians themselves, mathematical astronomy was simply another method of calculating astronomical events.
Given that mathematical astronomy was not a theory for the Babylonians, was there another type of astronomy which they did think of as a theory? I suggest that there was and that it is to be found in the schematic astronomical tradition.33 As a reminder, Babylonian schematic astronomy presents a fully self-consistent set of numerical schemes for selected astronomical phenomena, such as the change in the length of daylight over the course of the year and the change in the duration of visibility of the moon during the night over the course of a month. Schematic astronomical texts are always written in the third person—they provide descriptions of these variations, not instructions of how to calculate a specific phenomenon from them. And, crucially, schematic astronomy was expanded over time to provide mathematical descriptions of additional aspects of astronomy through the logical application of mathematical methods to the well-established basic principles of schematic astronomy.
As an example of the expansion of schematic astronomy to include new astronomical topics, let us consider a scheme for the rising times of the signs of the zodiac which was developed during the last half of the 1st millennium BC (Steele 2017a). This scheme relates the culmination of ziqpu stars which cross the meridian at known intervals with the rising of a sign of the zodiac or a part thereof. The rising time scheme itself it constructed from the length of daylight scheme found in schematic astronomy and applied to the concept of the signs of the zodiac, which was developed in the late 5th century BC. The scheme is presented in several different forms—some of which are simple lists, whilst others present longer prose descriptions along with astrological material—all of which are written as third-person descriptions, never as second-person instructions for calculating. These texts, therefore, represent an expansion of schematic astronomy into a new area and make use of recently developed astronomical concepts such as the zodiac, but remain fully consistent with the basic principles of schematic astronomy.
Alongside the astronomical theory presented in the schematic astronomical tradition, I suggest that the lists of astrological associations represent a theory of astrology. These lists codify and expand long-established traditions linking things like the individual planets, the quarters of the moon, wind directions, and constellations with counterparts such as countries, cities, the rise and fall of the values of commodities in the market, and weather. These traditions are found embedded within the celestial omens listed in Enūma Anu Enlil and other early texts,34 but are only rarely articulated before the Late Babylonian period. In this late period, however, the Babylonian scribes produced numerous lists of astrological associations between planets, constellations, and the signs of the zodiac, and countries, cities, parts of the human body, illnesses, the ingredients for medical remedies, the maximum length of life, the cause of death of an individual, and much more. Most often these lists simply juxtapose the two parts of the association; in a few cases the term ‘for’ (ana) is inserted between the two. In addition to the lists of astrological associations, other texts present further foundational material for astrology, such as statements and lists of the geometrical relationships between signs of the zodiac, lists of the so-called bīt niṣirti (‘place of protection’) of the planets where they have special significance, and the division of each month and sign of the zodiac into five unequal length parts which are associated with the planets (the so-called ‘terms’).
We have clear evidence that the astrological theory presented in these texts did indeed form the foundation for astrological practice. For example, texts presenting instructions for predicting weather and increases and decreases in the value of commodities in the marker from the positions and phenomena of the planets draw directly upon the associations given in these texts. Similarly, astral medicine texts apply the associations between the signs of the zodiac and ingredients for making remedies found in the lists of associations. Indeed, some of these texts combine both these associations with numerical schemes which are built out of the schematic astronomical tradition to predict which ingredients to use to treat a patient depending upon which day it is. Thus, we can see that the scribes drew upon both the theory of astronomy presented in the texts of schematic astronomy and the theory of astrology presented in the lists of astrological associations to construct practical astrological tools.
Final remarks
My aim in this paper has been to explore whether Babylonian astral science was ‘theoretical’ in nature, and, if so, to try to identify where we can find these Babylonian theories. As I have discussed, the first question must be divided into two: first, whether Babylonian astral science embodies aspects of what we would define as a theoretical science, such as forms of theoretical reasoning and detailed astronomical understanding, and, second, whether the Babylonians themselves had a body of knowledge which they viewed as being something like theories of astronomy and astrology. I have argued that the answer to both is in the affirmative, but that where we find theory is different for each one: We see theory in the analogical reasoning and the use of generalised models throughout Babylonian astronomy, in the interest in testing computational models against observation, and, most obviously, in the clear understanding of the astronomy of solar, lunar, and planetary motion and the resulting phenomena that they exhibit found within mathematical astronomy. They, I argue, however, saw the schematic astronomical tradition as the presentation of their theory of the celestial realm, providing a simple, self-consistent numerical description of astronomical phenomena, and the lists of astrological associations, geometrical relationships between zodiacal signs, etc., as providing the theory underlying astrological practice.
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1
These terms are all culturally dependent and, in some cases, may not exist within a culture at all. See, for example, Rochberg (2016) on whether or not the Babylonians had a concept of ‘nature’.
2
In some respects, Crombie’s and Gregory’s words hardly differ from those found in early modern histories of science written before the rediscovery of the cuneiform material. For example, the English clergyman and antiquarian George Costard (1710–82) contrasts the ‘registers’ of eclipse observations kept by the ‘Chaldeans’ (that is, the Babylonians) with a Greek ‘Science built upon strict demonstrative Principles’ (Costard 1746: 21–3). For Costard, observation is not science, and astronomy only becomes a science when geometry is applied to it, something that only the Greeks did: ‘Geometry being improved by them, and them alone, into a Science, and applied to the Heavens, they became the true and proper Authors of every Thing deserving the Name of Astronomy’ (Costard 1746: 156). For accounts of Babylonian astronomy written before the discovery of the cuneiform material and their legacy in the historiography of the field, see Steele (2022).
3
The history of scholarship on Babylonian astronomy between the 1880s and the 1950s is reviewed in de Jong (2016) and Steele (2016).
4
These authors do not define what they mean by science, probably in large part because they understood that Babylonian astronomy—in particular Babylonian mathematical astronomy—is not close to being a borderline case under what they would consider to be any sensible definition of science.
5
I use the term ‘astral sciences’ as a catch-all to refer to scholarly practices which fall under the modern categories of astronomy, astrology and celestial divination, cosmology, and certain aspects of meteorology. In addition to the tablets from Babylonia, at least a thousand tablets concerning astronomy and astrology are known from cities in Assyria (principally Nineveh, Aššur, and Huzirina) dating to the 8th and 7th centuries BC. The tablets from Assyria include copies of standard works, such as lists of celestial omens and the compendium known as MUL.APIN, as well as correspondence between scholars and the king dealing with the interpretation of observed celestial phenomena as omens.
6
Almost all these tablets were either purchased on the antiquities market in the 1870s and 1880s or else were unscientifically excavated. Most are now in the collection of the British Museum.
7
The Akkadian name of the Astronomical Diaries translates as ‘regular watching’. For editions of the Diaries, see Sachs & Hunger (1988, 1989, 1996) and Hunger (2022). On the creation of the Diary genre in around 600 BC and their subsequent development, see Steele (2019). For the compilation of the Astronomical Diaries from preliminary observational reports, see Mitsuma (2015).
8
The name ‘lunar six’ is due to Sachs (1948).
9
For editions many of these compilation texts, see Hunger (2001).
10
For editions of known Goal-Year Texts, see Hunger (2006).
11
We can trace a transition from recording either the observed dates of the solstices, equinoxes, and Sirius phenomena or predicted dates with the marker ‘not seen’ to unmarked predicted dates in the early 3rd century BC (Steele forthcoming b). For the evidence for the prediction of these phenomena in the late texts and the methods by which these predictions were made, see Neugebauer (1948) and Sachs (1952).
12
BM 45728 Obv. 5–6; edition by Steele (2025). In the edition and translation, text within square brackets is lost on the tablet due to surface damage but can be restored based upon context and parallels. In the translation, text within curly parentheses are glosses added by the translator to aid the reader.
13
BM 42282+42294 Obv. 6–10; edition in Brack-Bernsen & Hunger (2008).
14
For editions of the Almanacs and Normal Star Almanacs, see Hunger (2014).
15
For an edition and translation of MUL.APIN with a detailed commentary, see Hunger & Steele (2019).
16
The only exception to this rule is found in MUL.APIN, where there are a few procedures which are written as second-person instructions. But those instructions tell the reader how to expand a numerical scheme to all months of the year, for example. They are not instructions for using the scheme to calculate astronomical phenomena.
17
For a study of the Horoscopes and editions of many examples, see Rochberg (1998).
18
In a later work, Kuhn (1977) did list the characteristics of what he considered a ‘good scientific theory’ (in contrast to a poor one): that it be accurate, consistent, broad in scope, simple, and fruitful of new research findings.
19
MUL.APIN I iv 31–37; translation by Hunger & Steele (2019: 143).
20
MUL.APIN II i 1–6; translation by Hunger & Steele (2019: 143).
21
As I have discussed elsewhere (e.g., Steele 2000a), the system cannot have been developed independently for solar eclipses because the occurrence of visible solar eclipses at any given location is too infrequent and too irregular to allow the information necessary to set up the system to be derived from observation.
22
This meaning differs from how Rochberg uses the term ‘model’ in her later work (e.g., Rochberg 2016, 2018), where she draws upon work in cognitive theory and in the philosophy of science which considers models to be human-generated cognitive objects which allow us to ask selected questions that we wish to ask about the world, and discusses whether these are useful ideas for understanding the Babylonian material.
23
System A type schemes are known for all the planets and the moon; System B type schemes are attested for the outer planets (Mars, Jupiter, and Saturn) and the moon but not the inner planets.
24
In principle, this relationship holds for all the planetary systems. In practice, for reasons that are not fully understood, in some of the computed Mercury tables the rule was not applied as expected (Neugebauer 1955).
25
‘ACT’ in this quote refers to mathematical astronomy; it is taken from the title of Neugebauer’s (1955) book Astronomical Cuneiform Texts.
26
The three fragments are BM 42878, BM 45726+45807, and BM 46004. For an edition of this text, a reconstruction of the placement of the fragments, and a detailed analysis of its contents, see Steele & de Jong (2023).
27
The two tablets are BM 36599 and BM 36580+36737(+)47912. They are edited and studied in Aaboe & Sachs (1969), Britton (1989), and Aaboe et al. (1991).
28
29
BM 42127+46243. I will soon publish an edition of this tablet along with a detailed discussion of its content and significance.
30
See, in particular, Kugler (1900), but the same terminology is used in all of his publications.
32
Interestingly, van der Waerden used ‘rechnung’ when writing in German but ‘theory’ when writing in English. It may be significant that Ossendrijver (2012), in his publication of the procedure texts of mathematical astronomy, never talks of Babylonian lunar or planetary theories but instead of ‘calculations’ and ‘algorithms’ for calculating.
33
Brown (2000) already highlights the importance of the schematical astronomical tradition and points out that its aim was not to predict astronomical phenomena but instead, in his view, to present a model of an ‘ideal’ universe against which observation could be compared for divinatory purposes. He contrasts this with what he takes to be a later paradigm of astronomy in which astronomical prediction replaces these ideal models. Although I agree with Brown that the purpose of schematic astronomy was to provide a description of the universe, I disagree with his claim that this was for the purposes of divination alone. I also disagree with his idea that there was a switch between a paradigm in which schematic astronomy was used for divination to one of computational astronomy represented by the systems of goal-year and mathematical astronomy. Instead, it is clear that schematic astronomy continued to be of relevance—and continued to be developed—alongside other forms of astronomy. It did not become redundant or copied only for antiquarian reasons in the late period but remained a living tradition (Steele 2021a).
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DOI: 10.5871/jba/013.a32
Published on: 26 August 2025
Volume: 13
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This article introduces the thematic collection, ‘The critical role of governance for decarbonisation at pace: learning the lessons from SHAPE research’, edited by Sarah Birch, Hilary Graham, Andrew Jordan, Tim O’Riordan, and Henry Richards. With confirmation that global average temperatures in 2024 exceeded 1.5° above pre-industrial levels, and near continuous news of extreme weather events around the world, there seems little to dispute the characterisation of UN Secretary-General, António Guterres, that ‘every country must deliver and play their rightful part’. Guterres and many others point to the urgency of action, even though it is palpably sluggish. In the collection, we argue that SHAPE (Social Science, Humanities, and the Arts for People, Economy and environment) research provides the essential lynchpin for policymakers to understand people, societies, economies, and cultures and what works in practice to bring about the transformative changes needed to respond to this challenge. The common thread of this collection is governance. Governance provides the political and civic mechanisms to deliberate and make inclusive decisions based on evidence and collective judgements about our shared future. The collection features crucial policy insights drawn from SHAPE research to advance the principles and practices of consensual governance, and to help navigate ‘an exit off the highway to climate hell’.
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