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Babylonian and Seleucid Dates

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This page gives access to two conversion tables in Excel format (905 kB), with a copy in HTML format (2.57 MB), useful for determining the Julian equivalent of Babylonian and Seleucid civil dates in the Ptolemaic era. The dates of some important events early in the Ptolemaic era, such as the death of Alexander, and of a number of Seleucid events involving Ptolemaic princesses, can be determined from these tables.

Three tables are provided:

1) The standard conversion table generated by Parker & Dubberstein in 1956 (PD)
2) A corrected conversion table, consisting of PD overlaid by data from contemporary astronomical diaries, lunar tables, eclipse reports, eclipse predictions, goal year texts and horoscopes.
3) A difference table, showing the differences between the first two tables.

The second of these tables is also provided in a CSV text format.

Analysis of the Tables

The following notes give additional information on the processes used to generate these tables.

Parker-Dubberstein

The standard conversion table of PD was based on the calculated new moon tables for Babylon developed by Schoch, combined with tables for 1 Nisanu determined by Sidersky. Where there were discrepancies, Parker and Dubberstein started with Sidersky's number and calculated lunar months backwards and forwards till they reached agreement with Schoch's tables. The tables do not indicate which dates are taken directly from Schoch, or which are derived from Sidersky or by this interpolation process, nor have I tried to determine this. These tables replace and silently correct a previous version published in 1942. They should be understood to be accurate only to within a day. Parker and Dubberstein themselves estimated that their numbers were 70% accurate. Schoch's calculations have been superseded by other tables.

Moreover, the dates are for Babylon. Even if they are completely accurate for Babylon, and even if the start of the month outside Babylon was also determined by the same techniques, dates at points further west (e.g. Judea, Egypt) may occasionally be one day earlier, owing to the rotation of the earth, causing moonrise to be observed at a slightly later point in its cycle. In most cases these uncertainties do not matter, since Babylonian or Seleucid dates of Egyptian-related events are usually known only to the year, or occasionally to the month.

In recent years a considerable volume of contemporary Babylonian data has been published which allows large sections of the PD table to be confirmed or corrected. The corrected conversion table provided here is based on this data. In no case does the discrepancy between the PD calculations and the Babylonian data demonstrably exceed 1 day, as Parker and Dubberstein themselves expected.

I have no doubt that there are errors in these tables. They should only be regarded as a draft edition of a corrected table. The years 324-300 have been carefully crosschecked against the corrected table prepared by Tom Boiy in "Aspects chronologiques". Remaining discrepancies in this period represent points that I believe are in error in his table. Additionally, all years have been checked against the observed lunar first visibility dates given in Table 1 of L. J. Fatoohi et al., JHA 30 (1999) 51 and Table 1 of S. Stern, JHA 39 (2008) 1, and thre predicted dates given in Table 2 of Stern's article. As an indicator of reliability, I found about 50% more errors in my original version than I found in Boiy's table, and 8 out of 184 dates (2 of which were consequential to an initial error) were in error compared to Fatoohi et al. (4.3%); I found only one error in their table; Stern disagrees with them on four dates. For comparison, the error rate for the lunar first visibility dates predicted by PLSV compared to the Babylonian observations as given by Fatoohi et al. is 7.2%. Fatoohi et al., using their own software derived from the lunar ephemeris ELP2000-85, found that about 3.8% of the observations were early (they don't give an analysis of late observations). Stern, who used programs he considers more accurate than PLSV, found that about 8.15% of observed crescents were late or early and about 6.36% of predicted screscents wre early (none were certainly late).

The Babylonian data is incorporated in the corrected tables as follows.

Eclipses

The corrected tables have been primarily based on eclipse data in the diaries, and by optimising the match of monthly run lengths against the calculations of PD, as discussed below. Since I am not an astronomer, let alone familar with Babylonian astronomical terminology, I have not attempted to determine Julian dates through retrocalculation of lunar, planetary, sidereal or other data. However, many of the lunar visibility dates calculated by Fatoohi et al. and by Stern were based on the time given between sunset and moonrise on day 1 of the month in the Babylonian sources, or from other such data, which allows the equivalent Julian dates to be precisely determined in most cases. Where these dates are not determinable by the procedures given above, I have taken advantage of their results without calculating them independently. Lunar visibility dates that are not also eclipse dates are underlined on unbolded entries, usually in red.

The Julian date for the start of a Babylonian month can be determined with certainty for virtually any month in which an eclipse occurred, or was predicted on a Babylonian date that is either given directly or is unambiguously recoverable from surrounding dates. These months form the absolute anchors for the correlation. Observed eclipses are bolded and marked in red without underlining; predicted eclipses that were not observed, or whose observation status is uncertain, are bolded, underlined and marked in red.

Eclipses are taken from the astronomical diaries (AD) in volumes 1-III of Sachs & Hunger, the eclipse reports (ER) of volume V, the horoscopes (BH) reported by Rochberg, the eclipse observations (EO) of Huber & de Meis, and the eclipses reported in Stephenson (HER). If both lunar and solar eclipses occurred in the same month, observed eclipses are used rather than predicted eclipses.

The Babylonian dates in these reports are frequently not given explicitly in the surviving portion of the texts, or only survive in part. In the great majority of cases, however, the precise Julian dates can be recovered from the detailed eclipse description or from other astronomical data within the texts. There is, so far as I know, no reason to doubt the accuracy of these assignments. F. R. Stephenson & J. M. Steele, JHA 37 (2006) 55, is a detailed analysis of the astronomical data for a solar eclipse explicitly dated to 29 Addaru II SE 175 in BM 34034 and to 29 [lost] [x]75 SE in BM 45745, showing that the only matching eclipse in the years 750 BC to AD 100 is that of 15 April 136 BC, which is sufficient to establish an anchor point.

Since the algorithm for equating Babylonian months to lunations is fixed and well known in this period, the Julian date of an eclipse is sufficient to determine the equivalent Babylonian month and year. For this reason, I have not distinguished here between years and months which are explicitly given Babylonian dates and years or months which are only recovered by retrocalculation from the astronomical data. However, since the first day of the Babylonian month was usually determined by observation, the precise Babylonian date of an eclipse can only be estimated to a precision of +1 day unless the day number survives, or can be inferred from other data. For this reason, eclipse reports which cannot be associated with a specific day in the Babylonian month have not be used for the conversion tables.

Modern dates as given in Sachs & Hunger are also sometimes ambiguous, especially for lunar eclipses and predicted eclipses; e.g. it is not always immediately obvious whether a lunar eclipse on a certain date occurred between midnight and dawn or between sunset and midnight. Accordingly, the times have all been checked against Fred Espenak's historical eclipse tables. Any remaining ambiguities have been resolved in favour of the date that matches PD; there are very few such cases.

In order to justify the use of predicted eclipses it is necessary to determine the accuracy of the ability of the Babylonians to predict eclipses that were not actually observed. This problem is studied in J. M. Steele, Observations and Predictions of Eclipse Times by Early Astronomers (Dordrecht 2000) 68-75. Summary lists of timed predicted and observed eclipses recorded in Babylonian sources known to Steele are given by astronomical date in tables 2.4-2.8. Several eclipses are mentioned in more than one table.

Steele divided both lunar and solar eclipses into two categories, and determined the mean accuracy of the ability of the Babylonians to predict eclipses to be as follows:

In addition, Steele found two predicted lunar eclipses that simply did not occur; only one of these (-278 Nov 15) is in the Hellenistic period. A third (-225 July 17) is discussed below.

In short, the Babylonian eclipse algorithms are very reliable, though not perfect, and quite precise. The use of predicted eclipses as a reliable chronological anchor is based on these results.

As a measure of the completeness of coverage of my own research, Steele's tables were cross-checked against the eclipses found in the Astronomical Diaries (AD) or Eclipse Reports (ER) of Sachs & Hunger, in Rochberg's Babylonian Horoscopes (BH), in Stephenson's Historical Eclipse Records (HER) and in Huber & de Meis' Babylonian Eclipse Observations (EO). For all observed eclipses listed by Steele, and for most predicted eclipses, the source report was found, although quite a few of the eclipses, both predicted and observed, cannot be used for calendrical conversion because the Babylonian day number is not recoverable from the source text, as discussed above.

The following eclipse predictions given by Steele were not found in any of these sources, and represent additional potential synchronisms:

If you know where the reports of these predictions are published, please email me.

A very small number of Steele's dates appear to be in error, since Espenak indicates that no eclipses actually occurred on the date in question. In most cases the error is easily identifiable as an editorial blunder or a minor discrepancy; in one case (-122 Feb 7) a lunar eclipse prediction has been misfiled as a solar eclipse prediction. I am unable to account for the solar eclipse prediction listed by Steele for -182 Jun 7.

Three eclipses, two of them recorded in the same tablet, call for particular discussion.

The First Day of the Month

The tables reflect the general assumption that the start of the month was actually determined in this period by observation of the new crescent moon wherever possible. Recently, however, J. M. Steele in idem (ed.), Calendars and Years 133, has argued that this is not the case, but that the first day of the month was always based on the predicted date of the first crescent moon. Steele's argument is based on a comparison of observed and predicted dates for first crescents, which showed only two possible conflicts, both of which were, in Steele's view, arguably due to misreadings of characters that have only partially survived in the source text. Against this, S. Stern, JHA 39 (2008) 1 at 22 n. 30 notes that Steele relies on only about 50 examples, and that we should expect a very high correlation between observed and predicted dates if a prediction algorithm is any good.

More importantly, Stern observes that some 21 out of 331 observed new crescent moons were certainly late, while none of 110 predicted new crescent moons were late, and conversely that only 3 observed new crescent moons were certainly early, while at least 7 predicted new crescent moons were actually or most probably early. Stern holds, in my view correctly, that this difference shows that the conventional view is correct: that the start of the months were determined by a mixture of observation and prediction.

At the opposite extreme from Steele, L. Depuydt, in J. M. Steele (ed.), Calendars and Years 35 at 76 n. 43 and elsewhere has stated the view that "not even in Babylonian astronomy did first crescent visibility play a role as the beacon of computation [of the beginning of the lunar month], in spite of all kinds of indications to the contrary". His reasoning and evidence for this remarkable suggestion is as yet unpublished; based on Fatoohi's and Stern's results it seems highly unlikely to me. However, there are two weaker forms of this assertion that are more plausible and seem worth addressing. First, the calendar of the Babylonian astronomers may not have been the ordinary calendar in daily use in Babylon, and, second, months of the Babylonian calendar may not have been determined by first crescent visibility outside Babylon.

These questions can be answered, even though J. M. Steele in idem (ed.), Calendars and Years 133 at 139f. notes that the amount of non-astronomical calendrical data is very small. He cites sixth century cultic sacrifice records from Uruk as showing that 29-day months occurred in approximately the right ratio, and also letters asking for rapid notification from nearby cultic centers as to whether the month was 29 or 30 days. This establishes that the calendar months of the general populace were established by the local priests. In Babylon, these were certainly the priests of E-Sagila, which was the center of astronomical observation. The Diaries contain references to observations made at other sites, e.g. Borsippa, so in all likelihood Babylonian astronomical practice was standard at least throughout southern Mesopotamia.

To my knowledge, there is practically no evidence allowing us to decide whether the same answer applied to more distant regions in the Hellenistic period. For example, we have no data allowing us to decide whether the start of Antiochene lunar months were determined astronomically or more loosely in the usual Greek fashion. For the Achaemenid period, we have the Egyptian/Aramaic double dates of the Elephantine papyri, listed most recently by L. Depuydt, in J. M. Steele (ed.), Calendars and Years 35 at 55. Depuydt compares these to lunar conjunction; comparing the 12 unproblematic double dates to first visibility using PLSV, we get an accuracy of slightly less than 50%, comparable to the accuracy seen in Egyptian lunar dates and much less than the 90%+ accuracy of Babylonian dates. This suggests that months were determined using ad hoc techniques at sites that were too distant from an astronomical center to use ther results of astronomical techniques.

Month lengths

The length of a Babylonian month is usually determined from their convenient habit of recording whether a named month began after the 29th or the 30th day of the preceding month. Sachs and Hunger frequently provide summaries of each diary of the type "VI 0 = V 30", i.e. that the day before the start of month VI (Ululu) was day 30 of month V (Abu). These summaries must be used with care, since they are sometimes provided even though the surviving portion of the corresponding diary entry does not explicitly give this data. Once I realised this problem, I relied only on the diary translations.

Month lengths are not always recorded when naming a month, but they are standard in the astronomical diaries (if not always recoverable) and are common in the horoscopes and the lunar tables, and in the "lunarrr six" portion of the goal year texts. The diaries, goal year texts and horoscopes are regarded as primary sources, either directly reflecting source observations (horoscopes) or being the official redaction of the source observations (diaries and goal year texts). Sequences based on these month lengths are shown in red. Lunar tables are assumed to be derived from diaries, and hence are considered secondary sources. Sequences based on these month lengths, that are not also covered in part by diaries or horoscopes, are shown in green.

Clearly, an entry for day 29 in the diaries without a day 30 is not sufficient to assure a restoration of a 29-day month. Less obviously, a standalone entry for day 30 in the diaries is not sufficient to assure a restoration of a 30-day month, since the last day of the month could be called day 30 retrospectively, regardless of its length. In theory, however, it is possible to recover the lengths of 30 day months from the diaries if they record entries for days 29 and 30. I have not checked the diaries for this phenomenon. Note that this concern does not apply to contemporary documents such as letters or contracts; for example, the 30-day length of Aiaru 219 SE = 93 BC was recovered this way.

Month lengths show the difference between the start date of two consecutive months. Thus, the month preceding the first named month of a sequence must also be considered part of the sequence. The first month of a sequence, unnamed, is shown in brown (unless it contains an eclipse).

Month lengths can be correlated against the corresponding month lengths in PD. However this does not by itself allow us to fix the absolute dates of the months, even though the longer the sequence the likelier it is that the highest correlations do in fact represent absolute dates. The highest reliability is obtained if a sequence of months includes one or more months in which eclipses are observed.

Month-length adjustments

A basic assumption of the corrected table is that the standard correlations are not significantly in error, i.e. that the true start dates of Babylonian months do not differ from PD by more than a day, early or late, and that any such divergencies are corrected by a compensating divergence, usually in the next month but in any case within a very few months. Many of the sequences available in the source data show divergencies that are self-corrected in precisely this fashion.

Where a sequence of month lengths ends with a date that diverges from PD I have usually chosen the next available month in PD after the end of the sequence that would allow the appropriate compensation (29->30 or 30->29 days as appropriate). This is frequently an arbitrary choice, though, since first-cresent sightings could easily be missed it is likely that a 29 day month that became a 30 day month due to a missed sighting will be followed by a compensating 29 day month. Occasionally, eclipse data, or a long run of month lengths matching PD with a single early divergence, shows that a compensation is required before the start of the contemporary data. These adjustments have not been checked against modern lunar tables for plausibility. In essence, they were chosen to give the minimum possible divergence from PD. For these reasons, the merging of recorded month sequences with PD should be regarded as preliminary only.

There are three cases where this strategy was not possible. All involve exceptionally long runs in the source data surviving from Lunar table BM32327 = LT39. When complete, this table covered 32 years, from SE 62 to 93.

Source conflicts

The following source conflicts, indicated in magenta, were detected in preparing the corrected table.

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