Movable wAgj and numeration of lunar days in Ancient Egypt

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Oles Honchar Dnipro National University Dnipro

Department of World History

Movable wAgj and numeration of lunar days in Ancient Egypt

A. Puchkov, PhD Student

Annotation

The ancient Egyptians celebrated the wAgj feast, an integral part of the Osirian cult. Data from the Illahun archive evidence that there were two instances of it: a fixed one, which fell on a specific civil date, and a movable one associated with a specific phase of the moon. There is disagreement about the lunar day and month on which the movable feast took place. The aggregation of the Illahun lunar dates into a `date net' indicates that the disagreement is due both to peculiarities of the datasets of previous studies and to the incorrect numeration of lunar days in Parker's list, which has been the standard for more than 70 years. Analysis of the lists of lunar days from the Ptolemaic Period also reveals the erroneous position of one of the days; when it is set to the proper position, the symmetry of the phases relative to the day of full moon improves. Based on the corrected numeration of lunar days, it is concluded that the movable wAgj in the original list fell on the 17th day of the second month after the emergence of Sopdet (the heliacal rising of Sirius in modern terms). Further research is needed to examine the effect of the proposed correction on the chronology of the Middle Kingdom.

Keywords: movable wAgj feast, wAgj dates, lunar month, lunar days numeration, moon, phases, Sirius, heliacal rising

Анотація

О.В. Пучков. Рухомий wAgj і нумерація місячних діб у стародавньому Єгипті

Стародавні єгиптяни відзначали свято wAgj, невід'ємну частину культу Осіріса. Дані з архіву Іллахун свідчать про те, що існувало два його різновиди: фіксоване свято, яке припадало на конкретну цивільну дату, і рухоме, пов'язане з певною фазою Місяця. Існує розбіжність щодо доби та місяця, в які відбувалося рухоме свято. Агрегація місячних дат Іллахуна в “мережу дат” вказує на те, що розбіжність пов'язана як з особливостями наборів даних попередніх досліджень, так і з неправильною нумерацією місячних діб у списку Паркера, яка була стандартом понад 70 років. Аналіз списків місячних діб періоду Птолемеїв також виявляє помилкову позицію однієї з діб; при правильному її положенні покращується симетрія фаз відносно фази повного Місяця. На підставі виправленої нумерації місячних діб зроблено висновок, що рухомий wAgj в оригінальному списку припадав на 17-у добу другого місяця після появи Сопдет (геліакічного сходу Сіріуса за сучасними термінами). Потрібні подальші дослідження, щоб перевірити вплив запропонованої корекції на хронологію Середнього царства.

Ключові слова: рухомe свято wAgj, wAgj дати, нумерація місячних діб, Місяць, фази, Сіріус, геліакальний схід

The earliest attestations for wAgj occur in feast lists from private tombs of the 4^th Dynasty. Two different instances¹ of it are recorded in the Illahun archive: a civil one, fixed on I Axt 17/18²; and a lunar one, which fell on different civil days; therefore, it is often called `movable'. The lunar wAgj follows prt Spdt in the Middle Kingdom lists, and its dates were calculated by the Egyptians according to certain rules that need to be clarified.

Days of the lunar month (LM) had names, some of which denote the phase of the moon: Abd - `new crescent day'; dnjt - `first/last quarter day'; while some others contain a numeral corresponding to the ordinal number of the lunar day (LD): snt - `6<sup>th</sup> day'; smdt/mDdj-nt<sup>3</sup> - `15^th day', `day of full moon' [Parker 1950, 11-12, §36-41].

The movable wAgj dates are not accompanied by information about the corresponding lunar day, but pBerlin 10016 indicates that the feast took place two days after the full moon (2-nw n mDdj-nt) [Krauss 2006b, 425], and pBerlin 10165 reports a three-day interval between these events (II Smw 19 and II Smw 22, respectively) [Luft 1992, 101; Krauss 1994a, 8; Depuydt 2000, 177]. Thus, in the first case, the feast falls on LD 17 (= 15 + 2), and in the second, on LD 18 (= 15 + 3).

Due to the scarcity of documentary evidence, there is no consensus about the day of the movable wAgj among scholars: Krauss [1998, 53; 2006, 425; 2021, 95] believes that the feast falls on LD 17 (two days difference from the full moon); Luft's [1992, 201- 202] `date net' indicates that it was LD 18 (whereas the full moon unexpectedly falls on LD 16; two days difference); Depuydt [2000, 177] and Spalinger [1994, 49; 2013, 620] accept LD 18 (three days difference) following Luft.

The method used by Luft [1992, 201; 1994, 40-41] to find the lunar day number is to calculate the distance between LD 1, psD(n)tjw, and the sought phase/event. The distance method sounds good, but three date selection rules should be applied to obtain accurate results:

1. an original date of the phase from the document should be used, not a calculated one, since the calculation assumes a known fixed interval between phases, and this is not always true;

2. a document with conflicting dates (a discrepancy of two or more days) should be excluded;

3. dates of the same phase/event must be consistent within the acceptable error margin (less than one day), i.e., they must correspond approximately to the same lunar day.

Four sets of dates need to be checked:

I. psD(n)tjw. The event is mentioned in pBerlin 10090, pBerlin 10056 (presumably as the end of a month interval [6 times]) and 10056a, pBerlin 10006 (presumably as the end of a month interval). The dates from pBerlin 10003, pBerlin 10248 and pBerlin 10282 used by Luft to calculate psD(n)tjw are Abd originally and therefore they cannot be used (rule 1). There are no significant discrepancies in the dates. The dataset passes consistency check (Table 1).

Table 1

PsD(n)tjw dataset consistency check

Legend: ДLM - difference in lunar months; ДLM = ДD [diff. in days] : 29.53059 D/LM. Dev. - deviation in days from the expected same phase (row). Dev. = (ДLM - Round(ДLM)) * 29.53059 D/LM. Avg. dev. - adjustment value in days to bring the examined date (col.) into line with other dates (negative/positive = earlier/later dates).

II. Abd. The event is mentioned⁸ in pBerlin 10003, pBerlin 10248, pBerlin 10056 (presumably as the start of a month interval [6 times]; see n. 6), pBerlin 10006 (presumably as the start of a month interval), pBerlin 10282a and 10282b. The Abd - smdt pair from pBerlin 10282b shows significant inconsistency and should be excluded (rule 2). The dataset passes consistency check (Table 2).

Table 2

Abd dataset consistency check

III. smdt. The event is mentioned¹⁰ in pBerlin 10003, pBerlin 10165, pBerlin 10016, pBerlin 10282a and 10282b. The date from pBerlin 10282b should be excluded (see Abd). The consistency check (Table 3) indicates that the date from pBerlin 10165 needs to be corrected (II Smw 19 -> II Smw 20).

Table 3

Smdt dataset consistency check

IV. wAgj. The event is mentioned in pBerlin 10165, pBerlin 10016, pCairo 58065. There are no significant discrepancies in the dates. The dataset passes consistency check (Table 4).

Table 4

WAgj dataset consistency check

The distance method can now be applied to the selected dates to calculate the average LD for Abd, smdt, wAgj, if psD(n)tjw is LD 1 (see Table 5).

Table 5

Average LD calculation for Abd, smdt and wAgj, if psD(n)tjw is taken as LD

1. Legend: ДD - difference in days;

ДLM - difference in lunar months;

ДLM = ДD:29.53059 D/LM;

LD - lunar day number.

The Abd - psD(n)tjw pairs from pBerlin 10056 and pBerlin 10006 have been excluded from the calculation to achieve greater accuracy.

The results obtained explain the aforementioned contradictions: firstly, the three-day interval between smdt and wAgj from pBerlin 10165 turns out to be inconsistent with the rest of the data; secondly, as can be seen from Table 5, for all four psD(n)tjw dates, taken as LD 1, the same pattern of relative positions of Abd / smdt / wAgj (see `Avg. LD' rows) is observed: Abd / Abd + 14 / Abd + 16, where Abd varies from 1.36 to 1.96, therefore the full moon occurs at both LD 15 and LD 16, and wAgj two days after it, respectively. The discovered pattern indicates that if psD(n)tjw is taken as the reference point, then the same phase is distributed between two adjacent days of the lunar cycle, and if Abd is the reference point, then the phase falls on the same day. How to explain such a distribution for the standard psD(n)tjw = LD 1?

It is necessary to remember that Parker's [1950, 11-12, §36] list of days of the lunar month consists of 30 names, one for each lunar day. However, we know that a synodic month averages 29.53059 days (varies from 29.25 to 29.83 days), that is, if from the beginning of the lunar month the days are sequentially called by names from the list, then after two or three months a loss of synchronization with actual phases will be found. Therefore, in order to maintain synchronicity, the Egyptians had to skip one day in some¹³ months. What day could they skip? It is easy to demonstrate that this was one of the days of invisibility of the moon, prt Mn and psD(n)tjw, namely the second of them.

If the observer does not know exactly when the new lunar month will begin, he must turn to observations. Uncertainty regarding the phase exists only when the moon is not visible, and therefore, without calculations, it is not known exactly when a new crescent will appear - today or a day later. Thus, the first appearance of a new crescent is an obvious synchronization point, and in order for the lunar month to correspond to reality, the Egyptians had to use a simple rule: if today is the turn of the second day of the moon's invisibility, psD(n)tjw, but the new crescent has already appeared, psD(n)tjw is skipped, and the current day becomes Abd (and possibly vice versa). With this scheme, the new crescent always fell on Abd; psD(n)tjw functioned as an intercalary day, and its top position in the list of lunar days can be explained by the fact that the Egyptians regarded intercalary days as Hrjw days - `which are upon', `which are higher' [Erman and Grapow 1929 (Wb. III), 133] (for example, the epagomenal days of the civil calendar were called Hrjw-rnpt, `those over the year').

Obviously, the numbering of the days of the lunar month, starting from the intercalary day, does not make sense, while the numbering from the first day of the new crescent visibility, Abd, is, on the contrary, natural. Moreover, this numbering explains the temple service month intervals and the absence of psD(n)tjw in early private feast lists [Krauss 2006a, 386]; the month-feast, Abd, turns out to coincide with the real beginning of the corresponding month, and not with its second (or even third) day; the other phases are not delayed relative to the corresponding days, as in Parker's scheme [1950, 14, Fig. 10- 11; 3^rd day]. In the light of the foregoing, the sequence of days in Parker's list should not begin with number one, but with an unnumbered intercalary (Table 6).

Continuing the analysis of Parker's list, it should be noted that two instances of the quarter, dnjt (LD 7, LD 23), are separated by an overly long interval, 16 days, instead of the expected average interval of 29.53059 : 2 = 14.765 ? 15 days; and two instances of the unknown phase, sjAw (LD 14, LD 17), are not symmetrical with respect to the full moon: they are one and two days apart from it. This effect can only be caused by a superfluous day within the ranges of these two pairs, namely, the incorrect position of LD 16, mspr 2-nw, which got there by mistake. The list has an element with a similar name, mspr, so putting them side by side results in a sequence of mspr, mspr 2-nw being the first and second `rib' days. The corrected list of lunar days is as follows (Table 6, right side):

Table 6

New proposal for the sequence and numeration of lunar days

Differences from Parker's numeration are in square brackets.

Now mspr is accompanied by mspr 2-nw, creating the mspr-sequence; smdt is symmetrically surrounded by two sjAw, in which it is easy to recognize the preand postfull moon phases; the interval between quarters is also normalized²². If we recalculate Table 5, assuming Abd = LD 1, then wAgj falls on LD 17 (16.85); psD(n)tjw - on LD 30 (29.91); and smdt/mDdj-nt - on LD 15 (14.96), as indicated by its name. civil cult holiday ancient egyptian wagj moon sirius

As for the lunar month in which the movable wAgj was celebrated, data from the Illahun archive show that this feast took place approximately 60 days after the emergence of Sopdet (Table 7), that is, in the second (not in the first or third) lunar month after the heliacal rising.

Table 7

Movable wAgj dates from the Illahun archive

The prt Spdt dates (Memphis; arc. vis. 9°; 1460 y.) are given as ranges due to different estimates of reign dates. The interval between the lunar wAgj and prt Spdt averages 60 days.

Summarizing the above, the following conclusions can be drawn:

– it is necessary to return to the earlier views²⁵ that the original lunar month began with Abd;

– psD(n)tjw was an unnumbered intercalary day and headed the lunar month due to the fact that intercalary days were regarded by the Egyptians as Hrjw days, `which are upon/higher [time unit]';

– the movable wAgj in the Middle Kingdom and earlier took place on `day of the moon', jaH = LD 17, in the second lunar month after the heliacal rising of Sirius;

– the list of lunar days was corrupted sometime after the Middle Kingdom: mspr 2-nw, presumably as a result of the omission, was moved down to the position in which it appears in the lists of the Ptolemaic temples.

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