A comparison of a text found on the back of certain votive cubit rods with the hieroglyphs used as numerals in Ptolemaic...
Originally published in GM 192 (2003), 61−66.
Cryptic numerals on cubit rods Gyula Priskin A comparison of a text found on the back of certain votive cubit rods with the hieroglyphs used as numerals in Ptolemaic inscriptions reveals that the cryptic notation of numbers was already in use at the beginning of the Third Intermediate Period.
Introduction On one type of cubit rods that have come down to us from ancient Egypt we find numerous inscriptions. These artefacts, the earliest examples of which are dated to the New Kingdom, are called votive cubit rods, and are thought to have belonged to temple inventories as some sort of ceremonial objects.1 That these rods were not used in actual measurement is strongly suggested in the first place by the fact that they are all made of stone, while the functional rods, as far as we can judge from surviving specimens, were without exception fashioned from wood. 2 The nature of the inscriptions also makes us think that the votive rods had symbolic, rather than practical significance. A text inscribed on the top side, for example, tells us that what is written on these rods belongs to the magical lore of Thoth. Indeed, the other texts record the physical extentions of Egypt, the height of the flooding Nile at different locations, the variations of the land measure according to the nomes, and other similar information. Pierre Lacau and Henri Chevrier were the first to point out that many of these texts are of the same vein as those found in the White Chapel of Sesostris I (ca. 2000 BC), 3 and are somehow connected to the jubilee of the king’s reign, the Hb-sd festival. While the majority of the inscriptions on the votive cubit rods have been clarified and translated by Adelheid Schlott-Schwab,4 some texts pose sizeable difficulties of interpretation and are still to be properly understood. Here I attempt to shed some light on a piece of text that has so far eluded explanation completely. The text On the back of the cubit rods of Sheshonk I (ca. 950 BC) and Nectanebos II (ca. 350 BC) is preserved an enigmatic text, occupying four fingers (from the 16th to the 19th) and belonging to Text j in Schlott-Schwab’s categorization (see Fig. 1). A fragment displaying about one and a half fingers from the same text is also found on the rod that is registered in the Cairo catalogue by the number @ . .5 Since, however, the rods of 1
The most extensive study of votive cubit rods is found in A. Schlott-Schwab, Die Ausmasse Ägyptens nach altägyptischen Texten (Harrassowitz, Wiesbaden, 1981). See also S. Gabra, MDAIK 24 (1969), 129-135; A. Schwab-Schlott, MDAIK 28 (1972), 109-113; A-P. Zivie, RdÉ 29 (1977), 215-223 and BIFAO 71 (1972), 181188. 2 For these rods, see R. Lepsius, Die alt-aegyptische Elle und ihre Entheilung (Berlin, 1865), reprinted with an English translation by J. Degreef as The Ancient Egyptian Cubit and Its Subdivision (Museum Bookshop, London, 2001; edited by M. St. John), and M. St. John, Three Cubits Compared (Estoi, 2000). 3 P. Lacau & H. Chevrier, Une chapelle de Sésostris Ier à Karnak (Institut Français d’Archéologie Orientale, Cairo, 1956), pp. 217-248. 4 Schlott-Schwab, Ausmasse, pp. 30-65. 5 Schwab-Schlott, MDAIK 28, Tafel XXVI.
Originally published in GM 192 (2003), 61−66.
Figure 1 Fragments of votive rods of Sheshonk I (above) and Nectanebos II (below) displaying Text j1 [= Tafeln XIV and XIX in Schlott-Schwab Ausmasse]. On Sheshonk I’s rod the inscriptions run uniquely from right to left.
Sheshonk I and Nectanebos II are also fragmentary, we do not know if the four fingers under examination present the whole body of the text (I propose to call it Text j1), or it continues on the lost parts of the cubits. The fragmented signs in the 20th finger on Nectanebos II’s rod may be interpreted to suggest that the text does not terminate in the 19th finger but runs further, or alternatively, begins earlier on the right. To decide the direction of writing, the face of the hieroglyphs is not authoritative here, I think, because they may be deliberately reversed. The structure of the text is very simple: it is divided into nine groups – each consisting of three hieroglyphs – that are distributed in a 2–2–3–2 pattern as regards the fingers. The first two glyphs in each group are the same, , while the third one is different each time. For we may tentatively offer a phonetic value wnmD, especially on the basis of the hieroglyphic group in the 19th finger, which may form the first lexical unit of the text. The meaning of wnmD remains obscure, but there may be a parallel between this phrase and the equally puzzling expression wnhr that appears in Text a on the top side of the cubit rods,6 in the context ‘the power (mastery?) of the wnhr of the magic spells of Thoth’. As for the nine hieroglyphs constituting the third, varying element within each group, they almost certainly denote numbers, because for six of them we find exact 6
Schlott-Schwab, Ausmasse, p. 40.
Originally published in GM 192 (2003), 61−66.
matches in Ptolemaic texts at Dendera, Edfu, Esna and Kom Ombo used as cryptic numerals (see Table 1), while for the remaining three more or less plausible explanations can be presented why they signified numbers. In the light of this, it is all the more likely that the second hieroglyph should not be read phonetically at all, but has the numerical value 10; at present, however, no definite solution can be put forward on this point. If does read 10, then we have a list of numbers from 11 to 19. The traces ( and ) in the 20th finger on Nectanebos’ rod seem to support this interpretation, because they may be the remnants of and , and thus should perhaps read wn 9 and wn 10, the numbers preceding 11 in the list. Still, the meaning of wn remains unclear.
Cubit rods
Ptolemaic temples
Numeral
–
1 2 3 4 5
,
–
(6)
–
(7) 8
,
9
Table 1 Exact matches between signs in Text j1 on votive cubit rods and hieroglyphs used as numbers in Ptolemaic texts. The numerals in parentheses are uncertain.7
Possible origins of the numerical values of the signs I will in this section offer explanations for the numerical values of all the signs in Table 1, plus one more not featured in Text j1, but probably also having something to do in its origins with the cubit rods. Also, I will try to highlight points of connection between the signs for which no exact matches are found in Ptolemaic texts and the signs used with the same numerical value at that later time. While I believe that the explanations below – be they my own or put forward by others – are reasonable, and in certain cases very obvious, they also sometimes tend to be much speculative, so the Egyptian priests may have had entirely different ideas in mind when they selected a particular hieroglyph to be used in the cryptic writing of numbers.
7
For the numerals 2, 3, 4, 5 and 8 in Ptolemaic inscriptions see C. De Wit, CdÉ 74, (1962), 272-290 and S. Cauville, BIFAO 90 (1990), 83-114. For 9, A. Gutbub, Kôm Ombo vol. 1 (Institut Français d’Archéologie Orientale, Cairo, 1995) pp. 407-422.
Originally published in GM 192 (2003), 61−66.
=1 This may come from a pun between watt ‘uraeus’ and wa ‘one’, the first being replaced by the writing Dt ‘cobra’. 8 Perhaps an equally plausible derivation is from , a variant of . In this case, a parallel in Ptolemaic texts may be = 1, with a possible original . It is also a possibility, however, that was exclusively used to denote 11. =2 In every probability from the simple fact that it shows the two branches of a horn, as suggested by the variant .9 =3 It shows the three bAw birds. =4 The top part of this hieroglyph depicts an open-fronted shrine used at festivals, which was in all probability supported by four columns, 10 perhaps representing the four points of the compass. For the idea of four columns, we may cite here the writing ifdw sxnw ‘the four supports of the sky’. In Ptolemaic texts, the variant showing the temporary pavilion erected at the Hb-sd also occurs. This was rarely written , containing the phonetic element ifd ‘four’ or ‘square’.11 =5 The star has five rays.12 Horapollon says, however, that for the Egyptians the star signified the number 5 because there were five planets to ensure the order of the universe.13 It has also been conjectured that a pun between dwA ‘adore in the morning’ and diw ‘five’ lies behind the identification of the star with 5.14 , = 6? Originally phon. rcw perhaps came from a paronomasia with crcw ‘six’. Then it must be supposed that is a corrupt rendering of the other sign, although chronologically appears earlier on Sheshonk I’s rod. Such a mistake was perhaps easy to make because of an identification between ¦A-mri and Ptolemaic 15 snwt ‘Egypt’, the latter coming from the expression snwt ‘the 6th day of the lunar month’.
8
For general lexical information in this section I have drawn on the standard works of A. Gardiner, Egyptian Grammar (Griffith Institute, Oxford, 1994) and R. O. Faulkner, A Concise Dictionary of Middle Egyptian (Griffith Institute, Oxford, 1988). 9 H. W. Fairman, BIFAO 43 (1945), 51-138, 114 n. 3. 10 See the reconstruction of L. Borchardt, reproduced in B. Kemp, Ancient Egypt: Anatomy of a Civilization (Routledge, London, 1991), p. 96. 11 Fairman, BIFAO 43, 106, n. 2. 12 Fairman, BIFAO 43, 103 & 114. 13 Horapollon I. 13/c. See B. van de Walle & J. Vergote, CdÉ 35 (1943), 38-89; 54. 14 van de Walle & Vergote, CdÉ 35, 54; K. Sethe, ZÄS 47 (1910), 1-41; 17 15 cf. Fairman, BIFAO 43, 77, n. 1.
Originally published in GM 192 (2003), 61−66.
= 7? This sign eludes easy explanation. In Ptolemaic texts 7 was generally written by the human head , in all likelihood on account of the fact that there are seven orifices on it.16 A rare use of the head with the phonetic value anx was in the expression = 17 anx ntr nfr ‘long live the good god’, and on this basis perhaps a connection can be sought with anx ‘mirror’. (For the problems posed by the last two signs, see further below.) =8 This must come from one of Thoth’s epithets, ©Hwty nb 8 ‘Thoth, Lord of the Eight’, which in turn goes back to the name of his city, called #mnw ‘the city of 18 the eight’. , =9 This must derive from psDt ‘the company of nine gods, ennead’. Its equivalent at Dendera and Edfu is psD ‘shine’.19 = 10 This sign – @r ‘Horus’ – used in Ptolemaic texts does not appear in Text j1, but is featured in the list of gods on the top side of the rods (Text b), as the tenth god from the right following the deities of the ennead. Its numerical value may have therefore derived from this position.20 The signs in the 17th finger As far as the determination of the numerical values of the hieroglyphs in Table 1 is concerned, we only encounter difficulties in this finger, because exceptionally three groups are written in this rubric, and only for one of the third signs do we find a Ptolemaic equivalent ( = 5). Also, it seems that the order of the signs is mixed up, because the star should be placed at the top. Bearing in mind the overwhelming evidence that the star equalled 5 in Ptolemaic times, I would find it difficult to accept that we should read the signs as they are – , = 5, = 6, = 7 – and should contemplate a diachronic shift of meaning by which = 6 became = 5. Then the only ambiguity we are still left with is whether which one of the two later disused signs equalled six and which one stood for seven. I suppose that only , and have been interchanged, and the third sign is at its proper place. This is perhaps the simplest solution to the problem, although the possibility that equals 6 and , stands for 7 may not be ruled out categorically. Conclusion The purpose of the text we have examined therefore is in all probability to record the cryptic numerals from 1 to 9, or alternatively, the numbers from 11 to 19, beginning in 16
Fairman, BIFAO 43, 103. Fairman, BIFAO 43, 129. 18 Fairman, BIFAO 43, 105. 19 Fairman, BIFAO 43, 102. 20 cf. Fairman, BIFAO 43, 106, n. 2. 17
Originally published in GM 192 (2003), 61−66.
the 19th finger and ending in the 16th. This means that Text j1 is in fact a textual unit that makes sense on its own, although it may belong to a longer inscription the other part of which has been lost. The cryptographic numbers listed in these four fingers have been invented by priestly speculation – as the later Ptolemaic texts suggest – for use in cultically charged inscriptions. Now we must acknowledge, however, that the earliest example of this cryptic writing is found on Sheshonk I’s votive cubit rod and is dated consequently around 950 BC, some six hundred years before the Ptolemaic era. Given that votive cubit rods were beyond doubt made in the New Kingdom – though unfortunately none of the fragments from that period preserves Text j1 – the origins of this form of notation possibly go back even further in time.
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