Abstract
The two pyramids built during the Old Kingdom by the Fourth Dynasty King Sneferu at Dahshur are usually considered as two consecutive projects, the second – that of the Red Pyramid – being generated by a presumably failure of the first, the Bent Pyramid. In the present paper, we show that the archaeological proofs of such a scenario are far from obvious and that, on the contrary, a series of architectural, topographical, epigraphic, and astronomical hints point to a unitary project probably conceived from the very beginning in terms of the two pyramids and their annexes. Altogether the two pyramids are thus shown to form a conceptual, sacred landscape associated with the power of the Pharaoh and his afterlife.
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References
1.
This idea was first put in print by the first researcher to conduct serious investigation at Dahshur necropolis using modern methodology, the Egyptian Egyptologist Ahmed Fakhry. See A. Fakhry, The Monuments of Sneferu at Dahshur (Cairo: General Organization for Government Print Offices, 1959). The idea has since then been repeated in academic sources and popular literature without much further questioning. See, for example, I.E.S. Edwards, The Pyramids of Egypt , 3rd ed. (Harmondsworth: Penguin, 1993); M. Lehner, The Complete Pyramids (London: Thames & Hudson, 1997); M. Verner, The Pyramids: The Mystery, Culture, and Science of Egypt’s Great Monuments (New York: Grove Press, 2002). For a contrary opinion, namely, that the change of slope was not caused by structural problems in the Bent Pyramid, see A. Varille, A propos des pyramides de Snefrou (Cairo: IFAO, 1947), pp. 7–8, who wrote, “Tout d’abord la pyramide à été prévue, des le débout des travaux, pour avoir deux pentes. Tout y est l’expression d’une dualité.” More recently see, J.M. Parra, “Houni et Snéfrou: les pyramides de Meïdoum et Dahchour,” Göttinger Miszellen , 154, 1996, pp. 77–91; J.M. Parra, Historia de las pirámides de Egipto (Madrid: Editorial Complutense, 1997), pp. 114–5, for a similar opinion.
2.
G. Magli, Architecture, Astronomy and Sacred Landscape in Ancient Egypt (Cambridge: Cambridge University Press, 2013), pp. 57–71.
3.
As poetically expressed by R. Kapuściński, Imperium (Warsaw: Czytelnik, 1993).
4.
Egyptian chronology for the Old Kingdom is highly disputed. See, for example, J.A. Belmonte and M. Shaltout (eds), In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), Appendix I, pp. 339–46. The date selected, 2575 b.c. , are close to the ascension of Sneferu according to E. Hornung, R. Krauss and D.A. Warburton (eds), Ancient Egyptian Chronology (Handbuch der Orientalistik, 83; Berlin: Brill, 2006), who proposed the intervals 2568–2535 to 2543–2510 b.c. (the earliest ascension date at 2578 b.c. ) for his reign – a low chronology. Other dates published in the literature are a high chronology (2613–2589 b.c. ), according to I. Shaw (ed.), The Oxford History of Ancient Egypt (Oxford: Oxford University Press, 2000), or a very low one (2520–2470 b.c. ), according to A.Dodson and D.Hilton, The Complete Royal Families of Ancient Egypt (London: AUC Press, 2004). Another often referred to chronology for Sneferu is 2639/2604 to 2589/2554 b.c. according to J.Von Beckerath, Chronologie des pharaonischen Ägypten (Mainz: Philipp von Zabern, 1997). More recently, C. Bronk Ramsey, M.W. Dee, J.M. Rowland,T.F.G. Higham, S.A. Harris, F. Brock, A. Quiles, E.M. Wild, E.S. Marcus and A.J. Shortland, “Radiocarbon-based chronology for dynastic Egypt,” Science , 328, 2010, pp. 1554–7, have presented a Bayesian approach to the problem of radiocarbon dates showing that Ian Shaw’s chronology is perhaps the most realistic. However, they have used certain circular arguments and a poor statistics for the data of the Old Kingdom: see J.A. Belmonte, Pirámides, templos y estrellas: arqueología y astronomía en el Egipto antiguo (Barcelona: Crítica, 2012), pp. 332–5.
5.
For a discussion on the length of Sneferu’s reign, see: R. Krauss, “The length of Sneferu’s reign and how long it took to build the ‘red pyramid’,” Journal of Egyptian Archaeology , 82, 1996, pp. 43–50. The highest preserved date is the year of the 24th occasion (of the cattle count), Tnt or “tenet” for the ancient Egyptians. Prior to Sneferu’s reign cattle counts were handled once every 2 years, with a year after (the cattle count) between them. Reign lengths have often been calculated doubling the highest Tnt, accordingly. However, J.S. Nolan, “The original lunar calendar and cattle counts in Old Kingdom Egypt,” Aegyptiaca Helvetica , 17, 2003, pp. 75–97, has proven that this was not the case from the reign of Sneferu onwards, suggesting that there was one “year after” for an average of 2.83 years of (nearly a proportion 3:1). The 24th Tnt would then correspond to year 31 with a pessimistic margin of a couple of years.
6.
A. Ćwiek, “Date and Function of the So-Called Minor Step Pyramids,” Göttinger Miszellen , clxii, 1998, pp. 39–52. See also, A. Dobson, “The Multiple Pyramids of Snefru,” in B. Manley (ed.), The Seventy Great Mysteries of Ancient Egypt (London: Thames & Hudson, 2003), pp. 57–60. More recently, see R. Stadelmann, “Snofru: Builder and Unique Creator of the Pyramids of Seila and Meidum,” in O. El-Aguizy and M. Sherif Ali (eds), Echoes of Eternity: Studies Presented to Gaballa Aly Gaballa (Wiesbaden: Harrassowitz, 2010), pp. 31–8. For the recently excavated pyramid at Edfu (El Ghoneimiya), see: G. Marouard and H. Papazian, “The Edfu Pyramid Project: Recent Investigation at the Last Provincial Step Pyramid,” The Oriental Institute News and Notes , 213, 2012, pp. 3–9. Additionally, F.L. Borrego Gallardo, “Lord of Maat: Innovation and Change of the Egyptian Divine Kingship Under the Reign of Snefru,” ARYS: Antigüedad, Religiones y Sociedades , 12, 2014, in press, includes the most recent discussion on the topic.
7.
J.A. Belmonte, M. Shaltout and M. Fekri, “Astronomy and Landscape in Ancient Egypt: Challenging the Enigma of the Minor Step Pyramids,” Papers on Ancient Egypt (TdE) , 4, 2005, pp. 7–18.
8.
See Belmonte, op. cit. (ref. 4), Table 5.1. Several later pyramids were built with designs including very simple mathematical relationships such as a ratio 14:11, with a slope of c . 51°50½′ – Sneferu’s final project at Meidum, Khufu’s Great Pyramid or Niuserre’s one at Abusir – or the very comfortable Pythagorean triangle 3-4-5, slope of 53°7′48″ – Khaefre’s pyramid and the majority of Sixth Dynasty pyramids.
9.
D.A. Cintron, 2003, “A New Angle on Sneferu’s Pyramids,” who has argued that “the pyramid complex of Dahshur was designed as a unified whole from the beginning as a dual pyramid necropolis and that this design was carried out exactly to Sneferu’s satisfaction.” This paper is the unpublished outcome of a presentation at the 54th Annual Meeting of the American Research Centre of Egypt, in Cairo in 2003, <http://www.cintronics.com/pdffiles/SneferuPyramids.pdf>.
10.
For an earlier discussion on this topic, see A. Fakhry, The Pyramids (Chicago/London: University of Chicago Press, 1961), p. 73. For a detailed argument, see R. Stadelmann, “Snofru und die Pyramiden von Meidum und Dahshur,” Mitteilungen des Deutschen Archäologischen Instituts , 36, 1980, pp. 437–49.
11.
For a recent analysis of the Palermo Stone, see T.A.H. Wilkinson, Royal Annals of Ancient Egypt: The Palermo Stone and Its Associated Fragments (New York/London: Kegan Paul, 2000). For the Pyramid Texts, a classical work is R.O.Faulkner, The Ancient Egyptian Pyramid Texts (Oxford: Oxford University Press, 1969). For a more recent work on the topic, see J.P.Allen and P.Der Manuelian, The Ancient Egyptian Pyramid Texts: Writings from the Ancient World (Ann Arbor: Society of Biblical Literature, 2005).
12.
… the turning point in pyramid masonry came at the beginning of the Fourth Dynasty when at the Bent Pyramid the courses of the core were set horizontally for the first time and the casing blocks were set nearly so, …
D. Arnold, Building in Egypt: Pharaonic Stone Masonry (Oxford/New York: Oxford University Press, 1991), p. 159.
13.
Fakhry, op. cit. (ref. 1). Also relevant is Fakhry, op. cit. (ref. 10), p. 97, who was convinced that the Bent Pyramid – the upper chamber at the end of the western corridor – was the actual burial place of Sneferu.
14.
See the discussion on the tenet (Tnt) in ref. 5.
15.
See R. Stadelmann, Die ägyptischen Pyramiden. vom Ziegelbau zum Weltwunder (Mainz: Philipp von Zabern, 1985), and, more recently, R. Stadelmann, “Inscriptional Evidence for the Reign of Sneferu at Dahshur,” in H. Vymazalová and M. Bárta (eds), Chronology and Archaeology in Ancient Egypt : The Third Millennium b.c . (Prague: Czech Institute of Egyptology, 2008), pp. 104–10. See also Krauss, op. cit. (ref. 5).
16.
Once finished, this chamber was not aired and the more than probable problem generated by rarefied air and extreme heat was perhaps on the origin of the airshafts at Sneferu’s son Great Pyramid at Giza. See G. Magli and J.A. Belmonte, “Pyramids and Star, Facts, Conjectures and starry tales,” in J.A.Belmonte and M.Shaltout (eds), In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), pp. 305–22. For a more recent analysis, see M. Haase, “Dienten die oberen Schächte in der Cheops-Pyramide zur Belüftung der Grabkammer?,” in V.G. Callender, L. Bareš, M. Bárta, J. Janák and J. Krejčí (eds), Times, Signs and Pyramids: Studies in Honour of Miroslav Verner on the Occasion of his Seventieth Birthday (Prague: Faculty of Arts, Charles University in Prague, 2011), pp. 135–56.
17.
Fakhry, op. cit. (ref. 1) elaborated this idea, once the Bent Pyramid was clearly assigned to Sneferu. However, when reviewing this paper, César González-García has pointed out the fact that to solve a problem of instability by adding more weight to the structure was not a very clever idea. Even with the lesser slope, the amount of stone in the upper section of the Bent Pyramid would be ~67 percent of the one that would have been present providing the older slope was kept – saving only 10 percent of the total volume of stone of the pyramid – still being a huge additional weight for a building that was supposed to be under the risk of collapse.
18.
V. Maragioglio and C. Rinaldi, L’architettura delle piramidi Menfite , vol. 3 (Turin: Artale, 1963).
19.
However, Fakhry attributed the dismantling of the structure to the excavations of A.M.Hussein (1946–1949). These works were never published. The idea of a later earthquake would agree with Fakhry’s (see ref. 13) suggestion that the Bent Pyramid was his actual tomb.
20.
Curiously, according to S. Yoshimura, T. Nakawaga and S. Tonouchi, “Non-Destructive Pyramid Investigation (2)” (Studies in Egyptian Culture, vol. 8; Tokyo: Waseda University, 1988), data on micro-gravimetric prospects, there would be an additional chamber and corridor inside the Great Pyramid that are yet to be archaeologically confirmed. This has led Parra (2008), op. cit. (ref. 1, 2nd ed.), pp. 203–8, to suggest that perhaps Khufu imitated his father Sneferu’s western apartment in his own pyramid.
21.
G. Magli, “Geometry and Perspective in the Landscape of the Saqqara Pyramids,” APLIMAT Journal of Applied Mathematics , 3, 2009, pp. 147–59.
22.
G. Dreyer, Umm el-Qaab 1: Das prädynastische Königsgrab U-j und seine frühen Schriftzeugnisse (Mainz: DAI Archäologische Veröffentlichungen, 1998), p. 86.
23.
G. Magli, “From Abydos to the Valley of the Kings and Amarna: The Conception of Royal Funerary Landscapes in the New Kingdom,” Mediterranean Archaeology & Archaeometry , 11, 2011, pp. 23–36. It could be argued that the pyramids have sharp apexes instead of the slender slope of the ḏw sign, but during the New Kingdom, the equivalence was pretty obvious in the name of the Sphinx, Hor-em-akhet (see Figure 9).
24.
Senuseret III would have looked for an analogy with the “Mountain of Anubis” to the south of Umm el-Qab. See J.Wegner, “The Tomb of Senwosret III at Abydos: Considerations on the Origins and Development of the Royal Amduat Tomb,” in D. Silverman, W.K. Simpson and J. Wegner (eds), Archaism and Innovation: Studies in the Culture of Middle Kingdom Egypt (New Haven: Yale University Press, 2009), pp. 103–169.
25.
Magli, op. cit. (ref. 21). An updated and extended discussion on the topic can be followed in Magli, op. cit. (ref. 2). It is, however, worth mentioning that, according to José Lull and José Miguel Parra, the final accomplishment of a ḏw symbolism could be a later decision of Shepseskaf once the visualization of the idea was “obvious.”
26.
G. Magli, “The Snefru Projects and the Topography of Funerary Landscapes During the 12th Egyptian Dynasty,” Time and Mind , 5, 2011, 53–72.
27.
Lehner, op. cit. (ref. 1), pp. 34–5.
28.
J. Assmann, “Creation through Hieroglyphs: The Cosmic Grammatology of Ancient Egypt,” in S. La Porta and D. Shulman (eds), The Poetics of Grammar and the Metaphysics of Sound and Sign (Jerusalem Studies in Religion and Culture, 6; Leiden: Brill, 2007), pp. 17–34.
29.
S. Quirke, The Cult of Ra (London: Thames & Hudson, 2001), p. 116.
30.
The question of the names of the pyramids has been a matter of some debate. Some scholars would have read the name of this pyramid as “The Pyramid of Sneferu is Durable.” However, most recently, the second alternative, with the name of the pyramids as an appellative of the defunct king has received more support, but the question is far from being resolved. For a very interesting discussion on the different possibilities of reading the names of the pyramids, see H.G.Fisher, “On the Interpretation of Names of the Pyramids,” in H.G.Fisher (ed.), Egyptian Studies , III: Varia Nova (New York: Metropolitan Museum of Art, 1996), pp. 73–7.
31.
D.B. Redford, History and Chronology of the Eighteenth Dynasty of Egypt: Seven Studies (Toronto: University of Toronto Press, 1967), pp. 4–27.
32.
An excellent discussion on this topic can be followed in Katja Goebs’ PhD dissertation. This has been published as K. Goebs, Crowns in Egyptian Funerary Literature: Royalty, Rebirth, and Destruction (Oxford: Griffith Institute Monographs, 2008). Particularly relevant is the information collected in section 1.3, pp. 24–31.
33.
A. Moret, “Chartes d’immunité dans l’Ancien Empire égyptien,” Journal Asiatique , 11(10), 1917, pp. 359–447. This must be understood as a clue for a common project only. See also Magli, op. cit. (ref. 2), pp. 68–9.
34.
L. Borchardt, “Denkmäler des Alten Reiches (ausser den Statuen) im Museum von Kairo.” Catalogue Général des Antiquités Égyptiennes du Musée du Cairo I (Berlin: Reichsdruckerei, 1937).
35.
As already mentioned, the most recent analysis of the annals is: Wilkinson, op. cit. (ref. 11). There are three clear entries for the reign of Sneferu.
36.
Goebs, op. cit. (ref. 32), p. 25.
37.
Wilkinson, op. cit. (ref. 11), p. 142. However, according to the hieroglyphic copy in Urk. I, 236, 11, the sign would be Sma, and not rsy . This might include a certain hue in the reading.
38.
Wilkinson, op. cit. (ref. 11), pp. 144–5.
39.
There is no archaeological evidence of such a building. However, exactly the same solution would have been adopted at the beginning of the Middle Kingdom when Amenemhat I founded a new administrative capital Ittawy, “Who grabs the Two lands,” a few kilometres to the south of Dahshur, erecting a new necropolis nearby (present El-Lisht) where his pyramid and the one of his son Senuseret I would be constructed. Both monuments had names selected accordingly. See Lehner, op. cit. (ref. 1), 168–73. It is, however, fair to note, as Rolf Krauss pointed out, that the determinative of pyramid is not written in the relevant entry of the Palermo stone (see Figure 4), although the text is rather wordy in that particular section.
40.
See Stadelmann, 2008, op. cit. (ref. 15). Even if we suppose a nearly contemporary building, then some 9 years (between years of the 8th and 15th occasions) look reasonable time to prepare the terrain, excavate the huge pits of the lower chambers of the Red Pyramid, put in place the huge corbelled vaults of the ceilings of the lower rooms and prepare the foundation platforms and trenches to start settling the different layers. Interestingly, see W.S. Smith, “Inscriptional Evidence for the History of the Fourth Dynasty,” Journal of Near Eastern Studies , 11, 1952, pp. 113–28, for an earlier opinion that it seems impossible that the quarry marks could have been applied at the beginning of the construction of the Red Pyramid but rather when it was nearly completed.
41.
Krauss (private communication, 2014) has argued that if any pyramid symbolized anything it was presumably not on the basis of its building materials . It could reasonably be argued that the Red Pyramid was cased with white limestone and the “final” aspect of the pyramid would have been that of a white shining gem. However, while the casing of the Bent Pyramid is almost intact, that of the Red Pyramid has nearly completely disappeared (see Figure 2). Perhaps, the pyramid was left unfinished due to the death of the king in his year 31, or it is indeed possible that there was no intention of completely casing it in white limestone. Only some sections of the lowest courses have survived in situ, which is surprising considering that the general idea is that the casing blocks of Tura limestone of the Red Pyramid were used to burn lime in Roman times. Curiously, the white limestone pyramidion (a tiny fraction of the total casing) was found in fragments during the excavations of the funerary temple, and under this consideration, it would be reasonable to assume that more rubble of the rest of the hypothetical white limestone casing should have been found on the site if this was ever finished. Interestingly, when just excavated, the pyramidion showed traces of a red pigment that could be either painting or rock oxidation, see Stadelmann, 1985, op. cit. (ref. 15). If they were rests of painting, it may after all suggest that the Red Pyramid could have been painted red once finished.
42.
This idea was first defended by Cintron, op. cit. (ref. 9).
43.
A comprehensive summary of the idea can be found in J.A.Belmonte, M.Shaltout and M. Fekri, “Astronomy, Landscape and Symbolism: A Study on the Orientations of Ancient Egyptian Temples,” in J.A. Belmonte and M. Shaltout (eds), In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), pp. 211–82. The origin of Egyptian archaeoastronomy can be traced to the year 1894 with the publication of J. N. Lockyer, The Dawn of Astronomy (New edition; New York: Garland Publishing, 1993). However, a discussion on the first serious attempts to analyse Egyptian sacred building orientations can be followed in E.C. Krupp, “Light in the Temples,” in C.L.N. Ruggles (ed.) Records in Stone, Papers in Memory of Alexander Thom (Cambridge: Cambridge University Press, 1988), pp. 473–99. An important preliminary study on the orientation of temples is also provided by C. Leitz, Studien zur ägyptischen Astronomie (Wiesbaden: Ägyptologischen Abhandlungen Band, 49, 1991).
44.
For the so-called stellar simultaneous transit theory, see K. Spence, “Ancient Egyptian Chronology and the Astronomical Orientation of Pyramids,” Nature , 408, 2000, pp. 320–4; J.A. Belmonte, “On the Orientation of the Old Kingdom Pyramids,” Archaeoastronomy , 26, 2001, S1–20. A recent updating of the theory has been outlined by Belmonte, op. cit. (ref. 4), pp. 169–214. This would still work independently of the validity, or not, of the error versus time trend (related to precession) originally defended by Spence. For the “stretching of the cord ceremony,” see J.A. Belmonte, M.A. Molinero and N. Miranda, “Unveiling Seshat: New Insights into the Stretching of the Cord Ceremony,” in J.A.Belmonte and M.Shaltout (eds), In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), pp. 193–210. See also Figure 6.
45.
For Meskhetyu, see J. Lull and J.A. Belmonte, “A Firmament Above Thebes: Uncovering the Constellations of Ancient Egyptians,” Journal for the History of Astronomy , 37, 2006, pp. 373–92 (and references therein); or the most recent updated and enlarged J. Lull and J.A. Belmonte, “The Constellations of Ancient Egypt,” in J.A. Belmonte and M. Shaltout (eds), In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), pp. 153–92.
46.
Allen and Der Manuelian, op. cit. (ref. 11), pp. 11–2.
47.
Herschel wrote the following in a letter to James:
The inclination of the passages I used to think quite satisfactorily accounted for by being able to see Alpha Draconis through them; now you have shown a practical and assuredly very natural reason in pointing out 26° as the “angle of rest,” facilitating the sliding down of great weights without incurring a “down-rush,” and directly subserving the intention of blocking up the access to the burial chamber.
See R. Krauss, “La orientación de los corredores de las pirámides egipcias según John Herschel,” in J. Lull (ed.) Trabajos de arqueoastronomóa: ejemplos de África, América, Europa y Oceanía (Gandía: Agrupación astronómica de La Safor, 2006), pp. 185–92.
48.
There is a discrepancy between our own datum on the slope of the Red Pyramid northern corridor (checked on site with a precision of ¼°) and other measurements reported in the literature which give a value of c. 26°34′, see R.Krauss, “Weisen die Pyramidenkorridore den Weg zum Himmel?,” Studien zur altägyptischen Kultur , 38, 2009, 151–9, Table 1. If this were the correct number for the slope, it would possibly mean that the ratio 2:1 was already an innovation of Sneferu’s reign. In this sense, it is worth noticing that the alignment to Thuban was more precise for the pyramid of Meidum, where the corridor has a slope of ~28° with an average deviation from the north of −18′, giving a declination of 88°30′, accurately corresponding to the declination of α Draconis c . 2600 b.c. This star presumably belonged to one of the “Mooring Post” constellations of the ancient Egyptians. See Belmonte, op. cit. (ref. 4), Table 3.1. The ascending corridor of the western apartment of the Bent Pyramid will be discussed later on, see (ref. 60).
49.
In a contribution to the SEAC XIII conference hold in Isili (Sardinia) in June 2005. See J.A. Belmonte and M.P. Zedda, “Light and Shadows on the Pyramids,” in M. Zedda and J.A. Belmonte (eds) Light and Shadows in Cultural Astronomy (Cagliari: Agorà Nuragica, 2007), pp. 188–196.
50.
The inspiration came from the work of D. Magdolen, “The Solar Origin of the Sacred Triangle in Ancient Egypt,” Studien zur Altägyptischen Kultur , 28, 2000, 207–17.
51.
For the definition of astronomical terms that could be useful for Egyptology, see M.Shaltout and J.A. Belmonte, “Introduction: Under Ancient Egyptian Skies,” in J.A. Belmonte and M.Shaltout (eds) In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), pp. 11–26.
52.
For whatever reason, the pyramids of Amenemhat I in El-Lisht and that of Amenemhat III in Dahshur were built with slopes very close to the lower section of the Bent Pyramid, thus having an identical solar phenomenology. See also Magli, op. cit. (ref. 26). At the beginning of the Middle Kingdom, Wepet Renpet was happening in dates close to another very important station of the solar cycle: the winter solstice.
53.
It has been suggested that this slope obeyed a design that followed a Pythagorean triangle of 20-21-29. See C. Rossi, Architecture and Mathematics in Ancient Egypt (Cambridge: Cambridge University Press, 2004). However, this mathematical approach does not explain why this new slope was selected. Actually, the two explanations are not mutually exclusive since there is no doubt that in practice, Egyptian architects used rational fractions to express angles.
54.
However, Rossi, op. cit. (ref. 53), has argued – indeed without further evidence – that the pyramidion found at the Red Pyramid temple would actually have been the one originally built for the Bent Pyramid prior to the change of slope, which was later abandoned and, for unknown reasons, deposited in the final resting place of Sneferu at the Red Pyramid complex.
55.
This was first proposed by Belmonte and Zedda, op. cit. (ref. 49).
56.
For a discussion on the solar origin of the civil calendar, see J.A. Belmonte, “Some Open Questions on the Egyptian Calendar: An Astronomer’s View,” Trabajos de Egiptología (Papers on Ancient Egypt), 2, 2003, pp. 7–56. For an updated version of this work, see J.A. Belmonte “The Egyptian Calendar: Keeping Ma’at on Earth,” in J.A. Belmonte and M. Shaltout (eds) In Search of Cosmic Order, Selected Essays on Egyptian Archaeoastronomy (Cairo: Supreme Council of Antiquities Press, 2009), pp. 73–130. Alternatively, L. Depuydt, Civil and Lunar Calendar in Ancient Egypt (Leuven: Orientalia Lovaniensia Analecta, 77, 1997) defends the very importance of the moon in Egyptian calendrics, while A-S.Von Bomhard, The Egyptian Calendar, A Work for Eternity (London: Periplus Publishing London Ltd., 1999), defends a stellar origin based on Sirius observations. A.Spalinger, “Egyptian Festival Dating and the Moon,” in J.M. Steele and A. Imhausen (eds), Under one Sky (Münster: Ugarit Verlag, 2002), pp. 379–404, offers an open discussion on the topic.
57.
For a complete discussion on the errors, see Belmonte (2003), op. cit. (ref. 56).
58.
According to J. Kahl, Ra is My Lord: Searching for the Rise of the Sun God at the Dawn of Egyptian History (Wiesbaden: Harrassowitz, 2007). Also relevant is R. Krauss, “Stellar and Solar Components in Ancient Egyptian Mythology and Royal Ideology,” in M. Rappenglück and B. Rappenglück (eds), Astronomy and Power (British Archaeological Report International Series, 2015), in press.
59.
Bronk Ramsey et al. op cit. (ref. 4) has fixed a date between 2691 and 2651 b.c. for the ascent of Netjerkhet, according to a set of radiocarbon dates of his reign.
60.
The civil calendar moves 1 day ahead every 4 years with respect to the Gregorian proleptic calendar. The 2-day error – corresponding to 8 years – is due to the fact that the latter is only an average of the actual tropical year of 365.2425 days in antiquity. In this respect, we have so far not dealt with the two distinct slopes of the corridor reaching the western apartment of the Bent Pyramid of Sneferu. This started with a slope of 24°17′ but reached the surface of the pyramid western face at an inclination of 30°9′ (see Table 1 and Figure 7). These correspond to “declinations” of 11° and 14½°, respectively. The only relevant one would in principle be the latter since this was the one reaching the surface. There is hardly any relevant star at that declination for the epoch of Sneferu. If, on the contrary, we consider an alternative solar alignment, this declination would fit to the sun at 30 April or 13 August in the Gregorian proleptic calendar. We could speculate that either of these two dates was relevant for Sneferu’s reign (perhaps his date of ascension to the throne or something similar). However, if 20 May is to be considered as a possibility for Wepet Renpet sometime during the reign of Sneferu, these two dates would correspond to IV Shemu 15 and III Akhet 25 in the civil calendar of the time, respectively. The former does not seem relevant apart from being the mid-month of Mesore, the month celebrating the birth of the sun. The latter corresponds to the minor Middle Kingdom festival of Sspt itrw whose relevance we simply do not know although it was certainly linked to the important festival of Peret Sopdet. Before anyone else arguing in this respect, it is worth noting that 13 August and 30 April were especially relevant dates in Mesoamerican calendrics. We indeed believe that this is pure chance!
61.
Bronk Ramsey et al., op. cit. (ref. 4). Two dates have been previously discussed for the inauguration of the civil calendar: c . 2750 b.c. for the first Pharaohs of the Second Dynasty and c . 2690 b.c. for the reign of Khasekhemuy. This would give either 2622 or 2562 b.c. , with a margin of ±8 years, for Sneferu’s eighth Tnt. This offers two possibilities for Sneferu’s 31-year reign: c . 2632–2601 ± 8 b.c. or c . 2573–2542 ± 8 b.c. , in relatively good agreement with the standard high and low chronologies considered so far (see ref. 4). The authors would tend to support the lower one since Belmonte, op. cit. (ref. 4), pp. 335–8, has proposed, on an archaeoastronomical basis, c . 2550 ± 10 b.c. as the date for the ascension of Khufu, the Great Pyramid builder and son and successor of Sneferu.
62.
The small pyramid has a slope of c . 44°30′. This would give a declination of 20°21′, which corresponds to 22 May in the Gregorian proleptic calendar. This may suggest that the satellite pyramid could have been planned, or at least started, 8 years prior to the other components of the complex with a similar slope (i.e. the upper layers of the Bent Pyramid and the Red Pyramid). This is indeed plausible. However, considering the margin of error of ±8 years, this hypothesis must be viewed with caution.
63.
Belmonte, op. cit. (ref. 4), Table 5.1.
64.
O. Neugebauer, The Exact Sciences in Antiquity (New York: Dover, 1969).
65.
R. Krauss, Astronomische Konzepte und Jenseitsvorstellungen in den Pyramidentexten , (Wiesbaben: Ägyptologische Abhandlung Band, 59, 1997).
66.
For the Coffin Text’s astronomical aspects see: P. Wallin, Celestial Cycles. Astronomical Concepts of Regeneration in the Ancient Egyptian Coffin Texts (Uppsala: University of Uppsala Press, 2002).
67.
Goebs, op. cit. (ref. 32).
68.
For the White Crown, see Goebs, op. cit. (ref. 32), p. 154, who argues that: “when used as an item of insignia with cosmic connotations, the HDt seems to refer almost exclusively to the luminosity of the moon or stars at night,” as well as: “in the cosmic context of the early funerary literature, the crown designation HDt hence appears to have been chosen specifically to express lunar or stellar light – the latter including the radiance of Horus as the morning (or evening) star.”
69.
See Goebs, op. cit. (ref. 32), pp. 204–5, who argues that the Red Crown ought be related to the red light of dawn or sun’s disc at sunrise, since “of the four attestations of dSrt ‘Red Crown’ in the Pyramid Texts, two occur in the so-called Cannibal Spell, the most obvious and revealing spell in relation to blood and slaughter.” However, according to Pyramid Text spelling 243, the White Crown appears after “devouring” the Red Crown, posing some doubts on this identification (R. Krauss, private communication, 2014). For Krauss, the White Crown would certainly be Venus as “Morning Star” while he speculates with the idea that the Red Crown would also be a “stellar entity” and should be interpreted as Venus “Evening Star.”
70.
Although quite speculative and without epigraphic support, it is hypothesized by New York University Egyptologist Patricia Blackwell Gary and “Astronomy” senior editor Richard Talcott that the shapes of the ancient Egyptian pyramid and obelisk were derived from natural phenomena associated with the sun. The pyramid and obelisk might have been inspired by previously overlooked astronomical phenomena connected with sunrise and sunset: the zodiacal light and sun pillars, respectively. P. Blackwell Gary and R. Talcott, “Stargazing in Ancient Egypt,” Astronomy , 2010, pp. 63–7.
71.
See, M. Vázquez and J.M. Vaquero, “Aurorae Observed at the Canary Islands,” Solar Physics , 267, 2010, pp. 431–44. For example, in February 1872, a notable aurora was observed in Cairo and as far as Aswan. According to M.Vázquez (private communication, 2014), the number of auroras (aurorae) increases with the terrestrial latitude. However, low-latitude events have been often reported associated with strong solar storms. For Northern Africa, H.M. Basurah, “Records of Aurora in the Islamic Chronicles During 9th-16th Centuries,” Journal of Atmospheric and Solar Terrestrial Physics , 68, 2006, pp. 937–41, has reported seven events – from Arab sources – between the ninth and the sixteenth centuries. More recently, M.Vázquez et al. (now in preparation), indicate a minimum of 10 observations of aurorae in Northern Africa for the period a.d . 1600−2015 from different western sources. They tend to be clustered in short activity episodes (from weeks to few years) separated by approximately 100-year intervals (a cadence comparable to total solar eclipses). Interestingly, K. McKraken, J. Beer, F. Steinhilber and J. Abreu, “The Heliosphere in Time,” Space Science Review , 176, 2013, pp. 59–71, have shown that a maximum of solar activity was possibly present during the epoch of formation of the Egyptian state in the first half of the Third Millennium b.c. , in contrast to the most recent centuries when a minimum has been produced. Hence, a larger number of low-latitude aurorae would have been expected when the celestial eschatology of the Pyramid Texts was developed.
72.
Goebs, op. cit. (ref. 32), p. 155.
73.
If, instead, dawn is considered as a comprehensive alternative for the crown of the north, the green nature of this might refer to the “green flash” phenomenon happening immediately before sunrise and sunset, also observable – although for very brief moments – at mid-latitudes clear skies. However, as one of the referees has suggested “green” can be a usual euphemism for “red”; see, for example, J.E. Quack, “Mit griiner Tinte rot schreiben,” Göttinger Miszellen , 165, 1998, pp. 7–8. The reason would be the general colour symbolism, which is most likely due not to any physical phenomena but perhaps to the warmness of the colour as such.
74.
Krauss (private communication, 2014) has argued that to identify the White and Red Crowns with the zodiacal light and the aurora borealis, respectively, the related Pyramid and Coffin Texts must be interpreted accordingly. Egyptological multiplicity of approaches is fine, as long as the sources allow it. The fact that the authors are impressed by the zodiacal light and the aurora borealis does not mean that the ancient Egyptians were similarly impressed. The (real) problem is to show from the sources that they were similarly impressed. It is relevant, in this sense, the astonishing apparent silence of Egyptian sources about conspicuous and certainly impressive astronomical phenomena such as eclipses or comets. However, as one of the referees has suggested, this silence could simply be due to chances of preservation. Such information would mostly have been recorded on papyrus in libraries which we know existed but are now lost. Hence, one may not expect everything to have been monumentalized in stone. Interestingly, the fact that the Egyptians must have had many records of eclipses, at least in the Greco-Roman period, is explicitly mentioned by Seneca, Questiones naturales VII, III, 1–2.
75.
A fact could certainly be relevant: many Fourth and some Fifth Dynasty pyramids were cased with pink granite in their lower courses, notably that of Menkaure: see Arnold, op. cit. (ref. 12), p. 169. A pyramid cased with white limestone in its upper layers and with pink granite in the lower ones would certainly have had an aspect mimicking the double crown of Egypt, the sxmty, integrating both the White, HDt, and Red, dSrt, crowns of Upper and Lower Egypt, respectively. Hence, we may speculate with the idea that Sneferu’s symbolism would have been somehow followed by his direct descendants although in a different level. Other aspects of landscape symbolism were also followed by the Pharaohs of later dynasties; see, for example, G. Magli, “Topography, Astronomy and Dynastic History in the Alignments of the Pyramid Fields of the Old Kingdom,” Mediterranean Archaeology & Archaeometry , 10, 2010, pp. 59–74; D. Jeffreys, “The Topography of Heliopolis and Memphis: Some Cognitive Aspects,” in D. Polz (ed.) Beitrage zur Kulturgeschichte Ägyptens, R. Stadelmann gewidmet (Mainz: Philipp von Zabern, 1998), pp. 63–71.
76.
The best orientation accuracy would be achieved one generation later by Sneferu’s son Khufu in his pyramid complex at Giza. See E. Nell and C.L. Ruggles, “The Orientation of the Giza Pyramids and Associated Structures,” Journal for the History of Astronomy , 45, 2014, 308–69, for a state-of-the-art approach to this question.
77.
Sneferu’s Red Pyramid superstructure had presumably been started shortly before the year of the 15th occasion (year 19 or 20 of his reign) as shown by mason-marks located in the southwest corner of the monument. Hence, its construction lasted a dozen years or so. See Krauss, op. cit. (ref. 5) and Stadelmann, op. cit. (ref. 15).
78.
See M. Shaltout, J.A. Belmonte and M. Fekri, “On the Orientation of Ancient Egyptian Temples: (3) Key Points in Lower Egypt and Siwa Oasis,” Journal for the History of Astronomy , 38, 2007, Vol. 2, 141–60 (Part I) and Vol. 4, 413–42 (Part II); G. Magli, “Akhet Khufu: Archaeoastronomical Hints at a Common Project of the Two Main Pyramids of Giza,” Nexus Network Journal , 11, 2008, pp. 35–50. Also relevant for the inspiration of the idea is R.H.Wilkinson, Symbol and Magic in Ancient Egypt (London: Thames and Hudson, 1994).
79.
And indeed, in both cases, the orientation errors of the two main pyramids differ from each other by a mere 3′, close to the normal resolving power of the human eye, in agreement with a contemporaneous planning. See Table 1 and Nell and Ruggles, op. cit. (ref. 76). However, P. Tallet and G. Marouard, “The Harbour of Khufu on the Red Sea Coast at Wadi al-Jarf, Egypt,” Near Eastern Archaeology , 77, 2014, pp. 4–14, have found a papyrus, contemporaneous to Cheops’ reign, with a text where Axt xfw is mentioned with a single determinative of a pyramid (as in later sources). This, according to José Lull (private communication, 2014), would be a point against the duality of the complex. Arguably, many pyramid complexes included more than one pyramid (although just a single “big” one in most cases) and were always named with a single determinative with the notable exception of the – indeed later and not contemporaneous – use of the double determinative in the case of Kha-Sneferu. This question will indeed need further exploration in the future.
80.
For Khufu’s dates, see Belmonte, op. cit. (ref. 4), Table 8.1 Also relevant would be Tallet and Marouard, op. cit. (ref. 79).
81.
The name has also been read as “Khefren is a great (of heaven).” For a lengthy discussion on the topic, the name of the second pyramid of Giza included, see Belmonte et al., op. cit. (ref. 43).
82.
M. Roaf, “Mesopotamian Kings and the Built Environment,” in J.A. Hill, P. Jones and A.J. Morales (eds), Experiencing Power, Generating Authority (Philadelphia: University of Pennsylvania Press, 2013), pp. 331–59.