A response to J.Wall's examination of 'The Star Alignment Hypothesis for the Great Pyramid Shafts'

The true meaning and implications of these explicitly stellar names only become apparent in the earliest surviving royal funerary texts inscribed within pyramids from the end of Dyn 5.  Unis the king, purified himself with the cool water of the stars and bathed in the starry firmament §138, the 'Imperishable Stars' raised Unas aloft §139, and Unas guided the 'Imperishable Stars' §373. Unas was born as a star, and he appeared as a star §262. Unas opened his place in the sky among the stars of the sky, for he was the Lone or Unique Star §251.  Atum, the 'father' of Unas, assigned Unas to the excellent and wise gods, the 'Imperishable Stars' §380.  He was a son of Sopdet (personification of Sirius, the brightest star in their sky) §458, and was given a warrant as Great Power by Sah (Orion), 'father of the gods' §408.

Referring to Utterance 273-4, Badawy states: "At least one of the pyramid spells mentioning Orion belongs to the older stock since it occurs in the context of the so-called Cannibal Hymn." (Badawy 1964: 199).

It is Sah (sAH, 'Orion') who has given me his warrant;  it is Mesekhtiu (msxtiw, the 7-star asterism 'the Plough' / 'Big Dipper' in Ursa Major) which has made a path for me to the western horizon;  it is Sopdet (spdt, 'Sirius') who greets me as the birth of a god.  CT 482

Thus says Sah (sAH, 'Orion') to me: You have acquired all their powers, you have forgotten nothing.  CT 236-9

From the pyramids of Unis and Teti (Sethe Vol 1: 212; §406c):"....for both skies go around (in service) for him and the two shores* serve him. Unis is the most controlling power, who controls the controlling powers; Unis is the sacred image who is most sacred of sacred images.........Unis is the god who is senior to the senior ones, for thousands serve him and hundreds present offering to him; for he has been given title as the greatest controlling power by Orion (sAH), the gods' father; for Unis has reappeared in the sky and is crowned as lord of the Akhet. W 180b (T 275b)

*Allen note:  "the term "both skies" refers to the two parts of the sky, north and south of the Winding Canal, and the 'two shores' are those of the Nile:  the passage indicates that sky and earth are in the deceased's service."

Deep underground beneath the Dyn 3, step pyramid of Netjerikhet, are three panels showing Netjerikhet running or standing in various shrines. On the middle panel Netjerikhet is shown striding or running, carrying the flail and the mks, a container holding the imit-pr document (lit. 'that which is in the house' or that which constitutes the house'. In the royal realm, it appears to entitle the king to claim over the property he circuits - the Two Lands - Egypt. In front of the king is the 'White Shrine / Palace' (aH-HD) of the Great Ones (wrw)

On either side of the king at the bottom of the panel, are a set of three semi circular territorial stone-markers (Dnbw) - one set in the north and the other in the south. Behind the king are two sky boundary markers in the form of two halves of the 'sky' sign N1 (mdnb) that stands for the limits of the sky. The king in the ritual Hb-sd run, goes around the territorial markers holding the title deed, legitimizing his rule of the terrestrial and celestial realms.

The king traveled from north to south and south to north when he visited the sacred sites in Upper and Lower Egypt - the 'Two Lands' he ruled over, and in his sed-festival, he went around the semi circular boundary stones in the north and south of his sed-festival court (the sun 'traveled' from north to south and from south to north in the annual solar cycle).

Sah as 'father of the gods', in the earliest Pyramid Texts, gave the title deed to the king legitimizing his rule in the celestial realm.

Netjerikhet is seen holding the title deed that legitimizes his rule over the Two Lands and the Two Skies - the north and south skies.  This title deed seems to have been authorized by his divine ancestors symbolized by the baboon sitting in the 'White Shrine / Palace of the Great Ones'. The baboon is wearing a cross that can mean 'great' (wr). The 'great ones' inside the shrine / palace, is simply written with three swallows (wrw)  (in the Pyramid Texts, swallows are the Imperishable Stars, the followers of Osiris, who had an identity of the one in Sah).

"there is no one who bars him from the White Palace of the great ones at the Beaten Path of Stars (msqt sHdw, perhaps the ecliptic or the Milky Way) - for look, Unis has reached the sky's height." W 172.

"Helck argued that the collective body of royal ancestors could be represented as a white baboon whose role was to transfer lordship of the land to the succeeding king.  Since wr can mean not only 'great' but also 'the greatest' or 'oldest ones', denoting gods, but also suggesting divinized ancestors."  (Friedman 1995)

During the reign of Khufu, the top of the upper southern shaft was facing an area of the sky due south where Sah 'stood' upright as he 'strode' across the southern sky.  Sah, as the 'father of the gods' had the authority to legitimize the king's celestial rule, perhaps similar to the transfer of power by 'the greatest' or 'oldest ones', denoting gods, the divinized ancestors, to Netjerikhet.  Khufu, the Dual King of the Two Lands, not only had direct access through the dual shafts to the two skies - the north and south, but perhaps also through the south shaft, to Sah who seems to represent the collective authority of all the gods and divine ancestors of the king when he bestows the title 'greatest controlling power' on the king.

This same idea is carried on into the Middle Kingdom:

.....I find Sah standing on the path with the staff in his hand, and I set up the staff and receive it, and I am a god by means of it.  He gives me the staff which is in his hand, and he says:  'Give me my son, for it is he who rises in peace;  you shall be ennobled before your throne, for you are my son, the lord of my house'.  CT 470

It is Sah (sAH, 'Orion') who has given me his warrant;  it is Mesekhtiu (msxtiw, 'Plough' / 'Big Dipper') which has made a path for me to the western horizon;  it is Sopdet (spdt, 'Sirius') who greets me as the birth of a god.  CT 482

Slope geometry

Wall makes two assumptions when he selected the data used in the calculations for his star alignments.  First he assumes the alignments are according to the overall angle of the more or less straight section of the shafts, but he ignores the actual angle of the shaft outlet at the top end.  The angle of incline at the top of the shafts is crucial because that tells us what area of the sky the top of the shafts were actually facing.  Secondly, he assumes the angle of the nearest seqed to the overall angle was the actual intended angle.  Both his assumptions have the effect of skewing the resulting astronomically derived dates, making it appear as if the shafts have widely differing dates.

The star alignment proposal is based on the ancient Egyptian idea of the ba (bA, 'soul').

"It was necessary for the deceased to journey from the tomb to rejoin his ka if he was to become transformed into an Akh, and since the physical body could not do this it was the duty of the ba.........In order for the physical bodies of the deceased to survive in the afterlife, they had to be reunited with the ba every night, and Spell 89 of the Book of the Dead recommended that a golden ba-bird be should be placed on the chest of of the mummy in order to facilitate this reunion."  (BM Dictionary of AE, 2002 (1995).

The ba was depicted as a human headed bird in later texts - a vignette on the Dyn 18 Nebqed papyrus, shows the 'opening the mouth' ritual at the tomb entrance, and a long shaft connected to the burial chamber where a mummiform coffin lies on a 'bed'. Fluttering in the shaft is a human headed ba-bird (the ba of the deceased).

An inscription from four Dyn 5 pyramids allude to the king's ba ascending along a path, through the doors of the sky, and into the company of the gods: 

Faulkner:  How good it is for those who see, how comforting it is for those who hear when Osiris the overseer of the gods arises! You have your tomb, O King, which belongs to the heart of Him whose seats are hidden; he opens for you the doors of the sky, he throws open for you the doors of the firmament(?), he makes a road for you that you may ascend by means of it into the company of the gods, you being alive in your bird shape.  PT 667A §1943; Sethe Vol 2: 468

Allen:  How beautiful to the sight, how satisfying to the hearing, is Osiris’s stance," is in the mouth of your tomb’s gods, Neith. He of the injured heart and inaccessible places shall open for you the sky’s doorway and pull open for you the Cool Water’s doorway. He shall make you a path, that you might emerge on it amongst the gods, alive in your ba.  Nt 243 (P 279, M 199, N 340)

We know from the royal funerary texts inscribed within four Dyn 6 pyramids, that the AE thought of stars as the bas of the kings - 'She of a Thousand Bas' (xA-bA.s): Nut, whose "Thousand Bas" are the stars of the night sky.

Assuming Khufu's ba left his pyramid through the shafts, what did he see as he exited from the top end?  - in other words what areas of the sky were the top ends of the shafts facing - its the crucial survey data from the top of the shafts that determines the angle for possible stellar alignments.

The outlet at the top of the upper southern shaft was facing an area of the sky the distinctive 3-star asterism ('Orion's Belt') in the centre of Orion crossed due south at its highest point in the sky, c.2570 BC.  The top end of the upper northern shaft was facing an area of the sky where the North or Pole Star, Thuban, reached at its highest point in the sky c. 2570 BC due north.

Both shafts have the same astronomically derived date, and according to the Oxford History of AE, c. 2570 BC is consistent with Khufu's reign (2589 - 2566 BC +- 50 years).

For the upper southern shaft, Wall only examines the possibility of an alignment with the star Alnitak, but inexplicably, fails to consider Badawy's original proposal of an alignment to 'Orion's belt', effectively skewing the results of the calculations.  The 'calculations' are very precise - accurate to 0.01 degs (36 arc seconds), but the results are only as good as the data fed into them.

Based on his assumptions for the angle of incline of the two upper shafts and his choice of the star, Alnitak, Wall (after Tonkin) obtained the dates 2364 (north shaft / Thuban) and 2492 (south shaft / Alnitak), but as has been demonstrated, an equally convincing alternative to Wall's assumptions and choice of Alnitak, give the same date for both shafts that is well within Khufu's reign.  This means he has certainly not invalidated Badawy's original idea.

Alexander Badawy's original proposal for the shafts aligning with a significant star, the North or Pole Star Thuban in the northern sky, and the distinctive 3-star asterism in Orion crossing the southern sky, used an unfortunate 'scribal' error in Petrie's survey data (44.5 degs instead of the correct 45 degs for the upper southern shaft).  According to Gantenbrink's survey, the angles of inclines for the upper shafts are 45 degs for the southern, and 31.2 degs (the top 11m / 36 ft) for the northern shaft.  Using these corrected values, the resulting date c. 2570 BC for both shafts, is fully consistent with Khufu's reign.

Wall also examines the lower shafts, and wrongly assumes "each has the same principal angle so that, if extended, like those from the King’s Chamber, each would have had the same exit height." - he assumes the "principal angle" for both shafts is 39.47 degs based on sqd 8 palms 2 fingers, but does not explain why the ancient Egyptians chose not to use a whole palm seqed like the two upper shafts - sqd 7 and sqd 11, that were probably used for the basic layout of the design.  Why would a seqed with a precison down to a finger be chosen for the lower shafts?  It is much simpler to use a whole number seqed, sqd 8 or sqd 9, rather than sqd 8 palms 2 fingers.

Wall cannot claim that both lower shafts had "....the same principal angle so that, if extended, like those from the King’s Chamber, each would have had the same exit height." - his unsubstantiated assertion completely ignores the uncertainty of Gantenbrink's and Petrie's survey data - possible range of angles for the slopes of the initial inclined section of the south shaft are 37.5.....39.6 degs, and for the north shaft, 38.5.....43.6 degs.  Neither Gantenbrink nor Petrie measured the angle of the slopes of the upper sections of the shafts.

Gantenbrink used a 'Rope Climber' that carried a high-resolution, numeric-digital instrument designed to measure the shaft's angle of ascent. It pulled itself up the shafts along the cable of the Upaut-2 robot, which was fitted with a laser guidance system.

Gantenbrink measured the length of the north shaft, and its angle of incline up to the first bend of the lower inclined section. The shaft begins with a horizontal section 1.93m long, and an inclined section about 16.57m long.  His 1994 MDIAK article states the angle of incline is 39.124 degs +- 2 degs that was determined with 14 individual measurements over a length of 15m.  His web site published five years later has the following data:  the drawing of the north shaft has the text, "angle uncertain!", and Gantenbrink states in his 'Findings' section:  "Based on 14 measurements made over a distance of 17 meters, the shaft's angle of ascent fluctuates between 33.3 degs and 40.1 degs. Block No. 4 clearly shows that a change in the angle was made at this point. To that end, the builders even cut the shaft 2 cm deep into the beginning of the floor block.  The extreme angle fluctuations and the changes made to Block No. 4 would seem to indicate that, at this point, the ancient Egyptians ran into a conflict with the Great Gallery, which was being constructed at the same time, and thus were unable to adhere exactly to the originally intended shaft angle. Only further measurements in the still unexplored upper areas of the shaft will tell whether the intended angle is several degrees smaller than that of the southern shaft, or whether both shafts were to be constructed at the same angle, that is, quasi-symmetrically."

According to these figures, the slope of the lower inclined section varies from 33.3 - 40.1 degs, with a possible overall angle of 39.124 degs +-2 degs, and to complicate matters further, Gantenbrink drew the shaft with about a 43.6 deg slope.  Gantenbrink's robot, Uphaut-2, did not go beyond the first bend of the inclined section, which means most of the length of the shaft to the top was not measured. In 2003 Hawass continued the exploration of the upper section of the north shaft but AFAIK, any measurements of the length and angle of the slope, have not yet been officially published.  He states in a 2005 article "We also sent the robot into the northern airshaft and found that after 20m the shaft bent and continued for another 8m. This bend may indicate that it was designed to miss the grand gallery and it also explains that it was carved during the construction of the pyramid. The robot continued for another 60m and then stopped in front of a door with two copper handles. It is the same distance as the door in the southern shaft with two copper handles."  Hawass's figures are not reliable as they are rounded up, 20 + 8 + 60 = 88m - for example, the first figure of 20m should be 18.5m, a rounding up of 1.5m!

As Gantenbrink was careful to point out:  "Only further measurements in the still unexplored upper areas of the shaft will tell whether the intended angle is several degrees smaller than that of the southern shaft, or whether both shafts were to be constructed at the same angle, that is, quasi-symmetrically."

Gantenbrink on the lower southern shaft: "......the shaft inclines at an average angle of 39.6078 degs, which we determined by taking 24 measurements over a distance of 28 meters."
The inclined section of the shaft up to the closure stone is about 59.45m (195 ft) long, but Gantenbrink only measured the first 28m (92 ft), which still leaves another 29.49m (97 ft). The upper northern shaft for example has a slight change of angle for at least the last 11m (36 ft), so its possible the lower shafts also have different angles of inclines for the top sections.

According to Petrie, the mean angle of incline for the lower section of the southern shaft is 38.47 degs  (tantalizingly close to the 38.15 degs slope of a shaft taking the shortest route to the exterior of the pyramid), and the mean angle for the northern shaft,  37.47 degs.  Petrie was a  meticulous surveyor, but had the disadvantage of only being able to measure the beginning of the lower inclined sections - he was not able to measure further up the shafts as Gantenbrink did.

Robert Bauval has proposed that the lower southern shaft was aligned with Sirius.  If the upper shaft was 'targeting' 'Orion's belt', the top opening was facing 'Orion's belt' due south around 2570.  The lower shaft was constructed a few years earlier when Sirius was about 38.8 - 39 degs alt. due south, which fits within the possible range of angles of inclines for the lower southern shaft.

Its also possible the original design of the lower shafts may have been symmetrical, but without more survey data this cannot be confirmed, making it difficult to investigate the lower northern shaft for alignments with any confidence.

The accuracy of astronomically derived dates for the shafts, depends on at least three variables:

1.  how accurately the AE surveyors could measure a star or asterism due south or north.

2.  how accurately the builders could build the shafts according to the architect's design

3.  to what extent have the angles of incline been affected by subsidence within the pyramid's superstructure over 4500 years

Its difficult to assess by how much these variables affect the dates, but if they are taken into account, the uncertainty factor is probably similar to the archeologically derived dates accurate to +- 50 years for the Old Kingdom.

If the two southern shafts were intentionally aligned with Sirius and Orion's belt, it would share a common theme found in the royal funerary inscriptions preserved inside pyramids from the end of Dyn 5.  The texts, known as sAxw (lit. 'akh-makers'), were to ensure the king became an effective Akh and achieve eternal life.

Both Sah (sAH), the personification of the large, distinctive constellation of Orion (or at least some part of it), and Sopdet (spdt), the personification of Sirius, the brightest star in their sky after the sun, crossed the southern part of the sky together, and are also paired together in the earliest texts:

Sah has become encircled by the Duat, as the Living One (the sun) became clean in the Akhet;  Sopdet has become encircled by the Duat, as the Living One became clean in the Akhet:  This Unis has become encircled by the Duat, as the Living One became clean in the Akhet.  He has become akh for them, he has grown cool for them, inside the arms of his father, inside the arms of Atum.  W 149 (PT 216);  Sethe Vol. 1: 86;  §151.

You (Teti) shall touch (sAH) the sky like Sah (sAH, 'Orion'), your ba shall be sharp (spd) like Sopdet (spdt, 'Sirius').  T 228 (PT 412);  §723

The sky shall conceive you with Sah, the morning-star shall give you birth with Sah.  Live!  Live, as the gods have commanded you live.  With Sah in the eastern arm of the sky shall you go up, with Sah in the western arm of the sky shall you go down.  Sopdet, whose places are clean, is the third of you two:  she is the one who will lead you two in the Marsh of Reeds to the perfect paths of the sky.  P 38 (N 9);   PT 442  §819

As Sah's birth should not be barred, you should not bar this Pepi when he comes to the place where you are.  As Sopdet's birth should not be barred, you should not bar this Pepi when he comes to the place where you are.  P 508;  PT 569  §1436

Sah will give him his arm, Sopdet will receive his hand.  P 524;  PT 582  §1561

The sky's two reedfloats have been set for the Sun, that he may go on high from east to west to the midst of his brothers the gods.  Sah is his brother, Sopdet is his sister, and he will sit between them in this world forever.  Nt 277

May N be encircled by Sah, by Sopdet and by the Morning Star, may they set you within the arms of your mother Nut, may they save you from the rage of the dead who go head-downwards, for you are not among them and you shall not be among them, ...... CT 44

My mother is Sopdet, and she prepares my path, she sets up a stairway to this very great plain of Nenmut for my ascent from the Valley of the Mountain of the Sehseh-bird on the north within my river banks, at the place whence Sah issues.  I find Sah standing in my path with his staff of rank? in his hand;  I accept from him and I will be a god by means of it.  He gives me his staff which is in his hand, and I will cause the strong ones(?) to tremble by means of it, I will spit on(?) the great ones by means of it, it will make me noble in the presence of Sopdet, it will make me secure in the Mansion of Sah.  I ascend and appear as a god, my signs of rank are on me, and I will make the lands of the Fenkhu impotent through them.  I sit on a throne within the shrine and make summons to Sah that he should come to me:  O Sah, come and see me!......Come Sah, and see me..... Come Sah, and bring me these two shares of mine of the cuts of meat........Come, be a spirit, be equipped' - so says Sah to me........they shall assemble the Children of the Red Crown, being noble in the house of the Two Souls; who given suck in the Mansion of Sah ...... Sah speaks.  You have spoken truly - so says Sah to me ...... CT 469

Spell for reaching Sah.  ........O Sopdet my soul, make my path ready, set up a stairway to the great plain, for you are my mother(?), and Hu is at (the place) whence Sah issues.  I find Sah standing on the path with the staff in his hand, and I set up the staff and receive it, and I am a god by means of it.  He gives me the staff which is in his hand, and he says:  'Give me my son, for it is he who rises in peace;  you shall be ennobled before your throne, for you are my son, the lord of my house'.  CT 470

It is Sah who has given me his warrant;  it is Mesekhtiu / Plough / Big Dipper which has made a path for me to the western horizon;  it is Sopdet who greets me as the birth of a god.  CT 482

As Sah's birth should not be barred, you should not bar this Pepi when he comes to the place where you are.  As Sopdet's birth should not be barred, you should not bar this Pepi when he comes to the place where you are.  P 508;  PT 569  §1436

In northern Egypt, the heliacal rising of Sirius (spdt), took place around June 26th +- 2 days during the OK, and roughly coincided with when the ancient Egyptians expected the beginning of the annual inundation of the Nile at Abu (Aswan) in southern Egypt.  The exact timing of the inundation varied, as it depended on when the monsoon rains fell on the Abyssinian plateau, but it normally began around the time of the summer solstice at the end of June. (summer solstice c.2570 BC, about the 26th of June;  heliacal rising of Sirius, also around 26-27 June).

Sah (sAH, 'Orion') and Sopdet (spdt, 'Sirius') were closely associated with the important ancient Egyptian calendar and the beginning of the year already in the OK:

This Pepi has come to you, lord of the sky.  This Pepi has come to you, Osiris.  This Pepi will wipe your face and clothe you with a god's clothing, having become clean for you in Djedit (Ddt, necropolis of Iunu).  Sothis (spdt, 'Sirius'), your daughter whom you have desired, [who makes] your [fresh vegetables (rnpwt) in] her identity of the year (rnpt), is the one who led this Pepi when this Pepi came to you.  P 327  (PT 477  §964-5 P;  Sethe Vol 2: 39)   ('year' = D21 (r) N35 (n) Q3 (p) X1 (t) + ideo. M4 (rnpt))

(note:  a possible play on words between 'fresh vegetables' (rnpwt.k) and 'year' (rnpt))

RECITATION:  Ho, Pepi!  You are the big star that is Orion's companion, who travels the sky with Sah and rows the Duat with Osiris.  You shall emerge in the eastern side of the sky, renewed at your proper season and rejuvenated in your time, Nut having given you birth with Sah, the year having put your headband on you with Osiris.  P 317 (T 213; M 290; N 464);  PT 466  §882

Middle Kingdom reference linking spdt to the year and the beginning of the year:

Sah (sAH,'Orion') speaks:  'He is my son, older than I (sic)' - so says Sah '....N, who is pure and young, and Sopdet (spdt, 'Sirius') bore him, (even) she the young (rnpii), she of the year (rnpt), a goddess from her birth who is at the start of the year... CT 689  §319 Vol 2: 253

(note:  a possible play on words between 'young' (rnpii), and 'year' (rnpt))

Sopdet (spdt, 'Sirius') may have been associated with the inundation as far back as the first dynasty.  An ivory plate from the reign of king Djer shows a cow with a feather (H6) between the horns, and above the 'feather', a dark disk.  Below the cow are three plants on a horizontal base similar to M8, ideogram for the Akhet season (Axt. 'inundation (season)').

Conclusion

Wall:  "If any celestial significance is to be attributed to the shafts it should be of a general orientation towards the northern and southern skies, which is supported by the fact that Khufu’s successor’s pyramid name contains “sehdu ‘firmament’ or ‘starry sky’."

The translation of the name of Djedefra's pyramid, 'Radjedef belongs to the firmament / starry sky', is at least 30 years old (Hornung has it in his 'History of AE').  Wall again fails to give modern translations by acknowledged experts in the ancient Egyptian language of the Old Kingdom.  The Dyn 4 pyramid of Djedefra, son of Khufu, was named: 'Djedefre is a shining star' (Strudwick 2005); ‘Radjedef's star’ (J.P. Allen 1998); 'The Pyramid which is the sehdu-star' (Baines & Malek 1986); 'Djedefre is a sehed-star' (Edwards 1985).

Wall's critique is flawed - he misrepresents a respected authority by only quoting half his sentence, he carefully selects his 'evidence', but ignores other equally valid evidence that necessitates different interpretations.  He assumes too much, he ignores or seems unaware of the uncertainties of the survey data, and lack of data for crucial sections of the lower shafts, and for not even considering the crucial survey data for the top ends of the upper shafts that define specific areas of the sky the top ends are actually facing.