Shafting the stars

or

Never mind the quality, feel the width   ^[1]

By John Wall

Publisher's note:  Wall's rebuttal here is well reasoned and well composed.  Tedder's argument nips around the edges of the real topic in a vain attempt at casting doubt on the latest research into the heretofore enigmatic shafts of Khufu's pyramid at Giza.  They remain a mystery so long as we look at them as "star shafts" intended to launch the king's soul into the heavens.  No one can find evidence to support this because, quite simply, it wasn't the purpose of the shafts.  When one looks closely at the subject though, and applies simple, objective rules to the argument (as I do with my article on this site entitled, "The Nature of a Good Shafts Theory") one can easily see the glaring flaws in Tedder's criticisms. -- A. Sakovich

My JHA 38 (2007) article ‘The Star Alignment Hypothesis for the Great Pyramid Shafts’ has been criticised by Tedder.

Although not published until 2007, my article reached its final form before submission in the middle of 2006, after a somewhat leisurely gestation over the previous few years. Everything can be improved but there is, however, nothing in the critique that leads me to change my conclusion that the shafts in the Great Pyramid were not intended to ‘target’ the culminations of various stars.

Tedder provides extensive background about the modern study of the shafts which, although not without interest, is largely irrelevant. There are no extant Egyptian texts that make any reference to them, an absence that, within reason, permits many possible explanations of their original purpose.

Compiling information is straightforward enough, even if sometimes time consuming; analysis and the formulation of conclusions is, however, more difficult. Tedder’s diligence in the former is outweighed by flaws in the latter. His critique contains a large number of references from various periods in Egyptian history, and also from studies in modern Egyptology. But his attempts to analyse and determine the relative importance and/or significance of this material are erratic; never mind the quality, feel the width. He also perpetrates a number of logical fallacies, which I have identified, as well as making frequent use of argument from authority.

It is important to state that I believe that the four shafts should be treated as a ‘set’. It is not known whether those from the Kings Chamber were originally blocked like those from the Queens Chamber; the latter, of course, terminate in the masonry. However, in other respects they share common characteristics. Consequently, I consider that it is methodologically sound to contemplate, and subsequently examine, a common purpose.

Tedder begins by accusing me of being disingenuous:

the title of the article implies he is examining THE star alignment hypothesis, but inexplicably fails to state WHOSE star alignment hypothesis - although he does not actually state this, it turns out he is only examining Robert Bauval's ideas on the shafts, while virtually ignoring the original 'stellar destiny of the pharaoh' proposal by Egyptologist, Alexander Badawy, in 1954 - a clever strategy, as the unwary could be misled into believing Wall has invalidated the 'star alignment hypothosis'  after apparent flaws in Robert Bauval's theory are pointed out.

Let me remind the reader that my article begins with the following statement:

The purpose of this article is to examine the contention that “…an increasing number of Egyptologists are now accepting that they (the shafts) may be aligned towards star culminations”. (p199)

Note the use of the word “shafts”. Or was I misplaced in my assumption that the reader would recognise the use of the plural as a reference to all four shafts?

Tedder’s section Background information on the shafts provides lengthy quotes that are not considered relevant (see above). Badawy’s studies addressed only the Kings Chamber shafts and Badawy proposed different functions for the shafts: one targeting a star, the other an asterism.

In Cosmology Tedder immediately sets up a straw man:

He seeks to show that star culminations were of no interest to the ancient Egyptians in the Old Kingdom and that the horizon was the most important part of their sky.

The final sentence of that section of the article states:

We therefore lack evidence that culminations were of major interest and/or importance in that era, although this is an argument from silence.

He then claims that:

Wall cites names of pyramids he believes allude to the horizon, but inexplicably fails to cite translations by acknowledged experts that again weaken this argument.

Scholars are not always in agreement on such points. There are variations in translations and, in the case of the Great Pyramid, there’s also Baines and Malek’s[2] ‘The Pyramid which is the Place of Sunrise and Sunset’ (the horizon), Goedicke’s[3] ‘…it has to be taken as (western) horizon of Khufu’ or Edwards[4] ‘Cheops is one belonging to the horizon.’

The translations mentioned by Tedder include:

‘the place of Snefru's appearance’, and ‘the southern place of Snefru's appearance’ (J.P. Allen)

'Sneferu Gleams', and The Southern Pyramid 'Sneferu Gleams' (Edwards)

'The Shining Pyramid', and 'The Southern Shining Pyramid' (Baines & Malek)

If the name does incorporate an ‘astronomical’ reference then ‘appearance’ suggests ‘horizon’. Despite Tedder’s reference to Baines and Malek’s and Edwards translations of the names of the 4th dynasty Dahshur pyramids he inexplicably fails to include their translations of Akhet Khufu (given above). ‘Gleams’ or ‘shining’ both suggest the sun; a pyramid encased in brilliant white Tura limestone would be dazzling during the day – like the sun. Most translations suggest ‘horizon’; none suggests star culminations.

Within a number of quotes Tedder suggests that:

Translating 'Akhet' simply as 'horizon' may not convey the true meaning of the Akhet, as the Akhet extends far below the horizon.

That may well be the case, but there is nothing in it to indicate star culminations.

Tedder goes on to suggest:

Alternative translations of the name of Sahura's pyramid / complex, xa-bA-sAHwra:

‘the place where Sahure's manifestation appears’ (J.P. Allen)

'The ba of Sahure gleams' (Edwards)

Again, as with Sneferu's pyramids, this name can simply mean the pyramid itself was a shining / gleaming manifestation of the king's ba.

As I mentioned previously, however, ‘appears’, in a context where it is believed that an ‘astronomical’ meaning is implied, suggests ‘horizon’; again, there is nothing here to suggest star culminations.

He does not mention that my article notes that ‘contemporary royal names; Khafre, “Appearing like Re”, contains the hieroglyph of the sun rising over a hill, as does the name of the late third dynasty king Khaba.’ (p199)

Tedder then gives a long list of stellar references from various periods: another excellent example of assembly of information unaccompanied by relevant analysis; never mind the quality, feel the width. It is possibly an example of argumentum verbosium.

Faulkner[5] concluded, of the Pyramid Texts, that:

…behind this lay a very ancient stratum of stellar religion, in which the stars were regarded as gods or as the souls of the blessed dead…

while Edwards[6] poetically outlined the syncretic nature of Egyptian religion:

That conservatism so noticeable in Egyptian art is even more emphasized in matters of religion; elements which had once been admitted into the canon continued side by side with later innovations, even though they were logically superfluous and sometimes irreconcilable…..The impression made on the modern mind is that of a people searching in the dark for a key to truth and, having found not one but many keys resembling the pattern of the lock, retaining all lest perchance the appropriate one should be discarded.

Tedder’s references succeed only in corroborating this!

In Slope Geometry there’s immediately another straw man:

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.

My article states that ‘Gantenbrink did succeed in establishing the shafts’ principal angles of slope’ (p199); and it was these angles that were used in my article. The variation of slope (which Tedder discusses) implies that choice played some part in the construction. Although Tedder omits any mention of this point, my article later (p200-2) suggests how the principal angles of the shafts could have been determined; If Tedder wishes to propose a ‘correction’ or ‘fine tuning’ in order to obtain the angle of the final part of the shaft, he would have to explain why that slope wasn’t used earlier; suggestions of incompetence do not satisfactorily address this question. My article explains the grounds for my assumption that seqeds were employed (p200); considering a maximum difference of 0.88%, this is reasonable. The analysis performed later (p203) – which is not addressed by Tedder – results in wide date ranges for the shafts; from 100 to over 250 years.

Tedder then moves away from critiquing my work, and instead tries to make a case for Badawy’s proposal (which I have discussed above).

Tedder claims that:

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.

As mentioned above, I believe that the shafts should be taken as a ‘set’.

Later, Tedder states:

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 precision 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.

Based on the analysis my conclusion is correct. I am unsure as to why I should provide an explanation for the particular slope chosen. It is, as the article identifies (p204), 14:17.

Tedder goes on to note that:

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 .

The Shaft Alignment Dates section (p200-1) of my article discusses the observation of culminations. This is, of course, entirely hypothetical; there is no evidence for this being undertaken in the Old Kingdom . Whilst the builders were capable of extremely high quality work, they sometimes followed the old adage of ‘out of sight, out of mind.’ My article provides tables showing that the tolerances on the potential dates from the shafts were, as noted above, from 100 to over 250 years. (p203)

Tedder then states:

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.

and follows this with another lengthy set of quotes; once again never mind the quality, feel the width.

Tedder begins his Conclusion by commenting that I have used a translation by Hornung of the name of Djedefre’s pyramid that is now some thirty years old. This translation appears in a 2001 work by Quirke (who references Helck in the Lexicon), a date contemporary with the works referenced by Tedder.

Tedder continues:

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.

The quote from Allen is considered valid and the supporting evidence reinforces the conclusion. There is 4th dynasty evidence to definitely, as well as probably, demonstrate the importance of the horizon at that time. In contrast there is little evidence for the importance of culminations at that time.

I discuss the various areas where uncertainty prevails in my article. More, and better, data is always welcome, but we can work only with what is available to us. The question of the slopes of the top ends of the shafts has been addressed above.

Pausing only to discuss astronomical dating (which I have addressed above), Tedder concludes with:

Badaway's proposal that the upper shafts were 'targeting' stars is certainly not proven, but based on the compelling circumstantial evidence and the sparse textual evidence, it still remains a feasible theory put forward by an experienced Egyptologist, that explains the purpose of the shafts.

On the basis that Badawy was proposing that the shafts targeted a star and an asterism, this statement is incorrect.

Whether it is contended that the shafts (two or four) ‘target’ the culminations of stars or asterisms, there are several important conditions that have to be met.

1. Evidence must be provided to invalidate the conclusion that ‘We therefore lack evidence that culminations were of major interest and/or importance in that era, although this is an argument from silence.’ The important word is ‘major’; the shafts were not easy to incorporate and must have required a very compelling justification. I get the impression that Tedder fallaciously believes that by casting doubt on whether some terms refer to the horizon, references to star culminations can be assumed as a valid alternative. It is a non sequitor to assume that ‘evidenced A’ being uncertain means that ‘unevidenced B’ is certain.

2. There has to be evidence for an adequate ‘infrastructure’ which could have undertaken the necessary astronomical observations. The lack of physical evidence for a temple in a certain era (which may lie under a later structure or a modern settlement) can be remedied by a textual record of a priest of that temple. Similarly, astronomical ‘records’ may not survive but there should be some indication of those who performed the observations. My article has a section (and see Note 22), Astronomical Observations (p202-3), which explores that subject and concludes ‘If it was of sufficient importance for a man to have the skills, and to spend almost three months “observing”, to be able to “align” the shafts, this would have been identified somewhere in the titulary.’ (p203) In hindsight it would have been appropriate to reference Quirke’s[7] analysis of the title of the High Priest of Heliopolis which indicates that it may have been ‘He who Sees the Great One’ in the Old Kingdom rather than the more familiar ‘Greatest of Seers’.

Tedder’s critique, overall, is little more than a straw man. It is easy to dispute the interpretation of terms – as do many Egyptologists. He can also argue about the measurements of the slopes of the shafts, their geometry, the abilities of the builders and potential astronomical dating, and, by this method, he seeks to cast doubt on the whole work.

He has not, however, refuted my conclusion that ‘there are too many areas where a culmination-alignment hypothesis lacks support.’ (p205)