The findings in the above titled paper, which was supported in the same Nature issue by an article from Dr. Owen Gingerich, the veteran astronomer from Harvard , have been vented in the international press in at least 20 countries and in hundreds of dot.com news-lists as a major Egyptological event. In the paper the author, Dr. Kate Spence of the Faculty of Oriental Studies at the University of Cambridge, well-known to British viewers for her appearance on BBC Horizon ‘Atlantis Reborn’ and other ancient history programmes, makes the following claims:
- Dating the Giza Pyramids: That the Egyptian pyramids at Giza have never been accurately dated.
- Simultaneous Transit Method: That the method used by the ancient builders in their attempt to determine true north was by aligning a plumb-line to the ‘invisible line’ formed by the great circle passing through the star Kochab ( b Ursa Minor) and Mizar ( z Ursa Major) and to the north-south axis of the west or east side of each pyramid.
- Misalignments of Pyramids as a Function of Precession: That this method produced a misalignment ‘error’ of the west or east side of each pyramid which can be explained as a function of the precessional drift of the ‘invisible line’ away from the north celestial pole.
- Anchoring the Old Kingdom chronology: That the date for the start of construction of the Great Pyramid can be fixed by her dating method to 2478 BC +/- 5 years and can serve as an anchor for the Old Kingdom chronology.
One of the great appeals of Spence’s thesis, especially concerning item (c) above, is that it offers a mathematical ‘model’ showing on X-Y graphs the relationship between precessional drift and the misalignment of the pyramids which can be evaluated per se. At first sight the two neatly parallel lines, which represent respectively the misalignments of the pyramids and the Precessional Drift plotted against time, appear to confirm her theory in a way that clinches the deal for the scientifically-minded. On closer examination, however, the paper reveals flaws and errors, inconsistencies and unjustified assumptions that undermine the originality and validity of the claims that Spence was allowed to make in Nature.
Let us examine these claims:
Dating the Giza Pyramids.
First the claim that the pyramids at Giza have never been accurately dated before is not correct. Spence simply ignores the scientists and researchers who came before her. As one eminent astronomer put it to me, this was not very ‘polite’. In 1838 Sir John Herschel was the first to use precession to attempt to date the Great Pyramid by using the pole star, Thuban; and was followed by the Scottish astronomer Charles Piazzi Smyth in 1865 who used the same method . More recently, in 1964, astronomer Virginia Trimble and Egyptologist Alexander Badawy used precession to determine the stellar alignments of the so-called air-shafts of the “King’s Chamber” of the Great Pyramid by referring to data from Petrie’s 1881 survey, and computed that these shafts were sloped to Delta Orionis in the south and Alpha Draconis in the north at about 2600 BC . In 1990 I also used the same data to compute that the southern shaft of the Queen’s Chamber was sloped towards Sirius in c. 2750 BC . However, in 1993 the slopes of these shafts were more accurately measured by the German engineer Rudolf Gantenbrink, and with this new data I obtained a date of 2450 BC +/- 25 years for all four shafts . This date was confirmed in 1995 by the Scottish astronomer, Dr. Mary Bruck, although she assumed a +/- 60 years margin of error . A simple calculation shows that this estimate falls within the 2478 BC +/- 5 years date claimed by Kate Spence. Adding as brief paragraph or footnote to her paper to cover this historical background would have given it the scholarly ethics it sorely lacks on this specific issue, but as I understand it, it was apparently the referees of Nature advised against it.
It must be remembered that the Pyramids of Giza are, astronomically speaking, equinoctial monuments and thus any methods using the azimuth change of stars are bound to be fraught with much uncertainty. This, inter alia, is because the misalignment error could very simply be due to surveying and constructional problems, and/or naked-eye limits of resolution, rather than the result of the precessional drift. In any case, Spence’s method is by no means novel. Several years ago, in 1984, the astronomer Steven C. Haack of Nebraska University introduced the idea of using the precessional drift of stars to define a new chronology for the Pyramid Age . And although Haack used the azimuth at the horizon rather than azimuth at the celestial pole, the method is fundamentally the same. It also must be mentioned that Haack’s method was used again by French astronomer Karine Gadre in 1998 . Using the east horizon rather than the pole region is, in fact, more justified (if perhaps less accurate), for it is well-known that the south and north sides of the pyramid are more accurately aligned to the cardinal directions that the east and west sides . For example, the south side is only 1′ 57″ S of W as opposed to a 2′ 30″ W of N for the west side which Spence’s used . The real problem, however, with azimuth methods such as proposed by Haack and Spence is that the accuracy required for naked-eye observations is, in practice, almost impossible to achieve . The astronomer Brad Schaefer from Texas University rightly pointed out that the scatter about Spence’s theoretical curve is ~ 2 arc-minutes on the X-Y graphs displayed, yet the stars she uses are faint enough that their perceived naked-eye appearance is about the same size . Schaefer also pointed out that the accuracies of naked-eye sightings required by Kate Spence are theoretical and cannot be achieved in practice ‘because with the perceived size of the stars and the speed of motion, it is impossible for the human eye to get the 25 second timing accuracy required’ .
Furthermore, there is a mathematical error in Spence’s paper pointed out by the astronomer Dennis Rawlins of Baltimore and his colleague Keith Pickering of DIO magazine. In their own words, ‘Spence (or Stephenson [the astronomer whose calculations Spence used]) correctly computed that the inter-star line between Kochab and Mizar moves past the North Celestial Pole at 27’ per century, but that is not the rate at which the azimuth of the vertical line between them changes. To get the rate of azimuth, you must divide by the cosine of the latitude, which in this case yields an azimuth change of 31′ per century.” Pickering and Rawlins suggested a better solution: “to wait until Thuban (the ‘classical’ Egyptian pole star) and nearby star 10 Draconis are at equal altitude, and bisect the small angle between them. This method yields a change of 27.4 arcmin/century, which is much closer to the 28 arcmin per century change of the pyramids themselves.”  I asked the astronomer Dr. Ed Krupp of the Griffith Observatory what he made of this error, and this was his comments: ‘I know Dennis Rawlins well enough to figure he is likely to be right on this count. If my understanding of the error is correct, Kate Spence’s use of pyramid construction chronology can no longer be used in support of her pyramid alignment proposal.’  This elementary error has, in fact, been now acknowledged by Dr. Owen Gingerich, the Harvard astronomer who originally promoted Kate Spence’s paper. Gingerich confirmed that ‘there is a small error in Kate Spence’s paper on this point, which compresses the time scale on each side of the zero point by about 15%.’ 
For the record, in 1995 the astronomer Dr. Mary Bruck pointed out that although in archaeoastronomy the dating of ancient monuments is generally performed from azimuth observations, this cannot be satisfactorily applied to the Egyptian pyramids because they ‘are oriented towards the cardinal points of the sky, directions which do not alter with time. The visible effect of precession, if it exists, must be looked for in evidence of stellar altitudes rather than azimuth.’ . Thus the change in declination, not of azimuth, of stars measured at the meridian is the correct method to be used. Fortunately the Great Pyramid contains numerous tunnels and shafts inclined towards the meridian. If any of these were directed to stars, and if we know which stars might have been used, then we are provided with the correct means to attempt to date this monument. This is precisely the reason why in 1964 Dr. Trimble and Dr. Badawy used the so-called ‘air-shafts’ of the Great Pyramid for dating purposes. Among Egyptologists and, later among astronomers, the possible stellar links of the shafts received serious attention because of the well-known association of Orion to the rebirth cult of the Pyramid Age . The fact that the ‘astral shafts’ were not used as actual sighting devices because of various features that impeded such a possibility, was not seen as an obstacle to this theory, since pyramid specialists such as Dr. I.E.S. Edwards rightly argued that, like many other features in Egyptian monuments, the shafts essentially served a symbolic and magical function. And although these days there are the occasional voices raised in protest against this conclusion (chief among them Rudolf Gantenbrink and Dr. Zahi Hawass ), there is nonetheless overwhelming support for the stellar association of the shafts coming from both the Egyptological and astronomical professions . In any case, for Kate Spence to have completely ignored in her paper this important issue and the eminent scientists who had worked on it, is not just a reflection of some inexplicable ‘oversight’ or academic ‘impoliteness’ but also highlights a very worrying trend amongst scientific editors and referees to opt for ‘economy and simplicity’ in an article at the expense of historical facts, irrespective of the validity or acceptance of the theory. Kate Spence, however, apparently now claims that her paper in Nature was intended to merely ‘test’ her views in the scientific community, but this is a very lame excuse for ignoring or being economical with the facts in such a blatant manner. At any rate such a motive was most certainly not made explicit or implicit in her original article, hence the huge reaction by the scientific media, which, upon seeing the supporting article in Nature by Dr. Owen Gingerich, readily accepted Spence’s findings as scientifically proven facts.
The Simultaneous Transit Method:
Spence claims to have started with a blank-slate approach to find the stars that could be used for the so-called Simultaneous Transit Method. Apparently after a series of trials and errors she happened on the stars Kochab in Ursa Minor and Mizar in Ursa Major and noted that these two stars were directly above each other in c. 2467 BC. She then called the imaginary line that joined these two stars the ‘invisible chord’. In actual fact, however, the idea of an ‘invisible chord’ between Kochab and Mizar is depicted in several diagrams of my earlier publications, albeit not for the same purpose but rather in connection with the simultaneous rising of Orion’s belt in the east and the Great Pyramid only . It should be pointed out that although there is ample evidence in the ancient Egyptian texts that Orion was observed at rising, there is, in contrast, absolutely no textual support to suggest that Kochab or Mizar, simultaneously or otherwise, were used for aligning pyramids to true north. To be entirely honest about this, the ancient methods are unknown, and if these were indeed stellar, we simply cannot tell which stars they used. In my opinion single star transits using a star in Orion or the star Sirius (which are mentioned in the texts) could have done just as well as the northern stars in simultaneous transit proposed by Spence. As for the Simultaneous Transit Method itself, there is a logic that escapes me in Spence’s paper. Her reasoning, if I understand it well, shows that the Great Pyramid (Khufu) at Giza was the best aligned to true north using the ‘invisible chord’ in c. 2478 BC +/- 5 years on the west side (running south to north). Spence arrived at this conclusion by matching the 2.8 arc-minutes westerly misalignment of this side of the pyramid to the westerly angular distance of her so-called ‘invisible chord’ measured from the north celestial pole. She then reasoned that the pyramids that were built earlier would have greater westerly misalignments than Khufu’s, and that those built later would have greater easterly misalignment. She then goes on to say that there is evidence that shows that the techniques and precision of sighting and fixing the alignment of pyramids were the same throughout the Pyramid Age, and also states that such precision should have improved after the Great Pyramid. But surveying and setting-out precision, however, goes hand in hand with construction standards. And here, contrary to what Spence assumed, there is considerable evidence that the standards of engineering of pyramid-building were lower before Khufu’s reign, and deteriorated very rapidly again after the 4th Dynasty. Thus to ignore this and then to consider only the surveying aspect is, to me, being ‘selective’ with the evidence. There are also religious and cultic issues to consider in this matter. It must be appreciated that the astronomical alignment of pyramids was essentially a religious matter, carried out according to strict religious rituals and fixed religious dates. A pyramid project was, after all, an enterprise that would require many years to plan and several decades to construct, and thus the site preparation including the astronomical alignments were carefully and meticulously implemented according to a long-established tradition. Now according to Spence, in order for her theory to work, she had to assume that some of the alignments on the ‘invisible chord’ were taken with Kochab at upper culmination and Mizar at lower culmination; and others taken in reverse, that is with Mizar now at upper culmination and Kochab at lower culmination. The astronomer R.H. Van Gent pointed out, however, that ‘there is no period in the year when both situation can be clearly viewed on the same night’ [HASTRO-L Sat.18 Nov. 2000]. Furthermore also for the theory to work, Spence had to also assume that in some cases it was the north-south axis of the west side of the pyramid that was aligned to the ‘invisible chord’ and that in other cases it was the north-south axis of the east side. Such assumptions, however, would have required radical changes in the rituals and also radical changes in the religious dates between the successive reigns of Khufu and Khafre, which would be somewhat inconsistent with how religious bodies normally behave on such matter, especially in antiquity. Even today, for example, Islamic priests would be extremely reluctant to alter the astronomical computations related to the feast of Ramadan, as much as Roman Catholics abhor any change the astronomical calculations for dating Easter each year. There is, too, another ‘Catch-22’ reasoning by Kate Spence that does not seem to add up, and it is this: in order for the ancient Egyptian priest-astronomers to know which stars culminated simultaneous on and/or near the great circle going through the celestial north pole (meridian), they obviously had to know beforehand where the north celestial pole was in the first place. This would imply that they already had a means to establish true (or near-true north)!
Misalignments as a function of Precession:
Most of the objections are dealt with in items (a) and (b) above. Apart from these, there are other miscellaneous factors that undermine Spence’s method. For example the problem of parallax has been mentioned. Aiming a plumb-line at an ‘invisible chord’ adjoining two stars which are some 22° away from each other is rather a tricky business to say the least, as just a slight uneven blinking of the viewers eyelids can cause a parallax effect on the plumb-line, especially in the pitch-dark conditions such as required by Spence’s method . On the other hand the measuring of the declination of a single star using a simple inclinometer for aligning the shafts or tunnels in the Great Pyramid does not carry this parallax problem.
Anchoring the Old Kingdom chronology:
Using the 2.8 arc-minute misalignment of the Great Pyramid’s north-south axis of the west side, and equating to the precessional drift of her ‘invisible chord’, and assuming that construction began on the second year after alignment, Kate Spence dates the monument to 2478 BC, allowing a +/- 5 years margin of error which, she then claims, she will refine to +/- 1 year after more field research. To begin with, even if her method was valid, the date of 2478 BC must immediately be adjusted now by 15 % over one century, thus to c. 2463 BC to account for the latitude/cosine factor error as pointed out by Owen Gingerich. Furthermore allowing only a +/- 5 years (let alone +/- 1 year!) margin of error is, I think, somewhat unrealistic, for this demands an accuracy of 1.35 arc-minutes with naked-eye observations which, in practical terms, cannot be achieved according to astronomer Brad Schaefer. Regarding this point, astrophysicist Chris Doran of the Cavendish Laboratory at the University of Cambridge, also suggested that a +/- 20 years margin of error would be more acceptable in these circumstances .
All in all Kate Spence put forward an interesting proposal as to how the ancient pyramid builders might have attempted to align their pyramids to the meridian. But that is all. There are far too many uncertainties and errors in her paper to sustain her other proposals that such a method can anchor Old Kingdom chronologies. As for the dating of the Great Pyramid, I maintain that the best estimate is still 2450 BC +/- 25 years as obtained with the inclination of the shafts. I note, however, that Kate Spence is preparing a larger paper for an archaeological journal in which she may account for the various points made here and presumably elsewhere. Meanwhile she must be commended for drawing attention to this fascinating but highly neglected topic.
- NATURE 408, 16 Nov.2000 pp.297-8, Plotting the Pyramids, by Owen Gingerich.
- Piazza Smyth, The Great Pyramid (4th edition) reprint of the 1880 ed. Published by W. Isbister, London (Our Inheritance in the Great Pyramid), by Dell Publ. NY 1990, p.368.
- Virginia Trimble, Astronomical investigation concerning the so-called Air-shafts of Cheops’s Pyramid, in Mitteilungen der Institut Fur Orientforschung, Band x, Heft 2/3. pp.183-7, 1964.
- Robert G. Bauval, The seeding of the star-gods: a fertility rite inside Cheop’s Pyramid?, in Discussion In Egyptology vol. 16, 1990, pp. 21-5.
- Robert G. Bauval, Cheop’s Pyramid: A new dating using the latest astronomical Data, in Discussions In Egyptology vol. 26, 1993, pp. 5-6.
- Dr. Mary T. Bruck, Can the Great Pyramid be astronomically dated?, in Journal of the British Astronomical Association, vol. 105, 4, 1995, pp. 161-4.
- Steven C. Haack, The Astronomical orientation of the Egyptian Pyramids, in Archaeoatronomy, vol. 7 (Journal for The History of Astronomy, XV, 1984).
- Karine Gadre, L’Orientation astronomique des Pyramides d’Egypte, l’Ordre Celeste recree, Edition La Maison de Vie, 1998, ISBN 2 909 816 29X.
- Somers Clarke & R. Engelbach, Ancient Egyptian Construction and Architecture, Dover Publ. NY 1990 (from 1930 ed.), p.68.
- Brad Schaefer, HASTRO-L, Sat. 9 Dec. 2000.
- Brad Schaefer, in private communication with author.
- Keith Pickering and Dennis Rawlins, HASTRO-L, 9 Dec. 2000.
- Ed Krupp in private communication with author.
- Owen Gingerich in private communication with author.
- Mary T. Bruck, Op.cit.
- R.O. Faulkner, The King and the Star-Religion in the Pyramid Texts, J.N.E.S. xxv, 1966, pp.153-161. See also Jane B. Sellers, The Death of Gods in Ancient Egypt,Penguin 1992; and R.A. Wells, Sothis and the Satet Temple on Elephantine: A direct Connection, SAK 12, 1985; also BSAK 4, 1990
- See Dr.Zahi Hawass, article on Website entitled the Gold Pyramidion to Cap Khufu’s Pyramid (http://guardians.net/hawass/millennium1.htm)
- See for example I.E.S. Edwards, The Pyramids of Egypt, Penguin 1993 ed., p. 284-5. Also E.C. Krupp, Echoes of the Ancient Skies, Oxford University Press 1993, pp.102-5.
- Robert G. Bauval & Adrian Gilbert, The Orion Mystery, William Heinemann hardback ed., fig. 15a and p. 279. Here is the quote from p.279: ” In a previous article by R. Bauval (DE 28 1994), it was shown how the rising of the star Zeta Orionis in the east coincided with the meridian passage of the star Kochab in Ursa Minor… It follows, therefore, that the heliacal rising i.e. rebirth, of Zeta Orionis, the ancient builders could predict this all important event –the ‘rebirth’ of the star– by observing… the upper culmination of Kochab. This would strongly suggest that the heliacal risings of stars were not merely determined by waiting patiently for their rising at dawn –which could be frustrated by haze over the horizon, clouds and excessive refraction– but by cleverly using the circumpolar stars as markers on a sort of ‘star clock’, with a given meridian upper or lower culmination of specific circumpolar stars ‘marking’, as it were, the time of heliacal rising of another, non-circumpolar star.”
- A simple demonstration is to look at your extended hand with your thumb upright and aim with both eyes open at an object in the distance; then close the left and right eye. The thumb will appear to change position relative to the object in the distance. Usually the right eye is dominant, but this is not always the case. Such parallax errors are easily made when dealing with naked-eye observations at night using rods or plumb-lines.
- Private communication with the author.