Technical examinations:
The shafts

After our attempt to find a link between Giza and Osiris failed, we are forced to examine other possibilities. It might be possible that the Egyptians reconstructed Orion although it had noting to do with Osiris at that time. So if we can prove this, Bauvals Osiris-idea might be wrong, but the Orion theory still remains valid.
Therefore we will now examine Bauval's "technical" evidence step by step. Unfortunately it is very theoretical and might be difficult to understand in some places. If something is difficult to understand, or if there are still questions, please contact me.

Shafts/Stars?

As an introduction, a few words about the general idea and methodology of dating something "with stars". And about some of the problems which might occur.

To point at a star

Fig. 11 - Target of shafts

As mentioned in he introduction there are four tiny shafts in the Great Pyramid whose functions are unknown. Before Bauval several researchers had the idea that these shafts could have a symbolic connection with the stars. If they are intended as exits for the different souls (Ach/Ka/Ba) they could point in the general direction of the destination of the soul, which would probably be the highest point a star reaches in the south (the so-called culmination point).
The northern shafts can, of course, point in two directions. The constellations high in the north never set, so they describe small circles around the celestial pole. So a shaft could aim at the highest or lowest point of the circle, the upper or lower culmiantion.
The pyramid builders must have designed such shafts to match their current view of the sky. And if we now know at which star each shaft should point, we can calculate when the star reached the same angle in the sky as the shaft. This would be the date of the design. And because there are four shafts we can use statistics to average out any building errors which probably occurred.

Evidence for star-targeting-idea may be a precise north/south-course of both southern shafts. But one theory can certainly be rejected: These shafts could never have been used to look at a star. They go horizontally for the first few metres, and then bend upwards. Additionally they have several horizontal bends so there was never a direct view of the sky.

Shaft and accuracy

The slope of the shafts was first accurately measured by Rudolf Gantenbrink; in 1993 he worked under contract to the "Deutsches Ärchäologisches Institut" (DAI) to clear, check and measure the shafts. He used several small robot vehicles and his most famous discovery is surely the stone object blocking the southern shaft from the Queen's chamber. This blocking stone has been the centre of much heated debate and speculation. But this object is not discussed on these pages.
His robot UPUAUT II, in combination with another vehicle, permitted measurement of the inclinations to an accuracy of 1/20 or 3'. Gantenbrink gave these values personally to Robert Bauval and also published them in the official journal of the DAI, the "Mitteilungen des deutschen Archäologischen Instituts Abteilung Kairo" (MDAIK)t[1]. I mention his because it becomes important a little bit later...
Gantenbrink writes that the inclinations of the upper shafts could be measured by drawing a line between the beginning and end of the shaft, and that the shafts, although bending horizontally, were extremely precise. With a laser measuring device he didn't find any differences in the width of the shafts of greater than 0.005 m.
Even more fantastic is the fact that the beginning and the end of a shaft are precisely on one line, even though the shafts bend inbetween![2]

The situation with the lower shafts is a bit different. The northern shaft shows settling which might have occurred due to an earthquake during the building phase, Gantenbrink therefore says that the current shaft inclination might vary from the planned angle by up to 2. The southern shaft, on the other hand, has the same accuracy seen in the upper shafts. Gantenbrink measured the shaft at 24 points over 30 metres and could find no deviation greater than 12' from the average.[3]
This gives a good overview of how carefully the Egyptian engineers and builders dealt with the shafts. The following table summarises the "official" inclinations for the shafts.
BTW: I will sometimes use the "official abbreviations" of the shaft names, as defined by Rainer Stadelmann, on the following pages.

Shaft Abbr. Inclination
King North nSK 3236'08"
King South sSK 4500'00"
Queen North nSR 3907'28"
Queen South sSR 3936'28"

Tab. 1 - Shaft inclinations MDAIK

Dating - how?

As previously stated Bauval is convinced that the shafts point at the culmination points of stars. He emphasizes several times in his book how necessary it is to "watch the meridianal passage" of a star. This was certainly necessary for the builders, but it is not required when calculating these points with a computer program. All you need is the declination of a star (its distance to the celestial equator) ) at the intended time. Then simply add a beta = (90 - latitude) and voila, you have the meridianal elevation without "watching the meridianal passage". Fortunately the declination is a value all astronomical programs show first.
If the angle of the shaft (inclination) is identical to the elevation of the star you've got your date. With this method you can also calculate the required declination for such a match: Inclination - beta = required declination.
With circumpolar stars you have to use (180 - declination - beta) to get the elevation, and (180 - elevation - beta) to get the declination.
To calculate the positions of the stars I used the program Redshift 3 which also performs calculation of precession and star movement. I checked the values with another program, Sky Map Pro 7. The values of both programs differed only in the area of seconds, therefore I'm only using the data from Red Shift.

Strange aberrations...

When I compared Bauval's data with the official MDAIK values I became irritated. Bauval produced three publications after Gantenbrink's discovery. Two articles in the "open" journal Discussions in Egyptology (DE), No. 26 and 27, and his book The Orion Mystery (OM). And all thre publications had different values. And all were different from the values in MDAIK:

Shaftt Inc. Bauval Inc. MDAIK Difference
King North DE26: 3228'16"
OM  : 3238'00" / 3228' *
3236'08" DE26: 7'52"
OM  : -2'08" / - 8'08"
King South 4500'00" 4500'00" -
Queen North DE27: 4000'00"
OM  :3900'00" **
3907'28" DE27: +52'32"
OM  : -07'28"
Queen South 3930'00" 3936'28" -06'28"
Tab. 2 - Data Bauval/MDAIK

* : *: In the German paperback edition Bauval uses two values: One in the table on p. 200 with the "more correct" value of 3238', later, eg. in Figure 20 on p. 240 he uses a grossly wrong value of 3228' (N.B.The Crown paperback uses 3228' consistently)
**: On p. 201 Bauval notes that there are no measurements available at the moment, so he has to use an estimated value of 39. Later he uses this value as if it was a measured angle.

These differences are peculiar, particularly as Bauval identifies Gantenbrink as the source. The origin of these incorrect values is unclear. Oh, and by the way, a difference of 10' produces a shift of constructional date of about 50 years, therefore they're not negligible.

Confusion

The "normal" way to date such a shaft would be to calculate the year in which a match between shaft inclination and star elevation took place. If the values of the different shafts are close together and the differences could be explained with building tolerances we have our date.
Bauval does nothing like this. Instead, he produces "Epochs" which he never completely explains. And he doesn't calculate exact matches, but talks of "good confirmation of the epoch 2475 BC". But what is the definition of a "good confirmation"? Either there is a match, or there isn't.

These "Epochs" are a further source of confusion - they don't match! After I compared the values in two English versions of Bauval's book with the German edition by Knaur and the values in DE , I got these epochs:

Shaft Epoch Knaur Ep. English DE
King North 2450 2425 2425
King South 2445 2475 2475
Queen South 2450 2400 2450
Tab. 3 - differing "Epochs"

The German version of the book seems to be wrong, therefore I will only use the English values for the shafts sSK and nSK . The shaft sSR is another matter, because here we have a match between the German epoch and DE 27. In reading this article I found out that Bauval used a grossly wrong inclination so I think he used a reworked epoch for his book. Therefore I will also use the English book values.

The Stars

Let`s now get to the positions of the stars and the inclination of the shafts. As a reminder I will repeat Bauval's statements concerning the shafts:

1 "In 1964 Egyptologist A. Badaway and astronomer V. Trimble discovered that the small "air shaft" in the northern wall of the King's Chamber seems to point at the circumpolar stars. Bauval modified the idea to the effect that this shaft once aimed directly at the pole star of the pyramid age, Thuban (Alpha Draconis): "This means that the shaft points very nearly toward the north celestial pole, about which the circumpolar stars seem to revolve. It is also of interest to note that, at the time the pyramid was built, the pole was marked by a bright star about as accurately as Polaris (alpha Ursae Minoris) now marks it."[4]
2 Badaway and Trimble came similarly to the idea that the southern shaft of the King's Chamber aimed in the direction of Orion. Although they used old, and incorrect, values (measured by Petrie in the 1880's and with an angular error of 30 minutes) they found an indisputable correlation between the highest southern elevation of Orion's belt and the inclination of the shaft around the assumed date of pyramid building. Bauval used the latest values and could calculate from them that the correlation was greatest around the year 2450 BCE. At that time the shaft aims directly at the westernmost star of Orion's belt, Bauval therefore claimed that this shaft directly aims at the star Al-Nitak or Zeta Orionis.[5]
3 After Rudolf Gantenbrink had demonstrated with his robot, "Upuaut II", that the shafts from the Queen's Chamber had not been abandoned after a few metres, Bauval also associated them with star-symbolic representations. The southern shaft should aim directly at the highest elevation of Sirius in the year 2450 BCE! OK, this isn't new, the oldest publication I could find was from 1919 by the German engineer Albert Neuburger. But due to the imprecise measurements available at that time he couldn't verify it..[6]
4 The northern shaft, on the other hand, points at Ursa Minor or, to be more precise, at its second brightest star Beta Ursa Minor: ""to the head of Ursa Minor, the celestial adze of Horus, also called the 'adze of Upuaut'."[7]

Let's now compare these ideas with the astronomical reality. I will come to Bauval's "epoch-method" later. In the following table I calculated the most important astronomical values for the four stars for the year 2450 BCE, declination, elevation and positional error, and the correct year of the match. After that we can ask the questions

Star Decl. Elev. Shaft Error Nec. Decl. Corr. Year
Thuban 8801' 3157' 3236' -39' 8720' -2326
Al Nitak -1449' 4449' 45 -11' -1502' -2496
Sirius -2042' 3920' 3936' -16' -2026' -2348
Kochab 8038' 3920' 3907' +13' 8051' -2385
Tab. 4 - Star- and Shaft dates compared

Interesting: At a first glance we can see that not a single star is anywhere near Bauval's suggested time of 2450 BCE. Three stars are in the region around 2300 BCE, one is near to 2500 BCE. The average is 2389 BCE, 61 years later than Bauval's dream time.
Even worse: With the exception of one star (al-Nitak) all the shafts cluster around a date of 2350 BCE, with a standard error of 20.33 years. Normally this star would be regarded as exceptional and a date of 2350 BCE accepted - 100 years away from Bauval's dream time.

Another problem as an aside: The shafts span an era of more than 160 years. This is longer than some dynasties! And it is more than double the time between Djoser's pyramid and Khufu's! You cannot date anything with such an interval; it is close to scientific quackery.

Bauvals Methodology

But how DOES Bauval get his values? Easy, he doesn't average dates but epochs. An epoch for Bauval seems to have 25 years, and if you take the average of the three epochs Bauval uses (2425, 2400 and 2475 BCE) you get 2433 BCE which can be classified as "epoch of 2450 BCE".
And what are these epochs??? Well, nothing more than a trick to eliminate unwanted deviations. These epochs work like the British voting system: All that counts is "in or out" (of course, all values are "in" according to Bauval). If a value is "in epoch 2400 BCE" he deals with it as if it IS 2400 BCE Strange method, he doesn't deal with the real errors here, he smoothes out the differences. Unfortunately this is nothing you would expect in a scientific work. I will show later how this should be done correctly.
According to Bauval the reason for the epochs are building mistakes. Because of these errors we can never get the intended year for the match, all we can get is the epoch during which such a match took place.
The way Bauval explains his epochs leads to the suggestion that they are "centred", which means that the epoch "2450 BCE" goes from 2437.5 to 2462.5.

Let us now take a look at Bauval's epochs. As we can see not a single star lies within its designated epoch, to see this look at the following table. In it I've calculated the matching year and the difference from the middle and rim of the epoch:

Shaft Epoch corr. Year Dev. to center Dev. to border
King North 2425 2326 99 a 86,5 a
King South 2475 2496 21 a 8,5 a
Queen South 2400 2348 52 a 39,5 a
Tab. 5 - Bauvals "Epochs" and Star dates

Oops! No value is near its designated epoch. All are wrong, there is no hope. Or is there? At the beginning I was wondering about the different values Bauval used for the inclinations. Could there be a reason behind these changes??? Let's recalculate the above table with Bauval's inclinations...

Star Shaft Inc. Bauval Nec. Decl. Year Difference
Thuban King North 3228' 8731' 2360 -34 a
Al Nitak King South 4500' 45 2496 0
Sirius Queen South 3930' -2031' 2375 -27 a
Kochab Queen North 3900' 8059' 2344 +41 a
Tab. 6 - Star- und Shaftdates Bauval compared

Well you could knock me over with a feather, Bauval's "correction" places two critical values 34 and 27 years nearer to their desired dates. Only one value worsened: the Kochab match got slightly younger - but Bauval doesn't use this star for his epoch dating!
If we now take the average of the 3 stars used by Bauval we get the year 2410 BCE, much nearer to his desired date...

An aside: My colleague in the battle against the fringe, Rainer Lorenz, once interviewed Rudolf Gantenbrink for a newspaper article. In this interview Gantenbrink did not speak well of Bauval, because he had given him this values explicitly as Bauval had requested of him several times on the phone. Consequently, he had been very angry when Bauval had used these grossly wrong values and had asked himself, and Rainer, why he had done this? Well, now we know :-)

But even this operation does't do much for Bauval's epochs. if we assign these star dates to epochs we get:

Shaft corr. Epoch korrekt with Bauv. values
King North 2325 2350
King South 2500 2500
Queen South 2450 2350
Epochen
Tab. 7 - correct Epochs

...this gives us an average epoch of 2400 BCE :-)The diagram on the side shows, how the correct dates (lower markers) are moved to the desired epochs due to the strange shifting of the original values...

How to do it right?

Bauval used epochs because of building errors which could have occurred. There is nothing wrong with this, just the contrary. Tolerances are always used when evaluating such results. But not the way Bauval did it!
The correct method looks like this:

  1. Take the inclination
  2. Add/subtract the error interval (+/- 15')
  3. Calculate the necessary declinations for these three values
  4. Calculate the matching years for these values
  5. Do this for all the shafts
  6. Get an average value with +/- errors from them

In the following table I will do this for all four shafts and use Bauval's gigantic tolerance of +/- 15':

Star Shaft Elev Decl. Year max. Decl. min. Decl. max. year min. year
Thuban King North 3157' 8720' -2326 8735' 8705 -2370 -2283
Al Nitak King South 4449' -1502' -2496 -1517' -1447' -2547 -2445
Sirius Queen South 3920' -2026' -2348 -2041' -2011' -2430 -2265
Kochab Queen North 3900' 8059' -2344 8114' 8044 -2415 -2265
Tab. 8 - Error Intervalls

The +/- error intervals according to Bauvals absurd building tolerance are:

Star Shaft Year + -
Thuban King North -2326 44 a 43 a
Al Nitak King South -2496 51 a 51 a
Sirius Queen South -2348 82 a 83 a
Kochab Queen North -2344 71 a 79 a
Error diagram
Tab. 9 - +/- Error intervalls

The tolerances span an era of 300 years, the individual tolerances are between 90 and 170 years as you see on the graph: The values just look silly. No sensible person could get an average out of such statistical cluttering. it's nothing more than white noise. Clearly the shafts were never designed to point at specific stars. By the way: The horizontal red line in the diagram is the year Bauval gets from these values.
If we reduce the error intervals as Gantenbrink's measurements suggest the picture gets worse, as the overlapping of the tolerances would also be reduced.

Conclusion

The overall impression of the shafts is extremely negative. All the shafts point, more or less, at their dedicated stars - but nowhere near 2450 BCE! And never at the same time! Not a single star reaches the necessary position during Bauval's pyramid building age. Even when you calculate an average from the four dates you get 2400 BCE, 50 years away from Bauval's date

The shafts are definitely unusable for dating the pyramid building epoch as they span an era longer than many dynasties. Even if the new calculations by Kate Spence should point to a later pyramid building era, Bauval can claim no credit. If you use his method with the correct values you will never get anywhere near 2450 BCE. Perhaps this is the reason why all these ideas of calculating construction dates from shaft elevations were dismissed during the last 30, 40 years?

The whole story of dating with shafts doesn't work. Only one shaft, King's South is anywhere near a date which could have been in the pyramid era. And this one dates to 2496 BCE and is smack in the middle between the "conservative" date of 2550 and Bauvals dream date. With an error interval of about +/- 50 years. When you take into consideration that when the pyramid was started in 2x50 they would have reached the height of the King's Chamber around 2x65-2x70 BCE, so 2550 would fit the error interval better than 2450.

Remarks:
[1] Stadelmann, Rainer, & Gantenbrink, Rudolf; Die sogenannten Luftkanäle der Cheopspyramide; Modellkorridore für den Aufstieg des Königs in den Himmel, MDAIK 50, 1994 p. 285-294
[2] ibd. p. 293
[3] ibd. p. 293 f
[4] Bauval/Gilbert p. 238
[5] ibd.
[6] ibd.
[7] ibd. p. 270 f
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