PART 6 (second half)

The King’s Run (continued)

Several times I have come across the question “If the star shafts in the Great Pyramid were so important why does not every pyramid have them ?

My answer to this would be :
First I need to be fairly sure what the purpose of the shafts was. Without this, it is a bit hard to proceed !

Most pyramids had satellite pyramids inside their enclosures, but the Great Pyramid did not. The star shafts enabled the job of the satellite pyramid to be performed in what Khufu believed was a better way.

The satellite pyramid enabled the King’s Run by providing a burial chamber in the southern sky and the southern sky markers. The King’s Run was important as it was a critical ritual in the afterlife Heb Sed. The shafts brought the sky markers into the burial chamber to satisfy the King’s Run requirements.

Khafre’s Pyramid had two shafts, one in the north wall and one opposite in the south wall.

The short shafts came only from the Pyramid masonry - meaning that the pyramid itself would have to have represented all the sky markers that Khufu used.

Khufu’s marker stars were Orion’s Belt for the south sky and Mizar-Thuban-Kocab for the north sky.

A fundamental question arises “How could Khafre’s pyramid by itself possibly represent the two sets of three sky markers in the skies, one north and one south ??

For just one pyramid on its own this is not credible . – but as a combined set of three, that is another matter. Three pyramids as a unit could represent Orion’s Belt when looking south and the same three pyramids as a unit could represent Kocab-Thuban-Mizar (KTM) when looking north.


Fig 1

(This hypothesis may sound unlikely, but there are several supporting facts !)

Of course there would need to be a third pyramid to make such triple star representations. Menkaure’s pyramid was not yet built.

But Khafre was indeed expecting Menkaure’s pyramid to be built exactly according to the Giza plan (see above thread entitled ’ Djedefre’s Other Angle’) .

Yet there is another possibility . . .

Khafre may have built his own small pyramid as a guarantee until (or unless) Menkaure built his.

When Petrie surveyed Menkaure’s Pyramid he was under the impression that it was built over a small pre-existing pyramid.


Fig 2 from [www.wonders-of-the-world.net]

From his report1 :
From all the details it seems that the Third Pyramid was first begun no larger than some of the small Pyramids on the same hill. That it had a passage descending as usual, with a large lintel block over it; and running horizontally in the rock, into a rock-cut chamber, whose roof was 74” above the passage floor. That after this was made, the builders, for some reason, determined on enlarging the Pyramid before it was cased, and on deepening the chamber. They accordingly cut a fresh passage, from the new floor level of the chamber, working this passage from the inside outward. They not only deepened the chamber, but also cut the sloping passage to the lower, granite-lined, coffer chamber; for the granite lining could not be put in until the second chamber had been deepened to its present extent; so the granite chamber must be part of the second design, or is perhaps in itself a third design. The old entrance passage was then built over on the outside, and the greater part of its height blocked up. The blocking that remains is clearly ancient, as it consists of large blocks wedged in by chips, and worn by passing over the tops. On one block is a saw cut, 6 inches deep in part, running vertically on the face; this cut must therefore have been made by the Pyramid builders, before they used the block for filling the passage.

The large lintel at the top of the original shaft suggests an entrance on the side of the smaller pyramid.

It seems unlikely that Menkaure would first build a smallish pyramid without an adequate burial chamber, and then completely remodel the inside and double the size.

One piece of information would be helpful. The azimuth of the shaft, which does not appear in Petrie’s report, might match that of Khafre’s pyramid. If about +5 minutes it would be Khafre’s, if about +14 minutes it would be Menkaure’s. Until more proof is found, the idea that Khafre himself built a small third pyramid at Giza is not confirmed.

After Khufu it is generally accepted that Nebka became king. He, like Khufu and Khafre just before him, wanted a giant pyramid. He was not, I guess, interested to complete the smallish G3 at the family necropolis of Giza. Instead he started at Zawiyet El Aryan but must have died soon after. Menkaure was likely in a hurry and gladly completed the job of G3 at Giza !

So for the deceased King Khafre to perform his King’s Run within the burial chamber he would start in the northern half of the chamber (= northern ‘sky’) and pass by the shaft there. By virtue of the counterpart (plus some magic!) the three northern markers would be passed.
Then he would move around the south half of the chamber, the ‘southern sky’, and pass by the shaft there. Here the counterpart in the south would provide the markers. He would then be deemed to have ‘gone round’ these markers. Finally he would have returned back to the northern half for the required rituals.

Now I need to demonstrate these sky-ground counterparts.

The Orion Correlation Theory

The OCT of Robert Bauval first proposed the matching of the three main Giza pyramids with Orion’s Belt.

He did not really give a credible reason why Orion’s Belt had such importance. But the Heb Sed requirement for run markers does now provide that important purpose.

The Great Pyramid with its two shafts, one from Orion’s Belt and one from the asterism Mizar-Thuban-Kocab tell us where to look in the sky for the Heb Sed markers. The OCT looked at only one set of 3 stars. It was not balanced - only half the story!
This more balanced dual representation of the three marker stars, north plus south, makes more sense.

Bauval got many arguments regarding the angle made by the three stars of Orion’s belt because they did not quite match that of the pyramids on the ground at Giza .
Here are two of them :
The bend at the centre star was 172.5 deg in the sky and the pyramids on the ground had 168.5 deg. The discrepancy was put down to measurement difficulties.

However the northern KTM trio had an angle at the centre of 164.5 deg.
In order get a dual representation, an average or mid-way was used. The average or midway of 172.5 deg and 164.5 deg was 168.5 deg – as exactly on the ground at Giza.



Fig 3. Comparison of the angle sizes :

The average or midway position resembled both of the 3 star asterisms and was used on the ground at Giza.

Another problem : The orientation of the line joining the first and third pyramid apexes on the ground was 52.25 deg to east-west. But at the south meridian, the orientation of the first to third Belt stars was 14.5 deg to the horizon. Bauval solved this ‘awkward’ mismatch by winding back time to around 11000BC to get the Belt at this same angle as at Giza.

So at culmination we had the Belt angle, Alnitak-Alnilam line, was at 14.5 deg to the horizon. At the culmination of Kocab in the north the Kocab–Mizar line was vertical at 90 deg to the horizon around the epoch of Khafre.

Fig 4 the orientation of KTM due north :



Fig 5 The orientation of the Belt stars due south :




In order get a dual representation, an average was again used. The average or midway of 14.5 and 90 is 52.25 degrees to the horizon.
This averaged angle to east-west was exactly the one used on the ground at Giza between G3 and G1

Fig 6 : The orientation of the three main Giza Pyramids



(So each star group needed to rotate 37.75 deg, KTM clockwise and the Belt anti-clockwise to get to the required averaged orientation of 52.25 deg.)

At the averaged position, the two 3 star asterisms both had the same orientation in the sky, so that this could be dually represented on the ground at Giza.

This dual correlation hypothesis is saying that OCT is ‘half’ right - but it is not the full story !

Some years ago Chris Tedder wrote that there was no need to look to 11,500BC for a match of Orion’s Belt’s orientation to that on the ground at Giza. He wrote that this orientation for the Belt could have been found at the epoch of Giza pyramids by looking in the south east sky. Unfortunately Bauval dismissed this idea in his book The Egypt Code p109 writing “there is not a shred of textual evidence to support it”.

I think what Bauval also meant was that he saw no reason for Tedder’s match to the east, but he did see a reason for the match due south at around 11,500 BC.

But of course he would not have heard of the fact that 52.25 deg was the average orientation of 90 and 14.5, and that this was a more likely reason for the 52.25 deg orientation to east-west at Giza.

It is the use of these two averaged angles 52.25 deg and 168.5 deg at Giza that created the strange base sizes of Khafre’s and Menkaure’s pyramid ; 411 and 201 cubits respectively. Some people have argued that G3 base should have been 200 cubits or even 196 cubits. But it was because the angle between the apexes of 52.25 deg dictated this base length for G3.

Counterparts in the sky

Now , I would like to look again at the fundamental question identified above : “How could Khafre’s pyramid by itself possibly represent the two sets of three sky markers in the skies, one north and one south ??

First the north : As above here is a copy of the counterpart of Khafre’s pyramid at the celestial pole presented earlier :



Fig 7 Counterpart in the north

The diagram above, based on the sky software, shows the counterpart of Khafre’s pyramid at the celestial pole as discussed before. The square is fixed in the sky like the pyramid on the ground. The stars rotated and returned to this position once per day.

To comply with the ‘averaged’ orientation, the stars needed to be rotated 37.75 deg clockwise from culmination, which was 52.25 deg to east-west – as shown below.
Notice that the three stars KTM were now inside the square . Thus the counterpart of Khafre’s Pyramid at the pole ‘contained’ the 3 markers – and by itself represented the three markers.

Just compare the revised counterpart position of Khafre’s pyramid in the sky with the plan of Giza necropolis on the ground

Fig 8 Counterpart North at the ‘averaged’ orientation :







Fig 9 Researchgate, Plan of Giza plateau, Mark Lehner

Looking at the square in the sky picture and the Giza map below it, the pyramid of Khafre had a match with Thuban, as expected. The Great Pyramid had a match with Kocab and Menkaure’s pyramid had a match with Mizar. All within the counterpart square of Khafre’s pyramid !

Now for the south . . .

The Belt orientation needed to go from 14.5 deg to the horizon to 52.25 deg to the horizon to get to its ‘averaged’ orientation. It required the same azimuth rotation of 37.75 deg so that the orientation changed to 14.5 + 37.75 which is 52.25 deg to the horizon - the angle copied at Giza.

Here is Chris Tedder’s diagram of the situation looking south down the meridian. The 3 Belt stars can be seen oriented at 52.25 deg to the horizon parallel to the three pyramids at Giza :

Fig 10 Chris Tedder webpage



We have an exact match !

Below a square has been drawn around the three stars of the Belt on a printout from the Sky software as per scene above. This creates a counterpart looking south - as was done for the north. We get this :

Fig. 11 The southern counterpart from Sky software.







Compare the sky with the plan at Giza. The purpose of this square is just to show that a counterpart of Khafre around Orion’s Belt can by itself represent the three marker stars in the southern half of the sky, just as in the north.

So in this way, Khafre’s pyramid was able to represent the KTM stars looking north and the Belt stars looking south – both with the same orientation as copied at Giza.

This result was achieved with just a pair of little 13 inch deep shafts in the burial chamber - and a bit of magic ! Compare this to the complex engineering of the star shafts in the Kings Chamber of the Great Pyramid. Pure genius !

Now here’s a subsequent question. Is there any evidence that the builders at Giza demonstrated their link to the match in the sky at 52.25 deg south of east. ?

Well, yes there is - the positioning of Djedefre's pyramid (see my post Djedefre’s Other Angle above) ! Looking down this direction at night from Djedefre’s pyramid over Menkaure’s pyramid, up to and above the horizon, the Belt would have appeared there at some time in the night with the same orientation in the sky as at Giza on the ground.



Fig 12 : from Robin Cook. Right, the Djedefre Angle from Abu Roash. Left, the view in the sky down the line.


Area C

Khafre’s complex had no equivalent of the Queen’s Chamber to follow the days and years, but built his own calendar system right behind the pyramid. It was located symmetrically with the Pyramid.
Called by some the workmen’s barracks, or craft workshops, only because no other credible explanation for it existed. However there would be no need to put barracks in that position behind the Pyramid.
Also called galleries, but it is the walls that are important not the spaces between them.

Have a look the plan of Giza labelled fig 9 above . The Area C is directly west and central to Khafre’s pyramid.

Here is a close up :

Fig 13 Conard and Lehner Survey of Area C



Lehner thought they were like the teeth of a comb. 73 identical and equally spaced walls (8.5c apart) were lined up behind the pyramid on a ridge. Plus one more wall separated to the north near the label ‘gallery 76’.

(The galleries he labelled -1 and -2 were not satisfactorily identified because a Modern Road was laid around the southern end of the structure.)

At right angles to these were 20 more little walls with spacing of 6c. This includes the two end walls. (The diagram above shows an assumption how the end walls looked as there are no remnants of them.)

If each of the 73 walls represented one day, and if each of the 20 walls at right angles to them represented one time span of 73 days, we have a calendar.

Because, 20 x 73 comes to 1460 which is 4 years of 365 days. Add one for the fourth year - the single separated wall - to make 1461 for the 4 year cycle.
By this method the days and years could be counted for the timing of the afterlife Heb Seds.
.
This number 1461 matched the 1461 for Djoser’s outer wall - both were on the west side.
Fig 14 The heads of the Area C walls



Petrie, and later Lehner, conducted excavations of Area C4. They found traces of white gypsum plaster and red ochre. It is likely that the front 'heads' of the walls were covered with white plaster. Perhaps they had a red line also. Stone blocks were laid between each head. See above my sketch of the ends of the walls looking west - based on the data.


Conclusion

• Once again the requirements of the afterlife Heb Sed dictated many design features of the pyramids.
• They determined important aspects of the architecture at Giza: the number of main pyramids (3), the base sizes of them, the spacing and the angles between them. Also: the chambers, the temples, and the statues of Khafre and gods.
• The OCT was lacking a credible reason for it, but the Heb Sed requirement of Khafre provides one.
• The base orientation of Khafre’s pyramid base was reversed to get a dual representation. i.e. Kocab at the top produced a similar ‘look’ of the 3 stars in the north and Orion’s Belt in the south.

Through this ‘new’ lens of the afterlife Heb Sed, many features of the pyramids that were mysterious before suddenly can be explained. This has been my experience in all the Parts of this article.
Whether any of these new interpretations will be accepted by Egyptologists I actually doubt ! But if there is a student out there who thinks they are worthy of a thesis, they are welcome to use them. A little credit mention would suffice !

References :
1. Petrie Pyramids and Temples of Gizeh [www.ronaldbirdsall.com]
2. Robert Bauval, The Orion Mystery [archive.org]
3. Chris Tedder sites.google.com
4. Conard and Lehner The 1988/1989 Excavation of Petrie’s Workmen’s Barracks at Giza [www.academia.edu]