They [the builders] were apparently able to dictate … the small dimensions of the Third Pyramid, despite the presumed desire of Menkaura [Mycerinos] to have a monument equal to those of his predecessors

— J. A. R. Legon in Discussions In Egyptology

At Giza we are confronted by a set of monuments which bear every sign of intelligent design, yet we are ignorant of the principles upon which these designs were based.

— R. Cook, The Pyramids of Giza

I A Peculiar Offset

In 1982, the day after I had visited the pyramid of Unas, I went to another familiar haunt, the Cairo Museum of Egyptian Antiquities. My objective was the east wing of the ground floor, where most of the Pyramid Age relics were kept.

The Museum is an extraordinary place, in the heart of Cairo on the bustling north side of Tahrir Square, and entering its courtyard is like finding a sanctuary from the madness of the traffic outside. The present building was designed at the turn of the century by the French architect, Marcel Dourgnon; not unexpectedly there is a distinctly French feel about the place, due not least to the mausoleum of Mariette. He had asked that his remains be entombed in a sarcophagus and kept in the gardens of the Museum; recently his statue has been repaired and now dominates the crowds as they stream into what was once his exclusive domain. In a country becoming more fundamental by the hour, Mariette’s statue looks strangely out of place, a relic of a colonial past Egyptians would have preferred to do without. The gardens at the entrance of the Museum are full of pharaonic relics, which would receive pride of place anywhere else. There is no more room inside the building so many statues and sarcophagi are left to the mercy of the city’s terrible pollution and the groping fingers of thousands of tourists. On the east side of the Museum is a local school, where two sarcophagi serve as school benches and a third as a rubbish bin.

I walked through the main hall and made my way to the pyramidion (benben) of Amenemhet III’s pyramid. This is dated to c. 1850BC and once stood on top of the king’s now crumbled pyramid at Dashour.1 It is made of highly polished black granite and has two lines of inscriptions around its base. These, as well as the winged disc and eyes of the Horus symbol, include the figure of Osiris-Sahu (Orion) with a star in his outstretched hand. Before entering the east gallery which contains the Old Kingdom relics, I came across a statue of Menkaura, builder of the third pyramid of Giza. Though small in size, it is beautifully cut from green schist. The king seems to radiate a powerful authority and a strange intensity of feeling, very characteristic of Old Kingdom statuary art. Menkaura is presented on each side by a goddess; both display an odd sense of tenderness mingled with pride in the way they hold on to Menkaura’s arms. Clearly, such kings were not the tyrants they are sometimes made out but were regarded as deified rulers to be loved and glorified.

Passing into the famous Room 42 which contains many Fourth Dynasty relics, I immediately saw the splendid statue of Khafra; builder of the second pyramid. This is cut from a single block of black diorite, a granite stone which is extremely hard to work. Yet the statue is so finely polished that it looks like metal; it is considered by some as one of the world’s great works of art. The sculptor who worked the stone must have been the Michelangelo of his time; how he sculpted diorite to such perfection with only copper tools remains a puzzle. Khafra sits on a throne, his face radiating both authority and love, depending from which side you observe it. His head is embraced by the open wings of a Horus hawk which rests on Khafra’s shoulders. I felt that even the ornate and beautiful relics from Tutankhamun’s tomb did not have such haunting beauty.

I walked around the gallery taking in as many impressions as I could, then my eyes caught something else: a large poster on the north wall — an aerial photograph of the Giza pyramids. The tag indicated that it had been taken by the Egyptian air force, probably in the 1950s, and was the first aerial view I had seen from directly above the Giza site. Before looking at this poster, I had not paid much attention to the curious offset of Menkaura’s pyramid from the south-west alignment of the two larger pyramids. But now, looking from high up over the site, it stuck out like an out-of-plumb frame on a wall. I had worked as a setting-out building engineer a few years before,2 and my eyes were trained to focus on such anomalies in site layouts. The pyramid of Menkaura, I felt, was not quite where it ought to be. I asked the guard if I could take a photograph of the poster and got a smile and nod, with the usual military style salute which indicated bakshish was in order. I was using a black-and-white film with a fast 50mm lens on my old Olympus. I raised the camera and clicked only once. This idle snapshot was to change the course of my life.

The short holiday over, I returned to work in Saudi Arabia. In Riyadh I had the film developed and ordered several large copies of the aerial photograph of the Giza pyramids. I was intrigued by the offset of Menkaura’s pyramid and wanted to try to solve the riddle. Most of my friends in Saudi were in the construction industry — civil engineers, architects, planners — and I felt that their opinion might help. My aim was to see if we could agree on the reasons for the odd layout plan of the three pyramids.

12. Analysis of the Giza Layout Plan

As I had thought, most of those who looked at the photograph made the same observation: the three pyramids were each set along their own meridian (north-south) axes and everyone noticed the south-west diagonal along which the two larger pyramids are set. They agreed that this indicated a unified plan. Then came the confusion I had anticipated: they wondered why the third pyramid was so much smaller than the other two, and, even more puzzling, why it was slightly offset east of the south-west diagonal line which linked the two larger pyramids. All agreed that the size and offset of the Menkaura pyramid had been a deliberate choice by the architect. The question was why?

II An Architectural Plan

I decided to give copies of the picture to another group of friends not involved in construction work, but with some understanding of an artistic or a poetic nature. I wanted to see if they would ask the same questions. This time, however, I traced in black ink the south-west diagonal line which linked the two larger pyramids, and extended the line to the Menkaura pyramid to show the curious offset. I also provided them with the assumed sequence of building: Khufu (Cheops with the Great Pyramid), then Khafra (Chephren with the second pyramid) and Menkaura (Mycerinos with the smaller third pyramid). I was listening for questions as to why this last pyramid was much smaller and was offset from the south-west axis of the other two larger ones. The replies confirmed what the other group had deduced: the size and offset of Menkaura’s pyramid seemed a deliberate choice by the architect. This group, however, was more concerned to discover why Menkaura’s pyramid was so much smaller. I dished out the standard reply: Menkaura probably was short of resources. They were not satisfied, nor was I, but it was as good an explanation as any. Yet on what evidence did this lack-of-resources hypothesis rest? As far as I could make out, there was none. Egyptologists think that Menkaura ruled for just as long as his two predecessors at Giza and was described as an equal to Khufu and Khafra, his eternal cronies. I offered another standard answer: Menkaura was in a hurry, so he built a smaller pyramid. Again I had to agree that there was really no evidence for this conclusion. The pyramid must have taken several years to build — seven to ten years on conservative estimates3 — so how could Menkaura have been in a hurry? Was he a sick man? Again no evidence. His statues show him as healthy and strong.

I saw the point that this second group was trying to make: whichever way you looked at it, it didn’t make sense for Menkaura to have settled for a much smaller pyramid. He most likely had the same autocratic power and resources as his immediate predecessors. In any case, the concept of economy was alien to them; resources meant plenty of able men and plenty of limestone quarries, both of which Menkaura certainly had. His predecessors would also have left much behind to make his task easier: ready open quarries, tools, accommodation for workers, sledges and so forth (what construction companies today call the ‘preliminaries’), and a wealth of experience gained by trial and error.4 Yet even considering the unlikely possibility that Menkaura did not have the same power and resources as Khufu and Khafra, why should he build an ‘inferior’ pyramid at Giza to advertise this fact to posterity? There was plenty of land elsewhere. Menkaura’s pyramid is by no means small, but the others are twice as tall and ten times as massive, reducing it to the status of dwarf. Why would he have settled for this?

One thing was certain: Menkaura knew that his pyramid was going to be much smaller than the other two at Giza. Such monuments have to be planned well in advance, and Menkaura must have approved the plan. Why approve a plan which would make him look inferior to his two predecessors? Whichever way we looked at it, there were flaws in the explanations. Perhaps we were looking at this pyramid, indeed any pyramid, in the wrong way. We were looking at each pyramid individually when we should have been looking at them as part of a unified project. All that we had to do was to think of the pyramids not as belonging to this or that pharaoh, but as a conglomerate of monuments devised as a unified plan. What was more likely is that the pharaonic state saw itself as custodian of the Memphite Necropolis as a whole, and that the chain of pyramids there were seen not as individual tombs but as an ensemble expressing the supreme ideologies of their rebirth cult. All the pyramids together made up the Necropolis or land of the dead; more accurately, they made up the Duat, the ‘place where Osiris-Sahu is’. But how was the Necropolis linked to the stars of Osiris?

Returning to the Giza group, I saw that the questions had to be rephrased: Why did the master plan specify two large pyramids and one smaller? Why offset the smallest to the east? Now the answer became obvious: these ‘anomalies’ were not anomalies at all but constraints imposed in the planning, design and layout of a master plan which were reflected in the third pyramid. The next question was, therefore, were these constraints imposed by engineering or site problems or by religious considerations?

Trained in construction planning of layout, where the client’s brief and the contours and area of the site, among other factors, imposed constraints on size and location of buildings, I knew by experience that many things which later appear as anomalies to others, are often planned aspects of the design. Even though no answer was as yet evident as to why the third pyramid was relatively small and offset from the south-west alignment of the two others, we could apply the process of strategic thinking in reverse: trace back what could have imposed those two criteria on the layout of the Giza pyramids.

There had been something else about the aerial photograph which now began to intrigue me, something important though it was not actually in the photograph: the River Nile. Not far to the east side of the Giza plateau was the lush Nile Valley and beyond it the city of Cairo. The river flows from the south to branch off just past Cairo into the wide Delta of Lower Egypt. The Nile’s course, as French Egyptologist Jean-Philippe Lauer points out, ‘flows quite exactly towards the north’.5 In short, apart from the natural bends and kinks on its course, the river flow is meridional. Lauer also showed that all mastaba tombs from the First Dynasty onwards were orientated roughly south-north, parallel to the axis of the Nile. From the Fourth Dynasty, ‘the orientation of pyramids reached a precision that was truly extraordinary’.6 How, asked Lauer, did the ancient builders achieve such accurate south-north alignments? He believed the answer was that the ancients made use of stellar observations at the meridian transit of certain stars. Others before him, such as Edwards and the astronomer Zbynek Zäba, agreed with Lauer’s hypothesis.7 Zäba had also argued that the pyramid builders not only used stars for alignment but that they might also have been aware of precession.8

I knew that each pyramid at Giza was set so that the sides of its square faced a cardinal point. This meant that the monument was, intentionally or not, a fixed compass, easily directing due east, north, west or south depending on which side of the square base one stood. Despite this, the main axis of the pyramid ran along its meridian, especially looking from north to south. This is obvious because the entrance to the pyramid was always on the north face, so a visitor proceeded southward into it. The meridian was therefore the primary criterion for the original design and layout of the group. Yet here was another ‘anomaly’: the three pyramids of Giza, each set on a meridian, do not align together on a main meridian when seen as a group but are in alignment along their southwest axis, with the third pyramid offset to the east. What induced the architects to produce this odd layout?

The first factor to consider was the ground conditions of the Giza plateau, to see if the geology and contours of the site had forced this anomalous decision. But I knew the Giza plateau well, and there was nothing that would have prevented the planners from placing the three monuments in a row along a main meridian axis. Indeed, this would probably have been the easier choice.9 Placing the three pyramids in a north-south axis would have meant two major quarries to the east and west of the project, which could have been used throughout the duration of the works. It would also, of course, have facilitated the alignment problem, with the need to set only one pyramid, the first, along a meridian. The alignment of the other two would merely have meant projecting the line farther south.

In the absence of major engineering constraints, there was really only one answer to the apparently illogical choice: the constraints or criteria which had determined the layout principle were based not on engineering logistics but on religious considerations. But what could these be? Most of the architect friends I consulted agreed on a symbolic rather than practical reason for the plan of the Giza group. They pointed out that most monuments — and especially intensely geometrical ones such as the pyramids — were charged with symbolic connotations. This often applied to the place where they were sited, its orientation and relative position to the geography of the area. In this case, the obvious geography and alignment to consider was the course of the Nile. The architects pointed out that the socalled Historical Axis of Paris, which extends from the Louvre to the new district of La Defense and goes through the Champs Elyseés, was orientated relative to the flow of the Seine adjacent to the Louvre.10 Similarly in Washington DC, the main axis of Pennsylvania Avenue which the French architect, L’Enfant, had aligned, constituted another historical axis linking the White House with the Capitol; it, too, took account of the direction of flow of the ‘sacred’ Potomac River.11 The pyramid builders of Memphis undoubtedly considered the meridional flow of the Nile when planning the Memphite Necropolis. But at Giza the general alignment of the three pyramids was not meridional but through a south-west axis.

Some explanation had to be found. The monuments were obviously of such importance to religious ideologies that any explanation had to correlate with the supreme belief in the rebirth of the kings who commissioned the project.

A common denominator was clearly at play here, yet it seemed to escape engineering logistics. Some other scientific discipline was required. The obvious astronomical layout of each pyramid, based on stellar observations, suggested that we should consider the alignments and layouts of the pyramids from the viewpoint of astronomy as well. I decided it was time to take a good long look at the stars.

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