Here I am, O Ra (Sun-God), I am your son, I am a soul … a star of gold …
Pyramid Texts, lines 886–9
Modern archaeological scholars have cultivated a pristine ignorance of astronomical thought, some of them actually ignorant of the precession [of stars] itself.
G. de Santillana, Hamlet’s Mill, p.66
I The Solar Theory
As we have noted, the true pyramid was prefigured in the step-pyramid of Zoser, the earliest large stone building yet discovered. It marked a turning-point in the development of Egyptian civilisation, which was approaching its zenith with the dramatic rise of the Fourth Dynasty. Zoser’s monument required a huge leap in imagination as well as in technology and labour organisation, and it moved Egyptian funerary architecture in one giant leap from mud-brick mastabas towards the grandiose true pyramids.
The overwhelming consensus of Egyptologists is that the step-pyramid was a development of the mastaba but, unlike mastabas and the earlier burial pits, the step-pyramids were designed to be seen from afar and their outside look was as important as their internal burial chambers. The theory that the step-pyramids served as cosmic symbols is not revolutionary.1 All over the world there are structures with a similar shape and meaning, from the stupas of south-east Asia to the stepped pyramids of central Mexico. They are invariably derived from the same basic archetype: the mountain or ladder from which the celestial world could be reached or which could serve as a platform for the sacerdotal duty of monarchs and rulers: a common concept in the sacred mythology of almost every nation. It was also part of the Egyptian heritage, for the hill of Annu was regarded in similar terms; it was the holy hill of Atum rising from the primal sea, and on its top stood his sacred pillar crowned with the Benben Stone, his sacred seed.
We do not know what originally stood on top of Zoser’s step-pyramid but it may have been a replica of the Benben Stone,2 which would be in keeping with the overall symbolism of the Pyramid Age. What we do know is that the later, true pyramids were capped with replicas of the Benben, for this was the name given to their crowning pyramidions. Examples can be seen today in the Cairo Museum,3 which provide further evidence, if any were needed, that pyramid building was more than the creation of elaborate tombs.
The association of the Benben with Heliopolis, whose name means ‘the city of the sun’,4 has led some Egyptologists to conclude that the pyramid shape is essentially a solar symbol, that it represents rays of the sun coming down to earth through the clouds. Thus the pyramid symbolises a crude stone ramp leading the pharaoh home to the sun. This is a relatively recent hypothesis and is an extension of the step-pyramid/ladder of the planets theory. It is repeated by Dr Edwards in his Pyramids of Egypt where he quotes Alexandre Moret: ‘These great triangles forming the sides of the Pyramids seem to fall from the sky like the beams of the sun when its disk, though veiled by storm, pierces the clouds and lets down to earth a ladder of rays.’5
Commenting on this, Dr Edwards adds:
When standing on the road to Saqqara and gazing westwards at the Pyramid plateau, it is possible to see the sun’s rays striking downwards through a gap in the clouds at about the same angle as the slope of the Great Pyramid. The impression made on the mind by the scene is that the immaterial prototype and the material replica are here ranged side by side.6
This ‘pyramid = the sun’s rays’ hypothesis has become deeply entrenched as a historical ‘fact’ and is quoted whenever the pyramids are discussed. However, this theory (and it is only a theory) unwittingly diverted the attention of researchers from the real symbolic purpose of these monuments. But we must first consider the history of true pyramid building, beginning with the work of Sneferu, first king of the Fourth Dynasty.
II The Sneferu Enigma
In the space of 500 years, from about 2700BC to c. 2200BC, more than thirty million tons of rock, enough to build Windsor Castle a hundred times over, was moved around the western desert near modern Cairo. It was used to construct pyramids,7 some of which, like the Great Pyramid at Giza, are well over 140 metres high. They formed a huge royal cemetery for ancient Memphis, which we now call the Memphite Necropolis.8 During this Pyramid Age, also known as the Old Kingdom, hordes of Egyptians worked like ants on this gigantic building site, while an equally large army of masons, goldsmiths, painters and scribes chipped, melted, brushed and scribbled away to prepare for the royal funerals.
To give some idea of the scale of these works, in 1980 an English-language newspaper in Saudi Arabi announced that a Franco-American consortium had signed a large contract to build the new University of Riyadh. The term ‘large’ hardly did justice to the sheer scale of the project: it was the largest single fixed-price contract awarded to a contractor in the history of constructional engineering and was valued at over US$1 billion. The logistics involved were staggering: 8000 workers on site, millions of cubic metres of rock and soil to move and hundreds of thousands of cubic metres of concrete to be poured. Even the site offices were on a monumental scale and an Olympic-sized swimming-pool and other leisure facilities would be provided for the staff.
Yet the Riyadh University project was modest in comparison with what happened at Dashour and Giza nearly 4500 years ago. When we compare the technology and resources available now — gigantic tower cranes, bulldozers and excavators, hydraulic cranes and so on — the unsatisfactory nature of the consensus view of Egyptologists concerning the pyramids becomes apparent. To refer to the gigantic pyramid complexes at Giza and Dashour as ‘royal cemeteries’ with ‘royal tombs’ is like calling the Palace of Versailles a house, or St Peter’s in Rome a chapel. The building of the pyramids shows that the Pyramid Age was remarkable for great technological ability and daring innovation. But what exactly was the Pyramid Age? What sort of golden age was it?
According to Dr Edwards, ‘the Pyramid Age, par excellence … covers the period beginning with the Third Dynasty and ending with the Sixth Dynasty.’9 During this time some twenty-eight pyramid complexes were built along a stretch of desert running from Abu Ruwash in the north to Meidum in the south, the whole contained in an area about eighty kilometres long by some four kilometres wide. Yet such statistics are misleading, for they do not give us a balanced picture. It is often overlooked that most of the building took place in a very short period, the Fourth Dynasty, when seven of the twenty-eight pyramids were built; but such is the scale of these giant monuments that they account for more than 75 per cent of the total thirty million tons of material used during the entire Pyramid Age. Five of the seven, three at Giza and two at Dashour, have survived more or less intact to this day.
The first king of the Fourth Dynasty was Sneferu, father of Cheops. For reasons which Egyptologists have not yet determined, Sneferu and his architects abandoned the step-pyramid and launched the daring and huge smooth-sided pyramid design. Most scholars do agree that the motives for this dramatic change were religious, but what these motives were is not so evident. What is certain is that Sneferu’s venture made the step-pyramid builders of the Third Dynasty look like village contractors. His builders raised not one but two gigantic pyramids, which, from present evidence, no other pharaoh ever attempted, before or after Sneferu. In addition to this massive building programme, Egyptologists believe that Sneferu’s builders were able to satisfy him on another constructional enterprise; the upgrading of the step-pyramid at Meidum into a true pyramid by filling in the steps with masonry and adding the smooth casing-blocks.10 But there is still much controversy surrounding this theory, and the Meidum pyramid, begun in the Third Dynasty and so far south of the Memphite Necropolis proper, cannot be treated in the same way as the other Fourth Dynasty pyramids.
To get a good idea of the engineering revolution which Sneferu initiated, compare the step-pyramid of Zoser, employing some 850,000 tons of material,11 with Sneferu’s two giants at Dashour, which together used nearly nine million tons. This amazing upsurge in engineering and organisational prowess has defied explanation, but it is obvious that something important inspired Sneferu, something which perhaps involved the thinking of the great master-builder-cum-priest — Imhotep. It is not simply the increase in scale but the fact that the technology was suddenly available to raise large blocks of stone, some weighing several tons, to a height of nearly 100 metres.12 To make up the core of these pyramids, large blocks of hard limestone were quarried, transported, dressed, stacked then placed in perfect geometrical shapes which they have retained until today.13 The question becomes not whether the pyramids were just tombs but what changed at the opening of Sneferu’s reign that made it possible and indeed imperative to build pyramids on such a scale.
The textbooks do not provide a satisfactory answer to this question; they overlook the significance of the huge increase in activity during Sneferu’s reign. Dr Jaromir Malek of the Griffith Institute at Oxford, in a recent book on the pyramids of Egypt, passes quickly over this subject, though he does say that ‘the innovations introduced at the time [of the IVth Dynasty] were so wide-ranging that they must have had their origins in the sphere of religion rather than technology.’14 Previously the renowned architect and Egyptologist, Dr Alexander Badawy, had merely written: ‘At Meydum a true pyramid was obtained by filling up the steps of a layer pyramid … At Dashur Sneferu erected on a square base two true pyramids, one called the Rhomboidal (Bent) … It has been, however, observed that the upper part of this pyramid is poorly built … presumably finished in a hurry.’15
To describe the building activities at Dashour as being carried out ‘in a hurry’ is something of an understatement. If Sneferu’s builders had only the same resources as their predecessors at their disposal — and there is no good reason to assume otherwise — they were in something more than a hurry. To make things even more difficult, the building activities were carried out on three sites: the two at Dashour which are two kilometres apart, and a third at Meidum, fifty kilometres further south, at least one day’s journey up-river. Even if the work on the three sites was perfectly planned, there had to be a huge and complex organisation behind the scenes which would tax even today’s large contractors. To cut, move and place nine million tons of limestone blocks in the space of perhaps two decades, in an epoch which did not know the wheel or the pulley and had no iron tools, is a factor which merits close scrutiny. Let us consider the scale of this achievement in the context of the Fourth Dynasty.
III The Golden Age of the Fourth Dynasty
What, therefore, could have happened c. 2650BC when Sneferu came to power and founded the great Fourth Dynasty? Dr Edwards was the first to bring some sense of proportion to the Sneferu enigma, in 1947. Prior to his analysis, Egyptologists were faced with a perplexing situation, which involved the solitary Meidum pyramid in the extreme south of the Memphite Necropolis, originally built as a step-monument and later converted into a true, smooth-faced pyramid.16
There are no contemporary writings on the Meidum pyramid or elsewhere which give the name of its owner. However, in a temple nearby was found what Egyptologists technically call ‘graffiti’ (scribbles made by some passer-by). The graffiti were dated to the Eighteenth Dynasty — some 1200 years after the reign of Sneferu — and indicate that at that time (c. 1400BC) the Meidum pyramid was considered to belong to Sneferu.17 Dr Edwards translated the graffiti, apparently written by a scribe called Aa-Kheper-Resenb, who lived during the reign of Tuthmoses III: ‘… in the forty-first year of the reign of Tuthmosis III … I came to see the beautiful temple of King Sneferu.…’ Edwards also refers to graffiti from times earlier than this, as far back as the Fifth Dynasty (some 250 years after the reign of Sneferu), which mention his name in connection with Meidum.18 This would normally be sufficient evidence to attribute the Meidum pyramid to Sneferu but there were the two other pyramids at Dashour to consider, with the ‘southern … certainly built by Sneferu’19 and evidence that strongly suggests he also built the northern one. An inscription found not far from Dashour dating from the reign of King Pepi I of the Sixth Dynasty, mentions the ‘two pyramids of Sneferu’.20 This was an official inscription, part of a royal decree exempting the priests of Sneferu from paying taxes, which must be regarded as sound evidence. Yet another, also found at Dashour and dating from the Fifth Dynasty, mentions the ‘southern pyramid of Sneferu’.21 Read together, these inscriptions imply that there were two pyramids, a southern and a northern, which belonged to Sneferu. The question then was, which pyramid should be considered the southern: the more southerly of the pair at Dashour, also called the bent pyramid because its angle of slope changes halfway up, or that at Meidum? Finally, on the tomb of a priest associated with the southern pyramid at Dashour, there is an inscription referring to the ‘southern pyramid of Sneferu’.22 This confirmed that the Dashour pyramid was the southern pyramid of Sneferu, and that its northern partner was also at Dashour. So where did the Meidum pyramid fit in? Egyptologists were at a loss.
Dr Edwards proposed a way out of this archaeological impasse. He pointed out that although ownership of two pyramids was unique to Sneferu, it could perhaps be understood to ‘symbolise his sovereignty over Upper and Lower Egypt’; three pyramids, however, ‘would seem to have no justification, practical or symbolic’.23 It was a bold admission that archaeological evidence can be misleading. Edwards then proposed that until new evidence came to light, Egyptologists should consider Sneferu as the owner of the two Dashour pyramids, but that he had probably only converted the Meidum pyramid from a step-monument into a true pyramid.
It made good sense; the supposed builder of the original step-pyramid at Meidum was now said to have been the elusive Huni. Since Huni seemed to have reigned just before Sneferu, and would have been expected to have a pyramid of his own, this attribution meant that the Sneferu enigma could be regarded as sorted out and Egyptologists could get on with other pyramid problems.
But although Edwards’s theory for Meidum made rational and even poetic sense, he issued the warning that since no inscriptions, either contemporary or of a later epoch, linked the mysterious Huni with the Meidum pyramid, it ‘does not follow that his pyramid was indeed the step pyramid of Meydum …’24
This leads to the next problem: why did Sneferu build two pyramids when all other kings before and after him were satisfied with one? Did he intend to be buried in two places? Perhaps it is the words ‘owned’ and ‘belonged’ which are misleading. Could it be that the pyramids were not regarded as belonging to any particular king but rather to the royal lineage and the cult as a whole? Sneferu may have built two pyramids and converted a third, but perhaps they were not ‘his’ as we have hitherto thought. After all, medieval cathedrals, although built during the reigns of specific monarchs, do not belong to them even if they were interred in them.
If the ownership consensus of Egyptologists is to stand, how is it that Sneferu, who built two and perhaps even three pyramids, did not make it clear to posterity that he was the owner? There was plenty of space outside and in the Dashour pyramids for inscriptions to have been carved in capital letters. But none of the Fourth Dynasty kings put his name on the pyramid he supposedly owned. There is not one contemporary, official inscription, not even inside the Great Pyramid.
Ask yourself, if you had built the greatest tomb in history, after several decades of effort and cost, would you leave everyone guessing who had performed such a feat? It was not that the pyramid builders did not like official inscriptions on their monuments. From King Unas (last king of the Fifth Dynasty) onwards, pyramids had hundreds and hundreds of official inscriptions, leaving us in no doubt which kings built them.25 Was it that Fourth Dynasty Egyptians could not write? Wrong again; many inscriptions exist in the vicinity of pyramids dated to the Fourth Dynasty and before. In the chapel of Queen Meresankh many hieroglyphic texts can still be seen. So this omission in the Fourth Dynasty pyramids is extremely odd and contrasts with the earlier mastabas and the inscribed pyramids of later dynasties.
Why did Sneferu, Khufu (Cheops) and the others not inscribe their pyramids? Never mind posterity, why leave the gods guessing who was responsible for these fine monuments? Did the Fourth Dynasty kings not regard themselves as individual owners of the pyramids? Is it possible that all the Fourth Dynasty pyramids were part of a single scheme, which required the building of seven different pyramids at specific locations?
The Fourth Dynasty as a whole is exceptional and stands out from the rest of the Pyramid Age. It seems to have arrived like the Egyptian phoenix who brings a new golden age, and over a short period of time carried out a magnificent programme of civil engineering, achieving a scale and standard of workmanship unparalleled until modern times.26 Then, just as suddenly, it ended. The textbooks speak of ‘religious upheavals’ and ‘civil wars’,27 but there is no evidence of these. If we are to find the answer we need to go back to the roots of pyramid research and question everything we have been told. Let us begin by looking again at the dating of the pyramids.
IV The Dating of the Pyramid Age
In the 1940s modern chronologists reshuffled the study of Ancient Egypt when they moved the early dynastic epoch forward by a millennium. Prior to this, the First Dynasty was thought to have begun earlier than today’s estimates. In the 1830s Champollion, the father of scientific Egyptology and decipherer of the hieroglyphics, believed that the First Dynasty began c. 5867BC. Later the German Egyptologist, Karl Lepsius, moved this to 3892BC. Then Mariette, writing in the 1870s, reverted to 5004BC. Finally his colleague, Dr Brugsch, settled for 4400BC. Brugsch had apparently based his calculations on the simplistic assumption that there are, on average, three generations in each century,28 but, for lack of anything better, his system was accepted for many decades by most Egyptologists.
Then in the 1940s the dating of the First Dynasty was again adjusted to c. 3100BC. This is constantly refined to 3150BC, 3300BC, 2900BC and so on, leaving us confused about what system we are to consider definitive. In any event, it should now be clear that the science of Egyptian chronology is far from perfect and relies on evidence dependent on personal interpretations and subjectivity. It is far from exact without tools that science has to offer, such as carbon dating and, in the case of symbolic architecture based on astronomical alignment as with the pyramids, the use of precession calculations.29 Without them we wonder how early Egyptologists were able to establish such precise dates as ‘5004BC, and ‘5867BC’. Today chronologists use the prefix ‘circa’ (c.) before a suspect date is given, to warn of a plus or minus variation. Yet we see such bold datings as the start of Sneferu’s reign, given as c. 2686BC; c. 2584BC; c. 2614BC.30 Not only are such figures misleading with their implications of accuracy, but evidence is rarely offered as to their computation. The earlier the epoch, the less accurate are such conventional dating systems, and concerning the Pyramid Age such estimates could easily be a century out, or more.31
In a letter we received from Dr Edwards during the preparation of this book, the date of c. 2600BC for Khufu’s (Cheops’s) reign was deemed ‘most satisfactory’.32 But the latest data, obtained in May 1993, from Rudolf Gantenbrink’s laser measurements of the shafts in the Great Pyramid confirmed that even this ‘most satisfactory’ date may have to be adjusted by some 150 years to c. 2450BC,33 to the time when those shafts were built.
When the pharaoh Sneferu came to power, the western desert near his capital at Memphis had already sprouted a few step-pyramids in the Memphite Necropolis. Today only that of Zoser remains. Much farther south was the lone step-pyramid of Meidum. Also in the Memphite Necropolis were many mastaba tombs, and farther north was the holy city of Heliopolis with its powerful priesthood. This was roughly the situation at the opening of the Fourth Dynasty.
Sneferu’s bold decision to alter the traditional step-pyramid design resulted in the building of two gigantic true pyramids at Dashour. The credit should not necessarily go to Sneferu but, most likely, to his architect-priest who was either the legendary Imhotep or his successor. Imhotep is generally credited with the invention of stone masonry and the science of medicine. But Dr Edwards rightly pointed out that his title of Chief of the Observers suggests that he was an ancient astronomer who studied the motion of the stars.34 This title was often assumed by the high priest of Heliopolis, which suggests that Imhotep, and those great masters like him, filled the function of high priest of that holy city.35 Having so successfully completed the Zoser step-pyramid complex, Imhotep, or his successor, was possibly fired by an even greater ambition: a unified master plan for the Memphite Necropolis which would allow full development of the royal rebirth cult.36
Sneferu is said to have died after reigning for nearly thirty-four years. With the coronation of his son, Khufu (Cheops), pyramid building was to reach its apotheosis.
V The Three Great Pyramids of Giza
Sneferu seems to have died peacefully c. 2480BC,37 leaving his legacy of the two giant pyramids at Dashour. Some twenty-one kilometres north of Dashour was the elevated rocky plateau of Giza (the Mokattam Formation).38 This plateau extended about 2.2 kilometres from north to south and about 1.1 kilometres across. It sloped gently from west to east, then dropped sharply near the contours of the Nile Valley.39 It was on this imposing site that the eldest son of Sneferu, Khufu, launched the most ambitious engineering project in the history of building, which, with its two partners there, was to become the greatest wonder of the ancient world.
There is no satisfactory explanation why Khufu did not follow in his father’s footsteps and build his pyramid at Dashour or indeed at Saqqara, where the ancestral step-pyramids and mastaba tombs were located. The easy answer is that the dominant position of the Giza plateau inspired him and his architect found the site ideal for a pyramid which would transcend those of Sneferu. But if this is true, why did Sneferu himself not select Giza instead of Dashour? Dashour is not much nearer to Memphis than Giza is and is a rather low site hardly visible from the palm groves which surround Memphis.40 Indeed, uninformed visitors today are surprised to be told that there are two great pyramids other than those at Giza. So why did Khufu choose Giza, a site so far from his father’s tomb? Perhaps he did not ‘choose’ Giza as such; perhaps it was already part of a master plan, intended to expand from south to north, devised during his father’s reign? Georges Goyon, who was personal Egyptologist to King Farouk, was of the opinion that the Giza site was ‘certainly chosen by the priest-astronomers because of certain religious and scientific factors’, yet what these were Goyon does not tell us. We agree, however, that religion and astronomy motivated the ancient builders to move to Giza.
VI The Great Pyramid
Even today, in its ruined form and lacking almost all its glistening white casing-stones, the Great Pyramid is staggering. It broods over the surrounding desert and suburbs of modern Cairo, seeming more like some strange feature of the landscape than the work of human hands; indeed, more like a geometrical mountain than a building. The mathematician and journalist P. D. Ouspensky visited Giza for the first time in 1914, shortly before the outbreak of the First World War and wrote of the experience:
The plateau is reached by a winding and ascending road which goes through a cutting in the rock. Having walked to the end of this road you find yourself on a level with the pyramids, before the so-called Pyramid of Cheops (Khufu), on the same side as the entrance into it. To the right in the distance is the second pyramid, and behind it, the third.
Here, having ascended to the pyramids, you are in a different world, not in the world you were in ten minutes ago. There, fields, foliage, palms, were still about you. Here it is a different country, a different landscape, a kingdom of sand and stone. This is the desert. The transition is sharp and unexpected.
… The incomprehensible past became the present and felt quite close to me, as if I could stretch out my arm into it, and our present disappeared and became strange, alien and distant.41
The Great Pyramid of Khufu, like the other pyramids, stands four-square, but it is in all its detail the most perfect. The first exhaustive survey of the monument in modern times was carried out by Sir Flinders Petrie in 1880–2. He used the latest equipment of the time and approached his task with great thoroughness. He found that the sides of the pyramid were indeed lined up almost exactly with the cardinal points of the compass: north, south, east and west. (The accuracy of this alignment is incredible, with an average discrepancy of only about three minutes of arc in any direction; this is a variation of less than 0.06 per cent.) He also measured the sides of the base as being 230.25 metres for the north side; 230.44 metres for the south, 230.38 for the east, and 230.35 for the west. Thus, although no side is identical to any other, the difference between the longest and shortest is only nineteen centimetres, less than 0.08 per cent of the average length.
Such degrees of accuracy, both in orientation towards the cardinal points and in keeping the base square and the sloping side perfect, are little short of miraculous when you consider the size of the structure. Its perimeter is almost one kilometre, with an area of over 53,000 square metres, enough to fit into it the cathedrals of Florence, Milan and St Peters, as well as Westminster Abbey and St Paul’s.42 It is indeed doubtful whether any of these later buildings exhibit the same accuracy as the Great Pyramid in their orientation or their structural execution. Although the pyramid contains several chambers, it is by no means a hollow building; it is mostly solid masonry and constructed from approximately 2.5 million limestone blocks. On average these weigh about 2.6 tons, to give a total mass of over 6.3 million tons.43
We can simply marvel at the craftsmanship and technological abilities of these ancient builders, for they not only orientated their monument towards the four cardinal points and kept the plan square and the slopes true, but they cased its four sloping faces with finely polished white limestone from the quarries at Tura on the other side of the Nile. Judging by the few facing stones remaining at the foot of the north side of the pyramid, these were even larger than those used in the core of the building and weighed some fifteen tons each. They were set so closely together that the blade of a knife could not fit between them. The casing-blocks were removed by the Arabs from the thirteenth century AD (some say to build the mosques of Cairo), but when intact the pyramid must have looked even more spectacular than it does today, glittering like a jewel in the sunlight.
It is now quite easy to clamber up and down the narrow corridors leading into the pyramids, for banisters are provided and there are wooden ramps with metal footings. The Giza pyramids are also electrically lit inside. Such luxuries were introduced in the 1940s, but exploration was not so easy for earlier travellers, as Ouspensky lamented in 1914:
The floor is very slippery; there are no steps, but on the polished stone there are horizontal notches, worn smooth, into which it is possible to put one’s feet sideways. Moreover, the floor is covered with fine sand and it is very difficult to keep oneself from sliding the whole way down. The Bedouin guide clambers down in front. In one hand he holds a lighted candle; the other he stretches out to you. You go down this sloping well in a bent attitude. The descent seems rather long — at last it ends.44
One thing that has not changed, of course, is the low height of the ceiling and the steepness of the gradient of this passage; it is only about 1.19 metres high and 1.04 metres wide and is sloped at 26 degrees 31 minutes 23 seconds to the horizontal. The passage plunges downwards, through the core of the pyramid and then through the bedrock that lies beneath it, for a total of 105.15 metres. It carries on horizontally for a further 8.83 metres before terminating in a roughly hewn chamber. The purpose of this chamber is unknown and the subject of much debate. It seems to be unfinished, and this has given rise to the so-called ‘abandonment theory’. According to its proponents, this underground cavern was planned as the burial chamber of the king; for whatever reason and while the pyramid was still in its early stages of construction, this plan was abandoned in favour of building a new chamber high inside the pyramid itself (the Queen’s Chamber). Later on this too was abandoned; a further corridor (the Grand Gallery) and a third room (the King’s Chamber) being built. It is believed that the king was eventually buried in this last chamber, which contains a large sarcophagus, but no remains of the king’s mummy or his funeral goods have been found and it is assumed that the pyramid was looted.
The abandonment theory has a certain attraction, but it runs against many practical requirements of building engineering. To have changed the design of the pyramid halfway through would have presented its engineers with nearly insurmountable problems. To have altered the design twice seems inconceivable, particularly when these alterations involved building the Grand Gallery, itself an extraordinary achievement, as well as the King’s Chamber. We believe that the King’s and Queen’s Chambers, as well as the Grand Gallery which links them, were all part and parcel of the original design for the pyramid and were indeed essential features. There is no hard evidence to prove that the subterranean chamber was ever intended as the burial chamber of the king; indeed it may have been in existence before the pyramid was built as part of an earlier structure on the same site. We cannot be sure that this was so, but it is certainly facile to assume it was abandoned for technical reasons. The Egyptians were experts at building underground chambers and would not easily have been deterred from burying the king under the pyramid had that been his wish.
These days visitors are not allowed into the underground chamber; roughly eighteen metres from the entrance to the pyramid an ascending corridor begins. It is another back-breaking journey of approximately forty metres at a gradient of more than twenty-six degrees. As with the descending corridor, it runs exactly north-south (i.e., it is meridional). At the top of this corridor is the heart of the pyramid, the Grand Gallery, but before climbing this, a short journey along the horizontal corridor brings you into the Queen’s Chamber.
As with so much of the Great Pyramid, the function of the Queen’s Chamber remains a mystery. The academic consensus is that it was intended as the burial chamber of the king but, like the underground chamber, it was abandoned; it has recently been suggested that its entrance was too small to allow the granite coffer (now in the King’s Chamber) to enter it.45 This argument is not really tenable; a pharaoh capable of having such a massive and perfect pyramid built was unlikely to have altered his plans because someone had made his sarcophagus too large. Abandoning all this work for such a reason does not fit the probabilities.
The Queen’s Chamber is not very large; only 5.74 metres from east to west and 5.23 metres north to south, its ceiling rising to an apex of 6.22 metres above floor level. In the east wall there is a niche, closely resembling a mirab (the prayer niche found in many mosques). The back of this niche has been cut away by treasure-hunters who no doubt hoped to find a secret chamber beyond. However, this is not the case; the niche was probably used originally to hold a statue of the king.46 The walls are of carefully fitted, smooth limestone blocks. Though not as large or as elaborately finished as the King’s Chamber, the Queen’s Chamber looks no more abandoned than the rest of the pyramid. As it lies exactly on the pyramid’s east—west axis, the Queen’s Chamber must have been an important aspect, and it seems inconceivable that the Ancient Egyptians would have built it only to abandon it at the last moment.
The particular features of interest both to us and to Rudolf Gantenbrink are the two so-called ‘air-shafts’ in this chamber, which have for many years been seen as supporting the abandonment theory. These shafts, which have their counterparts in the King’s Chamber above, were first discovered behind the walls of the chamber by a British engineer named Waynman Dixon in 1872.47 As in the King’s Chamber, one shaft is directed to the south and the other to the north. Further investigation soon revealed that, unlike those in the King’s Chamber, these shafts do not run through to the outside of the pyramid, proving that they could never have functioned as ventilators as some have supposed.48 In 1881 they were carefully investigated by Petrie, who measured their slopes and lengths with a clinometer. He concluded that they were not very long and that they seemed to serve no practical purpose. This was good ammunition for the abandonists, who concluded that the reason the shafts did not penetrate to the outside of the pyramid was that they were abandoned at the same time as the Queen’s Chamber. The matter might have rested here had not Rudolf Gantenbrink proved that the shafts were much longer than hitherto assumed.49
Running from the level of the Queen’s Chamber up to that of the King’s Chamber is the amazing architectural creation known as the Grand Gallery. This is in many ways the most elaborate and mysterious feature of the whole internal system of the Great Pyramid, and words can scarcely do it justice. It is enormously impressive. It runs upwards at the same angle as the ascending corridor but instead of being a narrow, crouched tunnel it is 8.53 metres high. When you are inside, it gives the impression of being even higher as it sweeps towards the King’s Chamber at the top end. It is a very curious structure indeed, for though it looks rather like a massive staircase, there are no steps as such. Yet it appears highly functional and was carefully finished in finely smoothed Tura limestone. Again Ouspensky provides a good description:
In the construction of this upper corridor-staircase there is much that is difficult to understand and that at once strikes the eye. In examining it I very soon understood that this corridor is the key to the whole pyramid. From the place where I stood, it could be seen that the upper corridor was very high, and along its sides, like the banisters of a staircase, were broad stone parapets, descending to the ground, that is to the level where I stood. The floor of the corridor did not reach down to the ground, being cut short … at about a man’s height from the floor. In order to get into the corridor from where I stood, one had to go up first by one of the side parapets and then drop down to the ‘staircase’ itself. I call this corridor a ‘staircase’ only because it ascends steeply. It has no steps, only worn-down notches for the feet. Feeling that the floor behind you falls away, you begin to climb, holding on to one of the ‘parapets’.50
Ascending the Grand Gallery is easier now, for there are short metal steps on either side leading from the level of the Queen’s Chamber to the level of its floor. There are also handrails to help you up (and down) and a wooden ramp on the floor with metal anti-slip treads.
Although the Grand Gallery is now easier to explore, it is still overwhelmingly mysterious, especially when one realises that this curious room was ancient even in the days of Antony and Cleopatra. The walls are corbelled, so that the Grand Gallery becomes narrower towards its ceiling, and its cross-section design seems to echo the curious niche inside the Queen’s Chamber, also corbelled. As with so much Egyptian architecture, it looks so ancient that it seems almost modern. There is a quasi-inhuman quality about the Grand Gallery that is hard to explain, as though it were not intended for people to walk up and down but to serve some other specialised or specific function. Many have remarked that the Grand Gallery looks like part of a machine, whose function is beyond us.
This is not a recent observation; the Neoplatonist Proclus drew attention to this in his fourth century commentary on Plato’s Timaeus.51 He claims that the Great Pyramid served as an astronomical observatory before it was completed, and that it was used as some sighting device for looking at the skies. This idea was taken up by a Victorian writer, Richard A. Proctor, who wrote The Great Pyramid: Observatory, Tomb and Temple, published in 1883.52 He pointed out how the various corridors could have been used for observing the stars while the pyramid was being built; in particular, he suggested that the Grand Gallery could have been used to record the transits of stars. Proctor believed that the slots in the parapets were used to fix the position of a movable ramp used in this work. To understand this, it has to be remembered that because the Gallery is meridionally aligned to the southern sky, it could indeed have been used in this way at some time before the top part of the pyramid was built.
Then again, as some modern Egyptologists tell us, it may simply have been used for storing granite portcullis slabs. If so, the Egyptians went to enormous trouble to build such a store-room when a rough chamber would have sufficed. No one, however, has the answer to the riddle of the Grand Gallery and perhaps no one ever will.
Ascending the Grand Gallery brings one to the King’s Chamber. Technologically this is the finest structure of all: it measures 10.46 metres from east to west and 5.23 metres north to south; its height is 5.81 metres. It can therefore be seen that while its floor area is exactly a double square of side 5.23 metres, it is just a little too high to be a double cube. Unlike the Queen’s Chamber, which is lined with limestone, this is of smooth black granite brought from Aswan in Upper Egypt.53 Whoever was responsible for building it was a master mason indeed. The granite blocks which make up the walls and ceiling weigh about thirty tons each and are perfectly smooth-faced. No mortar was used in jointing but, as with the casing-stones on the outside of the pyramid, the blocks were so perfectly cut and fitted that a knife blade will not fit between the joints. Fine jointing such as this would have been difficult with large limestone blocks; with huge granite blocks it is little short of incredible.
At the western end of the chamber is the mysterious granite sarcophagus. Although it is believed that this was the final resting-place of Khufu, there is not the slightest evidence of a corpse having been in that chamber, not a sign of embalming material or fragment of any artefact. No clue, however miniscule, has ever been found in this chamber or anywhere else in the Great Pyramid. This has led many to suppose that we have not yet found the true burial chamber of Khufu. Whatever the case, the sarcophagus in the King’s Chamber has been badly damaged by souvenir hunters chipping pieces from its edges.
Finally, there are the two air-shafts of the King’s Chamber to be considered. As in the Queen’s Chamber, these rise from the north and south walls but they shoot right through the pyramid to emerge on its exterior. The four shafts found in the two chambers are all quite narrow, only some 20 × 20 centimetres in cross-section The belief that they were ventilators is a curious idea for a burial vault, and one not repeated in any of the other pyramids. As these shafts are central to our thesis, we will be returning to them later in greater detail. For the present, the consensus is that they were not intended to keep the pyramid ventilated, although one of the achievements of Rudolf Gantenbrink and his team was the fitting of ventilators in the shafts of the King’s Chamber; this brought the humidity down from a stifling 90 per cent to 60 per cent, the same as outside. This is important when you consider the thousands of tourists passing through these chambers every day, each exhaling water vapour.
The completion of the Great Pyramid marked the high point of the Pyramid Age. When complete, it stood 147 metres (481 feet) high, some fifty metres higher than the larger of Sneferu’s pyramids at Dashour, or equivalent to adding an extra fifteen-storey building on top. It also required that Khufu’s workmen quarry and raise two million tons of stone more than the amount needed to build either of the Dashour pyramids. That Khufu was very serious about his pyramid is borne out by such textual information as we have about him.
There is, in the Berlin Museum, a document called the Westcar Papyrus. It dates from the New Kingdom but is undoubtedly a copy of a Fifth Dynasty original, for it tells the story of how this dynasty was ordained by the divine intervention of Ra, the sun god. The story takes place in the Fourth Dynasty during the reign of Khufu.
Wanting to be entertained, Khufu asks one of his sons, Djedef-Hor, to bring to him a magician called Djedi, an old wise man ‘of one hundred and ten … who knows the number of the secret chambers of Thoth. Now His Majesty King Cheops (Khufu) spent all his time trying to find out the number of secret chambers of the sanctuary of Thoth so as to have the same for his own “horizon” …’ He was therefore eager to meet the old magician. Horizon here means the Great Pyramid, for it bore the name ‘the horizon of Khufu’.54Thoth, of course, was the ancient god of wisdom, depicted with an ibis head, who was reputed to have invented science and the system of hieroglyphic writing. His famous books, forty-two in number, were supposedly kept at Heliopolis and formed the basis of the state rebirth cult. In later times, Thoth was identified with the Greek god Hermes and was said to have been responsible for the planning and construction of the Great Pyramid.55 When the magician Djedi arrives at court, Cheops asks him to perform some magical stunts and interrogates him: ‘It is also said that you know the number of the secret chambers of the sanctuary of Thoth …’. To this Djedi replies: ‘Please, I do not know their number, O king my Lord, but I know the place where it is … there is a chest made of flint in the building called “the inventory” in Heliopolis. It is in this chest.’ Djedi then says that he cannot get it and neither can the king; only three as yet unborn kings in the womb of a priestess of Heliopolis will have that privilege. These are the first three kings of the Fifth Dynasty: Userkaf, Sahura and Neferirkara.
Unfortunately, the Westcar Papyrus does not tell us what happened to the chest in Heliopolis or whether Khufu did obtain it and use the information it contained in the building of his pyramid. We are left wondering whether he did discover a secret chamber of Thoth at Heliopolis and, as is hinted in the papyrus, build a secret chamber of his own inside the Great Pyramid.
Work went on at Giza long after the death of Khufu. He was succeeded by Khafra (Chephren): who built another giant pyramid next to the Great Pyramid. Though only a few metres short of the first, the second appears taller because it stands on a slightly higher part of the Giza plateau. After Khafra came Menkaura (Mycerinos), who built a smaller pyramid, 65.5 metres in height. By any other standards, the third pyramid is a giant, but it is dwarfed by its neighbours on the Giza plateau.
Six kilometres north-west of Giza is Abu Ruwash, where a son of Khufu, King Djedefra, built his pyramid, but this has not survived time and plunder. It is now a pitiful heap of rubble and hardly recognisable as a pyramid. Its dimensions are not known for sure, but it seems to have been a large structure, perhaps similar in size to that of Menkaura at Giza. Another obscure pharaoh named Nebka, perhaps a brother or son of Khufu, planned a pyramid at Zawyat Al Aryan, a site about five kilometres south-east of Giza. It was either never finished or was dismantled in later epochs and used as a ready-made quarry.56 With Nebka the Fourth Dynasty came to an end. What happened next is unknown to Egyptologists; we are faced with an apparent loss of will and consequent decline in pyramid building after the Fourth Dynasty.
To put their achievements into context, it may help to compare the sizes of their known pyramids. The table gives the approximate size and mass for each.
HEIGHTS AND MASS OF FOURTH DYNASTY PYRAMIDS
Zawyat Al Aryan
To this twenty-one million tons must be added the mass of rock to raise boundary walls, temples, causeways and other structures forming part of a pyramid complex. We can conservatively add a further one million tons of limestone and granite, and this twenty-two million tons57 represents more than 80 per cent of the rock used during the whole Pyramid Age. The Fourth Dynasty, literally, towers above those which preceded and followed it.
VII The Collapse of the Fourth Dynasty
Jaromir Malek, director of the Griffith Institute of the Ashmolean Museum, has claimed that we do not need knowledge of architecture or history to know which pyramid came first:
It is enough to look at their present silhouettes: the step pyramid … is of the Third Dynasty … the pyramids proper which present a clean and sharp outline against the sky date from the Fourth Dynasty; those of the Fifth and Sixth Dynasties are now ragged shapes resembling huge piles of stone block and rubble …58
It is obvious to anyone visiting the pyramids that after the Fourth Dynasty there was a sharp decline in the skill of pyramid building. The kings of the Fifth Dynasty built five small pyramids at Abusir, about nine kilometres south-east of Giza, and a further two small pyramids at Saqqara, not far from Zoser’s step-pyramid. All of these were rather poorly constructed, and the workmanship of the inner core, which has mostly collapsed, is very much shoddier than that of their illustrious predecessors of the Fourth Dynasty. All the Fifth Dynasty pyramids are now mere heaps of rubble, some more like mounds than pyramids.59 Four small pyramids were built by the Sixth Dynasty pharaohs at Saqqara, all about fifty-three metres high and of even shoddier workmanship. With these last ‘the Pyramid Age par excellence’, as Edwards puts it, came to a close.60
The Fifth and Sixth Dynasty pyramids required some 2.75 million tons of limestone for their construction, less than half the mass of Khufu’s pyramid at Giza. This, and the obviously shoddy workmanship involved, implies that something drastic must have happened at the close of the Fourth Dynasty, something as inexplicable as the sudden emergence of the Fourth Dynasty with the rise of Sneferu and his ambitious project at Dashour.
The Fifth and Sixth Dynasty builders had the experience of the great Fourth Dynasty to fall back on, so from an engineering point of view we would have expected a progression and not a regression in the skills of raising monumental pyramids. Some Egyptologists believe the problem was one of social upheaval or economics. But if the later dynasties could not match the Fourth in the scale of the projects they undertook, at least they should have been able to sustain the quality of workmanship.
It is almost as though Egypt experienced a technological exodus at the end of the Fourth Dynasty, a brain and skill drain that depleted the pharaonic state. During the Fourth Dynasty, the Egyptians were supreme master builders, then suddenly, within a generation or so of their demise, there was an amazing loss of skill in the art of pyramid building. This is so pronounced that even the most conservative of architectural Egyptologists, Dr Alexander Badawy, describes the Abusir pyramids as being ‘strikingly poorer than the megalithic Fourth Dynasty structures’.61 Visitors to the Abusir site are hard pressed to believe that such pitiful heaps were once geometrical pyramids.
Egyptologists still debate the events that led to what they call the collapse between the end of the Fourth and the start of the Fifth Dynasty. They talk of socio-political upheaval, but Dr Malek claims that ‘the Old Kingdom was not brought to its knees by an upheaval caused by a popular uprising … no large-scale invasion from abroad took place.…’ He believes that there occurred a weakening of the state’s authority caused by a ‘gradual shift in the ownership of land from the central authority to cult and temple establishments and the nobility as a whole’.62 Yet, as far as we know, there is no evidence to confirm this; there are no land deeds or decrees to support such contentions. Edwards, on the other hand, feels that there was a violent cultural or religious change which caused a shift in authority to the priests of Ra, the sun god, whose centre was at Heliopolis. But he, too, admits that ‘documentary records are lacking’ to support this theory.63 If the truth is told, nobody knows what happened; conventional reasoning cannot explain the evidence we have before us. All we can say is that whatever happened at the end of the Fourth Dynasty caused the eventual collapse, as Malek describes it, of the great Pyramid Age.
The Giza pyramids are the crowning achievement of Ancient Egypt and the ancient world. It also seems that the dynamic momentum set by the Fourth Dynasty was slow in fading; although Fifth and Sixth Dynasty pyramids were smaller and shoddier, the urge to build them was still there, and we get the impression that it was not a collapse that occurred but something more like the handing over of the state’s authority to a less experienced government after a large-scale event.
VIII Evidence of a Master Plan
In 1934, towards the end of the Great Depression, a successful American architect, James A. Kane, visited Dr John Wilson, then director of the Oriental Institute at the University of Chicago. Kane had brought a large folder containing detailed drawings, calculations and a geo-survey analysis, not for a new office block or some mansion in New England, but of the Giza plateau and the three great pyramids which stand on it. Wilson’s first reaction was to try to persuade Kane to drop this hopeless business of ‘solving the mystery of the pyramids’ but then, in his own words: ‘I found myself constantly falling back to the cry of “coincidence”! Now coincidence may be invoked once or even twice, but when several divergent elements coincide and coincide again, coincidence becomes conformity rather than chance.’64
What the architect was showing him seemed obvious: the Giza pyramids, seen as a whole, were built in accordance with an architectural master plan. In his thesis, ‘The Ancient Building Science’, Kane was presenting a detailed analysis of the geo-architectural aspects of the Giza pyramids which showed conclusively that each of the three great pyramids was part of a single, unified plan, one which must have been devised from the outset of the great enterprise at Giza. We do not propose to go into the details of his analysis, but Kane saw that the three Giza pyramids were developed from a plan based upon geometrical and surveying principles which he believed were related to astronomical observations. Even in the 1930s, most Egyptologists were aware that the pyramids were set out and orientated using astronomical observations. For example, the bases of the pyramids are all set along meridians, so that each side of their square bases faces one of the four cardinal points. That the entrances to the pyramids are virtually all on their north faces, and that their internal systems are designed to run along their north to south axes, indicates that this meridional setting was paramount.
Recently the American archaeologist, Martin Isler, reiterated this fact in connection with Khufu’s pyramid, saying ‘accurate orientation could only have been achieved by using celestial bodies’.65 The accuracy is indeed stunning; there is an average deviation of only 1.8 arc minutes, minimal for such a large monument.66 The celestial body or bodies which served as the orientation target could not have been the large discs of the sun or moon (as Isler supposed) but must have been a pinpoint of light, which strongly implies a star. Edwards adds support to this stellar hypothesis with the opinion that ‘it seems more likely that the high degree of accuracy was achieved by astral rather than by solar observations’.67 This becomes obvious when we know that the Ancient Egyptians were avid stargazers. The priests watched the night sky not only for religious reasons but for telling time by the rising of stars and their culmination as markers to some natural star-clock mechanism based on the apparent daily and annual motion of the stars. R. O. Faulkner, the ‘definitive’ translator of the Pyramid Texts, also writes that ‘it is well known that the Ancient Egyptians took great interest in the stars, not only for practical purposes … but inscribing star-maps and tables in their coffins and tombs … in which the stars were regarded as gods or as the souls of the blessed dead.’68 Indeed it has often been demonstrated, not least by Dr Edwards, that the meridian line to set a pyramid’s square base could best be achieved by observing the stars. Everything points to astral methods having been used, not only because of the accuracy this gives but because we know that the Ancient Egyptians had, at the outset of the Pyramid Age, a strong stellar religion deriving from an ancestral cult.69
All this might seem obvious to us, but James Kane’s ideas made little headway in Egyptology circles. Although he published his thesis, it was put to one side and forgotten. Several decades later, in 1984, the American Research Centre in Egypt (ARCE) launched the Giza Plateau Mapping Project. This was to be carried out during two seasons in the period 1984 to 1986. The team leader was Mark Lehner, an American-born Egyptologist from Yale University. Two major reports were published in ARCE newsletters in Egypt before Lehner published his full report in a prestigious German Egyptological journal.
Lehner’s reports are largely based on surveying and geological data. Curiously and in view of his earlier literary work,70 he was not much concerned with the cultic aspects of whatever plan might exist, nor indeed with the symbolic architectural and astronomical messages the monuments might contain; his focus was on the geomorphy of the site and the need to determine exact co-ordinates for the analysis of geological formations in the Giza plateau. While many waited for new physical evidence for what some engineers already suspected — that the Giza pyramids were part of a unified master plan — all that came out of the 1984–6 surveys was a mass of complex geological and surveying data which raised more questions than it answered. Although Dr Lehner had performed an excellent geological and land-survey exercise, the burning questions related to a unified plan were not answered but further obfuscated by technical jargon. Yet he was awe-struck by the grand scale of the pyramids of Giza and Dashour which the Fourth Dynasty raised, and wrote that ‘when graphed against time, this brief period of the most monumental architecture stands out as a sharp peak dwarfing the material invested for royal construction prior or subsequent to the reigns of these kings’.71 Lehner later reported that an obvious diagonal alignment existed running just east and close to the monuments. This line projects from the south-east corner of the first pyramid (Khufu) to the south-east corner of the third pyramid (Menkaura), later referred to as the ‘Lehner line’ by other researchers.72
Kane and now Lehner were thus pioneers of a new avenue of research and people began to think about a unified ground plan for Giza. They were not the only ones to think along these lines; at least two other researchers pursued it further and their results were more extraordinary still.
IX A Unified Ground Plan
As is often the case with valid theories which evolve from the convergence of diverse data, the ‘master plan theory’ had popped up even before Lehner’s survey was finished. A similar suggestion had come from John Legon, a self-employed physicist living in Surrey, England. He first expounded its basis in the Reports of the Archaeology Society of Staten Island.73 In 1988, and in greater detail, he wrote a paper entitled ‘A Ground Plan at Giza’ and this was published in the Oxford journal Discussions In Egyptology.74Legon investigated the ‘possibility of a positional relationship between the three pyramids’ at Giza.
His thesis was passed to me late in 1988 by Dr Edwards, who seemed interested in Legon’s theory of a unified plan at Giza, which was as follows:
The placing of the three pyramids in a single ground plan was obviously an ambitious project, and one which indicates that the architects and builders of the Fourth Dynasty had a much greater control … than had hitherto been recognised. They were apparently able to dictate, for example, the small dimensions of the Third Pyramid, despite the presumed desire of Menkaura to have a monument equal to those of his predecessors. Since the three large pyramids of Meydum and Dashur appear all to have been built by Sneferu, it seems possible that at the outset, Khufu himself might have aspired to the construction of the three pyramids of Giza in a single unified ground plan.75
Legon showed mathematically that the three Giza pyramids fitted inside a rectangular perimeter having the north-south side as 1732 cubits76 and the east-west side as 1414 cubits. It occurred to him that a basic modular unit of 1000 cubits was used, and could be expressed as 1000 √3 and 1000 √2. Since these sides were of a right-angled triangle, the diagonal could be expressed as 1000 √5. He concluded that such geometrical and mathematical harmony could not be the product of coincidence. The notion of a master plan at Giza was now getting strong support from other quarters, but Legon, intent on proving that there was evidence of a master plan, also omitted to investigate the religious or cultic motives for it.77 The question that still hung in the air was, and still is, what does the master plan express?
In February 1988 a teacher and geologist, Robin J. Cook, published a paper entitled ‘The Giza Pyramid: A Design Study’.78 Cook expanded on the findings of Lehner and Legon and added some ideas of his own to show that ‘the Giza pyramids were designed according to a system of geometrical ideas, and that the site was planned as a whole …’ Cook pointed out that a geometrical axial system could be shown to link the central pyramid, that of Khafra, with the small satellite pyramids next to the first and third pyramids. The main angles exposed were 60 degrees and 26.5 degrees; 60 degrees is the angle of the isosceles triangle and 26.5 degrees is produced by the diagonal of the double-square. This angle of 26.5 degrees could also be found in the main passageways of the Great Pyramid and the double-square of the floor of the King’s Chamber; again defying the limits of coincidence. Cook, unlike Legon and certainly unlike Lehner earlier, sensed a powerful symbolism behind the plan, evidence which revealed the use of geometrical and geo-architectural patterns to express an ancient system of numerical philosophy. He rightly observed that:
The Giza Pyramids represent a symbolic statement written in stone and the language of a mathematical philosophy. The Giza group probably represents a symbolic expression of the Heliopolitan myth [my emphasis] …79
Yet Cook seemed unable to say what the symbolic statement was that was written in stone.80 He and Legon had demonstrated the advanced state of Egyptian geometry at the time the pyramids were built and that it could be applied in practical ways, but this was not enough to explain the Giza pyramids or their layout.
It seems we need to look further for these answers, not at Giza but in the small Fifth and Sixth Dynasty pyramids at Saqqara. There are inscribed, inside the little pyramid of Unas, some extraordinary texts.