When I first picked up Louis Charpentier’s book called “The Mysteries of Chartres Cathedral” in June, 1985, I could taste it deep within my ribs. It was an indescribable food – not quite esoteric – just indescribably inspiring – but I had to wait three more years before it was my turn to experience the beneficence of the place itself. And yet I could taste it as if it were just down the road from our hotel in Auckland. This echoed my feelings about Chartres back in 1971 when Kenneth Clark commented on it in his series called “Civilization”. I confess again: Chartres lives in my heart and the feeling is that it has always been there. Its presence defies logic, expectation and all theories I have ever had about knowledge. Moreover, there is no one on Earth that I can think of – whether friend or enemy – who I do not wish could visit Chartres at least for one day in their lives. Chartres is for everyone. Every word that Charpentier committed to print was an affirmation of a knowledge so deep it was as if I had been born with it. And if I was born with it, so too must the rest of humanity be born with it. But it felt as if it were imprisoned in an infernal darkness. My urge was to descend into my own depths and wrest it from its jailor provided I could overcome the two greatest adversaries: time and fatigue. Like all living things knowledge wants to grow. We are the effects of that growth even when most of the root system of such knowledge remains submerged in the unconscious. Significant knowledge is not merely a matter of connecting the dots or finding a correspondence between an effect and a cause. Significant knowledge enlightens one’s whole being – even if ultimate causes remain unknown. A blind hen will continue to scratch around for a grain of corn. But even a blind hen can be illuminated from within while the corn is eventually felt with a single swipe of its claw. In searching for a geometry that accounts for human form, a form capable of supporting minds that could engineer Chartres, I felt like that blind hen.
In one passage Charpentier recounted an experience he’d had in a Paris suburb in 1964. In the blink of an eye my entire feeling about the world, how it is constructed; about human culture and even human nature, was changed forever. The change was as significant as the ‘Big Dream’ that occurred out on Long Island in the fall of 1980, mentioned in the earlier posts. As it turns out they were thematically related. Before that dream, which felt more like a template of the real than a dream, I had some knowledge in my head, but it was dim, like seeds that had fallen on barren ground and could not blossom into the light. I still had no key with which to fertilize the soil. The Big Dream had introduced me to a new kind of knowing: knowing what I am and what has formed me, directly, from within. It was an inner seeing and an inner drama, within which I was both participant and observer. But it too was a seed that was growing only slowly out of a state that could be called ‘the trauma of rebirth’, into a new adolescence of ‘knowing’ and learning to trust that knowledge in a world so often warped by a labyrinth of projections that fire us away from ourselves – not just psychologically, but also physically. We often search for ‘truth’ as if it were something other than what we are. And to add to the mystery, it took me exactly 12 years to fully recollect the 1980 dream! A lot of inventive perseverance was required to cajole it from its hiding places. But this implied it was already committed to some form of long-term memory – a bit like the root system of a tree. It was up to me get down there and examine the roots without damaging them. Recollecting the dream was a lot like giving birth. It was a long labor.
To my surprise, Charpentier invoked the “grail” in introducing the prime principle of the book, Chartres’ secret perhaps; its quintessence. I could not have guessed that the mere mention of the ‘grail’ could have so profound an effect. I had not yet read Wolfram von Eschenbach’s “Parzival”, written alongside the final reconstruction of Chartres from 1195 to 1220, after the fire of 1194. Apparently he wrote it right there on the site. I knew almost nothing about the Knights Templar. Perhaps that was a good thing because my innocence blinded me to the controversy that swirled about their place in history. I had no idea Eschenbach himself may have been a Templar. I had no familiarity with Wagner’s operas that concerned the Grail. I had gone straight to Mahler in my youth and never got back to Wagner. So, not only did I have no idea what the “Grail” meant to the Gothic Age, but I did not have a clue what it was at all. So, when Charpentier drew a parallel between the cathedral itself and the Grail, initially I was astonished. Or was I? I think I was astonished that it rang so true! My connection to Charpentier’s book was mystical. Chartres must be a node on the body of the Earth and human knowledge must be much more than what we imagine.
I knew the Grail was a vessel of some kind but had not thought of a cathedral as a vessel that had assumed the function of the Grail. My own view of all churches other than Chartres has been mired since childhood in a murky backwater of preciousness – an allergic reaction of the mind to the falsity of my own religious up-bringing. Finding the grail to be almost as ‘precious’, subconsciously, it was a stimulating association, an antedote perhaps, to an ingrained – but tired – rationalism that had not yet entirely shed its skin and was still encumbering my quest for psychological freedom. I could see that Charpentier had more faith in the ‘Grail’ than I did, but it was Chartres that beckoned me.
However, it wasn’t until I had come upon key references to the Eye of Horus – particularly in the Vth Dynasty Pyramid Texts of the Egyptians – that the meaning of the “Grail” started to become clear. The Grail, like the Eye of Horus, is not a ‘thing’ per se. A cup, or stone urn, or gold chalice are all ‘symbols’ – no matter how beautifully they may have been crafted by human ingenuity. The 1980 dream ws pushing me to look more deeply behind the symbol – if possible. The ‘Grail’, or “Gral”, could not be identified with a specific object, anymore than the God of the universe could be identified solely with the Sun, or the ‘personality’ solely with the physical body. The Grail is universal, of which things are ‘symbols’ only, likenesses, to borrow a term from Goethe, means that facilitate a much more mysterious end. However, the right vessel, properly rectified, can have the effect of enhancing or inducing a metamorphosis, a qualitative change or transmutation in a living being. This can range from art to a cathedral, to a relationship or even a shock of some kind. More to the point, the Grail facilitates an event, an experience – or perhaps ‘revelation’ would be a better term – that pushes the boundary-stones of the ‘self’ (one’s own natural ‘grail’) to a limit of comprehension. At this limit, all ‘understanding’ undergoes an inversion. Appearances, once considered self-evident, find themselves re-absorbed by a source too mysterious and too powerful to name. But yet it is experienced vividly and directly. After this inversion, communication also changes. You know what you wish to communicate but a new language is required to properly represent it. Having seen directly, one can no longer speak directly. Cabalistic language arises by necessity. It is not arbitrary. One thinks of the legends surrounding Moses who was said to have been the only one among the Hebrew who had ‘looked directly into the Sun’! Metaphors aside, the feeling is that Moses had been illuminated from within, initiated in some fashion to the law of his being: man’s relationship with the surrounding cosmos. Below is a sculpted image of Moses at the north-west entrance to Chartres.
With Chartres and any other building that echoes the eternal spirit, there is the feeling that everything essential was put into the world all at once. Was there a key that the Master Craftsman kept in his pocket – or did he just keep it in his mind? Did he inherit it? Did he discover it? Perhaps it was rediscovered? But what was it? What was this key?
Here Moses holds a pillar. A winged dragon (French, “wouivre”), not unlike the winged serpent of the Egyptians, has ascended the pillar. The Spirit of the World has been gathered from the Earth and concentrated. Presumably it is concentrated according to the ‘table of the law’ that he holds as well: a rectangle with a rounded end that exactly resembles the floor plan of the choir at Chartres (Fig X). The concentrated spirit then rises up the pillar, a symbol for the human spine. It penetrates and purifies (refines) the inner man and opens the inner eye. In Egypt that Winged Serpent or Uraeus was always feminine and was variously Isis, Neith, Uatchet and so forth. It blossomed at the summit of its journey as the Eye of Horus and was symbolized (in part) by the Uraeus that projected from the brow of the Pharaoh.
In this image we see Seti I of the XIXth Dynasty making an offering of Maat, neter of Truth, Cosmic Balance. The Uraeus extends from Seti’s brow as if it has blossomed from the khepresh helmet, itself capable of conducting and concentrating magnetic energy. His hands have been reversed. His left hand is on his right wrist and offers Maat. The right hand is on his left wrist and seems to invoke protection. The hands are extensions of the heart and what seems to be shown here is not only what is in the heart – the effect of each heart circuit and the decussation of vital energy, vital breath – but he is both giving and receiving simultaneously. Maat represents balance or cosmic equilibrium. There is perhaps no greater balance than that between receiving and giving; systole and diastole; inhalation, exhalation. She herself seems to have two right hands and holds the Ankh. Therefore the secret of ‘Truth’ and ‘Balance’ is that it ‘gives and maintains life’. We read a similar passage in the Berlin Papyrus: “I have come to you, I am Thoth [Maat’s masculine counterpart], my two hands united to carry Maat…you make Maat rest on your head in order that she may take her seat on your forehead….you exist because Maat exists,…and vice versa.” I should just add here a comment by Lucie Lamy, the stepdaughter of Schwaller de Lubicz – though I did not come upon this until about 1988 – “Maat is the greatest treasure that a being might wish for.” (egyptian mysteries, p. 51) She calls Maat “Cosmic Consciousness”. Not surprisingly, perhaps, if you slipped those lines into Parzival but replaced the word Maat with Grail, you would never know the difference. Cosmic consciousness transmutes encyclopedic knowledge.
Next, is an image I concocted in 1992, once I had enough information to create a head from nothing. That was the year I felt released from the labor of recollecting the Big Dream. Finally I felt I had gotten it out. For reasons that may not have been altogether clear, we also left Manhattan and moved to Nova Scotia Canada.
I used the angles of ‘squared-circle’ geometry and the golden section as generated within a 2:1 rectangle. I left the lines visible to provide a sense of something intelligent arising from the void as if it were a self-organized vessel that accumulates the light, thereby piercing the world of appearances as if all at once. At that moment the head struck me as the ultimate mystery. But I believed I could conjure it up through the basic geometerical ingredients I had gathered from 1985 through 1991.
By 1992, I knew there was a long tradition that linked the Grail to the human head, an inestimable vessel of transmutation. In the Welsh version of the Grail, a head on a platter replaces a cup! The head is what is being served at the feast. The appearance of the Grail is supposed to prompt a question from the hero: “Who or what do you serve with the Grail?” The miracle of the human head or the Grail, is a means only – a passage perhaps.
In Egypt the head was associated with Horus, Ra, Atum-Ra and Osiris. At Rosslyn Chapel in Scotland, the Grail is associated with the Sun and the head. In Western astrology the Sun is said to be ‘exalted’ in Aries. Aries is also said to ‘rule’ the head. In any case, I will use the face of this young woman shown next as a standard for the fundamental geometry I have found present in all faces, the means by which the head and face self-organize with amazing consistency. The geometry has nuances, face by face, and yet always plays with the same fundamental principles! Here it is without the geometrical lines and markings in place, which I will show later.
The quest for the Grail is itself an out-and-out adventure if ever there was one because the experience cannot be distinguished from one’s own transformation. When Parzival failed to transform his own brutish character, he found himself wandering in an interminable and senseless wasteland, pining for the Grail that he himself had forfeited. What, then, is this ‘Grail’ that we variously label: ‘cup’, ‘head’, ‘Eye of Horus’?
In the West, we insist upon reducing everything with a name to a physical thing that can be labelled and pointed to. We have a conscious infatuation with the “tangible object”. In my view this infatuation is not merely a product of empirical science or the advent of the modern ‘scientific method’. Rather, to me, the scientific method is a product of an infatuation with the ‘tangible object’, an infatuation that has been with us for a long time. We cling to our ‘attachments’ and from a practical point of view, often with obvious reasons. During the Middle Ages pilgrims were obsessed with ‘relics’, tangible ‘proofs’, hard evidence that the divine was at work on Earth in a specific place and time. This obsession became the basis of Christian Dogma, which is why influential spiritual leaders such as Saint Bernard of Citeaux, who helped inspire the movement that lead to the Gothic Cathedrals, constantly reminded everybody that a cathedral is but a means only. The end is the spiritual perfection of the individual pilgrim who is making a passage, a journey.
There are some realities that reveal their natures on another plane of consciousness, arising from a much more intangible source – a plane of teeming potential, many-named and multi-natured – as if it were the mother of all ‘things’ and with which we find ourselves inextricably entangled. Today we sometimes speak of a ‘teeming vacuum substrate’ as if it were pregnant with possibility and not merely a desolate void dotted with separate ‘things’. Heisenberg’s Uncertainty Relation is as much pregnant as it is ambiguous. At the root of the Uncertainty Relation and the Grail there is an enigma: the measurable and the immeasurable arise together in an ineffable embrace. This is a quality they share with the 2:1 rectangle. Its width is 1; its length is 2; its perimeter is 6. But its diagonal is the immeasurable or incommensurable square root of 5, namely: 2.236067978…. But it seems that these opposites are in a complementary relationship with each other which, by degree, become amplified into the process of life.
The Aborigines of Australia referred to a spirit plane called the Dreamtime. Special practices were required for the spirit to enter the Dreamtime – which was a quest for knowledge and power. Controversy swirls about that entrance like a smoky fire – its burning glow so terrifying and yet so desirable at the same time! The Dreamtime must be experienced in order to transcend the controversy. The Egyptians referred to something called the Duat, the passageway to the Netherworld. In the language of Christianity there is talk of ‘spirit state’, a term that echoes the strange, yet beautiful landscape of the very ancient Pyramid Texts which deal with the purification and transformation of the “ka” or “double”. The Buddhists also speak about a plane of existence that is for the spirit alone. Extraordinary discipline is required to enter that world – a world where compassion becomes complete. The Naassenes also referred to a realm that was for the spirit only. Everything else had to be left behind. The serpent-in-the-spine, ‘wound around the tree of knowledge in the midst of Eden’, was the energy that got one there. All the truths in Parzival also feel as if they were woven from the fabric of a vast and multifarious dream state, as if the entire adventure was one collective initiation into the explosion we call ‘life’ – an explosion that erupts with all its agonies, joys, triumphs and humiliations as if from the black womb of Wisdom herself, whether she be called Night, Nut, the Great Mother, the Barren One, Black Virgin, Sophia, Isis, Mut, Hathor, Neith, Athena, Mary, Saint Anne or the Eye of Horus. In the Pyramid Texts the Eye of Horus is always depicted as feminine in gender! So was the Goddess Kundalini – that notoriously mysterious serpent power coiled up in the sacrum. Eventually, the Eye performs the function of a womb-like protective sphere that guards and transmutes the essence. Significantly, when Parzival encounters his ailing Uncle, the Grail King, suffering the pains of an enigmatic illness that nothing can cure – not even the Grail itself – he fails to inquire about the nature of the illness with compassion. He is supposed to ask a question. The humility of a question asked in the right manner is the sole antidote to the pride that afflicts Anfortas. Compassion cannot be faked. Nor can it be prompted. It also cannot be forced. But without compassion enlightenment will abort itself; the lotus flower will not open. As soon as we start to talk about the Grail, like the Egyptian Eye of Horus, we are talking about something All-embracing, but yet is witnessed by individuals at specific moments in time. When the soul is imprisoned – often by a pride that loves to wear many masks – compassion opens the locks letting the genie out of the bottle – but only at the right time.
Whatever name is invoked and whatever shape humans choose to represent it, the Grail remains enigmatic because in it the opposites seethe and boil until cooked to perfection. Then the cycle must start all over again. The spiritual trek is not for sissies. Along the way Dionysus and all his cohorts may tempt even the boldest among us with the dread we call ‘madness’, the very boundary that separates hell from heaven and falsity from truth. More dangerous than madness itself are the labels that attempt to define it. Nothing gets in the way of what the Zen masters call ‘satori’ like labels. Labels are intellectual turns within the walls of the labyrinth.
“Three Tables bore the Grail”.
Anyway, back in 1964 there had been a ritual gathering of “the Society for the Study of Traditional Sciences”, the “Friends of Atlantis” , on a property in a suburb of Paris. It involved lighting a fire, chanting and perambulating in a circle with beribboned sticks and colored dress. Someone gave a speech during which he invoked the ‘traditional enigma’ when mentioning the carpenter who had been responsible for saving many of the church spires ravaged by the Battles of 1944. Charpentier had to paraphrase the ‘enigma’ and recounted it two ways. I will mention the second way first:
“Three tables bore the Grail, a round one, a square one and a rectangular. All three have the same perimeter and their Number is 21”. (The Mysteries of Chartres Cathedral, p.92, p.133)
In this context – with the mention of 3 Tables – it is difficult not to think of Hermes Trismegistos or Thrice-Greatest Hermes, especially when one bears in mind that Hermes means Her-mes or Hr-ms which meant in Egyptian: ‘the birth of Horus’! And if one wants to be even more technical at this stage, one can see this really means the ‘rebirth of Osiris-as-Horus’. Charpentier uses the past tense: ‘bore the Grail’. The religion centered on Horus and Isis probably initiated the Egyptian civilization around 4200 B.C. or so when the Sirian Calendar was established based on the heliacal rising of Sirius every 365.25 days. This was the star of Isis. However, Thoth-Hermes was treated by the Egyptians in a special way. When Ra was created it was Thoth and Maat who brought him up out of the void and established his size and so forth. The Egyptians attributed all sizes, all periodicities, all measure and all design, ultimately to Thoth and Maat. It would have been Thoth who would have established the 3 tables that bore the Grail. The imagination still wants to know what the ‘Grail’ was or continues to be. Were they thinking of the genesis of Sun, Moon, Earth, Saturn, et al? This would seem to be the ‘Grail Castle’, like Castle Mundsalvaesche in Parzival. Castle Mundsalvaesche also invokes a magical mountain of some kind as well. In the Pyramid Texts Atum becomes the Primeval Hill, the Primordial Hillock. He rises up like a Pyramid out of the Nun (void) as a primordial mound. Long before Chartres was a cathedral, the place itself was famous for its mound. Its water, the vegetation, etc., was legendary. The Druids practiced a secret form of baptism, initiation rituals in a crypt within the mound. Supposedly a dolmen is buried within it to enhance its spiritual and healing properties. The current cathedral is simply one of a long history of beneficent manifestations associated with the hillock, tertre, or ancient mound of Chartres. The Great Pyramid was a legendary mountain known throughout history. Supposedly the building itself has been built around a 30 meter high hillock that was as legendary as Chartres. These places are like special nodes on the face of the Earth’s sacred geography where the current that bathes everything comes to a special head with special properties. Chartres is definitely one of those places. So is Gizeh. There are a few lakes in New Zealand with this sort of endowment. I know a place in Nova Scotia, Canada that is like this. The soil was once part of Africa. It is red and pink. An extraordinary peace and well-being penetrates mind and body in the summer. It also boasts the world’s highest tides.
Were they thinking of man’s genesis in the image of the three tables when they spoke of the Grail? Were they thinking of the manner by which ‘God fashioned Adam on his Potter’s Wheel’ as depicted at Chartres echoing the way the Ram-Headed Egyptian neter, Khnum, fashioned a man and his double (ka) also on a Potter’s Wheel? The emphasis at Chartres was on Adam’s head. Chartres was under the spell of Plato’s Timaeus at that time. Plato saw the gods fashioning the World Soul first as a sphere. The head was created in imitation of both World Soul and the Eternal Living Being who was spherical. The body then followed as a matter of practical necessity to stabilize the spherical head. Incidentally, at Luxor, Khnum creates the King also with two right hands, not unlike the image of Maat above who gives the key of life (Ankh). But in any case Charpentier is quick to point out within the context of this past tense, “bore the Grail”, that:
“… even the bare mention of the Grail shows clearly that there is no question of trifling and that this “trade secret” had, in its application, an initiatory significance and, especially in the case of a cathedral, a bearing on initiatory action.” (ibid, p.133)
An All-embracing roundness becomes square through division and differentiation. Squareness involves acceleration. Acceleration is an aspect of inverse square forces such as gravity. So with the square, gravity or ‘self-gravity’, is born and things become separate and differentiated. There is now competition in a shared field. Gravity acts a bit like Seth was said to act. He stole the Eye of Horus and swallowed it. Horus has to get it back again. Christ had to descend into hell to win back the light. The opposites are born, like Horus and Seth, male and female, light and dark, war and peace, matter and spirit through the square or ‘square-ness’, which includes electromagnetic radiation. Matter steals the light which is reborn in the belly of the Sun. When accumulated in the head and heart it too can be reborn until the whole being is a vessel full of light.
The rectangular table is mentioned last. In Parzival, Parzival himself arrives at Castle Mundsalvaesche as if by fate or possibly by chance. He is taken into an immense square hall that was probably a cube. He was then witness to the Grail Procession. It is quite mysterious, but the Grail was carried in procession by the world’s most radiant and beautiful woman, Repanse de Schoye, from one room – not seen – through the square room where a stupendous feast was manifest, and the Grail was then carried on to a third room, also unseen. So the square appears to be what makes invisible spirit, visible. The circle and rectangle appear to be associated with invisibility.
Charpentier then pointed out the following:
“The rectangular table is that of the Eucharist. The mystical table, Christian, that which supports the altar and, indeed, the choirs of Christian churches are as a rule rectangular. There have been other rectangular tables, as in Egyptian and Greek temples…But the choir at Chartres is rectangular.” (ibid)
Best to note right away that the choir at Chartres was once completely blocked by a gorgeous, thick, stone ‘rood’ screen, not removed until 1763. No one – not even the Knights Templar – were allowed entrance to this most holy place except the ‘High Priest’ and even then, like ancient Egypt and Solomon’s Temple, only once a year! It was the place of the High Altar. Clearly this choir had gathered up something so pure, so vital that the temple priests did not want to violate or disturb it in any way. It was acting like a dolmen, a spiritual fertility stone. The ‘Grail’ was traditionally associated with fertility. The Eucharist invokes some sort of sacrifice, often associated with altars. In Christianity the sacrifice was that of Christ, by which his blood and his flesh were capable of ‘feeding’ others. But it has to be mentioned that the builders of Chartres placed no crucifixes in the Cathedral. The Templars did not share the Christian view of the crucifixion. Nor did they share the Christian view of Christ.
When Eucharist, altar and choir are put together with the idea of rebirth, or a second birth, the notion of 3 tables suddenly becomes fundamental. Charpentier continued with a relentless penetration into the mystery that already had me under its spell but which was not yet fully radiant: you want your ‘tree of knowledge’ to liberate and purify the soul, but it is easy to be confused by the mysteries. When myth is used to convey eternal truths, we tend to latch onto the symbol and fail to sense the process for which it is a vital metaphor only. Often science itself becomes trapped by its own myths: assumptions that cannot be verified because we lack the time and instruments to measure what is infinite or, conversely, what is infinitesimal. So we accept theories as if they were axiomatic. There is a very fine line between effective symbol and even unintended propaganda!
“There without doubt was the way into the mystery of the cathedral’s construction. But it was still necessary to solve the riddle of the Number 21. The answer is simple in fact. We are to read, not 21 but 2 and 1. We are confronted then, with a rectangular table whose length is twice its width.” (Mysteries of Chartres Cathedral, p 93)
All Roads Lead to 2 x 1
Charpentier had confirmed what I had already met with in Dozci’s book, that Egyptian and Greek temples were based on 2:1 tables, because as Vitruvius had noted, this was the foundation for human proportions. But it is well to remember that the Greeks spent some time on the Egyptian throne (after 305 B.C.?)! They fully restored places like Dendera and Edfu. Now Charpentier added that the 2:1 rectangle was somehow the key to the equivalence of the 3 Tables ‘that bore the Grail’; 3 phases of one essence – the three parts of the one philosophy, the one mystery, perhaps – one miracle like the body of Shiva, shimmering with trillions of luminous parts.
So, each unexpected fork in the road had arrived at the same destination: a rectangular table with a length that was twice its width. For me it was like a universal omphalos, only it was a rectangle. I wish I could describe how it felt upon arrival, when I first stumbled in to touch the ‘cosmic chip’. All I could do was stand there and accept. There was nothing to say. No comments proved fruitful. Initially I tried to hide it: the omnipotence of its simplicity. When I tried to talk to others about it I turned into a stammering fool. At last I had cause to truly keep my nervous lips sealed. I wanted to share my excitement, but I was going to have to get to work, not squander the propitiousness of the moment on talk. A strange silence binds the tongue of acceptance – especially in restless people like me – always afflicted by dissatisfaction. New Zealand was a nice part of the world to be confronted with such an enigmatic experience. What do you do? You breathe and enjoy the stillness. You ask: “How can this be”? But there is no answer. It just is. Such a relief! It’s like the Sun rising after a frigid dawn. The frost melts and drips back into the roots of living things. Green abounds. You see at last that meekness does not mean weakness. Having been an outcast, you feel as if you have reinherited the Earth, the place where ‘above’ and ‘below’ unite. You yourself are that point of union. If Vitruvius was right, I wanted to prove it. We are born of that 2:1 tablet, where 1 has become 2 and then everything happens between them like the bellows of the Tao, the heart of the Tai’chi. An ovum is neutral until fertilized by a sperm with equal DNA. Then suddenly its neutrality is gone. Meiosis, once suspended, converts to an endless mitosis until death shuts down the ‘water factory’ and the 2:1 becomes the final looking-glass.
With this rectangular table, you feel your own worthiness above you, below you; within you and all around you. And when you trace out two equal circles within each of the two squares, it is hard not to think of the Sun and Moon just separating after New Moon; or the first cell replicating its own nuclear information and then suddenly dividing into two, new, equal ‘daughter’ cells. Right away nuances abound, it is true. Nothing is ever quite identical to anything else, but yet there is the Platonic hint of perfection that surrounds that division. The whole story starts to tell itself, like a river issuing from an immense glacier, one droplet at a time, until it has become a swelling flood.
Solomon had used a 2:1 table (20 x 40 cubits) as far as the Holy of Holies, which was itself a cube with 20 cubits on each side. Geometrically speaking, a cube is a good starting point within which to construct the human head. One immediately thinks of the famous “Ka’aba” in Mecca: that perfect black cube that inspires an involuntary perambulation in imitation of the fundamental motion of celestial bodies when the infinity of space is transformed into the periodicity of time! A black cube is the Great One, the nameless Allah, Atum, Amun, Amen who precedes even the Sun itself: whose invisible essence is enveloped by the infinity of the female. A sphere set in a cube is the next step.
And if the volume of the cube is taken as unity (1), the volume of the sphere within it will be .5236, the same relative value as the royal cubit the Egyptians used for the Great Pyramid of Gizeh. When pi is 3.1416 m, the royal cubit becomes 3.1416/6 = .5236 m.
I will return to this number 5236 again and again. But it cannot be emphasized enough that the dimemsions of the King’s Chamber in the Great Pyramid are 5.236 x 10.472 meters. Since the perimeter of a 2:1 rectangle is 6 times its own width, the perimeter of the KC is 6 x 5.236 = 31.416 meters. The Great Pyramid squares the circle but rests on a square base. The King’s Chamber, deep within it, is proportioned 2 x 1. In Solomon’s Temple, one imagines that the 2:1 purifies the entrance to the cube, wherein spirit gathers. This is the head of the Temple. It was also the place of the “Oracle”. In Egypt, Osiris was called “The Herald of the Year”. At Dendera, the Osiris-King (or surrogate High Priest) entered the 2:1 rectangular Sanctuary of the Barque once a year, as the Oracle. The Oracle is a consummate revelation in some of man’s greatest civilizations – such as Tibet and Egypt – that ‘Holiness’ arises from wholeness. I realized early on that I was looking for a geometry that reflected the circumstances and details of that wholeness. Tradition has called such a geometry: “sacred”. I was aware that I was looking for a geometry that was capable of uniting and harmonizing outside with inside; above with below; female with male. I developed a habit early on. Whenever I stumbled upon an interesting number or relation, I automatically checked for its reciprocal: its inverse value or the manner by which it had divided unity. When multiplied together unity is restored. For example, the reciprocal of 1.618, the golden number, is .618 and when multiplied together you get:
1.618 x .618 = 1
The reciprocal of .5236 is 1.90985 or nearly 1.91, a number we will see ahead. If you take the width of the KC as 5.236, then:
1.91 x 5.236 = 10 meters and 191 x .5236 = 100 meters.
Twice 191 is 382 and 3.82 divides 10 by the golden section with 6.18
3.82 + 6.18 = 10.
The circumference of a circle with diameter 10 meters is 31.416 meters which is identical with the perimeter of the KC.
The Ark of the Covenant
The Ark of the Covenant was ostensibly kept inside this ‘Holy Cube’ at the end of Solomon’s Temple and so could be part and parcel of the “Oracle”, the crystal ball of wholeness. Like the King’s Chamber, this Cube was supposedly completely empty except for the coffer called the Ark of the Covenant. The Ark was called variously, the ark of the testimony (e.g. Exodus 25:22); the ark of God; the ark of the covenant. In Kings 8:1, it is called ‘the ark of the covenant of the Lord’. In Kings 8:4 it is called ‘the ark of the Lord”. In Kings 8:6 it says it was placed in “his place”, “into the oracle of the house, to the most holy place…” It is of interest to note that in Kings 8:9, it is stated that “There was nothing in the ark save the two tables of stone, which Moses put there at Horeb, when the Lord made a covenant with the children of Israel, when they came out of the land of Egypt”. In Exodus, it is stated that only the ‘testimony’ is to be put into the ark. The testimony was given to Moses at the top of Mount Sinai. Mountains are often associated with enlightenment, testimonials, salvation and so forth. The Grail Castle is called Mundsalvaesche or Salvation Mountain. The Pyramid was a human mountain wherein an extraordinary form of salvation was to take place. The Osiris-King, according to the Pyramid Texts was not seeking his own salvation for himself alone.
It was only years later (2000) that I came upon more than one reference to the Ark which was described as being 2 x 4 x 2 feet in size (e.g “The Hiram Key, 1997). By that point it came as no surprise to learn that the Ark may have been based on a 2:1 table. In Exodus, it is given quite different proportions, namely: 2.5 x 1.5 x 1.5 cubits. However, the Court of the Tabernacle that housed the Ark when the Jews were wandering in the desert, was proportioned 1:2. The table built for offerings was also 1 x 2 x 1.5 or perhaps 20.6″ x 41.2″ x 30.92”.
The Ark is featured in a singular way at Chartres at its north-west entrance, as if it had been regarded with special interest by its builders, The Order of the Temple, or “Knights Templar”. Incidentally, while the south-east entrance to Chartres features Christ, the north-west entrance features Saint-Anne holding the infant, Virgin Mary, as if somehow the key to the whole mystery was the axis drawn across the transepts from Saint Anne to Christ.
The general public was at one time forbidden to enter by the north-west entrance that features Moses among others on the left and the Ark, among other things on the right. One thinks of Nut holding Isis in ancient Egypt. Isis and Mary have much in common. Dogma should not permit itself to obscure this fact. The Cathedral of Chartres was named “Notre Dame de Chartres.” The emphasis and the dedication was placed upon the purity and rectitude of the vessel within which the soul and spirit of each pilgrim was intended to be immersed. This was to enhance Nature’s potential for the ultimate gift: that of a second birth; the birth in spirit; a qualitative exaltation of one’s very existence.
To further this purpose, it seems the builders may have chosen their measures carefully. It should be mentioned that the internal width across the transepts has been given by Etienne Houvet as exactly 61.8 meters. When, in 1985, I was using the 5 x 10 rectangle in centimeters, I did not yet know about this measure. I cannot convey the excitement I felt when I first encountered this 61.8 meters around 1989 or so. Just as it is unlikely that the 31.416 meter perimeter of the King’s Chamber was an accident, I doubt very much that the 61.8 meter width of the transepts at Chartres is an accident. 61.8 is the golden section of exactly 100 meters. 31.416 meters is a perfect circumference for a circle with diameter of 10 meters. If you establish a 100 meter 2:1 rectangle, as shown here, and take its golden section from point S at the entrance to the Nave, 61.8 meters falls exactly at the entrance to the Choir, or point T. So you have a square, OPKL that is 61.8 x 61.8 meters. In this square, the Nave with its Labyrinth, and the transepts as far as T, are included. After that it is forbidden territory, like Solomon’s Holy of Holies. The Cathedral prepares you. In the midst of the transepts you are penetrated by the three great Rose Windows. Then, when all personal projections and the virus of superstition have been caught in the same ‘cup’; when a threshold has then been reached, one can say that this is the true goal of ‘alchemy’: the moment when metamorphosis is possible. The Rood Screen guarded that possibility. In the figure of the female shown further down, you can see the identical golden rectangle. T marks the navel and the crown of the head corresponds to the round point of the choir. Between Saint Anne and Christ is the means of his incarnation: the Pelvic Vesica is inscribed within the golden rectangle Everybody was allowed within the OPKL square. Only the highest priest was allowed past point T, into the sacred part of the temple.
When we stand just south of position “T” we are so uplifted; so filled with awe and Grace that we naturally wonder at times just exactly how the builders went about this construction. We want to know if there was a seed, a germ that like an acorn could rise to exactly the right height, producing exactly the right proportion of ‘foliage’ with which the the Sun is transmuted. Rather than feeling overwhelmed or inflated with the audacity of the achievement, instead we are fulfilled; we are filled with peace and with Grace that sets a whole new standard within us. Size by itself is nothing. The scale must also be a proportion. The 61.8 meters must be in harmony with the wholeness and that wholeness must embrace the Earth, the Moon, the Sun and so forth. The whole ogive springs from a delicate but precise elevation. The feeling is that it could not be any higher or any lower without feeling either too heavy or too unhinged. Then we find that it is exactly 25.57 meters from the paving stones. But as soon as you apply the principle of the square root of 3, like a key, the door is unlocked. With a hypotenuse of 2 we can quickly know the base of a triangle from which the elevations are built up. I calculated 14.765 m which differed from Charpentier only slightly, but significantly. What we agree on, however, is that the measure seems to derive from Gizeh, Egypt. I will return to this ahead, when discussing the Sphinx in better detail. Charpentier did not note the link between the Sphinx height and a shadow cast by that height at Noon on the Equinox and the ‘square’ table at Chartres. He did note the same number for the base of the Great Pyramid, however.
So it is with considerable interest that we contemplate a Latin inscription on the pillar under the sculpture of the Ark across from Moses at the ‘North-West Gate’, that Charpentier reminds us was also called the ‘Gate of the Initiates’. Initiation must occur on multiple levels and by degree until the highest state has been achieved. The light must accumulate, which is why patience is treated as a virtue among all spiritual traditions. There is much to tempt impatience out of its den. In any case, the translation from the Latin seems to indicate that it was intended for temple builders and was furnished by Canseliet who once noted that it was not intended to be eloquent:
- You are to work through the Ark. (Archa Cederis)
- Here things take their course. (Hic Amititur)
- You are to work through the Ark. (Archa Cederis)
Whether the Ark was a 1 x 2 construction or a 2.5 x 1.5 construction, this inscription rang true for me immediately. Nothing has inspired me to press forward with a geometry of human proportions quite like this simple instruction – or reminder – to the builders of possibly my favorite sanctuary on earth. In the image below, which I photographed at the end of May, 1988, you can see part of this inscription, still well-preserved, carved on the smooth rim of the pillars under the sculptures of the Ark. It is easy to miss this sculpture as it is small and a ladder is essential to get up to its level. I would not have noticed it had Charpentier not drawn attention to it in his book. Note the open lid of the coffer on the left revealing two Tables of testimony (or Law) as stated in the Old Testament. What is not mentioned in the Old Testament, however, is a sphere of some kind to the right of the tables. Charpentier also made no mention of that sphere. I noticed it only when examining the photo that I had blown up and is now on the wall. Lomas and Knight mention that 3 things were put in the Ark, the two tables but also Yahweh himself.
This sphere is an interpretive addition made by the Grand Master or Master Craftsman at Chartres. The only reason for adding it would have been if the builders believed it was somehow the essence of the entire work; too important to leave out. Of course we know that the Ark was supposed to house the divine presence, the Lord of Hosts, God. For Plato there was no better way to represent God than a sphere. We see spheres in the sacred barques of the Egyptians and references such as “Spirit in the Dndrw Barque” in the Pyramid Texts. But in the Pyramid Texts, the King himself has become that spirit. And that spirit is also the Eye of Horus.
They may also have felt it was important to portray the antiquity of the principle of the Ark that likely predated the time of the Old Testament. The sacred barques of the Egyptians, such as the Hennu Boat, seem to be as old as the Pyramid Texts that, in turn, are probably much older than the first dynasties. The hand of the clock points to a legacy that had returned to the Nile after some sort of hiatus. It is highly likely to me that the Hebrew were a part of that legacy that now dissolves into pre-history, frustrating the instincts of many of us who know knowledge did not start formally with the Greeks, but predated them by untold millenia. The Ark itself was taken out of Egypt by Moses, so ostensibly it represented critical knowledge inherited from the Egyptian civilization toward the end of the 18th Dynasty.
To learn that the Ark may have been 2×4 feet is significant in light of this entire discussion. One could say: “Here things take their course. You are to work through the principle: 1:2. Everything emerges from it and everything returns to it.” And ‘Ark’ (arc, archa) is also a circle. Geometers imitate the circles of Nature with their compasses. Circles and squares bring measure into the world. The circle is the first enclosure where time and space function together with periodicity and rhythm. Things become differentiated with the square. With the 2:1, everything is related to everything else. It relates, purifies, transcends and transforms. In Exodus the altar was a 5 x 5 cubit square. The offering table was 1 x 2 cubits. It received only sacred objects.
In the sculpture here on the south side of the north-west porch, the side of the ark is proportioned 1 x 3. The whole Temple of Solomon was 1 x 3 or 20 x 60 cubits. It ws divided as 1/3rd and 2/3rds. The Holy of Holies was 1/3rd and the rest 2/3rds. If the cube was the oracle, it is important to note that the head has a close affinity with the cube. Egyptians, Tibetans, Hebrew, Aborigines, all used specific head gear to enhance the flow of energy in the head for the occasion of the annual oracle. The human head is part and parcel of divination, not at all of the coffee table variety. Rather the purpose of the divination was to keep above and below in the right balance. This is a profound dimension of the Grail itself, which concerns spirit as much as flesh and time as much as physical space or mass. It unites them in the place: the place where a meaningful God dwells.
The Templars were also interested in the “Grail”, that mysterious vessel or ‘stone’ that is both cornucopia and altar simultaneously, or perhaps alternately. It is also well-known that the Templars apparently worshiped a recondite head called the “Baphomet”, in some way connected to the means by which wisdom enters the world from all around and is gathered up into a living testament. The head was supposed to have brought fertility to the land: the source of riches, growth, health and strength. It even made the trees blossom. These gifts were also attributed to the Grail as if the Baphomet and Grail were one and the same. In Egypt one thinks of the head of Atum-Ra. In Greece one thinks of Apollo or Zeus. Then there was Orpheus and the Celtic “Bran”. There was Osiris, Geb, Horus, Rahu of India…In Egypt, Nut was the immense black sky that contained all the stars. Geb was the Earth. Atum became Geb on his way to becoming man. The most conspicuous link between God and Man has always been the head. The skull is certainly reminiscent of a gral, a bowl, a vessel undergoing a mysterious transmutation drawing power from the roots of the spine.
The building of a cathedral is a testament to a total knowledge; not its final goal, but a means by which the spirit of the pilgrim can be perfected, quickened; purified, lifted up toward sublimity. It offers an unparalleled relief; to feel again the well-spring of the divine that can be forgotten in the humdrum.
The cathedral was designed to testify to specific laws by which the ‘Grail’ reveals itself to the world. The image of the head will not go away easily. Remember in Greece that old saying: Athena was born fully grown from the head of Zeus. Athena was the Egyptian Neith who was linked to the Eye of Horus. Plato dedicated the Timaeus to Neith. Neith was knowledge, wisdom, Sia. In the Pyramid Texts the King becomes Sia. He departs this world as Sia and sits at the ‘right hand of Re.’ “I become Sia who bears the god’s book, who is at the right hand of Re; O you who are protected by my hand, it is I who say what is in the heart of the Great One [feminine Goddess], in the Festival of Red Linen. I even I, am Sia, who is at the right hand of Re…” (PT 268).
Here is the image of Christ at the South-East Gate of Chartres (some 62 meters across from Saint Anne), hand upraised in protection, holding the god’s book. He is very, very human. Like Seti I of the XIXth Dynasty in Egypt, one thing he is protecting is the “truth”. In Egypt this was accomplished during earthly life and was extended into the Netherworld after death. In the Gospel of John, Christ declares to Pilate that his Kingdom is not of this world. The feeling that I get was that the Templars were seeing Christ much more the way the Egyptians saw the Horus-King. The Festival of Red Linen refers to a pure, new state of ‘weaving’. Throughout the Pyramid Texts it is stated over and over again that the Eye of Horus is woven into being after having been dismembered by Seth, or the Greek Typhon. Red is royal and also refers to the Red Crown of the North. At times the Eye of Horus and Red and White Crowns were treated as identical!!! Just as the Procession of the Grail in the square hall of Mundsalvaesche was a festive occasion, so too was the reconstitution of the Eye of Horus through the ‘magic’ of the weaving. But this weaving occurs on the plane of spirit; the realm known to the ka. To experience it, a candidate required special training. Red was symbolic of that training, a harbinger of what was to come; the ‘sacrifice’ that introduces the spirit.
The Phoenix and the Stone
To add to the mystery, in Parzival, the Grail was closely connected to the Phoenix. The Phoenix was connected to a ‘stone’ treated as altogether magical and difficult to name: “lapis exilis” being but one example. The stone possessed an essence most pure. It is by virtue of this stone that the Phoenix burns itself to ashes; which done, it rises again as lovely as before. And in this fashion, it molts its feathers. This pure “Stone” was also called “The Grail” (Parzival, p. 239, Penguin Edition). The ‘Phoenix’, moreover, is common to every religion, every mythology and ultimately, probably, to every true science that will ever be throughout history – from chaotic transitions to bifurcation points that reach thresholds of stability where suddenly everything breaks down; what was familiar is shed; what has gone stale, is emptied out. The spirit gives itself up and withdraws. And just when all is lost, when every attachment has been dissolved back into the vacuum; when faith itself feels forsaken; when isolation feels like extermination: then comes the restoration. The tides are not arbitrary. Diastole and systole are not exceptions. They are the law of reconciliation, the rhythm between ‘same’ and ‘different’. The Phoenix is also common to the rite of the Eucharist and the Table of the Last Supper, where 12 surround a 13th. 13 is not only the essence, but it is also the resurrection when the pantheon of 12 collapses; when the wound pierces the heart. Like the Red Linen the blood carries a red tincture. To be seen, the vessel must be pierced; the old vase broke.
In Egypt the ‘stone’ was called the Benben Stone and the Phoenix was called the Bennu Bird. The Bennu Bird and Benben Stone were related to the essence of the Great Pyramid and were concerned as much with time as space. When time and space unite you have living processes and the adventure that trundles through life, death and the magic of rebirth. The 2:1 rectangular King’s Chamber deep in the body of the Great Pyramid may have been built around 2,700 B.C., long, long before Christianity. The Choir at Chartres has an astonishing precedent!
Altars were places of burnt offerings, the greatest being the self-sacrifice of the Phoenix itself. It ‘burnt itself to ash upon the Stone’. The Grail, then, is the essence of the Phoenix, the Bennu Bird. Pyramid means ‘fire-in-the-middle-of-the-earth’. Benben comes from bnn bnn, which is the verb to rise, or rise again. When attached to other words it was used symbolically. For example bnn-loaf of the Pyramid Texts refers to the principle in bread that makes it rise. The Egyptians used symbols differently than we do. The bnn-loaf actually was another term for the Eye of Horus! When the bnn-loaf was invoked they were referring to the inner power of resurrection: the capacity for the fallen Osiris to rise again as Horus, the way warm bread rises and expands. But I did not know the relationship between the Phoenix and the Stone until about 1992. Clarifying the true nature of the ‘crucifixion’ is another matter that slips beyond the scope of this entry, as fundamental and fascinating as it is. Admittedly, however, if we misrepresent the meaning of the crucifixion we distort the meaning of the gift called “resurrection”. Under repressive dogmas it is difficult to hear one’s own instincts and the crucifixion becomes severely maligned. It can be used as propaganda as a substitute for the hard won struggle to rescue truth from the thorns that protect every cherished thing. There were no crucifixes at Chartres!!! Chartres is a place of unvarnished generosity. Because it expresses the root of being, it lifts everybody above the mundane sphere. It is not designed to yank the vulnerable pilgrim away from what they are – no matter who they are. Rather it is designed to restore what they are. What Authoritarianism displaces, Chartres recovers with incomparable grace. Chartres gives you back your life…and then some….I would love to name it the “Place of the Restoration”, but it would scarcely benefit from any more names.
The Road to the King’s Chamber
The King’s Chamber was based on a 10 x 20 cubit rectangular table, pictured below (ABCD). In Fig X we see its width (10 cubits), length (20 cubits), height (11.18 cubits or 1/2 its diagonal) and three diagonals (15, 22.36 and 25 cubits). It offers a timeless example of the ‘3 Tables that bear the Grail’. Its perimeter is 31.416 meters or pi x 10. A circle with the same perimeter is 10 meters in diameter. A square with the same perimeter is simply 3/4 the length or 7.854 meters, which is also the diagonal of the end walls (AH = 1.5 x Unity = 15 cubits = 7.854 m). In the standing adult, 3/4th the height falls right in the middle of the Thoracic Vesica Piscis (TU in the next Fig below). This is the spot where you place the hand to restart a heart that has experienced cardiac arrest. Moreover, it appears that the coffer is placed at the 3/4th mark of the KC which is over the east-west center of the whole Pyramid, while remaining south of center. We can note that 1.309 x 4 = 5.236; 1.309 x 8 = 10.472; 1.309 x 6 = 7.854; 1.309 x 24 = 31.416. We will use 1.309 and 24 just ahead as a simple way to create the 3 Grail Tables.
It is well worth emphasizing that the KC height is 1.118 x Unity (1.118 x 10 = 11.18 cubits = 1.118 x 5.236 = 5.854 meters). The relationship between the ‘great diagonal’ 13.09 m and length 10.472 m is the Major 3rd in the diatonic scale of music, 1.25 or 5/4 or 25/20, a figure we saw in the previous post when situating the mouth in the standing adult: namely the diagonal of a double square(2.236) divided by the square of 1.118034 (1.25) = 1.7888 = 2.236/1.25 = 2/1.118. This 1.7888 is measured from the soles of the feet when the height is “2”. In the image below we see three convergences on the mouth. We see the horizontal line of the square with equal perimeter to the circle with diameter equal to her height (2). We see the Thoracic Vesica Piscis converge on the same spot. And we also see that Height/1.118 = 1.7888 which is also right on the opening of the mouth. We will look at more convergences ahead.
Since mention has just been made again of 3/4th the height or 1.5 x unity, the diagonal of the end wall of the KC, I will just mention now that it is important to relate the Aortic Arch, 1.618, to the center of the heart/lung complex, 1.5:
1.618/1.5 = 1.07866 = 1.3333/1.236
This ratio 1.07866 ends up determining the relative size of the male Thoracic Vesica which is proportionally larger than the female. This 1.07866 will also become the radius of a circle placed over the center of the heart. When raised up to the Ideal Angle of botany, the male arms measure that radius. In the image here I have shown that the average female armspan is a little shy of the ‘ideal’. I will return to this interesting constellation of harmonies ahead.
The ratio 5/4 will prove important again just ahead when we use it in one method for squaring the circle, in conjunction with 1.309, the ratio that frames the wood stela of Ra-Horachty seen in the previous post. 1.309 is great because not only is it 1/2 of 2.618 (the square of the golden number), but it is the relationship between two of the most important divisions within the 2:1 paradigm, the golden number and golden section:
1.618/1.236 = 1.309 = 10/7.64 = 10.472/8
Just as importantly, we find that the ratio for the royal cubit emerges as a resolution between 1.309 and the square of 1.118 or 1.25 (5/4):
1.309/1.25 = 1.0472 = 3.1416/3
This ratio captures the relationship between a circle and the hexagon that it inscribes as well as the 2:1 rectangle whose length is the same as the diameter of the circle. A circle with diameter 10 has a circumference that is 31.416. A 2:1 with length 10 has a circumference that is 30. 31.416/30 = 1.0472. The circle da Vinci portrays in his famous illustration is the smaller perimeter that equals the hexagon or 2:1 rectangle. The Square, EFGH, is in fact 1.0472 x greater in size than Circle A or Hexagon A or the prime 2:1 rectangle with length = height of figure. When I set about to examine the proportions of human anatomy I decided to include some pertinent statistical averages. In men the common arm spans are larger than the square drawn by da Vinci. One is 1.03 and the other is 1.045 which is close to 1.0472, what Schwaller calls the “Ideal Armspan” because of the importance of the Royal Cubit Principle. But with time I realized I had to center the circle over the heart and lower the angle of the arms slightly.
An Interesting Number Series
1.309 appears naturally in Line 1, Col XIV, in a very interesting Fibonacci-like series that I will call Series E. We see all the numbers mentioned above in the same series. I will introduce it here so we can refer to it throughout.
Note how this series starts. It is 1, 5, 6… Five characterizes it and pentagonal geometry opens the golden proportion family. 1 is common to any Fibonacci series. When 5 and 1 are added together you get 6. 6/5 = 1.2 and 1.2 x 2.618 = 3.1416, an excellent version of pi that appears on Line 24, under the 1309 column. In any case 118, 309, 1309, all occur on Line 1 of this series. 382, 618, 1618, 2618, etc. all appear on Line 2. 5236 occurs on Line 4 and 10472 occurs on Line 8. 31416 occurs on Line 24.
The ratio 1.309 plays a significant role in the layout of the brain – among other places – as we will see. It centers itself over the critical (partial) decussation site where both olfactory and optic information cross over to opposite hemispheres of the brain. This is the same part of the head (or brain) where the ancients pictured the “Eye” taking root. It appears to divide the long axis of the brain by the golden section, marked here as 1:1.618 and indicated by EF of the Prime 2:1 rectangle, ABCD. If the smaller circle centered over the decussation site is taken as 2, the larger, complete circle will be 2.618 and 2.618/2 = 1.309, which is here AB, CD, etc. The decussation is finished after leaving the .309 zone. Note that the visual cortex reassociates optic information at the back of the brain between the two circles. Both the eyes and visual cortex areas are exactly bound by the Prime 2:1, ABCD (in red), so the diagonals of the 2:1 rectangle are generating a complementary relationship between right and left ; and front and back, analogous to the operation of the four legs of a horse. A large part of ‘intelligence’ is information processing that goes on below the level of conscious awareness. Here we see complementary information processing that must balance the energies that enter the eyes in a dynamic way. The human brain is about 80% optical. An eagle is about 95% optical. A snake is about 95% olfactory. Note the eyes are contained within a 29.1 degree wedge. Every synodical month the Earth and Moon travel through 29.1 degrees around the Sun. This is approximately 76,000,000,000 meters or 16.18 m raised to the 9th power. So this image here also pictures the orbit of Earth + Moon in one synodic month. The synodic month is represented by an infradian clock that may be situated a little above the optic tract in the suprachiasmatic nucleus of the hypothalamus. In women this is about 29 days and leads to a monthly ovulation in a cycle that alternates between right and left ovaries month by month. A woman can feel this alternation.
One imagines decussation as being a form of ‘weaving’, a warp and weft that binds, counterbalances and focuses energy that will become ‘information’ and rhythm; the Egyptian “Sia” that transmutes into knowledge and finally wisdom. Wisdom is so full and so all-embracing that the transmutation was symbolically expressed by a perfume released as if by a flower, such as the lotus bloom. The Egyptians spoke of the ‘perfume (sty) of the Eye of Horus’ that purifies the face (Hr). But really this is a symbol only. The ‘perfume’ is an attempt to describe spirit-state, that is so exquisite and so unique it does not lend itself to normal language. Light witnessed by the ka does not behave like normal reflected light. It behaves like a light that has originated from within and does not reflect off forms. Rather it illuminates the forms from within. It is like an exquisite healing radiation.
So the head is one place where this transmutation occurs and decussation is one way that energy is accumulated and amplified becoming the ‘alchemy of the mind/brain’, caught within the vessel of the skull – a gral or grail in its own right. Not surprisingly then, the same ratios show up in the human face through which the data that will become information is admitted into the vessel of the head: the ‘control center of the Central Nervous System’. Here we see three faces – all different, and yet the same proportional ratios dominate.
In the first one we see that the head cube is divided in half by 1.309 through the pupil of the eye. The lower half of the head divides by the golden section at the mouth into .5 and .809. The whole head cube is divided by the golden section into 1 and 1.618 at the tip of the nose that also passes through the Temporal Mandibular Joint (TMJ) and entrance to the ear. The Prime Square ABCD starts at the chin and brow. To the tip of the nose is .309. So from the tip of the nose to the back of the head is 1.309 + 1.309 = 2.618. The entire slope of the nose is contained within the .309 margin. Just as we saw optic decussation in this zone in the brain, so yoga teaches a way to alternate the breath through each nostril. This stimulates the decussation site in the brain, but when both sides become equal in strength, it can have the effect of provoking the kundalini in the sacrum. Olfactory is a powerful sense and operates on a potent electromagnetic double current when strengthened.
The next image is of the woman shown earlier. This introduces the overall geometry. Once again the lower half of the head has been divided by the golden section at the mouth. But this head divides in half at the upper eyelashes. Then everything falls in place from there. First of all notice that if the whole head height is 2, then from the crown down to the mouth is 1.618 and the remainder is .382. This is a remarkable dovetail with the fact that when we took the whole height of the adult and divided it by 1.118 we got 1.7888 out of ‘2’, which falls right on the mouth, dividing the body the other way: from bottom up, leaving .2111456 from the mouth to the crown. Now we are in the head with a 2:1 that is 13/100 of the whole height. This we take for ‘2’ and when we divide it at the mouth remarkably from the crown to the mouth will be 1.618 and the remainder will be .382.
I will not speak for anyone else, but I regard this face as a revelation. I am amazed by its harmonies and this set of numbers is but one variation only; one selection within the same face. It can be broken down into several types of harmonics. Endless ramifications. Her face is like a window into a world of enormous spiritual and psychological complexity involving themes of mythic proportions.
In this incredibly articulate face, from the mouth to the upper eyelashes is .618. Note the degree to which the diagonals of various double squares shape this face. The nose is circumscribed by the diagonals of the Prime 2:1, ABCD. Its maximum width (QR) also is 1/3rd of Unity (AB), in imitation of the width of the Thoracic Vesica Piscis in the adult that frames the chest, ribs, lungs and heart. The horizontal ‘prime’ 2:1, IJGH, shapes the sides and slope of the upper mouth/lips, precisely. They also pin the corners of the mouth (x and y). The diagonals of the smaller 2:1, KLCD, circumscribe and determine the slope of the lower mouth/lips – also precisely. The corners of the mouth are limited horizontally by the 2:1, abcd. Its golden section opens the mouth – yet another contributor to all the geometric factors that open the mouth. The ears join this face at exactly the boundaries of the golden rectangle, WXYZ. The eyebrow height is set by 1.118 x unity. The Third Eye where the Eye of Horus takes root, is usually described as being between the brows and behind the eyes. So 1.118 is involved within the Square of the face, in the placement of the Third Eye. The latitude of the tops of the upper eyelid and tops of the ears is 1.0472.
In the earlier image of the whole standing adult we also divided the height as 2 into 1.618 and .382. This division occurred at the aortic arch of the heart where chemoreceptors convey the state of the blood to the medulla oblongata in the lower brainstem and also where the recurrent laryngeal nerve wraps around the arch and also where the arterial, oxygenated blood leaves the heart. The 1.618 latitude also marks the horizontal armspan as if the arms were an expression, like branches of a tree, of the heart itself. It seems this 1.618 point also marks the trachea where it divides into the bronchial tubes. The chen sign of the Egyptians is likely taken at this point through a cross-section just above the bronchi. So the mouth is to the whole head what the Aortic Arch is to the whole body, but inverted, upside-down. The mouth must be where above and below meet. And when they meet there is an interface that breathes, eats, drinks, chews, and articulates the sounds and ideas emitted from the vocal cords that are innervated from the brainstem. The relationship between the mouth-jaw measure and the Aortic Arch-to-crown measure is as 1:7.69. The 7.69 is measured from the crown to the Aortic Arch and the 1 is measured from the base of the jaw to the crease of the mouth.
The relationship between crown to mouth and feet to Aortic arch is meaningful enough to warrant a deeper glance right here at the gap between mouth and Aortic Arch. 1.7888 – 1.618 = .17082. This happens to be the reciprocal of 5.854 which is also the height of the KC in meters and is derived from the formula: 1.118 x .5236 = .5854. This comes from the royal cubit.
In the standing adult, the height (2) divided by 1.118 = 1.7888, the position of the mouth from the soles of the feet. In this zone you have clavicles, neck and probably C2 to T2 in the vertebral column. You have the arms. The blood departs from the main aorta and feeds arms and head. The rest heads down.
Next we see this face a little closer up with the numbers altered, to reflect different values, but the same proportions of course.
Note how the 2:1 rectangle, IJKL, when golden-sectioned in both directions (ut and MN), marks the nostrils and mouth opening: both ways for air to get in and out of the body. The unity circles or arcs of the golden section (Q1&Q) literally shape the “V” of the upper mouth/lip. The smaller 2:1, abzy, when golden-sectioned, marks the bottom edge of the lower lip. When jaw-to-mouth is unity, the 2:1 IJKL is 1.309 x 2.618. So, in the case of the face, what splits open the mouth is the golden section of the smaller, ‘half’ 2:1 IJKL and the division of the whole height of the head AD, taken as ‘2’, into 1.618 and .382. In this image here the whole height is 5.236 and so the mouth divides the whole into 1 + 4.236. All these numbers appear in Series E.
It is quite interesting to note that the height from base of head to mouth is 1 and the width of the mouth here is 1.309 or rectangle: MNKL. So MNKL is a 1.309 x 1 rectangle, the same shape as the Ra-Horachty image, just set on its side. We can recall that the harp in that image featured an Ennead of strings (9 strings, but 10 tuning keys, where the 10th could only be Horus liberated from the 9). One thinks of the old biblical pronouncement at the beginning of the Gospel of John: “In the beginning is the Word…” In the Pyramid Texts, on one occasion great importance is attached between ‘word’ and liberation. The lips were portrayed as the meeting of the Two Enneads, undoubtedly one above and one below: “My lips are the Two Enneads; I am the Great Word; I am one who is loosed; I am one who ought to be loosed, and I am loosed from all things evil.” (PT 1100). When this woman was a youngster she used to write on the walls of her bedroom. She was precociously, deeply concerned with “Truth”. She often ‘exclaimed’ in her writing with capital letters. This also characterized her manner of speaking for many years as an adolescent. It was as if the Great Word were a seed that was fulfilling its growth through her. She felt profound responsibility for this unfoldment of the Word. She experienced it as a calling with great urgency. She did not want to deviate from what she called ‘the Truth’. I should also mention here that in the ‘Big Dream’ I have been referring to throughout this blog, specific words at one point brought about a critical transformation or change of state. They were spoken in a unique way that could be described as the indigenous origin of ‘ritual’. But it was a ritual with transformative power like a conversion. Exactly 9 words were spoken by 2 individuals simultaneously; one female, one male. It was as if an all-embracing field of force moved like a wave and brought both voices and both throats into a form of sublime coherence. It had a truly beautiful numinosity to it even though there was little time to contemplate that beauty. The changes sped along at their own inimitable pace. But I thought it important to note that the words spoken were 9, in 3, rhythmic, groups of 3. One immediately thinks of the 9 bows, the 9 monarchs, the 9 potencies, the 9 movers of the Egyptian Ennead. 9 is very compatible with 3, 6 and 12. It is also a square number. So it bridges diverse worlds together in an effective, organizing and powerful way. It’s like a pump. The Pituitary is the Master Endocrine Gland and produces 9 hormones. Hormones are stimulators, activators, potencies, regulators, The Pituitary stalk drops down from the golden section point of the brain, just below the optic chiasm. It appears to be divided into two lobes by the golden section: anterior which is not part of the CNS and posterior, which is part of the CNS. The posterior lobe produces 2 hormones; the anterior produces 7.
24-method of Squaring-the-Circle
This ratio, 1.309, has become so important, I will introduce what I call the ’24-method’ for ‘squaring-the-circle’ here so it can be seen. But I will go into detail later.
The way to create this image is to simply golden-section the Prime 2:1, ABCD (5 x 10), into 3.82 (BF) and 6.18 FC). You then center a circle on the navel, point I. You take 3.82 as its radius. You inscribe a circle with diameter 7.64. Its’ perimeter will be:
7.64 x 3.1415927 = 24
The relationship between 7.64 and 10 is 1.309, so the reciprocal of 1.309 is .764. It is easy to use whole numbers to create a square and 2:1 rectangle that are 24 on the perimeter. The square is 6 x 6 and the 2:1 is 4 x 8. 10/8 = 1.25, the Major 3rd in music; and 10/6 is 1.66666, very close to A-natural (440). This paradigm is packed with geometrical information that gives it remarkable self-focusing properties. For the moment I should just mention that I am rounding up 3.82 and 7.64 as in Series E. In fact they are both irrationals and appear in this paradigm as 10/2.618034 = 3.81966 and 10/1.309016 = 7.63932.
7.63932 x 3.1416 = 23.999 ~ 24
The way to ‘square-the-circle’ with the prime 5 x 10 2:1 is through the golden proportion. An ‘irrational’ diameter x the irrational pi produces a whole number; in this case 24. This is an inversion. Normally we think of pi as irrational and operating at the limitless circumference of a circle. We think of the diameter as being finite. But here the diameter becomes ‘irrational’ and the circumference becomes ’24’. 24 is a nice number. We have used it to divide the ‘circle’ of the day for a long time. The hour has relevance in human rhythms.
In any case, it is the golden division within the 5 x 10 rectangle that sets the scale of the 3 Tables. But it is as if the 5 x 10 is the underlying support of the ‘3 Tables that bear the grail’. This will have consequences when we look at the nanometric scale of the tubulin protein dimers (4 x 4 x 8 nanometers in volume) which may be information-processing automata in the cell, but also the scarab beetle that undergoes a metamorphosis from worm to winged insect of extraordinary beauty. This does not just happen out of thin air. There must be geometrical forms that facilitate this remarkable transformation of form. Something is ordering it in its cocoon.
1.309 is acting as a key of transformation and we can recall that it is the relationship between 1.618 and 1.236: respectively within a 2:1 rectangle, its golden number and its golden section. 1.236 is also the width of its cousin golden rectangle within which the female Pelvic Vesica is constructed. So 1.236 in the female is the relationship between heart and lungs above and womb below. When it is related to the golden number we get 1.309, at the headwater of Column XIV of Series E.
This image is remarkable. The 5 x 10 rectangle that generated the circle with circumference 24, remains active in shaping the scarab. It measures its width if the middle claws were tucked in slightly to touch the body. But the whole length is framed precisely by the 4 x 8 rectangle which extends a little above the 5 x 10 by the ratio 1.0472. The “1” or 7.64 circle exactly limits the antennae. The 4 x 8 (EFGH) determines the main width of the body minus the middle claws. The foreclaws are limited by the 4 x 8 for extent, but are shaped by the diagonal of the prime 5 x 10 for angle of attachment to the body. They are in a precise complementary relationship with the opposite hind claw also determined by the diagonal of the Prime 5 x 10. The Square, IJKL, cuts through the eyes and marks details of the rear claws.
But the key to this entire image is the relationship between the Circle with a circumference of 24 and the Prime 5 x 10 that created it. 10/7.64 = 1.309. This then allows the other 2 tables with perimeters of 24 to be generated. They are all centered upon the navel of the 5 x 10, or 6.18 from the base DC. There is the distinct feeling that the golden section is at work in the process of metamorphosis that transforms the worm into a winged insect. The squaring-of-the-circle is the geometrical means by which this is facilitated. Through this geometry, what was in the worm is conserved. Through the 3 tables the geometry can blossom, sharing the characteristics of all three tables. Looked at this way, there is a striking parallel between the Egyptian symbolism of the scarab “Khepera” and the Grail. Automatically, then, we have to conclude that there is an even older parallel between the Eye of Horus and the Grail. The Eye of Horus at one point in the Pyramid Texts was said to ‘go up from the head of Seth’. If it takes 3 tables to bear the ‘grail’, one must empathize with the Egyptian tendency to give one phenomenon many ‘names’. Each name refers to different aspects of its nature. The Egyptians were confident of unity and appeared not to be reductionists. I think we have projected our own western reductionism on a civilization that we did not understand. Their spiritual preoccupation was with the final metamorphosis into pure spirit.
King’s Chamber and Scarab “Khepera”
In the next image, which I have reconstructed based upon several sources, we see the widths of the King and Queen’s Chambers, which are both 10 cubits or 5.236 meters . We cannot see their respective lengths from this angle, but the King’s Chamber is 10.472 meters long or twice its width as shown above. The Queen’s Chamber is perhaps 5.74 meters long. It is situated about 22 meters above the base, while the KC seems to be 44 meters above the base: another 2:1 ratio. All these numbers appear in Series E. One can see that the chamber with its stone coffer is capable of being hermetically sealed. It is a grand climb to get up to it. The dotted lines indicate shafts that point to Thuban of Alpha Draconis to the north and to one of the stars of Orion’s belt to the south. The whole set up looks like a self-enclosure with a perimeter of 31.416 meters, designed to liberate, to loose the spirit from all attachments. How significant, then, to learn that the geometric shape of this chamber of transformation should be proportioned 1 x 2 or, 10 x 20 royal cubits, or 5.236 x 10.472 meters.
The Tomb of Seti I and the 2:1 Rectangle
In the historic struggle to interpret the stellar symbols invoked on the famous ceiling of Seti I’s tomb in the Valley of the Kings, its geometry is usually overlooked. The ceiling appears to depict the entrance to the Duat, the Gate to the Netherworld, the Ladder of the God, or just the King’s Gate. But it is also obvious that the central drama within which we can discern a rotation, as if we were watching the northern heavens known as the Imperishables, rotate around the pole of the precession of the equinoxes, has been framed within a 2:1 rectangle! The rectangle ABCD is an exact 2:1. Its’ most important features are marked by the golden section. EF marks the horizontal division so that BF is 1 and FA is 1.618. The figure of the “Osiris-King” with up-raised arm is literally marking the golden section itself and the loop or break in the ‘harpoon/lasso’ being used by Horus. In Egypt the term ‘harpoon’ usually associated with Sokar and the Cavern of Sokar, was another name for ’30’, indicating the involvement of time in the process of metamorphosis. The “Bull of Heaven”, as it is called in the Pyramid Texts, probably referring to the resurrection of Osiris/Orion, is clearly dependent upon this golden proportion! It does seem in this instance that the Bull is an aspect of the Big Dipper known back then as Meskheti.
Vertically, the ‘thigh bone’, or mnj.t, being stabilized or guarded by the pregnant Isis-Hippo with pendulous breasts, as Horus the redeemer/warrior/shooter climbs it, is 1 while everything above Horus to the tips of the Bull’s horns is 1.618. When the thigh bone or Mooring Post, or ‘ship’s peg’, or ‘nose-bone’ of the Eye of Horus is taken as “1” the full length of this ‘Gate to the Netherworld’ or “King’s Gate”, AB, is 5.236, the same number that measures the GP profile when the base is 2 and the apothems are 1.618.
The thigh-bone or Mooring Post, or ship’s peg – the mnj.t went by different names – shown in the lower right corner of the Seti I ceiling, refers to Isis or Nephthys in the Pyramid Texts. They were usually associated with Sirius in Canis Major near the cusp of the southern horizon at that time. So what Horus seems to be climbing is an axis, a cosmic pillar that represents the resurrection of Osiris associated with Orion that rises about an hour before Sirius – but in the south (Seth) – up into the Northern Sky (Horus) where the Imperishable stars of the Northern Hemisphere make a circle around the north celestial pole.
In images of the Eye of Horus, which consisted of segments, the part that looks like this very same ‘mnj.t’ was given a value of 1. It was treated as the seed or root of the whole Eye. The Oudja Eye was subdivided into 64 parts, echoing the 64 hexagrams of the I Ching, the ‘book of changes’ or ‘transformations’, like the Egyptian ‘khepera’ symbolized by the scarab beetle. When all the divisions are added back up they only sum to 63, not 64. Curiously in the I Ching, Hexagram #63 is titled “After Completion”, while Hexagram #64 is titled “Before Completion”. There is an inversion on the difference between 64 and 63 which is 1. The I Ching does not actually end, suggesting that the number 64 is circular, one reason it has been called a totality number. I will have to continue the discussion of 64 at a later point, but it is interesting that the Earth’s rotation rate at the Equator is 1/64th its mean speed around the Sun: 29.786/.4651 = 64. 64 also has an exquisite internal structure when regarded in terms of its powers. A later post! It involves the number 1236.
The “1” missing, referred to as “qd”, but portrayed as the ‘mnj.t’ in the Seti I ceiling, becomes the seed of the new and the means of resurrection through the impregnation of Isis (“Horus who is in Sothis”, PT 1636) depicted here as a pregnant Hippo. Horus is the seed, but it is portrayed as being within Isis/Sothis/Sirius who was in association with the fallen or dead Osiris (Orion). The drama has and always will be a spiritual drama that becomes the ‘second birth’ during life, but a final resurrection after mummification following the body’s demise. This essence or seed that has impregnated the Hippo – who really could also be the mother of Isis, Nut, is also referred to in the same Utterance as the ‘Spirit-in-the-Dndrw-bark’. (PT 1637). Incidentally, I believe the Templars were aware of the parallel between Mary and Isis and Saint Anne and Nut. There is plenty to say about Nut from the Pyramid Texts, but not right here. The “Black Virgin” is closer to Nut, the immense Great One, than Isis, who was more localized as Sirius A, the brightest star also known as the Beautiful Star. It is true. It even has a quality that surpasses Venus and Saturn to the naked eye.
This play upon unity is the root of the future Eye or Eye of Horus and this has been reflected within a 2:1 window, or gate, or door in the Seti I ceiling! I mention this here only to emphasize that in two of the greatest architectural wonders of all time: the Great Pyramid with its King’s Chamber and Chartres, the 2:1 is depicted as the key, the gateway to the heavenly realm. It is depicted in the same way in the tomb of Seti I. At Dendera it is the shape of the Sanctuary of the Barque (5.5 x 11 meters), the predecessor to the Ark of the Covenant. So the 2:1 boasts an ancient legacy that seems to dissolve into an unknowable prehistory. Little wonder the group that celebrated on that suburban Paris lawn, back in 1964, called themselves “The Friends of Atlantis”. The Traditional Sciences refer to the eternal, through which ‘things take their course’: the principles that create us and support us and have nothing to do with personal will. This is the relief and the beauty of it. Simplicity is the root of genuine power. It is also the root of all adaptation and what we call ‘invention’. The Grail could only be carried by the world’s most beautiful, most upright and most chaste female. She is a spiritual fountain that overflows its own boundaries. The Grail is in an inverse relationship with pride or what today we call the inflation of the ego: Goliath, Seth. Pride always seems to go before a fall, even as the Ark keeps trundling along the old, old road: now desolate, now bleached of all color, now resplendent with light and bursting with a jungle of sound and form; now caught in a cataclysm of human blood; only to be once again trundled down another valley of green.
Above I have indicated the mnj.t and its ‘number’, 1/64. It is my understanding that “t” indicates the feminine determinative. So the Isis- Hippopotamus and mnj.t or Mooring Post, or ‘thigh of the Horus Eye’, must be taken together as a complex, interpretive symbol. The “Enduring Bull of the Wild Bulls”, or ‘Great Wild Bull’ (PT 1146), or Foremost of the Westerners’ (ibid) which the King becomes in the Pyramid Texts, is also assimilated to the Big Dipper, so that what had been perishable becomes imperishable, what had stolen and dismembered the Eye of Horus, has been tethered, tamed and redeemed. Seth and Horus have been reconciled through the agency of the scales of truth and the words of power known to Isis. Seth obviously has much in common with the Minotaur encountered by Theseus with his short sword at the center of the Labyrinth fashioned by Daedalus.
But in the midst of all this celestial symbolism, the Egyptians did not overlook the fundamental importance of the 2:1 ratio, the octave in music. The 2:1 gate is the portal, the stairway, the window, the means to get there. The entire drama is contained within it. What emerges from that gate is the spirit of the king.
Splitting Open the Mouth
There is such a crush of information that could be conveyed at this point. It is so complicated and yet unity does prevail! The Egyptians performed a ritual upon the Mummy, and undoubtedly on candidates for the second birth during life as well, whereby the ‘mouth was split open’ using the ‘thigh of the Eye of Hor’, also called the hook of Upuat which means ‘opener of the ways’. In Egypt one unified symbol bore within it many ways to say the same thing. The opening of the mouth seems to be operating on more than one level. The Egyptians were masters of geometry. So the position of the mouth in the human body becomes important as we will see. By splitting open the mouth one was also opening the Eye of Horus. The Pyramid Texts use the term interchangeably! If the width of the King’s Chamber is taken as “1”, its height is 1.118 or the root of 5 divided by 2. In the body, the position of the mouth is determined by dividing the height of the Prime 2:1 by 1.118. In this respect, one could suggest, geometrically speaking, that 1.118 (1/2 the diagonal of a double square) is acting like the Adze of Iron used to symbolically ‘split open the mouth’ or “eye”. One could suggest that 1.118, by dividing the height, is splitting open the mouth of the double (ka), freeing it from its mummified cocoon! 1.118 is also acting as the’ thigh of the Eye of Hor’, that splits open the eye and facilitates the ascension of the spirit of the king. The feeling is that the hook of Upuat, the mnj.t, the thigh of the Horus Eye, is really the ratio 1.118 or the relationship between the diagonal of a 2:1 rectangle and its length (or 1/2 diagonal and its width.) One could also suggest that the King’s Chamber deep within the ‘earth’ of the Great Pyramid, was not designed for aesthetical reasons. It was concealed in deepest darkness. Rather, it was designed to accumulate the Earth’s telluric current, the Serpent Current, the “wouivre” of the Gauls, and subsequently transform that energy into a Lotus Bloom, the Golden Flower of Iseion – other names for the Eye of Horus. The splitting open of the mouth or eye was a metaphor for the final, culminating metamorphosis of the life of the ka that had observed Maat, accomplished its rebirths, learned the nature of things, expressed that knowledge through words uttered from the mouth truthfully, reflecting the Pyramid Texts which stated: ‘Say that which is, do not say that which is not, for the god detests falsity of words’ (PT1160-61). It is then possible not to allow oneself to be held back by the powers of the Earth at the moment of resurrection. The King’s Chamber was designed with complete simplicity and purpose – to open the gate; to split open the ‘mouth of the god’ as it was often stated.
In this XIXth Dynasty image from the ceiling of Seti I’s tomb, (Fig), we have proof beyond all doubt that the Egyptians were employing the golden number and golden section – both of which are determined from the diagonal of a double square – long, long before the Greeks. The Greeks inherited knowledge of the Golden Section and its role in the whole principle of resurrection, from the Egyptians. They did not discover or invent it as many history books insist. They were taught or reminded, perhaps, that the 2:1 was the Alpha and the Omega of all becoming and that the golden proportion mediates this becoming as a matter of course. And not only does it create and sustain us; not only does it give us the capacity to be fair and wise; but it also fills us with wonder when we sense what is beyond all transitory forms. The golden proportion is a means by which the Ark can stay on course – in life on earth by mediating Goliath – and as the way to enter immortal realms. The ancients believed this principle, whether we do or not.
The Templars and Egypt?
The Great Pyramid had been blasted open in the 9th Century by the Arabs and the King’s Chamber investigated – revealing nothing inside it but a simple stone coffer within a 2:1 rectangular chamber. The Templars were organized by 1114 A.D, but founding members had likely been in the Holy Land starting around 1100 after the 1099 conquest of Jerusalem. The first Nine Knights Templar returned from the Holy Land around 1128 A.D. Chartres experienced a terrible fire quite as of the Phoenix were right on time, and the West Front with south tower was gotten underway. The Holy Land was returned to the Muslims, presumably by the Templars, in 1187-8. After that, as ‘things took their course’, the Gothic Flowering exploded into being like a bifurcation of lotus blooms carved in stone.
Entering the Cathedral of Chartres is a unique experience. One learns that true peace is not quiescence. Rather, it is creative, dynamic and fully alive. It does not confine or burden either heart or mind. Rather, it relieves all burdens almost immediately. Suddenly the universe with all its conflicts and troubles, feels right. Love becomes reality. Dream becomes actuality. The indescribable fills the heart with its immediate presence! What is ‘above’ feels rooted in the here and now; and what is ‘below’ feels exalted, strong and fresh. Longing ceases and the soul must only learn to endure fulfillment. To know that other ‘pilgrims’ are feeling exactly what you are feeling only enhances the wealth, urging the soul to share more. At Chartres there is nothing to hoard, nothing to covet, nothing to hide. For shame itself is flushed from all its hiding places. What an accomplishment! If the builders of this Cathedral returned from the Holy Land with a secret, after dwelling for some 28 years in and around the eastern end of the Mediterranean Sea, then they revealed all when they committed that secret to the stones that built up Chartres. The secret now radiates from every part of it. It is imparted to even the most callous visitor with every breath taken. One is inclined to believe that the Templars must have spent a goodly part of that 28 years somewhere in Egypt.
I will demonstrate in a later post that the new scale upon which the present cathedral was built, depended from data that appears to have come directly from Gizeh, including the Great Sphinx.
Kely and I stayed 3 days at Chartres. We spent every waking minute around or inside the Cathedral. When it was time to leave, being a rather emotional creature by nature, I experienced an impossible grief that has never quite vacated my system. Floods of tears accompanied the drive to La Havre and the journey across the English Channel to England. Nothing since – with a few rare exceptions – has equaled the spiritual grace offered by Chartres in its totality. I will discuss these exceptions at a future point. I feel quite fortunate, however, that I can say that the Big Dream of 1980 shared something with Chartres, so that taken together they redefined for me the true nature of the Phoenix. Life and death are inextricably bound due to the mystery of the third. When the medievals spoke of Hermes Trismegistos, “Thrice-Greatest”, they were speaking of this third part, when the Phoenix is reborn.
Charpentier goes on to describe how a 2:1 table possesses the root of transformation from an angular to a circular table, in other words the 2:1 rectangle has the capacity to ‘square-the-circle’. Its capacity to construct the golden number infallibly was one thing. But the ability to square the circle seemed to penetrate more deeply into my system. But with time I realized that the golden section itself was the way to ‘square-the-circle’, which I have demonstrated below. The entire construction begins with the 5 x 10 rectangle, ABCD. The compass starts on A, is opened to AB and swung into a 10-meter diameter circle that crosses the diagonal at E. Its circumference is 31.416 meters, exactly the same as the perimeter of the King’s Chamber inside the Great Pyramid . EC then becomes the golden section, 6.18, and is swung into a second circle (diameter 12.36068) that cuts BC at F, dividing BC into 3.82 and 6.18, which relate as 1:1.618. But the arc of 6.18 also cuts AD at G. AG can be computed by subtracting 3.6327, calculated by Pythagorean Theorem, from 10.
The new length 6.367 then becomes the radius of a new circle with diameter, 12.734 a figure that we recognize in the Earth’s diameter. The Earth’s Equatorial diameter is 12,756.28 km and its Polar Diameter is about 12,713.5 km, so 12,734 km constitutes a reasonable mean between the two. In any case the Square, HJLK, clearly has a perimeter of 40 and a circle with diameter 12,734 has a circumference of about 40.005040. For the purposes of building in stone or even wood this is more than sufficient accuracy. What really matters here is how the golden section serves as the means to create a circle with the same perimeter as the square. It is the means by which matter and spirit appear to unite, thereby opening a portal of some kind: a passage. Note that the whole operation basically occurs within the 2:3 rectangle, HJCI, and we saw in the previous post that a 2/3 rectangle frames the entire Vesica Piscis complex with its 3 double squares and two overlapping circles with a total of 3 radii, where one is shared becoming the home of the heart and lungs as well as the womb! The Prime 2:1, ABCD, constitutes a 1/3rd part of HJCI. The Square, HJLK, is 2/3rds of it.
It is the hypotenuse, 6.18, of the triangle, GCD, that acts as the ‘bridge’ to the circle with the same perimeter as the square. 618 occurs naturally on Line 2, Column XI of Series E under 309. The dual squares within the Prime 2:1, ABCD, through the agency of its diagonal, both generate and unify complementary worlds: circle and square. The key to this function is the golden section, 6.18/10. It is well worth emphasizing that the arc of 6.18 cuts opposite sides of the ABCD 2:1 rectangle at points F and G, differently. This is the consequence of a shift in angle from upright, or 90 Deg, to 36 Deg or the angle formed by GCD. 36 Deg is 1/10th of a circle, so pentagonal and decagonal geometry are also related to squared-circle relations. The Pentagon and 5-pointed star ‘open’ golden section relations in a most beautiful manner, but it will have to wait for another entry. In any case, from AB down, BF is 3.82 while AG is 6.367. Their relationship is 1.66666, which is the same as that found in a 3-4-5 triangle between its base and its hypotenuse. 5/3 = 1.66666… Here we are using the long ‘5’ (6.367) segment as the radius of a circle with circumference equal to the 40 perimeter square. Ahead I will use the shorter ‘3’ (3.82) segment from the opposite side of the 2:1 rectangle as the radius of a circle with circumference equal to 24. In Series E, 31416 occurs on Line 24 in Column XIV. The circle will be centered right on the navel of the figure to be or 6.18 from the soles of the feet (CD of the Prime 2:1). Naturally 40/24 = 5/3 = 1.66666. I should also point out that 6.367/618 = 1.03. This in fact is one statistically typical armspan found particularly in women where the armspan is 1.03 x height. The horizontal armspan, then, is in a sense ‘squaring-the-circle’. Of particular importance is the difference between the radii of the two circles. In this instance it is 6.367-5 = 1.367 and we can note the archetypal relationship between the difference and the longer radius: 6.367/1.367 = ~ 4.6576 or nearly 4.66.
Robert Lawlor, who with Deborah Lawlor, translated Schwaller’s “Temple in Man” and “Temple of Man” into English, reminded me in 1990 that the Number 21 might also refer to Phi itself, the 21st letter of the Greek alphabet. The enigma is then complete. The golden proportion, phi, is the means within the 2:1 rectangle to Square-the-Circle. I do not think there is any doubt whatsoever, that as early as the 4th Dynasty (Cheops, et al) when the Gizeh Pyramids were built, the Egyptian priests, mathematicians and architects were manipulating the golden section and squared-circle geometry together with other interrelated geometrical functions, to transform the telluric or ‘serpent’ current that had been collected and concentrated by the Earth, within the Pyramid, in order to open a celestial portal or door to the firmament through which the spirit-form of the candidate – his transformed or purified ka – could pass on into the immortal realm of the Netherworld. This intention is made adequately and even enthusiastically, joyously clear in the Pyramid Texts of the 5th and 6th Dynasties. Beyond the transient ‘pains of death’ experienced by the passion of Osiris, the Egyptians rejoiced with a faith that can only be called sublime.
So, if we start with a Prime 2:1 rectangle that is 5 x 10, Unity will swing a circle with a diameter of 10 meters and a circumference of 31.416 meters.
These are naturally occurring numbers in Series E, with 1309, 2618, 5236, 10472 and 31416 all occurring under Column XIV. These numbers dominate the size of the King’s Chamber in the GP in meters! The perimeter of the 5.236 x 10.472 meter KC is 31.416 meters. In the image above, the circle-in-the-square is 10 and its perimeter is 31.416 – the same as the 2:1 Table of the King’s Chamber. When the Squared-Circle is carried out by the arc of the golden section, 6.18, a circle is generated with 40 meters on its circumference, the same as the 10 x 10 square that bounds the circle-in-the-square. The KC, then, is a decimal fraction of the Circle-in-the-Earth-Square! This seems to constitute an inner gate where a passage takes place to an absolute world – a world entered through the Duat that resembles the Aboriginal Dreamtime. In the Great Pyramid shown earlier we can see that the comparable difference between square and circle is 60 cubits or 31.416 meters and the height of 280 cubits divided by 60 cubits is 4.666.
But what is most remarkable here is that the same 60 cubit (31.416 meters) difference is turned into a 2:1 rectangular enclosure in the manner of the Egyptian Cavern of Sokar – an ancient rendering of the well-known uroboros or snake-that-bites-its-tail. We can also observe that if the base of the Pyramid is 230.384 meters, or 440 royal cubits, then it has an interesting relationship with both the length of the Sphinx and the length of the King’s Chamber. If the KC length is taken as unity, then the GP base is 22. When the diameter of a circle is 7, its’ perimeter will be 22. 7 x 10.472 = 73.33 meters or about 240 feet. The Sphinx is traditionally considered to be about 240 feet long or say, 73+ meters. So the Great Sphinx is in a pi relationship with the solid base of the Pyramid.
73.3 x 3.1416 = 230.384
The base length of the GP can be placed around the Sphinx in a circle making the Sphinx the diameter of that circle. With the length of the KC as unity, the relationship will be 22/7. 73.3 meters is also 1/2 the height of the Pyramid set on top of a 1/2 meter platform. S0, 73.3 x 2 = 146.6 = 280 cubits. If this is an image of the Earth, then the Sphinx measures from the equator to about 30 Deg latitude, the position of its actual location on the Earth’s surface. We will look at the possible significance of its 66 foot height at another point.
When the serpent of time bites its tail, rebirth is close at hand. The self-enclosure becomes its own altar, its own “pyr”. This was called a ‘stone whose essence was most pure’. This is a fascinating image. In the upper register we see 3 chests. Within each chest circularity is invoked. At the upper right corner a serpent spits ‘fire’ into each chest. So the serpent fire, like the kundalini, replaces the Phoenix or is the agency of the Phoenix. It is burning three parts: a head, a wing and the loins of an animal. One thinks of Horus, Thoth and Seth. Below the candidate is over on his side, not unlike descriptions of Osiris in the Pyramid Texts and Anfortas in Parzival. On his head is a scarab, so this man is undergoing a metamorphosis in the self-enclosure of the uroboros that co-ordinates time and energy. The kundalini is a 3-fold refining fire sometimes descriptive of Aries, Leo and Sagittarius: Head, heart, loins. The wing was probably the wing of Thoth who is sometimes called the heart of Ra, but usually the spiritual heart or ib. Eventually the Man-scarab will stand up again in triumph having shed the former husks of his forms and arise as a spirit.
This enclosure very much invokes the function of the King’s Chamber itself. Not only is the perimeter 31.416 meters or 60 cubits, where 60 is a common number for measuring time, but 31.416 meters is also exactly 1236.84 Br. inches. In 100 years there are 1236.8 synodic months. Half the perimeter is 618.42 inches symbolic of 50 years and 618.42 synodic months. 1/4 of the perimeter is 309.2 inches symbolic of 25 years and 309.2 synodic months. All these numbers are found in Column XI of Series E. There is the feeling that the King’s Chamber was also a clock and that the clock was tuned to both small and great cycles of time. It acted like Solomon’s Holy of Holies which was closed up all year except once, admitting the High Priest alone to enter its pristine state like an oracle. Here is what Eschenbach says about the ‘stone’, as if the stone were acting like a ‘pyr’ or an accumulation of electromagnetic energy capable of undergoing a metamorphosis:
“By virtue of this Stone the Phoenix is burned to ashes, in which he is reborn. – Thus does the Phoenix molt its feathers! Which done, it shines bright and lovely as before! … This Stone is also called “The Grail”. (Parzival, p. 239)
We all know the Phoenix burns itself to ash in a singular act of self-immolation upon an altar of its own making. The Grail, then, is the essence of the Phoenix itself, the mystery of the eternal spirit within. It molts; it does not die! The coffer within the King’s Chamber has been called a ‘fount of spirit’. For the Egyptians at least, the Squared-Circle seemed to act as an eternal gate when Circle and Square have been reunited. The King’s Chamber must have been seen as the Cavern of Osiris/Sokar within which that union is realized. Much can be said about this famous chamber – especially when one examines the Pyramid Texts – but I will have to do this at a later point – it is too detailed. What should be said, however, is that when ‘circle’ and ‘square’ are reunited, all the opposites are reunited. In Egypt, Horus was the Eye or Circle; Seth was the Square, the one who dismembers, opposes, obstructs and imprisons the coveted luminary: the principle by which light (and sound) become intelligible. Seth is the matter pole that must transform passion into wisdom. When the Two Combatants, as they were called, are reconciled by Thoth-Hermes through the agency of Isis – undoubtedly by way of the altar or 2:1 Table – the “Eye” is restored; the Phoenix is reborn; the scarab transforms from a worm into a winged insect of startling beauty.
EARTH + MOON
In the image below we see the Moon adjacent to the Earth. And we see that it has repeated the same Squared-Circle pattern as the image just seen above. Now the Earth itself is the Circle-in-the Square and the Moon’s radius marks a circle with the same circumference as the square that bounds the Earth! So it is now the Moon’s radius of about 1738 km that is acting like the 60 cubits or 31.416 meters of the Great Pyramid. In the very ancient renewal myth known in Mesopatamia, India, Cambodia and so forth, as the “Churning of the Sea of Milk”, the Moon itself is treated as if it were a goblet or grail. The Moon’s synodic cycle is treated as if it were part and parcel of the Phoenix cycle of which we are participants. The New Moon is the phase in the synodic month (29.53 days) when the moment of renewal takes place following the ‘death’ of the previous cycle. This occurs to an even more pronounced degree with the progressed New Moon that occurs every 29.53 years and so is nearly coincident with the Saturn transit around the Sun.
So now we have a proportional progression between the two images through 4/π or 1.27324… To get from the ‘Circle-in-the-Earth-Square’ to the Circle that passes through the Moon’s radius we square 1.27324 to 1.6211 which we can see is not far off the golden proportion, 1.618!! In fact they relate as 1:1.0019. This constitutes an important progression because the square of the coefficient 4/pi would seem to indicate that Moon and Earth are very much in a shared field that is well-proportioned. Today astronomers refer to the binary team, Earth + Moon, as “Mearth”. The fact that they have a shared center of mass (SCOM) 1700 km or so below the Earth’s surface will be seen to have extraordinary interest when we examine the angled armspan of the human adult in better detail ahead. Meanwhile, we can see the following:
280/60 = 1.2732/.2732 = 4.66 = 8105/1738
We can also note that the perimeter of the Earth is here shown as 40,000 km, which I took as a convenient mean. The perimeter of the Hexagon inscribed within the Earth’s perimeter is 40,000/1.0472 = 38,200 km. This is about 1/10th of the separation between the Earth and the Moon. But more importantly it is the same number in the metric system as the short length when we golden section the height of the 5 x 10 rectangle (6.18 + 3.82). This 3.82 is the radius of the circle that we used in the ’24-method’ shown earlier for squaring-the-circle. I will also note here that the Escape Velocity at the Sun’s surface is 618 km/s. If that figure is squared, you get 382,000 sq km/sxs. If you unfolded all those little square kilometers you would have the distance between Earth and Moon. The Sun’s Escape velocity is an effect of its mass and radius in a gravitational field. The gravitational acceleration of that mass-energy requires that an object must reach a speed of 618 km/s if it is going to escape the accelerated fall into the Sun. The Sun’s gravitational field embraces or envelops the Earth and Moon and all other bodies in the Solar System, but falls off in strength as an effect of the square of the distance. A square is a surface and because it is curved it has self-focusing properties. The Sun’s mass determines all circular speeds and all escape velocities at any distance from the Sun just by itself. So, it is quite interesting to see that if you took the golden section of a 500 x 1000 km 2:1 rectangle, it would give the km in seconds of the Sun’s V-escape. In the case of the Earth, if you took a 2:1 rectangle that was 5 x 10 km and extrapolated its diagonal, it would give the exact speed also in seconds, namely 11.18 km/s. That is the speed required to escape the Earth’s Equator!!! It is about 11.2 km/s at the poles.
Since we have just established the image of the Moon adjacent the Earth, this is a good moment to introduce again the image of the male armspan in relative numbers within a 1 x 2 Prime rectangle. This Fig is densely packed with information. The hands of the horizontal armspan rest right on the 1.618 latitude. I have marked with red the angled radii from the center of the Thoracic Vesica Piscis to the centers of the two ‘Moons’ through which the red circle passes. Each radius is 1.078689. This is also the width within which the Thoracic Vesica is inscribed. I’ve marked that ab and the rectangle width is xz. When in the upper position, angled 21.25 deg off the horizontal, the hand exactly forms the radius of the Moon. The two hands together, ignoring the small asymmetry between arm lengths in most people, makes up the Moon’s diameter. I arrived at the 1.078689 by some trial and error over about a year’s time. I had to stumble on the Ideal Botanical Angle first in Ghyka. The Ideal Angle divides a circle by the golden section, here, 137.5 deg on top and 222.5 below. This Squared-Circle formula only works at this angle, when it forms the radius to the center of the heart. At one point I began to realize that the relationship between the center of the heart (1.5 from the ground) and the Aortic Arch and horizontal armspan (1.618 from ground) was crucial. It related the center of the thorax and specific muscle of the heart (probably constrictive) to the Aortic Arch – a very special part of the heart complex where the blood branches off to head, arms and then lower body. It is also relating the center of the Vesica Piscis that makes us breathe with the maximum width of the human body: its armspan. I finally began to relate them and then found 1.07868 in other places such as multiplying the two categories of most common male armspans:
1.03007 x 1.0472 = 1.07869 = 1.618/1.5
This suggested to me that the ratio between 1.618 and 1.5 was inducing an electromagnetic acceleration – in waves. This acceleration had the capacity to both pump blood and nourish muscles capable of doing work through the hands and arms. There was a limit set upon the relationship between diastole and systole that was self-regulating and this self-regulation was determined by the relationship between 1.5 and 1.618. But I did not see the relationship to the Earth/Moon situation until I started to superimpose all measures in meters over the AU imagining that the height of the human was “15”, meaning 150,000,000 km. This gave an armspan at the Ideal Angle of about 150,000,000 x 1.078689 = 161,800,000 km. If man can be considered the measure of all things then this was highly symbolic because the maximim span the arms could take was this limit at this angle. The total diameter of the heart circle would then be 323,600,000 km or about 2.163 AU. But there is far more here than initially meets the eye. The hand is in the same proportion to the whole radius – from the tip of the fingers to the center of the heart – as the Moon’s radius is to the sum: Moon Radius + Earth Radius. In actual terms this can be written 1738 + 6366 = 8104 and 8104/1738 = 4.66. If we return to the Great Pyramid for a second we see the analogy: 280/60 = 4.66. But we also saw that the squared circle exactly cuts the mouth of the standing adult which is about 2/1.118, or 1.7888 from the ground. So now hand, mouth-to-crown, tip of GP are all acting similarly. They are the difference between circle and square with same perimeters! They express a difference that participates in, or remains connected to, a sameness! Same and different complement one another like Yang and Yin. The two hands are in a complementary relationship like the two hemispheres of the brain. The two square moons, waxing and waning, complement each other. The New Moon and Full Moon complement each other as seed and fruit.
By some conservation law, in the male, what did not go into preparing a womb for hatching a new human being, has gone into a slightly expanded Thoracic Vesica that heightens its ‘mouth’ to the nostrils instead of the mouth. It also drops the opposite pole down into the sacrum. This might incline the male to seek yoga as a means to raise the kundalini from its conservation cave in the sacrum. A male might well go about spiritual development differently than a female.
I should also note that from the ground 1.078689 measures exactly to the top of the head of the femur that is inserted into the SI of the pelvis. 1.0472 is the lower part of that oval. From the top down, 10.78689 measures to the base of the sex organ. 1.0472 is the bottom limit of the pelvic structure. There is much more to discuss, but I will wait until we have a more magnified image. What I should say,though, is that I did not see this Earth/Moon participation until I was measuring the AU (Astronomical Unit) for around April 17 (1998) or so, or about 150,108,000 km. This gave excellent measures of Earth and Moon. So I fine-tuned the body until I could see the constants at work – such as 1.078689. When I did this, the Earth’s surface cuts off the wrists according to squared-circle proportions. The inner core of the earth is exactly contained within the male Thoracic Vesica. And the Shared Center of Mass between Earth and Moon exactly corresponds to the width of the golden rectangle within which the female Pelvic Vesica is inscribed. This convinced me to use that width, 1.236, to find the male Pelvic Vesica, by simply dividing 1.236 by 1.078689 = 1.145835. This worked perfectly for the male pelvis! It is marked here as ‘wy’ but I have not drawn the pelvic circle in to avoid over-crowding.
On one last harmonic note, we can observe the following if we take the Au for 15 or 1.5:
1.5/1.309 = 1.1459! The position of the center of the Thorax divided by that incredible number of metamorphosis that helps square the circle by the 24 method, gives the ratio for the male Pelvic Vesica. These numbers suggest that humans are eager for spiritual metamorphosis. But specific conditions are needed to take the potential reservoir of energy up to where it can be transformed; the crysallis from which the butterfly can go free.
The Golden Proportion
One of the most beautiful things to contemplate about the Golden Proportion is its all-embracing consistency. One imagines an infinite hologram and in phi-proportioned intervals, phi itself is the warp and weft that binds together the microcosm and macrocosm so that in the end they act as one, whole, eternal, living being. One name the Egyptians gave this all-embracing warp and weft, mapped out by the golden proportion, was the Net. The Net was kept in the ‘Temple of the Net’ in Khemenu, presided over by the great Neter known as Thoth, the brilliant Ibis-Headed partner to Maat, the Goddess of Truth. I will not embark upon a discussion of Thoth here as it will require a separate entry in its own right. However, it is well known that Thoth was associated with the Moon. But he can no more be identified withe the Moon itself than Ra could be identified with the Sun. Thoth was associated with the complete synodic month and in this sense he was the master of time as much as he was the master of geometry. He allotted the proportions, sizes and speeds to the celestial bodies. The synodic month is also an exponent of the Astronomical Unit which determines the speed the Earth + Moon are traveling in their orbit around the Sun. This is about 29.786 km (statistical mean). A good number to associate with Thoth is 29.53. This number is common to both days and meters. I will return to this when we look at the scale and elevations of Chartres, where 29.53 meters sets a complete standard. But it is also evident at Gizeh at the base of the Great Pyramid and in a shadow cast by the 66 foot height of the Sphinx. In both instances Squared-Circle geometry is involved. Incredibly, and I suppose, marvelously, we are born through the agency of this number. It is also the agency of rebirth. The Grail is not just a cornucopia of profusion; the Grail governs rebirth. It is the vessel that ‘captures the ash’.
When any of us entertain concepts or experiences of wholeness, peak experiences that happen all too infrequently, the subject is delicate, because all of us are attuned a little differently. However, there is a danger in presuming that everything in our world is disconnected from everything else and that the moral sense of oneness and a shared responsibility for the Earth and its inhabitants is largely illusory. This casts us into a gloomy environment of mutual indifference and a planet of sharks where literally we cannot feel an interconnection with the whole. Sanity and health is surely experiencing the mean that mediates between the One and the Many; an interconnectedness and a separateness; the circle and the square.
The Proportion: .618
In view of the dominance of the number 6.18 (or .618 0r 61.8% of anything), I was immediately struck by the figure given by Etienne Houvet for the internal width across the transepts at Chartres. He suggests an exact figure of 61.8 meters without commenting on the coincidence! Charpentier also did not mention this coincidence. I immediately sought out the best ground plan I could find and reconstructed it according to measures from more than one source. I felt if there was a 61.8 meter width, there had to be a 100 meter length that also featured the interior of the Cathedral. This would provide an interior Golden Rectangle (IJKL), the symbolism of which would go something like this: Virgin + Child = Incarnation. According to this idea the golden rectangle, EFGH, comprises the interior of the transepts and the immediate start of the Nave just beyond the towers, all the way to include the interior limit of the choir. The Apse that surrounds the choir, exceeds this golden rectangle. Meanwhile, it also seemed that an overall 2:1 rectangle (ABCD) with its sister Golden Rectangle (EFGH), had been established, but using the Egyptian Royal Cubit. The 2:1 would be in the order of 130.9 cubits by 261.8 cubits and the Golden Rectangle, 161.8 x 261.8 cubits, which is the golden number by the square of the golden number.
It is interesting to contemplate the scale of Chartres. The West Front of the Parthenon is 30.922 meters or 1 second of arc at the Equator. This would suggest that the internal span across the transepts at Chartres comprised not only two Parthenon – which also refers to a Virgin Birth (Athenos Parthenos) – but also 2 seconds of arc at the Equator ( 40,075,035/1,296,000 = 30.922 m and 30.922 + 30.922 = 61.84 m). I will be coming back to this number again when constructing the female canon of proportions. It shows up in the most unexpected way when one superimposes the 2:1 principle over the Astronomical Unit, so that the height of the figure is the Astronomical Unit itself. I should also note that Chartres turns out to be a convergence of meaningful scales, where we realize that measures themselves are proportions. There are harmonious proportions and there are stressful or even destructive proportions. The number 309 is instructive with 618. In 25 years there are 309.2 synodic months. In 50 years there are 618.42 synodic months. It is quite interesting to observe the occasions when the meter uses the same numbers as time cycles. The most important is 29.53 meters which sets the scale for the interior of Chartres and its elevations. This is the synodic month in days but also measures a critical time cycle in years that seems to determine the Egyptian Sed Festival of Regeneration. The numbers 309, 618 and 927 make an important appearance when the canon of the female is superimposed over the Astronomical Unit that I often round up to 150,000,000 km or even a little higher as if ‘tuning’ a remarkable ‘celestial mechanical’ harp string. Sometimes I just take it as 500 light seconds which is about 149,896,229 km. The mean AU is about 149, 587, 870 km. But the Earth is only ever at that distance a couple of days each year. I should repeat again that it is quite significant that 61.8 meters links the north-west door (left) to the south-east door (right). At the north-west is Saint Anne and at the south-east is Christ who we just saw earlier holding a book and with hand up-raised. 100 meters measures the sacred part of the Cathedral from the entrance to the Nave up to the internal limit of the Choir. 6.18 x 100 is a perfect golden rectangle. In the female, the Pelvic Vesica is inscribed within the golden rectangle. The Thoracic Vesica is inscribed within the 2:1.
The Measure of All Things.
By 1998 I had come to feel that the mean AU of nearly 150,000,000 km was an incredibly important key to life. It was the optimum distance from a G2-yellow star at which a dynamic balance had been struck between light, heat, gravity, circular velocity, temperature variation, water optimization and the capacity for organic compounds to build up into complex living structures able to sustain themselves over longish periods of time.
I thought it was important to examine the distance using the meter within the context of the growing geometry. The reward for using the geometry, as if it were a lens of some kind, has proven ‘immeasurable’. Right away it invokes Series E. When we take the golden section we have the appearance of ‘927’, the same number that measures around the socket stone base of the Great Pyramid. It appears in Line 3, Column 11 of Series E. Since I was already using the scale 43,200 between Earth and GP, I decided to ‘focus’ the AU by using a distance that was the Moon’s diameter x 43,200. So this came out in 1998 to about April 16 or 17 when the Earth is about 150,163,200 km from the Sun. I backed it up to April 16 for a host of other reasons and often use 150,108,000 km instead of the mean of 149,597,870. What matters is that this is about 500 light seconds or 149,896,229 km. 500 appears on Line 1, Column XII of Series E. The golden section gives two adjacent numbers in km from Series E on Line 3, the ’15’ and ‘1500’ line, namely: 57,300,000 + 92,700,oo0 km.
This exercise proved important because it eventually led me to correct the angle of the up-raised arms and forced me to realize that the right angle aligned them with the center of the heart. This angle was determined by dividing a circle centered over the heart by the golden section (137.5/222.5 degrees). It was then that I could see that the hands were participating like the Moon and the head above the mouth, and the 31.416 meters above the GP square that becomes the perimeter of the King’s Chamber, in Squared-Circle relations. This in turn helped me to further understand the way the Egyptians had depicted the hands in bas-relief inside temples and tombs. Just as they had manipulated 1.118, they also were manipulating the geometry of the hands.
Moreover, it is the perimeter of a square generated by a shadow cast by the Sphinx at Noon on the Equinox. Just as startling, it is the identical perimeter around the square treated by Charpentier as the key ‘Square Grail Table’ referred to earlier on. He found it to be 23.193 m on a side or 92.772 for perimeter. The shadow cast by a 66 foot height at Noon on the Equinox at the latitude of the Great Sphinx, is 11.598 which gives 23.196 on a side and 92.78 for perimeter.
When we measure the golden section for April 16/98, when I first tried this experiment, it gave about 150,108,000/1.618 = 92,773,795 km. This ‘AU’ of 150,108,000, is interesting in that when divided by 43,200, the same scale the GP is to the Earth, it gives the diameter of the Moon. So when we perform the Vesica Piscis for the pelvis and size of the female womb, we get 92,773,795/3 = 30,924,598 km. This might possibly tie the number ‘309‘ to the formative aspect of the Sun/Moon/Earth triad. The synodical month is entirely dependent upon this triad. It does not exist without the triadic relationship among the 3 bodies. So their sizes and distances of separation become important. Geometry coheres their differences in spacetime.
There really is such a curious feeling of harmony in this image! The Thoracic Vesica is about 25,000,000 km across. So we take the number 25 and we make it years. In that time there are 309.2 synodical months. Recall the female rule: “one ovum per month”. In 25 years we have 309.2 ovulations. And in this one image we have both numbers: 25 and 309. They relate through 1.236, which appears on Line 4 in Column XI under 309, 618 and 927. The Pelvic Vesica is inscribed within 927 as 1/3rd of it. A complete cycle is 1236.8 synodical months or 100 years. It is also the inches in the King’s Chamber. It is the width of a Golden Rectangle when the height is 2, so it relates Prime 2:1 to Golden Rectangle. Finding these numbers in Series E awakened the amazing sensation that there was an inevitability to life forming in our Solar System. I realized the set up among Sun, Earth and Moon was following rules that were poorly understood, but well worth exploring. The geometry was acting like a creative lens. It was letting me see things that I could not see otherwise.
Another observation is worth making here. The average female height in North America is apparently, delightfully enough, 1.618 meters. To obtain the mean diameter for the width of the Pelvic Vesica, one divides first by 1.618 giving 1 meter exactly, and then one divides by 3. So, in effect one is dividing 1.618 by 4.854, another fascinating number that we do not have time for here. The width becomes 33.33 cm. This in fact is not far from 30.9 cm and they relates as: 33.33/30.9 = 1.78964. This ratio will become one of the most important in this work, because relative to unity, it is the width that determines the male Thoracic Vesica. If the female is 1, the male is 1.0786. This also becomes the radius of the heart circle, just referred to above, that in turn determines the arm span of the up-raised arms. Note that 1.0786 x 150,000,000 = 161,800,000 km. The entire canon comes full circle through the golden number when it is laid over ‘or measures’ the position of the Earth and Moon relative to the Sun. But the arms span measures even more as we will see at the end of this post.
The Charisma of the Golden Number
Overall Charpentier was both elegant and sparing with numbers. He knew full-well the general reader’s anathema for math. Understandably. All knowledge is relative. I recall all too well what it took to get through Roger Penrose’s “Shadows of the Mind” (1994). That it was well worth the effort does not alleviate the level of punishment endured trying to follow half a dozen mathematical arguments needed to understand some of the roots of nothing less than consciousness itself. But when it comes to the golden number it is important to be tireless. It even makes an appearance in the behavior of tubulin protein at the nanometric scale, not overlooked by Penrose in his work on quantum behavior. Phi is surely part and parcel of what holds us together and may well be a transcendental bridge between behaviors and states such as spirit and body; quantum and relativistic; statistical uncertainty and rigorous determinism. Phi captivates us, not because of any intentional show on its part, but becaue of the way it resolves tensions, differences, behaviors, scales, growths and by a natural means, keeps proliferation within bounds.
The golden number (1.618) divided by its own reciprocal (.618) gives 2.618 which is the square of the golden number or 1.618 x 1.618. Note that 10/2.618 = 3.82. Things manifest through squares by way of some form of acceleration. The acceleration is a self-amplification. Energy starts to behave like matter as it accumulates through feedback loops or self-feeding circuits. Squares gestate energy. From the square of the golden number, 2.618, Charpentier points out the following gem:
2.618 x 12/10 = 3.1416
He did not realize that this equation is the basis of the perimeter of the King’s Chamber in the Great Pyramid, where 31.416 meters is equal to 60 royal cubits. A royal cubit is simply the perimeter, 3.1416 divided by 6 = .5236 m. A circle with the same perimeter as the King’s Chamber has a diameter of exactly 10 meters. A 2:1 rectangle with the same perimeter as the 10 meter circle has 10 cubits for its width which means 5.236 meters using a cubit of .5236 m which we see in the diagram below.
.5236 relates to .5 m as 1.0472 to 1. Schwaller has called this the ideal armspan though typically it is expressed in real humans as 1.045. I have one arm that is 1.047. Eventually I incorporated this “Ideal Armspan’ in the male geometry. Since the KC has the same perimeter as a circle with diameter 10 meters, it makes sense to divide it by 12 seeing as 12 has already made it into the universal formula featured by both Schwaller and Charpentier.
1/2 the width is 2.618 meters which is 1/100th part of the walk around the labyrinth at Chartres. This means 2.618 meters constitutes one sign of the Zodiac at the scale of the King’s Chamber. It also means that a 1/12th part of the division of the Duat is here taken as the square of the golden number, 2.618 meters. This also suggests, of course, that the meter adopted by the French during Napoleon’s time, was the same meter used in the King’s Chamber. Isaac Newton availed himself of these measures in order to determine the size of the Earth so he could calculate the gravitational constant.
Best to tarry here for a moment. A crush of data has piled up. With the 1/2 base already set as 1.618 (220 cubits), I have calculated unity and turned it into a Cube, here figured as ABCD. The KC with its coffer is within the Cube with the Queen’s Chamber. Note that the Subterranean Chamber is set by a Root-2 rectangle as if it were in fact the root of the Cube. Within Unity the floor of the K.C. is set by the golden section as if it were a gate. The Grand Gallery goes up to the Golden Section. In another post I will suggest what I think the significance of this Cube actually is as it pertains to the head and the meaning the head held for the ancient world. Note that the width of the QC is the same as the King’s Chamber. Both are 5.236 meters wide. I have indicated both the coffer and niche in the KC and QC respectively.
I should note that it took a long time for me to discover where to apply the Squared-Circle formula in human anatomy. But when I finally found an application, the reward was substantial.
It was R.A Schwaller who noted that this formula is built into the Egyptian gates also called sba. The pylons are 12, taken together; the opening is 10 and the height is 31.416. Notice in Fig of the Great Pyramid that the difference between square and circle is 60 cubits or 31.416 meters which is here marked TS, NQ and PO. So this 31.416 meters has been enclosed within the massive body of the pyramid as a 2:1 rectangle with perimeter equal to that difference. The 60 cubits is to the whole height of the Pyramid (280) what the Moon’s radius is to the Moon + Earth radius, which gives the ratio, 1:4.66. We will come upon this ratio in more than one location as we proceed. It appears to be quite fundamental.
I would like to now proceed to an examination of how the 2:1 can be used to ‘square-the-circle’ also using the golden section of the Prime 2:1 but in a different manner that offers a plethora of relationships. Then we will look at some interesting phenomena that reflects this geometry, one of which includes the geometry of the scarab. But it also seems to be involved in focusing the lens of the eye; in the structure of the magnetosphere; in the function of the tiny tubulin protein ‘dimer’ that makes up microtubules in the cell’s centriole; in the newborn human infant. Then we will look at some geometry applied to a few faces. We will then look at the armspan and discuss the role of the SCOM between Moon and Earth and the proportions of the standing adult. Let’s take a close look at this 24-method for squaring-the-circle. It is quite a dynamic jewel that may offer the support base for metamorphosis.
Once again we start by golden-sectioning the Prime 2:1, ABCD. We then take 3.82 as the radius of a circle that we will inscribe right on the navel that is 6.18 from the base of the Prime 2:1. That 3.82 is the height divided by 2.618, or the square of the golden number. That gives a diameter of 7.64 or to be more exact: 2 x 3.81966 = 7.63932 The circumference surrounding this diameter is7.63932 x 3.1416 = 23.999688 or nearly 24. Hence the name the 24 method. In Series E 764 appears as a whole number and we can use modern Pi to calculate the circumference: 7.64 x 3.141592654 = 24.001. We can now proceed to square the circle with whole numbers. A square with 6 on the side is 24 in perimeter. A 2:1 rectangle with 24 for perimeter is 4 for width and 8 for length. Naturally 7.64/6 = 1.2733 = 4/pi. The number relationships here are marvelous. You have 2, 3, 4, 5,6, 7.64, 8, 10. You have 3.82 and 6.18. The two rectangles relate as the Major 3rd, 5/4. But this paradigm presented me with a real surprise because it appears that Nature actually uses it to build up remarkable forms of life and function.
Below we see the head, Thoracic Vesica and Pelvic Vesica laid over the ’24-technique’ for ‘squaring-the-circle’.
Other examples serve to highlight the importance of this geometry, born from the golden section of a Prime 2:1 rectangle. It’s as if the golden section of the Prime 2:1 supports the Three Grail Tables as if it were a foundation or underlying scaffolding. The scarab is perhaps one of the most remarkable example of this geometry. It is so intricate and precise I will have to leave the reader to follow it themselves. I must paoint out the diagonals and head size however.
Below I have shown a more fundamental application of the ‘Squared-Circle’. What has been squared is the Prime Circle itself, with diameter equal to the height of the figure or the length of the Prime 1:2, AC.
This figure is now getting packed with information, and like Nature herself, it becomes important to keep track of themes – or to observe how themes keep track of themselves! The base of this drawing is twice the golden number, or 1.618 x 2 = 3.236. We saw earlier that by extending the diagonal of a double square by its width and bisecting it we obtained 1.618 infallibly. Now this diagonal + 1 has become the base of a ‘Great Pyramid’ and a 2:1 rectangle that is 1.618 x 3.236. The top part of the 2:1 marks the horizontal armspan and cuts through the Aortic Arch where blood leaves the heart to feed the arms and hands like sap feeding the branches, leaves, flowers and fruits of a tree or plant. It is important to note that Nature distributes branches, leaves, blossoms, seeds, fruits and buds around the stalk or trunk in accordance with the golden proportion. They are even separated around a 360 degree circle by the golden section, dividing the circle into segments, 222.5 deg and 137.5 deg which has been called ‘ “Ideal Angle” in botany. We will see the implications of this angle just ahead when we examine the upraised arms that act as a radius of a circle that is centered in the heart at 3/4th the height of a standing adult. At this point the ratio between 1.618 and 1.5 becomes a key not only to proportion but also to function. Proportion is as much an exponent of function as function is a product of proportion. They arise together.
The height of the large pyramid, bka, is 2.06 and 2.06/2 = 1.03, a very common arm span among men and women relative to the height. So the height of this all-embracing ‘Great Pyramid’ has also offered the horizontal armspan of the figure.
We next move to the highlighted Great Pyramid, TUO. Its base is the same as the width of the golden rectangle, GIJK, that determines the size of the Pelvic Vesica. Its’ 1/2-base is .618; its base is 1.236. Its apothem or angled side (hypotenuse) is Unity itself, 1; and its height is the square root of .618 which is .78615 which is .618 x 1.272. We can also use 4/pi as the means to obtain the height of the smaller pyramid TUO and it would give, .7868. When we add 1 to this we get the height from the soles of the feet which would be 1.7868 that is very close to 1.7888. Note that if we slide TUO up so that its base rests on the navel it will exactly touch the vertex of the head. That suggests a recapitulation of the distance from pubic bone to navel from the mouth to the crown of the head. This is simultaneously a play upon the golden section relative to unity and the difference between square and circle that have the same perimeter.
We should now take a closer look at the square, WXYZ, that has the same perimeter as a circle with diameter equal to 2, the height of the figure and the Prime 2:1 rectangle, ABCD. It falls on the same latitude as the ‘mouth’ of the Thoracic Vesica and appears to be the same as the overall formula that is 1.7888 from the soles of the feet computed as Height/1.118. We know the diameter of the circle is 2 so the circumference is 2 pi or 6.283185. To get the sides of the square we divide by 4 giving 1.5708. To obtain the distance from the pubic bone it is 1/2 this or .7854. With unity added, it is 1.7854. The Vesica opens at 1.5 + .28867 = 1.78867, the closest to the overall formula of 1.7888. What we seem to have here is a group of convergences that together share statistical nuances. Those nuances, in a watery solution, would generate undulations that build extraordinary dynamism into the mouth. The dynamic range cannot be too extreme or it presents the problem of rupturing a stcructure. But if it is kept within bounds – especially at its resting stage, then the mouth is active with subtle undulations that make it both attractive and alive. The distance between square and circle here is .2146. This is the approximate distance between the vertex and opening of the mouth. Its reciprocal is 4.6598. Eventually I came to call a modified version of this number the Squared-Circle-Modulus because of its regulatory importance in several orders of reality. It also plays a role in establishing the size and function of the hands relative to the whole arm when together they are the radius of the Heart Circle shown already, but which I’ll come back to. I will note again that if you add together the diameters of the Earth + Moon and divide by the Moon you get the following: 12734 + 3474.8/3474.8 = 4.6646… So the Moon is to the Earth+Moon what the distance from the mouth to the vertex is to the whole height of the body.
So in this image we now see four convergences on the mouth. They are all remarkable. Each offers to the mouth their own dynamic function and spectrum of reality and needs. The Pyramid TUO is very impressive in that the center of its base corresponds to the base of the spine. So, in effect, the height of this pyramid measures the whole spine right up to the top of the neck and base of the skull. This signifies that the skull occupies the same span: .2146 or 1/4.66 of the whole height. The larynx is contained in the upper peak of the pyramid where ideas are given form and then ‘sent’ to the mouth for articulation and amplification. The mouth controls the dynamics that arise from the Vesica Piscis – including diaphragm located around the 3/4th line. This Pyramid TUO suggests that we speak with our entire spines. Everything that we are reaches a peak at the mouth. Words seem to radiate away from the pyramid’s apex. They fly away like ‘light’ from a beacon. The upper half of the Pelvic Vesica is within the Pyramid, as if the pyramid, TUO, were gestating in the female everything from words to a new human being. But the same pyramid also contains the entire Thoracic Vesica Piscis, suggesting that this pyramid alchemizes these basic functions. The entire brain, meanwhile is contained wholly in the difference between square WOLM and the circle with radius 1 or Unity. Another way to put this is to say that with the base on the pubic bone and base of the spine, the difference between the Squared-Circle Pyramid that culminates on the vertex of the head and the Golden Rectangle pyramid that culminates on the mouth, comprises the brain and includes eyes, ears, nose, etc. The brain is the intermediate world between circle and square. Now the ancients called the Squared-Circle a ‘gate’. We see descriptions of the “King’s Gate” in the Pyramid Texts. The term, “sba” refers to star and gate as well as Great Teaching. The Great Pyramid was situated precisely within a stellar environment. What is being gestated is a metamorphosis. The brain was liquified and extracted during mummification, but the heart was left in the mummy. The double or ka was concerned with the Word and that the Word be founded upon Truth. The ka had no more need of the brain. What concerned it was what was within the heart.