SQUARING THE CIRCLE: An Ancient Legacy
In the previous post I attempted to show some critical and diverse examples whereby squared-circle relations seem to be regulating aspects of Nature that have influenced the very ability for life-forms to evolve, flourish and enjoy the copious fruits of conscious experience. There appears to be a consistent and all-encompassing geometry that even extends down into the subatomic world. The golden number and its family seems to act as the ‘Royal Family’ of that all-embracing Net of Life or web of circumstances within which spirit, the essence, the pure heart of the ‘stone’ is caught and is able to grow. The Egyptians and the builders of Chartres seem to have taken this All-embracing net of life further and through knowledgeable architecture accumulated energies – the serpent power – to induce a qualitative leap in being, symbolized by the scarab Khepera. It seems that an underlying geometry must be capable of such a metamorphosis. Something must hold the Eye together. One factor that we know is always involved is the arc of a circle. Most especially we have seen that arcs from opposite corners of a 2:1 Table will divide its diagonal by the golden section. Before we look at another method for squaring-the-circle, that I call the “24-method”, let’s go back to Chartres for a moment and ponder a small sculpture on a pillar diagonal from the sculpture of Moses at the north-west entrance, the Gate of the Initiates as it has been called. This sculpture is remarkable in more than one way. It is important to read the Old Testament carefully in order to appreciate this sculpture.
The sculpture at Chartres depicts the Ark of the Covenant being pulled by a pair of oxen, not on a cart as stated in the bible, but affixed to wheels. It is not proportioned as stated in the Bible nor as others have reported. It seems to be 1 x 3 when viewed from the side: the same proportions as the whole of Solomon’s Temple (20 x 60 cubits). Moreover, it has two Tables of the Law within it and something else that is not mentioned in the Bible: it has a sphere of some kind to the right of the Tables (chipped by vandals in the sculpture).
Now, the Tables were supposedly written on both sides – laws composed by God and written by his own finger and delivered to Moses – alone. ‘Both’ sides probably means the Ten Commandments for the people, on one side, and esoteric, cabalistic mathematical laws for temple builders written on the other side. Temples were the science of that era, just as they were in Egypt, India, Cambodia, Mexico, Greece, Rome and the Gothic period in France. The sphere might be the Earth, the Sun, the Moon, The Egyptian “Aten” or any circular body, including Plato’s Eternal Living Being who, according to the Timaeus, had man made in his image or likeness through the means of a sphere. This was accomplished by way of the human head. The sphere could represent the Hebrew, Yahweh, but it could just as easily represent the Egyptian Eye of Horus or the ‘Spirit-in-the-Dndrw-Bark’ mentioned in the Pyramid Texts (e.g. PT 1637). Generally speaking, it would seem that the sphere points to the head in some way: the origin, the means, the way man is made in the likeness of ‘God’, the cosmos. But it also could just as easily refer to the principle of a circle swung by a compass. A circle in a sense refers to the whole, totality, the All, Spirit. But it is also a first enclosure; the first Grail Table. The perimeter of the King’s Chamber is the same as a circle with diameter 10 meters. Circles are intuitive, natural, instinctive, mysterious. The square is analytical, and is a play of the opposites. It is strategic and differentiated. It uses reason and sets down rules. The 2:1 is revelation; the Alpha and the Omega.
This head is Atum-Ra, Ra-Horachty and also “man”. The Sphinx reunites and joins above and below; around and within; matter and spirit; square and circle; space and time. One also thinks of the head of Adam. In Egypt, like Genesis, it was the Ram-headed Khnum who was said to fashion both man and his ka on a Potter’s Wheel. This is in imitation of the Earth spinning on its axis, the means by which life processes are ‘sculpted’ by cycles of time and space. The Sphinx faces east where everything rises. What is on the Earth’s surface is sculpted by everything that comes from the horizon – including the mysterious “sty” or ‘perfume’ of the Eye of Horus. This perfume is caught by the vase of life, the Grail. In Egypt the first act of catching the perfume, the celestial waters, was performed by Nut; and in a sense the last entity to become ‘pregnant’ with the accomplished spirit of the ‘king’, was also Nut, Saint Anne of the New Testament: the Black Virgin who contains all the stars – mysteriously nourishing their fires with her eternal womb.
Note below the similarity between various forms and the vase that sits on top of Nut’s head. Of particular interest is the shape of the scarab’s dungball. One imagines that the Egyptians noted these forms in detail as they formulated their unique style of hieroglyphic writing.
The head is the perfect container, the vase that transforms and regulates everything else. In the Ptolemaic Period the Egyptians depicted the head of Ra with a stylized scarab to symbolize the transformational gift of the head. The ears are like the handles of a vase.
The image of Ra’s head is quite informative indicating that the interaction between Greek imagination and traditional Egyptian principles was at times subtle. I have shown in the sutures of the skull and scarab similar geometrical ratios as employed in this interesting head and triadic crown. If the jaw to base of crown is ‘1’, from jaw to stylized scarab or brain cavity is .618. .382 includes the stylized eyes of the scarab. The crown of Thrice-Greatest Hermes rises up from between the eyes to complete an underlying 2:1 construction. In the skull and scarab the sutures seem to bridge .618 to .714. In the sba
gate construction .714 measures the height of the pylons within a 2:1 construction, upon which the lintel sits. So .714 represents the opening of the gate, the height, 31.416/44.
The head is sculpted by the world and in turn ‘sculpts’ the world. Its power and its influence are in evidence even at an early age. Personally, I remember almost the instant when the ‘head’ woke up in my mind – as if it were a miracle. I was hitch hiking with my camera from Big Sur to Yosemite, California. It was April and I had just seen Jacques Cousteau speak at Berkeley University. He was exhorting the crowd to fight on behalf of Nature and the Earth at exactly the moment when warplanes were carpet bombing Cambodia in one of the darkest advances of the Viet Nam war. I had been picked up by a hyper individual who had just gotten back from Viet Nam. He was headed back to Oregon. He could not stop his out-pouring of emotion that was bursting from a perspective shift that had finally reached a threshold. He declared the whole war a complete waste. A total tragedy. He said he thought he had served as his solemn duty to the United States. But now that he had seen the extent of the damage, how misguided it was; what the war had done to people, flora, fauna and social order, he felt he now had to do something positive to compensate the insanity. So he was going back to Oregon to be a doctor. After many hours under a boiling sun I was picked up on a dusty stretch of road by a pick-up truck.
This is the head of a 12–year old boy I encountered in the back of the pick-up truck when I was making my way through an endless stretch of grape fields. He was a farm worker and had no rights. What amazed me during the ride was how life in California – the hot sun, wicked pesticides that had scarred his arms, long hours of labor, picking grapes – had sculpted his face, his head and the emotions that clutched his heart. I have never
forgotten that boy – his head – the dignity granted by God and promised by Jefferson’s Declaration of Independence, but betrayed by one’s fellow humans. Twelve years old and the Potter’s Wheel was already leaving its marks severely. Man has an enormous influence on what life sculpts so long as we never forget the ‘clay’ that turns upon that wheel. This Mexican boy is a continuous reminder to me that each head is a child of the ‘eternal living one’ and is endowed by life with certain inalienable rights. The Sphinx echoes the heads of the ages. There is no head that the Sphinx does not reflect. It is absolutely fascinating that some Grail Romances depict the Grail itself as a head. Sometimes the head acts as an oracle. The Templars themselves ostensibly worshipped a head called the Baphomet. Some have interpreted the ‘Baphomet’ as ‘Father of Understanding”.
When you examine the skull, you wonder immediately whether ‘understanding’ would happen at all without the golden section. The golden section is a dynamic process: a relationship. It is not a thing, like a crystal. It breathes with infinity. It conducts and radiates the cosmic fire. Understanding rests on the cosmos; not merely shape, but also a dimensionless well of potential energy. Note how the golden section of the brain itself divides right at the Pituitary Cavity sunk in the sphenoid bone. The carotid artery bends around the Pituitary and then radiates into anterior and posterior cerebral arteries like branches of a tree. The whole composite brain/skull structure seems to be centered or rooted in that Pituitary Cavity.
The Egyptian Nut, who carries the first vase that catches the well of potential energy dispensed in quantum ‘bits’ by the recondite vacuum, was also called the Great Well in the Pyramid Texts.
Utterance 368 is a protection text that invokes first and last principles. It is a remarkable text but requires some background information first before presenting it in full. However, it is best to at least introduce a part of it so that some images start to seep in:
“Your mother Nut has spread herself over you in her name of St-pt, she has caused you to be a god to your foe in your name of ‘God’, she will protect you in her name of ‘Great Well’, for you are the greatest of her children. Geb is gracious to you; he has loved you and protected you, he has given you your head, he has caused Thoth to reassemble you so that what was on you comes to an end.” (PT 638-639)
One can see that the notion of ‘the son of God’ is at least as ancient as the Pyramid Texts and refers to a universal principle that involves a metamorphosis in a context of critical protection. One imagines the Pyramids were built to offer that protection. Geb was Nut’s male counterpart and was associated with the Earth that had become fertile with seed. It is Geb in this instance who gives the candidate his head. Thoth (Greek, Hermes) reassembles the whole being, an analogy to the reconstitution of the Phoenix and the Eye of Horus. This brings an end to the ‘ash’ stage, the apparent death phase. So Thoth and the head are associated with the means by which the ‘King’ is reconstituted. This of course refers to the ka or double, the assumption being that it lives on after the demise of the physical form.
Here you see the morphological similarity among inverted head, 12-day embryo, the eye and the 26-day embryo. The shape of the embryo is never lost. It remains in the brain. The similarity between the eye and the 12-day embryo is particularly striking. The embryonic endoderm + ectoderm is acting like the lens of the eye. And the primitive yolk sac is acting like the vitreous body of the eye. This strongly suggests that within a spherical container electromagnetic forces self-focus in a way that organizes information in biological material. That information is able to self-replicate as a living structure grows. In the brain which we are looking at inverted, the region of the Pituitary, White Anterior Commissure, hypothalamus, Third Ventricle, median eminence, optic chiasm, suprachiasmatic nucleus, mamillary bodies, etc. are involved in that central self-focusing region – acting as a sort of command central for many processes of the whole body. Within the Egyptian Mysteries, the Eye of Horus played a similar role for the soul, the ka and the spirit of the candidate. Its reconstitution was the goal of the Egyptian Way.
Now under the sculpture of the Ark at Chartres there is a Latin inscription, presumably for initiates, since it is at the North-west Gate. It is on the right hand side (south) as you mount the porch steps. I had to find a ladder to get up high enough to photograph it. So you must look for it or you will miss it.
“Archa Cederis. Hic Amittitur. Archa Cederis”. According to Eugene Canseliet, this translates in the following manner:
“You are to work through the Ark. Here things take their course. You are to work through the Ark”.
In the image below you can see the letters of the Latin clearly. But who among us has thought of ‘working through the Ark’? And no mention has ever been made of placing a sphere in the Ark. Head, arcs, circles that become squares, orbits that maintain living things … the rotundity of the cosmos … a resonance chamber that transmutes all the motions there are to be … a compass that swings out arcs and imitates circles…
The Ark of the Covenant
“You are to work through the ark”. Immediately one imagines there is an intended play upon the word Archa. One meaning is the arc of a circle, the role played by a compass in geometry. After all, it was 1195-1220. Plato’s influence was profound at Chartres as was Pythagoras who supposedly spent 22 years in Egypt. The secret of the circle is part spatial and part temporal. The circle also refers to the secret of cycles and hence the cycle of the Phoenix. But the Ark was also associated with the Oracle by which ‘God’ made known his will. Therefore it was associated with revelation, dreams, mediumism, holism.
The Ark of the Covenant was ostensibly kept inside the 20 x 20 x 20 cubit Holy of Holies at the end of a 20 x 40 cubit 2:1 Table in Solomon’s Temple also called the “Oracle”, the crystal ball of wholeness. Note the archetypal relationship between a Cube and the Sphere it houses: it is .5236 from Series E, the same as the Royal Cubit. The cubit depends from π. It is the result of dividing the circle by 6. 3.1416/6 = .5236. The width of the King’s Chamber was 5.236 meters. The cubit as 1/6th the circumference of a circle – in the case of the King’s Chamber – depends upon a diameter of exactly one meter. This meter is 39.37 inches. Since this is the meter used today we must conclude that the French elected to go with the Egyptian meter when in the 18th and 19th centuries we could not find agreement on the length of the meter. The Earth has too many variations in its surface. In those days there were no satellites.
The whole Temple of Solomon is 20 x 60 cubits; measures we are now familiar with. The King’s Chamber has a perimeter equal to the length of the Temple of Solomon, if the same cubit was employed. This perimeter is 60 cubits or 31.416 meters. And this 31.416 meters is the difference between square and circle in the Great Pyramid and so represents the proportion of the ‘squared-circle-modulus’ (SCM) or 1/4.66 of the Pyramid Height of 280 cubits.
Like the King’s Chamber, this Cube was supposedly completely empty except for the Ark. 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”.
Another passage from Charpentier has haunted me since 1985 – sometimes the sign of an eternal clue; one that does not die even in the abyss of doubt. For Charpentier the Ark carried much more than just the Ten Commandments. He believes it was a repository of measures. To puff ourselves up, we love to believe that Temple builders were barely standing upon the shoulders of flint-carrying Neanderthals. Ironically, however, the mass of us do not hold this view because we ourselves are actually capable of building bombs, or computer chips and artificial hearts. But rather, not only can the bulk of us not build bombs and computer chips, but we are irked by the fact that we cannot even design a porch let alone a temple. It is we who have lost the knowledge and significance of the relation between man and cosmos and so we are determined that ancient man could not have been capable of it either. It is us who see the Ark as a magic talisman, not as a means, a blueprint for constructing a House of God within which man is raised up. But it has always been historically unfair for contemporary cynicism, ignorance or just self-satisfaction, to disparage the accomplishments of earlier generations.
But no matter, there is no doubt about the Latin inscription at Chartres. ‘You are to work through the Ark’.
“Workmen are indispensable of course, but so is measure. Higher or lower, the pyramid of Cheops is only a fine heap of stones….One must have at one’s disposal a valid measure, a common denominator between world and man. It would seem that as regards the Tables of the Law, this was a unit of measurement which was laid in the Ark in the form of Aaron’s Rod, the living baton. It vanished in Solomon’s time.” (Mysteries of Chartres, p. 64).
The mention of the pyramid is appropriate since the square table at Chartres, 23.193 x 23.193, implying a round table with the same perimeter with a diameter of 29.53 meters – easy to remember because it names the days in the Synodical month – is simply 1/10th the socket stone measures of the Great Pyramid. I have no doubt that the Hebrew took the measures of the Great Pyramid out of Egypt and had them placed in the Ark. If certain measures are lost the relation between matter and spirit can be lost. Man then reverts to a primitive level that loses the capacity to regenerate spiritually. The balance is lost; the covenant broken; the cycle of the Phoenix becomes impotent. So convinced was Charpentier that the Ark contained some invaluable measure or system of measures, that he believed the Ark in some crucial respect was recovered by the Templars after the First Crusade:
“There are no proofs of a removal of the Ark, or of a replica, into France. None except those that one does not look at because they are under your nose – the Gothic Cathedrals.” (ibid, p77)
Note again that Unity here – the ‘mouth’ of the triangle – is 14.765 meters. This implies the diameter of a circle that is 29.53 meters. In this image I have concentrated only on the equilateral upon which the entire ogival arch rests, the first elevation and the highest point. It was Jean Favier who pointed out that the highest keystone was a little more than 36 meters. This would fit the use of the Square Root of 6 – the next root function beyond the square root of 5. 2.44948 x 14.765 = 36.1667 meters. Note how awkward these root functions are. They are infinite values to the right of the decimal point. But within a 2:1 construction, with just a line and stakes, one can be sure that one has ‘caught’ the infinite in the proportion produced by the 2:1 itself. Also, note again that the first elevation of 9.794 represents the acceleration rate of gravity at the Earth’s surface in one second of time. So the cathedral also gives the second. A few extra centimeters and it will give the fall rate for the latitude of Chartres which is a little faster due to the Earth’s flattening. I suggest that the building has set the second by the first elevation. Acknowledging the acceleration rate for gravity, is juxtaposed to the understanding of how that gravity is overcome; how the spirit is raised. The Cathedral is a crucible within which the essence of the stone is purified through a perfect quickening that escapes the serpentine coils of the Earth. In the first elevation you have a triangle that gives the Earth’s radius, the fall of gravity and the means of overcoming it through spiritual enlightenment. Charpentier rightly points out that what determines the first elevation is the ratio for the Minor 3rd in music, 6/5 or 1.2, recalling that 6/5 x 2.618 gives π. Once again we see the participation of 1.2 in the generation of π that can be used in squaring the circle. 2.618 is the square of the golden number. The feeling is that the square of phi is a special acceleration that is transcended when augmented by 1.2. The first development of Series E is 1 + 5 = 6 and 6/5 = 1.2. The King’s Chamber is a decimal play upon this principle: 12 x 2.618 = 31.416 or 1.2 x 26.18 = 31.416 or .12 x 261.8 = 31.416. The walk through the Chartres’ Labyrinth is 261.8.
In this image you see the simple basis of the meter. The Earth Circle (EF) is squared (ABCD). A circle (HG) is placed in the square. The diameter of the circle (HG) and the side of the square (ABCD) are the same. The outer circle is 1.27324 x larger than the diameter of the inner circle and side of square. The side of the square and diameter of the inner circle are divided by 10,000,000 which is a large decimal number that boils down to a human measure – known to laborers and temple builders alike as essentially ½ a fathom, ½ an armspan. If somebody is my height which is 179.52 cm, I have an armspan that is almost 1.0472 my height.
1.0472 x 179.52 = 188 cm = 1.88 m
Half of this gives a measure of about .94 m or 37 inches. This is shy of the meter and a little larger than the yard.
The meter directly measures the Earth. The King’s Chamber is a decimal fraction of the Circle-in-the-Earth-Square. Its perimeter is a 1/1,000,000th part of this inner circle’s circumference. This is the inner circle of the alchemical ‘Pelican’. In the Pyramid Texts this Pelican is referred to as the King’s mother. This has nothing to do with one’s earthly or biological mother. Therefore it is the place of thick darkness within the Great Pyramid where the Pelican transforms the King’s soul into an eternal spirit that makes pregnant the womb of Nut. This pregnancy within Nut is referred to by different symbols – all referring to fermentation as a principle: beer, bread that rises, Winepress God, the bnn that fertilizes as an analogy to sperm, etc. This spirit then passes out of the Pyramid – the fire kindled in the earth. The Pyramid protects the metamorphosis so that it becomes an inner gate indicated by the perimeter of the circle as 31.416 meters. The whole Pyramid enclosure, then, is acting like the Alchemical Pelican, the great womb of the cosmic mother. Eventually it becomes pregnant with and gives birth to the Eye of Horus.
This image of the Pyramid is identical to that of the ‘Squared-Earth’, it is just set at a smaller scale; 1:43,200. And this we have seen is a key member of
27 54 108 216 432 864 1728 3456 6912 13824 27,648 55,296 110,592
This scale is what creates a difference between circle and square at the top of the pyramid that is 60 cubits or 31.416 meters. And it is this that then becomes the hermetically sealed enclosure of the King’s Chamber while also being the circumference of a circle with diameter equal to 10 meters.
A Master Measure
As far as the history of architecture goes, this meter is a master measure. It does not need to be belabored, but the Pyramid did involve labor to build. This 31.416 meters – which is 60 cubits – was extracted from the difference between the radius of the circle and ½ the square. That difference relates to the whole height – of which it is a part – as 1:4.66 just as the Moon (which makes things pregnant) relates to Earth + Moon as 1:4.66. And just as Capra’s nucleon speed relates to the speed of light in the vacuum as 1:4.657 as if it too were that which captures energy or light and makes the vacuum pregnant. What gives the Great Pyramid its bulk, its weight and its visible mass are the nucleons, not the photons that heap up into varying fluxes of concentration in the vacuum; nor the massless gravitons. So the internal mass and the specific gravity that heaps up in the pyramid concentrates energy and that energy becomes active, the way the yolk of an egg becomes active with electromagnetic and hence electrochemical processes. This occurs in the empty spaces of the various corridors and rooms, which then act the way the megalithic dolmenic chambers acted.
These chambers accumulated energy that was utilized by the Druids and others for purposes of spiritual initiation into the higher states of human existence.
The King’s Chamber is completely lined with granite – a very high-pitched stone that has a high quartz content. Quartz is capable of conducting piezoelectric current when subjected to a compression – decompression cycle that the mass of the Pyramid would undergo just by terrestrial tidal gravity alone. The whole Earth’s crust breathes with gravity. It is quite dynamical because of the influence of the Moon which shares a center of gravitational mass with the Earth 1700 km below the Earth’s surface. This focal point is always shifting because the Earth rotates faster than the Moon orbits the shared center. So the internal center and the combined outer influences of Sun and Moon acting together make for a potent variation cycle that is memorized by biological material active on the Earth’s surface – a surface that is intermediate between outer gravitational cycles and inner gravitational cycles. In humans the Circadian and Infradian biological clocks are located in the suprachiasmatic nucleus on either side of the anterior walls of the Third Ventricle just above the optic chiasma. This is part of that self-focusing region of the brain that is quite important in directing many aspects of our life. Moreover, two shafts also target the King’s Chamber: one from Orion and the other from Alpha Draconis. These shafts perfectly fit the description of the way the ‘perfume’ of the Eye of Horus comes from the horizon of Amun and is captured, concentrated by and in the Stone which will eventually reconstitute itself as the Eye of Horus. This internal quickening of the ‘egg’ is what the Egyptians meant by the bnn and hence Benben Stone. In the Pyramid Texts it adopts many names one of which is the work of Sokar and Isis.
Most readers will sense that the Great Pyramid is an Arq Ur or Great Measure. That the difference at the summit of this ‘Mundsalvaesche’ between square and circle should be none other than 31.416 meters – the very meter used today – is a master stroke of scale. But to incorporate that very masterful measure into the perimeter of one of the most mysterious and talked about chambers on Earth – the King’s Chamber – is also a masterpiece of knowledge and of the relationship between matter and its behavior and spirit and its behavior. This is not to be compared to rocket science. It is not to be compared to nuclear weapons nor nuclear reactors which will drive hair driers and T.V. sets. This is a spiritual science capable of balancing and healing the Earth and its inhabitants. This is not easy to do. Illness persists more readily than the knowledge that can cure it. Best, then, to preserve the cure through thick and thin.
Below I have placed a Unity Cube in the Pyramid as if it were the starting point of the entire construction. In that cube is the head of Atum who becomes Geb and eventually man himself. The relationship between this ‘source’ and the pyramid is the golden number. So the ½ base is 1.618 and the apothem is 2.618 while the height and sides of the cube are unity. The King’s Chamber is found at the golden section point of the cube taken in three directions! On that basis I decided to see what part of the head corresponded to the King’s Chamber, Queen’s Chamber and Subterranean Chamber.
It will require a separate post to expound upon. However, it is clear that the Suprachiasmatic nucleus does fall within the King’s Chamber. It does seem that the ‘root’ of the Uraeus falls in the King’s Chamber. It seems that the whole brain rallies around a ‘seed’ of some kind that then escapes the ‘coiled serpent’ to borrow a term from the Pyramid Texts.
Moreover, the Unity Cube extends as a Root of 2 rectangle very precisely down to the Subterranean Chamber as if the Subterranean Chamber were acting as a root. We can see this relationship below between a ‘germ’ taken as Unity and its root, which becomes the square root of 2. In the case of the Great Pyramid it is as if the Vagus Nerve were rooting itself in the Aortic Arch which we know corresponds to the golden number, 1.618, in the whole canon. The same root 2 rectangle also contains the spine as far as the first Thoracic Vertebra. Nerves from these first 8 vertebrae innervate the heart stimulating it to beat faster. The Vagus Nerve reaches the heart from the medulla oblongata via an anterior route.
With this simple scheme it is very significant to see the Uraeus emerging from the brow on the golden section of the Unity Cube. We can recall from the previous post that the Uraeus also rests on the golden section of a head cube in a Karnak bas relief shown below. Note that the Grand Gallery rises up to and rests upon the golden section latitude of the Unity Cube. This also corresponds to the top of the cerebral peduncle. The King’s Chamber is the meeting of the forebrain and anterior extremity of the thalamic complex and Third Ventricle.
Here I have taken the serpent itself as “1”, so it is “2” to the vertex. From base of Uraeus to base of jaw is 3.236. The relationship is 1:1.618 just like the floor of the KC in the Unity Cube. The KC appears to be about 44 meters from the platform. Here, the 44 meters is represented as .618 of the Unity Cube, or in other words as the Golden Section. This corresponds to exactly 84 royal cubits. The Queen’s Chamber appears to be 42 cubits above the ground.
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. The top of the mountain is meant symbolically. What is really meant is that the serpent is raised up in the Wild Mountain. The infra structure of the Great Pyramid seems designed to raise subterranean energies up to the King’ Chamber. The wilderness is teeming with savage life-force. Its power must be tamed, and raised. It is drawn up the spine; into the old brainstem; over the cerebral peduncle; through the Thalamus via a slit corresponding to the Third Ventricle; and finally into the narrow domain where forebrain and thalamus meet. It is as if the candidate has returned to the fetus – its cause; its germ; its origin in the womb of Nut. From this the Eye of Horus will be reborn. It is Seth, often symbolized by an ox who must ‘carry’ the Eye forevermore. It is Horus who must overcome Seth without killing him and who must place him ‘under the king’, ‘under the eye’. The Eye was sometimes depicted as being carried in an Ark or Barque. ‘You are to work through the Ark’ could perhaps be stated otherwise. ‘Here things take their course. You are to work through the Eye of Horus.’ But one could also say: ‘Here things take their course. You are to work through the Grail.’
“Take me with you O Horus; ferry me over, O Thoth, on the tip of your wing as Sokar who presides over the Bark of Righteousness. Horus is not asleep behind the canal, Thoth is not boatless; nor am I boatless, for I possess the Eye of Horus”. (PT 1429)
The boat, the Ark, the Bark of Maāt or Righteousness – the means of passage – is one and the same as the Eye of Horus. In ancient Egypt the King was expected to work through the ‘Observances of Maāt’. He was to follow the path of the ‘Bark of Maāt’. This was also called the “Right Way” in the Pyramid Texts. When you follow this path, the ‘path of righteousness’, then things naturally take their course. The start point of this path and the end point of the path seems to be the 2:1 Table. In the Great Pyramid this is the King’s Chamber.
During the whole process the candidate sometimes feels as if he were going to go mad as there is much that must be shed; much that must be burned to ash, much that must be exposed in the wilderness. The ‘madness’ accompanies the loss of one’s initial frame of reference. This is Dionysius. Chaos precedes order as if by magic. Just when you think chaos will rip apart mind, soul and body, it transforms, self-organizes into the Eye by which one is delivered: through a brilliantly ordered self-amplification. Since color is involved it seems that electromagnetism must be part and parcel of the ordered self-amplification in some sort of hermetically-sealed sphere of protection. There is a remarkable image of the scarab pushing the Eye (dung-ball) out of the pyramidal mountain where it has been reconstituted. The image shows the transformation from a 3-4-5 triangle to an equilateral triangle. The equilateral is featured at the site of the Sphinx. I will have to show this image in another post. It was first identified by Schwaller de Lubicz and constituted one of the most important breakthroughs in his understanding of the ancient Egyptians. The King is depicted as the hypotenuse of the 3-4-5 triangle, which is to say as the number 5. A serpent that is undulating forms the remainder of the triangle. So you have serpent = 3 +4 = 7 + King = 5, giving 7 + 5 = 12 for the full triangle. With the arms reaching up over the head the hypotenuse becomes 6 establishing the ratio 6/5 and an equilateral triangle is then formed. The Templars used to portray an Eye within an equilateral triangle. The equilateral triangle is relevant at the latitude of the Great Sphinx where the Sun casts a shadow at Noon on the Equinox that is 60 degrees.
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. 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. Moreover, it cannot be stated enough times that the internal measure of the cathedral that joins Christ to Saint Anne is none other than 61.8 meters. This is a remarkable measure. It is 2 seconds of arc of terrestrial surface. Half is 30.9 m. 1,296,000 x 30.9 = 40,046,400 m. The diameter of this circle is 12,747,165 m. If you divided this diameter by 1,296,000 you would get 9.835. This is the fall rate of gravity at the North Pole in seconds of time, or 9.835 m/s². It is always worth repeating that the escape velocity at the Sun’s surface happens to be 618 km/s or 10,000 greater than the span across the transepts at Chartres. The Earth’s escape velocity is 11.18 km/s which is 100 times greater than the height of the North Tower at Chartres, or, 11,180/111.8 = 100. 61.8 alsp participates in a golden rectangle the height of which is 100 meters. The theme of Chartres seems to be the vessel that captures a complete cycle: the incarnation; the rebirth in spirit and the final liberation or resurrection of the spirit. In this sense to work through the Ark is to work through the complete cycle of the Eye of Horus.
Whether the Ark was a 1 x 2 construction or a 2.5 x 1.5 construction, this inscription rang true for me immediately. I suppose I took it on faith. It was said that ‘God himself wrote the law on both sides of the tables of testimony thereby forming a covenant with both Moses and the Hebrew people. Both sides must mean exoteric and esoteric. The Ten Commandments are relevant for social behavior but cannot teach a Master Craftsman how to build a Temple, let alone a place like Karnak, or Luxor, or Chartres or the interior design of the Great Pyramid. 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. The emphasis was on ‘work’. This was not art for its own sake. This was work, Virgo, precision, structure, purity of design, efficacy of function; the capacity to heal, the art of perfection and a confidence in that function that keeps all detail spare. It is easy to miss this sculpture as it is small and a ladder is essential to get up to its level in order to photograph it.
I would not have noticed it had Charpentier not drawn attention to it in his book. It is well worth looking for it if you can get to Chartres. Note the conspicuous sphere next to the two damaged Tables of Testimony. I am not yet sure why Charpentier did not mention the sphere. I noticed it only when examining the photo that I had enlarged and is now on the wall. Lomas and Knight (1997) mention that 3 things were put in the Ark, the two tables of testimony, but also Yahweh himself. And they also mention that the Ark was proportioned 2 x 4.
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 who is in the Dndrw Barque” in the Pyramid Texts (PT 1637). But in the Pyramid Texts, the King himself has become that spirit. And that spirit is also the Eye of Horus. It is my best guess that the sphere represents the ultimate relation between God and man. This is the real basis of the covenant. The Eye of Horus, the All-Embracing sphere is the means by which the covenant is established. The Ark is the support which links time to space.
They may also have felt it was important to portray the antiquity of the principle of 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 millennia. 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 was 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 repeat 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 worshipped 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).
If one is looking for a good definition of ‘humanity’ I can offer a clue. Humanity is that extra gift in man that offers transpersonal inspiration; an inspiration that the individual or a group of individuals endeavor to bequeath to successive generations long after they themselves have left the delights of Earth. Charpentier has left just such an inspiration. And Chartres is what inspired him. Under the discussion of the Ark of the Covenant and the way it was portrayed by the “image-maker” at Chartres, Charpentier points out without apology, without couching his conviction:
“There is more in the Gothic than a series of technical solutions. There is a building of temples that are gates to the Kingdom of God; and this requires a higher science than that of calculation of forces and resistances. It demands knowledge of the laws of numbers, matter, spirit and, if it is to work in the souls of men, knowledge of the laws of physiology and psychology. Someone revealed all this. If it is not the Ark, if it is not the Tables of the Law, the knights Templar must have brought back an extraordinary initiatory document to the West.” (Mysteries of Chartres Cathedral, p.77-78).
In 1985 I took this passage seriously. I already believed that it all worked together. My 1980 dream demonstrated sufficiently to me that man was the being of grand unification. The question was: what were those ‘laws’? And the answer inevitably started with the 2:1 and the arcs swung by a compass within and around that 2:1 construction. Everything grows from the 2:1, right from the first cell division of 1 into 2. It also seemed possible that the Ark contained information derived from Egypt; Tables of Numbers such as Series A, Series E and so forth. It seems it could have given the Earth’s size and rotation rate; the Moon’s size and distance from Earth; the Sun’s size and distance from Earth. The Templars apparently taught Columbus that the Earth was round. They may also have taught him its size and how to navigate its seas. Man must be in harmony with his Earth or we could not survive the vicissitudes. One seed must grow into a diversity that remains in harmony with all its parts, including man himself.
If, for example, the Templars were taken to Egypt by, say, the Fatimids, it is possible that they were shown the implications of a shadow cast by the Great Sphinx and any obelisk that was 66 feet high and placed at the latitude of the Sphinx or its neighboring temple. In round figures the shadow cast would have been 11.6 meters. The theme of the Sphinx’s location is 6. A 60° angle is cast by the Sphinx at Noon on the Equinox. The 11.6 shadow can be doubled into a square with 23.2 meters on a side. A circle can be put in this square with a diameter of 23.2 meters. This diameter can be taken 60,000,000 times and will give a diameter of:
23.2 x 60,000,000 = 1,392,000,000 meters.
Today astronomy texts give a diameter of the Sun, the Egyptian Aten, as 1,392,000 km.
If we take the Moon’s diameter as 3476 km or 11404176.67 feet and divided it by a member of Series A
11404176.67 ÷ 172800 = 66 feet.
The shadow cast at the latitude of the Sphinx is about 60.025° and gives a length of 38.064649 feet or 11.602 meters.
23.2 x 4 = 92.8 meters.
92.8 x 432,000 = 40,096 km = Earth’s Equator.
In essence then, the 66 Foot Sphinx and its shadow are giving 3 figures at once: the size of the Earth, the Moon and the Sun:
29.53 x 432,000 = 12,756 km = Earth Diameter
66 Ft x 172800 = 11404800 feet = Moon Diameter
11.6 x 2 x 60,000,000 = 1,392,000 km = Sun’s Diameter.
The Sphinx gives the square. When we square the circle we get a diameter of 29.53 m and a radius of 14.765 meters which also sets the scale for the elevations at Chartres. 29.53 is easy to remember because it is also the number of days in the synodical month. In this instance 1 meter corresponds to 1 day.
In the next post we will go directly to what I call the “24-method” for squaring the circle.