Squared Circle Dynamics.

Prelude: Proportion, the forgotten Key.

It is May 4, 2010. I am attempting to finish the last of 13 initial posts that introduces work on the geometry that has shaped we humans in a fundamental sense, obviously over a long evolutionary period of time. This leg of the journey has itself been strange, unexpected and difficult. This past winter has been the most painful and problematical winter of my life. I truly feel lucky to be alive and am well aware that many people around the planet during the same time period were less fortunate than myself. Meanwhile others have exploded like miraculous trees resplendent with growth.

Since this work began in May, 1985, I have noticed a pattern. Every time – almost without exception – when I have made some sort of breakthrough, found a missing clue, or had an important factor brought to my attention that I had failed to see, extreme circumstances have accompanied each breakthrough, each act of recognition. It is literally as if the work were proceeding by a sort of ‘existential yoga’, an extreme alternation between breathing in and breathing out; between diastole and systole. Or, like  the growth of a tree,  it has progressed in cycles, one ring at a time.  Creation and destruction alternate. These discoveries have encompassed more of my being than merely intellect alone. It has not been an intellectual yoga, nor merely a physical yoga. Rather it has felt like a yoga of the soul. It has not been an encyclopedic experience. Rather it has been a cathartic one that I could not circumvent. For example, even as late as 1998, I was not paying attention to the Solar Plexus, its number (1.33333 ×Unity or 2/3 of the Height) and its function. So I had a dream so graphic, so primordial in its violence and seriousness that that very day, I located the Solar Plexus and made it part of the canon from that point on. It corresponds to the Major 5th in our diatonic musical scale.

The details have been dense. I have had to leave most of them out of this blog. I have included the factors that have made the greatest impression on me. To me, the laws of proportion operating in our immediate world, including the Solar System, have been downplayed by our entire social order. When we refer back to ‘Golden Ages’ in our past, we frequently do not realize that what made them ‘Golden Ages’ was probably – more than any other factor – their reverence and enthusiasm for the universal proportions that have created us and offer us life, health and strength. When we deviate too far from these proportional rules, disease of every denomination sets in and we look back with a vague sentimentality at societies which understood the value and the fundamental reality of proportion. The time will come again when the philosophy of “More is Better” will yield by necessity to “Proportion is best”.  Until that time the individual has some personal freedom to strengthen him or herself with the knowledge of harmony that is ever-present in the universe that holds us in its embrace. We are free to take the sophistication of that harmony to heart.

Prime Principles: 2:1 Rectangle, Golden Rectangle, Square, Circle.

Between 2004 and 2006, I gradually settled upon what I came to believe was a Prime Principle, or perhaps it was a tight little cluster of principles operating together within a Prime Principle. Within this principle a  conservation law seems to be at work between female and male, the limit of which has been set by the golden proportion. Even though an embryo develops over the course of 266 days in an apparent linear sequence, in fact the geometry at work is not linear. It is a self-interacting present tense. The geometry works as a whole and evolves as a whole through these principle elements. It is probably safe to say that these geometrical principles are a class of “Platonic Forms”. They are so interdependent that it is very difficult to isolate and describe the parts within the whole. However the difficulty of analysis and explanation is worth tackling and transforming into  themes if they help clarify understanding. Personally I feel it has been essential for me to at least lay out the  prime principles and eliminate the vague belief that somehow our bodies, minds and the solar system that acts as a host to our existence, are all just part of a big accident. But there often seems to be a mutually exclusive relationship between words and geometrical forms. A 2:1 rectangle is already acting like a great ‘word’ that is too eloquent for analysis. A golden rectangle is another ‘word’ that does not want to be decomposed or ‘explained’. But yet these words are part and parcel of the Prime Principle.  With the 2:1 rectangle (ABCD) as the start point, the golden rectangle (EFGH) becomes a  limit within which everything unfolds and matures.  The square (MNOP) that is the double of the Prime 2:1 and the circle within it, act as maximum spatial limits with some nuances within which a 1.236 × 1.236 square (IJUT) is centered.  So the 1.236 square relates to the Prime Square as 1:1.618. The square IJUT offers exceptional stability and harmony. The female Pelvic Vesica Piscis is inscribed within it. If it has an area of “1”, the Prime Square has an area of 2.618 or the square of phi.

The difference between their areas is  simply 4 – 1.52786 = 2.472135.  All these values appear in Series E: 1528 in Line 8, Column X and 2472 next to it in Column XI. 1.618 and 2.618 are next to each other on Line 2 under Columns XIII and XIV.

This exceptional harmony and stability becomes the place of the womb from which we all emerge. This is the language of geometry The words I am using now spring from its interacting web and pour out of its vesicas like water from a deep well. But it took me a long time to learn its language. The mystery is not the language of geometry itself, which is a language of  givens: inevitable rules that Nature must obey once energy has condensed into material patterns. The mystery is what attracted me to learn the language to begin with. I believe I was looking for a foundation that was missing in my life. I was looking for the basis of health, strength, body, mind, soul and the interconnections between us and our greater environment. With time I came to believe that specific fundamental proportions were acting on my mind like medicaments. The medicament allows the mind to see in the dark through and beyond the trivia. Like a golden arrow it is able to pierce the maize of forms that often bind us up like chains.

1. Female Program First

As early as 1985 I felt that the female geometry preceded the male geometry. So I started with the female. For one thing, we all come from the female, so it made sense to see if  it was possible to find out why in a geometric sense. Why might also suggest how – also in a geometric sense.

At that point I was guided mostly by intuition. It was intuition that seemed to know in an archetypal sense that things were whole and this started with the Earth. I soon could see that the Earth’s spherical nature was interconnected with a wider celestial field. In fact Earth, Moon and Sun could be said to be acting as one mass-energy triad that is both separated and not separated simultaneously. The  center of mass of all three bodies is deep within the violent turmoil of the Sun’s mass even as the shared center of mass between Earth + Moon is deep in the Earth’s mass some 1700 km below its surface.  The Sun possesses about 99.87% of all the mass of the entire solar system. I had to get used to the idea that though we were tearing around the Sun some 150,000,000 km away at a mean speed of 29.786 km/s (107,229 km/hr), we were immersed in the Sun’s field and it was the Sun’s mass that was setting the speed at which we were rolling around it with our companion the Moon.  Right away I knew that 29.786 was both a measure and a proportion. 29,786 meters of travel in one second was in a context. It was also a 10,000th part of the speed of light. 10,000 is a square number. Gravity is an inverse square force. Every proportion has its reciprocal. Every path seemed to want to come back upon itself. That’s why I kept comparing the geometry to yoga. Everything we do, or think, or feel – every pathway keeps returning to the center of the meditation. All that matters is the quality of the meditation. Every sentient creature meditates.

In embryology it is said that the female program is primal. The male program will not begin until a sperm brings in a determining factor. Otherwise the female program will proceed. I wanted to know what geometrical factors allowed that program to unfold. In geometry, both female and male start with the 2:1 rectangle. In a healthy female, as the height remains constant – say ‘2’ – the maximum width within which the maximum Vesica for the Pelvic/Womb complex would be constructed, is that of the golden rectangle and golden section, namely 1.236. This is also the mean navel position for all humans and is simply 2 ÷ 1.618 = 1.236. This becomes the width of the golden rectangle within which the ‘ideal’ or ‘mean’  female Pelvic Vesica is inscribed. I will repeat though, when I started to draw these figures, if I was off the 1.236 width even a small amount, the proportions looked wrong and it appeared that the  function was wrong. I am not talking about being overweight. I mean proportion. It is the proportional relationship among 1, 2 and 1.236 that generates right function. It is right function that makes memorizing 1, 2 and 1.236 worthwhile. It is right function that makes 1.236 a good medicament to feed the mind.  It is because it is defined by the golden proportion, 1.618 (2 ÷ 1.618 = 1.236), that it is acting as a proportional limit. It is this proportional limit that forms a key part of what I am calling the Prime Principle. In all Fibonacci and Fibonacci-like series, 1.618 is the proportional limit of the series. After Column 13 or so, every adjacent pair of numbers will be in a relationship that is 1:1.618 or its reciprocal: .618. In the Prime Fibonacci Series an example is 233/144 = 1.618 and 144/233 = .618. Or, 377/233 = 1.618, etc.

0, 1,  1,  2,  3,  5,  8,  13,  21,  34,  55,  89,  144,  233,  377,  610, etc, ….

In the context of the equally primal 2:1 rectangle, this limit, 1.618, is expressed as the relationship between the Height, “2”, and the width of the golden rectangle, 1.236. In the context of the Prime Square shown earlier, the same relationship is established horizontally, the basis of the arm span according to Vitruvius. In the image below I have highlighted the female Pelvic Vesica complex by itself. It is contained within the golden rectangle, GIJK. It is inscribed across TU over the center of the whole body. The overlap that creates the Vesica has a width that is 1/3 of 1.236 or .412, here ‘vw’. Meanwhile you can just make out circle “VW” and its Thoracic Vesica that is centered on the middle of the heart. This has a width of “1”, or Unity. In this one image, all the basic keys are present even before discussing the proportions of the head. The fact that the female Thoracic Vesica is inscribed within Unity merits contemplation. Since the art of archery tends to be guided by the heart and breath one wonders if the female is more ‘unified’ when she aims the bow. It is said that women possess a better aim with the bow than men. The male Thoracic Vesica, as seen already, is inscribed within 1.078689. This is a harmonious ratio, but it might displace the male somewhat both physically and mentally.

In the female, then, the relationship between her Thoracic Vesica and her Pelvic Vesica is as 1:1.236. At a very early stage I felt this proportion, 1.236,  was one of the most fundamental building blocks of  life on Earth. And in fact, an instinct dictated that it was probably one of the building blocks of life anywhere in the universe: any universe; any conceivable spacetime milieu. Moreover it relates to time as well. There are not 12 months in a year. There are 12.3685 synodical months in a year and 1236.85 synodical months in 100 years. Recall there are 1236.85 inches in the perimeter of the King’s Chamber (31.416 m ×39.37 = 1236.8479 inches).  This ratio 1.236… is an irrational, an incommensurable value. It is open-ended and invokes process, relationship, self-interaction, the co-ordination of space and time. It heralds the year, suggesting that the year itself is the foundation of life. It is an organic envelope within which life forces are mustered and self-organize in rhythm with the year through the ‘number’ 1236.

Another situation that convinced me of its importance was its appearance in the powers that compose the number 64. The I Ching has 64 Hexagrams and I have often marveled at the level of accuracy with which the I Ching will ‘self-focus’ on a situation. The I Ching ‘knows’ the seeds of everything within which proportional information is encoded, stored and will unfold. The figure below is a rich vein of gold in the world of number. One could contemplate it for hours. The numbers that compose the value 1.236 are dynamical. They are versatile. They are harmonious. They appear to be multi-dimensional. There is no way to rationally ‘measure’ the value of the triadic group: 2, 1.618 and 1.236. These ratios are not things. They exist solely in a context among things. They are a triadic web of relationships. The reality they impart is in the proportional relationship among a group of entities.

To see 1236 appear in the powers for 64 is fascinating. As 4 cuts in half to 2, the power 3 doubles to 6 as if making a qualitative leap internally. While 64 conserves its identity, its appearance or composition appears to undergo a metamorphosis. Recall the I Ching is called The Chinese Book of Changes. ‘64‘ accommodates continuous change and transformation even when heavily constrained. 6 itself is perfect and equals both 1 + 2 + 3 and 1 × 2 × 3.  In the segment of the Table of Lambda shown at the bottom, 64 is in the 216 Column of Series A (27, 54, 108, 216, 432, 864…etc.) 2160 shows up in Nature as the diameter of the Moon in miles. It is the approximate years in one Astrological Age in the Cycle of the Precession of the Equinoxes (total cycle almost 26,000 years). It is next to 432. Recall the scale of the Great Pyramid to the Earth is 1:43,200 and the Moon’s diameter to the Astronomical Unit for around April 17 is 1:43,200. If the AU is made into a 2:1 rectangle, which I did to erect the canon of human proportions, the Moon’s diameter fits into Unity 21,600 times. There are about 21,600 nautical miles in the Earth’s equator.  216 is also next to 108 and the Sun’s diameter fits into the AU for April 21, namely 1.00493 AU, or 1,392,000 × 108 = 1.004934 AU = 150,336,000 km. And note that the ratio between the speed of a particle rotating around the terrestrial axis at the equator and the Circular Velocity at 1 Astronomical Unit, is 1:64 or 29.786 ÷ .4651 = 64.  In the one segment of this famous Table of Lambda shown above, 64 and 216 relate to one another and the phenomenal world in a dynamic way. For the ancient Egyptians, the original Horus Eye, or Wadjet Eye, consisted of 64 parts before it was dismembered by the Sethian force of differentiation and opposition such as we find in the polarized forces of nature. Just as the I Ching acts as an oracle, so the Holy of Holies of Solomon’s fabled Temple that had been designed to house the Ark of the Covenant, was also called the oracle. It is likely that in ancient Egypt the Eye of Horus, like the Ark of the Covenant, was linked to the principle of the oracle, which is to say the cosmic wholeness of time and space. For the ancients the Year was sacred. Osiris was called The Herald of the Year. The year of course is established by the Sun at a distance of 1 Astronomical Unit (149,597,870 km) from the Sun’s center of mass. This determines how long it will take for an orbiting body to complete one revolution. By the equivalence principle of gravity, this rate of revolution is not determined by the orbiting body itself, only by the radius from the Sun, the Sun’s mass and the internal application of the gravitational constant. So our distance from the Sun is fundamental. This is why I started to lay the growing geometry over the Astronomical Unit so that the AU itself equaled the height of the figure.

The height, then was acting as the radius that bound us to an orbit. I used the metric system to study what numbers emerged and then related those numbers to Series E that I have introduced in earlier posts.

I have also highlighted 137.5° of the Heart Circle, the radius of which is rooted also in the center of the heart which is 1.5 from the soles of the feet or 3/4th the Height. Interestingly, 3/4th the AU is only a small distance beyond the Venus Orbit (.723) that is almost a perfect circle (.0068 eccentricity). When the arms are dropped down the side of the body, the finger tips touch the Mercury orbit which has a large eccentricity (.206).

137.5°/222.5° is the golden section of a circle; 222.5 ÷ 137.5 =1.618. The golden proportion seems to generate correct tone or tonus in muscle development through right proportion in the skeletal structure. Meanwhile 3/4th the height or 1.5 × Unity, where the heart is positioned, corresponds to what in music we call the Major 4th, when a fundamental is augmented by 1.3333 × fundamental by reducing the string length to 3/4th or 75% of the original length. This is a reminder of the inverse relationship between frequency and length (or wavelength). From Middle C the Major 4th will be something like 352 v/s. The Fifth will be say 396. In our bodies this is the Solar Plexus at 2/3rd the height. So through differences of acceleration, the body and mind as a whole seek to restore Unity or balance. This Principle is the basic drama of life. Note the Fifth × Fourth = 2 = 1.3333 ×1.5. This is a classic or archetypal example of harmony that relates human morphology directly to our diatonic musical scale. Here the octave is the Height of the figure which I am also taking as the separation between Earth and Sun.

2. Shared-Center-of-Mass and 1.236.

The 1.236 circle which contains the female Pelvic Vesica Piscis also coincides with the SCOM circle (diameter TU) that we have seen in earlier posts. The SCOM circle is the Shared-Center-of-Mass Circle established about 1700 km below the Earth’s surface. It is the gravitational center-of-mass of “Mearth”, or Earth + Moon, which are in a squared-circle relationship with each other, even as their own centers of mass are separated by 384,401 km on average. If the Earth diameter is 1, the Moon’s diameter is .2732. 1.2732 or 4/pi is the signature ratio that defines the squared-circle. And with the Moon’s diameter as 27.32% of the Earth’s diameter, recall that there are 27.3217 days in 1 Sidereal Month which is the rate of motion of the Moon around the shared-center-of-mass and is also the rate of rotation around its own axis! In the image above I have squared the overall circle with the inner 2:1 rectangle, ‘bazx’. The ‘Great Pyramid’ that links square and circle together here has base ‘xz’. Its 1/2-base is the same as ‘xb’ and is 1.5708. The whole base is 1.5708 × 2 = 3.1416. Because this is relative to a Prime 2:1 rectangle, if this 3.1416 was collapsed into a circle its diameter would be “1” which is the diameter of the Unity Circle, “VW”, or Unity of the Prime 2:1, ABCD, within which the female Thoracic Vesica Piscis is inscribed! The height of this pyramid coincides with the height of the body or its vertex and so is 1.5708 × 1.27324 = 2. We can see how the squared-circle here harmonizes with the heart and solar plexus and the two great intervals of music through the octave (Height): 1.5708 × 1.27324 = 2 = 1.33333 × 1.5. This squared-circle pyramid precisely encloses the SCOM and 1.236 circle, adding to the overall harmony, equilibrium and stability of the female Pelvic Vesica Piscis. Meanwhile this 3.1416 rectangle is enclosed by a slightly larger golden number rectangle and its larger ‘Great Pyramid’ with base equal to 1.618 × 2 = 3.236.  Note that 1.618, 3.236, 1.5708 and 3.1416 all appear in Series E. Also note that the SCOM circle is enclosed by the 3.1416 pyramid but it reaches up and touches the golden number 2:1 rectangle or 1.618, adding even more to its overall harmony and stability.

Side of Squared-Orbital-Circle = Circumference of Thoracic Vesica Circle

I will summarize one point with the Astronomical Unit in mind. ‘xz’ is the side of a square with perimeter equal to the Earth’s orbital circle around the Sun, with the Sun positioned at the figure’s feet. If you take that length, here 3.1416, and collapse it into a circle, it is exactly the Unity Circle within which the Thoracic Vesica Piscis is inscribed! This houses heart, lungs, throat, spine, kidneys, pancreas, stomach, liver, spleen, etc. It opens on her mouth above and the navel below.  This is a remarkable example of a harmonious enclosure. For life to form, an enclosure is essential. Here we see proportional envelopes within envelopes, all related through basic harmonies. It is particularly beautiful to see the side of the square with the same perimeter as the Earth Orbital Circle become the circumference of the Unity Circle within which the Thoracic Vesica Piscis is inscribed. If we perform the same operation with the Great Pyramid of Gizeh the results are enlightening. The solid base is 440 cubits which is 230.384 meters. If we collapse that into a circle it will have a diameter of 440 ÷ 3.1416 = 140 cubits = 73.3 meters or about 240.48 feet. This is the length of the Great Sphinx which is often given as an even 240 feet. It is also 1/2 the height of the Pyramid measured from the top of the platform. This means it measures symbolically to the same latitude at which the Sphinx and Great Pyramid are situated on the Earth’s surface, which is nearly 30 degrees North Latitude.  The lion’s body of the Sphinx measures the Unity circle of the canon as if it were measuring the genesis of the heart, the abode of the Sun, symbolized by the lion.  The Sphinx, looked at this way, seems to be heralding and describing human cosmogenesis which itself is the basis of the second birth, or rebirth in spirit highlighted in the New Testament.

3. Astronomical Unit. Earth. Human Canon

In the canon of proportions the Earth’s radius can be taken as the distance from the center of the heart at 3/4 the height (1.5) as far as the wrists, where the pulse is. The hand then proportionally represents the radius of the Moon. The two hands together measure the diameter of the Moon. Recall from earlier posts that Thoth of Egypt was said to carry – with two hands united – the Moon, the Eye of Horus and at other times Maāt. Since the Egyptians were masters of geometry, it seems clear that what Maāt, the Eye of Horus and the Moon have in common is the underlying principle of the ‘squaring-of-the-circle’, which at Chartres Cathedral was associated in turn with the Grail. I repeat, this proportional analogy is determined by squared-circle dynamics. In the drawing below, relative to 1 and 2, the breakdown of the arm/hand is .8472 and .23148. In Series E, 8472 is next to 5236, on Line 4, Columns XIV and XV. The value of the royal cubit used in the Great Pyramid with the meter, is .5236 meter. Note too that 1236 is on Line 4, as is 3236, and also the number that coincides with the Fine Structure Constant so important in physics: 1/137.036, here appearing under Column XVI as 13708. Line 4 seems to be foundational, imparting enormous stability to a variety of forces. In physics we tend to refer to Four Forces of Nature just as the Greeks referred to Four Elements; and just as psychology refers to the Quaternary as a basic structural archetype of the psyche or Self.

I found this relationship by examining the Astronomical Unit for around April 22 (1998), or say: 1.00496 AU, or about 150,339,903 km. It happens that this position is coincident with an AU of  the Sun’s Diameter × 108! And recall the Moon’s diameter fits into 1.00377 AU 43,200 times. 108 and 432 are on either side of 216 in Series A. I will not open up a discussion of the “100-factor” now, but just bear in mind that 100 is a square number and is likely referring to inverse square forces that are radius-dependent.  In any case for here, I am introducing the base numbers like 432, but I am encountering it often as 43,200. Note in the image above that the archetypal male hand is here .23148 of Unity and .23148 is the reciprocal of 4.32 which is 432/100.

Meanwhile, .23148, the relative length of the hand here, represents the Squared-Circle Modulus that we have seen in earlier posts (see P12). It is in a strict relationship with the whole radius that emanates from the center of the heart in the Thoracic Vesica Piscis out to the finger tips of the male armspan. So to get that radius it is simply .23148 × 4.66 = 1.078689 = 1.618 ÷ 1.5. This ratio, 1.078689, started to appear again and again as I proceeded. I soon found that it was one of the most important keys that accounted for fundamental differences between male and female construction. It relates the golden number, 1.618, to the center of the Thoracic Vesica, 1.5. It is 2/3 × 1.618 = 1.0786891.618 ÷ 1.5. The number in the Great Pyramid that is comparable to .23148 we have seen already is 31.416 meters and this was collapsed into the 2:1 rectangular King’s Chamber where it became its perimeter, or 60 cubits. So the perimeter of the King’s Chamber is to the height of the whole GP what the hand here is to the radius of the Heart Circle which is derived from the Astronomical Unit for about April 21-22 and the Sun’s Diameter × 108. This in turn harmonizes with 10,000 × Diameter (Earth + Moon). Just as 100 is the square of 10, so 10,000 is the square of 100.

Using the Ideal Botanical Angle for the position of the upraised arms within a circle centered over the heart, the maximum, or ideal armspan, for the male canon laid over the Astronomical Unit (about 150,339,903 km or 1.00496 AU), would be 162,170,000 km or exactly 10,000 times the combined diameters of Earth + Moon or 12741 + 3476 = 16,217 km. The appearance of this number explains why I laid the Earth over the center of the heart, to see how its internal proportions would break down. This number is interesting in view of the fact that the square of the prime ratio, 1.27324, is none other than 1.621138…This relates to the golden number as 1:1.001918…The principle here that is so fascinating is to see Squared-Circle dynamics govern both the proportion of the human hand and the proportional relationship between the Moon’s radius and the radius of the Earth+Moon combined! But that is not all.  This same proportion seems to occur between the speed of light and Capra’s nucleon speed (c/64,374 = 4.657) that we saw in earlier posts. When slightly adjusted it gives the following progression shown in Post 12:

1. 29.433199 ×  4.655832137.036 (Fine Structure Constant)

2.     137.036 ×  4.655831 = 638.016454

3.  638.0164 ×   4.655831 = 2,970.496774

4. 2,970.4967 × 4.655831 = 13,830.13091

5.  13,830.13 ×   4.655831 = 64,390.75197 (Capra Nucleon Velocity)

6. 64,390.75 ×  4.655831 = 299,792.458 (speed of light)

7. 299,792.458 × 4.655831 = 1,395,783 (solar diameter+ hot corona)

This would seem to point to an interdependence between ‘speed’ (or rate of agitation) and radius. They are inversely related. And it is this complementary, inverse relationship between proximity (or radius) and momentum that helps to bring about the self-focusing properties of mass-energy without which there would likely be no coordinated cognition. The same complementary pair also composes one of the most archetypal examples of the Uncertainty Relation of Heisenberg. This makes the self-focusing property of consciousness dynamical, suspenseful and always in flux. What generates stability is the dynamic properties of proportion that give recurrent form and pattern to what is in flux.  It is remarkable that Capra’s mean speed for terrestrial nucleons should be in the proportion of squared-circle relations with the speed of light in the vacuum. In this instance the speed of light is acting like the whole radius (Earth + Moon, 1.2732, the whole arm, the whole pyramid height, etc). The nucleon speed is acting like the hand, the perimeter of the King’s Chamber, the mouth to vertex, the Moon, etc. It is tempting to picture the squaring-of-the-circle as playing a role in the way mass concentrates itself, proportionally, relative to the speed of massless energy in the vacuum (299,792.458 km/s). It would suggest that the speed of light is an intrinsic property of the vacuum and when it is altered, geometry plays a role, literally collapsing and curving spacetime around itself. At this stage proportion becomes a property of spacetime curvature due to self-confinement. It is not simply a patina scratched upon abstract space or abstract time. It is fundamentally involved in the transformation of the spacetime vacuum. This brings us close to the seeds of metamorphosis.

Recall from earlier posts that, as we can see in the image below, the mouth of the adult is opened or resolved by the Squared-Circle dynamic of the Height circle which is 1/2 the Orbital Circle just referred to. The square with equal perimeter to the Height Circle, centered over the pubic bone, exactly cuts the mouth (side ‘hg’). So the SCM in this case (1/4.66) is the span from the mouth to the vertex (.2146). The overall radius is from vertex to pubic bone. The ‘Great Pyramid’ that corresponds to this squared-circle dynamic has base ‘cd’ seen in the male image below. This creates a 2:1 rectangle, ‘hgdc’, that is .7854 x 1.5708 in relative size.

With these proportions the Earth’s solid Inner Core fits perfectly within the female Thoracic Vesica Piscis and it fits the male Thoracic Vesica as if contained within the ribs. In the male it sits right on the 2/3 latitude or the Solar Plexus! When the Pelvic Vesica is centered over the pubic bone its upper mouth coincides with the Solar Plexus also. In the female it is just inside the Inner Core Circle. The Earth’s surface here coincides with the pulse point on the wrist. The tawny concentric coincides with the Moon’s radius.

The male Thoracic Vesica is proportionally larger than the female by a ratio of 1.078689 which I will come back to ahead, as it is a prime component in the overall principle being presented here. Not only does it indicate differences between male and female but it is also the means of conservation of energy between the genders.

In the image above we see the SCOM circle surrounding the Outer Core Circle. It coincides with the width of the Golden Rectangle, PQ.

If the SCOM circle is dropped down from the heart to right over the center of the female body (as seen below) it coincides with the same circle within which the Pelvic Vesica Piscis is inscribed, namely 1.236! In fact the SCOM circle is frequently given as 73% of the Earth radius. Here that would be 73% of .8472 which is none other than .618456. Doubled, this gives 1.2369. This is very close to the number that gives the synodical months in the year: 12.3685.

It is from this Vesica that all human beings emerge after 9 months of gestation. And 9 months is almost 73% of 12.3685. This 1.236 circle also harmonizes with the golden number at PQ or LM, as mentioned above, because 1/2 of 1.236 is 6.18, so 1 + .618 = 1.618. If we had not started with the Prime 2:1 rectangle, ABCD, and proceeded to build everything from it, the proportional value of the SCOM circle of Earth + Moon would have been completely missed. Moreover, I had to adapt the Ideal Angle of botany to the upraised arms to discover a radius centered in the middle of the Thoracic Vesica. Had I not laid this paradigm over the Astronomical Unit for April 17-22, I would not have hit on a radius of 1.078689. The whole male canon focused as if all at once through this number which I found through application to the base AU of 150,000,000 and a ‘Heart Circle’ of 161,800,000 km.

It was then that I realized Earth + Moon was about 16,217 km. Having faith in the decimal system I immediately laid the Earth + Moon over the Thoracic Vesica. Since the center of gravity and the Earth’s dipole magnetic field are both linked to the Earth’s core, it made sense to place the Earth over the heart. The heart is both pendulum-like and an electromagnetic generator. Moreover we believe the Earth’s core is mostly iron and nickel. The heart pumps blood. Blood is red due to its iron content. It is iron that transports oxygen and carbon dioxide. The proportionally perfect fit of the Inner Core is striking in this regard. The Outer Core is molten and its relative motion as the Earth spins, may generate the dipole field that passes through the Inner Core and out through the ionosphere. Who knows how much of this movement of the molten core might perhaps be affected by the SCOM circle changing position deep within the Earth as the Earth rotates on its axis.

This SCOM circle (RS above and TU further below) is also contained by the Squared-Circle ‘Great Pyramid’ that joins the circle of the Earth’s orbit to the square with the same perimeter. This circle bridges 1.5708 to 1.618. 1.618 marks the Aortic Arch of the heart and also we can see the arms rising from this level in imitation of branches of a tree.

The difference between Orbital Circle and Square (‘xbaz’ is the upper half of the square) is 2 – 1.5708 = .4292. This marks what could be called the ‘mouth’ of the heart where all the blood will be discharged to feed all parts of the body’s vascular system. It is line ‘ba’ of the inner 2:1 with base ‘xz’. Recall ‘ba’ here is 3.1416 relative to the Prime 2:1 rectangle, ABCD. We have already seen that the difference between the Height Circle and square with equal perimeter falls on the actual mouth of both male and female and is exactly 1/2 of .4292, namely .2146. We see this .2146 in the female above in two places: (a) mouth-to-vertex; (b) her hand. Note how the “GP” with base .618 + .618 = 1.236, falls on the mouth also. The apothem of this pyramid is Unity itself. The harmonies that set the opening of the mouth are not merely functional. They are not merely inevitable. They are also beautiful and radiate a mix of joie de vivre and authority. This unity that falls on the mouth is not only the diameter of the Thoraic Vesica Circle, it is also the diameter of a circle with a circumference equal to the base of the pyramid (3.1416) that reconciles square and orbital circle of the Earth with equal perimeters.

So we have the internal mouth of the heart in the Thorax arising from the ‘squared-orbital circle’  and the external mouth in the head arising from the squared height-circle! What is absorbed through the external mouth will be internally released from the ‘mouth’ of the heart as glucose, blood proteins, electrolytes, oxygen and so forth. This is some cycle that Nature has offered us as a gift! Below we see PQ of the square, PQTU, cutting the mouth. The Circle with diameter OV or the Height, is simply 1/2 the diameter of the Earth’s orbit around the Sun. So this is an important example of dimidiation. Through it the theme of the ‘mouth’ is replicated. The upper, smaller is the mouth of the body; the larger, lower, is the ‘mouth of the heart’! In the image here, the orbital path is passing right through the wrists where it intersects the Earth-Circle. And when we speak of ‘Height’ here, we are referring to the distance from the Earth to the Sun. In 1998, the exact Astronomical Unit coincided with April 4 and again around October 5th.

In the Great Pyramid we saw that this same difference between circle and square was 60 cubits or 31.416 meters and that it was collapsed into a perimeter of a 2:1 rectangle that became the King’s Chamber. The King’s Chamber has been associated with a ceremony called “Splitting Open the Mouth”. Here in our anatomy, this same geometrical configuration is the apparent cause of the split that opens the mouth or by which the opening of the mouth has been resolved. But we can see that the squared-circle dynamic also applies to the ‘mouth-of-the-heart’. It also applies to the proportions of the hands which at the ideal angle emanate from the heart – reinforcing, perhaps, the spontaneous significance of a handshake. Moreover, when we place our hands together in prayer mode over the heart, it is as if we are returning them to their place of origin. This might offer the key to the way the hands have been depicted in an Egyptian bas relief of Seti I making an offering of Maāt. His hands have been reversed on his wrists! His left hand is on his right wrist and holds the offering of Maāt. His right hand is on his left wrist and seems to invoke protection.

Crossing the hands unites them like all forms of decussation or weaving. It is probably a symbolic gesture portraying the principle of what the Hopi People called a One Heart. Maāt is the principle of harmony, unity, cosmic equilibrium and a heart that has achieved truth. Maāt herself looks as if both her hands are right hands. The right hand gives. So she is in the mode of giving life since she holds the Ankh, Key of Life. This is the life that comes from a balanced heart and is reflected in hands whose purpose is united. The helmet and Uraeus indicate that the head has been anointed; that all the chakras have been opened and that the King is offering life and truth back to the gods. In other instances the King is depicted as Thoth who carries the reconstituted Eye of Horus with both hands united. Without Maāt the Eye of Horus cannot be reconstituted.  The Eye of Horus is the wholeness that unites above and below, around and within. It is the covenant between spirit and matter.

When we bring our hands together over the heart, in a sense we are re-enacting a fundamental principle. The Thorax has traditionally been associated with both Sun (heart) and Moon (breasts). When we open our arms and hands out, like we see in these drawings, we are expressing the Moon at the square phase when separated from the Sun. But when we bring our hands in to the heart we our giving expression to New Moon when Sun and Moon conjunct. The fact that the Sun and Moon appear the same size in the sky now takes on significance. When the two hands are united, they are not just completing the Moon, they are uniting Sun and Moon in one place: the center of the Thorax.

The progressed New Moon is an internal event that offers the possibility in some for a mystical marriage of male and female. When this occurs there is both acceleration and metamorphosis often experienced as a spiritual rebirth of momentous significance for the individual. Just prior to the exact conjunction, the Phoenix seems to swallow itself into thick darkness where it is reduced to abysmal ash. The body can feel exhausted – at the end of its time – weak and even infirm. But moments after New Moon a new light is reborn and a new orientation to the universe is established. This new cycle will last about 27 years before it begins to disintegrate. In some schools the heart has been called a Chamber of Initiation. This implies that Sun and Moon are playing a role during their conjunction in the rebirth process. This second birth is spiritual and psychological in nature.

The fact that squared-circle dynamics are present in Earth/Moon relations and hand/arm relations suggests that we might be able to formulate a principle from this. The difference between square and circle with equal perimeter seems to create an opening, a portal of some kind: a place of passage. Because of the geometry involved the portal is multi-dimensional and escapes being merely a piece of plumbing – a term I’ve seen used by the medical establishment. As suggested by the image of Seti I, crossing the hands indicates that a candidate is acting with a transpersonal will through a body that has been illuminated.

Given the importance of the 1.236 circle and the squared-circle dynamic, it is quite elegant to see that very circle dovetail with the ‘Great Pyramid’ that reconciles square and ‘height’ circle in this canon, while also falling on the latitude of the golden number from which the arms spring and from which the arteries will sprout.

4. The ratio 1.078689

With the heart circle and Thoracic Vesica Piscis both centered on the latitude of 1.5 it made complete sense to relate 1.618 to 1.5. This is the same as taking 2/3 of 1.618, what I call a harmony of a harmony. 1.618 ÷ 1.5 = 1.078689. As it turns out this has become one of the most important of all ratios. Not only is it the radius of the heart circle, but it is the width within which the male Thoracic Vesica Piscis is inscribed.

It is also the ratio between the Solar Plexus and the Navel: 1.3333 ÷ 1.236 = 1.078689. This latter ratio is just as significant as 1.618 ÷ 1.5. This region deals with the assimilation and refinement of the very nutrition that the liver will give to the heart to distribute to all parts of the body. The Solar Plexus is also at the center of a circle formed by the short length of the Prime Golden Section (2 – 1.236 = .764) . Here it would have a diameter of .764/3.1416 = .243188. This circle is perfectly contained by the Thoracic Vesica. It contains kidneys, adrenal glands, pancreas, a lot of the liver, much of the spleen and stomach as well as the duodenum. Deep emotion, anger, instinct and anxiety seem to arise from this center. It is very powerful and reflects the health and state of the whole system. It seems to be the center of some sort of instinctual guidance system.

What is great about 1.5 is that it receives from both below and above. Physically it draws down air from the lungs above and nutrients from the small intestine and liver from below. Each cell will depend on both oxygen and glucose in order to function and in order to maintain consciousness. There is an analogy to the Cathedral of Chartres here. If you stood a human form on the latitude of the equator with the vertex on the North Pole, the latitude of 1.5 where the heart is would coincide with the latitude of Chartres! The source of Chartres’ incomparable energy was said to be both above and below. Moreover, in the Middle Ages a pilgrimage route had been set up that apparently started at Compostela (Spain) and proceeded to Toulouse, then Orleans, then Chartres, then Paris, Amiens and finally Rosslyn, Scotland (see Rosslyn, Tim-Wallace Murphy and Marilyn Hopkins, 1999) . Chartres was apparently the cathedral that corresponded to the heart and the heart chakra. Exactly as I experienced it when there, it was known as the center of love and compassion and tended to awaken those aspects of our nature in those who visited it. It was considered to be the Abode of the Sun. It was given the color green, symbolic of initiation and rebirth. In my experience red, gold, blue and black are also closely associated with initiation and rebirth, so color must be looked at interactively. Though blue seems to be particularly important when it comes to the fortuitous mystical marriage of male and female.  I’m not sure that this coveted inner experience would occur at all if the well-known blue did not appear. It is a blue like no other blues. It is a direct, inner blue as if arising from the void directly, a direct radiance. It illuminates from within and by synchronistic resonance, or perhaps a quantum coherent radiance of some kind, it fills all parts of a chamber of initiation as if it were a hologram. In any case it is an inimitable blue as if obeying a cosmic law that the Egyptians associated with Hathor, wife of Horus. Hathor was more like the Christian “Mary” than any other Egyptian Neter with the possible exception of Isis. Not surprisingly, Chartres is more famous for its blue stained glass windows than it is for green. All to say, 1.078689 is particularly important as it seems to point to an inner refinement – a spiritualization, perhaps, of the inner activity of the body. And this suggests a law. A law suggests a potential. The body seems to be a natural transformer. Proportion seems to be the way it transforms. But we must feed that potential properly! We cannot feed it artificial foods and chemicals or the very architecture by which it has evolved will be damaged and its higher, subtler gifts, squandered. The same could be said of knowledge. It helps to feed the mind and soul truth. That is why I regard ratios like 1.618, 1.236, 1.27324, 1.5, 1.309, 1.62, 1.3333, 1.2, 4.66, 3.66, .381966, 1.078689, etc, to act as medicaments for the mind and soul. They act like catalysts, mantras, seeds all wrapped up in one. The span between 1.618 and 1.5 appears to house the thymus gland that begins to disappear after age 40, but may be hinting at a higher expression of that aspect of the heart as one ages.  Since the ratio 1.078689 also appears to establish a gimbals effect that enables us to walk upright and also defines the lower limit of male sexuality when measured from the crown or vice-versa, it is quite significant that it is also the ratio that expresses the prime difference between the male Thoracic Vesica Piscis and the female Thoracic Vesica! One important aspect of this 1.078689 ratio can be linked to 108/100, two factors we saw above.

(1.237324)² ÷ 1.081.5 = 1.621138 ÷ 1.08 = 1.618 ÷ 1.078689

From this simple formula we can see that at 1.5 or 3/2, the same proportion that governs the creation of a Vesica Piscis and also governs male blood pressure that will be exerted against the Aortic Arch, acts as a point of convergence between the square of 4/pi (1.6211389) and the golden number, 1.618 through 1.08 and 1.078689 respectively.

A width of 1.078689 is too large for the female Thoracic Vesica and a radius of 1.078689 is also too long for her up-raised armspan.  This brings us to the next principle.

5. Conservation of Energy, Function and Proportion between 1 & 2 and 1.236.

It seems that a conservation law is at work among the differences between male and female. What is conserved is the overall relationship between unity and 1.236 which is contained within the relationship between 1 and 2 so that 1 × 1.236 = 1.236 = 2 ÷ 1.618. The 2 by 1.236 golden rectangle is acting like the limit of a Fibonacci Series. The relationship between width and height cannot be changed. It has reached a limit; that of the golden proportion, here, 2/1.236. So if the male Pelvic Vesica is proportionally less than the female, the conserved energy will show up somewhere else.  One immediate place it will show up is the Thoracic Vesica Piscis and slightly longer arms.

It became apparent, after a little trial and error, that a very reasonable male Thoracic Vesica Piscis would be 1.078689 and that by the overall conservation law it made sense that the female 1.236 Pelvic Vesica ought to be reduced in the male by about the same amount, namely: 1.236 ÷ 1.078689 = 1.145898. With Unity of the Prime 1:2 as “1” the male Thoracic Vesica will then be 1.078689 ÷ 3 = .359563. And the male Pelvic Vesica Piscis will be 1.145898 ÷ 3 = .382, a number that we are now familiar with as it is the golden section with .618 of a prime .5 x 1 or 5 x 10 rectangle when it is 3.82 and 6.18.

Above we see the male plan without the figure in place. We can see in this image that point “Y” has assumed special significance and we should not be surprised to see Christ at Chartres on his throne within a Vesica Piscis. If Chartres truly represented the place of the heart on an ancient pilgrimage route known to our ancestors, then one imagines that this vesica at the Royal Portal of Chartres was intended to represent the heart itself. To master the heart, the abode of the Sun, is to become King. We might also suggest that we are all born from the physical mother through the Pelvic Vesica, but we are reborn in spirit through the Vesica that houses the heart.

Below I have put the figure in place and have highlighted both vesicas. It is important to note in this instance that the male Pelvic Vesica Piscis is both 1/3rd of 1.145898 and it is also Unity or 1 ÷ 2.618 = .382. 2.618 is the square of the golden number and offers stability as well as an acceleration.

This width within which the male Pelvic Vesica is inscribed appears naturally in Series E on Line 6, Column X as 1146, below 382 and 764, the numbers that create the 24-method for squaring the circle that we saw in an earlier post.

Each circle that composes the Pelvic Vesica is 2/3rd of 1.146 and so has a diameter of .764, the diameter of a circle with circumference, “24”. And when .764 is collapsed into a circle it forms the Solar Plexus circle centered on 2/3 the height!

The 24-method can be seen again below. It is constructed through the golden section of a Prime 5 x 10 rectangle so that 3.82 becomes the radius of a circle with a circumference equal to square (6 x 6) and rectangle (4 x 8): ‘three tables that bear the Grail’. It will complicate the figure too much to lay these three tables over the main figure but I will do so in another forum. It was important to mention the link to 7.64 and the 24-method here since 3.82 has shown up as the width of the male Pelvic Vesica Piscis. His hips are as harmonious as the female, just different. He is a bit more stream-lined since he does not have to gestate a child for 9 months.

To repeat, the radius of the circle shown above is .382 or 3.82 for a 5 × 10 rectangle. In a 10 × 20 Prime 2:1 rectangle that I used for drawing all these major figures, this means the 3 ‘grail tables’ derived from the 24-method can be inscribed easily in the upper half of the body over the golden section of a 5 × 10 rectangle. This point coincides once again with the Aortic Arch or top of the heart – the latitude from which the arms spring as well as the Common Carotid Artery and Subclavian arteries. Meanwhile 1/3rd of 1.146 gives .382 or 3.82 in the drawings. This is also the rather special distance from the Aortic Arch to the Vertex or crown of the head (2 – 1.618 = .382). It is also Unity ÷ 2.618, while also being the radius of the circle with perimeter equal to 24 from which we can derive square and 2:1 rectangle with equal perimeter easily. Once again it has uniquely exceptional harmonies. In the subatomic world of quantum resonances at the nanometric scale I strongly believe that the tubulin protein dimer subunits that compose microtubules, are always in association with ‘parent’  5 × 10 nm structures that they relate to through the golden section of the parent  5 × 10. I suggest this might contribute to geometry-based states of synchronistic resonance that further contributes to quantum coherence at this scale thus linking brain matter to consciousness in a way that is both patterned and asymmetric simultaneously. In micro-imaging I have seen 50 x 100 nm structures, but I am currently not aware of where  5 x 10 nm structures might be hanging out.

So to summarize this principle of conservation between male and female, it seems to me that a limit has been set by the golden rectangle, relative to 2 in a 2:1 rectangle. This suggests that ratios like 1.236 and 1.618 are involved in curvature, whereby a system feeds energy back into itself and in this way builds up energy, interacts with itself and so produces a sense of a conscious ‘now’ through this self-interaction. In this manner, rather than dissipating energy, it conserves energy and in waves amplifies that energy. Any change of state affects everything else by degree.

When the Egyptians depicted the proportions 1.236 x 1.618 in certain meaningful images they were demonstrating an understanding of this important law of conservation/transformation. Through laws of harmony contained within a fundamental enclosure, the ultimate metamorphosis takes place, symbolized by the eyes that frame the Chen sign. The ratio between 1.236 and 1.618 is 1.309 that appears on Line 1 of Series E and heads up the all-important XIVth Column. The presence of the harp in this image of Ra-Horachty strongly emphasizes the role of harmony in facilitating the metamorphosis depicted under the arch of heaven at the top of the image. I will just repeat here that there are 9 strings probably symbolizing the Great Ennead or Nine Bows, Nine Monarchs, Nine Powers. But there are 10 tuning keys that act like the vertebrae of the spine descending from the head as if the harp owes its genesis to the head and is symbolic of how the spine functions: as if it were a musical instrument. The 10th key probably represents the 10th Neter, Horus and the ultimate goal of ancient Egyptian religious culture was the rebirth of the Eye of Horus. This image is worthy of an entire analysis. And it is framed by 1.236 x 1.618 which depicts the complete cycle: from the incarnation of Atum-Ra through the head and the Great Ennead, followed by rebirth or the second birth, and culminating with the final resurrection as Horus, the 10th. The play on 10 is the return to a new ‘1’, so it is where Atum and Horus meet again but on a new basis. ‘Man‘ is what occurs between Atum and Horus. (Incidentally, I have re-colored this image selectively in order to highlight specific themes and repair a little damage.)

With the temple practice of yoga, the idea was to conserve and accumulate energy through what the ancients called Maāt, a specific form of ‘meekness’, by which the accumulated energy could open up the higher centers of one’s potential being. Maāt was also associated with the laws of harmony by which cosmic equilibrium was effected.

In the male, one of the most most striking differences from the female is the fact that the mouth of his Thoracic Vesica Piscis falls on his nostrils. Note how the nostrils are being emphasized in the Egyptian image from Hour Ten of what is in the Duat above. The male Vesica is inscribed within a width of 1.078689, whereas the female Thoracic Vesica is inscribed within Unity of the Prime 2:1 rectangle. 1.078689 is, as already stated, the harmony of a harmony, as it is 2/3rds of the golden proportion, 1.618 or it is 1.618 ÷ 1.5 = 1.078689. In the canon this is the top of the heart divided by the middle of the heart which is also the center of the Thoracic Vesica Piscis. 1.078689 is also the radius of the Heart Circle centered over the same point: 1.5 from the soles of the feet. Because the male Thoracic Vesica is proportionally slightly larger than the female, the mouth of the Vesica reaches the nostrils instead of the actual opening of the mouth. In this image here you see the square and the golden rectangle pyramid converging precisely on the mouth the way they do with the female. But the mouth of the Thoracic Vesica Piscis seems to flare the nostrils. It seems to link nostrils to navel.

It is worth pointing out that when I first started to do yoga, it was a spontaneous occurrence. It was not easy, but entered my life as a necessity. I was a tense, restless individual, very raw and very disturbed. I felt like a repository of lies and had multiple allergies to add irritation to irritation. After two 4-day fasts (water only) in the same year in New York City, I gradually drifted toward yoga following a few false starts. The fasts were not just successful. It is no exaggeration to say that I could not have proceeded with the yoga without first correcting my diet. The first fast was a revelation. I owe a great deal to that fast and the moral support offered by Carlton Fredericks in New York who supplied the conviction that a fast was positive and important. It helped restore my nervous system and encouraged me to fix up my convoluted posture!  Fredericks was frequently on the radio at that time as well, so the support was social. After the first fast my body felt luminous and my heart felt light and unburdened. Some instinct gradually lead me to alternate the breathing through the nostrils once the yoga got underway. I would pinch one, inhale and then hold the breath. By alternating nostril by nostril I became aware of a powerful stimulation to both sides of the body. Eventually I ended up holding my breath for very long periods of time. I had to learn patience. I had to learn to quiet my mind. At the peak of the yoga cycle I was holding my breath for as long as 2 minutes – again by some unknown instinct. I do not know why I started this practice of holding the breath. Initially it was a deep relaxant that allowed me to correct my posture by loosening up overly tense muscles. It also enabled me to get control over patterns of anxiety that dominated a period of about two years. It also caused me to control my restlessness which included restless thoughts and ambitions. Only later did I learn that this alternation of the nostrils was an established practice known for hundreds of years! In the image you see the exact convergence of the two Vesica Circles just at the nose. Then the two circles diverge as if into each nostril, suggesting that the geometry itself promotes the alternation and that it is the geometry that generates the instinct to breathe in this fashion. The Vesica itself wants to be filled with life force and may hold onto the breath in order to maximize its capacity gradually. Moreover, breathing like this through the nostrils stimulates the olfactory apparatus one side at a time. The olfactory system dominates the serpent and it is the serpent force (kundalini) that is being awakened from the base of the spine in certain forms of advanced yoga. Ironically, the higher self springs from the simplest, most primitive part of our being. By accepting the serpent within, it can be transformed. By repressing it, it becomes monstrous and compulsive.

In the long run the effect was powerful. It gradually integrated and flooded, or activated, my entire system. When I see this configuration of the male Thoracic Vesica, I immediately wonder if it is an innate instinct in the male to draw the kundalini up from the spine because of this ‘pumping’ action of the Thoracic Vesica. If circumstances build up sufficiently in specific individuals they may find themselves predisposed by an inner necessity to draw the kundalini up like drawing a ‘fiery water’ up from an unknown well. In the enlargement below we get the feeling that the Principle of the Pyramid accumulates the ‘fiery water’ in that well. The sacrum is the well itself and the spine is the well shaft. The breathing acts like bellows fanning embers into flames. Initially these flames will ‘burn the Phoenix to ash’ causing considerable anxiety in the aspirant. It pumps and fans the ‘fire’. It strengthens the ‘winds’ that circulate through the body and energize the double (Egyptian “ka”). The breathing techniques of yoga were known in China as the circulation of the light, the ‘Chi’. This led eventually to the production of the “golden flower”. In Egypt, where the spiritual quest was on a scale grand enough to invite misunderstanding everywhere, the ‘son of a god’ principle was universal. The association between the raising of the Min, the serpent force, the light and the golden flower is stated explicitly: “…I am a god and the son of a god, I am a flower that issued from the Nile, a golden flower that issued from Iseion…” (PT 544)

In India, around 500 B.C., Gautama Siddhārtha ‘Buddha’ also used a flower as the symbol of enlightenment and proceeded to set up places where people could go to learn how to raise up this inner power so that the lotus could bloom from the head and heart. Once you have steeped yourself in the Pyramid Texts long enough and grasped their use of interactive symbolic intent, it becomes clear that the golden flower of Iseion is the Eye of Horus which the candidate, the ‘son of a god’, has become. He becomes Thoth. He becomes Shezmu, the winepress god, mysterious of forms; he becomes the ‘spirit-in-the-Dndrw-bark’, which may be what the image-maker at Chartres was showing in the sculpture of the Ark of the Covenant at the North-west entrance.  The Ark is probably here carrying the Eye of Horus, the whole secret of the ancient world; its whole reason for being: the principle by which enlightenment becomes actual and not merely the stuff of fairy tales or myth. Here, ‘gods’ or ‘neters’ have become completely integrated. One has transformed illusion into truth and being. In Egypt this was the Eye of Horus.

In the image below which we have seen before with the magnetosphere, it is important to note that when the whole image is contained within a 2:1 rectangle, the section above takes it to 1.118 which is the same proportions as the side walls (long sides) of the King’s Chamber in the Great Pyramid. It is possible in the image below that the ‘image maker’ is using human practices of yoga as a symbol to portray the strengthening of the ‘wind’ that circulates through the Pyramid just as it circulates through the human body and ka. This may be telling us what is being accomplished by the construction of the King’s Chamber in the Great Pyramid. It is also an important coincidence that the height of the King’s Chamber is determined by ½ its own diagonal giving 2.236068 ÷ 2 = 1.118. The diagonal of the end wall with width “1” and height “1.118” is none other than 1.5. I have shown this in previous posts.

This is the prime formula for determining the opening of the mouth in both male and female canons. 2 ÷ 1.118 = 1.7888 (see previous post).

When it was time for the double to be raised, or undergo its resurrection, the Egyptians performed a concomitant ceremony called “Splitting Open the Mouth”. An adze of iron was used for the mouth. The ceremony was important, but at the same time it is crucial to point out that it was only a parallel symbolic gesture performed upon the mummy and/or a candidate for the second birth. What was really going on was the ‘Eye’ was being ‘split open’. And the portal to the Netherworld was being ‘split open’. The “King’s Gate” was being split open. The egg was being broken by the ‘harpoon of Sokar’ made of iron. All this is in the Pyramid Texts. And in fact they meant that the magnetic field that had been ‘sharpened’ in the Broad Hall was opening the mouth, the Eye, the Cavern, the egg. In the case of the King’s Chamber, that sharpening (self-focusing resolution?) was associated with a 2:1 rectangular floor and ceiling and an end wall that is 1 × 1.118 with a side wall that was 2 × 1.118.  The Christian Middle Ages called the 2:1 Table the “mystical table’ and “The Table of Revelation” for good reason. They inherited this legacy from the Egyptians. One way to describe the function of the King’s Chamber in terms of symbolic geometry is to say it was designed to split open the mouth of the god (neter). This is the portal to the Netherworld. In the case of the King’s Chamber two long shafts were built that run down from the apothem to the north and south walls of the KC in the shape of adzes. The south one targeted Orion’s belt and the northern one targeted Thuban of Alpha Draconis, the pole star at that time. These shafts were helping to build up energy in the King’s Chamber (Cavern of Sokar) within which a final metamorphosis was to take place. The metamorphosis was into spirit state.

The Pyramid Texts discuss catching the efflux from Orion. But other texts mention catching the perfume of the Eye of Horus that comes from the Horizon of Amun. It was caught in a vase as if the vase were the earliest form of the Grail that begins the incredible transformation that leads not only to the birth of consciousness but to the enlightenment  of the human spirit. So it is as if the King’s Chamber were the ultimate alchemical retort that was catching and accumulating a variety of energies to ‘split open the mouth’. In Utterance 422 it is said: “O King, go that you may be a spirit and have power as a god, as the successor of Osiris” (PT 752). “I am this Eye of Horus which is stronger than men and mightier than the gods. Horus lifts me up; Seth raises me.” (PT 1147-48)

“He has appeared upon the Stone, upon his throne, he has sharpened the iron by means of his spirit…I open for him the gate that keeps out the plebs…your bread is the t-wr-loaf, your bread is in the Broad Hall…O King, raise yourself as Min….” (PT 1945-1948)

This passage immediately invokes the image of Christ on his throne over the Royal Portal at Chartres framed by the Vesica Piscis and surrounded by the Four Evangelists who seem to represent the four Fixed Signs of astrology: Taurus, Leo, Scorpio and Aquarius.

Min is the principle of earthly power associated with the Bull, hence Minotaur (Taurus). It has been raised up and redeemed. It becomes the power that strengthens and sharpens the iron and the wind (magnetic field). This becomes nourishment and energy for resurrection. The symbol is both ‘bread and wine’ which possess a shared capacity to ferment and ‘raise the spirits’. So they are intended symbolically. The bread and wine go back to the Egyptians, I repeat, as symbols. The symbol has spiritual intent and has nothing to do with the physical practice of drinking wine or eating bread. Through yoga, the body can accumulate comparable energies whereby it opens inner gates, inner portals that widen the spiritual being of the practitioner.

“This is this cavern of yours, the Broad Hall. O Osiris this King, which brings the wind that it may strengthen the north-wind and lift you up as Osiris this King. The Wine-press god comes to you bearing grape-juice….” (PT 1551-1552)

The Wine-press god is Shesmu known to be related to the inner powers of the Eye of Horus – among other things – and mysterious of forms. To say he is the winepress god is to say that he is the mysterious principle that acts within the Benben Stone, the power to accumulate, ‘ferment’ and rise. Once again this raising is related to the Egyptian principle of resurrection as well as the true principle of the Crown, the throne, that which links above to below and vice versa. But they did not say, as the Christian version does, that it is a bodily resurrection. They explicitly state at other points – again and again – that it is the ka, or double, that is raised up by these winds that have been strengthened and “sharpened”. The north in this instance refers to the fact that the dipole magnetic field enters from the north where there is an excess of electrons as well as a stronger gravitational acceleration than that encountered at the equator. Yoga also sharpens the winds of the body-temple. This strengthens mind and health if done properly.

Let’s just take a quick glance at the head in profile to see what the construction of the olfactory complex looks like – recalling that the serpent brain is 95% olfactory in character. The ‘serpent’ is what is being raised within the spine. The serpent represents what is earliest, most primordial, most basic. It is highly dependent because it is cold-blooded.  The Hopi People called snakes ‘their brothers’. They performed sacred ceremonies with snakes – some of them poisonous – to discover their own spiritual status – namely, which leaders were One Hearts and which ones had ‘split hearts’, indicating ulterior designs born of fears from having departed from the will of the Creator. So the serpent in us represents what is simplest, purest, most balanced and uncomplicated.

When we examine a cut through the head that slices the middle of the olfactory bulb we see that it divides the whole section by the golden section.

As we move backward to the White Anterior Commissure shown here in orange we see that the golden section moves up so that the olfactory complex from bulb to WAC – where olfactory ramifications cross over to the opposite side of the head – moves with the golden section. It slopes up with the sloping skull, maintaining the golden division within the rudimentary olfactory complex! I have indicated the bulb as “1” and “1.618” and the WAC as “.382” and “.618”.

In the close up image below you can see the prominence of the olfactory nerves that pass through the perforations in the cribriform plate of the ethmoid bone into the olfactory bulb. They resemble living roots and in some respect that is what they are. An intensification of the breathing, by alternating the nostrils, stimulates this ‘olfactory root system’. Electrical signals enter the bulb and pass down the tract. Some go directly to the opposite bulb without any other detour. It is as if the olfactory bulbs were a brain onto itself. The signals get from bulb to bulb via the WAC. This ‘primitive’ part of our system activates the entire spine and awakens the serpent force that can also assume other names. The idea is to transform it until it obtains ‘wings’, the ‘winged wouivre’ of Moses at Chartres; but also the ‘golden flower that issued from the Nile, from Iseion’. I should note that early on in the embryo, GnRH precursor neurons migrate from ahead of and below the bulbs along little nerves (medial to the olfactory tracts) called Nervus Terminalis to positions in the hypothalamus that are above the optic tract and behind the olfactory. These neurons will eventually stimulate ovulation. As I have said already, the male does not have an ovulatory apparatus. But he does have an inner cycle that in the past assumed the form of inner spiritual initiations that integrated the spiritual aspect of the male soul, the anima. These initiations were like internal acts of self-fertilization, greatly enhancing the individual’s understanding of his entire being – including the feminine side of his soul. The ‘olfactory brain’ offers the means of returning to the primordial embryo, from which rebirth becomes an internal reality. The clock that he obeys is the same as the female. To be exact it will take about 29.53 years to complete each cycle: Phoenix to Phoenix, pNew Moon to pNew Moon.

Notice below how the WAC resembles a mouth when viewed from the front. If the whole diameter of the brain at this cut is 1 the WAC (orange) is approximately .382 which is the same proportion as the male Pelvic Vesica within the width of the Prime 2:1. The width of the Lateral Ventricles which produce about 50% of the total cerebrospinal fluid (CSF) is .236 and .382/.236 = 1.618. The central WAC is part of a .236 square with the lateral ventricles at the top of the Third Ventricle that produces 10% of the CSF. In this image within the circle, the golden section falls on the optic chiasm under the WAC. But WAC and Lateral Ventricles share a golden rectangle as if they had been central to the brain’s evolution from the beginning. The individual who raises the serpent in the wilderness is, in a profound sense, returning to the origin of his being and there must confront disproportionate powers that will have to be wrestled with and transformed. This is Goliath, the Minotaur, Seth, the winged beast encountered by Carlos Castaneda during his experiments with the sorcerer Don Juan.

The more I looked into Egypt the more I became convinced that the Pyramids were designed to fulfill the spiritual quest of the ancients. They were designed to both strengthen and sharpen the winds – meaning the electrical and magnetic winds that the double could attract and sharpen more.  By ‘sharpen’, the Pyramid Texts probably mean focus, self-focus, resolve, or transform into the Eye of Horus which appears as a sphere – not unlike the overall image of an ovum. In fact the Eye of Horus acts a little like the ovum within which the first marriage of male and female ignites the birth and growth of the zygote. The Eye of Horus is the vessel of a mystical marriage of male and female, above and below, behind and in front, body and spirit, numinous and overflowing, like descriptions of the Grail.

When you compare the image above with the images below it seems clear that the Uraeus is at the same level as the White Anterior Commissure as if this were the true mouth that was being split open in the Broad Hall, the Cavern of Sokar or Osiris by the process of sharpening, or heightening, or resolving the magnetic field that the cavern has accumulated. But it seems clear that this is the King’s Chamber and that the Great Pyramid must be enclosing the head of Atum, or Geb, or Seth, or Horus, or Ra. It is as if the head of the Sphinx were announcing the opus behind it. Hugues de Payens of the Templars had three black heads on a gold field for his Côtes of Arms. The cube is the perfect container of the spherical head. The Pyramid envelops it. If the Cube is Unity, the Pyramid grows organically from that cube – that head – by the golden number. There are two implications that can be drawn from this. Both olfactory and the golden number are implicated in the ancient, mysterious and legendary ‘raising ceremonies’, still preserved today in organizations like the Masons. These are internal experiences that produce internal transformations: qualitative changes in one’s being and in one’s sense of participating in a deeper frame of reference beyond the boundary of the merely physical and its multifarious appearances. The archetypes reveal themselves; become known and integrated. The serpent is assimilated and no longer behaves like a split-off function projecting irrational terror out into the natural and social milieu; compulsive appetite; insatiable greed, etc.

This places the WAC in the King’s Chamber, and the Uraeus comes out from about that level.

The Coffer is located just under the WAC as if the WAC were itself the principle that sharpens and raises the double from a prone position to an upright position.

One extraordinary coincidence that might reinforce the possibility that the Pyramid builders were enclosing the principle of the head – so dear to Plato in the 4th Century B.C. – is that in this scheme the Subterranean Chamber corresponds to the place where the Common Carotid Artery leaves the  all-important Aortic Arch that registers the state of the blood and heart and is linked to both vocal cords and medulla oblongata. The Queen’s Chamber in this scheme receives the information from the Aortic Arch via the Vagus Nerve, which terminates approximately where the mysterious “Great Niche” is inside the Queen’s Chamber. In the anatomy of the Medulla Oblongata this might correspond to the nucleus ambiguus where diverse functions converge – some of them unknown. For the double, this might be the origin of the name David, which symbolized the ancient spiritual achievement of linking the head to the heart. When the Hopi People spoke of a One Heart they meant he whose heart and head are united, acting together. When Carl Jung was visiting the southwest of the U.S. in the 1930’s I believe, he met a Pueblo Chief named Ochwiay Biano. Biano told Jung the Pueblo thought the whites were all mad. Jung asked him why they thought all the whites were mad. Biano said because the whites think with their heads. Jung said “of course we think with our heads. What else do we think with”? Biano replied: “We Pueblo don’t think with ours heads. We think here.” And he pointed to his heart. The point seems to be that the restless scheming of the mind divides or fractures the heart and fills it with ängst, fear and anxiety.

The Pyramid is directly related to the purity of the Eye of Horus in the Pyramid Texts. Probably the Eye was reconstituted by the Pyramid. What better means to sharpen the iron than with the principle of the Eye. According to this image, it also seemed to link the head and heart, thereby allowing them to go together. In this sense, the spirit was freed and could feel part of the entire all-embracing net of existence.

So it is well worthwhile to note again the morphological similarity between the Earth’s magnetosphere and the eye. In the image below I have laid the 24-method for squaring-the-circle very precisely over the Eye. The 3 ‘grail tables’ go far to account for the function of the lens of the eye. This reinforces the conviction that squared-circle geometry is part and parcel of fundamental self-focusing properties of the eye, but undoubtedly also perception in general and the power of cognition itself.

Below we see the morphological similarity between the magnetosphere and the serpent or lizard:

King’s Chamber and Tradition of Rebirth

There is no doubt in my mind that despite all hearsay, all opinion, all belief, all convention, the King’s Chamber in the Great Pyramid of Gizeh was not used as a conventional tomb by anyone. The tradition of rebirth that goes by many names, has left a trail of misunderstanding behind it through no fault of its own. People are more enamored of the idea of an extravagant tomb – a final resting place for the Pharaoh’s mummy and his personal jewels – than they are of the enterprise during life that concerned his accomplishment as a spiritual being. If we ourselves do not aspire toward the regeneration of the soul – let alone the regeneration of an immortal spirit – we can hardly be expected to be interested in such an aspiration in others: not even a Pharaoh. In fact we may disregard such a quest as bogus. All we are really interested in is the fabulous life of the King upon which we project almost anything we wish. We have more or less done the same thing with Christ. Moreover, nailing his near-dead body to a cross with a crown of thorns jabbing the sacred line of the ancient Egyptian headband or crown, does little to improve the principle and capacity for all of us to regenerate and strengthen our spiritual potential.

Ancient Egypt has been poorly represented in the West – until we get in trouble. Then once again we pry open Pandora’s Box seeking wisdom and from the box pours a cornucopia of beauty, mystery and multiple enigmas. There are some questions that cannot be answered. Everything depends upon the way the question is posed. Then the question will open gates. It is the quality of the journey – the way the questions open the heart – that matters. The answers are existential; the flow of life that they open. Ask the right question and the transformation inevitably begins. Mastering the cycles is the trickiest part. We all love creation and despise destruction, but the two will always be complementary on Earth. Extraordinary sophistication is needed to transform them into one thing only, what the Egyptians called Unas; what the Chinese called the Tao or Great Ultimate.

The turning point in my amazingly well-ordered 1980 dream, took place the instant I stopped demanding and instead asked a question in complete supplication. But this humility was simply a natural part of the ritual. I had no choice but to be meek. The question triggered the conversion. Asking this question was probably the surprise of my life.  It has not really helped me live my life better since. If anything it has only made my life more burdensome. Its content is bound to be controversial, not because it is innately so but because it will be interpreted as so once metaphors turn into the ‘swords of projection’. It touches off deep layers in all of us: layers under pressure – often repressed and often unable to bloom. What matters to me is that prior to the dream I lacked an inner being. I was a drifter, wild, inconsistent, lost. I was pretentious. I was cut off from my roots. I could not put down new roots in school, in Nature, reading, acting.  My inner self was aggravated and reminded me of a room without lights. I moved through life with an exaggerated passion but no real compassion. I could not be still. I could not shed my masks. I could not discriminate with guts. The quality of the dream was spectacular. It was and is the immeasurable gift. It was like relining a well so that the ground water that was there all along could finally be drunk and enjoyed. I didn’t seem to have done anything to deserve it except keep a journal in which I wrote down the truth every day as it happened to me.  I let the truth of my life heap up within: like fermenting grapes into wine. But I accepted the gift instantly because I had to and because it was unmistakably genuine, unmistakably overflowing with gratitude; unmistakably joyful. I had been spiritually so starved that I had no choice but to allow this rebirth to refresh my entire system. With this gift I cannot advise anybody. I never could, I just wanted to, even though I knew better. But what I can do better than before the dream, is share. I can let others be who they are a little better than before. I can appreciate their rights, their loves, their fears, their luck, their misfortunes, their gifts and their limitations.

As I write these words, the clock has come full circle. It is almost 29.53 years later. Suspense again crackles in the air like that dense flashing that precedes a violent thunderstorm. Every cell quivers in an ocean of electricity even as my body seeks to wither into another cocoon. Does a second birth offer a bit more faith than those days when everything seemed stretched into a wasteland?  I think so. I just don’t know how to measure it. The measure is life itself which is now being shared with billions around the planet. It is a life well worth protecting with thought, strength, integrity and collective sophistication.

May 4, 2010

The Gateway of the Human Body

In 1995 I took another concentrated foray into the female canon. I made some real progress, but was still disturbed that several things were off. Several features were entirely unaccounted for and this had the effect of keeping my mind dim. I was amazed how resistant it was to revealing itself. What I recall, however, was that the new discoveries were momentous for me personally. There are too many details for this post. But this implied that I could not give up the pursuit. Nor could I account for my perseverance. Why did I want to know the geometry of our form so badly? This crossroads taught me that I didn’t know myself. I realized that all I could do was discover myself everyday. I had some sort of penetrating belief that seemed to have me in its grip: the human form is not an accident. It was the way it was for a variety of interactive reasons. I knew a fundamental geometry was guiding it and I also knew that the same geometry influenced man’s spiritual longings. I believed the ‘uncertainty relation’, presented around 1925, was contained within the geometry.  What was measurable and immeasurable co-existed in one system. This is an aspect of our duality. Because I was initially working at such a small scale with pencil and sketch pad, precision was critical. If I was off the tiniest amount it looked ugly, wrong, dysfunctional and even worthless. That fall I built up a very complex geometry and yet still, it lacked something fundamental. I did not get discouraged, however. I had faith – a faith that I did not have in any other field. I simply believed I was going to find something that would make a difference. When the work was interrupted in a rather disastrous way from 2006 to 2009, I admit my faith was shaken. But even so my belief seems to be inextinguishable. Set against the difficulties of my life, I admit, this belief is mysterious, like the relationship between a mother and a child.

The Challenge

Developing this work was a long meandering road where things continuously went in and out of focus. Sometimes the whole focus would go completely and the work would stop for months. But it was always in the back of my mind and I was always alert to fresh clues that might help me to account for some feature that could in turn be perfected. This was especially the case with the arms and hands. I was looking for a principle. I knew the brain was dedicating a disproportionately large number of cells to the function of both mouth/lips and hands/arms. In order to harness so much energy that was then applied to multiple tasks requiring intricate skill, I felt the geometry of the hands, arms, shoulders, but also the mouth, lips and jaw, had to be exceptionally flexible, adaptable, harmonious and effective. What would that be and why was it eluding me? Moreover, these activities involving intricate patterns of muscle action, operated through feedback loops that were being managed by the brain and in fact the whole head. Something had to be capable of this. For several years I had been quite taken by what I came to call the Squared Circle Modulus, a silly term really. I was interested because I knew that the speed of an electron in the First Bohr Radius (ground state) was determined by the Fine Structure Constant. Essentially this number 1/137 was itself determined by dividing the square of the fundamental unit of electric charge by the product of the speed of light, Planck’s Constant and 4π × electrical permittivity in free space. So it looks like this:

I understood this value was important in regulating many functions and many relations in the universe including biological interactions. This latter cannot be emphasized enough. So this gave a speed of about 2188 km/s at the ground state of the electron in the First Bohr Radius. 2188 is the product of the Squared Circle Modulus raised to the 5th power, so, approximately:

4.65583 x 4.65583 x 4.65583 x 4.65583 x 4.65583 =  c/137 ~ 2188 km/s

This prompted me to start a progression – it mattered little initially what the progression might signify. All that mattered to me was that the SCM (~ 4.66 refined to 4.655831) was acting like a vital coefficient. It seemed to be as important as the golden number, only it seemed to be regulating ‘speed’ (momentum) relative to the vacuum and was relating the constant that is relevant at the quantum scale to the constant that was relevant to relativistic physics. One immediate consequence of this speed or momentum was that it also set the diameters of things. For example if you divided the Sun’s diameter by 137 you get the diameter of the White Dwarf, Sirius B, that has collapsed from 1.05 Solar Masses to a white dwarf that is super dense but no longer producing enough light or photons that can counter the gravitational force of the mass of the star. Degenerate electrons and their speeds as well as electrical repulsion among each other have blocked further collapse of the star. But overall its previous hydrostatic equilibrium has been replaced by a new equilibrium set, at least ostensibly, by the Fine Structure Constant. So ‘speed’ is part and parcel of radius, or diameter, or degree of separation. The small heaps up to the large; quantum effects heap up into classical effects; microscopic heaps up into macroscopic and they remain interdependent.

By 2000, I felt that one key ratio that described this reciprocity or mutual interdependence between quantum mechanical and classical, or small and large, was the SCM, set around 4.6558, but with built-in variables.

When I realized that the Prime Squared Circle (PQTU over circle OV) of the canon seen below, cut through the mouth and that the mouth of the adult in both canons was being reinforced by so many important geometrical functions, I decided to take the SCM seriously and be on a continuous lookout for where it might show up.

Moreover, the Fine Structure Constant was being related to the square of electric charge which bound protons and electrons together. This relationship dominates biology. I decided to start one step before alpha, the Fine Structure Constant. It was something like 29.4332 which, coincidentally, in Earth years is the number of the Saturn transit around the Sun. But in the 1980’s 1/29.43 was close to one of the ‘running’ coupling constants relevant at the scale of the electroweak force, so that when related to alpha (known as the “weak mixing angle”) it was something like .21478 or 29.4332/137.036 = 1/4.6558 .  But now it is thought to be more like .22 for the W particles or .23 for the neutral “Z” particle. This interested me immediately, because as I developed the arms and hands at the Ideal Botanical Angle in a circle set over the center of the Thoracic Vesica, I found a range in the hands that extended from the mouth-to-vertex measure, that was: .2146 to .22 to .23148, the latter being the maximum for a male; the female being more in the .2146 or .22 range.  However, I decided I would keep 29.43 in case it referred to something subtle at that scale. I then progressed through 137.036 until it reached the Capra nucleon speed which I upped to 64,390 and then to the speed of light at 299,792.458 km/s and from there to 1,395,783 which is strangely close to the diameter of our Sun if you include the super hot layer that extends past its immediate surface.

1. 29.433199 ×  4.655831137.036 (Fine Structure Constant)

2.     137.036 ×  4.655831 = 638.016454

3.  638.0164 ×   4.655831 = 2,970.496774

4. 2,970.4967 × 4.655831 = 13,830.13091

5.  13,830.13 × 4.655831 = 64,390.75197 (Capra Nucleon Velocity)

6. 64,390.75 × 4.655831 = 299,792.458 (speed of light)

7. 299,792.458 × 4.655831 = 1,395,783 (solar diameter)

Naturally, then, in view of this rather deep progression, that even suggests a vital diameter for a G2-yellow star, the fact that (Earth + Moon) ÷ Moon  should yield the SCM (4.66) and that the human mouth also gives the same relationship as do the hands relative to the radius of the heart circle, I could not ignore its significance nor its use at Chartres, the Parthenon and the Great Pyramid.  Particularly striking is the fact that this measure of 60 cubits in the Great Pyramid, where 280/60 = 4.666 becomes the internal perimeter of the King’s Chamber. So they have taken a length, a height which is also a difference, and have collapsed it into an enclosure. In the Pyramid Texts they talk about strengthening the winds in the Broad Hall of Osiris (PT 1551). With further references to iron one soon realizes they were referring to the Earth’s magnetic field and probably the accumulation of electrostatic energy, not to drive light bulbs or hair dryers, but for the purposes of spiritual baptism in a medium quite different from water. The King’s Chamber is a hydrophobic cavern if ever there was one! It seems they were trying to ‘strengthen the winds’ by a very precise amount and this amount was derived from some knowledge regarding Squared-Circle geometry, the basis of the whole Great Pyramid. This is one of the great mysteries of the Great Pyramid. Why did the builders use squared-circle relations for its design? And why did they take the difference between circle and square and make it the perimeter of the enclosure of the King’s Chamber? What did they believe this proportion of the height (1/4.66) would accomplish deep within the body of the pyramid, the great Primordial Mound or Hillock of Khepera?

I also found it intriguing to see a parallel between Capra’s nucleon speed and the speed of light.

64,390/29.4332 = 2187.66 = 299,792.458/137.036

It suggested to me that squared-circle relations were involved at a fundamental level with the Uncertainty Relation in determining the scale and momentum associated with the generation of nucleons relative to the vacuum where c sets a limit for massless energy. It also seemed to be saying something about the birth of matter – the relationship between spatial confinement and rate of motion or agitation. It also indicated that the speed 2188 km/s for the electron at the First Bohr Radius was being reinforced from 2 directions: out and in. The nucleon speed was the matter pole and was being divided by the coupling strength at the scale of the electroweak force while the speed of light was being divided by the Fine Structure Constant, the coupling strength at the outer limit of the atom. They were converging at the speed of the electron at the First Bohr Radius. The atom was self-regulating, self-adjusting in a vast cosmic soup. The relationship between c and the Capra nucleon momentum struck me as fundamental. So to see it come up as the SCM (1/4.66) – one key to squared-circle-dynamics – suggested that squared circle dynamics were a critical aspect of self-organization relative to the vacuum at a fundamental level. It seems the Egyptians were thinking at that level when they built the pyramid and wrote out the Pyramid Texts in some of the 5th and 6th Dynasty pyramids.

What I find potentially interesting about this equation:

64,390/29.4332 = 2187.66 = 299,792.458/137.036

if it has any serious merit under at least some conditions, is that the electron speed in the First Bohr Radius (ground state) can be arrived at two ways. One way is dividing the speed of light in the vacuum by alpha (137.036) and the other is to divide the mean nucleon speed on Earth by the value of what has been called alpa-2 or say 29.4332. This would seem to suggest that an equilibrium has been set on the basis of squared-circle geometry within an atomic field. The mean nucleon speed is to Alpha-2 what the speed of light is to Alpha. The electron has adjusted by speed and radius as it ‘vibrates’ electrically around the nucleus that is many orders of magnitude removed from the nucleus under terrestrial conditions. Apparently the mean electron speed on Earth is something like 1,000 km/s. This is about 1/64th the nucleon speed. And at the First Bohr Radius it is about 1/29.433 of the nucleon speed. By analogy, the Earth/Moon pair has a mean circular velocity for 1 AU of 29.78 km/s while the Moon moves about 1.018 km/s. So their relationship is about 1/29.25. Moreover the Earth’s Equator moves about .4651 km/s which compares to its circular velocity as 1/64. The coincidence of the appearance of both ratios: 64 and 29 is striking to say the least of it. The continuity of these number-proportions is in part what the Egyptians meant by decussation of above and below; around and within as well as what they meant by the principle of Maat or Cosmic Equilibrium. The numbers point to inversions between macro and micro in such fashion that their behaviors are bound together in a shared field.

The relationship between c and the Capra nucleon speed is the same as the relationship between alpha 2 and alpha. So their relationship may be simply .2146 in an ideal or threshold situation. In the case of the human body – especially the position of the mouth – it seems that this .2146 is close to exact and that multiple geometrical resolutions converge on, or reinforce, the same position set by squared-circle dynamics. An atomic field, at a fundamental level, must be reacting to its environment both internally and externally through a squared-circle paradigm. It is so important that it keeps recapitulating itself all the way to a standing adult human who is bound together by electromagnetic energies but also is constrained to experience the gravitational cycles that influence the Earth’s surface continuously. Still, I admit, I was very surprised to see the Prime Squared-Circle (by perimeter) fall exactly on the mouth

and to see the authority, stability and beauty that it imparts. But I was also surprised to see the formula: Height (2) ÷ 1.118 = 1.7888, converge with the strict Squared-Circle formula. The Squared-Circle formula gives 1.7854. Their relationship is 1.001934784… If this same ratio is applied to the AU, incidentally, one gets exactly 500 light seconds or 149,896,229 km for 1.001934784 AU.

As I worked I felt more like a temple architect than I did a physiologist. So when a region was dim, I myself felt dim. And by some truly mysterious correspondence, the ‘temple’ felt dim. What temple? The answer to this was long in coming. But obviously the temple was acting like the Grail: it was overflowing with information. It was the place of life; where, in mysterious cycles, the Phoenix came to roost upon the altar. Every day despite discovery and exploration I had to confront my own limitations; my own ignorance. Furthermore, my life circumstances were always on edge. There was no real security. Nothing was normal. My routines were not normal. I often felt like Hephaestus locked in a cave far from the daily bustle, chained to a rock with nothing but a pencil and pad of paper or a ruler, mylar and a compass. A guard never left the shadows of the cave, a spear in his hand and a sign always hanging around his neck: DRAW – ON PAIN OF DEATH. But gradually it was my fate to come to terms with the fact that the human body was the basis of the temple design. The temple strengthened the ‘winds’ and lifted the human spirit above the darknesses of psyche and body.

Full concentration and hours of laborious searching were essential to find missing clues. I was not interested in the anatomy of corpses. I wanted to see directly into the underlying principle, the cause – that which was supporting what we call our anatomy – but also that which was supporting the soul; whether it be comparable to the Egyptian “ka” or not. I was also on the continuous hunt for any clues that might help me to understand the inner nature and even cause of the 1980 dream in which I experienced a new order of ‘seeing’. I knew the progressed New Moon was involved because it had set the clock, the timing of the event. I knew the entire dream had acted like a dynamic inner seed in which the ‘self’ had been reborn after an unexpected internal self-fertilization. I knew something quite unique had happened to my heart as well. And this change of heart was what I had craved both consciously and unconsciously all my life. I did not know anything about the tradition of a ‘second birth’ because I was uncomfortable with the Bible and never had the right circumstances to settle into any meditative state long enough to let it sink in. But I was on the path of the second birth anyway – despite all ignorance. It took years for me to understand that Parzival was a story about the second birth. What was violent, ignorant and crude was undergoing a transformation into a higher, more refined state of being within which the spiritual self was awakened. At this point one no longer has a human mother, nor a human father. This ‘more than human state’ is an experience and should probably be classed, according to the tradition of such experiences, as spiritual empiricism. But it occurs on an advanced level of spiritual development that requires considerable commitment and sacrifice, dangerous under normal social conditions as it is capable of disrupting one’s entire social existence: family life and career. This explains why certain societies set up monasteries and a decision was required to enter the discipline of a monastery. I started to realize that the male had an inner female program that at specific times needed to be integrated. That integration process was on a clock. The clock was the same as the female clock. When in ‘progressed’ mode it was a 29.53 year cycle. The male, at such times, may not be giving birth to a physical baby, but he is capable of giving birth to another form of ‘infant’ that traditionally goes by different names.  In any case the 1980 dream inspired and compelled me to understand the underlying basis of body and double, since it appeared as if for the moment of the progressed New Moon, the body had ‘stepped aside’ long enough for the ‘double’ to undergo a qualitative change of state.

Between 1997 and 1998 during which I did all the heavy foundation work for a garden that surrounded our house – a garden destroyed by a hurricane in 2003 – I realized the heart region of the canon of the female was still dead. So was the region of the Solar Plexus that I did not quite yet realize was 2/3rd the height. I realized I was still trying to go about the anatomy as if needing to please physiologists. I was not listening to my own spectrum of instincts with unreserved courage. For this reason I started to drag some astronomy books into the house and exposed myself to the latest data, images of the Earth’s magnetic field and the Earth in profile. I reread about the Earth’s core, the outer core, the iron and nickel. I then looked into theories about stars, white dwarfs, supernovas, how iron is formed – under what conditions and the meaning of 56 nucleons which possess some sort of stability that blocks further fusion in a star. I then learned how to work a few gravity equations and equations involving Planck’s Constant, the speed of light and so forth. All this had the effect of sensitizing me to a feeling of how we grow from a single cell packed with information to a grown adult; in other words the path between microscopic and macroscopic. I was quickly aware that I had been changed by my 1980 dream permanently. I was no longer capable of reductionism. I could not reduce ‘mind’ to ‘brain chemistry’. I could not reduce “Self” to body or even personality. I could not even reduce it to an astrological chart. The Self seemed to have an open boundary where spirit and matter met and danced. I could not reduce psychology to the choreography of hormones. I saw hormones as agents, liaisons, connectors in a spectrum of activity that was ultimately not computable even when constrained by geometries that held all of it together and allowed it to relate back to itself through a dizzying array of feedback loops.

I was struck by the amount of controversy that prevailed in physics, in psychology and also in theories about the nature of consciousness itself. The more I read the more I came to believe that the geometry was providing the means within which all the controversy was operating and within which even deep principles like Heisenberg’s Uncertainty Relation were being housed. When I attempted to understand what aspects of energy and mathematics were blocking Grand Unification Schemes that tried to unite the Four Forces of Nature into one equation or scheme, my mind was flung wide open and I started to see the Earth’s surface with fresh eyes. I started to see many things with fresh eyes. This state of open-mindedness was first and foremost an act of faith. It was a belief that things are actually unified in ways that transcend ‘normal’ appearances – including ‘mathematical appearances’. And these forces that unify had extended to the human body and in fact were underlying its evolution and function from the beginning. I also believed they were responsible for what we call health and that illness sets in when unity has been disrupted, obstructed and when the parts within the whole have become excessively separated from one another. A lot of factors can disrupt, obstruct and separate. In ancient Egypt, this was Seth. Seth was the obstruction of unity; the disruption of harmony; the separation of the opposites engendering a state of antagonism, anger, frustration and opposition. In the moral sphere Seth opposed justice. This focused unity that I had some inborn faith in, also extended to the surrounding environment. When things go out of focus, the environment assumes a specter of evil or hostility. When things are in balance, the same environment will appear beneficent. I worked from the assumption that the relationship between inside and outside sought harmony by its inner nature.

The Meter

By this point I was already treating the meter as both a finite measure and a proportion. Its greatness was as a proportion. The 39.37 inches meant nothing in and of itself. But I also became interested in the meter as a principle. It had been derived from a principle that society tended not to offer as part of the ‘Metric How-To Manual’. I had been struck somewhere between 1989 and 1997 by a combination of the writings of Peter Tompkins and R.A. Schwaller de Lubicz, who presented a whole new way of looking at ancient Egypt. Schwaller had spent some 15 years in Egypt while Europe was embroiled in turbulent disarray. And he examined the Temple of Luxor with a fine tooth comb in an atmosphere of peace and sanity. During that time he insisted that he found not just a few isolated occurrences, but thousands of examples where the meter had been used as a measure!!! According to his stepdaughter, Lucy Lamy, the meter was in evidence in mastabas as early as the First Dynasty!  I was slow to come to grips with the implications of this discovery. But in any case when I reviewed the ‘history’ of the meter I realized that there was no way anyone could match the Egyptian meter by going out with instruments – even satellites – and boiling down the Earth’s size to exactly that known to the Egyptians. There were too many variations in the surface. Whoever made the solemn decision to select a meter of 39.37 inches, it is in my view a credit to their sense of history and the often underground debt owed by the entire Western World to the conscience, wisdom, knowledge and ability to preserve records for which the Egyptians were famous. Sir Isaac Newton (1642-1727) did not have to wait for the meter to be established in Europe to learn the size of the Earth from which he could compute its mass. All he had to do was send people to the King’s Chamber and measure it carefully. However, this would not have done much good were he not also in possession of the principle that would allow him to deduce the scale of the measures reported. If the KC was built in a uniform way; and if it was in fact supposed to be a manifestation of the royal cubit, then its perimeter would have been the same as a circle with a diameter of exactly 10 meters. That meter would have been 39.37 inches if the cubit was .5236 meter. Provided Newton was aware the Egyptians had derived the meter from squaring the Earth polar circle, and provided he knew the scale of the King’s Chamber, then he could deduce the size of the Earth – for the purposes of finding its mass – by simply knowing that the 10 meter circle is the circle-in-the-square so that the square has a perimeter of 40, instead of 31.416. The Earth’s circumference, then, would be 40 and some zeros. There is a tradition that even goes back to Herodotus and Aristotle that the Earth could be measured as 40,000,000 which obviously refers to the meter.

This history of measures is fascinating. I for one am deeply moved that the Europeans in the 19th Century (1793-1799) would pay homage to the Egyptians by adopting the principle of the Squared-Circle represented by the meter which is simply the side of the square divided by 10,000,000 which brings it into the range of the human armspan. Attempts were made to measure the meter prior to 1793, but these measures were not in agreement with each other. A provisional measure was adopted in 1793 and basically stuck. What is extraordinary is that this provisional measure should be the same as that used by the First Dynasty Egyptians. As it turns out the meter is shy of the actual terrestrial Polar Circumference. So there are more than 40,000,000 meters in that circumference. However, what really matters is that it expresses a principle that we do not know enough about. That is Squared-Circle relations in geometry.

With or without the imperfect history of the meter, I had already taken to the meter in 1985 when starting the baby steps of the female canon. It was a language that I found eloquent. Every time I constructed a 5 x 10 cm rectangle and performed the golden section which brought out 3.82 and 6.18, something felt right immediately. I believed that the meter was maintaining a principle and I believed the principle was deep. I was eventually intrigued naturally to learn that the mean height of the female in North America is actually about 1.618 meters (an American is a little taller than a Canadian) so that the mean navel position for a modern North American female might be about 1 meter which is very close to the length of a pendulum that beats the second of time (.997 m).  One meter, by the way, is about the mean tidal flux on the ocean. The Earth’s crust rises and falls around 20 cm, but on the ocean the tidal flux is about 1 meter. In some areas of shore the land configuration is such that the tidal flux is much, much higher (e.g. 15.25 meters in Minas Basin, Nova Scotia), but the ocean flux is about a meter.

One day back in January, 1998 I was interested in actually being able to compute circular velocity so I could get a feel for the equivalence principle in gravity. And I realized that the Earth was only at the position of the mean Astronomical Unit (149,597,870 km) twice a year (April 4th and Oct 5th, 1998). I obtained charts for all the positions of Earth + Moon for 1998 and started to come to terms with the difference between a statistical mean and the reality of a full year of time. Time is definitely a fourth dimension in all this work. But it is not as easy to demonstrate its effects. Prose and other forms of writing are good at conveying the role of time in the spiritual development of a human. I am quite conscious of time during certain phases of important cycles. But at other points, I almost become oblivious to time. Time measures energy and process. Without process we are nothing; without it we lack depth. Everything great undergoes a process. In physics time is an inseparable component in all measurements.

The Astronomical Unit: A Critical Separation:  ~ 150,000,000 km

I realized the AU was close to 500 light seconds, but also the number 15 in the metric system. So the full diameter of the Earth’s orbit was nearly 1000 light seconds. In terms of time two photons leaving the Sun at the same time but traveling in opposite directions would end up covering the 1000 light seconds in 500 seconds of time. But spatially it was 1000 seconds worth of light travel giving around 299,200,000 km. I often reduce zeros in order to study the principle of the behavior of the number. Then I restore them to attempt to understand the function at hand. Obviously the 150,000,000 km separation between Sun and Earth is critical. I cannot imagine anybody alive on the planet today who does not feel sensitive to that distance of separation. We know how easily drought can set into a region. We know what fire can do on a massive scale. We know what too much ice and snow can do. We know what too much rain can do. We know what happens when the range in temperature is too severe. We know what happens when the body is overheated or cooled down below 98.6° F. Our metabolic efficiency is altered dangerously. We know what happens when parts of the food chain are wiped out due to excess heat, sunlight, ozone depletion, or other forms of imbalance. We know how quickly sunlight can damage skin and eyes. All of us know, the more we learn about neighboring planets, that the Earth’s surface is delicate. What it supports is delicate. The water cycles that it maintains are unique. The atmospheric composition is unique. The green life supported by all these features is unique. Since man lives on the Earth’s surface, it struck me that I had to pay more attention to the Astronomical Unit (AU) and that I ought to superimpose the growing geometry over the AU and see what numbers break down. Not only that. I needed to see where they broke down. In the back of my mind I expected I would find things but had no idea what, or how what was found would help to fine-tune the system of proportions I was hunting for. I was certain the numbers would offer insight into the behavior of the meter; behavior that was interactive and operating in an entirely meaningful context. I felt it would suggest something about how the whole was self-focusing into its parts. And how the parts were managing the all-important feedback loops that permitted a living system to grow, respond, adapt, learn and possibly perform that leap in consciousness that transforms the humdrum into something special.

Since living things like to grow toward the light source, I began to get a feel for the seed at the Earth’s surface growing toward the Sun. I also kept in the back of my mind a sort of holographic notion of ‘made-in-the-image-of’. I imagined the entire Sun/Moon/Earth relationship as being recapitulated at a specific scale relevant to biological molecules, even as far down as the scale of the tubulin protein dimers and smaller. One half the dimer is only dealing with some 55,000 Daltons of mass. But presumably one could talk about 1 Dalton or two or three when discussing hydrogen bonds. But even so, there was a limit before the nucleons were too remote from electrons to be part of the physical process. The charge between nucleons and electrons was critical and the speeds of the mass-energy were important because they contributed to the reality of stability and dependability upon which the bio-chemical interchanges and growth progressions relied. The more I thought about the Earth’s surface and its atmosphere the more convinced I was that the geometry was a superb scope or lens with which to examine the underlying resolutions of approximately 500 light seconds; 150,000,000 km, 92,955,600 miles, etc.

I will repeat, left to my own instincts, I believed the AU could be examined in the image of the human body as if a prime geometry were being recapitulated, scale-by-scale, until a seed was born in optimum conditions: conditions where life-energies could self-focus and maintain themselves long enough to establish conscious memory of the existence of that life-structure. The whole seed was in the embrace of the entire principle of the year, which of course can be construed as a circle. In the case of Neptune and Venus it really is a circle. In the case of the Earth there is some eccentricity off a mean circle by nearly 2,500,000 km in either direction (perihelion/aphelion). In the case of the Earth perihelion is around 147,100,000 km from the Sun and aphelion is about 152,102,100 km from the Sun. I drew this eccentricity into the geometrical illustrations of the canon but the eye cannot pick it out easily. It appears to be a circle. I show ½ the circle only to conserve space.

By 1998 one word began to dominate my mind: resolution. I started to picture the entire solar system as a massive self-focusing system that sought resolution among parts within a single whole, with time always functioning as a fourth dimension!! A quick glance at just a few initial figures is immediately interesting, if initially awkward for the mind. Above we see the following: 150,000,000 km, 75,000,000 km, 92,707,045 km, 57,300,000 km. We also see 309 light seconds, 191 light seconds, 500 light seconds. We note immediately that all these numbers appear in the first few lines of Series E.

191, 309 and 500 are all in a row from Column X to XII on Line I. 573 and 927 are next to each other on Line 3 Columns X and XI. 1500 is also on Line 3 next to 927 in Column XII. 309 appears again when we divide 927 by 3 to obtain the female Pelvic Vesica Piscis. 309, is a lunar number. Note 75,000,000 km is 250 light seconds. In 25 years there are 309 synodical months. In 75 years there are 927 synodical months. In 50 years there are 618 synodical months. In 1000 years there are 1236 synodical months. These numbers seem to be expressing the way what has been resolved at the Earth’s surface self-focuses as a result of both spatial interaction and the flow of time which gestates and grows, cyclically. The year does not divide into even numbers. It is not 12 Synodical Months; it is 12.3682369 Synodical Months per year (equinox to equinox). With the appearance of this 1236 number right away one feels that an organic process is at work. Organic processes tend to be characterized by the golden number. Time is the trajectory of the process. So there should be no surprise that the golden section family shows up in measures of time. The synodical month is creative and dynamic. In the year there are 1.2368 x 10 synodical months. The year is a product of the decimal and golden section functions.

We can see these angles again below with the figure in place. I have outlined in red the Ideal Angle and selected the 137.5° sector of the Heart Circle also in red.

At the Earth’s surface the whole, it seemed to me, was being implied in the parts as if through a means of self-focus that uniquely balanced gravity with electromagnetism with the subtle co-operation of the strong nuclear force that provided the mass that as an ensemble was being controlled by the Sun’s mass-gravity and also the gravitational influence of our nearest neighbor, the Moon. At the Earth’s surface the acceleration of gravity is strong enough at 9.78 m/s² (Equator) to hold mass to the Earth’s surface – despite the overwhelming gravity of the Sun. But the Sun is causing the Earth and Moon to fall together toward the Sun continuously, balanced by the centrifugal momentum of the circular speed almost as if the planets were being pumped or pulsed around the Sun as if via a gigantic heartbeat. I know nothing about gravity waves, but it makes sense that gravity would move in waves given its effects. I have been intrigued for some time at the relationship between the 160 minute pulse reported back in January, 1976 in the New York Times and the Earth ionospheric ‘shout’ said to be 69 times a day. I already described in an earlier post the use of this 9/69 ratio to determine the head size relative to the body height and found it to be perfect for situating the mouth by several, converging geometrical pathways. I use it (.13043478) instead of the more whole 13/100. This is an example of extreme precision in the canon that I felt the mouth warranted. Remember, the mouth to vertex measure is the basis of the SCM ratio. It is divided into the distance from the vertex to the pubic bone. The implications of this 9/69 association between the Earth ‘shout’ and the solar pulse, is that our image of how the Sun is affecting gravity may not be telling the whole story. We might have an imperfect understanding of the vacuum and we may not understand entirely how it gravity is operating and that it may be influencing the planets as if it had a double cycle: diastole and systole. The further implication is that only at the Earth’s surface has a balance been struck that permits human pulses and human oscillations to endure. There has to be some critical cross-over effect or exchange between gravity and electromagnetism that, at the Earth’s surface, has assumed a creative function within a creative ‘equilibrium’. This also affects the mind – how we think and record perceptions.

In the image below the circle being squared is OV. The square with the same perimeter is PQTU. The 2:1 rectangle that passes through the mouth and pubic bone is PQNM and has a value of .7854 × 1.5708.  The pyramid MON unites circle and square. The span that recapitulates the 60 cubits of the Great Pyramid is here seen from the mouth to point O at the vertex. Here it is .2146. The Pyramid that has its apex on the mouth has a base RS which is identical to the width of the golden rectangle and we will see ahead is synonymous with the ‘Shared-center-of-Mass’ circle inside the Earth – that the Earth and Moon

create together. I should also point out right here that the female hand falls shy of the circumference of the Heart Circle but seems to be identical to the mouth-vertex measure (~ .2146 of Unity)! The male hand appears to be – in certain categories – a little longer than the mouth-vertex measure. This vertex-mouth measure is archetypal. It is precise and can be used as a module if desired. It is simply 2 – 1.785398163 = .214601836. The reciprocal of this is 4.65979. Just as the hand has some mobility at the wrist, so does the jaw have some mobility below this point. The mouth is as active as the hands.  The Moon also has mobility while sharing in a common center of mass within the Earth and participating in the same ratio with the Earth that the hands do to the Heart Circle.

I will return to the subject of the mouth ahead. This is one part of our system that not only pertains to the physical world. It also has relevance in the spiritual world and seems to act as some sort of gate or portal between spirit and matter. It’s quite amazing really. The ancient Egyptians were very particular about speech and about the relationship between the heart and the mouth; between Ra and Thoth; and Ra and Ptah. When they stressed the manner with which something was spoken, they were stressing the quality or state of the heart. And this affected speech: the relation between square and circle.


The vacuum must be playing a role in the way constants have been set and the way quantum mechanical behavior works with macroscopic, relativistic behavior. We must contend with degrees of curvature of space-time and that can create problems for mathematics when we attempt to deal with energies approaching a ‘0’- point. What seems to happen is that ‘focus’ is lost. ‘Resolution’ vanishes and we have to back away from notions about a ‘o’ point or the idea of absolute singularities. It then seems that a family of constants adjust to one another until they have reached an agreement of some kind. It seems that geometry must be playing a role as the field , pattern or bridge that links the two scales or behaviors together. One archetypal geometry, intuited by humans for eons, is squared-circle geometry. The ancient Egyptians went to great lengths to build the Great Pyramid in accordance with this geometry.

A Template

Below I have drawn the template for the male canon of proportions. The semicircle here represents about 6.18425 synodical months or 182.625 days. Recall that the golden section of the synodical month is the 19th day, or 18.25133 days. All children can draw semi-circles. What makes this semi-circle interesting is that it measures 6.184 synodical months. The synodical month determines the female ovulatory clock, which is to say 6 ovulations, 3 per ovary in the period of this semi-circle. It is important to emphasize that Nature has synchronized the synodical month to the golden section number. And recall that in the North American female, the golden section of the average body height is 1 meter + .618 meter. When the Height is Unity, the golden section is .382 + .618 = 1. Note that the relative male Pelvic Vesica is .382 of Unity, where unity is ½ the height or in other words is the width of the Prime 2:1 rectangle. The female is .412 or 1.236/3. I should also note that the surface gravity of the Moon is exactly the same as the mean height of an American or British woman. It is 1.62 m/s². In this instance the length 1.62 meters is dependent upon the fourth dimension of 1 second. At Chartres the First Elevation has special meaning – being 9.79 meters – when one includes the dimension of time. I personally cannot ignore 1 second of time, because for decades my heart rate has been 60 beats per minute or 1 beat per second. The First Elevation at Chartres is interesting because it corresponds fairly closely to the surface gravity at the Earth’s Equator. The means by which the elevations are calculated is through triangulation. The base of the triangle seems to be derived from the Great Pyramid as alluded to by Charpentier who did not have the benefit of knowing the 1925 Cole Survey. The base of the triangle is ½ of 29.53 or 14.765 m. The first hypotenuse is 1.2 x 14.765 which gives 17.718. Through Pythagorean Theorem, we can easily compute the right angled height to the first elevation which ends up being the square root of 95.922299 = 9.793993 m. By adding about 2 cm the builders would have the surface gravity at Chartres where the center of the Earth’s mass is a little nearer than at the equator. So more distance would be covered by a falling object in the same time frame. But the point is, 1.62 m is not just a spatial measure. In the case of a North American or British woman, it is the average height that can be seen in the context of 1 second. The Moon’s gravity is about 1/6th that of the Earth’s.

1.236 is .618 x 2. Also note that the Escape Velocity from the surface of the Sun is ~ 618 km/s. This is c/485.4 or c ÷ (300 x 1.618). The head square shown here in white is based upon 9/69 where 69 is the height or ~ 150,000,000 km.

This idea of resolution or self-focus – especially with the continuous appearance of the golden section family of numbers – convinced me that scientists were incorrect to dismiss the Moon’s measures and even apparent angular diameter in the sky as seen from Earth as accidental or meaningless. There has been a tendency to reduce the Moon to various categories or labels that have rendered it dead and of no special significance as if the Earth would just be going along fine without it. To tell you the truth, this attitude toward a key member of this self-focusing system, causes me considerable discomfort. The notion that we all have bigger and better things to worry about than the Moon is itself a deception. We all have jobs to get to during the day. But that does not mean it is necessary to leave the baby to drown in the bath water or fall down three flights of steps. What is small and right under our noses is often what is most important. A tiny baby will grow. And who knows what it will grow into? It seems that the collective maternal instincts of humanity are still being diluted by an overly flaunted arrogance spawned by the domination of male aggression. The ancient Egyptians associated perhaps their most productive, wise and efficient “neter” with the complete Synodical Month, which depends from the triadic relationship among Sun, Moon and Earth. Within a fascinating African group known as the Dogon, each tribe was allotted a planet. The most important tribe, the Aru, chose the Moon over the Sun as their ‘planet’. They said it kept them humble, but I believe it was because they knew the role the Moon played in secret male initiations that guided them into spirit state. They knew it governed cycles of renewal critical to human well-being.

The heart is also perhaps more important than it seems. It is more than just a physical pump. Consciousness itself is affected by heart rhythm. I was driving a car on a tight road south of Route 3 on the way to Elizabeth, New Jersey, many years ago. I was in the right lane. Suddenly, the largest truck I have ever seen came barreling down an on ramp and did not slow down. He was supposed to yield and did not. The next thing I knew the front of my station wagon was under the body of his truck. Time altered in the twinkling of an eye. I believe I held my breath and slowed my heart rate involuntarily. It felt as if death was an instant away. At that moment I felt myself leaving my body. I was just expanding or floating outside my body as if my heart had stopped. My conscious attention was smeared out so that I felt two places at once: outside the car looking in and inside my body looking out. I had no idea what to do. Then I felt a counterforce surround the car. It was a unique experience. It acted like a bubble that was at the same time a buffer. This counterforce pressured me to jerk the wheel with the bubble in short, little, leftward jabs. Time remained completely altered. My entire identity was out of commission because my heart was as if stopped. Somehow, the car was ‘bumped’ out from under the truck which never saw me. His rear wheels did not make contact with the car. I jerked the car out of his way right over to the concrete median without hitting the median. He roared off. All the other cars had nearly stopped and were now far behind. They must have expected an accident. I nursed my way to the next off ramp. I took the car onto a flat dirt area facing south. I turned off the ignition. I still had no identity. And then suddenly my heart reaccelerated. It pumped so hard that it knocked violently against my sternum like a hammer against a rock. I could not control it. Finally I let out my emotions. I must have stayed there a half an hour before I felt it was safe to keep going. It was as if all the blood had left the heart and gone somewhere else. I knew the time only because I consulted the car clock to decide whether I should return to New York or keep going to Elizabeth.

Now, Kely was walking down Ninth Avenue in New York City just below Port Authority at the time I was encountering the truck. At the moment I was under the truck she was assailed by terror. Her heart appeared to stop. She stopped dead on the sidewalk as people swerved around her. She knew mentally that I was in mortal danger. Her heart would not go. Then, as suddenly, the danger passed. Her heart reaccelerated and pounded violently in her chest. When she felt normalized she resumed her stride down Ninth Avenue, believing I was okay. She recalls this incident like it was yesterday. It was vivid and memorable. Later I spoke to her on the phone and told her about the incident. She described what happened to her on Ninth Avenue. We both realized that it was another example of synchronicity. I had already had a few such experiences. But this was the closest brush with death and the only time I felt at least partially out of the body. Two principles are operating here at once. The heart appears to be synchronized to states of consciousness and to the stream of consciousness and to the perspective that distinguishes between objective and subjective reality. This can undergo metamorphosis. But two human beings, separated by spatial distance that would require time to breach, can experience an event simultaneously due to some type of non-local connecting principle. One imagines some form of quantum entanglement that keeps them in a common state even when separated by distance that blocks ‘normal’ communication. This quantum entanglement is an aspect of what I mean by self-focus and the heart participates in that act of self-focus or resolution. Moreover it is in a dual relationship – between the vacuum substrate and the macroscopic, ‘outside’ world. This undoubtedly is a composite effect of both distribution of blood and electromagnetic lines of force that emanate from and thread through the heart. The heart must supply glucose to cells of muscles and the brain for consciousness to be sustained on Earth. But iron is the key with 4 Nitrogen atoms in hemoglobin, by which oxygen is carried. The brain needs a constant oxygen supply. Oxygen is needed to convert glucose eventually to ATP molecules. So the heart is synchronized to the way the body supports consciousness. Synchronicity between two hearts separated by real distance has to be accounted for on another basis. However, this dimension of synchronicity had a profound effect on my decision to superimpose the growing geometry over the Astronomical Unit. In this ‘lens’ I wanted to see what geometrical language was spoken by the meter as a proportional measure.

For a very long time astrologers keep placing a ‘coalescence’ of Sun and Moon in the chest as well as behind the eyes in the head. So the conjunction of Sun and Moon is pictured in the thorax, what the Egyptians called the “hatys”. The heart is in the midst and the two lunar breasts are to either side where blood becomes milk. Red becomes white. We think again of the grand unification of the white and red crowns of north and south in ancient Egypt. The neter responsible for their union was Thoth who was at times referred to as “The Heart of Ra.” Note how this entire image below is supported by or rooted in the heart. Also note that when we are looking at a right profile it is the White Crown over the Red Crown. When looking at the left profile it is the Red Crown over the White Crown. The Red was associated with the North and the White with the South. In the Pyramid Texts the Two Crowns were frequently identified with the Eye of Horus as if they were part of the same metamorphosis. The Crown in ancient Egypt had a spiritual significance not unlike the great headdresses of the Aboriginal people of North America.

As we go forward we will just bear this in mind on many levels simultaneously. It doesn’t really matter what one believes. Science is constrained to try and seek evidence even for what we don’t understand. There must be some reason why astrologers for so many years have placed Sun and Moon together in the thorax. And this involves iron because of the chief role played by iron in the transport of oxygen. The Earth’s core is predominantly iron and nickel both of which can have 56 nucleons in their nuclei. 56 nucleons are especially stable. The Earth’s core has been called a self-exciting dynamo. And this self-exciting field extends far beyond the Earth’s surface. So it is passing through all living things, rocks, atmosphere, water and so forth.

When I learned that the Moon was in a squared-circle relationship with the Earth and that it shared a center of mass with the Earth, my attitude changed permanently. When I found that Capra’s ‘nucleon speed’, calculated with the aid of the uncertainty relation, was in the same relationship to the speed of light as the Moon was to the Earth + Moon, namely something like 4.657 for c/64,400, and 16,216/3476 = 4.66 for Earth and Moon, I did not think it was a mere chance event. Rather, I saw it as a resolution that has enabled life to form and develop on the Earth’s surface. Even if we do not completely understand exactly what holds the mass-carriers in their compressed, agitated states where the 64,400 km/s worth of ‘speed’ has become trapped, the proportional relationship between it and the massless constant C (299,792.458 km/s) strikes me as highly significant because squared-circle relations indicate that an internal balance has been struck between two tendencies: massless volatility versus massive, compressed internal agitation. In a star this balance contributes to an overall hydrostatic equilibrium that maintains the shape of the star and its longevity. This hydrostatic equilibrium must also be contributing to the integrity of the solar system as well, remembering that the electromagnetic force falls off also by an inverse square ratio and so weakens quickly. Gravity holds the planets in their orbits. But when we get down to individual atoms at the Earth’s surface, we find that electromagnetic forces are once again powerful and dominate bio-chemical processes. The parameters of these relationships are clearly tight. The margins are narrow. Life is conditioned and for many of us ostensibly quite unfree. For humans, freedom is more a state of balance – the Egyptian Maāt – than it is unrestricted movement or just restlessness for its own sake. Dynamic, cyclic balance holds a more profound key and what I believe I have stumbled upon is the importance of squared-circle dynamics in the establishment of that balance. In that sense, the Great Pyramid with its expression of squared-circle dynamics, could also be called The Stone of Maāt. There is no good reason not to do this. But it could also be called the House of the Benben Stone because of the effects of squared-circle dynamics. We saw in earlier posts that in the canon of proportions squared-circle dynamics have manifested in some important places.  One is the adult mouth. The other is the wrists that separate hands from arms. This same dynamic at the Great Pyramid separates square from circle or 280 cubits from 220 cubits, yielding 60 cubits that the builders made into the perimeter of the King’s Chamber. This 60 cubits is 31.416 meters, the meter Lucy Lamy points out was being employed with the royal cubit in the First Dynasties of Egypt.  At the Earth’s surface the feeling is that there is a cross-over effect between the strength of gravity and the strength of the electromagnetic force. That is why the Fine Structure Constant is so important. It defines the strength of the electromagnetic interaction at the First Bohr Radius and beyond.

In this image above note that the Earth + Moon is about 16,210 km or 16,210,000 m. I’ll mention again that the average female height in the United States is about 162 cm. It’s the same in Britain. There are different ways to consider the radius of the Earth and Moon. I still see 3474.8 as the Moon’s diameter, but also 3476 km. The radius of the Earth with the same volume as the ellipsoid that has been measured quite carefully with new techniques, is about 6,371 000 meters.

6,371 + 1737.4  = 8108.4

When doubled you have 16,216.8 km. One important factor to recall in all this is that the 1.62 number is also a square number: (4/π)² = (1.2732395) ² = 1.621138. Since 1.2732395 is the squared-circle principle itself, namely 40/31.416 = 1.2732395, it is important to realize that this number 1.62 may well be an effect of the inverse square force of gravity. And it is quite interesting to see that 1.62 m/s² shows up on the Moon’s surface as its surface gravity. I already cited an example of synchronicity between a man and a woman above. Others will have even more spectacular examples to report in their own lives. There is no good reason that the second of time does not act to synchronize spatial states and states of consciousness between distances separated as much as 376,300 km (between surfaces of Moon and Earth). Physicists predict non-local connecting principles over much greater distances than that. Our entanglement with the Moon may be much more than meets the eye. Moreover, terrestrial consciousness may have been entangled with the Moon much longer than we realize. It is probably so deep in our memory that in fact it is trans-racial and even trans-gender. We should go to sophisticated lengths to protect the Moon. At no time should it ever be treated as a garbage dump or be used for target practice. Right now we face one of the greatest tests and greatest opportunities in human history to learn how to set aside all self-destructive tendencies and be sure to treat the Moon with care and precision.

The second and ½ second may be critically synchronized among several factors. For example it’s possible that heart rate is synchronized to ATP production which is synchronized to the way the cell metabolism utilizes glucose in the input of energy that augments the photon strength that is caught and amplified by microtubules in the cell’s centriole. First the microtubules may experience quantum coherence over a geographical region that concerns the center of conscious attention. When a threshold has been reached, the wavefunction may well become unstable such as we find at moments of bifurcation in systems theories. Roger Penrose suggests (1994, 1996) that the internal instability as more mass-energy is engaged in the wavefunction, causes the collapse of the wavefunction via quantum gravity, forcing the wavefunction to choose a particular state over a set of possible states characteristic of quantum wavefunctions. I believe tidal gravity or quantum scale effects of tidal gravity routinely collapse these wavefunctions in such fashion that they generate or encode engrams by which the brain learns, remembers, recalls, and is able to react.

It is well worth remembering that the liver manufactures the glucose but it does not distribute it with regularity and force to the rest of the system. It is the heart that pumps the glucose to all points in the anatomical field that require it. So the fact that this heart circle is centered over the middle of the thorax is quite significant.

Ideal Botanical Angle

When I set to work from several different angles I eventually found that when I set the angle of the upraised arms at the Ideal Botanical Angle within a circle centered over the heart and used an AU that was the Moon x 43,200, in imitation of the scale of the Great Pyramid to the Earth, I found that armspan to be:

150,111,360 x 1.078689 = 161,979,392

If I used an Earth position of 150,338,000 km I could get an upraised armspan of about:

150,338,000 x 1.078689 = 162,168,000 km.

This date corresponded to 1.004947 AU or in 1998, April 21, or 17 days from the mean.

With this armspan I was back to the mean height of a woman in North America and Britain, the square of 4/π, and the Moon’s surface gravity. Within the Prime 2:1 of approximately 75,000,000 x 150,000,000, every other value could be known. But what really mattered was that when I applied the squared circle principle to the arm at this angle, it gave a good approximation of the Earth + Moon at a higher decimal scale. The Earth would be about 127,366,403.8 km or 10,000 x the Earth. This measured out to the wrist just about exactly where we take our pulses. So the very spot where we measure or count our pulse corresponds to the Earth’s surface, or perhaps a shade below it. The Moon’s radius then corresponds to the hand and up to that pulse. Because of this fact, it made complete sense to me that I was supposed to be studying the armspan within a circle placed over the center of the Thoracic Vesica Piscis. The thrust generated by the ratio between the Aortic Arch (with its critical chemoreceptors that communicate through the vagus nerve to the brainstem) and the center of the heart that we use to restart a stopped heart seemed to be determining the ‘ideal’ radius of this “Heart Circle” which also was determining the width within which the Thoracic Vesica Piscis of the male was being inscribed. This was 1.618 ÷ 1.5 = 1.078689 = 2/3 x 1.618. Many roads were leading to 1.078689 including the Solar Plexus/Navel or 1.33333 ÷ 1.236068. One of the beauties of this is reflected in the cross-over equation where musical intervals cross with these illustrious members of the phi-family. It is worth showing the equation:

1.618 ÷ 1.5 = 1.078689 = 1.3333 ÷ 1.236068

So that:                      1.618 × 1.236068 = 2 = 1.5 ×1.33333

What has been defined here is the octave which in our Prime 2:1 rectangle corresponds to the Height of the figure. Specifically here it corresponds to the AU for say, April 21, or about 150,338,000 km. In names we might paraphrase:

the aortic arch × the navel = the heart center × the solar plexus.

In the image below 1.078689 is measuring from the center of the heart to points F and E which correspond to the center of each ‘Moon’ circle. So theoretically the hands + wrist are measuring the radius of the Moon which is in a squared-circle relationship with the Earth. Since the Moon wanders off what is left is the Earth’s surface. The wrist imparts considerable mobility and dexterity to the hand. The pulse we feel on the Earth would seem to be a result of a relation between various interacting gravitational influences – both inner and outer. The heart attempts to regulate its pulse while also being flexible within that confluence of gravitational pressures coming from within the Earth and outside the Earth.

1.07868 is also measuring from the ground to the top of the femur heads where they plug into the pelvic bone. From the crown downwards, 1.078689 measures to the base of the male sex organ. Between the two is .15737 which is close to 1/10th of the squared circle with 1.5708 on a side. In any case, this one measure (1.07868) stabilizes walking. It defines male sexuality, it provides the width (here “xz”) within which the male Thoracic Vesica is generated; it defines the proportion for the leg as it joins and supports the pelvis; it is the radius of the Heart Circle that measures the armspan at the Ideal Angle of Botany – which is a spatial effect involving shared light on a common stalk where the sharing divides by the golden number into 137.5° and 222.5°. It will also offer the basis by which we will calculate the width of the male Pelvic Vesica Piscis coming up. All this arises from one position: the center of the chest which, within the Prime 2:1 rectangle, is 1.5 or ¾ of 2, .75 of the Height.

1.078689 also appears with 1.236 in a rather interesting way. Together they form a rectangle that frames the triangular sacrum in the male pelvis. In the image below you can see that 1.078689 is “op”. “on” is 1.236. From LM down to the tip of the coccyx is 1.618 and from ON up, it is 1.618 to the top of the scrum ‘op’. The entire male pelvic complex is framed by an exact 3:2 rectangle, the very same rectangle that frames a Vesica Piscis construction. Note that the tops of the femur heads divide the whole pelvic complex in ½. From the ground to PS is 1.078689 × Unity of the Prime 2:1. In turn QR or PS also divides the sacrum in ½. The femur head comes in at an angle only as far as rectangle ‘opmn’ that frames the triangular sacrum. If the width across the Greater Trochanters of the femurs is 3, the width across the Iliac Crests is 2.618. Their relationship is 1.1459 which is the same as the male Pelvic Vesica Piscis derived from dividing 1.236 by 1.078689. Recall again that the reciprocal of 1.078689 is .927. The reciprocal of .078689 is 12.708, another member of Series E like 927.

The Earth and the Thorax.

There are a few surprises associated with this system of proportions that in fact are quite precise and worth examining now while everything is fresh. Scientists are fairly sure that they now know the boundaries of the solid iron inner core of the Earth and the molten outer core that might be responsible, through movement, for the self-exciting dynamo currents that activate the Earth’s main magnetic field. The heart in some respects – with the lungs – is a child of the Earth’s field. So once the Earth and Moon had been ‘named’ in this Heart Circle, and demarcated at the pulse of the wrist, it made sense to test both the Earth’s cores (inner and outer) and the SCOM circle (about 1700 km below the Earth’s surface) and see where they fell in the two canons. We’ll start with the male because only the male uses a circle of 1.078689 and also establishes the width of the Thoracic Vesica through the same ratio: 1.078689 × Unity.

In this figure above I have highlighted the exact relative size of the Earth’s solid Inner Core once the ‘Earth Measure’ had been established out to the wrists. The Inner Core is thought to have a radius of about 1221 km and a diameter of 2442 km or just over 19% of the Earth’s diameter ( ~ equatorial diameter ÷ 5.236) (here ML). So within our 2:1 archetype above we can easily break down the proportions. The female Thoracic Vesica will be .3333 and we see it in orange passing through the male mouth. The male Thoracic Vesica is .359563 and we see it in blue forming the outside skin of the chest and passes through his nostrils. The inner core is about .32473118 and seems to be just contained by the ribs! The fit is quite remarkable. Recall again that the Earth’s surface here is where wrist and hand meet and where ‘Earth’ and ‘Moon’ are touching. In the metric system the Earth and Moon measures are ‘named’ quite precisely when the  arms are lifted up at an angle identical to the Ideal Angle of botany that divides a circle by the golden section. As it turns out the hand is in the same ratio to the whole radius as the Moon is to the Earth + Moon. That ratio is of course the SCM. The radius of this circle is centered in the heart. The hand represents the difference, once again, between circle and square.

Below we see the way the Inner Core fits the female canon. The fit is tighter and simpler. It is as if the solid iron/nickel core were determining the proportion that links Sun and Moon together in the thorax: namely heart (blood) and breasts (milk). The way the inner core fits is so striking, it really does raise questions: about iron; about the term ‘core’; about why the Egyptians kept only the heart in the body after death; about why the Egyptians were so concerned about the dramatic event called “psychostasia” where they depicted the heart being weighed before the Hall of Judgment before the ka was free to move on to other realms. The heart was weighed against the Feather of Maāt which could be summed up as balance between above and below; inside and outside. It could be called truth or truthful speech. It could be called justice and also precision in following the Observances of Maāt as they were called. Are we to conclude from this image that the Inner Core here points to the accomplished truth of the personality; its very core and that everything depends upon what is in the heart?

Note below how the Moon’s circle encompasses knees and hands even as the female hands and arms are, relatively, a little shorter than the male hands and arms. The Earth surface corresponds to the pulse on the wrist. The hands then imitate the Moon. In 29.53 days the Moon travels around the Earth a distance of about 2,610,543 km while in the same time period at the Equator a particle is rotated about 1,186,682.6 km. The relationship between the two is about 2.2. The Sun exerts 2.2 times more inverse square gravity on the Moon than the Earth does and the Moon exerts about 2.18 times more tidal gravity on the Earth’s surface than the Sun does on the Earth’s surface. There are about 2.2 days between the Sidereal Month and Synodical Month. At Chartres, the proportions of the transepts are as 1 to 2.2, or about 61.8 ÷ 28. The ratio between the Moon’s Vc (Circular Velocity) around the Earth and a particle rotating at the Earth’s equator is 2.2. The mean speed of all terrestrial electrons is about 1,000 km/s and at the First Bohr Radius it is about 2,188 as determined by the Fine Structure Constant. Their relationship is 1:2.188.

In the image above I highlighted the Thoracic Vesica and Pelvic Vesica, not the Earth’s Outer Core. I widened the Earth Circle to the hand and then marked it with a white line to highlight the hands. The pulse is between the white line and the hand. I have indicated the orbits of Mercury, Venus and Earth/Moon. The Venus orbit seems to support the diaphragm and gets under the heart. Curiously it is venous pressure that causes the blood to return to the heart and 1/4th of it returns by volume to the liver first via a specialized portal vein that extracts nutrients from the small intestine through the capillaries. When the liver has worked these nutrients it then sends the blood to the heart. The liver is highly vascular. It is in the Solar Plexus region and recall that the center of the heart × the solar plexus = 2 or 1.5 × 1.3333 = 2 and 1.618 × 1.236 = 2. In music, the Major 4th × the Major 5th = 2, the octave.

Below we see the Inner Core and Outer Core together. The total diameter is about 6962 km with a radius from the center of the Earth of about 3481 which is a mere 5 km larger than the Moon’s Diameter. So 2 Moon’s fit next to each other in the Inner/Outer Core complex, thought to be predominantly iron and nickel and constitutes around 54.63% of the Earth’s diameter (12,742 km).

It is an interesting observation that this Outer Core Circle cuts off the crown of the skull a little above the hairline. This suggests the way the Egyptians (and even the Gothic Period with Saint Remy at Reims Cathedral in France), excised the crown of the skull though they cut more deeply than this. Presumably they then made an offering of it to God. It was as if they were answering the age-old ‘grail’ question: “Who or what do you serve with the Grail?”  Now, in the brain everything is inverted. The feet and legs and hands and mouth are all upside down along the Rolandic Fissure in the cerebral cortex. They are motor-sensory termination points. They have to be there because they retain specialized engrams that pertain to specific activities that will involve hands, wrists, feet, legs, and so forth. Where this crown has been excised suggests that the individual is not living for his or her own will. Everything they do is in the service of the Divine Will. In this sense one could argue that our civilization is the exact inversion of the ancient Egyptian Way. Nothing was Luciferian; nothing was rebellion. This may also indicate a state of Grace; a spiritual state whereby the individual had been physically ‘dead’, paralyzed, crucified, and then subsequently spiritually liberated through the conservation of energy normally engaged in our most prized motor-sensory activities. In the Pyramid Texts we read all the time about the stoppage of these activities. That energy is conserved and augments and strengthens the energy in the Broad Hall, Cavern of Osiris, Cavern of Sokar, etc. Yoga is often a first step toward this type of inhibition and stoppage of mind, motor-sensory, restlessness, trivia, etc. The energy can then be used to amplify and build spiritual potential capable of opening higher centers.  Note too, that the same Outer Core Circle marks the base of the sacrum, the very bone thought to contain the extra energy of the Goddess Kundalini that male initiation practices very much wish to raise up from the ‘wilderness’ within which it is enclosed. The initial awakening or stirring of the kundalini is a lot like awakening the Medusa from a deep sleep. There is a point of terror where one truly wishes the path had not been embarked upon at all! However, once awake, there is no turning back and one must muster the courage to swallow the consequences of the gift of that extra measure of pristine force. If it progresses naturally the Medusa will transform into the most beautiful of all things – a beauty overflowing with surprise.

Note below how the OC neatly contains two Moons. The contours of the

upraised shoulder muscles precisely follow the top curvature of both circles. The Inner Core appears to support the shoulders and arms while the ‘Outer Core” appears to move them as if like ball-bearings around the Inner Core. Note also that if the 1.078689 width contains the male Thoracic Vesica, the Outer Core is contained by about  .926 which is Unity ÷ 1.07991.

SCOM Circle and Golden Rectangle.

In this figure below I have put in the Shared-Center-of –Mass Circle (SCOM). According to this system of proportions it has a diameter that is identical to the width of the Prime golden rectangle, which brings us full circle. We are all the way back to where I started in 1985, with two rectangles: the Prime 2:1 and its cousin 2 × 1.236.  The SCOM Circle is set at about 73% of the Earth’s Diameter with a mean separation between centers of mass of Earth and Moon set at 384,401 km. Note the value of the Fine Structure Constant: it is 1/137 or ~ .0073.

Moreover, note below that 73 appears in Line 1 at Column VIII. 8472 is in Line 4 next to 5236 and next to 8472 is 13708, the reciprocal of 73 and both describing the value of the Fine Structure Constant. The royal cubit as a spatial measure seems to be related to the Fine Structure Constant via the square of the golden number or 2.618.

In the male canon this upraised armspan that gives the metric measure of Earth + Moon (for AU of 150,338,000 km) has a relative radius of 1.078689 × Unity. When we divide this the way Earth and Moon divide we have about .8472 (Column XV, Line 4) and .23148 for the male. This is a bit large for the female. We get the relative proportion of the SCOM Circle by taking 73% of .8472 = .618456 (Line 2, Column XI). When doubled this gives 1.236912 (Line 4, Column XI). What is remarkable about this is when we consider how many synodical months there are in ½ the year, or the semi-circle of the Earth+Moon orbit. It is 182.6211 ÷ 29.53066 = 6.184118. One feels that this proportion that links 73% to 6.184118 implicates the SCOM circle in the process of gestation. There are 12.3682369 synodical months in the year. 73% of that is 9.02 which is about 266.6 days. The average number of days for human gestation is usually given as 266. Gestation is an internal process and we have seen that it is internalized within the Pelvic Vesica Piscis, the same shape we see Christ framed by at Chartres. The two circles that overlap to create the female Pelvic Vesica are contained within the Golden Rectangle with width 1.236. Clearly the proportion of the SCOM circle must be playing an internal role in stimulating a cycle of gravitational pressure variation that converges at the Earth’s surface so that external gravity and internal gravity interact.

The Earth’s surface is acting like a gigantic spherical drum. It is as if we are all born from that drum. It is continuously undulating. Perhaps it could be called an ellipsoidal tympanic undulation. And this undulation proceeds in cyclic waves governed by constantly changing relations among Earth, Moon and Sun. Tidal variation cycles are particularly strong and generate particularly ‘affective’ waves that stimulate everything on Earth. There is no depth, no position, no proportional situation that could exceed the harmony suggested by the location of the Earth/Moon SCOM below the Earth’s surface so that it occupies about 73% of the whole diameter. I also think that the ratio of 1:100 with the value of the Fine Structure Constant is probably not a meaningless coincidence. Particularly striking about these harmonies is the way decimal relations dovetail with the preponderance of the golden proportion. The names of the numbers remain. What changes are the numbers of zeros to the right of the name. The meter is a decimal measure. It is taking the value of the squared-Earth-circle and dividing it by the decimal function (namely 10,000,000 for the side of the square).

The SCOM circle is the same circle that is divided by 3 to obtain the width of the female Pelvic Vesica Piscis! The relationship between the SCOM Circle and the male Pelvic Vesica is found through the value 1.078689 which measures the armspan in the position of the Ideal Angle giving the golden number in the AU Canon (namely 150,000,000 × 1.078689 = 161,800,000 km) , and also the width within which the male Thoracic Vesica is constructed! This is a highly unifying ratio as we have been seeing, but here we see that:

Male Pelvic Vesica = (SCOM ÷ 1.078689)/3

This amounts to inscribing the Pelvic Vesica of the male within  1.236 ÷ 1.078689 = 1.14583536. Another way to put this is just as interesting. The Vesica width itself  is simply 1.236 divided by twice the golden number or 1.236 ÷ 3.236 = .381966 or ~.382.  .382 is 1 ÷ 2.618.  We just saw 1.14583 earlier in the proportions of the Pelvic Complex. Across the Greater Trochanters is 3 and across the lateral edges of the Iliac crests is 2.618. 3/2.618 = 1.1459. The height is 2. When this number, 1.1459 is divided by 3 we get .382 of Unity for the hips compared to the female .412. I repeat,  .382 is Unity divided by the square of the golden number or 2.618. The golden number and its family shape function, efficiency and beauty. The golden number is not just a division. It is not static. It is the consequence of growth which is under pressure from the environment and from within. It is subject to gravitational pressure variation cycles. The result is a dynamic, adaptable pattern of reactions through which consciousness accumulates experience.

In the female there is a coincidence between the SCOM circle shown here as RS and several things at once. Note the joyful beauty that seems to arise so simply from the Aortic Arch (at IJ). This corresponds to the golden number measured

from the ground but also the top of the SCOM circle when it is centered over the midpoint or pubic bone instead of over the heart. It takes on special significance when placed over the midpoint of the body. The top of this circle of course exactly coincides with the golden number. The arms proper rise up from this golden number position. So you have golden number (1.618) and golden section (1.236 = RS) working together and meeting at the top of the heart – the Aortic Arch on line IJ. I repeat, the Aortic Arch is the top of the aorta. It is under a lot of pressure. It has chemoreceptors that send information back to the brainstem to inform the CNS of the state of the blood. The recurrent laryngeal nerve also wraps around the Aortic Arch as if adhering to an ancient history whereby the state of the heart and speech are united. I often catch myself ‘talking from my heart’. I have little consciousness of talking from my head. The heart seems to shape my words almost like a large voice box that pumps out words and sentences – what the ancient Egyptians referred to as “Words of Power”. Of course this also involves the lungs. The Vagus Nerve (n.10) is dominant in linking these central functions to the brainstem. But whereas I am highly aware of the role of heart, lungs, throat and tongue in driving words, I have no awareness whatsoever of the brain and its motor drive in shaping or originating words. It all seems hidden in the head as if the head were the most occult of all places not unlike the ancient conception and function of the Holy of Holies. This is one reason why I used the golden number to situate the ‘head of Atum’ inside the Great Pyramid as if it itself were the ’cause’ of the Pyramid and the means by which the Great Ennead of Egypt fashioned man in the image of Atum-Ra.

As echoed in Plato’s Timaeus, the head is the means by which man is made in that likeness. What is great about the Great Pyramid is to see how it links head to heart with this scheme. Recall the Hebrew “David” meant “Beloved of God: he who has linked his head to his heart”. In the image above, the Subterranean Chamber corresponds to the point where the Common Carotid artery departs the Aortic Arch. The Common Carotid Artery will nourish the head and brain with blood. On another level, linking head to heart refers to an advanced spiritual state that involves a metamorphosis of the ka, or double.

Note also how the Pelvic Vesica Piscis is involved in shaping the Greater Trochanters of the femurs. The curvature of the Vesica determines the relationship between the femurs and the Iliacs. The mouth of the Pelvic Vesica nearly coincides with the center of the Solar Plexus in the female (1.3333) and exactly coincides with it in the case of the male!  This is the midpoint between the kidneys and is also the midpoint of the abdominal circle that had once been the short length of the Prime Golden Section (.764 out of 2).

The breasts and heart are wholly contained within the SCOM circle as well as most of the Earth’s Inner Core when it is placed in this fashion. In the woman, the Pelvic Vesica and womb seem to be perfectly integrated with the entire Thoracic Complex that does not depart from Unity. The more you look at his image the more joyful it makes you feel. Moreover, the Thoracic Vesica Piscis falls right on the mouth, whereas with the male it falls on the nostrils as if inviting advanced, highly directed yoga. One imagines that the woman might do yoga for quite different reasons. But the most impressive feature of all, when the SCOM circle is placed over the pubic bone, it that it coincides with the width within which the Pelvic Vesica Piscis is defined. It is inside this Vesica that we are all gestated in 9 Synodical Months or ~ 266 days.

In the image above I have also noted one more point of unity in the female canon. Her hand appears to be exactly coincident with the span from mouth-to-vertex, which also seems to be the full height of the heart and this proportion corresponds to the SCM – identical to the 31.416 meter difference at the top of the Great Pyramid and the proportional relationship between the Capra nucleon speed and the speed of light in the vacuum.

It seems that the woman is less likely to exceed the 1.03 armspan than the male. I have kept the maximum Heart Circle here for comparative reasons. Like the navel there is likely an oscillation between male and female which oscillates around the exact .618034 in the case of the navel and between 1 and 1.0472 in the case of the armspan. The female tends to be around .625 and the male around .605 for the navel. It is likely the same with the arms and one must go individual by individual. The SCOM Circle itself would appear to be following a principle. But if so I stumbled upon it by accident. The accident occurred when attempting to understand what proportion might guide the male arms and hands besides just a tendency to do rougher labor work. I was imagining a conservation law within the Prime construction 2:1 + 2:1.236. The final constraints are 2 and 1.236 which relate as 1.618, the limit of all Fibonacci series. It is a natural, if wonderful, occurrence. If the female program is first and if the pelvic region must dominate for all of humanity to be born into the world, then by a conservation law, energy will be taken from some other areas. And if the male must develop higher speed and longer hands and arms with wider chest and bigger lungs, then energy will be taken from his pelvic region which will swivel less and be more stream-lined. At the same time, being more compact it may be that it concentrates energy in the sacrum and stores it up like a reserve. This inner Yin energy then beckons. It longs to be released from its dark, deep prison. Some men must descend into their own darkness to release ‘Persephone from the grip of Hades’.

The sense of descent in the sacrum is very pronounced. And once one enters the Pelvic Box the descent goes down to 1.618 of 2 (from ‘LM’ down to ‘nm’). The symbolism is quite remarkable. The heroes of many a myth – including that of Christianity – must descend into hell in order to be reborn. You have Lucifer; you have Orpheus; you have Theseus; you have Christ; you have Jonah. All must descend into the dark ‘house of yin’; house of Hades; “hell”, “purgatory”, the “Chaos”, etc. At the point of the Golden Number a conversion takes place. With increased confinement, the energy must accelerate and demands release. The Genie begs to be released from the V-shaped bottle! Really ‘Seth’ becomes ‘Horus’. ‘Lucifer’ converts to, or transforms into, ‘Christ’, etc. It is the two poles of one individual that undergoes the conversion. From deepest despair, alienation and a feeling of having been totally forsaken, one is resurrected to a state of exaltation. One is knocked down onto the ground – helplessly glued to the black earth. And then one is miraculously ‘raised’ back up again by unseen hands and experiences a great expansion of being. When this experience occurs in a dream it feels ‘religious’, ‘numinous’. It is impossible to convey because most of us only know the qualities from the outside. When you experience it from the inside everything changes. You see everything differently quite as if you were seeing ‘quantum effects’ directly, not merely reflected in macroscopic appearances. Nothing gets easier, really, but things just feel right at last. You discover that you yourself are the central drama of the self. This of course makes it more difficult to lean on outside illusions, but it can make one feel more isolated. You find you speak a language different from others when you feel it should not be different.

I’m quite surprised that so much triumphant joy would rise up from this image. This was not intended. I only intended to find the principles that delineated the differences between male and female forms. Her joy seems to be rooted in what is ‘right’. And what is ‘right’ has here been determined solely by the geometrical interactions that took me from 1985 to 2006 to find. Note how the SCOM Circle links the inner pyramid with ½-base equal to 1.5708 to the 2:1 rectangle with dimensions 1.618 x 3.236. 1.618/1.5708 = 1.03005. This is a good mean horizontal armspan for females. The radius of the SCOM circle reaches up to 1.618 but it is exactly contained within the 1.5708 pyramid. Its top or outlet coincides with the Aortic Arch of the heart. This is the root of the blood vessels that will cause the arms and hands to grow!


We have seen one method for squaring the circle already. We are now going to look at another method that starts with the same Prime 2:1 rectangle, ABCD. This time it will build the three grail tables on top of itself as if it were their mother. In fact the 2:1 acts like the mother and the father, not unlike Hexagrams #1 and #2 of the I Ching, which are complete inversions of one another. Line 1 is all solid light lines (yang) and #2 consists of all broken, dark, Yin lines. They could be considered the “bellows” of Lao Tzu from which the myriad creatures enter the world. This is one way to look at the first two numbers, 1 and 2, of Column I of Series E, or the next two: 5 and 10. The golden number, 1.618, is named by Column XIII. We will see just ahead that tubulin protein dimer subunits assemble into 13 slightly skewed columns to form

microtubules. The 13 columns close up a hollow core interior consisting of ‘ordered water’ that is free of all ions. It also seems to have a 3 nanometer thick layer of ordered water surrounding the tubes as if insulating them. The total diameter may be 29 nm which suggests some sort of optimum resonance capacity that might harmonize with hydrogen bonds in DNA. Some think the ordered water may be the site of an event called ‘superadiance’ in which all the photons achieve a common resonance or quantum state. This might be a critical aspect of consciousness. Microtubules seem to have multiple functions that range from mitosis to synaptic repair, to memory, to information processing, to consciousness itself. But I wanted to emphasize that they form in 13 columns and the tubules themselves bundle in a circle of 9 MT’s per bundle. When you cut open a column and flatten it you see the dimers are staggered and when counted they have been grouped in a pttern that divides into 5 and 8 which give 13. The golden proportion may be the means by which superadiance ignites consciousness in waves.

Squaring-the-Circle: 24-Method

We start by swinging the unity circle around point A and where it intersects the diagonal AC we mark E. We then golden section BC by swinging the compass from CE to CF.

This divides BC into BF and FC, where BF is 3.81966 and FC is 6.18034. By now we are very familiar with this pair of numbers. We can note that (6.18)² = 38.1966 so their golden section relationship remains harmonious in diverse ways. We now take 3.81966 as the radius of a circle that we create around the navel, marked here as “I”. Its diameter (NO) will be 7.64. 382 and 618 appear next to each other on Line 2 in Series E and 764 appears under 382 on Line 4 in Series E, immediately before 1236. All this suggests that these numbers are part of a process, a dynamic web that is regulated by the golden number. So in the image above we see the 3 grail tables centered over the navel. The circle has a diameter of 7.64. The square has 6 on a side. The 2:1 rectangle is 4 x 8. The trick is finding the diameter of the circle with circumference equal to the others, which is 24.  The way to do it without computation is to golden section the Prime 5 x 10 rectangle. Series E rounds 3.81966 to 3.82. If we took the actual golden section as 3.81966 and doubled it we would get 7.639320119. If we multiplied this by pi from Series E we would get 7.639320119 x 3.1416 = 23.999688. This is close to 7.64 x 3.1415926 = 24.00176. If we split the difference we can use 7.64 and 24.

The more I work Series E the more convinced I am that it was one ‘Net of Numbers’ known to Moses and housed in the Ark of the Covenant. Under Column III on Line 4, we find 24, because 4 × 6 = 24. 7 steps away is 764 under Column X, a new Unity, often heralded by ‘7’ steps.  22/π gives 7. So 24/π gives 7.64. 7.64 is the diameter of a circle with a circumference of 24. This establishes a pattern between Columns III and X. Take Line 6, Column III. It is 36 and 36 ÷ π = 11.46. Line 8, Column III is 48. And 48 divided by π gives 15.28. Line 24, it is 144 for perimeter with a diameter of 144 ÷ π = 45.84 of Column X. So Column III gives the circumference and Column X gives the diameter.

I’ll just briefly mention another way that Series E can ‘square-the-circle’. As an example I’ll just take a number from Line 2. If we take, say 6.18 and make it the diameter of a circle we can find the square with equal perimeter by tripling Line 2 to Line 6 and counting over 2 Columns to Column XIII which is 4854. What we find is that 6.18 × 3.1416 = 4.854 × 4. If you take 1000 from Column XII, Line 2 and go down to Line 6, Column XIV you find 7854. By using the decimal system we can see that 10 × 3.1416 = 7.854 × 4. So the exact squared-circle ratio 4/pi (or 1.27324) is built into Series E. 6.18 ÷ 1.27324 = 4.854. Another example would be 7.64 of Line 4. Go to Line 12 (or 4 × 3) and count over 2 Columns to Column XII. There you find 6000. So 7.64 × 3.1416 = 6 × 4 and 7.64 ÷ 1.27324 = 6

Let’s return to 24 for perimeter.

Line I above 24 is 6 and 24 is on Line 4. 4 x 6 gives 24. The circle has just been squared. The 2:1 with the same perimeter is easy: it is the inverse: 24/6 = 4. The 2:1 will be 4 x 8.  We should just dwell on Line 4 for a moment. We are looking to square the circle and what better line to look to than ‘4’. ‘4’ means squareness. Now in the K.C. the square with equal perimeter to the 5.236 x 10.472 perimeter is 3/4th its length which is 7.854 of Line 6, Column XIV. 24 is the corner of the first 3 x 4 rectangle: Line 4, Column 3. So 4 x 6 gives 24. Then Columns X and XI give 764 and 1236 which we have seen are the golden section of a 1 x 2 rectangle .764 + 1.236 = 2. But 7.64 is now seen to square the circle when it is the diameter of a circle and 6 is the side of a square. A rectangle that is 4 x 8 then completes the 3rd Grail Table:

4 x 6 = 24 = 8 x 3.

Line 4 goes on to give 5236 again, the royal cubit value and then 13708 in Column XVI which is the square of 4 and a member of the power of 2 Series. 13708 is a valuable archetype because in physics it invokes the dimensionless coupling constant, 1/137.036, (Fine Structure Constant) that determines the strength for the electromagnetic interaction at about the first Bohr Radius. This strength is relevant in biology because it determines the coupling strengths among electrons of biochemicals critical for life-structures and life processes. For example, the creation of ATP from oxygen, glucose and phosphate bonds, is a high speed operation. The brain and muscles need trillions of these phosphate bonds to transfer information while thinking, moving and so forth. So the speed of the bonding and transfer process is critical for optimum function. The electron speed has to be just right if it is to function properly and is determined by the Fine Structure Constant as c/137 = 2188 km/s. We have already seen the importance of 2.618 in the calculation of π as 6/5 x 2.618 = 3.1416. This appears in Series E under Column XIV, the royal cubit column, on Line 24. Once again ‘24’ gives a circumference. 24 hours is a circumference of time and space. But 5.236 is Unity in the King’s Chamber, or 52.36 cm. 52.36 x 2.618 = 137.08.

137 is also a reasonable measure for the overall length of Chartres excluding the Saint Piat Chapel. It is simply 5.236 x 26.18 which is the diameter of a circle with the same surface as the Chartres/Sphinx square with 23.193 m on a side.

Note that 84.72, 68.54 and 137 all appear in Series E. In cubits they appear again as 161.8, 130.9 and 261.8 respectively. My guess is that the builders of Chartres possessed this Series E and understood it in a way that I have only a glimmering of.

If you look at Column XVI you see 6854 in Line 2. This is the overall width for the 2:1 rectangle that measures the whole cathedral. 84.72 is the width of its cousin golden rectangle with length 137 meters. 8472 is next to 5236 on Line 4. 137 is under Column XVI. To find the square with the same perimeter as this all-embracing 2:1, it is just

68.54 x 6 ÷ 4 = 411.24 ÷ 4 = 102.81.

Now, 411.24 appears as 41124 under Column XVI on Line 12. The square with equal perimeter is 10281 under Column XVI on Line 3. It is well worth mentioning that the South Tower at Chartres has been measured from its base to the point of the steeple as 102.64 meters. The difference here is 17 cm. This is a small enough discrepancy over ~ 337 feet, to consider seriously the possibility that the South Tower is also the length of the side of a square with the same perimeter as the commanding 137.08 x 68.54 m rectangle. For centuries the South Tower has been regarded with special reverence. There is a simplicity and harmony that satisfies immediately. It seems very likely that the height was taken from the measure of a square with the same perimeter as the overall 2:1 that frames the complete cathedral. And as we know from the human body, this length is ¾ the height or 1.5 x its width of 68.54 meters. In our anatomy this is the place of the heart, the center of the Thoracic Vesica Piscis. I think many visitors to Chartres would agree that the South Tower goes straight to the heart.

Here is another fine example of the Three Grail Tables. The diameter of a circle with the same perimeter as the 102.81 square and 137 x 68.54 rectangle is found on Line 1, Column XIV as 130.9 meters. So you take 41124 of Column XVI, Line 12 and divide it by 31416 of Line 24, Column XIV to get Line 1, Column XIV. This is still a play upon ‘24’ because 24 Lines separates 1309 from 31416. Meanwhile if you take 130.9 as a diameter of a circle Series E will find for you the circumference and the square and 2:1 rectangle with the same perimeter. That shared perimeter is Line 12, Column XVI: 411.24 Given the importance of the 100 x 61.8 meter golden rectangle for measuring interior measures including the transepts, it is worth noting the harmonious difference between 100 and 130.9. It is 30.9 which is ½ the transepts. And 30.9 is very close to 1 second of arc at the Earth’s equator and is also ½ of 61.8, the exact internal width across the transepts.  A quick way to know the 2:1 and circle with equal perimeter is through the ratio of the common arm-span and the royal cubit: 137.08 ÷ 1.0472 = 130.9 so that 137.08/130.9 = 1.0472. The difference between 137.08 and 130.9 is exactly 6.18 meters or a tenth part of the interior measure across the transepts. Chartres is an endlessly self-interacting crucible of harmony that seems to be feeding itself with the inner wisdom revealed by Series E.

Again we have another pattern. Line 12 gives the perimeter while Line 1 gives the diameter but 2 columns back. Let’s take 809 of Column XIII we will find the perimeter on Line 12 at Column XV as 25416. 500 of Line 1, Column 12 will have a perimeter of 15708 on Line 12 at Column XIV. And this goes on until it goes out of phase. Series E is continuously ‘squaring-the-circle’ undoubtedly because of the presence of the golden number. So we can see a sort of inversion occurring here. When we are on the right in the vertical Column 3 we have the perimeter. When we go to the larger numbers in Column X we find the diameter. But when we are in the horizontal Line 1 we have the diameter and when we head down to the larger numbers we find the perimeters on Line 12.

137.036 is an interesting number. If you take the SCM as a constant ratio, say 4.6558 it creates a curious progression.

29.433 x 4.6558 = 137.036

137.036 x 4.6558 = 638.0122

638.0122 x 4.6558 = 2970.4572

2970.4572 x 4.6558 = 13,829.85463

13,829.85463 x 4.6558 = 64,389

64,389 x 4.6558 = 299,792

6 steps gets from a speed that is close to the Earth’s circular velocity to the speed of light. This is ~ 4.6558 raised to the power of 6 or 10,185

Curiously, Sirius B used to be about the Sun’s size and has now collapsed into a White Dwarf with a diameter that is 80% that of Earth which is about 10,185 km. If we divided the diameter of Sirius B by 4.66 we would get 2188 which is the speed of electrons in the First Bohr Radius or 299,792/137. A White Dwarf is thought to be held up from complete gravitational collapse by a ‘gas’ of degenerate electrons. What bet their speed averages to about 2188 km/s and that determines its size. In other words the Fine Structure Constant is affecting the collapse ratio of a White Dwarf. And the SCM is involved in establishing a progression.

The more one works these numbers the more one thinks of the phrase under the sculpture of the Ark at Chartres: “Here things take their course. You are to work through the Ark.” “Archa Cederis”. According to what we are seeing, “archa” must refer to the relationship between the circle and everything else. When things divide square-ness sets in. Square-ness is part and parcel of inverse square law forces: gravity and electromagnetism. Gravity and electromagnetism hold together the solar system, the planets and biological structures. The nucleus of the atom with their nucleons hold together the matter. And according to Capra the speed of that matter in its confined state is around 64,374 km/s. This number occupies a position in the little chart just shown above. Its relationship to the constant c is the SCM: ~ 4.6558, which is derived from the ideal SCM, 4.666 or 1.27324/.27324.

According to this number, this relationship, 4.66, the speed of light in the vacuum is being altered when energy (E) is bent or curved (Archa) into some type of enclosure or self-enclosure. The E reacts to its own enclosure and eventually will feel the reaction. It will become conscious of the reaction when a threshold has been reached. The square suggests an acceleration which is radius dependent within a field. The circle is in part a reaction to the square and vice versa. It seems that when they are in balance – when they have the same perimeters – something focuses. What focuses is an energy. Something opens up. The Eye opens and sees. When our vision is blurry we feel ill. So health and resolution are equal. And resolution seems to depend in part from squared-circle resolution. The underlying geometry is the basis of health. The etymology of the English “health” goes back to heath and the heather that is found there. This in turn came from a more ancient root denoting open, unploughed country. So health was originally associated with the most natural and unrestricted state of life. This would be the place of the Wild Mountain. The geometry that gives form would have to remain in communication with what is wild to preserve health. The golden number and squared circle geometry are probably doing just that and in fact this open relationship between what is wild and what is contained is likely a good way to characterize their function.

Let’s review this 24-method for squaring the circle.

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 (BF) as its radius. You inscribe a circle with diameter 7.64. Its’ perimeter will be:

7.64 x 3.1415927 = 24

The relationship between 10 and 7.64 is 1.309, so the reciprocal of 1.309 is .764. Recall that 1.618 ÷ 1.236 = 1.309. And this ratio framed the Ra-Horachty stele from the earlier post. I cannot emphasize the importance of this ratio enough. It should be emblazoned on a flag and be seen fluttering in the wind outside churches and courts of law. 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 (which is the square of 1.118), the Major 3rd in music; and 10/6 is 1.66666, very close to A-natural (440) (440/264 = 1.66666). This paradigm is packed with geometrical information that gives it remarkable self-focusing properties.  For the moment I should just mention again that I am rounding up 3.82 and 7.64 as in Series E. In fact they are bothirrationals 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 times 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. 24 hours sets the Circadian rhythms in the brain which according to the paradigm we have just seen fall in the King’s Chamber: Note how the floor of the KC divides the Unity Cube into .382 and .618! This is also the level of the Great Step.

The floor of the Queen’s Chamber corresponds precisely to the Foramen Magnum which is where the spine plugs into the brain proper.

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. Three tables bore the Grail. The Grail is the essence (in the Stone) by which the Phoenix is burned to ash and from which it rises again as lovely as before!

1.309 is acting as a key of transformation and this must have something to do with 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. So here it is the relationship between parent and child; Prime 2:1 and grail circle: 10 ÷ 7.64 = 1.309.  We can also see in Series E that these numbers are lined up through a diagonal from 1236 to 1500 to 1618 to 1309. And we can note further that 1.618 ÷ 1.5 = 1.078689, the width that contains the male Thoracic Vesica and is also the armspan set at the Idea Angle of botany which divides a circle by the golden section (137.5° + 222.5°).

If I were asked to be as specific as possible as to what I think “archa” refers to in the Latin inscription at Chartres, I think I would say the arcs that swing out the golden section and golden number within a 2:1 rectangle that in turn generate the three grail tables. The Ark that contains the root of transformation from an angular to circular table is the 2:1 rectangle. Through it things take their course. Concern for equality of perimeter seems to reflect a concern for the conservation of energy or spirit throughout the transformations within the 3 tables; the 3 phases.

This image is remarkable. This beautiful insect, carefully chosen by the Egyptians as one of the symbols of the entire opus of man’s metamorphosis, has arisen from a worm through this combination of three enclosures set over the ‘navel’ of the prime 2:1. This 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 fore claws 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 legs/claws. The precision of these interactive forms can only be expected in view of the precision of the scarab’s natural beauty.

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 = 1.618/1.236. 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. It is the feeling that the golden proportion is the “Stone” itself, the essence most pure, born in the midst of the activity of the 2:1 rectangle. The entire 5 x 10 seems to focus itself at the navel as if it were a new umbilical link to the 3 new Grail Tables. The volatile urge within the worm awakens and flows through the portal of that umbilical link as if magically. The 3 Tables that bear the grail limit themselves as they distribute the extrusion of energy among the three shared formats: square, circle, 2:1 rectangle. The 2:1 is the key to the limits and function of the main body of the insect. But the circle with equal perimeter carefully limits the antenna and the rear of the body.

The squaring-of-the-circle is the geometrical means by which this whole distribution of vital energy is facilitated and the golden section is the way the circle-is-squared. 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 as well as the underlying Prime 2:1. 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. This occurs when the plurality of names returns to the unity of spirit. The golden proportion and the squaring of the circle seem to be the means by which this metamorphosis takes place.

This paradigm also lends itself to a reinterpretation of the ‘brazen serpent’. There is the feeling that the 3 grail tables, generated through the golden section of a prime 2:1 rectangle, is the means by which the serpent is raised in the wilderness. The wilderness does not simply mean ‘sin’. It refers to the Wild Mountain of the Grail romances; untamed forces; the chaos of the alchemist that provides the extra energy for spiritual transformation once it has caught itself, like the uroboros, in its own ‘grail vessel’.

It is worth looking at other examples of where these 3 grail tables supported by the navel of a prime 2:1 rectangle, seem to be functioning. One overriding feature that seems to be common to all examples is the capacity to self-focus the diverse energies supported by the four tables in response to the surrounding environment. Obviously this self-focusing capacity must start small: at the microscopic scale. So I’ll show the tubulin protein ‘dimer’ first, based on drawings now familiar to many. According to Stuart Hameroff, who initiated the interest in the role of microtubules in the phenomenon of consciousness, these drawings are really quite schematic, ‘cartoons’ as he now calls them. But I will apply them to the ideal geometry anyway in order to illustrate the principle.

The world of tubulin protein is a science unto itself because they are at the border between quantum and relativistic scales.  They straddle and ‘partake’ of both behaviors – probably by alternation like most phenomena we know of. To the human mind this alternation can appear as contradictory. Being at the border between quantum and classical behaviors, they in a sense, appear to embody the ‘gap’ in our knowledge of how the mathematical descriptions of the two behaviors unite. Because Stuart Hameroff and Roger Penrose have persisted in their determination to explain the role played by microtubules in the physiology and physics of consciousness – in an effort to unify mind and brain matter – it is worth at least glancing at an image of one subunit known to be a double sphere occupying a tiny space that is 4 x 8 x 4 nanometers. Because they assemble into tubes consisting of 13 columns, they appear to either side as 2:1 constructions. They contain a hydrophobic pocket that houses a single, relatively free electron that moves back and forth between the alpha and beta spheres – a bit like a built-in switch! Hameroff now tells us that these hydrophobic pockets may be located in various parts of the double sphere. This schematic diagram here, then, is a sort of geometrical ‘what if?’, where the geometry can be seen as a bridge, a continuity that links the basic dimer subunit of cytoskeletal microtubules all the way to the newborn human infant. The geometry might play a role in the internal self-organization of all early one-celled creatures which are capable of learning and reacting in accordance with that learned state to the changing environment that engulfs them. According to this model, the golden section gets the ball rolling and may well be the means by which the learning and adapting takes place, making of a living thing something much more than just a crystal.

Note that ordered water, that behaves like crystal, is surrounding the tubes and is contained within the tubes’ cores, but the hydrophobic pocket has no water in it at all. Its electrostatic properties have expelled water entirely from the pocket where one single electron is housed. The change in dipole state of the dimer results in a change in position of the electron. This is accompanied by a change in shape or conformation of the dimer so that it appears to open and close or nod at its ‘mouth’. In the image above I have shown it in transition between the two positions and am offering a geometrical solution as to how it distributes its self-organizing mass during the conformational shifting. In its open state it is 4 x 8. In its closed state it may go down to a shared distribution between hexagon and square with equal perimeter – meaning 24 nm. I am also suggesting that the hydrophobic pocket may be 1.888 nm which is the overlap of both golden sections taken up and down, so that 8 ÷ 4.236 = 1.888. 4.236 is the golden number cubed, which invokes a volume and enclosure of a high order of harmony. This might play a role in expelling the water from the pocket. This is a zone of optimum stability and harmony that keeps the slightly larger (56,000 Dalton) Alpha sphere in contact with the slightly smaller (54,500 Dalton) Beta sphere. I should also note again that each tube consists of 13 columns of dimers (slightly skewed or staggered) but microtubules assemble in groups of 9, yet another example of an Ennead. Since MT’s are involved in separating self-replicated DNA during mitosis, this Ennead is quite fundamental. It also appears in the tail piece of the sperm and so is involved with a sort of whip-like and rotational locomotion that guides the sperm in its journey toward fertilization.  9 can handle a fundamental acceleration/deceleration cycle generated by 3 x 3. This is highly creative and interactive.

To help picture the scale of operation here, note that 4 nm is 1/100 the wavelength of violet light and 8 nm is about 1/100 the wavelength of infrared. Each dimer contains about 900 amino acids; 450 per monosphere, already displaying the fundamental properties of 2:1. The conformational shifting of the dimers when assembled into tubes is important because it seems to correspond to different states of electrical polarization. In this way they may well be capable of processing electrical information and conducting that information within the cell and possibly to the synapses. But the tubes are also capable of becoming insulated by ordered water that may allow their hollow cores to act as wave guidance systems or super-radiance devices whereby quantum coherence becomes a possibility. With 9 also involved with the 13 columns we have a rather complete picture of self-regulating, self-organization and information processing. Recall that the golden number names itself in Series E at Column 13, Line 2. I won’t go any further into the mathematics of the quantum wavefunction here (see Roger Penrose for clear explanations in “Shadows of the Mind”, 1994)) and how MT’s may be involved with all their golden proportion relations, but it is worth mentioning that for decades (after 1971?) Stuart Hameroff believed that anesthetics were working by seeping the chemical into the hydrophobic pockets of MT dimers, binding up the free electron and shutting off consciousness. And this is how the idea got going. There is so much more to say about the behavior of microtubules in the cytoplasm of the cell. There is the cell’s sol/gel cycle involving calcium. There is a metabolic input. There is the notion of feedback loops that would set up an amplification wave needed to generate the quantum wavefunction but also to contribute to the collapse of the wavefunction that causes matter to ‘choose’ a particular state over an array of possible states described by probability distributions.  What I wanted to do here was to show the possible role of geometry even at this tiny scale, in guiding the morphology within which quantum coherence might be able to thrive thereby allowing mind and brain to cyclically act as ‘one’ while yet retaining the principle of difference through alternation, dipole behavior, and of course the underlying exclusion principle of Pauli. I sometimes feel that the golden number retains the secret key that allows a stream of consciousness to be maintained because it divides things unequally. This staggered asymmetry – yet harmony – allows what is separated to be joined in a mobius like action that feeds back into itself. There is no learning like self-learning. But self-learning is also the suspense of self-transformation – or at least the potential for it. Just plain proliferation does not mean relatedness. The golden proportion and its family allows continuous relationships among parts whereby proportion becomes the secret ‘glue’ of the conscious present. As I have said repeatedly, the secret asymmetrical, but harmonious, signature of the golden proportion is .618.

Now let’s look at a similar shape but at a larger scale: same geometry. This is the very familiar human fetus. Though much larger in size it still conforms to the same shape as

the dimers and is also prone to ‘nodding’. Its height is wholly contained within the ‘8’ rectangle (in blue here), but its width including large forehead and lower dorsal region, fill out the original width of the Prime ‘5 x 10’ rectangle: and once again, with amazing precision! The arms, ears, eyes and heart are contained precisely in the area corresponding to the hydrophobic pocket of the dimer as if this slot which is 8/4.236 or simply 1 over the golden number cubed, were of particular importance. Here the heart is regulated perhaps. All the needs of all growing cells will have to be supplied by the heart which distributes everything through the blood. In this pocket a pressure differential is established and regulated which is one reason why electron ‘speed’ in the First Bohr Radius is so crucial. It is part of the efficiency with which oxygen and carbon dioxide are managed by hemoglobin and the iron atom that is at the heart of hemoglobin.

Next we will look at the same set of tables as they apply to the newborn infant after 9 months gestation. First of all note that crown to knees fits in the 8×4. But the feet take it ‘back’ to the 10 × 5 (ABCD). The baby’s width, excluding the arms is exactly ½ the width of the 4 × 8, so ‘2’. But the height of the head is exactly ½ the width or ¼ the length of the 5 × 10! So the head is 1 × 1.25 or qr/ru. The throat of the baby, who does not have much of a neck, corresponds to the center of the thorax in the adult.

Now note how the heart occupies the upper half of the ‘hydrophobic pocket’. In the dimer the upper half would be in the Alpha sphere which is slightly larger than the Beta sphere and carries an excess of negative charge. The head is what develops most prominently first in the fetus and is proportionally large. So presumably the head is carrying a higher charge than the caudal pole. It would appear to contain the seed from which all other growth extrudes. Here the heart is lodged between the golden section of the 5 × 10,

the center of the entire complex of smaller grail tables and the golden section of the 4 x 8, indicated by mn. The infant’s navel is the center of the 5 × 10 where the diagonals cross and the genitalia are at the lower point of golden section of the 5 ×10. To summarize, here we see a real co-operation between the 4 x 8 rectangle and 5 × 10 rectangle. Particularly striking is the head that has its height determined by the 5 × 10 and its width determined by the 4 × 8. The process of dimidiation of the 2:1 rectangles seems to be in evidence all the way to the adult. Note that the heart seems to be angled by the diagonal EG, which is upper right to lower left of the 4 × 8 rectangle. The two hands appear to be ‘plucking’ the invisible diagonals of the 4 × 8 as if they were musical strings – the strings that make the baby want to sing.

Next I have shown the morphological similarity between a global magnetohydrodynamic simulation of the Earth’s Magnetosphere and the human eye. I have placed the same tables in the upper half of a 2:1/hexagonal image that embraces the whole eye right to the cornea. The ‘hydrophobic’ pocket falls on the anterior half of the lens. The lens complex with cornea and so forth distributes its functions right through the grail complex as if the self-focusing properties of the tables were their most important feature.

What is important about this morphological comparison is the way the Earth is acting similarly to the lens of the human eye. When the geometry is added it seems we are looking at the means by which energy has been gathered up, or gathers itself up, and self-focuses through the ‘grail tables’. Comparable shapes result within differences of density and medium. But basic ingredients remain the same. Clearly for the medium to self-focus, the grail tables must build up an inner pressure: some of which is electrostatic. This then resolves the material into an ordered state which in the case of the eye permits perception.

The Magnetosphere looks different when examined from different points of view and in different ways. One rather extraordinary cross-section strongly resembles a lizard. The Earth seems to be acting like an electromagnet in the position of the nostrils above the mouth. Snakes and presumably lizards are 95% olfactory in character, which is to say their cerebral cortical development is 95% olfactory derived. A human is 80% visual. An eagle is 95% visual! So it is fascinating to see a common geometry at both ends of the sensory spectrum.

There is the sense of electromagnetic self-organization that involves decussation of electric current that weaves together these forms including volume. Once a vessel has formed around the energy that has crossed over and curved back upon itself, it is then able to build up. As it builds up consciousness becomes increasingly dominant as if it were the reaction to both internal and external stimuli. In this image the Earth acts like a seed around which lines of force gather. The creature always seems to have been formed around this little seed as if consciousness itself was vastly greater than the seed through which it is threaded!

In the image below one can see that the decussation of optic and olfactory is stacked on top of each other at the same site. It is marked by EF which is the golden section division of the Prime 2:1, ABCD. I have put in the ‘7.64’ circle to point out that it seems to create the boundary for the visual re-association area of the cerebral cortex. The ratio that dominates this boundary is once again 1.309 or 1.618/1.236.

Note that the angle separating the eyes is the same angle found in the Synodical Month, namely 29.1°. This angle runs to the back of the head. So in 29.53 days from New Moon to New Moon, the Earth and Moon together travel through 29.1°. And from the Sidereal Month (27.3217 days) to the Synodical Month (29.53066 days), the Moon travels 29.1° in 2.2 days.

Here in a slice through the brain at the level of the optic chiasm, we see the 29.1° recapitulated again.

With a feeling for the morphological shape of the magnetosphere, I would like to show the ‘teardrop’ shape that is familiar to many as an analogy to a rather intriguing image of Hour Ten of what is in the Duat of the Egyptians. We see an unmistakable portrayal of a well-known breathing technique practiced at advanced stages of ‘spiritual yoga’ where the intention has become the reconstitution of the Eye of Horus. The technique involves raising the kundalini by alternating breathing through the nostrils. The finger is used to pinch one nostril while one cycle is performed by the other. What happens is that the electromagnetic pathways stimulated by the very primordial olfactory decussation mechanism at the White Anterior Commissure, eventually with respiration and heart rate registered in the pons and medulla oblongata, stimulate the spine and provoke the

kundalini in the sacrum. This raises the ‘serpent in the wilderness’ – suggesting there can be a constellation of chaotic psycho-spiritual forces which makes available a large amount of energy. This then reaches an apotheosis in the realm of the ka whereby the Eye of Horus self-organizes around the mystical marriage of Horus and Isis eventually resulting in spirit-state or spirit-form.  What is striking here is that the two figures are not seated on anything concrete. There is no question that the figure on the right is using the right hand and arm to ‘pinch’ one nostril while the figure on the left is using the left arm and hand to pinch the opposite nostril. There are two serpents for the two halves of the spine. I placed the teardrop-shaped image of the magnetosphere below it to suggest how this great form has been recapitulated in a human endeavor on earth with a certain instinctual self-knowledge. With this breathing technique, it is not smell that matters but rather the meeting of various forces that converge electromagnetically to stimulate the kundalini. This undoubtedly involves heart rate and chemoreceptors on the Aortic Arch which communicate information back to the Medulla Oblongata in the lower brainstem. This in turn will influence the spinal column and probably the state of the cerebrospinal fluid that bathes the brain and runs down to the sacrum creating a cranio-sacral pulse. CSF is formed in choroid plexi that receive blood and then remove large percentages of material from the blood, dripping a clear, colorless fluid with a lower specific gravity into the four ventricles of the brain. CSF is renewed around the brain about 4 times daily, which is about the same as the number of tides in a day.

The alternating breathing balances, amplifies and stimulates the complete cranio-sacral complex. It is as if it acts upon a hydraulic pump that primes the well of the sacrum, drawing that sacred fire-water up the spine in a wave that will reach the King’s Chamber in the head and reconstitute the eye.

Possibly one of the most beautiful, startling, pure, compelling, inspiring and direct expressions of this intention of the Egyptian way can be found in Utterance 524 of the Pyramid Texts (Faulkner translation is just fine for this one) from PT 1233 to PT 1243. Note also that the endeavor appears to be reuniting the Red and White Crowns which in various texts are referred to directly as the Eye of Horus. They mean of course its function and its purpose within a human life; not its ornamentation. Utterance 524 is called “a text concerning the Eye of Horus”. It is a great one. It is complete. It is startling and it helps to understand the meaning of the image above. It strikes me that the sphere you see materializing atop the two serpents is probably the same sphere the image maker sculpted into the Ark at Chartres. It is the same endeavor, the same purpose, the same transpersonal inspiration:

“I am he who prevents the gods from becoming weary in seeking the Eye of Horus; I searched for it in Pe, I found it in On [Heliopolis], I took it from the head of Seth in that place where they fought [meaning Horus and Seth]. O Horus, stretch out your arm to me; O Horus, take your Eye; may it go forth to you, may it go forth to you when I come to you. May the Eye of Horus come to you with me, upon me forever.” (PT 1242-43). The analogy between this and the story of David and Goliath is striking. David takes Goliath’s head after slaying him by hitting him with a single stone in the middle of the forehead. Goliath is very close to the story of Seth. Seth is the material force that takes the Eye and imprisons it. The candidate for spiritual metamorphosis must retrieve the Eye. In Egypt it was found on Seth’s head and must be returned to Atum – the Lord of the Horizon. The King’s work is not merely for himself; it is for the totality, gods included. We can recall that π is the ‘horizon’ of a circle the diameter of which is ‘1’. The King’s Chamber in meters has a perimeter of π x 10 or 3.1416 x 10 = 31.416 m. One imagines that they intended it to be an inner gate or portal (sba) that opens the road or way to Him of the Horizon, Atum, the original, eternal.

Entrance to the Netherworld and the Golden Section

With this in mind take a look at the famous ceiling of Seti I of the XIXth Dynasty in the Valley of the Kings. This ceiling image portrays the entrance to the Netherworld. It is very obviously designed. All I have done is highlight it.

ABCD is an exact 2:1 rectangle. It is the same as the ceiling of the King’s Chamber. This 2:1 captures a rotation of the heavens around a celestial pole that shows the summit of the circumpolar North Stars such as the Big Dipper, here shown as the Bull of Heaven chained or tethered like Seth to the ‘Thigh Bone of the Horus Eye’, guarded by the pregnant Hippo, Isis, with Draco? (Alpha Draconis?) (or Sobk perhaps?) surmounting her to join the rotation. The standing Osiris King with up-raised arm connecting sky to ground, is pointing to the exact golden section of the 2:1 rectangle – the portal to heaven. The Bull is exactly ½ the width (AD or BC) of the 2:1 ABCD, implying that it has a value here of 1.309 compared to the Thigh of the Horus Eye held by the Hippo with value ‘1’. The height of the standing King with up-raised arm is also 1.309.  In this context the full length of the opening is 5.236 and its width is 2.618. In Utterance 524 just mentioned at PT 1238-39 it is stated:

“Atum summons me to the sky, and I take the Eye of Horus to him. I am the son of Khnum [Ram-headed Divine Potter], and there is no evil which I have done. Long may this word be in your sight, O Re; hear it, O Bull of the Ennead, open up my road, make my seat spacious at the head of the gods, that I may take the Eye of Horus to him and that I may cause to reknit for him that which went forth from his head.” (PT 1238-38, p196-7 Faulkner).

Note, also that when the thigh-bone or thigh of the Horus Eye is taken as ‘1’ which it is when enumerated in the Wadjet Eye, it divides Unity also by the golden section so that the length overall equals 5.236 which is the same as the archetypal Pyramid Profile of the Great Pyramid. The top of the mnj.t or Thigh Bone is marked by the hands of Isis and the outermost curve of her pregnant belly. The total Eye is 64. It is then dismembered by Seth. When it is reconstituted it adds up to 63, not 64.

Unity remains the thigh bone of the Eye of Horus also known as ‘qd’ and “mnj.t” with a value of “1”. In the Seti I ceiling Horus mounts to the sky on the “thigh bone” itself, with the Bull supported by his harpoon and tethered by the mnj.t – the seed or essence of the Eye of Horus. In some instances the “thigh bone” is referred to as a Mooring Post. In the Pyramid Texts the Mooring Post refers explicitly to Isis or Nephthys. Isis was associated in turn with Sothis or the bright star Sirius. The suggestion is that the Egyptians were treating Sirius as some sort of celestial Mooring Post, in turn associated with the axis of rotation of the heavens.

It is this essence that has everything to do with the Grail – the essence of the stone by which the Phoenix purifies and renews itself and cannot die. This is the inspiration that caught the minds and souls of the Templars and formerly, the entire Egyptian Civilization. When the essence is known; when the keys to the kingdom have been recovered then ‘things take their course”. You work through the Ark which carries the Eye of Horus. It appears that the King’s Chamber was designed to act as just such a portal:


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

Series A

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.


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 purified, quickened, perfected and 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 human body can perform a similar function.

It is March 12th, 2010. The sun is blazing through a baby blue sky over Nova Scotia. It is cold and the resolution is flawless even as the Earth quakes and trembles as if in the midst of the labor of rebirth. All creatures must commiserate together even if only unconsciously – the magnitude of the labor is so great. As I attempt to penetrate the secrets of what makes cathedrals masterpieces of holism, and our bodies masterpieces of expression, it becomes increasingly urgent world-wide to transform our differences into a source of creative energy capable of protecting and enhancing the world’s highly interconnected web of resources. We cannot master these differences if we cannot master ourselves. Knowledge can inspire and guide. But it must reach down to the very depths of our shared humanity, a humanity that includes every creeping, peeping sentient creature here under the sky.

I have had occasion to reread sections of Louis Charpentier’s book on Chartres Cathedral and find it even more impressive than I remember back in 1985. It reminds me of the mountain of work that still lies before me. How do I contain the cornucopia? How do I represent the legacy? What do I choose to leave out, given that most people are already overstuffed with information? Charpentier invokes for me an inextinguishable path of transpersonal inspiration. You must not give up no matter how stony the path may get; no matter how many thorns may block your way. Belief guides your aching feet. The Sun lifts you. The basics do not abandon you.

The 2:1 Table can be given many names. From it arise all the contents of the cornucopia. We ourselves are that cornucopia. We ourselves arise from the 2:1. We ourselves are the Grail and its content and have the potential for some sort of qualitative leap, a ‘mutation’ of the soul if you like – even an improvement in our physical constitution. The spirit can heal an ailing vessel  from within. We ourselves are subject to the path of 3, three tables, three qualities bound by one essence. The 2:1 has been called the Mystical Table about which nothing can be said. But in my experience everything can be said about it. That’s the real problem: there isn’t anything that cannot be said about it! As the root of everything, the door through which phenomena enters the world and becomes square or round or square again, it is the parent(s) of everything. For this reason I will show two methods by which the 2:1 rectangle can ‘square-the-circle’. For several purposes at once, I will concentrate on equal perimeter for the time being. It has proven to have real relevance in this work. In this post I will show one method first. But we’ll take a short detour first. There is always a detour to make in the Labyrinth. But every path leads to the center and the center leads to the periphery.

The King’s Chamber Squares the Circle

For the sake of a legacy, that which is ancient, I will remind the reader again, that the King’s Chamber, 44 meters above ground in the Great Pyramid – built from 100 large blocks of granite, including 9 ceiling beams up to 29 feet long (50 tons each!) – is an exact 2:1 rectangular shape with a height that is ½ its own diagonal or 1.118 x Unity. I will also repeat that its dimensions, 5.236 x 10.472 meters, are derived from its perimeter which in meters names π, 31.416 meters. And this length that has become a 2:1 rectangular enclosure, comes from the difference between the square and circle with the same perimeter: the geometry that forms the basis of the Great Pyramid as a whole. Only ½ the configuration is above ground, so it is 280 cubits (radius) minus 220 cubits (square) leaving 60 cubits, which is 31.416 meters. Note that the basic configuration here above ground is based on a semi-circle around a 2:1 rectangle: JKPQ. The difference between semi-circle or radius and the 2:1 is TS, 60 cubits, or 31.416 meters. A 2:1 is 1/2 a square but also is itself a double square. Nature likes dimidiation.

In the previous post I showed the geometry of the ‘sba’ gate where the opening width is 10 and the height of the opening is 31.416. This is framed within an overall 2:1 construction. If the 31.416 height is turned into a circle, the width of the door will be its diameter. If that is turned into a 2:1 rectangle, it will be 5.236 x 10.472 in dimension (10 x 20 cubits) which we see in the illustration of the KC below.

The golden number squared is 2.618. 12 x 2.618 is 31.416. Recall the walk around the labyrinth at Chartres is about 261.8 meters or 500 cubits. The diameter of the labyrinth at Chartres is close to 13 meters. It’s possible that it was supposed to be 13.09 which is the Great Diagonal of the King’s Chamber (DG above). Here we can see that 13.09 meters measures the Labyrinth and the opening across the Royal Portal. It measures between the pillars of the Nave.

These numbers all appear together in a single Fibonacci-Series shown below. The depth and breadth of this series is one of the delights of this work. I have felt for some time that ancient sages have long known this series and had recourse to it. It strikes me that the Templars may very well have gotten their hands on the same series and were instructed as to how to use it. It is a unique play between the meter and the royal cubit. It starts simply as 1, 5, 6, 11… and then it also builds in the vertical plane with 2, 10, 12, 22, etc.; 3, 15, 18, 33, etc.; 4, 20, 24, 44, etc. Eventually it names the royal cubit (.5236, Line 4), the golden section (1.236, Line 4), the golden number (1.618, Line 2), 1.309 (Line 1) which is 1.618/1.236 and by Line 24 it names π as 31416. Note that the outside measure of the transepts at Chartres is 130.9 cubits (Line 1, Column XIV) or 68.54 meters that appears on Line 2, Column XVI. This Series E is a genuine cornucopia of number. Moreover, number and phenomena seem to arise together in an ineffable embrace

Series E is characterized by “5”, just as pentagonal geometry opens the golden proportion family. 1 is common to any Fibonacci series. It is as if this Series E represents a ‘leap’ of some kind: a qualitative transformation of the Prime Series which is 1, 1, 2, 3, 5, 8, 13, 21 … etc. 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.

At Chartres, 13.09 is also the radius of the round table with the same surface as the Chartres Square Table with 23.193 m on a side. It also seems to determine the round point of the choir. Now, if I’m right and a 100 meter table was really used for the interior measure of Chartres for Nave + Transepts + Choir, then it is interesting that 13 would correspond

to the proper proportion for the head of a figure that was 100 meters in height. I’ll come back to this when I discuss the head more specifically. I will mention again that the perimeter of the Chartres Square Table identified by Charpentier is about 92.772 meters. This is 1/10th the measure around the ‘socket’ stones of the Great Pyramid noted by William Fix in 1978 as 927.72161 m. When the Chartres square is multiplied by 432,000 one obtains a very reasonable measure for the Equatorial Circumference of the Earth: 92.772 x 432,000 = 40,077,504 meters. The scale of the Pyramid was set at 43,200 of the Earth. Charpentier did not have accurate data for the socket stone measure around the Great Pyramid. So he did not quite realize the exact correspondence between the Chartres Square and the socket stone perimeter of the Great Pyramid. But he sensed it. The number 927 that appears in Series E on Line 3, Column XI, under 618,  has turned out to be yet another important number.

Some cornucopia! The Grail feeds glutton and ascetic alike!  Let me just point out for now that if we take the Astronomical Unit for a date that is a little past April 4, the day of the mean (149,597,870 km), we can easily accept a round figure of 150,000,000 km. No astronomer will haggle over that. The Earth is only ever at the mean position twice a year, otherwise it is on on one side of it or the other with a range of nearly 2,500,000 km on either side. In Series E, 1500 is right next to 927 on Line 3. So if we perform our archetypal golden section to the AU that is 150,000,000 x 75,000,000 we get ~ 92,700,000 km. Around April 17 it will be 150,108,000 ÷ 1.618 = 92,773,000. When I laid the incomplete geometry for an image of the Earth+Moon orbiting the Sun in 1998, the numerical information brought Series E to life when I used the meter. I also found it instructive to use royal cubits and at other times, the “light-second” or 299,792.458 km.

When I collapsed the golden section value into a circle, I recognized it as the circle with the same perimeter as the Chartres Square and Great Pyramid Socket Stone Square that gives the Earth’s Equator. Same number, just a different scale. Above we see the width of the Pelvic Vesica as 30,924,598 km. Below we see the diameter of the circle with the same perimeter as the ‘Chartres Square': 92,773,794/3.1416 = 29,530,746 km.

I began to fine tune the geometry as if it were self-adjusting. The Vesica Piscis of course is 1/3rd of the interlocking circles. In the female it is 1/3rd of 1.236 or the large segment of the golden section. Here, this is say: 92,773,794. 1/3rd is then 30,924,598. At the Equator of the Earth 1 second of arc is 30.922 m, which is also the width of the Parthenon and ½ the transepts at Chartres. 309 appears on Line 1, Column XI. It is ½ of 618, 1/3rd of 927 and 1/4th of 1236. The measure across the Pelvic Vesica is 30,924,000 but the diameter of the Pelvic Circle is ~ 92,773,000 ÷ π = 29,530,000 km. As it turns out this is the circle with the same perimeter as the Chartres Square: 29.53 m with a radius of 14.765 m. This becomes the base of a triangle that determines the elevations of Chartres all the way to the ceiling keystone. Jean Favier mentions that near the Western Towers it exceeds 36 meters from floor to keystone. If a radius of 14.765 is used as unity of a 2:1 we can see that the Ogive springs from the square root of 3 at a height of 25.57 meters. The keystone height would seem to have used the square root of 6 which gives 36.167 meters – a very, very good guess for the intended height of the original ceiling. The root of 6 is the diagonal of a “Root-5” rectangle which displays very harmonious properties and simply arise through a progression that I will show in another post. I’ll just note the relationship between 30,924,000 and 29,530,000 is 1.0472, that of the royal cubit or pi/6 = .5236/5.

An Eternal Paradigm: 2:1

With the 2:1 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 having separated after  New Moon, or just about to enter conjunction; 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.

If all of this were merely an intellectual exercise and had nothing to do with life itself or the conditions by which life arises, then it would not matter all that much and our curiosity would be guiding us to other troughs to quench our thirst. But the 2:1 seems to be at the root of life: the well-spring of consciousness; and that very mysterious urge for transformation – for a qualitative leap in being. How does this mysterious leap gather itself up? What is the means by which it accumulates energy and then transforms one pattern or set of instructions into a new and different pattern or set of instructions? Why does it transform instead of self-destruct? This is an important question because some systems do self-destruct at points of great tension – bifurcation points where the transformation cannot be contained and the whole system breaks down. In the case of a great paradigm shift, how does consciousness act as a thread, a link that maintains continuity between the two paradigms? Something constant must underlie the pattern shift. In the Middle Ages, the Grail was the Stone that both burned the Phoenix to ash but also contained within it the capacity to restore it to its previous condition. Since the Phoenix self-immolates, the ‘Grail’, then, must be the spiritual essence of the Phoenix itself, not unlike the Egyptian notion of the “ka” or double. In this sense the double acts like a template, a pattern that does not die with the previous form.  ‘There is no such thing as death, only the transformation of form!’ This adage is a tradition. And what each new generation wants to know is whether or not it is true.


Charpentier went 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’. I found its capacity to construct the golden number infallibly was one thing, but the ability to square the circle seemed to penetrate more deeply into the mystery of self-organization. Then 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 Prime 5 x 10 rectangle, ABCD. The diagonal AC is put in place. The compass starts on A, is opened to AB and swung into a 10-meter diameter circle that crosses the diagonal at E. A is now also the center of the circle, PB, which is the length of the 2:1 or 10 meters. 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 the  opposite side of the 2:1, 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 40.0050. 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 10 x 10 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.

We can also recall that the Royal Portal at Chartres appears to be proportioned 2:3 also. In one common proportional ‘frame’, we have both operations: the Vesica Piscis, which at Chartres frames Christ on his throne, and the ‘squaring-of-the-circle’, which unites above and below, spirit and matter; male and female. In some traditions outside Christianity, this is the very definition of Christ on a universal basis. Christ is the triumph of ‘grand reunification’ after the tribulation of separation, alienation, disconnection, the profound and sometimes prolonged feeling of having been forsaken by the entire universe including the divine itself! There is also a phase in which one can feel forsaken by the feminine. This is a transitory separation that is the prelude to the archetypal mystical marriage in which the male consciousness is reunited with the bride of the soul. I suppose one could call this the transformation of the anima within.

Since so many of the numbers that appear above also appear in Series E, I will just note again how Series E starts. The first line is 1, 5, 6, 11, 17, 28, etc. The second line is 2, 10, 12, 22, 34, etc. So in effect this Series transforms horizontally via a leap from 1 to 5 and vertically by going from 1 to 2. It then proceeds from there. The golden number, 1.618, is named on Line 2, suggesting that it is necessary for 1 to divide into 2 before the golden number itself can be named. Here, it is Line 2, Column XIII. This Series E in fact gives square values that seem to be arrayed around a nucleus, 1000, of Line 2, Column XII. I will have to explain this interesting property later.

Given everything that has been said so far about this simple 2:1 rectangle, it is worth contemplating closely how it has squared the circle here. The first ingredient is the diagonal, AC. Then a circle is drawn around point A that cuts the diagonal at E. AE = AB which is Prime Unity or here, 5. This leaves 6.18 for the rest of the diagonal, EC. EC becomes the radius of a new circle with diameter 6.18 x 2 = 12.36068, centered on C. Now comes the most interesting part. This 6.18 radius, (the golden section and navel position of BC and the length of the Prime 5 x 10 rectangle), cuts the opposite side of the Prime 2:1, AD at G. So it has reached across the 2:1. This forms a new triangle: CGD

with 6.18 as its  hypotenuse and 5 (Unity) as its base. The short side is easy to calculate and turns out to be 3.6327, which is the square root of (6.18034)² – (5)² = 38.1966 – 25 = 13.1966, the square root of which is 3.6327. The angle formed by CGD, incidentally is that of the pentagonal triangle, 54°. So you have 54° + 90° + 36°. When this is doubled you have 54° + 54° + 72°.  This is also a way to construct a pentagon, by doubling GD. The remainder of AD is naturally 10 – 3.6327 = 6.36728. And it is this that becomes the radius of a circle with circumference equal to 40. The creative aspect of the 2:1 is also the way it generates dynamic equilibrium through complementary opposites that start with 1 becoming 2 and the diagonal that links opposite corners, A and C.

We have here 3 circles. The inner circle has a diameter of 10. The next circle is 12.36068. They relate as 1:1.236, the same length that determines the navel and the size of the Pelvic Vesica Piscis in the female. If the Thoracic Vesica is 1, the Pelvic Vesica in the female is 1.236, contained within the golden rectangle, EFGH. This golden rectangle holds more surprises ahead that I hope we will be able to get some handle on, as it involves gravity.

The third circle is 12.734. It relates to the inner circle as 12.734:10 or 4/π. And it relates to the middle circle as 12.734/12.36 = 1.03007. This latter ratio happens to be one category for a common male armspan in the horizontal position. The other most common is 1.045 which is probably from 1.0472. In my armspan, one is 1.03 and the other is 1.047. If you multiply them together you get the following:

1.03 x 1.0472 = 1.078689 = 1.618 ÷ 1.5 = 2/3x 1.618

This 1.078689 holds the key to the male anatomy and how it differs from the female. Note the reciprocal of 1.078689 is .927. With the AU-Canon as a template for the meter, one can see that ‘927’ concerns the generation of the female Pelvic Vesica and hence the womb. Even the number for the Pelvic Circle is a ‘lunar’ number, 29,530,000 km, the Synodical Month being 29.53 days. Through laws of harmony – the way spacetime is broken down into measures, the day and the meter find a relationship through this number 29.53.

Note, too, that there are only 4 points where the inner ‘10’ circle coincides with the square. At all other points, it is contained by the square. This seems to establish the four cardinal points which may act as outlets. The inner circle, on the other hand, is wholly contained within the 12.734 circle.  But the square itself pushes beyond the outer circle at its diagonal points which are 45° to the cardinal points. In contemplating the King’s Chamber from this perspective, one can see that it has the same diameter as the inner ’10’ circle. So it is ‘The Circle-in-the-Earth-Square” and is wholly contained within the Earth Circle. Since the King’s Chamber is located deep within the Great Pyramid and when it was found by Al Mamun in 820 A.D. all the passageways were plugged with heavy stones that could not be moved. The feeling is that the King’s Chamber was designed to be completely hermetically sealed so that it could accumulate the very energy discussed above, by which the Earth’s magnetic field, electrostatic energy and gravitational ‘self-energy as it is called today, could reach a threshold capable of inducing the coveted metamorphosis symbolized by the scarab “Khepere” (The Transformations of Re). The harmonies locked into the paradigm of the King’s Chamber appear to be such that the essence of the Stone (Grail) that ‘burns the Phoenix to ash’, is capable of perpetuating the link between body and ka in the act of spiritual rebirth. At the same time this is what was known as the entrance to the Duat or Gate to the Netherworld through the portal of the 2:1 paradigm; the sba.

In the image above I have laid out the basis of the female anatomy with head, thorax and pelvic vesica. There is a great deal of information in this one image but it will be too complicated for right here. The Thoracic Vesica is 1/3rd of Unity (AB) and the Pelvic Vesica is 1/3rd of 1.236 or the golden section of the height, 2 and width of the golden rectangle, EFGH. I have laid 3 ‘grail tables’ over the navel position, but will discuss them at a later stage. The mouth of the Thoracic Vesica falls exactly on the mouth of the archetypal head marked with a dotted line. I put this image in to provide a sense of how the figure  gathers itself up within the basic geometry and even at this early stage seems to want to spring to life. The golden section within a 2:1 paradigm contributes enormously to this well-spring of life.

In the image below we see the same basic paradigm applied to the Astronomical Unit. Here the golden section is playing an even deeper role. The short length that is around 57,338,563 km is collapsed into the abdominal circle that will contain key organs including pancreas and kidneys; while the larger segment, 92,773,794 km collapses into a circle that is 29,530,815 km and becomes the womb. It is a striking coincidence that the lunar number associated in days with the Synodical Month (29.53066 days) should show up in meters or kilometers in the Pelvic Vesica and Pelvic circle. A human gestates according to the Synodical Month in exactly 266 days or 9 synodical months. One can say, provisionally, that the Synodical Month (29.53 days) has a formative influence on human gestation. It determines ovulation. And when the golden section is divided by 3 we here have 30,922,000 km which is another lunar number. In 25 years there are 309.2 lunations or synodical months. The width of the Parthenon is 30.922 meters. The internal width of the transepts at Chartres is twice that, or about 61.8 m, or some say a few centimeters more.  One second of arc at the Earth’s Equator is 30.922 meters. The Parthenon is also based upon ‘squared-circle’ geometry but I will have to show it elsewhere.


Now take note of the difference between AG and AN. It is 1.3673 = 6.3673 – 5. And we can note an archetype here also worthy of contemplation. 6.3673 ÷ 1.3673 = 4.6578 = AG ÷ NG.

We have already seen this relationship in the Great Pyramid which I will now show again. The number that corresponds to 1.3673 is 60 cubits or 31.416 meters. This depends from the scale of 1: 43,200, proportioned to the size of the Earth. 432 is itself a member of an important number series I will call Series A, very familiar to the ancients. I will give some members right here:


27  54 108  216 432 864  1728 3456  6912  13,824  27,648  55,296  110,592

Best to note here that one prime interior measure at Chartres is from immediately inside the Royal Portal all the way to the interior Round Point of the Choir is 110.76 meters. Due to the Earth’s flattening, a degree of longitude lengthens by definition as one walks from the equator to the pole. At about 8° Lat the degree of longitude will be 110,591 meters (13th member of Series A). At 25° it will be about 110,764 meters. At Chartres itself a degree of Long is about 111,180 meters. This measure would be very easy to accommodate by simply starting from closer to the immediate door itself at the Royal Portal. Series A is amazing. In miles it gives the Moon’s diameter as 2160 miles or 11404800 feet. When this is divided by another member of the series, 172,800 you get:

11404800 ÷ 172800 = 66 feet

This is the height of the Great Sphinx and two obelisks that disappeared from Heliopolis near 1200 A.D. when the Templars were rebuilding Chartres. A shadow cast by that height at Noon on the Equinox would be ½ the Chartres Square: 11.5965 m.

Above I have marked the proportions where the ½-base is 1.618 = 220 cubits = 115.192 meters. The height is 280 cubits or about 146.6 meters plus a 1/2 – meter platform, totaling say 147.108 meters. The difference between the whole height and the square is 60 cubits or 31.416 meters. 280/60 = 4.666…

Since this is an important point I will also show this in a closer up version. It allows a better viewing of the King’s Chamber looking west. The 31.416 meters that can be seen at the top of the pyramid have been turned into the perimeter of the King’s Chamber. It is as if the whole intention was to take that 31.416 meters and turn it into the sba gate, the entrance to the Netherworld. But what the Pyramid Texts tell us is that the entrance into the Netherworld is  through and as the Eye of Horus. Therefore the King’s Chamber must be the place where the entire endeavor of the Egyptian Civilization reaches its apotheosis; namely the reconstitution of the Eye of Horus. The Egyptians saw this as an example of the principle of Maāt, or Cosmic Equilibrium. And they viewed the Squaring-of-the-Circle as a fundamental expression of Cosmic Equilibrium or Maāt.

Pi represents the horizon of a circle. Horachty meant Horus-of-the-Horizon. Sometimes Atum is referred to as “Him-of-the-Horizon”. The Berlin Papyrus suggests that the name is so mysterious that it cannot in fact be named or even uttered. It is experienced by the spirit of any candidate as too powerful and too mysterious or infinite to label. Encountering the horizon of Him in spirit form absorbs words, language, metaphors and was well-stated by the Hindu as just “that”. “That” is simply the essence of spirit that has shed the corporeal body and even, according to the Tibetans, the double or ka. Sages have long thought that pi, 3.1416… genuinely represents or points to that mysterious “Horizon”.

SQUARED-CIRCLE-MODULUS: 1.27324 ÷ .27324 = 4.659

Around 1999 I stumbled upon a few clues that turned my head and helped me solve a number of outstanding problems with both female and male geometry. This occurred after I had a preliminary drawing based upon the AU for April 16th, 1998 (~ 150,108,000 km). Two examples are particularly important. One is a macroscopic resolution which nevertheless has retained considerable mystery. It involves the proportional relationship between the Earth and the Moon. The other is a quantum-scale resolution that concerns the mean momentum energy associated with the nucleons (protons and neutrons) that compose the bulk of the Earth’s atomic mass.

Scientists do refer frequently now to “Mearth”, acknowledging that the behavior between the two bodies is not a typical planet/moon relationship but also possesses aspects of a binary planetary system. For example the Moon is always falling toward the Sun in a concave orbit and even when approaching the waxing square in its orbit around Earth, never goes convex to the Sun the way other moons do, for example around Jupiter and Saturn. Earth and Moon fall together toward the Sun a greater distance than ever the Moon climbs against the Earth in any given time frame. Now, let’s take the  mean diameter of the Earth as about 12,732 km and the diameter of the Moon as 3476 km. Together they add up to 16,208 km which is close to the number of (4/π) ² or 1.2732 x 1.2732 = 1.621. I have shown this above in the drawing of the Great Pyramid. 1.621 is just a little bigger than the golden number, 1.618, but geometers often consider ways that these two great factors work together or dovetail. If you add the Earth and Moon together and divide by the Moon you get: 16,208 ÷ 3476 = 4.66. The Moon is behaving exactly the way the 31.416 meters are behaving at the top of the Great Pyramid. It is important to emphasize that the Egyptians appeared to follow the soli-lunar cycle religiously – literally. They were not only aware of its physical influences, but were equally aware of its spiritual influences and so kept 29 altars, one for each day of the synodical month which is also the  female infradian biological clock.

In the image above I used an Earth radius of 6367 to be consistent with the Squared-Circle illustration shown earlier. I could also have used a cut through the Earth according to its tilt which would be about 6370.5. But for now I will stay closer to the mean for convenience.

The difference between the Moon and our Squared-Circle archetype is that the Moon and Earth have become separated by about 384,401 km between their respective centers of mass. THEY ALSO SHARE A COMMON CENTER OF MASS THAT IS LOCATED ~ 1700 KM BELOW THE EARTH’S SURFACE. This I am calling in the human canon, the SCOM circle or ‘Shared-center-of-Mass’ circle that we have already seen without comment. Its relative size within the final canon is remarkable because it coincides with the golden section! We have to discuss the Astronomical Unit first and how the separation between the Sun and Earth/Moon influenced details now incorporated into the geometry of the male in particular. Then we can appreciate the proportional size of the SCOM circle in the final canon. But that it coincides with the width of the golden rectangle is a remarkable example of the harmony among Earth, Moon and human anatomy.

The Moon is 27.3% of the Earth’s diameter or 3476/12,732 = .273123. It is instructive that the Sidereal Month is 27.3217 days or 27.32% of 100 days. After the mean period of human gestation which is 9 Synodical Months (265.77 days), there are almost 100 days remaining in the year (99.48). Incredibly, this remaining period is where the tradition of the progressed lunation cycle derives from because it shows that 1° approximately equals 1 day which approximately becomes 1 year. Perhaps this suggests that most of us ought to be able to reach 100 years of age if circumstances permit. It’s like an internal implicate clock that simply requires reasonable explicate expression – maintaining natural rhythms – to make it to 100.

Meanwhile the Moon during our time, has taken up a position in the sky where it has about the same angular diameter as the Sun when viewed from Earth. Most scientists of the last few hundred years have regarded this coincidence as meaningless. But as science begins to think more in terms of systems, webs of circumstances, patterns and phases within patterns, it is possible that we will come to see this coincidence as meaningful. My guess is that we will see a type of gravitational resolution in the order of a form of gravitational self-focusing. This is what an eye does. The eye does it largely in response to electromagnetic radiation or light. We will look at the geometry of the eye in a future post, once we have examined another method for squaring-the-circle. But at the level of planetary bodies, gravity plays a much bigger role and in fact the Earth and Moon are bound together in a very shared gravitational field. Just a planetary body on its own is an eye-like resolution. It is gathering spacetime around itself in a shared field. The Earth and Moon are completely immersed in the Sun’s field but the Moon’s tidal influence on the Earth is greater than the Sun’s. The Sun’s inverse square gravity is greater on the Moon than the Earth’s is even though the Earth is so much closer. The Moon’s tidal gravity is about 2.18 times greater than the Sun’s tidal gravity, while the Sun’s inverse square gravity is 2.2 times greater than the Earth’s is on the Moon. There is a form of decussation going on between tidal gravity and inverse square gravity. Tidal gravity is approximately an inverse cube force that is stronger across shorter distances. It is my conviction that this sets up a  tidal gravitational variation cycle around the Earth that helps set both Circadian and Infradian biological clocks located in the suprachiasmatic nucleus just above the optic chiasma in the hypothalamus. Shifting locations suddenly induces ‘jet-lag’. Probably the cause is upsetting the entire metabolic clock that has adjusted to the tidal gravitational variation cycle that stimulates very subtle levels of cell activity such as cytoskeletal microtubules which are involved with consciousness itself. So jet-lag involves even how we think and how our muscles work. It would take up too much space to theorize here how it came to be that the Moon and Earth share these crucial proportional relations. But it suggests to me a very ancient history when both bodies could be shaped together by the same forces operating in the same field. I don’t think the Moon came wandering in from outside. My guess is that the Moon and Earth were once so close together that they were able to be separated in a proportional manner. Now, not only is the Moon proportioned as .2146 or 1/4.659 of the combined diameters, but it has also taken up a position where it appears the same size as the Sun only from the surface of Earth. This suggests to me a form of symmetrical gravitational self-focusing in a shared field. This also increased the harmonious properties of the symmetry. But I am suggesting that this ‘4.66’ factor is not merely harmonious; it is fundamental. The builders of the Great Pyramid were very cognizant of it since they based the dimensions of the King’s Chamber very precisely upon this factor: 280 ÷ 4.66 = 60, or 146.4 ÷ 4.66 = 31.416 meters. And this we have seen is based upon a scale model of the Earth set at 1: 43,200. At Chartres and the Great Sphinx the scale is set at 1:432,000 instead. From an engineering point of view, Chartres could manage a 36 meter vault (118.65 feet) but not a 360 meter vault!!

Terrestrial Nucleon Speed

The next example of the involvement of squared-circle relations came as a real surprise. I had read Fritjof Capra’s “Tao of Physics” in 1981 and had come upon two pieces of information that were memorable but which I assumed were extremely ‘ballpark’ in intention. However, in 1999, when I came upon this proportional relationship between Earth and Moon, I was also checking physics because of the fact that gravity was presumed to be operating in the vacuum at the speed of light just like electromagnetic radiation. So gravitons were supposedly a bit like photons: massless, spin-2, etc. And it was thought they might couple at some point and operate in the vacuum together. At the nanometric scale of microtubules, I thought this might be interesting especially if quantum gravity was a real factor and was capable of ‘tripping’ the quantum wavefunction as it is called.

One day I just intuitively checked Capra’s ‘nucleon speed’ against the speed of light and gravity in the vacuum, believing that this had to be proportioned like any other significant factor that has contributed to the ability for our bodies to build up at the Earth’s surface into what we are today. Capra had given a strangely rounded figure for the ‘Heisenbergian momentum’ associated with the mean energy of all terrestrial nucleons (protons and neutrons) which make up the bulk of the mass of the Earth. We are to picture entities that are ‘boiling’ away in their extreme confinement, far removed from the First Bohr Radius where the electrons begin to be distributed in wave patterns around the nucleus. The nucleons can’t get too close together and can’t get too far apart. Either way there is a powerful force of repulsion or attraction keeping them locked in place in a state of extreme agitation that can be expressed in terms of ‘speed’ or ‘momentum’ relative to position as calculated by Heisenberg’s complementary Uncertainty Relation which makes use of Planck’s tiny little quantum constant as its frame of reference. Capra gave about 40,000 miles per second worth of momentum or speed. He did not make his calculation on the basis of color theory with quarks and gluons as factors in how that momentum energy would be distributed or shared. But I wrote him in 1999 and asked him if I could take the figure of  64,374 km/s seriously? I basically told him what I wanted to do with it. I also asked him about his electron speed that was close to 1,000 km/s compared to 2188 km/s for an electron in the First Bohr radius. Capra did not feel it was necessary to modify or place his figure in any sort of parenthesis. He clearly had confidence in basic rules that had allowed him to calculate such a figure for all the nucleons on Earth. The Earth is not very massive so there is nothing going on here within the atomic nucleus such as we see inside our Sun or larger stars if fusion-burning is the correct explanation for the way our Sun is powering its light.

Here is what is so interesting about a figure of 64,374 km/s. Apparently nothing can move through the vacuum faster than light which is about 299,792.458 km/s. A massless photon cannot exceed “c”. If its energy is increased it will increase its frequency, not its speed through the vacuum. It will increase its agitation while moving. The frequency is important because the visible light spectrum is only a tiny segment of the great spectrum of electromagnetic energy. And we humans are tuned to the visible spectrum to a high degree. So frequency matters to humans – among a host of things – such as temperature, atmosphere, oxygen supply, air pressure, gravity acceleration, etc. Our Earth is quite the ally, friend, nurse and sanctuary!

If gravity also moves at this rate (299,792 km/s), then it might be important to know the proportional relationship between the confined momentum of our mass-carriers – the same nuclei that support the atoms found in carbon, calcium, iron, potassium, chlorine, oxygen, hydrogen and so forth. These atoms then heap up together into real gravitational effects which become significant at the macroscopic scale. In our bodies each atom does not possess much gravity. Electromagnetic forces are relatively much, much stronger. One way to represent that strength is through speed. So that at the First Bohr Radius we can represent the energy and the strength of the electromagnetic interaction by dividing the speed of light by the very important Fine Structure Constant also known as ‘alpha’. Alpha has an effective value of 1/137 so that the speed of the electron in hydrogen can be calculated as c x 1/137 = 299,792.458 ÷ 137 = 2188.266 km/s. The relationship between the electron in the First Bohr Radius and all other electrons on Earth is approximately 2.188 or ~ 2.2. We had just said that the Sun exerts about 2.2 times more inverse square gravity on the Moon than Earth does and the Moon exerts about 2.18 times more tidal gravitational influence on the Earth than the Sun does. The Moon is moving 2.2 times faster in its orbit around the Earth than the Earth is moving at its Equator: 1.023/.4651 = 2.2. The Earth rotates faster in a day because it has far less distance to go. At the Equator it has to go about 40,075,035 meters. It does this in about a day. But the Moon has to go much further even though it is traveling 2.2 times faster. It has to make about 2,415,262.7 km to get around the Earth in its 27.3217 day Sidereal Orbit. This is about 60.26 times greater in distance. So, naturally, 60.26 ÷ 2.2 = 27.3, which is the days in the sidereal month, the Moon also being .273 or 27.32% of the Earth’s diameter. The Moon is locked into a synchronized roll as it orbits the Earth. It rotates the same rate that it revolves as if the friction (and gravitational resolutions) were acting like a fixed axle and it were a cart on wheels constrained to a gravitational path. But this imparts cyclic regularity to the Earth/Moon/Sun dynamic. For the ancients, the fixed regularity of these cycles of motion of Moon, Earth and our relationship to the Sun constituted the most basic laws governing all aspects of life on Earth. Everything was subsumed under these cycles of motion. The constellations like Sirius, Orion, the Great Bear, Alpha Draconis, Regulus and so forth mixed their influences in with this basic Triadic Paradigm. Man himself was sculpted on the Potter’ s Wheel by these cycles or arcs of motion.

These examinations encouraged me to treat Capra’s ‘nucleon second’ in a similar fashion. I was imagining an inversion where a balance was struck between macroscopic resolution (and regularity) and microscopic or quantum balance where, through confinement, the one energy slows down in one respect since it is changing from massless energy to mass-energy through the curvature and self-enclosure of spacetime, but by containing that energy forces it to speed up according to specific rules or at least proportions. I strongly believed that proportion would have to play a role because the vacuum was being involved in the curvature or self-gravity; or self-attraction process. The spacetime vacuum was involved and proportion was one indicator that described the involvement. It was curving itself and reacting to its own confinement; its own self-enclosure. I could easily picture the squared-circle effect as a self-reaction: a geometric tendency toward dynamic equilibrium akin to hydrostatic equilibrium. Well, one day I simply related Capra’s figure to the speed of light:

299,792.458 ÷ 64,374 = 4.657

I definitely gulped when I saw this. It invoked what we had just seen above with the way the 5 x 10 rectangle squared the circle:

6.3673 ÷ 1.3673 = 4.6578 = AG ÷ NG

With time I came to call this 4.6578 factor, the “Squared-Circle Modulus” (SCM) because I found a path from the Fine Structure Constant all the way through Capra’s nucleon speed to the speed of light with some interesting stops along the way – all through the number 4.6578 or there abouts. I will show this path later. As a ratio it was behaving similarly to the golden number. But what is this factor? And why do we find it also associated with the Earth/Moon proportions where by a sort of inversion, the Moon is acting analogously to the internal agitation or activity of the highly confined nucleons – the carriers of what we call mass-energy: energy that is densely confined and so starts to behave like matter? To repeat: in the one instance the SCM is referring to speed or a rate of propagation of an energy relative to the vacuum. In the case of nucleon momentum, it is not to be pictured like a speeding bullet moving from A to B. Rather it is a self-contained distribution of motion-energy, highly confined and relative to its position (or confinement). In the case of the Moon it primarily refers to diameter or the amount of space occupied by a celestial body in a gravitational field. In the case of the nucleons, the speed (64,374 km/s) is certainly offering resistance to gravitational collapse. It also seems to be imparting stability to the identity and lifespan of protons in particular. In the case of the Moon, speed is certainly playing a role in its position but the SCM is describing the volume of space that it occupies as if Earth and Moon had been sculpted proportionally out of a single mass. So what is so interesting here is the proportion itself, namely ~ .2146, or 1/4.66, that links speed to volume.

The Moon appeared to me like a point of macroscopic inversion in a gravitational field intimately shared with the Earth and dominated by the Sun which determines with its mass and distance the speed the Earth and Moon can travel around it (29.786 km/s as the mean).

10,000 ÷ (4.6578/1.619) =  3476 km

Ten thousand kilometers is the Circle-in-the-Earth square. 3476 is the Moon’s diameter. 1.619 is intermediate between the golden number and the square of 4/π.  4/π is 1.2732395… The square root of the golden number is  1.2720196. Their ratio is 1.000959, so they are very close. One could say that the square root of phi is involved in determining the height of the Great Pyramid and helps to set the difference between square and circle. Probably one of the most fundamental coincidences in the whole of geometry is that between 4/π and the square root of phi. When 4/π is used the corner angles of the Great Pyramid are about 51.854 Degrees.

Here is another observation that may add another section to Ariadne’s thread that helps us to keep connected inside the labyrinth of knowledge. We saw that to obtain the SCM- factor in the Great Pyramid – so that it was 31.416 meters – it meant dividing the Earth by 43,200. This gives a height of about 147.1469 including a 1/2-meter platform for the Earth’s Polar Radius. Minus the platform gives a height of 280 cubits. With a 220 cubit square 60 cubits remain. 60 x .5236 = 31.416 meters. We also saw that when we used an Astronomical Unit for the day the Earth is 150,108,000 km from the Sun very interesting numbers are spawned. We can also take the same AU and divide it by 43,200 since it is such an interesting proportion in its own right:

150,108,000 ÷ 43,200 = 3474.72 ~ Moon’s Diameter

Curiously, back in the 1980’s a team from MIT measured the Moon’s diameter and got 3474.8 km, not 3476 that we see most commonly in use today. I checked with a member of that team back in 2000 and he still insisted that the Moon’s diameter was 3474.8 km. But in any case it is close enough to make the point. Where there is life, harmony tends to be operating on multiple self-interacting levels and with effort humans can glean some of those levels and the nature of some of the harmonies themselves. This becomes quite intuitive, like composing music, and it is true that ultimately it is not prone to analysis because by its very nature it holds together as a web of existence, life, reality.  The life of a ‘thing’ is in the web that it shares with other ‘things’. In this instance you have two proportions dovetailing on an AU of about 150,108,000 km. When I used this date the numbers broke down harmonically in such a way that I started to fine tune the canon of human proportions by using those numbers! And when the Moon is used as a measuring rod, it measures the same distance 43,200 times. Moreover, the Sun measures to nearly the same distance 108 times, another member of Series A.

So what might be going on here? What might this tell us about squared-circle relations? And why did the Egyptians take the same difference that concerns us here – recalling that in a sense, the Capra speed is acting like a difference between mass-energy and massless energy – and turn it into an ‘empty’ enclosure as if it were an inversion of mass-energy, the mysterious Cavern of Sokar or Broad Hall of Osiris? Were they not attempting through the enclosure to bring about an acceleration, a quickening, a metamorphosis that they symbolized by the scarab beetle? Moreover, they often replaced the scarab with various forms of ‘bnbn’ which is none other than the Benben Stone brought by the Phoenix which in turn burns itself to ash in the House of the Phoenix only to rise again probably as Horus, symbolized by the falcon or the Eye of Horus. It seems these inner caverns were designed to accumulate energy, spirit as a food for the ka to facilitate the very ‘leap’, the very spiritual ‘mutation’ that many of us seem to crave. If the Capra nucleon speed refers to the matter pole (Egyptian “Seth”), perhaps the empty caverns were referring to the ‘spirit-pole’. The same proportion was being applied to opposite ends of the spectrum. This is a good point to mention Eschenbach’s definition of the Grail in Parzival.

The Grail and the Phoenix

So, this enclosure determined by the SCM, brings about the proportional size of the King’s Chamber. Not only has the difference of the Squared-Circle Modulus (SCM) become 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 synodical months. Half the perimeter is 618.42 inches symbolic of 50 years and 618.42 synodical months. 1/4 of the perimeter is 309.2 inches symbolic of 25 years and 309.2 synodical 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 in the thick darkness pregnant with suspense and mystery:

“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 self-enclosure is also the ‘altar’. Since there was nothing in the King’s Chamber except the coffer, the coffer was likely, then, one and the same as the altar upon which ‘the Phoenix burned itself to ash’. The Grail, then, is the essence of the Phoenix itself, the mystery of the eternal spirit within and its relationship with the surrounding universe, the Cosmic Web. It molts; it does not die! The coffer within the King’s Chamber has been called a ‘fount of spirit’. For the Egyptians and Gothic Builders at least, the Squared-Circle seemed to act as an eternal gate when Circle and Square have been reunited; when their difference has been transformed and possibly transcended. The King’s Chamber must have been seen as the Cavern of Osiris/Sokar within which that union and transformation is realized. The diagonals of rectangles have long been treated as transcendental functions. In the King’s Chamber you have 15 cubits in the end wall, 22.36 cubits in the floor and 25 cubits in the Great Diagonal which is also 13.09 meters – so prominent at Chartres. Recall that at Chartres the 13.09 circle seems to determine the internal round point of the choir. We can see 1309 below at the head of Column XIV, the same column that also contains 2618, 5236, 7854, 10472, 15708, 31416. The width of the King’s Chamber is 5.236 meters; its length is 10.472 meters and its perimeter is 31.416 meters.

So much more 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, probably in part due to the presence of the square root of phi (1.2720196…) in the radius of the circle (Height of the Great Pyramid). 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 be transformed from 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 supported by the 2:1 Table – the “Eye” is restored; the Phoenix is reborn; the scarab transforms from a worm into a winged insect of startling beauty. It is my belief that the ancient Egyptians believed in this metamorphosis sufficiently enough to build the Great Pyramid.


Before demonstrating the second method for squaring the circle that also starts with the 5 x 10 Prime 2:1 rectangle and also uses the golden section division of 3.82 and 6.18 (also from Series E, Line 2, Columns X & XI), I should just note the first prominent application of the SCM in a human being. It has already been alluded to, but now that a bit more has been discussed, it is worth looking at in better detail. We are interested in that difference between circle and square where a sort of inversion takes place at a limit. At the macroscopic limit we have the Moon that has assumed the same angular diameter in the sky as the Sun. The Moon has harmonized with the Earth to set the monthly rhythm that governs female ovulation that alternates month-by-month, ovary by ovary. It is a clock-like oscillation. In the male there are no ovaries but there is a longing in the depths of the psyche and soul for another form of birth that has likely contributed fundamental elements to initiation rites of all races and all creeds – in pursuit of the mystical marriage of the  inner man with the inner woman in such fashion that a gate opens for the spirit to find its passage into open territory. It is as if the ‘squared-circle’ were a fundamental analogy for the mystical marriage of male and female. When the marriage is successful a candidate experiences a state of exaltation that stands outside sexuality, but yet also overflows with a higher level of energy.

At the other pole we find another limit set by the mean rate or energy of agitation, movement, speed, in a state of severe confinement far removed from the electrons that mediate all biological activity that supports conscious life on Earth. This energy is deep in the atomic nucleus, where the mass-energy has reacted proportionally to its confinement. More important than the highly suggestive ‘speed’ offered by Capra, who made the calculation himself with the aid of Heisenberg’s Uncertainty Principle along with a few other factors, is its proportional relationship with the massless constant we call ‘c’ that also may determine the speed of gravity in the vacuum, if indeed gravity has an ‘exchange particle or mediator’, similar to photons. And that relation is 299,792.458 ÷ 64,374 =  4.657. But this is the squared-circle modulus (SCM). And it has shown up with the Moon – that is also partly a planet – and has determined several biological and possibly spiritual rhythms. So, (Earth + Moon) ÷ Moon = 4.66. At one pole the SCM applies to comparative  speeds and at the other pole it applies to comparative  diameters. Through an inversion the SCM relates speed to diameter. Earlier we saw how the ratio between Solar pulses and Earth shouts related as 9/69, just as the head relates to the whole body height as 9/69 or ~ 13/100. And since the Sun and Moon have the  same angular diameter when viewed from Earth, one wonders if the head is not a  marriage of both Sun and Moon and the respective ‘motions’ each imparts to the  head’s formation.

The SCM has also has shown up in a most fundamental way at the Great Pyramid – determining the dimensions of the King’s Chamber (perimeter = 60 cubits = 31.416 meters) – within which most likely occurred the apotheosis of the Pyramid Age. We see it below as the  difference between the radius of the circle TR (280 cubits) and the 1/2 square SR (220 cubits).

Now let’s look at the human female where the square PQTU replaces JKLM seen in the Pyramid image above. Let’s take the Prime Circle with length “2” (or 150,108,000 km) and let’s square that circle by equal perimeter and see where the SCM falls.

The circle is OV and when it is squared the square becomes PQTU. The difference between the 2:1 PQNM and the radius of the circle is clear. I did not put a letter in, in order to avoid cluttering the space. However we will take the measures arithmetically to satisfy all curiosity. But the first point is obvious.  The difference falls on the mouth of the adult. PQ passes right through the opening of the mouth. In other words the upper side of the square PQTU passes through the mouth of the standing adult. One could argue that the geometry of the squared-circle is the underlying cause of the position of the opening of the mouth of the standing adult. Incredibly, as some may know already, the King’s Chamber was associated with a recondite ceremony or ritual known as the “Opening of the Mouth”. It was also called “Splitting open the Mouth” and “Splitting open the Eye”. In human anatomy, however, the functions are so complex, that the mouth position would have to be caused by more than one factor alone. However, the coincidence with the squaring of the circle is a remarkable one.

The distance from the mouth to the vertex (O) is acting like the 31.416 meters at the top of the Great Pyramid that becomes the perimeter of the King’s Chamber. It is acting, proportionally, like the ‘nucleon second’ compared to the speed of light. By becoming denser the speed has been slowed and has also become absorbed into the properties of the nucleons in their condensed confinement. It is also acting, proportionally, like the Moon relative to the Earth + Moon, which stimulates and regulates biological processes probably in more than one way.

Now if the diameter of the circle is 2, its radius is 1. Its circumference will be 2π or 6.2831853. The square with equal perimeter will be 1.5708 on a side. Half that will be .7854. These numbers appear in Series E on Line 6 and Line 12:

If we add 1 to this .7854 we get the height from the ground: 1.7854. Another route to get to the mouth is to divide the height simply by 1.118 (1/2 the square root of 5) which goes in the opposite direction from the diagonal. The diagonal of a double square is obtained by multiplying the length by 1.118 giving 2.236. To obtain the mouth from the diagonal it is 2.236 ÷ (1.118) ² = 1.7888 = 2.236068 ÷ 5/4. The difference between this and 1.7854 is negligible. It is for all intents and purposes exactly coincident. So: 2 ÷ 1.118 = 1.7888 = 1 + .7854. Note that in the King’s Chamber the diagonal of the end wall is 7.854 meters. With this as the side of a square you have a perimeter of 7.854 x 4 = 31.416 which is the same as the King’s Chamber itself and also the same as a circle with diameter 10.

31.416 appears on Line 24, Column XIV above. The 3 Tables that bore the Grail are instantly evident in the King’s Chamber (Circle has diameter of 10; Square has side of 7.854; Rectangle is 5.236 × 10.472). How interesting that the same factors are literally opening the mouth of the standing adult! The ‘place of coincidence’ and the ‘line of difference’ are the very factors that open the mouth. In the Pyramid Texts the Egyptians refer to both ‘Opening the Mouth’ and ‘Splitting open the Mouth’. They also interchange this with ‘Splitting open the Eye’ by which they mean the Eye of Horus. But in an important reference to Sokar they also mention ‘splitting open the egg’.

I should mention that just as male blood pressure tends to be around 120/80 which is 3/2 or 1.5, the center of the thorax from the ground, the female blood pressure tends to be 110/70 which is 1.5708. The relationship between 1.618 and 1.5708 is 1.030048 – probably the most common female armspan. The male can be looked at as 1.618/1.5 = 1.078689, which I will make as the  overall armspan for the male as it is 1.03 × 1.0472 when in the angled position we have been seeing. The relationship between male and female blood pressure standards is none other than the ratio of the Royal Cubit: 1.5708 ÷ 1.5 = 1.0472 = π/3. The woman has a larger range and her systolic pressure is lower than the male. By a conservation law, these nuances show up in different functions.

Let’s check the ‘mouth’ of the female Thoracic Vesica. It divides unity by 3, so the horizontal cross is .333333 or WX here below. Half that will give the ½ base (WN) of an equilateral triangle or .16666666. The base of this triangle is shown below as WX. The apex is unmarked but falls on the mouth. 1/2 WX falls in the center of the heart, marked N.

The height of the triangle is easy to determine as it is the root of 3. So you have .1666666 × 1.73205 = .288675.  Since the middle of the Thoracic Vesica sits on the 1.5 latitude marked above, we add 1.5 to .288675 = 1.788675. So we now have the following: 1.7888, 1.7854, 1.788675. In the image above I have marked 1.7854 to label the upper side of the square with 1.5708 on a side. Once again they cannot be distinguished from one another. This is extraordinary harmony without any question. It is well worth enumerating.

A. Height divided by  half of the square root of 5 = 2 ÷ 1.118 = 1.7888

B. Squared-Circle falls at exactly 1 + .7854 = 1.7854

C. The mouth of the female Thoracic Vesica Piscis falls at 1.788675.

The fact that these prime geometrical factors converge on exactly the same point, indicates that the mouth is capable of genuine refinement as well as being a cornucopia of flow, an exchange between inside and outside, diastole and systole, inhalation and exhalation, inspiration and expiration. The mouth articulates and shapes what has been formulated in the vocal cords (throat) by the motor activity that comes from the brainstem via the recurrent laryngeal nerve that wraps around the Aortic Arch of the heart after having left the Vagus Nerve (N.X). The Aortic Arch is at the latitude of the golden number (1.618) from the ground. The Aortic Arch signals the medulla and pons as to the state of the blood: oxygen and carbon dioxide levels. It strikes me that the recurrent laryngeal nerve needs to maintain that somewhat cumbersome route to reach the larynx because it is related to  respiration and the emotions associated with respiration and heart rate. The lungs dominate the upper half of the Thoracic Vesica, demonstrating that they are formed within the unity circle. The breath supports the vocal apparatus. The heart is also very much involved with speech as is the brain and brainstem. Circuits that drive the larynx also pass through the heart and are undoubtedly related in a prime way to Nerve X, the Vagus Nerve.

The motor control of the larynx and mouth can be manipulated by yoga to conserve the almost automatic flow that engenders ideas, emotion and speech. When a peak is reached – especially when the kundalini is added to the equation – it is possible to experience some sort of mystical initiation. Here words are experienced differently. They have great power and authority and can bring about transformations. They induce dramatic changes. But it is as if your own will is not the source of the vocal energy. When the Tibetan kuden has donned his 30 pound helmet and has entered his oracular trance, he is capable of extremely powerful and authoritative displays of words. But later when he has recovered from his mediumistic trance he has no recollection of the counsel he gave. So the source of words has a mysterious origin and there is both consciously acquired knowledge and deeper levels of knowledge that can use the same vocal apparatus. To see these fundamental geometrical functions predetermining the position of the mouth indicates that the source is complex and in part transcendental. No wonder Saint John begins his gospel with “In the beginning is the word…” In the Pyramid Texts it is said at one point: “I am the Great Word”. And this Great Word had liberating effects!

It seems the best way to assimilate unusual information is thematically. The memory likes themes, probably because cognition itself holds together thematically; in patterns. So I should mention while we are here that there is yet another convergence on the mouth of note. This one is the tip of a GP-pyramid, the base of which is 1.236 or 2 × .618, the same span and same latitude within which the Pelvic Vesica Piscis is constructed, namely the  width of the Golden Rectangle, EFGH. In the accompanying illustration it is base RS set at the level of the pubic bone or ½ the height. The apex of the pyramid falls on the mouth. The apothem of the pyramid, moreover, is Unity.

This is another striking example of harmony, so proof is in order. If we put the compass point alternately on R and S, open it to Unity at E and F  and then swing it into two interpenetrating circles they will intersect on the mouth with the apothem of the pyramid as 1 and the ½ base as .618034. It is easy to calculate the height of this archetypal pyramid from the pubic bone. We just take the square root of (1 – .381966) = .6180434. So the square root of .618034 is .78615. We add unity to this to get the distance from the ground: 1.78615. Once again we can see how close these four convergences are:

A. Height divided by half of the square root of 5 = 2 ÷ 1.118 = 1.7888

B. Squared-Circle falls at exactly 1 + .7854 = 1.7854

C. The mouth of the female Thoracic Vesica Piscis is 1.788675.

D. The apex of the 1.236 pyramid is 1.78615

We can also go the 4/π route as well, giving .618034 × 1.27324 = .7869. When added to unity you have 1.7869.

These convergences are not inconsequential. They are not trivial geometrical components. Rather they are the most significant and fundamental geometrical components that relate directly and harmoniously to the Prime 2:1 that spawns and supports them.


It is quite interesting to see how versatile and harmonious .618 in fact is. And .618 is the signature of the golden number. It is the difference, the proportion that gives the golden number its meaning and operating capacity. The  reciprocal of .618 is 1.618, the golden number itself. The square of .618 is its own mate in the golden section: .381966 which will play the pivotal role in the second method coming up for squaring the circle. Recall that .618 ÷ .382 = 1.618. And .618, the ½-base of this golden rectangle pyramid, can be used two ways to obtain the height of the pyramid that reaches the mouth from the pubic bone. The square root of .618 gives a height of .7861 and so 1.7861 from the ground. And it also can be used as .618034 × 4/π = .7869 = 1.2732395 × .618034. This architecture is so strong and so flexible and so harmonious in the way inside relates to outside that growth, cell-division and multiple activities can co-function in a dynamic environment such as the Earth’s surface. The mouth’s versatility is astonishing.

In the meantime we can see that we are dealing here with several points of constructive harmony – especially the constructive use of .618. Not only is it ½ the base RS, but it is also SJ and RI. This links the pelvic bone (1/2-point) to the golden number (1.618) that marks the horizontal armspan and the Aortic Arch of the heart. So IJSR is an important 2:1 rectangle that works harmoniously with PQNM, another important 2:1 rectangle that links the Pelvic bone to the mouth very precisely. As archetypes they relate as follows:

1.5708/1.236068 = 1.2708. This number appears in Series E on Line 6, Column XV next to 7854 and .7854 is the height of this ‘1.236’ pyramid. .7854 × 1.618 = 1.2708.

I will confess to the reader that there are times when I wish I could assign a tone to each of these geometrical ratios. I then wish I could ‘play’ the orchestra of sounds that have come together in the human body. That way the experience could be direct and non-analytical. Here, the reader must supply much of their own imagination to experience the interactive significance of these fundamental ratios. What I have found is that contemplation has proven to be a little more important than analysis. But contemplation takes  time. In any case, there is no question that in the female, the golden rectangle, with width 1.236, plays a marvelous, even beautiful role, in the way it works with the Prime 1:2 rectangle. The mouth emerges as the fount of life and wisdom as the tradition insists! The geometry helps us to understand how it can be the source of wisdom.

The Human Face

It is now important to examine the geometry of the face to see where the mouth falls relative to its immediate environment and then see how that harmonizes with the 4 methods already cited which apply to the body as a whole. I will start with a brief synopsis of how I became convinced of one statistic that demonstrated that the head tended to be 13/100 of the whole height. I found this particularly interesting at Chartres because the 100 meters was in evidence as an important internal measure. Its diagonal seemed to be giving the height of the tallest tower (North). And the inside measure across the transepts suggested a golden rectangle was also determining important interior measures, namely 61.8 meters. The fact that a 13 meter circle was setting everything from the round point of the choir to the entrance to the Royal Portal and the diameter of the Labyrinth, I decided to take the 13/100 seriously. But then I came upon a curious work called “The Opening Eye” by Frank McGillion (1980) that referred to a New York Times article (mentioned earlier) from January, 1976, written by Walter Sullivan called “Doubts are raised on why the Sun shines.”  It discussed different scientific teams who had discovered a pulse in the Sun that was like a gigantic heartbeat – every 160 minutes – or 9 beats daily. Another impressive example of a Great Ennead. But this little book also mentioned something called an Earth ‘shout’ that is an electrostatic retort from the Earth’s ionosphere as if in response to the Sun’s pulses – or in any case a build up of electrostatic energy as if in a large resonance cavity. The Earth shout is 69 times a day (see L. Watson, The Gift of Unknown Things, 1977). The relationship between the Solar pulse and the Earth ionospheric ‘shout’ is 13/100, or more exactly .13043478… So I made this relationship between the Solar ‘heartbeat’ and the Earth ionospheric ‘shout’ the proportion of the human head.

Now I will introduce the head of a young woman without the geometry and will then put the geometry in to show the position of the mouth.

In the case of this young woman I have divided the height of the head in half at the rims of the upper eyelids. I have divided other faces in half at different points of the eye with equal success. But the first operation is to divide the particular head in half. That becomes the length of a 2:1 rectangle. The 2:1 is expanded to a golden rectangle (WXYZ) and it is also doubled to a Prime Square (EFGH). The Prime 2:1 (ABCD) is then able to be broken down into smaller 2:1 rectangles which can be further broken down by the golden section and so forth.

When the Prime square, EFGH, is divided in half at IJ through the upper eye lids, the mouth immediately becomes a very harmonious place geometrically-speaking. The diagonals IG and JH immediately determine the  angle of the upper lips. It is exact. I never associated the diagonals of a double square on its side with beauty. But here the angle formed by the descending diagonals is obviously creating a bewitching beauty. The angle HGI is 26.56°. The lower lip is further defined by another diagonal of a smaller 2:1 rectangle, KLCD, that also descends at 26.56°. KLCD is ¼ of the Prime 2:1 rectangles and 1/8th of the whole Prime square. By extending CK and DL, the base of the ear lobes are delimited, so in fact a larger pair of complementary 2:1 rectangles are involved linking V to D and U to C. These are 3/4th the Prime 2:1 rectangles and they also overlap, reaching across the Prime 2:1, ABCD.

The opening of the mouth can be looked at two ways: within the whole square and within a ¼ 2:1 rectangle, “abcd”, that exactly measures across the width of the mouth from corner to corner. So the width across the crease of the mouth is 1/4th of the Prime square and ½ of the Prime 2:1 rectangle. Its height is ½ the height of the whole head. The mouth is opened very precisely by the golden section of this 2:1 rectangle, ‘abcd’. ‘xd’ becomes .382 and ‘ax’ becomes .618. This means that from the vertex or crown of the head to the crease of the mouth is 1.618 and from the base of the head to the crease is .382. And 1.618 ÷ .382 = 4.236 = (1.618)³. Also notice that just like the Vesica Piscis the nose is exactly 1/3rd the width of the Prime 2:1 and 1/6th the width of the Prime Square. Its triangular shape is precisely determined by the diagonals of the Prime 2:1, ABCD. Meanwhile the ears meet the face exactly at the boundary of the golden rectangle. What is most striking for me about this geometry is the way the opened eyes from upper eyelids to xy, or the opening of the mouth, works with the golden section to produce the overall feeling of concentrated alertness and sense of purpose that this face exudes. The next remarkable observation is the coincidence of the intrafacial measure from mouth opening to vertex (1.618) and the overall measure within the body taken as a whole (.2146). Within the head  taken as 2 the SCM length is 1.618. Within the whole body height taken as 2, the same span is .2146. Two significant harmonies act together to open the mouth. According to the infrafacial geometry, the opened eyes play a significant role in determining te opening of the mouth in this particular person.

We can now readily compute the intrafacial position of the mouth and see how it relates to the other overall methods that integrate the mouth into the whole body. As it turns out with a total height of “2” for the body when we add the percentage of the whole represented by the base of the jaw to mouth portion, namely .0249085, to the height of the body as far as the base of the jaw or .8695652 we get .894473709 of the whole, so:

2 x .894473709 = 1.7889474

We can now add this to our list of geometrical factors responsible for opening the mouth.

A. Height divided by half of the square root of 5 = 2 ÷ 1.118 = 1.7888543

B. Squared-Circle falls at exactly 1 + .7854 = 1.7854

C. The mouth of the female Thoracic Vesica Piscis is 1.788675.

D. The apex of the 1.236 pyramid is 1.78615

We can also go the 4/π route as well, giving .618034 × 1.27324 = .7869. When added to unity you have 1.7869.

E. (.618 x 4/π) + 1 = 1.7869

F. Intrafacial location (.049821653) added to 1.73913 = 1.788947

First of all, note again that I did not use exactly 13/100 for the head size. I used the ratio between 9 and 69 sensing that this relationship between the Sun’s potential pulses and the Earth’s ionospheric response (which is also tidal by the way), is probably fundamental and helping to support electrical and magnetic brainwaves – rhythms that support patterns, themes and musical-like waves that support cognitive processes and memory patterns.

9/69 = .130434782

This leaves a body height to the base of the head of .869565217. The jaw-to-mouth % of the head is .190983 and this is .024910829 of the whole body. This is added to everything up to the jaw:

.024910829 + .869565217 = .894476029

This is 89.447% of the whole height or the height divided by 1.118 as we have seen. So, .894476 is the reciprocal of 1.118. Remember that 1.118 is the ½ diagonal of a 2:1 rectangle and is the ratio between length and diagonal. The height of the KC is 1.118 × Unity or 11.18 cubits or 5.854 meters.

With a height of “2” with this configuration we have from the ground:

.894476 × 2 = 1.788952

This next illustration shows how Nature has fine-tuned the sculpting of this face. The same ¼ 2:1, here IJKL, when golden sectioned the other way across ‘ut’ determines the opening of the nostrils. So in one rectangle, golden sectioned in both directions – down and up – what is determined is both points where air is taken in and breathed out. uM or tN have a value of 1/(1.618)³ or 1/4.236.  It is a particularly stable region and we will see with cytoskeletal microtubules that this region houses a relatively free electron in a hydrophobic pocket.  In the image above also note now the even smaller 2:1, here ‘abzy’. When it is golden-sectioned from below it forms the bottom limit of the lower lip.  The V of the upper lip that completes its beauty is formed by the golden section arcs of IJKL, the same arcs that determine the crease or opening of the mouth. When I make the jaw-to-mouth distance “1”, the mouth width is 1.309 and 1.309 is 1.618/1.236 = 1.309. We are back to the proportions of the Egyptian Ra-Horachty stele. The rectangle, MNKL is part of what makes this mouth beautiful, edited, functional. This individual happens to write very well, and tries very hard to articulate her truest thoughts and impressions. She is as gifted with imagination as with the desire for ‘truth’.

Splitting Open the Mouth = Splitting open the Eye.

It was mentioned earlier that the Egyptians used different phrases to say the same thing. One event or phenomenon had several aspects to it. So “Splitting open the Mouth” also was referred to as ‘Splitting open the Eye.” The Eye of Horus was depicted in various ways, one of the most important being the Uraeus on the brow. This was the raised serpent or kundalini. In an image from Karnak it is striking to see that the measure of the jaw-to-mouth is identical to the measure of the Uraeus itself that is seated on the brow. Note that the Uraeus (Maāt, Eye of Horus) sits on 3.236 from the base. Above it is 2 to the vertex. 3.236/2 = 1.618. So Splitting open the Mouth or ‘Splitting open the Eye’ also refers directly to the golden number and golden section of the whole head. In the Pyramid Texts it is stated that the Eye of Horus is recovered from the forehead of Seth. I will discuss this in more detail in future posts.

This image below combines these same geometrical factors with squared-circle relations and angles. I did this in 1990 to demonstrate a principle, not attempt to draw an actual head.

In the next post I will demonstrate another method for squaring the circle and how it seems to be used by Nature to work a few wonders. We will also return to the Astronomical Unit to get some clues about the male geometry and the origin of the heart. The human being is an unapologetically profound creature. Our depth cannot be separated from the geometry that supports us.

“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)

When I first read this I felt I had been involuntarily pulled into a ritual. The ritual was cosmic. It was a wave-action like a heart-beat. I accepted it before I understood it without knowing why.

By this time I was already thinking in terms of 3-ness because of my 1980 dream (that I’ve been referring to all along) which had occurred right on the occasion of what every tradition of astrology ever known has called the ‘progressed New Moon’. This is based on the synodical month which depends from 3 bodies: Sun, Moon and Earth. It is about 29.53 years from one pNM to the next, so a year corresponds to about 1° which ‘equals’ one day. Nature is a continuous relationship between storage and release; systole and diastole; enthalpy and entropy, accumulation and discharge, yin and yang, seed and flower; implicate and explicate. The pNM is the point of maximum contraction, the shedding of the old, the last vestige of exhalation, the seed, a new implicate order awaiting growth. But it also possesses the potential for  inner illumination; a light born from the darkest dark. This is the light of revelation; the “Fire of Saint John,” when one has been taken back to the seed and its mysterious and even formidable cavern, the Broad Hall of Osiris. In the image below where a five-fold serpent is biting its tail, the fallen Osiris figure has a scarab on his head – the symbol of spiritual metamorphosis. Above this cavern, the fire of 3 serpents is about to burn the enclosed contents of 3 chests containing head, wing and animal loins. One imagines three parts of the temple:

the court for the pelvis; the covered way for the spiritual heart and the secret sanctuaries for the head: the origin and place of return. At Chartres you have Nave, Transepts and Choir: Round, Square, Rectangular. One can speak of 3 fires: Sagittarius, Leo, Aries.

Though the progressed New Moon is the product of 3 bodies, the fruit of their harmony is a fourth. The fourth behaves differently from the other three. They are all recapitulated within it. In the inspired and well-known Emerald Tablet, the Sun is its father, the Moon its mother and the Earth is its nurse. The fourth that concerns us rather uniquely is none other than man, often symbolized by the head which distinguishes us.

At Gizeh there are three great pyramids; three chests ‘efficient for burning’; three “pyres” capable of reducing and purifying the ash of the Phoenix. The largest, shown below, canonizes the squaring-of-the-circle. The other two

celebrate other significant geometrical principles. But there are also 6 smaller pyramids, suggesting that behind the Sphinx you have the Great Ennead. Atum was said to become the Great Ennead. He was both Primordial Mound and Great Ennead. 9 is the square of 3. It is the sum of 3 + 3 + 3. It is a 3-fold wave of amplification that transforms into a 10th, Horus of Egypt: the spiritual essence that the Nine Bows release into the Netherworld.

Here we see 3 ruined pyramids next to the south-west pyramid (Mycerinus). There are three more small pyramids in front of the Great Pyramid seen here in the distance at the right, bringing the total to 9. Horus was the tenth. One imagines the three large pyramids to refer to Atum, Geb and Osiris. It is difficult not to think of the Great Sphinx as being both the fourth and the tenth. The Sphinx represents man “made in the image of – ”.

The human imagination is difficult to satisfy – but who would want it any other way?  Reductionism is the first step on the road to dictatorship. Better to take an alternative path with bare feet and the shirt on your back if it avoids the debacle of subjugating others in order to dominate their freedom. The Grail is like the number 64. It invokes totality. The welfare of the whole is in its embrace. And to celebrate that totality it spawns many children to bear witness to it. However everything great finds its own limitations. The Grail Castle did not open its gates to just anybody at any time. Wounds sometimes hold the sole key of entry. In Parzival a bleeding lance possesses as much mystery as the cornucopia that satisfies all the heart’s desires and quenches the thirst of monk and glutton alike! Parzival was supposed to ask about the lance and the blood that was dripping down its shaft. A lance pierces. It can kill. But it can also let something extra enter the vessel. This sets in motion a transformation. Passion, self-satisfaction and pride yield to spirit and its wider frame of reference that includes the tribulations and joys of others encountered beyond the boundary of one’s own vessel.

Were the builders 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 at Luxor, Egypt? 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. But in any case Charpentier is quick to point out within the context of his use of the 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)

Were the pyramids also built with a mind to initiatory action? And was the Eye of Horus the fruit and blossom of that action? Unadulterated instinct, of course, says “yes”. The politics of history and religion engages in polemics in order to promote a current brand name; a label. But this is just an earthly substitute for a spiritual frustration; initiation obstructed; the Eye shut up in darkness. At Chartres all such argument seems to cease. We are born from an earthly mother. But there is an essence that yearns for rebirth in spirit. This is a path, a quest, a journey. It proceeds in steps: traditionally three.


Note first, at the summit of the Pyramid, I have marked in the difference in meters between the square and the circle. It is 31.416 meters or 60 royal cubits. Recall from earlier posts that the 1/2-base is 220 cubits and the Pyramid Height is 280 cubits which is the radius of the circle with the same perimeter as the square. 280 – 220 = 60 and 60 royal cubits is 60 ×.5236 = 31.416 meters.  This becomes the perimeter of the King’s Chamber set at the point of golden section of the Unity Cube, ABCD, taken as “1” when the ½ base is 1.618 and apothem is 2.618. The Great Step is mounted at the north-south midpoint of the Pyramid. The King’s Chamber can now be seen as the module of the whole. Its width (10 cubits) fits into the difference between square and circle 6 times. It fits into the 1/2 base 22 times. It fits into the whole base 44 times. It fits into the height 28 times. It fits into the length of the Great Sphinx 14 times. Not only is the Sphinx length in a pi relationship with the Pyramid Base but the perimeter of the King’s Chamber names pi in meters as 31.416 meters (modern pi is 3.1415926…). Right away we have stumbled upon the three tables that bore the Grail – in the King’s Chamber itself. The round table has a diameter of exactly 10 meters. The square table has a side that is 3/4th the length of the King’s Chamber as shown in the previous post, or the diagonal of the end wall which is 15 cubits. 15 × 4 = 60 cubits = 31.416 meters. The rectangular table is 10 ×20 cubits with a perimeter that is 10 ×6 = 60 cubits = 20 × 3 = 31.416 meters. So when the start point is a circle with a diameter of 10 meters and circumference of 31.416 meters, the royal cubit can be used as the means to ‘square-the-circle’. One simply divides the circle by 6 using a 6-pointed star, and turns it into a 2:1 rectangle where the width is equal to 1/6th of the circle. The radius of the circle is 5 but the width of the KC will be 5.236. To find the square with equal perimeter of 60 cubits one can simply divide by 4 but it is worth noting that if the height of the walls are 1/2 the diagonal of the floor, the diagonal of the end wall will be exactly 15 cubits (7.854 meters) and this gives an equal perimeter of 60 cubits or 7.854 × 4 = 31.416 meters. The King’s Chamber is a celebration of the ‘three tables that bore the Grail’ all interconnected with each other in a single volume that incidentally is 1000 × 2.236068 cubits³ or 1000 times the square root of 5 = 2,236.068 cubits³ = 321 m³.

All this seems unnecessarily complicated initially. But in fact it is remarkably simple and even more remarkably harmonious. What is important, however, is to learn the significance of that 31.416 meter difference that we find at the scale of the Great Pyramid, which happens to be 1:43,200 compared to the Earth. Something about that 60 cubit difference between radius and 1/2 square was of fundamental importance to the Egyptians. It was considered so significant that they took that difference and made it the perimeter of the King’s Chamber, itself a fine example of the ‘3 tables that bore the Grail’! 60/220 = .2727. We can note immediately that our Moon bears the same ratio to the Earth as 60 does to 220. In mean terms: 3476/12,732 = .273. A common ratio used today is 3476/12,741 = .27282. I will come back to the Earth/Moon relationship as we proceed. At this stage of our understanding, this ‘squared-circle’ relationship between Earth and Moon is a genuine mystery and in my view raises significant questions about the real history of the two bodies. Harmonious forces were somehow able to ‘shape’ this relationship. I am certain that one aspect of the shaping was gravitational. Moreover, I would hazard that it was a shared gravitational field operating for a long time – almost as if the Moon were at one point within the Earth and a bit like a “polar body” in biology, was somehow expelled from the Earth. The analogy is very general because of the fundamental difference in scale. Nanometric forces are at work in an ovum for example. So electromagnetic energy is working with a volume overload. In the case of Earth and Moon a straight collision by a large entity (“Giant Impact Theory”) seems too accidental. Perhaps iron and magnetic fields played some unknown role with the Moon already pre-formed near or on the Earth surface during a precise phase of rapid self-gravity.

In the Great Pyramid there seem to be three levels. With the Unity Cube in the center, the Subterranean Chamber falls right on the square root of 2, quite as if it were acting as a root. The next level is the Queen’s Chamber that I will have to discuss at another time. The King’s Chamber rests on the golden section of the Unity Cube at 44 meters from the ground. The north wall of the KC is the golden section from North to south. And the East wall is the golden section from West to East! It is not easy to sum up the significance of this level of harmony. Moreover, historians tend not to credit the Egyptians with a knowledge of the golden proportion. But it looks as if the King’s Chamber has been situated in accordance with both ‘squared-circle’ geometry and the golden proportion. One could readily argue that they understood the relationship between these geometrical factors and the coveted spiritual metamorphosis symbolized by the scarab beetle, Khepera (“Transformations of Ra”) and the Eye of Horus. For now I will just introduce the theory that when the 1/2-base of the Great Pyramid is 220 cubits, the Unity Cube that the Pyramid encloses, will be almost 136 cubits or about 71.194 meters. The golden section of that “Unity” is 44.0012 meters. It seems the Queen’s Chamber is 22 meters from the ground and the King’s Chamber is 44 meters from the ground or the golden section of a Unity Cube. The Cube can be thought of as the Holy of Holies, such as at Solomon’s fabled temple. But in the case of the Great Pyramid, this Cube was enclosed by the principle of the squared-circle, pointing to an internal transformation or metamorphosis that the Egyptians regarded as significant, as it maintained a cosmic balance between ‘above’ and ‘below’. This they called Ma-at. Ma-at also meant ‘justice’ and ‘truth’. So the Great Pyramid was also a testament built in stone.

Three Tables

An All-embracing roundness becomes square through division and differentiation – possibly under pressure; a necessity in the cycle. The Grail is cyclic. Its source is eternal: the bountiful universe, the ‘black’ womb of Nut in ancient Egypt. Its action is tidal. Squareness involves acceleration. Acceleration is an aspect of inverse square forces such as gravity and electromagnetism. Squareness also involves 4-ness. We speak of 4 forces of Nature which have difficulty being unified mathematically. The ancients spoke of Four Elements. Psychologists speak of the Quaternary. So with squareness, gravity or ‘self-gravity’, is born and things become separate and differentiated: Atum becomes a separate ‘hill’. He surges up into being from unknown depths and distinguishes himself as a Primordial Hillock consisting of a Great Ennead of neters. Just as we speak of 9 planets that react to the Sun we also speak of 9 hormones that react and move and activate other processes in the body. Once things become separate and active, there is now competition in a shared field, and what is born is a quarrel, a struggle that demands a quest for harmony; a longing for peace. 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 creative hero has to overcome his own miserable inertia to win from it inspirations that ache to be born. The opposites strengthen themselves, 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, when the ‘Sun once again rises from its own dark ash’.

When the pilgrim arrived at Chartres – usually having endured multiple dangers to get there – he or she entered through the Royal Portal. I must mention that this was carefully designed and seems to have been acquired from the Egyptians and their generic gate known as the ‘sba’. It is normally constructed within a 2:1 rectangle with width 22 and height 44. The Opening is 10 with 6 for each pylon. The height of the door opening is

then 31.416, echoing the difference between circle and square at the Great Pyramid, namely 31.416 meters, the perimeter of the King’s Chamber. If that were collapsed into a circle its diameter would be the width of the opening, 10. This gate symbolizes the gate to the horizon of Atum, or sometimes referred to as Horachty, Horus-of-the-Horizon. In Christian terms it is the gate to Heaven. The pilgrim had made his way to Heaven-on- Earth. The Rose Window sits above the gate. Presumably, then, it represents the heavenly sphere, heavenly splendor. This would explain its emphasis on the color blue.

In the image below I have modified Charpentier’s original sketch of the three tables that bore the grail. He has made them of equal surface. I have added the circle with equal perimeter to show the difference. All my figures are in red. The 29.53 circle is the circle with the same perimeter as his square with diagonal 32.8. It adds to his overall length of 97.04 m by 3.36 meters, giving an overall length of 100.4 meters. I have indicated where I think exactly 100 meters has been applied by the builders. The square table seems to be encroaching slightly into the rood screen. The scheme seems to work. Charpentier gets 32.8 from the middle of the walls of the nave. The inside measure across the nave wall to wall is about 32.2. The 29.53 circle seems to give the length across the nave from the base of the pillars.

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)

Charpentier means that the original table was rectangular before it was rounded, probably in the image of the rounded crown of the head. But what matters for now is that he refers to the rectangular table as mystical, that of the Eucharist. As many know the Eucharist was symbolized by a white wafer which in numerous Grail stories was associated with the Grail or was carried by the Grail or was brought to the Grail as if the Grail were one and the same as the altar. The altar is the place of a sacrifice, offerings, making sacred. Here matter and spirit undergo an exchange. Each receives from the other. Here square and circle act as one. The altar keeps the essence pure. The Grail is inextricably bound up with the altar and with the essence. Everything about the altar must be effective, genuine. Altars were places associated with fire and incense. Originally they were associated with burnt offerings in imitation of the action of the Phoenix. 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! And how subtle one must learn to be if you wish to describe the world of spirit – that other plane where consciousness can feel more real than it does when saturated with a glut of tangible things. The meeting of the tangible with the intangible is the boundary of the enigma. Circle and square seek reconciliation. But at Chartres the choir is rectangular. In fact the whole cathedral seems to have been laid out by a 2:1 rectangle, but I could not see this all at once.

“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)

To repeat, the choir at Chartres, like the table held by Moses, is rounded at the NE extremity. But it started as a rectangle. It is likely the same with the whole cathedral. It is also important to note right away that this choir 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, as in 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 Bnbn of ancient Egypt. 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.

All Roads lead to the 2:1 Construction.

What is it to be called? A double square? A 2:1 rectangle? The octave? A magic carpet? A gate? A portal? A sacred enclosure? The Table of the Law? The Table of Rectification? I responded by learning different ways to illustrate it.  The Benben Stone? The Mystical Table? The Table of the Altar? The Tabernacle? The Table of the Sacrifice? What sacrifice? When God became man? When potential energy first coagulated and divided from One into Two and started the process of both differentiation and relationship? Everything about the 2:1 enthralled me. For some indeterminate spell I felt like the luckiest man on Earth. Charpentier

had reinforced what I had already met with in Doczi’s book, that Egyptian and Greek temples were based on 2:1 tables. As Vitruvius noted, this was the  foundation for human proportions. I was an instant convert. In fact I was not converted at all. The 2:1 rectangle and its keys and inner patterns, were already in me ready to be fertilized. The real fertilizer, what caused the seed to germinate, was the journey to New Zealand and the idea that the way into the construction of Chartres was none other than a 2:1 rectangle. I knew I had found the means for constructing the canon of a human being. But I had no idea that it was overflowing with geometrical information. The 2:1 is the cosmic chip. It is the means by which the web of circumstances arises from the great void. It is a generator, a processor, a purifier and a rectifier. My

confidence in the little 5 x 10 cm rectangles I was drawing several times a day began to grow in a way that felt mystical and practical simultaneously. It was a remarkable feeling the day I first expanded the 5 x 10 to 6.18 x 10 by simply dropping half the diagonal down from each corner to the adjacent corner adding .59 to each side giving:  .59 + .59 + 5 = 6.18. This is IJKL at Chartres. It was like being introduced to one’s true name. I did not see the length

across the transepts at Chartres until 1988 after I had been there. How can the heart fall in love with a number? 6.18 is not a number. It’s a proportion, a building block of life, as important as DNA!  I have never seen this 61.8 x 100 meter rectangle mentioned in print. Few people associate knowledge of the meter (39.37 inches) with the Gothic Age. But all my work indicates that not only was it known, but that along with the royal cubit it was partly responsible for the unique fertility of the time. The meter by its very definition comes from the principle of the ‘squaring-of-the-circle’!

It was not this measure across the transepts that gave me the idea to use a golden rectangle for the female pelvis. But when I found Houvet’s measure for the interior width of the transepts, I admit, my heart did nearly seem to stop. It was as thrilling as it gets in this business of human and architectural biometrics.

The 2:1 also seems to encompass the entire construction, excluding of course the Saint Piat Chapel at the extreme North East. It strikes me as quite possible that the Templars recovered both the royal cubit and the meter from the Holy Land if not Egypt itself. The Prime 2:1 here, ABCD, encompasses everything including the front steps and outside walls at the far end. It includes the main walls and inner porch, but requires the golden rectangle EFGH to include the outer porches, north west and south east. At Chartres, the 61.8 meter width across the transepts is an interior measure. It contributes enormously to the feeling acquired from being amidst the transepts. I have included the 29.53 circle around the labyrinth. It too is an inner measure. The beauty of this

ABCD rectangle above that appears to be 130.9 x 261.8 cubits in dimensions, is that it provides the overall form to the mass of the building. All that specific gravity! It is the foundation of the volume. It completely comprises the length of this magnificent Ark. Once this enclosure has been settled, the mind is at peace. The heart feels right. This is about 68.54 x 137.08 meters. Regarding length, nothing is excluded. This is the length overall of this ship of stone. To totally include the outer part of each porch, a golden rectangle is needed which takes it to 84.72 meters, able to encompass all steps that lead up to the porches. The measure across the outside porches minus the steps is 73.4 which is not far from the length of the Great Sphinx (73.15 meters). The 61.8 meter length is an inner experience, the inner width across the transepts. The 100 meter length that completes the golden rectangle, is also an inner measure between the towers and the rounded part of the choir. All visitors can feel the sacred nature of that measure at Chartres. When you enter the nave from between the towers you can see to the rounded inner extremity of the choir which is very close to 100 meters away, or say, 328 feet. When you mount the modest steps to enter at the Royal Portal you are entering an all-encompassing 2:1 rectangle. The mass of the building rises up within that enclosure.

You feel yourself between the two massive towers. They are also hollow. So they also ascend. They do not just descend. You then stand at a threshold between C and D. This is where I think the 100 meter rectangle also begins. Immediately you enter a smaller 2:1, ABCD above, that is perhaps 13.09 x 26.18 m in size. The first square prepares you for the Labyrinth that is contained within the second square. I have placed the larger 29.53 circle around the Labyrinth as it determines the elevations of the cathedral by using its radius as the base of a triangle that builds through its hypotenuse. The labyrinth is a long path that was probably intended to be exactly 261.8 meters long or 500 royal cubits. That is ten times the diameter of the circle with the same surface as the square with a perimeter of 92.7714 that I have indicated above. As one walks around the Labyrinth one is also inside the 13.09 x 26.18, 2:1 rectangle. As you proceed the rational faculty is expelled. What is instinctive, vital, moving, natural, propels you toward the center: the place of the nucleus where energy is most concentrated. When you get there you confront yourself. The darkness of the Minotaur is the darkness of Seth: a primal power that is accumulated and so offers energy to be utilized. In the Labyrinth one must confront this power and not deny it; not repress it. The ego is to be reigned in. Seth is to be brought down or laid low, but not destroyed! To destroy Seth is to destroy that extra energy that will be needed to take up the spine, the living pillar.

Vitruvius pays homage to the Greeks, 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. And now Charpentier added that the 2:1 rectangle was somehow the key to the equivalence of the 3 Tables ‘that bore the Grail’. 3 Tables – ? 3 phases or qualities of one essence, perhaps – the three parts of the one philosophy, the one mystery – one miracle like the body of Shiva, shimmering with billions of luminous parts. Initially I had to pinch myself. Something as simple as the relation between 1 and 2 was possibly the key to a place as fantastic as Chartres? Was it possible? Chartres grew from a table with a length twice its width and this table somehow was the means by which a round, square and rectangular table could all be calculated to have equal perimeters? And more: was I to assume that these tables also bore human characteristics a bit like Jung’s psychological “types” rooted in the deepest archetypes of the collective unconscious?

An unexpected destination

So, each unexpected fork in the road had arrived at the same destination: a rectangular table with a length that was twice its width. It was a work-horse with wings. The mystic germ capable of unfolding into visible life and returning to a world of spirit. The fount of the altar. For me it was like a universal omphalos, only it was a rectangle, a double square. I wish I could describe how it felt upon arrival, when I first stumbled in to the clearing to touch the ‘cosmic chip’. 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. They almost felt sorry for me and my childish drawings. It all looked so bare and insignificant on the page – like a boy’s torn school book! But finally 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. While Kely and Vincent Ward researched the Black Death that struck Europe around 1348 – about 30 odd years after the Inquisition against the builders of the Gothic Cathedrals – I asked myself about the simplicity of the 2:1 construction, the primordial octave: “How can this be”? But there is no answer. It just is. Such a relief! The 2:1 is not man’s doing. It’s the nature of things: the primordial flow. Drawing the 2:1 with precision was a bit 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. Weakness is the belief that impatience and might are all there is. 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. The body must be formed the same way. 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. It’s diagonal, so easy to draw, presents itself as a mystery, filling the soul with awe. And so you start to swing the compass. You learn to measure. From the 2:1 the golden rectangle evolves with such ease. In time you find more than one way to square the circle. The more you look, the more you see. Very gradually you realize: 1 and 2 are not numbers. This is not an enumeration. It is a cosmic process. It is a field of activity active in the void.

In the West, we insist upon reducing everything with a name to a physical thing that can be labeled 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’  for practical reasons, but when things become ‘fetishes’, the light soon fails to leave the rim of the cup. 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. Nature respects hierarchies, but there is a point when you can no longer wait around for the divine to send another savior, when what is called for is that you summon your own light from its own little hideout. I am the last to say that this is easy. The light assumes many forms and many roles.

The Grail and the Head

At one point by 1990 I had come upon enough references that compared the Grail to the head, that I was inspired to put all these ideas together in one place. At that stage I also knew that the Templars kept and  ‘worshipped’ a mysterious head called the Baphomet, possibly meaning ‘Father of Understanding’. I know nothing about this recondite head, but the whole discussion sparked my interest in the focusing powers of the head – by which I do not just mean the eyes. I mean a collective power for the mind to self-focus in singular acts of conscious awareness. I was amazed by it!  So I attempted to apply what I knew to create a head from nothing. 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 – overflowing all the walls of the inner labyrinth.  At that moment the head struck me as the ultimate mystery where everything is united in the ‘place’: that center of centers that could be called an ‘essence’ so pure it cannot be destroyed. The head also transmutes its own content to the point of overflowing the container, shedding its light on the world for better or for worse! This head above is one geometrical recipe with some elements common to all recipes. I chose a recipe that was relevant to the main theme. The squared-circle was doing something fundamental. It was not just a superstitious conceit.

In the Welsh version of the Grail, a head on a platter replaces a chalice! 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. We feel the Grail is linking two worlds: the visible and the invisible; the transitory and the eternal; the finite and the infinite.

In Egypt the head was associated with Horus, Ra, Atum-Ra and Osiris. At Roslyn 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 a complex way, the head absorbs the sun’s light, responds to its gravity and transmutes the energy into an endless field of activity. 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. What, then, is this ‘Grail’ that we variously label: ‘cup’, ‘head’, ‘Eye of Horus’, cathedral and that which overflows each of these containers?

The Ennead

When the Templars initially formed somewhere between 1100 and 1114, they formed in a group of Nine Knights. When they first planned Chartres, they intended to build Nine Towers. They ended up with two only. The Egyptians continuously refer to The Great Ennead above and the Great Ennead below or the Double Ennead. The Templars likely wished to demonstrate the Great Ennead here below that reflects the one above. Nine is the square of 3 and so brings about a transformation. It probably works in a double direction: spirit to matter and matter back to spirit. Nine supports the 10th, a new Unity.

Nine pyramids invoke nine planets. In 1976 the New York Times reported that scientists working independently in France and Russia discovered that the Sun was pulsing – in their words – quite as if it were simulating a gigantic heart beat. It discharged this gigantic pulse 9 times a day or every 160 minutes. As a sort of echo, perhaps, to this solar pulse our own ionosphere apparently builds up electrostatic energy in its ion population, which is discharged like an electrostatic ‘shout’, 69 times a day. The relationship between 69 and 9 is 7.666… or inversely, .1304347… When I found out that the mean size of the human head was 13/100 of the adult body height, I started to take this 9/69 relationship seriously. And in fact I eventually came to use the exact ratio of .1304347, as it helped refine the position of the mouth in the standing adult. I realized the Egyptians were discovering multiple properties in the principle of “9” and that the “9” pyramids, like the symbol of the Grail, were superabundant in meaning. 9 governs, regulates and transforms. The head is a magical cauldron that springs from the circular actions of 3-ness. How did Plato put it in the Timaeus? ‘The head is endowed with all the varieties of motion there were to be’, and for this reason the body was designed to serve the head, “the divinest part of us that controls all the rest.” (p. 60, Timaeus). One imagines that the 9 pulses have somehow been internalized in the head and that the 69 Earth shouts have translated into the body. It’s as if the 9 solar pulses were the source of the 69 shouts, just as the head is the source of the commands that govern and regulate the body.  The head also contains the Pituitary Gland that is divided into two parts: an anterior and a posterior. The former biosynthesizes 7 hormones and the latter, 2, so 9 when taken together. The posterior is part of the Central Nervous System. The anterior part is not. Most body processes are regulated by these 9 hormones or stimulators.

Castle Mundsalvaesche, home of the Grail, also invokes a magical mountain of some kind. 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. In PT 1652, it is said that Atum-Khoprer ‘became high on the height’. He rose up as the bnbn-stone in the Mansion of the Phoenix. The bnbn-stone is the Benben Stone brought by the Bennu Bird that appears to be a cyclic phenomenon associated with the Phoenix. As every school child knows: the Phoenix is famous for its uncompromising act of cyclic self-immolation. After it has burned itself to ash it rises again as resplendent as it was before.

But what is less familiar to everybody is the relationship between the Phoenix and the Grail. Eschenbach is fairly clear about it. The Grail, he says, is a stone by which the Templars of Mundsalvaesche are nourished. He stresses that they live by the essence of that stone which is particularly pure. He calls it Lapis Exillis. “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 dazzling bright and lovely as before!” Eschenbach then goes on to insist that anyone who sees the Stone is immediately made young again and that, by it, all illness is banished. “This Stone is also called “The Grail”. (p. 239, Parzival)

The similarity between this and Utterance 600 of the Pyramid Texts is striking. A prayer is being made for the king and his pyramid.

“O Atum-Khoprer, you became high on the height, you rose up as the bnbn-stone in the Mansion of the Phoenix in On, you spat out Shu, you expectorated Tefenet, and you set your arms about them as the arms of a ka-symbol, that your essence might be in them. O Atum, set your arms about the King, about this construction and about this pyramid as the arms of a ka-symbol, that the King’s essence may be in it, enduring forever.” (PT 1652-53).

The text goes on to invoke the protection of the Great Ennead which it calls the Nine Bows. Atum-Khoprer refers to the scarab beetle and its capacity to transform. The bnbn-stone takes its meaning from bn or bnn which has many meanings but the root is to rise, to fertilize, to make rise. There are two births that this can refer to: physical and spiritual. The essence here concerns spiritual rebirth. The pyramid was designed to keep the essence pure.  As if describing the powers of the Grail, PT 1278 says the following:

“A boon which Geb and Atum grant: that this pyramid and this temple be installed for me and for my double, and that this pyramid and temple be enclosed for me and for my double. This Eye of Horus is pure: may it belong (?) to me.”    (PT 1277-8)

The translator was unsure of the word ‘belong’. For the owner of the pyramid, the Eye of Horus must manifest; it cannot just be an expectation. Like the Grail, it does something. It bestows something upon the King and upon his double. What it bestows is the essence which is then protected. With this in mind we can return to the subject of the ‘squaring-of-the-circle’.

Sacred Mounds

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 ‘water 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 in a long history of beneficent manifestations associated with the hillock, tertre, or ancient mound of Chartres. The Great Pyramid was also a legendary mountain known throughout history. Supposedly the building itself has been built over and around a 30 meter high hillock that was as legendary as Chartres. The Great Pyramid is a celebration of the Squaring-of-the-Circle as if it were the key to keeping the Eye of Horus pure; the Grail effective. And it is this that nourishes the Templars.

Reflected in the faces of the men and women sculpted in stone at Chartres, you see a common horizon that liberates and uplifts. The peace is immense and tireless. It is a shared mound; a universal sanctuary: an immense reminder that echoes with the voices we cannot forget. Just reading Charpentier in 1985 – I was hooked. I couldn’t wait to get to Chartres. When I got there by the full moon at the end of May, 1988, not only was there no let down; it was the opposite. Chartres vastly exceeded anything I could have imagined about it. It transported Kely in the same way. Despite her burdens at that time – mostly financial and professional worry – I could see she was not expecting Chartres to be so exalting; so gracious; an immensity of love. What a gift to have bestowed on the generations who have lived since 1220 A.D. At Chartres you are not afraid to love. The word is fulfilled and carries no shame. I exist because I love. I am because I love. This has nothing to do with romanticism; nothing to do with sentimentality because at no time can the experience of Chartres be reduced. The overflow is superabundant. And somewhere the squared circle had already primed the pump of the everlasting as if a priori. Incredible really. Everything the heart already knows and the mind has already forgotten. And then you take your turn and climb the hill to Chartres. Am I exaggerating? No. Chartres exceeded in every way imaginable anything I had ever thought or learned about it before getting there. I’m afraid to put a photo in here because I am reluctant to reduce the energy of the place to an appearance; a category or stereotype of the mind. Something about Chartres exceeds all appearances and all history we have of it.

The Great Pyramid Principle

Of special interest here: if the ½-base is 1, the whole GP profile will be 5.236, the number of the royal cubit (.5236 m). And the difference between the ½ square and radius of the circle (TR) is TS which is 60 royal cubits or 31.416 meters. We can recall that the perimeter of the King’s Chamber is none other than 60 cubits or 31.416 meters! The question to be asked is what significance did the builders place on that difference between circle and square of equal perimeter? I am going to address this in more than one category as we proceed. As it turns out it appears to be fundamental. Also note in the image above that what links the height of the Pyramid (which can also be taken as the Earth’s radius or polar axis) to the 1/2 base of the defining triangle, is none other than the golden number which is very close to the square of the ‘squared-circle’ coefficient, 4/π or 1.27324… So, 1.618034 is close to 1.27324 x 1.27324 = 1.6211389… If you rounded the former up and the latter down, you would have about 1.62. Curiously, in meters, the mean height of an American or British female is 1.62 meters. And when you add the Moon and Earth together you get about 16,217 km. The meter is not only useful, it also carries within it an intrinsic harmony that allows diverse phenomena to function interactively. We will see this in other posts when we come to the circumstances of what we call the Astronomical Unit, or the mean distance that separates the Earth from the Sun (149,597,870 km). The AU can be roughly expressed as 500 “light-seconds” or just 150,000,000 km. “15” is an easy number to remember. And if a woman knows that her height is average, say 162 cm, she automatically knows the size of the Earth + Moon. She simply multiplies her height by 10,000,000. The decimal system can be pleasant.

When I first picked up Louis Charpentier’s book called “The Mysteries of Chartres Cathedral” in June, 1985, I could taste it somewhere deep inside me. It was an indescribable food – not quite esoteric – just an unprecedented inspiration – 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. Though its presence defies logic and all theories I have ever entertained about knowledge, somehow it is supposed to be there. Chartres is ‘heart-knowledge’ and resists all labels, all categories, all ways by which the mind disarms the living fire only to chain it to some cold part of the brain. The brain need not become a prison. But vigilance is required to keep the fires stoked. Moreover, there is no one on Earth who 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. I repeat, in some ineluctable way Chartres is supposed to exist. So every word that Charpentier committed to print seemed to be 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 have been born with it. But the secret of this knowledge 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. I lived under a cloak of terror that somehow I would run out of time. I had faith, but not enough to just drift through life without knowing the secret. I was not born illuminated. But I craved it.

I believed humanity had emerged through some sort of pattern; some sort of  means. Surely it was just a question of where to look. Like all living things knowledge wants to grow. We are the effects of that growth even when most of its root system 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. It is not mere imitation. 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. And 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, alluded to in the earlier posts. As it turns out they are 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’. Much remained hidden. I was learning how to trust that birth and the numinosity it had imparted, in a world that often seemed 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 whole 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. That labor challenged all my assumptions about everything: including the nature of consciousness itself. Chartres was similar. It erupted into my head and my soul like a magnificent genie escaping its bottle. Breath-taking magic. The Tree of Life.

West Front, with Royal Portal, Chartres. May, 1988.

The Grail

In recalling that night back in 1964, to my surprise, Charpentier invoked the “grail”. It was as if he had just introduced the prime principle of the book – Chartres’ secret perhaps; its quintessence – and in so doing had introduced the secret of ourselves. I could not have guessed that the 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 devastating fire of 1194 that destroyed everything north of the West Front. Apparently he wrote it right there on the site; his words organizing themselves with such unique color and zeal as if from the ashes of the former cathedral itself. In Parzival the Grail is given an unexpected definition a little more than half-way through the book (p.239). It had never occurred to me to link the ‘grail’ to the Phoenix, the most mysterious of all principles, but that is exactly what Eschenbach does as if an historic necessity had reduced the previous church to ash. Nor did I yet link the grail to the Vesica Piscis because I had not yet stumbled upon it. But that was to come soon enough. It is a Vesica that frames a triumphant Christ at the Royal Portal seen above in the central tympanum. And I certainly never thought to link the Grail to ‘squared-circle’ geometry as was done that night back in 1964 outside Paris.

I knew almost nothing about the Knights Templar, the ‘shadowy’ organization responsible for building Chartres. Perhaps that was a good thing because my innocence blinded me to the controversy that swirled about their place in history; their monumental confidence that others with less zeal labeled ‘audacity’, but without which, the Gothic Cathedrals would never have been built and the human spirit would not have been harnessed to so monumental a task. I had no idea Eschenbach himself may have been a Templar, nor what a Templar was, except that they had even attracted a fashionable scorn from the likes of Robin Hood. Defenders of the human spirit can be misunderstood faster than an arrow that has already left the bow of a defender of the people. Even in the age of chivalry! If justice is in the eye of the archer, his heart had better be blessed with discernment. But apparently misunderstanding did not prevent the Templars from being nourished by a “Stone” they called “Lapis Exillis”, also known as the Grail, a Stone purported to be “most pure”.

Moreover, I had no familiarity with the operas of Richard Wagner and his preoccupation with the Grail, so I didn’t even know what millions of others knew already, because when I was seventeen, I had gone straight from the Beatles, the Rolling Stones, Aretha Franklin, James Brown and Jim Morrison to Gustav Mahler (1860-1911). An English teacher in Toronto stuck a set of headphones on my ears and put on Mahler’s Second Symphony – to keep me quiet – and from the opening few bars, that was that. I never looked back to Wagner again. Extraordinary! Not only did I have no idea what the “Grail” meant to the Gothic Age, but I did not have a clue what it meant to anybody. 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! Suddenly it was a fit. The Templars were also known as “The Order of the Temple”. They were nourished by the temple itself which Vitruvius reminds us was once based upon human proportions.

It was not until 1996 that I came upon a passage from the Pyramid Texts, a passage interesting enough to convince me it was time to obtain a copy of the Faulkner edition that Kely hunted down and finally plopped on my desk in 1999.

“A boon which Geb and Atum grant: that this pyramid and temple be installed for me and for my double, and that this pyramid and temple be enclosed for me and for my double. This Eye of Horus is pure; may it belong (?) to me.”  (PT 1277-1278)

The grain of corn was within striking distance of the claw.

I had not come upon “Holy Blood, Holy Grail” (published in 1982) yet, so my mind did not have to grapple with situating the ‘Grail’ in a particular historical place and time; or attempting to narrow its grandeur down to a single bloodline; or a specific vessel claimed to have caught specific blood from a specific death. My imagination remained free to search for something universal in the spirit of any New Age before it starts to reduce itself to this ‘brand name’ or that Dogma, or this system or that superstition. My connection to Charpentier’s book was mystical from start to finish, as was my youthful connection to Mahler’s ‘biblical’ vision in music. In fact, other than the atmosphere that often shrouds the heavens surrounding the mountains, valleys and lakes of New Zealand, the Promethean scope of Mahler’s “Resurrection” Symphony reminds me more of Chartres than anything else I can think of. Chartres must be a node on the body of the Earth and human knowledge must be much more than what our science allows. A solar system and its planets must have self-focusing properties that elude our theories about life and the birth of cognition. Self-gravity and the way it reacts to what it gathers up must hold many a secret in its embrace. The homely uroboros is a superabundant symbol.

In the image above I am applying an ancient symbol to an important astronomical event. I made the head of the snake that bites its own tail the  difference in days and distance between the Sidereal (27.3217 d) and Synodical (29.53066 d) months. The 2.2089 day difference amounts to 29.1° of Moon travel or about 195,269 km around a center of mass it shares with the Earth perhaps 1700 km below the Earth’s surface. In one synodical month the Moon and Earth travel together 29.1° around the Sun or about 76,000,000 km. 195,269 and 76,000,000 relate as 1:389. When days are replaced by  years you get a 2.2089 year period in which the former cycle disintegrates. The soul withdraws like a worm into its cocoon. There it potentially undergoes a metamorphosis of some kind; a rebirth. A new 27.32 + 2.2089 year cycle then begins. In my life I have learned that this is a powerful cycle. I was unable to ignore it. It wrapped me up in a cocoon of its own making until I was momentarily paralyzed externally, while internally the contraction caused an accumulation, a quickening, a constellation of archetypal force, an agitation – and then a light went on and the cocoon was shed. The ‘grail’ has been associated with just such a cycle, often rounded up to ‘30’ years. All of mankind and the Earth itself are affected by this 30-year cycle. When an individual cycle coincides with a collective cycle, it can be particularly challenging. You can find yourself panting for breath at the side of the road with ‘loss’ your sole companion. In Egypt this was the Sed Festival of Regeneration. In the month, we tend to mark – at least unconsciously – 4 points of the cycle as if we had ‘squared-the-synodical-circle’. If we do that we have exceeded the sidereal circle of the Moon by 2.2089 days, but have a square that is about 7.38266 days on a side. This gives rise through the 90° angle to the waxing square, the Full Moon, the waning square and the New Moon. Three phases are similar in that all are visible. But the New Moon occurs in front of the Sun and cannot be seen. It is as if the Sun absorbs it or swallows it. In the case of an eclipse it is as if the Sun has been swallowed by the Moon. So this 2.2 day/year phase in the cycle is more than meets the eye.

Now, the Moon’s diameter is 27.32% of the mean diameter of the Earth (3476/12,732). Together they are 1 + .2732 = 1.2732 = 4/π. This means that in terms of diameter, Earth and Moon are in a ‘squared-circle’ relationship. I will come back to this rather interesting point ahead. It is too valuable to ignore.

I knew the Grail involved a vessel of some kind but had not thought of a cathedral as a vessel that had assumed the function of the Grail: an enclosure designed to initiate all of us into something extra. That extra is what makes us a little more than just human – at least in cycles. My own view of churches, other than Chartres, has been mired since childhood in a murky backwater of preciousness – an allergic reaction of my heart to the falsity of all the bizarre  projections that we had been told to take as true. The church irked me, which is why Chartres has been such an unexpected fork in the road. Finding the grail to be almost as ‘precious’, subconsciously, it was a stimulating association to entertain – between it and Chartres – an antidote perhaps, to an ingrained, but tired, rationalism that had not yet completely shed its skin and was still encumbering my need for psychological freedom. I could see that Charpentier had more faith in the ‘Grail’ than I did, but it was Chartres that beckoned me. It was Chartres that seemed to exceed anything anybody could ever say about it. That was the mystery for me and the preoccupation. It shares this superabundance with the Great Pyramid of Gizeh, the “boon” just mentioned above granted by Atum (Heaven) and Geb (Earth).  But my ears were cocked to any clues that might help to explain the superabundance – the way consciousness can exult in its own overflow – the way Chartres stimulated this overflow; how the builders could have been nourished by the same boon, the Stone most pure.

As it turned out, it wasn’t until I had started to come upon key references to the Eye of Horus – particularly in the 5th Dynasty Pyramid Texts of the Egyptians – that the meaning of the “Grail” started to become clearer. One thing Grail, Eye of Horus and Notre Dame de Chartres all have in common is that all three are always referred to as feminine. In male psychology, the “Anima” is also feminine

and can play an indispensable role in the process of psycho-spiritual metamorphosis. There are levels of transformation that cannot occur without the appearance of the anima-figure – especially when the anima herself undergoes a significant transfiguration. The ancients identified the anima with the action of the Moon and the mysterious influence of the synodical month. In India and Mesopotamia, a favorite myth known as The Churning of the Sea of Milk, makes the ‘grail’ the Moon itself, a goblet that renews the Golden Amrita that, like the Eye of Horus, sustains the gods themselves!  However, instinct dictated that 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 was pushing me to look more deeply behind the symbol – if possible – to feel out the web of circumstances within which ‘things’ arise and disappear again, including the anima herself.  I knew the ‘Grail’, or “Gral”, could not be identified with a single object, or even person, 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 surely universal, of which things are ‘symbols’ only, likenesses, to borrow a term from Goethe, a means that facilitates a much more mysterious passage: a particular testament, if you like. However, the right vessel, properly rectified, can have the effect of stimulating a metamorphosis, a qualitative change or transmutation in a living being. It could most certainly be a means of initiation in the fullest sense of that term, by which I do not mean empty ritual. This ‘vessel’ ranges from a ‘constellation’, to a solar system, to a planet, to a grotto, to a living skull, to a dream, to art, to a cathedral, to a relationship, to a mathematical insight, or even a shock of some kind that induces a supra-normal or exalted state of being. In the case of a revelation, vision or unusual dream, the Grail refers to the means, the mysterious spherical enclosure within which ‘Isis’, the ‘Magdalene’, ‘Lakshmi’ can do their work. The Grail is the All-embracing’. It can also refer to the whole body itself – the house of the soul – those  proportions alluded to by Vitruvius and illustrated in part by Leonardo.

Below, I have outlined just the barest elements of Leonardo’s ‘plan’. The 2:1, ABCD, is ½ the square that surrounds it. The 2:1 is then divided into 8 squares

or 4 smaller 2:1 rectangles. Further division proceeds from this.  The circle is centered on the male navel at  ~ 6/10 of the height.  Below, I have placed “A”& “B” to indicate where Leonardo has marked out the Prime 2:1 rectangle with two vertical lines at the elbows. Division occurs between 1 and 2. The crisis of separation is overcome by the ability to rejoin. He then subdivides it into

quarters through dimidiation. I have indicated the 2:1 below, marking it ABCD.

Leonardo’s marks are cutting the Prime 2:1 into halves: the pubic bone (1/2), then the knees (1/4), then at the nipples of the chest (3/4), then the head itself (1/8) or 7/8 of the whole height. He also cuts the square in half at the elbows, then that in half at the shoulders (which I have marked S and R). The circle, contrary to general opinion, is not the ‘squared-circle’. Rather it is a circle with the same perimeter as a hexagon inscribed in a circle with the same perimeter as the square! That ratio is specific. The hexagon and circle relate as 1: 1.0472, or 6:6.2832 which is also the relationship between the meter and the Egyptian “royal cubit” used in the Great Pyramid of Gizeh.

A circle that is 1 meter in diameter has a circumference of 3.1416 meters.  The Royal Cubit is 1/6th of that circle giving .5236 m. The relationship between the radius of the circle and the royal cubit is .5:.5236 or 1:1.0472 or 3:3.1416. This number, .5236, is quite important in this work. It assumes many different forms including relationships among volumes. Another classic example of where 5.236 appears can be seen in the profile of the Great Pyramid which incorporates the golden number, 1.618 when the 1/2 base is taken as Unity.

In this image “1” is 220 royal cubits. The total perimeter is 1 + 1 + 1.618 + 1.618 = 5.236. And 5.236 x 220 = 1152 cubits. I repeat that since the value of the royal cubit happens to be .5236 meter, it can be seen as a principle. When applied to the meter taken as a diameter it is 1/6th of the  circumference. That value, .5236 m, is the cubit of the Great Pyramid. There are 5.236 meters in the width of the King’s Chamber and 10.472 meters in its length. Because the King’s Chamber is an archetypal 2:1 rectangle, it is quite significant to see it incorporate 5.236 in meters. I will be more specific about the KC as we proceed. I wanted to show in this image that the Pyramidal enclosure – the boon granted by Atum and Geb –  has an archetypal value of 5.236 when the ‘mouth’ of the commanding triangle is taken as unity or 220 cubits. The 5.236 then appears again as Unity in the King’s Chamber. And incidentally, the King’s Chamber was given its name by Abdullah Al Mamun when he and his men broke into the Great Pyramid in 820 A.D. There is no indication that the Egyptians themselves ever used the name “King’s Chamber”. This is an important point. If we go by the Pyramid Texts it is more likely that it was referred to as the Cavern of Osiris; the Cavern of Sokar; or the Broad Hall of Osiris (e.g. see PT 1551, Faulkner). I should just point out that the width of the King’s Chamber fits into the 1/2-base 22 times and into the whole base 44 times. The length of the King’s Chamber fits into the whole base 440/20 = 22 times. What I am calling Unity here is 220 cubits or 22 widths of the KC. The 1/2 base was called the mouth of the triangle that gives the pyramid its character. A ‘mouth’ emits sounds generated by the voice. The mouth was also referred to as ‘The Mouth of Ra’ and was considered one way that the creation came into being. As reflected in the Hebrew alphabet, there are 22 partials to the human voice. So the width of the King’s Chamber can be treated as one partial of the mouth of Ra. If the length of the KC fits into the  whole base length 22 times, it fits into the length of the Sphinx 7 times. The Sphinx length fits into the height of the pyramid twice and the base length 3.1416 times. So the Sphinx may well have been intended to be 140 cubits in length or ~ 73.3 meters. 7 x 10.472 = 73.3 meters. 22 x 10.472 = 230.384. It is most likely not an accident that the Sphinx length is in a pi relationship with the solid base of the Great Pyramid. So with the length of the KC as “1” the Sphinx length is “7” and the base length of the GP is “22”.  The KC was likely conceived as the seed of the whole, where the Eye took root. It is the bnbn or Benben. The Benben is closely connected to the Phoenix which was said to bring the Benben Stone. To connect the King’s Chamber or Broad Hall of Osiris, with the Phoenix is to make of it a place of metamorphosis.

In illustrating Vitruvius’ principles Leonardo was being faithful to a fundamental simplicity that springs from the 2:1 construction itself. It is the principle of the 2:1 that fosters the simplicity and can hold together complexity. The 2:1 also gives the sense of vitality and authority to the figure. So there is a direct connection between simplicity and authority. Below, ABCD highlights the Prime 2:1 rectangle which I have cropped for emphasis. Every subtle nuance arises within the 2:1 construction.

In the image of the principle of the Royal Cubit below I have shown the Prime 2:1 rectangle, ABCD, with perimeter 30. I put in a hexagon, EFIGHJ, with each side and the radius equal to AB or Unity of the Prime 2:1. Since it has 6 sides, like the perimeter of the 2:1, which is 6 x Unity, its perimeter will also be 30. But the circle that circumscribes it will be 10 x 3.1416 = 31.416. The relationship between 31.416 and 30 is 1.0472. Any arc of 60° of the circle will relate to unity or a side of the hexagon as 5.236/5 = 1.0472. The circle da Vinci used in his illustration has the same perimeter as the Prime 2:1 (ABCD) and the hexagon (EFIGHJ) shown below. In the case of the King’s Chamber, clearly it corresponds to the perimeter of the circle and has a circumference of 31.416 meters and diameter, 10 meters.

The circle shown in the image above is important in the canon for both male and female. Its diameter is the same as the height of the individual and the Prime 2:1 rectangle. We are going to ‘square’ that circle further ahead. Suffice to say for now that the royal cubit is derived from dividing the circumference of a 1 meter circle by 6. So, 3.1416 ÷ 6 = .5236

Below I have shown the difference between the ‘squared-circle’ and the one used by da Vinci. The squared-circle is clearly larger. The red circle, Circle B, is the same as the red square, EFGH.

Note below how the leg of the figure is parted in exact accordance with the  diagonal (AC) of the double square: ABCD. This passes right through the pubic bone and also marks the base of the ribs.

Above I have marked the head as ¼ of the Prime width, Unity or AB. The shoulders are marked ½ of Unity. The verticals are marked for the height, 2. Note that the shaded triangle, ABC, is the same triangle used to determine the Golden Number when Unity is added to AC, so that: (1 + 2.236068) ÷ 2 = 1.618 = 3.236068 ÷ 2

To sum up what has been said above. The Royal Cubit is part and parcel of the whole discussion at hand. But I introduced it first since it came up. A circle with diameter 10 meters will have a circumference that is 31.416 meters. For a 2:1 rectangle to have the same perimeter it must have a width of 5.236 meters. 6 x 5.236 = 31.416. The intention inside the Great Pyramid was for the Prime 2:1 to have a perimeter equal to a 10 meter diameter circle. We will pick up from here ahead. The KC is a place of convergence of measures that meant something important to the Egyptians. It concerns the ‘squaring-of-the-circle’; the basis of the whole Great Pyramid.


The grail is responsible for an event, an exceptional 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, order itself reaches a threshold of instability. The familiar and the known are swallowed by an unknowable suspense, as external knowledge breaks down and changes its frame of reference. It is pointless to attempt to deprive the grail of all mysticism. It is the cup that overflows its own form through a mysterious transmutation. It is the vessel that knows both destruction and creation and the relationship between the two: the moment when the snake bites its tail; when the Phoenix rises again from its own ashes. At this limit, all ‘understanding’ undergoes an inversion. The terror that transforms into ecstasy cannot be measured. The Grail is mystical insofar as we do not know its ultimate boundary. Appearances, once considered self-evident by the  cerebral mind, find themselves re-absorbed by a source too mysterious and too powerful to name. But yet it is experienced vividly and directly. One is  both the cup and the flowing fluid that overflows its own ‘rim’. Inevitably the ‘Self’ and the ‘Grail’ have much in common. Which determines which. Chartres seems to respond to this question by urging  the soul to blossom from the heart.

Following this inversion between known and unknown – and perhaps between cerebral knowledge and heart-knowledge – 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, because all metaphors have also been inverted! Cabalistic language arises by necessity to convey mystical truth. 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 and man’s relationship with the surrounding cosmos. Below is a closer look at a sculpted image of Moses at the north-west entrance to Chartres. Note the winged dragon perched atop the pillar at the level of his eyes.

Before I had come to Charpentier’s enigma about the Grail, I first came upon this image of Moses. It was 36 months before I could photograph it myself. When I finally got there I was stopped in my tracks. Such figures! They redefined my understanding of art, of culture, and of the spirit in humanity that can even inhabit stone when it has become essential to do so. Some legacies must not be lost in space even if they have ended in time – and vice versa! I willingly allowed myself to be lifted into a time warp. What force had driven the hands capable of carving stone in such fashion that spirit could glow upon every face and radiate with such historic humility from every heart. Eyes that seem to gaze down eons of time! Beacons. A guiding geometry enveloped and then gently beckoned the soul out of the rock. Moses holds a  rounded Table of the Law.

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 unlocked that world that the Master Craftsman kept in his pocket? If there was a cosmic code, a great measure, the Egyptian “Arq Ur” – which was one name for the Great Sphinx – did he inherit it? Did he discover it? Perhaps it was rediscovered in Jerusalem or in Egypt, or in both, from about 1100 to 1128 A.D. But what was it: a key to unity perhaps, to the wholeness of things – that which enables harmony? Even language faltered in my mind when confronted with the magnitude of knowledge that erupted out of Chartres as if it were the Cornucopia of the World. Each page of Charpentier’s book reflected the awesome tone that resonated in each stone, each pillar, each figure, saturated with history… a legacy that all of us had inherited from men in the grip of some cosmic inspiration.

At the North-West Porch, 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 in the ground according to the plan you see below.

That which is lowest, the serpent, has been raised, lifted up, ‘redeemed’. Presumably it is concentrated according to the ‘table of the law’ that Moses holds as well: a rectangle with a rounded end that resembles aspects of the floor plan of Chartres shown above. In this image I have included the outside width of the Nave and a length that equals the diagonal of a 50 x 100 meter double square (111.8 m). This includes the complete interior Apse and the entrance to the Nave from the towers. The North Tower has been given a height of about 111.44 meters by Houvet. The diagonal of a 50 x 100 meter 2:1 rectangle is 111.8 meters. The difference is 36 centimeters. In the Renaissance it was rebuilt and with cross and Sun it supposedly reaches 115 meters, so those items are to be subtracted. The principle of the diagonal of a double square is so important that my guess is that this was the original intention. The diagonal, the square root of 5, is a transcendental function. To stand it up as a tower is to connect heaven and earth. It is the return of spirit to its own source. In one fell swoop the blind hen may have caught a grain of corn in its claw. The double square represents Above and Below. The diagonal is the link between the two. The “Brazen Serpent” makes this link. Every tradition, moreover, warns that the “Kundalini” is dangerous on a vital level. It can be provoked by advanced yoga techniques. The serpent image is an enigma, a warning and a promise. Life and death are dangerous. Forewarned is forearmed. Wisdom is still worth the risk if you feel the calling. Chartres is a testament to this calling.

The concentrated spirit (brazen serpent in the Bible) rises up the pillar (tower), 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. A profound parallel is being made between fundamental principles that dominated Egypt and the ‘life of Christ’. What is being implied is wisdom, frequently associated by the ancients with a serpent. Why? The serpent power refers to a pristine force stored up in the base of the spine that can be opened and lifted up to the heart and head. Here it can blossom, the moment of enlightenment of all religions. At the moment of enlightenment the darkness; the melancholic state of being lost in the wilderness with or without sin, is transformed into an inner light that permanently changes the individual. And it is true: that moment of enlightenment is worth more than any physical gold one could possess, no matter how comforting such gold may be! In this respect wisdom is not merely encyclopedic information. It is a transformation of being; a ‘way’. There are different ways to express the same path. A ‘Winged Wouivre’ is one way; the “Grail” is another.

In this image we see Seti I of the XIXth Dynasty of Egypt making an offering of Maāt, neter of Truth, Cosmic Balance. The Uraeus extends from Seti’s brow as if it has blossomed from the khepresh helmet, itself capable of attracting, conducting and concentrating magnetic energy. John Anthony West reminds me that no khepresh helmet has ever been found, but one thinks of the 30 pound helmets worn by the Tibetan kuden, or State Oracle, worn to induce an oracular trance every year in the Central Cathedral (when formerly in Tibet). In any case, in the bas relief above, the ‘brazen serpent’ has been mastered, raised and blooms like a lotus flower exuding its numinous perfume out into the world. His hands have been reversed. His left hand is on his right wrist and offers Maāt. 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. ‘He gives to the god what he receives from the god’. That is Maāt. It is a double action, again echoed in the double square. We seem to be getting a clue from more ancient members of humanity as to the inner secrets of the crucifixion, the principle of the cross or crossing; and how it amplifies or magnifies something of inestimable importance. Maāt represents balance or cosmic equilibrium. So does the cross. 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, here severely edited:

“I have come to you, I am Thoth [Maāt's masculine counterpart], my two hands united to carry Maāt…you make Maāt rest on your head in order that she may take her seat on your forehead….you exist because Maāt exists,…and vice versa.” This passage makes a direct link between Maāt and the Uraeus or raised serpent force. The cross, and crossing, link spirit to matter, and matter to spirit; circle to square and square to circle. It links above to below and around to within and vice versa. The breath imitates this; as does each beat of the heart. Maāt is not a ‘Platonic-like’ abstraction. She exists through each living being and each living being exists through her. That is the secret of the crossing, decussation, symbolized by exchanging the position of the hands in the bas relief. Life is woven into being by the crossing. In the crucifixion one is given new life.  After a dire separation, male and female are reunited. The essence is re-baptized. The spirit is born. One thinks of the crossing of the diagonals in a 2:1 rectangle. Each one is valued at 2.236068, the root of 5. When multiplied together you get 5, the number of life and sometimes of man himself! Moreover, 2 + 3 = 5 = 2.236068 × 2.236068. 2 + 3 = female + male. Maāt is offering ‘life’, the Ankh. In the canon of proportions the diagonals cross on the pubic bone: that which divides male from female sexuality and also provides the means of their reunion. From that reunion, often ecstatic, new life arises.

The towers are not merely ornaments or ‘let’s see who can build the highest spire’. To suggest this is a considerable affront to the Master Craftsman of Chartres, even if other churches succumbed to such dubious endeavors. The towers attracted energy above and crossed it over with energy below. A bishop, Monseigneur Pie, once said of Chartres: “Its source is below and above”. (Mysteries of Chartres, p. 29). For humans it is not possible to exaggerate the importance of the hands. Not only are they extensions of the heart. But they also are wired to the mind and brain. In a sense the hands express the union of head and heart. They are also connected to speech. Given that the hands are capable of such intricate, nonstop labor, one would imagine that a special geometry must command their creation and function. It took me several years to realize that ‘squared-circle’ geometry was playing a fundamental role in the proportion of the hands. But this meant placing the center of a circle over the heart, the cross of the Thoracic Vesica Piscis. I did not find this circle until December, 1997. I was looking at the heart as the center of the ‘archer’s bow’. If the heart was perturbed the arrow would not reach its target. The arrow could also be taken as a metaphor for the human spirit. The eye and the heart were guiding the arrow together: the hands were their sensitive servants. So I placed a circle over the heart and built it up in concentrics. I imagined it to be a bow. I then learned about something called the Ideal Angle in botany that divided a circle around a shared stalk or stem by the golden section. This division became the tension in the bow capable of firing an ‘arrow’. I knew an ‘arrow’ could assume different forms of expression: from writing words, to drawing pictures, to driving a car. I will return to this ahead. Moreover, words could escape by different routes!

Note below how the diagonals seem to shape and focus energy into the sacrum: the abode of the serpent energy. The diagonals crossing from below seem to want to open it up: to let the genie out of his bottle. There is an anterior and dorsal aspect to the same energy. Sexuality is anterior. The kundalini that can be raised for spiritual transformation is dorsal.

I should just add here a comment by Lucie Lamy, the stepdaughter of Schwaller de  Lubicz who carried out countless precise illustrations for his books: “Maāt is the greatest treasure that a being might wish for.” (egyptian mysteries, p. 51) She calls Maāt “Cosmic Consciousness”, which is clearly to be distinguished from mundane consciousness that comes and goes. Obviously the implication is that Maāt must be awakened. When she is awakened, the crossing becomes real. Not surprisingly, perhaps, if you slipped Lucie Lamy’s line into Parzival, but replaced the word Maāt with Grail, you would never know the difference. “The Grail is the greatest treasure that a being might wish for.” Is the true essence of the Grail the same as Maāt?

Cosmic consciousness transmutes knowledge into the greatest of all treasures. The Grail transmutes its contents to the point of overflowing. What overflows has become a qualitative transformation of being – an accomplishment unique in its own time. The overflow is the difference. Chartres clearly overflows its own tangible boundary-stones. It is also unique. The Winged-Serpent overflows the cross, the papyrus stalk of Uatchet, the pillar that he has ascended, the soaring obelisk. Speech overflows the throat that has created it. Love overflows the heart that spawns it. What can be accumulated can overflow. The maple key overflows the branch. The perfume of the rose easily escapes its thorny prison. But when Parzival took the miracle of this superabundance for granted and failed to rise up and ask in humility and compassion about the circumstances surrounding the Grail – including the uncured illness of his ailing uncle, the Grail King – he found himself wandering in a senseless wasteland having lost all sense of time and purpose until nearly consumed by his own anger. The grail is not just about abundance. It is also about the wound from which abundance springs. Gates don’t open without questions to turn the key. Without humility at the base, the towering tree will topple in the first strong wind. The Grail King and the Osiris King have much in common. The fallen pillar will rise again at the right moment in the cycle.

“Three Tables bore the Grail”.

In a state of almost pre-cognitive chaos – sometimes premonitory – I came upon Charpentier’s fortuitous recollection at some point in June, 1985, at the start of a bewitching New Zealand winter, the birds singing, the grass always green, Greenpeace in town getting ready to protest nuclear tests in island arc atolls with their feisty little ship, The Rainbow Warrior. So, back in 1964 there was a ritual gathering of “the Society for the Study of Traditional Sciences”, the “Friends of Atlantis”, on a property in a suburb of Paris. Somebody had faith in a civilization that, according to Plato, was thousands of years older than either Egypt or Greece. A fire was lit in the name of Saint John; there was chanting and perambulating in a circle with beribboned sticks and colored costumes. A speech was given during which the speaker 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, as eventually it will provide the scale of the cathedral and its elevations:

“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)

When I first read this, it was a brain-stopper. The whole world seemed to gather itself around it for a second or two and let out a sigh, leaving me to wrestle with the riddle. The unconscious seems to know its own cause before consciousness has identified the specifics. You feel before you ‘know’. This was a trade-secret that distinguished temple builders from all others,  not wishing anyone to cast doubt upon the secret itself, nor their own intentions – the ‘Stone most pure’. It was an enigma with many layers, many implications. It reminded me of a mobius strip or the Chen sign of the Egyptians, or the sacred ligature that united Horus and Seth, North and South – through the breath that weaves life and feeds the blood in the midst of the thorax. Something unlimited and highly differentiated was being united. In short, the image overflowed its own limits. It was not just ‘squared-circle’ geometry that I had encountered in both Doczi and Michell; rather it involved the authority of a third. The third was a rectangle. At the South-East Porch of Chartres, to the North of Christ who occupies the central position, Saint John can be seen holding a 2:1 rectangular tablet. They lit the fire of Saint John on that property outside Paris. The 2:1 has been associated with ‘revelation’.

Saint John is the second from the right. This is the only photo I could find for the moment. I have misplaced a better quality one. Saint John is holding a 2:1 rectangular book.

I already knew from Doczi that the Great Pyramid of Gizeh was based upon the  squaring of the circle by perimeter, but had not yet thought of a direct connection between the Great Pyramid and the Grail. I had never imagined any connection between the Great Pyramid and Chartres. As it turned out, the connection is not the least vague but entails actual measures. I needed to read Parzival first and then the Pyramid Texts to understand the context: what the ‘squared-circle’ might be expected to accomplish. The Phoenix makes a significant appearance in both Parzival and the Pyramid Texts (e.g. Utterance 600, PT 1652). I also did not know that the King’s Chamber within the Great Pyramid was concerned with ‘squaring-the-circle.’ In fact the KC circle is of genuine interest for us moderns. As mentioned already, a circle with the same perimeter as the 2:1 rectangular King’s Chamber itself has a diameter that is exactly 10 meters. I will be coming back to this point. Recall, that if you ‘squared-the-circumference-of the-Earth’, and then divided each side of the square by 10,000,000, you would have the meter, or say 39.37 inches. The meter is derived from a principle. The principle is the ‘Squaring-of-the-Earth-Circle’.

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. The synodical month depends from the Year, so this coincidence of the Heliacal Rising of Sirius every 365.25 days is a stunning convergence of harmonies. Sirius (8.7 light years away) has an invisible white dwarf orbiting it, adding a unique gravitational situation to the equation. By linking the Grail to Isis, the ancients were automatically taking Sirius into account.  This was the star of Isis also known as The Great Provider in her name “Sothis”. The Dogon of Africa called Sirius B, the white dwarf, Po Digitaria, or the granary of the world. Even though Sirius B could not be seen with the naked eye, the Dogon knew it was there.

Thoth-Hermes was treated by the Egyptians in a special way. When Ra was created, they proclaimed, it was Thoth and Maāt who brought him up out of the void and established his size and so forth. For the Egyptians Thoth and Maāt represented some form of vital harmony. The Egyptians attributed all sizes, all periodicities, all measure and all design, ultimately to Thoth and Maāt. This included the human body! It would have been Thoth who would have established the 3 tables that bore the Grail. The balance among them would have been the domain of Maāt. Thoth was also called “The Judge between the Two Combatants”, he ‘who reconciles Horus and Seth’. One imagines the Circle to be Horus; the Square to be Seth; and the rectangle to be Thoth. Because of the plethora of information associated with the temple, the Grail, I have to omit many, many details. The art of editing is not without pain.


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