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 = 1.078689 = 1.618 ÷ 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 × 4.655832 = 137.036 (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 ÷ 1.08 = 1.5 = 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