The Formal Search Begins in New Zealand (Post 4)
The Prime Mystery: 2:1
My first impression of New Zealand when we stepped off the plane on April 10, 1985, was not the brilliant green of the grass. It was the smell. I have never smelled anything like it anywhere else: a unique combination of honey, milk and the faintest trace of volcanic sulphur. Then I was swallowed by the green. The air was moist. The atmosphere was biblical. I learned at that time that “Kiwis” referred to their country as “God’s Own”, a fact they state with an inimitable modesty. While Vincent Ward and Kely got down to the task of researching the time of the Black Death – the ‘plague’ that struck Europe around 1348 A.D. – for the film that eventually was called “The Navigator: A Medieval Odyssey”, I sat down in the hotel room and seized the chance to begin searching for a formal geometry that would account for our collective anatomical features. I confess, there was an inexplicable spell cast by the middle ages that had me in its clasp. All I could do was open my eyes and unstop my ears to see if I could understand ‘why?’. The world had become a cornucopia of clues. For the moment New Zealand was its crucible. I had no idea how long my luck would last nor what I might do with any clues I might find. But then faith is a mighty magnet. Without realizing it I had just embarked on a pilgrimage that was to last for many years.
Any desire on my part to take the reader on a linear path in order to reach the destination I have in mind is doomed from the outset. The destination is really the path itself. A song by Gordon Lightfoot immediately comes to mind: “There are too many clues in this room.” When the clues build up with unexpected density what had been straight becomes round and even tortuous. It bends itself with its own gravity. The mind stops and is forced to make a decision. Infinity blocks the way. There are too many steps on the path; too many dots clamoring to be connected up like beads on a string; golden links glistening on Ariadne’s magic thread. The closer you look, the more you see. One of the implications of the Heisenberg Uncertainty Relation is that it takes infinite energy to probe down to the “0-point” suggesting that the “0-point” will never be more than hypothetical. We are barred from knowing anything about it except the mathematical constructions that we scratch out on the inner walls of the cerebral mind. Too much detail exceeds a limit and will stop itself. No one can tell the whole truth and nothing but the truth. The writer must edit and in editing he runs the risk of the reader believing the edit is the thing itself. Wisdom must lie in the choice of limits; if we really have a choice.
So when I started to swing the compass in New Zealand in May, 1985, I found myself in a blizzard of clues. It is impossible to convey all the influences that guided that compass; and moved the pencil along the edge of the ruler; and carefully punched the keys on the face of a brand new calculator. It took from 1985 to 2006 to finally rest my case or, in any case, take a rest. Actually, a few more details have crept in since then, as one would imagine! For me the geometry of human proportions acts a bit like a camera acts. It is a means, not an end in itself. The camera takes you on a journey. You have no idea who or what you will encounter. For me personally, it was the key that opened doors that otherwise I would not even have noticed. For example, without the geometry, Ancient Egypt invoked for me an airless museum full of silent mummies, dusty with exquisite jewels. With geometry as a lens, it was a revelation that changed my view of existence. Since mathematics was ostensibly not my first calling in life, this was quite an unexpected part of the journey that had begun in 1971 when I left Toronto.
I had inherited two books while still in New York in 1984. One came from an Egyptian born friend, named Wagui Takla, called “The Temple in Man” by R.A. Schwaller de Lubicz – a break-through work that reveals the basis of the famous Temple of Luxor in southern Egypt. Schwaller’s study of Luxor has taken the old adage, “man is the measure of all things”, to a whole new level for modern man. Moreover, it is safe to say that the first unexpected jolt I got in the search for a geometry of our anatomy came from the ancient knowledge of the temple. Innately this made complete sense to me, but learning what that basis was, was an altogether different matter. It required painstaking effort combined with repetition. I had intuited the link between man and temple in 1984 when I put together an exhibit of paintings in a friend’s apartment on Fifth Avenue above Barnes and Nobles book store. But I was balking at the idea that the link was a science. Moreover, when dealing with man, geometry also has a philosophical dimension. I was appropriately worried that a philosophical geometry would become an all-absorbing preoccupation. Yes, I was obsessed with the physical form. I wanted to get it right: the geometry that guides the genome; not the genome that guides the geometry. In the back of my mind I knew I was looking for a geometry that also accounted for the mysteries of the human mind: not to mention the soul; the Egyptian “ka”.
The second book came from Wagui’s friend, an innovative French architect named Paul. Paul insisted to me after seeing some of my paintings that it was time for me to know the geometry itself as a science so that it would be at my fingertips. I said to Paul: “The day it becomes a science is the day the art will stop”. He laughed. But as it turned out, I was right. The ‘science’ swallowed the art. You discover who you are one footstep at a time. Who knows, if I live long enough, like Jonah, the art may well be coughed back up again by the whale of science.
In any case the book Paul gave me was a marvelously illustrated treatise by György Doczi called “The Power of Limits” (1981). This was the most comprehensive work on the role of the Golden Proportion in Nature, art and architecture that I had ever encountered. But in it, a single passage entered my mind like a magnet, a magnet that helped open the door to Schwaller’s appraisal of the ancient Egyptians. It was at this time that I came upon Leonardo da Vinci’s famous drawing yet again – in “The Power of Limits”. Leonardo had illustrated principles mentioned` by Vitruvius in his First Century works on architecture and Doczi’s comment sunk into my imagination like a golden hook.
“In fact we are told by Vitruvius, the Roman architect mentioned in the previous chapter, that the ancient Greeks even laid out their temples according to human proportions. On this basis Vitruvius recommends that the length of a temple should be twice its width…” (György Doczi, The Power of Limits).
The length of a temple should be twice its width. The basis of our diatonic scale is the octave which raises the fundamental to twice its initial frequency by cutting a string length in 1/2. For example, 262 v/s becomes 524 v/s.
I should mention immediately that with a tradition firmly in place, at least since the time of the Greeks – that linked the basis of temples to human proportions – the controversy aroused in Europe by Schwaller’s on site research in southern Egypt, likely had nothing to do with the tradition per se. His research was suggesting that this tradition was far, far older than the Greeks and that in fact it was at least as old as Egypt, if not older still. The controversy was over the antiquity of the tradition. This implies a deeper and far more profound controversy that we encounter in Plato’s Timaeus: the age of man and his knowledge. Plato pointed out that the Egyptians regarded the Greeks as children because they had failed to keep records of their own history that went back thousands of years to a time when they were greater than the Egyptians themselves and a very heroic people in the bargain. A comparable and more contentious controversy swirls like a whirlwind to this day around the age of the Great Sphinx. For experienced men like John Anthony West, for whom Egypt is like a second home, the Sphinx is far, far older than conventional education dictates. The geological science is even in place to prove it. But many of us have trouble imagining what could have preceded the historicity of ancient Egypt, Sphinx included. It took the dedicated and thorough eyes of Schwaller to notice the nature of the erosion patterns on rock associated with the Great Sphinx: its own body and the surrounding rock. Nobody else realized it was water erosion in a place that had been a desert for thousands of years, with the Sphinx buried up to its neck in sand for a good proportion of that time. Geologist, Professor Robert Schoch, however, corroborated almost immediately that the deep patterns of erosion on the body of the Sphinx could only have been accomplished by rain water. With help from a small team and new technology, West and Schoch are now trying to improve their reckoning to see if they can suggest when the first carving of the Sphinx my have taken place. At stake is not merely the history of ancient Egypt, but man’s own self-image; our own age and evolution.
All historical controversy aside for the moment, for me what mattered immediately was the mention of the 2:1 rectangle. It was all too easy to get snared by the controversy and miss the cornerstone itself, the seed from which temple and man could sprout. And that is how it entered my system – like a seed. Just like that my whole being was permanently fertilized. I had experienced this kind of fertilization with the 1980 ‘Big Dream’ – especially the build up to it. At times it felt very strange. As a male, I was not used to feeling pregnant – especially with spirit. The impregnation by the reference to 2:1 did not feel intellectual, per se. Rather, it felt ‘mystical’, for want of a better term. I realized there was something called innate knowing that stood outside all political considerations. The 2:1 ratio was at the heart of that innate knowing in some fashion. But my instinct knew it before my mind did. My mind has always felt to me like a stranger in a strange land. But my instincts feel all too real.
Since the Greeks and the Romans had spent time on the throne in Egypt (the Greeks starting 305 B.C.), it stands to reason that both Greeks and Romans inherited the very principle just mentioned by Vitruvius from the Egyptians themselves! Schwaller’s life mission was to prove this point and reveal the goal of the knowledge built into the temple at the same time. The notion that a temple was constructed on the basis of human form was a great idea since temples were holy places designed to unite above with below, inside with outside, cosmos and man. They were built by men with a mind to exalting the human condition; ennobling the human spirit that so easily succumbs to the decadence of luxury and the brutality of hardship. Temples were oracles and places of healing; sanctuaries designed to rectify all that can go wrong with human civilization. They had the ability to transform what is base into a finer state of being and perfect the governing body. It struck me, then, that the mention of the ratio 2:1 had to have some significance. Not surprisingly, Schwaller also singles it out in “The Temple in Man” (translated by Deborah and Robert Lawlor, 1977) in connection with the Golden Proportion, Phi or 1.618…:
“All the constructions of Phi that can also be found as the starting point in Byzantine basilicas and in cathedrals always have as a basis the right triangle whose sides are 1 and 2 and whose hypotenuse, the square root of 5, is the diagonal of a double square.” (Temple in Man, p. 39)
The seed that had barely been planted had already begun to grow. It was important for me to adopt a new attitude. I had to verify everything as I went along. That removed it from a cloud of abstraction and made it tangible to me. Anything this fundamental had to be witnessed with one’s own eyes; interpreted with one’s own mind to eradicate all doubt from the outset. But I repeat, it was some unexplained instinct that quietly proclaimed the importance of this geometrical syntax: 2:1 rectangle; its diagonal, the square root of 5 or 2.236068… and the golden number, 1.618 where 1 + 2.236068 = 3.236068 and 3.236 ÷ 2 = 1.618.
Making this drawing was not drudgery. It was a ritual, guided by an instinct. The 2:1 rectangle, ABCD is drawn first. The diagonal AC is placed next. The compass is placed on A and opened to unity (AB). It is then swung into a circle that extends AC to CE. CE is then bisected by placing the compass on C and E and creating the two ‘X’s at F and H. A line is drawn between them. Where it intersects CE at G, CE has been cut in half. CG and EG both equal 1.618, the golden number. It is easy to calculate the diagonal AC by using Pythagorean Theorem:
(AC)² = (AB)² + (BC)²
(AC)² = 1 + 4
(AC)² = 5
AC = 2.236068 = square root of 5
This construction proved to be the tip of an iceberg too big to measure. However, it introduced me to a principle. The principle has permanently altered my outlook on the world. We exist because of proportion. Without proportion we could not function. Undoubtedly proportion is the secret of cognitive understanding as well because it mediates mere proliferation. Mere proliferation collapses too quickly – under its own weight – to support cognition, not to mention reasoning or imagination. It is the proportions within the web of life that make perceptions and sensations intelligible, meaningful and impart to those sensations qualities. The golden number might well be the standard of quality against which everything – whether conscious or unconscious – is measured. The proportions of the 2:1 rectangle contain the measures by which the golden number can be infallibly constructed without the need of a calculator. Not only was this the tip of an iceberg, but it possessed a glow that felt to me like the spirit in matter, capable of giving life to the proliferation of material atoms that on their own would simply throb like crystals in the void without yielding to the miracle of intelligence.
When we attempt to reduce a seed to its simplest terms we can succumb to the fetish of ‘one thing only’. With the 2:1 and its phi-construction, I had to deal with the fact that the diagonal also instantly spawned the golden proportion another way. Same construction; another variation. Leonardo called it the golden section and in fact the golden section has proven to be as ‘useful’ for developing the canon of human proportions as 1.618.
The start is the same: draw the 2:1 rectangle, ABCD. Each time you do it you learn what ‘meekness’ really means. It is completely free of polemics. Again, you place the compass on A and open it to B. You swing it until it cuts the extended diagonal at F and J. Now you place the compass on the complementary opposite corner, C, and open it to F where is has cut the diagonal AC. You swing out the larger circle with radius EC and eventually you learn that:
EC÷AB = 1.236068 = 2.236068 – 1
You also learn that 2 – 1.236 = .764 and that 1.236068 ÷ .764 = 1.618
When you create the golden section the other way, namely top down, you establish point L and you discover that a progression has been created:
BE ÷ EL = 1.618
This can be expressed in terms of the golden number and its powers:
BC/1.618 = EC; BC/2.618 = BE; BC/4.236 = EL; or, 2/1.618 = 1.236; 2/2.618 = .764; 2/4.236 = .472
This simple drawing where unity divides the diagonal of a double square into 1 and 1.236, was perhaps the single most important geometrical gesture of the entire body of work. It was the pump from which all the water could be drawn from the well. Here you see two circles that touch each other at F on the diagonal, AC. When CF is rotated to CE along the length of the 2:1, it divides 2 into 1.236 and .764 which relate as 1.618:1. So in one paradigm you immediately have an outflow of values that relate through the golden number: 1.236/.764 = 1.618 = 1.618/1 = 2/1.236
1.309: A Singular Branch of the Tree.
The progression just shown earlier takes us in toward the microcosm. When we go the other way we find that when the two circles divide the diagonal of a double square in this fashion they form an angle around which we can place a rectangle. The proportions of the rectangle, NOPQ, become 4.236 x 3.236 or
(1.618)³ x (1.618 + 1.618) which is the golden number cubed by the golden number doubled.
But this merely primes the pump. A quick tour around the garden reveals all sorts of family members that cannot be dispensed with. Eden has one tree but the tree has many branches bearing multiple fruits.
1.618/1.236 = 1.309 = 4.236/3.236 = 2/1.528
I recall the first time I stumbled upon 1.309. I knew it was important because it linked 1.618 to 1.236. It was their relationship: eternal, unalterable. It also bounded the complete golden section ‘image’. But like a shy fish, it quickly slipped beneath the waves and I had to patiently wait for it to surface again. Sometimes it wouldn’t surface for years! Finally, with help from ‘tradition’ it remained visible and its importance started to grow in my often beleaguered mind.
I soon learned that 1.236 marked the mean position of the human, adult navel. And I could see that we bent over at the navel because it was just at or above the tops of the pelvic bones (Iliac crests) and at the base of the spine. Through simple exploration I soon learned how to construct a golden rectangle by using the ½-diagonal of the double square. All at once the family started to grow. The full diagonal was 2.236 or the square root of 5. The half diagonal was 1.118. This meant it was Unity + .118. I started to memorize these figures like a school-boy. If I added .118 to each side of the width I would have:
.118 + 1 + .118 = 1.236 and 2/1.236 = 1.618.
So this was a golden rectangle (GHJK) with all sorts of properties demonstrated in various works. Little did I know that with a few more clues I would be able to construct the female in a somewhat ideal or primordial way. But I had to wait for those clues to present themselves. I was a novice. I never took any Fine Art courses at college. So I had no head start. But often ‘beginners have luck’. The functional and philosophical implications of the golden rectangle when derived from the Prime 2:1, ABCD, took weeks of contemplation. It is easy to create. You simply put the compass alternately on D and C and open it to F where the diagonals cross. So the radius is 2.236/2 = 1.118, one of the most important and ‘authoritative’ of all proportions to be extrapolated from the 2:1 paradigm. After only a few weeks of working with 1.118, I soon labeled it the “Magic Wand” of geometry. I meant both the 1/2-diagonal and the full diagonal. But what I really meant was the ratio. The length of a 2:1 x 1.118 is 2.236. The width x 1.118 is 1.118. I repeat, 1.118 is one of the most important ratios to be worked within the 2:1 paradigm. So with the compass open to CF and KF you drop it down from F to the base on both sides at K and J. This will then
expand Unity by .118 + .118 = .236, giving 1 + .236 = 1.236. So we now have two ways to arrive at 1.236, namely: 1 + .118 + .118 = 1.236 = 2.236 – 1. And 2/1.236 = 1.618. This has become a tablet of harmony. It possesses an inner consistency where parts within a single whole can act co-operatively while handling differentiated functions. The golden proportion ensures that it operates toward a common end. And in fact I began to suspect early on that it determines that end. It is the proportion itself that determines the end, the purpose, the goal which is nonetheless implied from the beginning; from the germ. And the germ, I sensed almost immediately, was the 2:1 Rectangle, ABCD. When we discuss what I call the Prime Fibonacci Series, we refer to the golden number, 1.618, as its limit. This does not refer to a quantitative limit, but rather it refers to a qualitative limit reached starting around Column XIII. It is the relation between two adjacent numbers from that point on.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597….
The early relationships oscillate above and below 1.618. But gradually that oscillation tightens up and by Column 13 or so, it becomes constant so that 233/144 = 1.618 = 610/377, etc. The golden number was implied in this summation series from the beginning. Through growth it gradually emerges. The limit of the relationship between the growing parts seems to set a tone, a quality, a constant and a meaning. Women understand the meaning of constancy when raising a growing child. The child knows he or she depends upon constancy. Phi is the root of that constancy. And 1.618 is a proportion. The quantities grow but the relationships remain constant. Meaning, purpose, ‘direction’ seem to be guided by the proportion. Proportional oscillation – through growth – is regulated and even transcended by Phi, 1.618.
Proportion: A Personal Paradigm Shift
I was already aware of proportion. But this family: 1, .118, .236, .472, .764, 1.118, 1.236, 1.309, 1.618, 2, 2.236, etc., constituted a qualitative shift in perspective. An important example of a proportion that my system was digesting and that was motivating me to pay attention to all important proportions such as this group, came from a 1974/79 work called “The Tao of Physics”, by Fritjof Capra. I read the book in 1981 because I was ordered to by a professor and healer, a woman with a face like an Iroquois medicine woman, named Mona Dayton. Like a shaman this tough, but compassionate woman guided me through a very tricky abyss just months before the Big Dream out on Long Island, New York. She could feel something coming, but didn’t know what it was. Seeing the body as a microcosm of much wider forces, she knew blocked nodes could be dangerous during specific phases in the cycles of spiritual transformation. She unblocked a very significant one and basically got me on my feet again so I could handle the final onslaught of force that was erupting from my unknown interior. She had given me her phone number, concerned that I might be swallowed by whatever it was that was rising up within me. One night I definitely fell into the black. My imagination convinced itself that I had no future, no path. Everything felt intractable and impregnable. I felt I would never succeed in penetrating the walls of conventionality, elitism, the American Dream or any other pocket of fertility that I might possibly make into a niche. I was a drifter with no home, no family, no place, no roots. I felt about to be extinguished. I found myself ankle deep in the Atlantic late at night. It was so dark the waves were barely visible under a moonless sky but I knew the type. I used to call them ‘dumpers’. To say ‘dangerous’ was an understatement. There was also a nasty current yanking at my feet. The ocean was hungry that night. Had it not been for Mona I’m not sure how far I would have allowed that snarling sea to tempt me. I turned around and looked for the nearest telephone in South Hampton. Once on the phone I just spat it out. I told her the truth. I told her I was at the end of the line. She ordered me over right away. She found the blockage and she also found a problematical relationship between speech and wholeness. At one point she had to order me to shut up. Once that torrential leak in my system called “words” was stopped, the energy broke through the blockage that she had found with her gifted fingers and hands. I will have to write up a special section on the whole story of Mona Dayton. It centers around an enormous whalebone I had found earlier in April right near the spot where I had waded out into the dark ocean that night. I was told about Mona by a school teacher who insisted we let Mona see the whale bone. And the story unfolds from there: the moment she saw it and placed her hands on its smooth top side. It looked like the sacrum of a Blue Whale: an object of mystery and impenetrable power. I keep it by me when I work whenever possible.
Once back in Manhattan, months later in 1981, I honored her request that I read Capra’s paradigm-shifting book. In it he provides two ‘speeds’ (Tao of Physics, pgs 58, 62), by which he means ‘energies’ that can be described as momentums as calculated by the Heisenberg Uncertainty Relation which involves statistical probabilities vis a vis position of a subatomic particle that has been confined to extremely small or compressed spaces (100,000 times more compressed than the first ‘electron shell around the atom) and reacts by accelerating its ‘wave-forms’ or whatever they might be. Capra examined the situation of all electrons on Earth and all nucleons (protons and neutrons) in terrestrial matter. I eventually wrote to Capra in 1999 and then consulted with other physicists to obtain an appraisal of the accuracy of these ‘speeds’ or rates of compressed agitation. The Earth is not undergoing fusion or fission or anything that spectacular. So in theory these mean speeds boiling away in the severely cramped quarters where ‘mass’ resides in the nucleus of atoms and around the atom, seemed plausible. After a few years of correspondence a ratio emerged between the nucleons and the electrons that was approximately:
64,000 km/s ÷ 1,000 km/s ~ 64
The values Capra gives are 40,000 miles and 600 miles which have a ratio of about 66.666. I later got confirmation of 1,000 km/s for electrons and have rounded the 64,374 down to 64,000 here for the sake of a principle. Of particular interest for this work is the direct relationship between the 40,000 miles/sec and the speed of light taken as 299,792 km/s. 40,000 miles translates to 64,374 km. And:
299,792.458 ÷ 64,374 = 4.657
As soon as we get to ‘Squared-Circle’ geometry we will revisit this figure, 4.657 (4.666 in its archetypal state), a curious ‘coincidence’ if ever there was one. Moreover, the golden section within a 2:1 rectangle can be employed to ‘square-the-circle’. When we examine the proportional relationship between Earth and Moon, we will see this figure 4.657 again. It is a number worth remembering. It appears in the Great Pyramid of Gizeh, in a way that can only be called remarkable. It offers a clue to one of the greatest mysteries of the pyramid and its function. This ratio determines the scale of the King’s Chamber, by setting its perimeter. This carries an important implication with it. The Egyptians chose the size of the King’s Chamber carefully. It was proportionally linked to the rest of the Great Pyramid taken as a whole, in a most meaningful way. To see the same ratio relate the speed of light to the internal speed of hadrons was remarkable. The protons and neutrons carry the bulk of what we call mass or matter. The speed of light refers to a speed in the vacuum attained only by massless particles like photons and maybe gravitons. The feeling is that the speed of light must be an intrinsic property of the vacuum and that the formation of matter must reflect a proportional transformation of the vacuum itself. If this is the case, then the proportional relationship between the speed of light and the speed of terrestrial nucleons takes on qualitative importance for the formation of life forms. In human anatomy the same proportion shows up in an equally remarkable way. For me it has been one of the most impressive surprises in this work.
I was already interested in the number 64 from C.G. Jung’s extraordinary volume of research and insight, some of which was stimulated by his fascinating and complex association with Wolfgang Pauli who around 1925 discovered the very fundamental Exclusion Principle in physics that essentially maintains the discrete integrity of the subatomic world. For Jung ‘64’ was a totality number. It is also the basis of the Chinese Book of Changes, an all-embracing analysis of existence if ever there was one. Later I learned it was also the ‘enumeration’ of the Egyptian Eye of Horus that had ramifications when interpreting the images painted on the ceilings of some of the famous tombs such as that of Seti I in the Valley of the Kings. I’ll come back to this ceiling. But just as fascinating, was to see ‘64’ show up in macroscopic terms. The mean speed of the Earth + Moon around the Sun is about 29.786 km/s for a mean radius of about 149,597,870 km from the Sun’s center of mass (1.99 × 10³° kg). And the mean rotation rate of a particle at the Earth’s equator is about .4651 km/s. The relation between the two velocities is:
29.786 ÷ .4651 = 64
I immediately concluded that the number 64 had within it an internal, functional ‘capacity’ to order things spherically in such a way that macroscopic and microscopic could harmonize; self-adjust in a flowing manner; get in step with one another. I even felt they were uniting quite as if quantum and relativistic behaviors were uniting in quick time bits or cycles. I also started to connect the number 64 to the term resolution or some self-focusing tendency.
Above you see a segment of the Table of Lambda. I have taken it only to column 7. In the I Ching it is said that all events occur in 6 stages. The 7th brings return. Here ‘7’ is 64, a key member of the ‘power of 2’ series. The top tier spawns an important series that I have taken only to 216 but it goes on to include other interesting numbers which I will label Series A:
27 54 108 216 432 864 1728 3456 6912 13824 etc…
The Egyptians used this series extensively. For example the scale of the Great Pyramid relative to the Earth’s size is as 1:43,200. At the Cathedral of Chartres, the radius of a circle used to determine the Cathedral’s elevations is set to the Earth’s Equatorial radius as 1:432,000, or 1/10th that of the Great Pyramid!
The height of the Sphinx – 66 feet – is scaled to the Moon’s diameter as 1: 172,800 where the Moon’s diameter is 2160 miles and 11,404,800 feet, so 11,404,800 ÷ 172800 = 66 feet. We can also note that the number 43200 will give a reasonable figure for the Astronomical Unit when unity is the Moon’s diameter:
3476 x 43,200 = 150,163,200 km = 1.0037 AU, which corresponds to the Earth’s position on April 17th. Moreover the Sun’s diameter fits into the AU 108 times, giving: 108 × 1,392,000 = 150,336,000 km = 1.0049 AU or April 20. All these numbers are members of Series A.
In the I Ching, Hexagram 64 does not end the Book. Rather it is called “Before Completion”! Hexagram #63 is called “After Completion” even though it precedes #64. One imagines that between 63 and 64 is the point where the snake bites its tail and where an inversion or conversion of some kind takes place. It is also quite interesting to show the powers that produce 64. They proceed as 1,2,3 as 8 dives to 4 and 4 to 2. And then there is a qualitative leap to 6. It is this leap that seems to create volume and some sort of metamorphosis. The numbers point to a redemptive process concealed within the enclosure that could be called 64 (and the 384 lines of the I Ching). I will just show the Oudja Eye of the Egyptians here but will comment on it later in more detail:
With this enumeration of the parts of the Eye, 1/64th has gone missing. It sums to 63/64 only. The part here worth 1/64 shows up in the ceiling of the tomb of Seti I. This mnj.t has been called ‘qd’ but also the ‘thigh bone of the Horus Eye’. It seems to act as a seed or root or support of the whole Eye. It was also referred to as a “Mooring-Post” where it also assumed ‘celestial’ significance for the ancient sages.
In any case these sorts of proportional patterns and progressions led me to believe that multiple ratios of this order had to be operating in man so that micro-processes could harmonize with macroscopic processes; gravity with electromagnetism and so forth. I was motivated to pay attention to proportions the way a musician pays attention to musical intervals, whether he knows the Fifth is 2/3 or the octave 1/2, or the Fourth 3/4 or not. Nonetheless he is paying attention with his ear. His language is the language of these intervals and their differences – the way they co-exist within a single scale.
An Unexpected Inspiration
In April, 1985 I took Doczi’s book with me to New Zealand. I bought a new “Temple in Man” by R.A. Schwaller in Auckland and began the baby steps of drawing circles, squares and rectangles. It did not take long for the seed sown by the reference to a temple with a length twice its width to germinate in my imagination on a more formal basis. The idea that the 2:1 rectangle was the basis of both human form and the temple, while also being capable, through “analytical or creative geometry”, of constructing the golden proportion, felt like a treasure trove of information where intuition and science ought to be able to meet. I had always liked geometry but never had it filled me with this level of excitement.
Chartres Cathedral: Sleeping Beauty Wakes Up
It was one more book, a 1966 work called “The Mysteries of Chartres Cathedral”, that really took the little spark smoldering in my imagination and transformed it into a glowing fire. It was written by Louis Charpentier and to this day is probably one of the most valuable gifts I’ve ever received. Vincent and Kely had not been able to use it for their research for the Navigator, so they called me in on an educated hunch and asked me to browse a table full of ‘rejects’. I will return to Charpentier’s inspired masterpiece ahead, where the 2:1 proportion plays a very special role. I had been taken by Chartres in 1971. Then it aroused my interest inexplicably in 1984 when I prepared my art exhibit. At that moment I realized that I had no idea how the architect had created it. But I knew it was an exalted understanding of both proportion and scale. How did I know this? I repeat, the feeling is that Chartres exists in all of us. It existed even before it was built. Do I mean it is a realization of Plato’s Forms? Is it an archetype that exists in potential and gradually grows into visibility when the minds of men have reached a threshold? I don’t know. I simply wish to be blunt about this. I felt an association with Chartres before I had even visited it. I felt it was in me from birth. By the time I got to New Zealand, it was nagging at me. Both Kely and Vincent sensed my discontent. Kely felt Charpentier’s book might address some of what was nagging at me, which is why she had the instinct to buy it in the first place. Before I return to Chartres and the next development in the canon of the female, I will make a quick detour to Egypt in 1989. This was after the Navigator had been in competition at Cannes, 1988, and was being screened at the Cairo Film Festival. The role of Egypt in inspiring an understanding of our anatomy cannot be appreciated without a little extra attention. That trip also led me by complete accident directly to the Pyramid of Unas. I arrived at Saqqara with a group of Norwegians who were very eager to see the famous Stepped Pyramid. But after we passed through this entrance that you see below, I suddenly came to an inexplicable halt.
A bit like a dog or mule, I had no desire to move. So the group trudged off to Zoser’s Pyramid, leaving me to fathom why I had stopped. It was a sort of canine sixth sense that made me move slowly, one step at a time, until I had arrived at a totally nondescript little ruin. I descended the nondescript steps, having no idea where I was. There on the walls were hieroglyphs so marvelously precise that I just stopped and stood there. I stood there in those cramped rooms for hours while the others were feasting on Zoser’s famous stepped pyramid. I had no inclination to leave those hieroglyphs inside the Pyramid of Unas. Only much later did I realize I had been face to face with the Pyramid Texts that were to occupy so much of my time after 1999. I had been so absorbed by them I never once thought of snapping a photograph! I’ll end this post here.