Sacred Geometry in Ancient Goddess Cultures (March 26th, 2024)

My new book can be pre-ordered from the publisher and other retailers.

In March next year my new book will be released (see publisher website). The book has been typeset and is out for printing, having been favorably reviewed by a peer group. (The original date was February, but printing schedules have had to be adjusted.)

figure: the punctuation of towers and western outlook. Possibly a funerial building for the king, it could be used as a living observatory and complex counting platform for studying the time periods of the sun, the moon, and even the planetary synods.

Some new material was added during production, including chapters on the design of Angkor Wat (chapter 9) and St Peter’s basilica in Rome (chapter 10), and some early articles on these can be accessed on this site, most easily through the search function.

As you can see, my books partly emerge through work presented on this website. This has been an important way of working. And whilst I am providing some ways of working that could be duplicated by others, at its heart, my purpose is to show that the celestial environment of our living planet appears to have been perfectly organized according to a numerical scheme.

My results do not rely on modern techniques yet I have had to avail myself of modern techniques and gadgets to work out what the ancient techniques arrived at over hundreds if not thousands of years.

My basic proposal is that ancient astronomers learned of the pattern of time in the sky by counting days and months between events on the horizon or amongst the fixed stars. Triangles enabled the planetary motions to be compared as ratios between synodic periods.

Continue reading “Sacred Geometry in Ancient Goddess Cultures (March 26th, 2024)”

Pauli’s Cosmic Dream

above: Wolfgang Pauli, ca. 1924. Wikipedia CC BY 4.0

Renowned psychiatrist Carl Jung had an intellectual friend in Wolfgang Pauli, a leading theoretical scientist in the development of quantum mechanics who had offered (with others) a third perspective to the deterministic physics of Newton and relativistic physics of Einstein. For example, Pauli’s Exclusion Principle explained how sub atomic particles of the same type could be connected to each other (entangled) on the level of the very small.

Dream analysis with Carl Jung opened Pauli up to the inner worlds of alchemy, archetypes, and dreams. Pauli recounted his dreams to Jung who would analyze their symbolism. One dream is of special interest here since it concerned a cosmic clock with two discs with a common center: one vertical and the other horizontal. The vertical disc was blue with a silver lining upon which were 32 divisions and the hand of a clock pointing to a division. The horizontal disc was divided into four differently colored quadrants, surrounded by a golden ring.

above: A visualization of Pauli’s report of his dream of the Cosmic Clock. The black bird would traditionally be a member of the Corvus or Crow family. In the original one sees 32 rings punctuating the outer ring. below: Jane Roberts colored it, noting it resembled Ezekiel’s vision. 

This reminded me of the 32 lunar months which take 945 days to complete so that each lunar month could be known in ancient times as 945/32 or 29.53125 days, only 57 seconds too long! The clock had three “pulses”, the first moving the hand on the scale of 32, the second pulse occurring after the hand had completed one revolution, after which, something golden and presumably the Sun, moving something on the golden ring, by 1/32 of its circumference. Pauli said the golden ring was black before the clock’s hand started moving, and it seems that Pauli experienced this goldenness as a principle of geometrical harmony. If the golden disc is the sun and, since the lunar month is the completed illumination of the moon by the sun, here the sun is lit up by the moon to become golden rather than black.

Such an apparatus would complete itself in 32 times 32 (1024) pulses, these taking 945 times 32 or 30,240 days. This long cycle is three times 10,080 which number is the diameter of the sublunary sphere (14) then 10,080 in the factorial Equal Perimeter model, a model which presents the size of the earth and moon whose diameters are in the ratio 11 to 3, the mean earth diameter of 7920 miles and moon diameter of 2160 miles. This model has been found present within many ancient monuments up to the modern era, hence expressing past cosmological knowledge. Though the vertical “face” of the clock is blue, the colors of the four horizontal quadrants were red, green, orange, and blue, each quadrant having an outward facing “monk” holding a pendulum that, by Pauli’s day, represented the counting of time as seconds, rather than as days.

The whole apparatus is held aloft by a black bird, and this can explain the 30,240 days as eighty synods of Saturn (378 days), the planet that moves (between its synodic loops each year) a similar distance on the Zodiac as the Moon moves in a single day, which is one reason why Saturn was called a god of Time. In the Greek Myths, the crow family were not black but white until the separation of the “world parents”, namely the ecliptic and equatorial planes, this separation of the parents being the cause of the long Precession of the Equinoxes in 25,920 years. More significantly, it is this separation that divides the solar year into four quadrants of the clock. The quadrants are separated by the four gates of the year: the spring and autumn equinoxes where the parents cross one another; and the summer and winter solstices where, outside of the Tropics, the sun is higher or lower in the sky, creating the four seasons.

Equating the 32 divisions in the dream with 32 lunar months has allowed what is a dream to be quantified and connected to the ancient model, in a new and factual way, where the golden ring is the Sun on the ecliptic and the bird is Saturn. Distance and Time become twin dimensions since the size of the earth and moon, in miles, are then related to the lunar month within this harmonious clock. Another boundary has also been crossed, between our conscious daytime experience, as factual, and our subconscious nighttime experience of dreaming, as imaginative. A model of time on Earth was communicated through Pauli’s dream life. Jung called it the Collective Unconscious and it is either (or both) a door to the higher intelligence responsible for the creation of time on earth or (and) to the ancient works of astronomy that had understood the world of time to be a numerical creation. For this reason, Sacred Geometry: Language of the Angels got its name.

Jung later discovered a similar dream emanating from the Christian mystic Guillaume (whose works inspired John Bunyan’s Pilgrim’s Progress). Guillaume’s “vision” was presented as a dialogue with an angel. The details are different but significantly, a small blue ball (said to represent ecclesiastical time) was floating in an golden sea of Eternity and manifesting the Trinity within the Zodiac of twelve signs (3 times 4), as 12 fishermen who together manifest the Trinity. Guillaume did not understand so the angel then talked about the three principal colors as being green, red, and gold, but abruptly stops, terminating further questioning. Jung had already found, in the number three within the Trinity a culturally dominant form of masculine thinking which came out in the dream as the color not mentioned, namely blue – the color of the “small” sphere in Guillaume’s and of the fourth blue quadrant in Pauli’s version. Blue is associated with the Goddess, portrayed in the cloak of Mary, the mother of Jesus.

The missing goddess figure is also found in Vishnu’s awakening to his creation of a new world through Prajapati, the first man. Prajapati emerges out of a lotus, a flower growing from Vishnu’s navel, a flower that had Brahma (the creator god) in its many petals. So long as Vishnu sleeps between creations, the goddess attended to him but when He awakens, she has disappeared (because she is considered the supreme reality of the creation). It was Pauli’s feminine side who had, thought Jung, like Eve revealed the cosmic clock to him.

In my forthcoming book: Sacred Geometry in Ancient Goddess Cultures (chapter 11), the harmonic model can be seen emerging from this cosmic clock of lunar month and year and the planetary synods resonating with these musically. The biblical Adam then emerges within a lunar octave of doubling from 45 (through 90, 180, 360, 720, 1440). The coordination of such stories of “first men” within scripture might not have happened through the diffusion of traditions but instead, it may subsist in something like Jung’s collective unconscious, that men dream through their feminine side (and women through their masculine side), as seen in these dreams. This makes sacred geometry in ancient matriarchal cultures significant today when masculine thinking has become so dominant. It is also interesting that the early Indian myth of Vishnu had the god sleeping at night and, as humans do , re-inventing the world during the day.

Cologne Cathedral Facade as Double Square

image: The Gothic cathedral of Cologne by night, by Robert Breuer CC-SA 3.0

On the matter of facades of Gothic cathedrals, I hark back to previous work (February 2018) on Cologne cathedral. This was published in a past website that was destroyed by its RAID backup system!

As we have seen with Chartres, some excellent lithographs with scales can often exist online from which one can interpret their sacred geometrical form and even the possible measures used to build that form. The Gothic norm for a facade seem more closely followed at Cologne facade which has two towers of (nearly) equal height.

We saw at Chartres that an underlying geometry using multiple squares may have been used to define a facade and bend it towards a suitable presentation of astronomical time, in a hidden world view that God’s heaven for the Earth is actually to be found in the sky as a pattern of time. This knowledge emerged with the megaliths and, in the medieval, it appeared again in monumental religious buildings built by masons who had inherited a passed-down but secret tradition.

A Prologue to Cathedral Music

In my book Matrix of Creation I observed that the Lunar Year of 12 months appear to be like Plato’s World Soul, of 6:8::9:12 only raised by a fifth (3/2) to be (9:12::13.5:18). The number 12 is then the 12 lunar months of the lunar year and the 13.5 are the 13.5 lunations which are the synodic period of Jupiter (398.88 days). The synod of Saturn (378 days) is then caught between the 12 and 13.5, near the geometric mean of the octave 9::18, as a location known to tuning theory as the upper Just tritone of 64/45 (= 1.422), a prime example of the diabolicus in music. That is the Moon appears to be a central part and factor of an astronomical instrumentality relating Jupiter and Saturn, the two outer gas giants of the solar system.

Without knowledge of geocentric astronomy, megalithic metrology, sacred geometry, and the study of numbers (the four higher parts or Quadrivium of the Traditional Arts), it is impossible to read such monuments, and the truths placed within them.

The Double Square

The properties of the double square, here proposed as a vertical 2 by 1 rectangle embracing the whole facade, are to be seen in many other posts you might want to reference (this link opens a new search tab). It seemed to me that the key orientation was the crossing of the lower square’s diagonals, a location where Chartres has its Rose Window and in this case, the domed top of a major rectangular window.

Referring to the diagram below, the bottom square is the cosmic octave’s “ballast” of 9 lunar months and the top square the “active portion” of an octave in which 12 lunar months (or lunar year) is the fourth note of the octave uplifted numerically by 3/2. Saturn’s synod of 12.8 months is 12.8/9 = 64/45, musically √2 which is the length of the lower square’s diagonals which cross the arch of the main window. The red arrow thus signifies by its arc the location of Saturn as the tritone (geometric mean) of the octave.

The Façade of Cologne as the double octave of Plato’s World Soul elevated by 3/2.

The left tower is slightly lower that the right, indicating that the Saturn synod (378) is less than the Jupiter synod (399). Musically, Jupiter is 3/2 is the fifth in the octave 9::18, numerically 13.5 lunar months. If one halves the right side of the upper square into two, this is where the fifth belongs and this point is also a whole tone (9/8) above the lunar year, whilst Saturn is 16/15 above the lunar year as 12.8 lunar months.

Plato’s World Soul, transformed

In a single figure, the transformation of Plato’s World Soul of 6:8::9:12, as simplest solution, then masked the hidden doctrine that, in lunar months, the very same is implemented in the relationship of the outer giant planets to the Moon as lunar year but trasformed by a musical fifth. The dominant and subdominant are the lunar year and Jupiter synod, with the Saturn synod providing the “satanic” tritone which acts in denial of the octave “god”. This octave of 19::18 has only survived in the Supplemental Glyphs of the Olmec (additional to long counts), who appear to have received it from the collapsing Bronze Age of the Eastern Mediterranean around 1500 BC (see my Sacred Number and the Lords of Time).

Abandoning the geocentric perspective of the planets for the heliocentric “washed away [this] baby with the bathwater”, that the moon was the intermediary in simple numbers of months of the principle of cosmic harmony in the higher worlds. Holding us back from seeing the old perspective is our fond belief that cosmic design was part of religious fantasies in which God, gods or angels had made the sky of the earth. Whilst we know so much about space, time has been neglected for its astronomical action upon the present moment within which change is the prime phenomena, as the Buddha said “change is the only thing that does not change.”

Earth and Moon within Westminster’s Coronation Pavement

Our modern globes are based upon political boundaries and geographical topography yet they had geometrical predecessors which described the world as an image, a diagram or schemata. By some act of intuition, an original Idea for the form of the Earth had become established as a simple two-dimensional geometry, very like eastern mandalas.

Figure 1 Photo of the Cosmati Pavement at Westminster Abbey
[Copyright: Dean and Chapter of Westminster]

Such a diagram came to be built into the Cosmati pavement of Westminster Abbey, this installed during the reign of Henry III as a gift from the Pope and one or more Cosmati master craftsmen. It was dedicated to the Saxon King (and Saint) Edward, the Confessor. This exotic pavement became the focus for the Coronations of subsequent English then British monarchs. Its presence at the heart of English then British king-making is part of what is called the Matter of Britain, one of many Mysteries as to the meaning of its design.

Continue reading “Earth and Moon within Westminster’s Coronation Pavement”

Developmental Roots below 6

Square roots turn out to have a strange relationship to the fundaments of the world. The square root of 2, found as the diagonal of a unit square, and the square root of 3 of the diametric across a cube; these are the simplest expressions of two and three dimensions, in area and volume. This can be shown graphically as:

The first two roots “open up” the possibilities of
three-dimensional space.
Continue reading “Developmental Roots below 6”

Double squares: Venus and the Golden Mean

The humble square, with side length equal to one unit, is like the number one. It’s area is one square unit and, when we add another identical square to one side, the double square appears. Above right the Egyptian Djed column is shown within a double square. The Djed is the rotating earth which the gods and demons have a tug of war over. This is also a key story in the Indian tradition, called The Churning of the Oceans, where the churning creates both the food of the gods (soma) and every wonderful thing that emerges upon the Earth. In this, the double square symbolized the northern and southern hemispheres of the Earth. The anthropomorphic form Djed shown above has elbows indicative of the Double square.

Figure 1 The churning of the ocean (Samudra Manthan in Sanskrit)

The Djed appears to be the general principle of rotation of, and apparent motion around, the earth.

The god Isis is (as a planet) Venus and is shown (fig.2) offering up the sun disk: another Djed is below, with her Ankh symbol of Life atop the Djed, now having female arms . This sun most probably points to the practical year as 365 days which is 5/8 of the Venus synod of 584 days. (This ratio of 1.6 is the sixth note of the octave 1 to 2.)

In figure 2, two female attendants provide the duality which one might take to be her two famous manifestations of (firstly) the brightest Evening Star, as the sun goes down, and then (after that) the brightest Morning Star before the sun rises. Above there is duality again with three baboons either side of the sun, perhaps representing the six visible planets: Moon, Venus and Mercury: Jupiter, Saturn, Mars and their “tug of war”.

Figure 2 The creation of Horus-Ra from out of an ankh with female arms atop a djed. from Budge 1899, also fig. 7.8 of Richard Heath, The Harmonic Origins of the World.

The numbers 5 and 8 are Fibonacci approximations {1 2 3 5 8 13 21 34 …} to the golden mean, a transcendent number {1.618034…} which rational numbers can only approximate. Venus and the Earth have clearly settled into orbits around the sun resonant with Fibonacci ratios since the Venus orbital period (224.701 days) is 8/13 of the solar year. And it is this fact that eventuates in what we see on Earth, namely the manifestations of Venus every 8/5 of a practical year. of 365 days.

Figure 3 The double square, its in-circle and out-circle manifesting golden rectangles around itself.

In this post, I developed a result sent to me, that a square drawn within the upper hemisphere of a circle must define a golden mean rectangle either side from its height of 1 and the remaining radius of 0.618034… and so it can be seen that the divine principle of the Golden Mean emanates from the double square, either side of each square, when the double square is embraced by a circle drawn from its center. Obviously, on Earth and between orbits (of Venus and Earth), the Golden Mean (also called Phi) has to be approximated by whole number ratios but the principle is present within the geometry and its out-circle. Schwaller de Lubicz thought the dynastic Egyptians held the Golden Mean to be “the fundamental scisson” (literally “scissor cut”) in the range one to two and, its reciprocal can be seen to share the portion over 1 (figure 3).

One can see that geometry and the early numbers would have been seen as two aspects of what we call space and time, in which “things” are separate from each other in Existence but somehow conjoined within Eternity. What we call order is in fact an achievement of harmony made possible by the arranging and fitting of parts to form a coherent whole. It is this insight which gave meaning to their study of geometry and numbers from the prehistoric onwards, into the recorded history of early civilizations. The meaning for Life on Earth became encoded within ancient and prehistoric symbols, whose geometrical and numerical language of expression went to the heart of phenomena.