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.

The Megalithic Numberspace

above: counting 37 lunar months six times to reach 222,
one month short of 223: the strong Saros eclipse period.

There is an interesting relationship between the multiple interpretations of a number as to its meaning, and the modern concept of namespace. In a namespace, one declares a space in which no two names will be identical and therefore each name is unique and this has to be so that, in computer namespaces such as web domain names, the routes to a domain can be variable but the destination needs to be a unique URL.

If sacred numbers had unique meanings then they would be like a namespace. Instead, being far more limited in variety, sacred numbers have more meanings, or interpretations, just as one might say that London has many linkages to other cities. In an ordinal number set, there are many relationships of a number to all the other numbers. This means whilst their are infinite numbers in the set of positive whole numbers, there are more than an infinity of relationships between the members of that set, such as shared number factors or squares, cubes, etc. of a number.

The mathematician Georg Cantor saw “doubly infinite” sets. Sets of relationships between members of an already infinite set, must themselves be more than infinite. He called infinite sets as aleph-zero and the sets of relationships within an infinite set (worlds of networking), he called aleph-one.

Originally, Cantor’s theory of transfinite numbers was regarded as counter-intuitive – even shocking.


However, in the world of sacred numbers, although there can be large numbers, in the megalithic the numbers were quite small; partly due to the difficulty that numbers-as-lengths were physically real while later numeracy abstracted numbers into symbols and, using powers of ten, modern integers are a series of place ordered numbers (not factors) in base 10, as with 12,960,000 – possible for the ancient Babylonians but, I believe, not expected for the early megalithic.

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Geometry 5: Easy application of numerical ratios

above: Le Manio Quadrilateral

This series is about how the megalithic, which had no written numbers or arithmetic, could process numbers, counted as “lengths of days”, using geometries and factorization.

My thanks to Dan Palmateer of Nova Scotia
for his graphics and dialogue for this series.

The last lesson showed how right triangles are at home within circles, having a diameter equal to their longest side whereupon their right angle sits upon the circumference. The two shorter sides sit upon either end of the diameter (Fig. 1a). Another approach (Fig. 1b) is to make the next longest side a radius, so creating a smaller circle in which some of the longest side is outside the circle. This arrangement forces the third side to be tangent to the radius of the new circle because of the right angle between the shorter sides. The scale of the circle is obviously larger in the second case.

Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius. diagram of Dan Palmateer.

Figure 1 (a) Right triangle within a circle, (b) Making a tangent from a radius.

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The Tetraktys as plan of planetary harmony and the four Elements

Figure 1 The elimination of 5 as a factor in the harmonic mountain for 36 lunar years, resolved using matrix units of one tenth of a month and the limit 360 units.

In a previous post I explored the astronomical matrix presented in The Harmonic Origins of the World with a view to reducing the harmonic between outer planets and the lunar year to a single harmonic register of Pythagorean fifths. This became possible when the 32 lunar month period was realized to be exactly 945 days but then that this, by the nature of Ernest McClain’s harmonic mountains (figure 1) must be 5/4 of two Saturn synods.

Using the lowest limit of 18 lunar months, the commensurability of the lunar year (12) with Saturn (12.8) and Jupiter (13.5) was “cleared” using tenths of a month, revealing Plato’s World Soul register of 6:8::9:12 but shifted just a fifth to 9:12::13.5:18, perhaps revealing why the Olmec and later Maya employed an 18 month “supplementary” calendar after some of their long counts.

By doubling the limit from 18 to three lunar years (36) the 13.5 is cleared to the 27 lunar months of two Jupiter synods, the lunar year must be doubled (24) and the 32 lunar month period is naturally within the register of figure 1 whilst 5/2 Saturn synods (2.5) must also complete in that period of 32 lunar months.

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Number Symbolism at Table des Marchands

Table des Marchands, a dolmen at Lochmariaquer, can explain how the Megalithic came to factorise 945 days as 32 lunar months by looking at the properties of the numbers three, four and five. At that latitude, the solstice angle of the sun on the horizon shone along the 5-side of a 3-4-5 triangle to east and west, seen clearly at the Crucuno Rectangle [post2post id=”237″].

Before numbers were individually notated (as with our 3, 4 and 5 rather than |||, |||| and |||||) and given positional notation (like our decimal seen in 945 and 27), numbers were lengths or marks and, when marks are compared to accurately measured lengths measured out in inches, feet, yards, etc. then each vertical mark would naturally have represented a single unit of length. This has not been appreciated as having been behind marks like the cuneiform for ONE; that it probably meant “one unit of length”.

Figure 1 The end and cap stone inside the dolmen Table des Marchands in which the elementary numbers in columns and rows perhaps inspired its attribution to the accounts of merchants
Locmariaquer (Morbihan, Bretagne, France) : la Table des Marchand, interieur.
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