The Metonic Period at Ushtogai Square

If one takes the figure of 940 feet (that is, 286.512 meters) as the side length factorizing 940 gives 20 x 47 and 47 (a prime number) times 5 gives 235 which is the number of lunar months in 19 solar years: the Metonic period. image by Google Earth

This is the larger of three bounding periods for the sun, moon, and earth. The lower boundary is exactly 19 eclipse years, called the Saros eclipse period of 18.03 solar years. . Within that range of 18-19 years lies the moon’s nodal period of 18.618 years, this being the time taken for the two lunar nodes, of the lunar orbit, to travel once backwards around the ecliptic. It is only at these nodal points that eclipses of sun and moon can occur, when both bodies are sitting on the nodes.

The first article on Ushtogai showed how, by daily counting all the tumuli in a special way, the 6800 days of the nodal period would keep a tally in days, to quantify where the nodes were on the ecliptic as well as predicting the lunar maximum and minimum standstills.

It now seems that, if the absolute size of the monument’s perimeter was able to count the 19-year Metonic, not by counting days but rather, counting the 235 lunar months of the Metonic period. The lunar month would then be 16 feet long. And, within that counting, one could also have counted the 223 lunar months between eclipses having the same appearance. The diameter of a circle drawn within the square would then have a diameter of 235 (lunar months) divided by 4 = 58.75 lunar months which, times the 16 feet per month, is the 940 feet of the square’s side length.

Figure 1. The size of Ushtogai Square, side length 940 feet, is 235 x 4 feet, making its perimeter able to count 235 lunar months of 16 feet.

In Cappadocia, present-day Turkey, this type of geometrical usage can be seen within a rock-cut church called Ayvali Kelise, only then in miniature to form a circular apse, just over 100 times smaller! The church was built in the early Christian period (see figure 2).

Figure 2 The Apse of Ayvali Kelise in Cappadocia, which presented the same geometry in miniature. [part of figure 7.5 from Sacred Geometry in Ancient Goddess Cultures.]

The Ushtagai Square has the basic form for the equal perimeter geometry. If so, that would form a tradition at least 10,000 years old. As a counting framework for the 18-19 solar year recurrences of aspects between the the Sun, Moon, Earth, eclipses and nodes the Square appears to be both a tour-de-force in a form of astronomy now largely forgotten.

Figure 3 Showing the circle equal in perimeter to the Ushtagai Square, the size of the Earth (in-circle of diameter 11) and Moon (four circles of diameter 3.)

As an earthwork where tumuli punctuate geometrical lines, it is a highly portable symbol of great time and a highly specific astronomical construction. It was an observatory and also a snapshot within celestial time, built just after the Ice Age had ended.

Alignment of Ushtogai Square to Vega

The Ushtagai Square is angled to fit an invisible three-by-three square aligned to the North Pole. This grid could be to help lay out the square but then why make it angled to the diagonal of the double squares within the grid?

Figure 1. A Google Earth image of Ushtogai from above with yellow lines along its sides conforming to a 3-by-3 square aligned to north. The square sides of the monument obviously follow the angle of the double squares within the grid.

Following on from the first article, for some time I have been looking at northerly alignments within megalithic monuments as a possible siting mechanism for the circumpolar stars.

For example, the Le Menec cromlech in Brittany is a large Type 1 egg that this series of articles explores as having been a sidereal observatory, whose outputs formed The Alignments of Carnac, to the east. Modern observatories use sidereal or star clocks, and the circumpolar stars around the North Pole are such a clock. These stars directly show the rotation of the earth, from which the sidereal day can be tracked. (please use the search box for “sidereal” and “circumpolar” for a range of articles about this)

Monuments such a Gobekli Tepe, that predate the familiar megalithic periods, alignments to the star Vega are particularly interesting: around 12.500 BC, the ice age had a lull and Vega was the pole star. The northern alignment of Gobekli’s enclosures B, C and D, suggest Vega was being tracked there, around 9900 BCE (years before the current era).

Figure 2. A typical T-shaped stone of Enclosure D at Gobekli showing a “vulture” . The star Vega, in the constellation Lyra, was seen as a vulture or “falling one” and, in the mid section, one sees a vulture and a round shape that is probably that star, once Pole Star, but now departed from the celestial North Pole. © DAI, Göbekli Tepe Project for UNESCO.

The Ushtogai Square is thought to be at least 8000 BC and if the above alignment of 26 degrees, for a double square, were used to see Vega above the NW side of the square, then that would need to be around 9200 BCE (according to my planetarium program CyberSky version 5, see figure 3).

Figure 3. The upper area is the north pole and Vega on the celestial earth, looking north. Below this, the earth-coloured panel (north at the top) shows the north-west side of the Square of tumuli as an alignment to Vega in 9200 BCE.

The last ice age ended with a Maximum, but people were soon move around Eurasia: on the steppes, in Ushtogay where nomadism could flourish, and in eastern Turkey at Gobekli Tepe, at the head of the forthcoming Neolithic revolution. Such monuments display an advanced astronomical alignment and counting culture. This makes prehistory a lot more interesting, as to how and why there was such an early interest in matters cosmic.

In January, my new book will be published pushing this story forward. One in a series on such matters, it is called Sacred Geometry in Ancient Goddess Cultures because the ice age tribes were often organized around women and some “goddess” cultures seem to have been very interested in sacred geometry*. Matrilineal tribes had a social structure able to live off the land and with a large natural workforce (an extended family who were not farmers) such groups could achieve monumental works such as the Ushtogai Square.

*Such geometries were studied in my earlier books, Sacred Number and the Lords of Time (2014) and Sacred Geometry: Language of the Angels (2021).


  1. A previous exploration of the geometry of Ushtogai, onto which my proposed alignment to Vega can be added, is found in this pdf: A massive neolithique geoglyph … orientation … to cardinal directions (on by Howard Crowhurst.
  2. To explore the Ushtogai site, and Kazakhstan in general, you might try Wild Tickets.
  3. Ushtogai can sometimes be written as Ushtogay when searching.

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.

Chartres 3: Design of West Façade

The design of the twin towers of Chartres point to an extraordinary understanding of its designers, quite unlike pre or modern understandings of the outer planets and their harmonic ratios. We have already seen a propensity for using the ordinary English foot to indicate days-as-feet within the structure. The Façade hosts what is perhaps the most famous “rose window”, though it was only in later centuries that it would be termed thus, as the cult of the Virgin Mary became more widespread. But this cathedral was strongly dedicated to the Virgin, when built.

The two towers are separated by the same distance as the rose window is above the footings, namely 100 feet, while the façade is 150 feet wide. This has led me to rationalize the façade as being six units across of 25 feet, while the façade appears to end (and the towers begin) 200 feet above the footings.

Interpretation of the western Facade as composed as towers 4 apart, width 6 apart and height 8 units, all of 25 feet. The Rose Window is held within two 3,4,5 triangles within a wall of 2 units square.

That is the façade was therefore designed as a three by four rectangle, the rose window centrally located within a square of side length 50 feet.

In simplest units of 50 feet, 8 by 6 becomes the proportion 4 by 3, with diagonals that are 10 units (that is, 250 feet) where the rose is at the crossings of those diagonals, held between two 3,4,5 triangles.

This first Pythagorean triangle holds all of the ratios of regular musical harmony, having 4/3 (fourth), 5/4 (major third), 6/5 (minor third) between its sides, which multiplied together equal 60 and summed equal 12.

NEXT: to come

Interpreting Chartres
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

Yet to come: the design of the Rose Window.

Chartres 2: the harmony in its towers

In the previous post, the difference in height of the two towers was seen to have an exoteric and an esoteric meaning. Exoterically, the taller tower is sometimes called the sun tower, probably because the globe at its top (below its cross) is about 365 feet-as-days (hence representing the sun and its year). From this fact, the lower tower was considered lunar , since the lunar year is “not as long” and so less high. However, one must go to the top of the cross on the lower tower to achieve the height of 354.367 feet-as-days (hence representing the moon and its year).

This article presents a deeper meaning, that the difference in the full heights of the two towers represents the musical intervals of the synods of Saturn and Jupiter, relative to the lunar year: cunningly encoded within the full height of the solar tower as the Saturn synod of 378 feet-as-days, which is 16/15 of the lunar year. To have made the taller tower higher, to achieve the Jupiter synod, was impractical so that, instead, Jupiter was symbolized by the lunar year of 12 lunar months while Saturn was 12 “months” of 28 days, the 336-foot high globe of the moon tower, as shown below.

The two towers have a deeper meaning regarding the two gas planets Jupiter and Saturn, representing their synods to the lunar year. These musical intervals of 9/8 (tone = Jupiter) and 16/15 (semitone = Saturn), are different by 132/128, the ratio of the cross relative to the lunar tower.

To achieve this, the lunar tower had to be built shorter by 135/128 so that the top of its cross could ride 354.367 feet-as-days (of the lunar year), from the base, and the cross could then represent the ratio, 135/128 in height, between the two intervals the synods make with the lunar year.

The globe is at 336 feet-as-days, which is 12 times 28 days, a month belonging to the Saturnian year of the Goddess culture recorded in Greek Myth, whilst we know the Cathedral was a major shrine to the Goddess and Child found in the Crypt beneath this rebuilt upper form of the Cathedral. In Hesiod’s cosmogony, from the Archaic period, Saturn was the previous ruler over the sky, a culture which kept patriarchal cultural norms at bay*. Zeus-Jupiter was suppressed by the Goddess culture’s view of time and its year of 364 days, of exactly 52 (7-day) weeks.

That the archaic month of 28 days, times 135/128, is accurately the lunar month of 29.53 days, suggests a combined influence of the outer planets on the Moon’s synodic period with the Sun of 29.53 days.

NEXT: design of the west façade

*see my forthcoming Sacred Geometry in Ancient Goddess Cultures.

Interpreting Chartres
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

Yet to come: the design of the Rose Window.

Chartres 1: the cosmic coding of its towers in height

The lunar crescent atop the “moon” tower’s cross.

Chartres, in north-west France, is a very special version of the Gothic transcept cathedral design. Having burnt down more than once, due to wooden ceilings, its reconstruction over many building seasons and different masonic teams, as funds permitted, would have needed strong organizing ideas to inform the work (as per Master Masons of Chartres by John James).

As shown below, Chartres main towers are unequal in height and the “western” facade itself does not align to east-west, as normal Christian churches do. The left tower is also higher than the right tower and, it has been said, the left represents the Sun and the right the Moon. The height of the left tower, to its globe below its cross, is indeed the solar year of 365 days in feet. But the height of the shorter right tower, to its own globe, is not the 354.367 days of the lunar year (of 12 months); rather, it is the top of its cross, sporting a crescent moon suggesting it is a moon tower, that is 354 and a third feet high.

The cosmic time coding of the two towers as solar year->lunar year between the globe’s height (on left in red) and the top of the cross (on right in blue). But the left tower also indicates the Saturn synod of 378 days to the top of its cross. The for-square rectangle, geometrically relating the solar (diagonal) and lunar years, is shown.

That is, the height of the lunar year in feet, from the same starting point as the solar tower’s height as the solar year, the lunar year would be to the top of the lunar cross, where the crescent is attached, and not to its globe. There is then a reasonable connection between the solar and lunar years and the two towers. However, it is also interesting to see the number of days, as feet, of the left tower to its own cross. It is exactly 378 feet, the synodic period of Saturn in days. Readers of my books and this site will remember that the ratio between the lunar year and Saturn synod is exactly 16/15: a musical semitone within the ancient tuning system called Just intonation.

This arrangement suggests Chartres was built to be a time-factored monument, which may be why the cathedral was aligned to midsummer sunrise (which was a megalithic norm) rather than being aligned east-west. Built on top of a solitary promontory, horizon events would have been clear across the flat fertile plains.

NEXT: the harmony in its towers

Interpreting Chartres
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

Yet to come: the design of the Rose Window.