counting – Page 2 – Sacred Number Sciences

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.

Utility of the Ushtogai Square to count the Nodal Period

Using Google Earth, a large landform was found in Kazakhstan (Dmitriy Dey, 2007); a square 940 feet across with diagonals, made of evenly spaced mounds. We will demonstrate how the square could have counted the lunar nodal period of 6800 days (18.617 solar years)

images courtesy of Wild Ticket

Counting the Lunar Nodal Period

One can see the side length of the square contains seventeen (17) mounds, with 16 even distances between the mounds. Were one to count each side as 17 mounds, then four times 17 gives 68 which reminds us of the 6800 days in the moon’s nodal period of 18.617 years. If 17 can be multiplied by 100, then one could count the nodal period in days, and to do this one notices that the diagonals have one central space, around which each of four arms are 10 mounds long.

The Ushtogai Square from above, north to the top.

Each side length of 17 mounds forms a triangle to the central space, perhaps for central control, with two sides (left and right) of 10 mounds each. As with our own decimal counting of units and tens (as in 12) there could have been a day marker placed in the center. On day 1, it was moved to the first mound on the left. Every day, the left marker moves towards the left corner mound. Upon reaching the corner, two things happen.

The day marker returns to the center and,
A ten-day marker then starts its own journey to the right hand corner.

The left-hand day counting would continue on the next day, for ten more days, whereupon the same action, incrementing the ten counter, would mark another ten days in a further step between mounds, towards the right hand corner.

After 100 days, the marker of ten-day periods has reached the right hand corner and a new hundred day marker is deployed, to record hundreds of days per mound. Only after the first 100 days is the hundred marker placed upon the left-hand corner mound (that might have represented 100 days after the maximum standstill of the moon.)

The counting scheme for one quarter of the nodal period, repeated in each quadrant to count 6800 days

All of the above is repeated, slowly moving the hundred-day counter from the left corner to the right, at which time the moon no longer exceeds the solar extremes of summer and winter solstice in its range of rising and setting every orbit of, on average, 27.32166 days.

In conclusion …

There is a very beautiful correspondence between the geometry of Ushtogai and the nodal period of the moon. But in a following article we will explore the parallel meaning of this monument as a counter of lunar months: to use the outer perimeter to study the Metonic and Saros eclipse periods.

There is a second article on Ustogai here.

For more information on this sort of astronomical counting in the prehistoric period, and of the details of the major time periods of the moon and sun,
these can be found in my books,
Sacred Number and the Lords of Time and
Sacred Geometry: Language of the Angels.

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.

Numbers of a Living Planet: Preface

The image above is Kurma avatara of Vishnu, below Mount Mandara, with Vasuki wrapped around it, during Samudra Manthana, the churning of the ocean of milk. ca 1870. Wikipedia.

It is impossible to talk of a creation outside of the time and space of Existence, though from it, other dimensions can be inferred such as an “Eternity” visible in the invariances of numbers and structures. It is this higher dimensionality that leads to

The recurrence of celestial time periods,
The mental powers to recognise manifested patterns,
The use of spatial geometries of alignment,
The numerate counting of time,
A phenomenology which is neither factual nor imaginary.

The quantification and qualification of Existence, adequately conducted, reveals harmonious structures within time and space, especially in the spacetime of our planetary system, when this system is as seen from our planet. The harmonious nature of our planetary system helped the late stone age to develop a large numerical and geometrical model of the world through counting astronomical recurrences. This model, which shaped ancient texts, implies that solar systems may have an inherent intelligence which makes them harmonious.

Harmony in a planetary system must therefore employ invariances already present in the number field, by exploiting the recurrent orbital interactions between planets and large Moons, this in a connected set of three-body problems. Before our exact sciences and instruments, prehistoric naked-eye astronomers could understand the planetary world by counting the duration of planetary time cycles: the subject my books explore. Through counted lengths of time, the megalithic age came to understand the invariances of the number field and so evolve an early and distinct type of numeracy. This numeracy lived on as the basis for the ancient Mysteries of the early civilizations, embodied in their Temples and in the Pythagorean approach to ordinal numbers and geometries, expressing the “number field” in two or three dimensions, areas and volumes. (see Sacred Geometry: Language of the Angels for an introduction to this)

Astronomical Rock Art at Stoupe Brow, Fylingdales

first published 28 October 2016

I recently came across Rock Art and Ritual by Brian Smith and Alan Walker, (subtitled Interpreting the Prehistoric landscapes of the North York Moors. Stroud: History Press 2008. 38.). It tells the story: Following a wildfire of many square miles of the North Yorkshire Moors, thought ecologically devastating, those interested in its few decorated stones headed out to see how these antiquities had fared.

Background

Fire had revealed many more stones carrying rock art or in organised groups. An urgent archaeological effort would be required before the inevitable regrowth of vegetation.

*Figure 1 Neolithic stone from Fylingdales Moor | Credit: Graham Lee, North York Moors National Park Authority.*

A photo of one stone in particular attracted my attention, at a site called Stoupe Brow (a.k.a. Brow Moor) near Fylingdales, North Yorkshire.

Angkor Wat: Observatory of the Moon and Sun

above: Front side of the main complex by Kheng Vungvuthy for Wikipedia

In her book on Angkor Wat, the Cambodian Hindu-style temple complex, Eleanor Mannikka found an architectural unit in use, of 10/7 feet, a cubit of 20/21 feet (itself an outlier of the Roman module of 24/25 feet, at 125/126 of the 0.96 root Roman foot).

She began to find counted lengths of this unit, as symbols of the astronomical periods (such as 27 29 33) and of the great Yuga time periods proposed within Vedic mythology. Hence Mannikka’s title of Angkor Wat: Time, Space, and Kingship (1996). Whilst the temple was built by the Khymer’s greatest king, their foundation myth indicates the kingly line was adopted by a matriarchal goddess tradition.

Tag: counting

The Metonic Period at Ushtogai Square

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Utility of the Ushtogai Square to count the Nodal Period