Released in January 2021, this book explores sacred building as the continuation of the megalithic: its astronomical knowledge, geometrical and metrological methodology and knowledge of the size of the Earth. The megalithic was our first numerate culture which discovered the main design design parameters for our existence, organised by higher intelligences called angels.
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).
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.
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).
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.
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)
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.
The Taj Mahal is perhaps the most recognizable building on earth. It was built by a Moghul king as a memorial for his dead queen and for love itself. The Mughals became famous for their architecture and the Persian notion of the sacred garden though their roots were in Central Asia.
I had been working on Angkor Wat, for my soon to be released book: Sacred Geometry in Ancient Goddess Cultures, where the dominant form of its three inner walls surrounding the inner sanctum were in the rectangular ratio of outer walls of six to five. A little later I came across a BBC program about the Mughals and construction of the Taj by a late Moghul ruler, indicating how this style almost certainly arose due the Central Asian influences and amongst these the Samanids and the Kwajaghan (meaning “Masters of Wisdom”). I had also been working on the facades of two major Gothic Cathedrals (see post), and when the dimensions of the façade of the Taj Mahal was established, it too had dimensions six to five. An online document decoding the Taj Mahal, established the likely unit of measure as the Gaz of 8/3 feet (a step of 2.5 feet of 16/15 English feet; the Persepolitan root foot *(see below: John Neal. 2017. 81-82 ). Here, the façade is 84 by 70 gaz.
A very significant feature of the six by five rectangle is that its perimeter is 2 times 11 (or 22) and in the Taj Mahal, 14 gaz times 22 equals 308 gaz as perimeter of the façade. Since π (or “pi”) was often taken to be 22/7, an equal perimeter of circle would require a radius 7 to be 22 in circumference or, in gaz, a radius of 49 gaz, again giving 308 gaz (821 + 1/3rd feet).
With Angkor Wat, this feature of a circle could be exploited to count time around the walkways of the rectangular walls, just as if time was flowing around a circle. But, in this case, the architecture is taking us on a symbolic journey. One can see how the central façade can “explain” the three outer rectangles to the towers left and right, and to the pinnacle boss of the onion dome, synonymous with Mughal architecture. But the basic form of equal perimeter involves a circle diameter 11 whose out-square equals 44, if π equals 22/7. The circle of equal perimeter is then a diameter of 14 since 14 x 22/7 = 44. The circle shown here is obviously the outer circle of equal perimeter, for which there must be a circle of 11 whose out-square is 44. Seven gaz times 11 equals 77 and this indeed gives the out-square (of EP) as 308. The inner circle (see below) can then be seen to be the size of the onion dome.
The equal perimeter geometry is, when magnified by 720, a model of the Earth and Moon in miles and, in Sacred Geometry: Language of the Angels, it was shown time and again that domed monuments were pictures of the Earth within a strong but hidden tradition. There also seems to be a correlation between the moon circle’s size (of 42 gaz) and the windows of the octagonal outer building surrounding the tomb itself, and also the two visible cupolas. In order to draw the two circles, it was necessary to draw the two diagonals of the rectangle and this gives a central point in the façade as being the upper central window, a phenomenon quite clear in Chartres (post # 3) where the diagonals of its 3 by 4 façade locate the center of the circular rose window.
The elevation of the Earth and Moon above the equal perimeter façade is surely of sublime design to celebrate love, resurrection. The octagon design takes its inspiration from the cosmology of Islam and beliefs concerning the afterlife.
Bibliography of Ancient Metrology
Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
Heath, Robin, and John Michell. Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients. Kempton, Ill.: Adventures Unlimited Press, 2006. Reprint edition of The Measure of Albion.
Heath, Richard. Sacred Geometry: Language of the Angels. Vermont: Inner Traditions 2022.
Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
—-. Ancient Metrology. Vol. 1, A Numerical Code—Metrological Continuity in Neolithic, Bronze, and Iron Age Europe. Glastonbury, England: Squeeze, 2016 – read 1.6 Pi and the World.
—-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
—-. Ancient Metrology, Vol. 3, The Worldwide Diffusion – Ancient Egyptian, and American Metrology. The Squeeze Press: 2024.
Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.
An essay by Richard Heath on the numbers found in the book
“Plato and the Quran”, by Noor Bosra.
SUMMARY
Multiplication of the consecutive numbers 1 to 6 equals 720 and this, applied, to the equal perimeter model, numerically scaled it up to the cosmic size of the Earth and Moon in miles. The Quranic formula, to instead multiply the numbers 3 to 8 and generate 20160, doubled the cosmic model’s 10080 and hence the whole geometry was doubled in scale. The further addition of the consecutive numbers 3 to 8, further signaled 33 years, pointing to the equal area model of the Solar Hero and to the Moon’s nodal period because, 33 divided by 18.618 equals √𝝅 = 1.778 and the area function squares that. This equality of a circle’s perimeter and a circle’s area to the same square can then be drawn to unite the cosmic model of Earth and Moon’s size, to the relationship of the Solar Hero period of 33 years, as the square, to a circle of radius 18.618 years, as appears quite clearly in the plan of Islam’s Dome of the Rock[1].
Chapter 23: The Seven Sleepers of the Cave
One of Noor Bosra’s key themes is that the Quran was composed out of the cultural context of the eastern Mediterranean, Arabia, the ancient Near East, and beyond. One example is the story, from different sources, of people who sleep in a cave to escape religious persecution. Waking after what appears to be a single night, they find many years have passed yet their bodies have not aged and the danger they hid from has now passed.
Noor Bosra provides comprehensive literary references, in a good order starting with the Quran’s chapter 18, the story running for 18 Suras. The situation for these verses was ironic, since they were demanded by Mohammad’s religious persecutors to demand proof that his source of knowledge was competent, or his revelations should be discredited. A further irony is that Mohammad often used to ascend to his favourite cave on Mount Hira, where many key recitations were uttered.
One previous story of the sleepers is about early Christians from Ephesus in Asia Minor. In 250 BCE the persecution was then from Rome. But a roughly similar story is found in an apocryphal Jewish text, written shortly after 110 BCE, about the prophet Jeremiah who slept in the desert alone for 66 years to escape a king. In contrast, the Christians slept for 372 years and the Quranic sleepers, 309 years.
The numbers 300 and 9:
“they remained in the cave three hundred years plus nine more”
On page 440 Noor Bosra finds, in 309, the number of lunar months in 25 solar years of 365.25 days, which was the Egyptian Sothic year (of the helical rising of Sirius) from which the Nile flood was predicted. Four Sothic years is 1461 days and the accounting for the extra quarter day per solar year might explain that, in the Quranic version, the sleepers are found with a Dog to protect their cave, just as the Jackel god Anubis protected the dead in Egyptian tombs, Sirius being the dog star.
In the ancient world, coincidences of astronomical cycles within a whole number of time periods made these “natural” numbers sacred and to be associated with archetypes such as a dog (the constellation Canis Major). 309 lunar months is just 6 days less than 25 whole solar years but what about 365 days?
The Egyptians had two other years of 360 and 365 days that, when combined, allowed them to establish historical dates for over 1000 years. And if we divide 309 lunar months (in days) by 365 days, the result is 24.99986 years, which is within 1.3 days of 25 years of 365 days. This then has a further resonance with the Venus synod of 584 days, since the latter is 8/5[2] (1.6) of 365 days, and their common factor of 73.
Noor Bosra explains how the Apis bull, one of the deepest Egyptian traditions, was connected to this golden mean, a proportion that enables a unique division of three points as two identical proportions: of the least to the middle as of the middle to the whole – a sort of holism. We should note that Noor provides excellent resources of background information regarding astronomical numbers, numerical traditions and historical facts.
The varied accounts of the number of sleepers
Noor tells us that in no previous versions of the sleeper story were there any strong references to the number of sleepers, while in the Quran, all the numbers are playfully doubted as between 3 to 8, as if none of the locals, who remembered them emerging from the cave, could quite remember. These varied accounts were,
3 [sleepers] and the 4th was their Dog and,
5 [sleepers] and the 6thwas their Dog and,
7 [sleepers] and the 8th was their Dog,
taking a form congruent with a rhyme-based puzzle on successive numbers between 3 and 8. Noor Bosra suggests these three couplets form a code when multiplied, to give 20160, or when added, to give 33.
The first clue for me was that, in multiplying successive numbers, a factorial process was indicated, similar to the factorial[3] for 6 (notated as 6!) that equals 720: an important harmonic prime which, when multiplied by the three numbers 3, 11, and 14, becomes the familiar geometry of equal perimeter of square and circle based upon π =22/7[4] , but here expanded by 720 in an ancient “cosmic” model of the relative size of the Earth and Moon (ratio 11/3), in units of miles containing 5280 feet. But first, what is the equal perimeter geometry of circle and square? Figure 1 shows that the approximation to π of 22/7 causes a radius r of 7 to lead to a circumference of 44 (2 πr) and that the square of equal perimeter then has a side length of 11 whose in circle is diameter 11.
Figure 1 The equal perimeter model of circle and square
When 11 is multiplied by 720, the diameter of the Earth is interpreted as being 7960 miles.
The circle equal in perimeter to the out square of the Earth is then to be interpreted as 14 multiplied by 720, or 10080 miles in diameter, the limits of the sub-lunary world and of sacred spaces.
The diameter of the Moon is then interpreted as 3 multiplied by 720 = 2160 miles.
This cosmic geometrical model[5] [John Michell 2008] is accurately the size of the mean (spherical) Earth and of the Moon, long before the scientific revolutions of the last millennium, both Islamic and European. It suggests our planet and moon conform to a numerical plan, as an accurate overall approximation.
But the Quran appears to have used the alternative way, provided by Noor Bosra on page 443, of specifying the cosmic perimeter model, using 3 x 4 x 5 x 6 x 7 x 8 = 20160 to replace 720 x 14 = 10080. This 20160 is twice the normal 10080 of the cosmic model so that, the diameter of the Earth must also be 11/14 of that: that is, 7920 doubled to 15840. The equal perimeter length must also then double from 31680 to 63360. The results (now in half miles of 2640 feet) enabled the rhyme-form puzzle to replace the factorial expansion of the simple geometry and create numbers exactly twice that of the cosmic geometry, as shown in figure 2. By doubling the numbers of the cosmic model, the traditional numbers associated with the cosmic model of the earth were hidden, while upgrading the previous versions to become the subject for the Quranic version, the seven sleepers of the cave, all sleeping through history to avoid persecution.
Figure 2 The simplest, cosmic and Quranic geometries, the Quranic differentiating itself from the cosmic using an alternative factorial form to double the cosmic numbers.
Adding the numbers of the Sleepers
Noor then adds the numbers 3 to 8 to get 33, the number associated with the Solar Hero who are, as with Jesus and Mithras, said to die after 33 years. [6] This number has a strange relationship to the Moon’s nodal period of 18.618 years in that, the ratio between these numbers is the square root of pi as 3.141679 that is 1.77248. For this reason a square of side 33 is equal in area to the circle of radius 18.618[7] – a unique situation for a whole number as small as 33. The creation a circle and square of equal area has in fact been proven impossible to achieve by algebraic geometrical methods but 33 and 18.618 provide a practical synthesis[8].
It should be no surprise that the Quran might have referred to the nodal cycle in this way, since Mount Hira provides an approximate span, to the east, of the moon’s maximum (extreme) moonrises every 18.618 years, to the north and south, when viewed from the Kaaba, which is right angles to the lunar maximum to the north[9]. If the square side, equal to the diameter of the Earth, is reused then the required unit is one 33rd of the diameter. 15840, divided by 33, equals a unit of 480 and 18.618 x 480 equals 8936.64 as a radius, and a diameter of twice that. Figure 3 shows the radius of the circle of equal area to the square if that is 33 years and the radius 18.618 years.
Figure 3 The Quranic geometry with the nodal period added, given Noor’s clue of adding the numbers between 3 and 8 to give 33 years
This equality of a circle’s perimeter and a circle’s area, to the same square, can then be drawn to unite the cosmic model of Earth and Moon’s size, to the relationship of the Solar Hero period of 33 years, as the square, to a circle of radius 18.618 years, as appears quite clearly in the plan of Islam’s Dome of the Rock in Jerusalem.
Figure 4 left: The plan of the Dome of the Rock. Right: The Dome itself with Dome of the Chain before it, from Heath, 2021. This bedrock is the scene of Mohammad’s Journey called Miraj[10].
There appears to be some continuity between the built heritage of the subsequent Islamic empire, and the Quran’s subliminal reference to the cosmic model doubled using the story of the seven sleepers to provide the numbers 20160 and 33 through the multiplication and addition of the numbers [3, 4, 5, 6, 7, 8], respectively, centuries before. Plato and the Quran therefore appears to be both an excellent introduction to the influences acting upon the Quran when composed but also to esoteric number traditions to which the Prophet was connected, deserving of further attention.
Bibliography
Bosra, Noor. Plato And The Quran: Number and Allegory from Ancient Mesopotamia and Greece to Islam. London: Noor Bosra Publishing. 2023.
Heath, Richard. Sacred Geometry: Language of the Angels. Rochester, Vt.: Inner Traditions, 2021
Michell, John. Dimensions of Paradise: Sacred Geometry, Ancient Science, and the Heavenly Order on Earth. Rochester, Vt.: Inner Traditions, 2008.
[2] The numbers 5 and 8 are early members of the Fibonacci series in which successive terms approximate the golden mean of 1.618034, in this case to 1.6.
[3] A factorial number is all the numbers up to its limit, so that factorial 3 (or 3!) equals 1 + 2 + 3 equalling 6
[4] Pronounced pi, π is the relationship between a circle’s perimeter and its diameter which if the diameter is 7 then the perimeter is accurately 22, leading to the ratio 22/7 widely adopted by early numerate cultures.
[6] This periodicity denotes the exact location of the sun east on rising, or west on setting, since the extra quarter day is closely the fraction 32/132 which equals 0.24 days while 132 = 4 x 33.
[7] First identified by Robin Heath, personal communication.
[8] then found within astronomical time as the Solar Hero of 33 years and Nodal period of 18.618, reach into the structure of the Metonic period (19 × 19.618 × 18.618) and Saros periods (19 × 18.6182), solar year (19.618 × 18.618), and eclipse year (18.6182), all in solar days.
[9] See chapter 8: The Focal Buildings of Islam of Sacred Number: Language of the Angels, page 185
[10] The Israʾand Miʿraj( Arabic: الإسراء والمعراج, al-’Isrā’ wal-Miʿrāj) are the two parts of a Night Journey that Muslims believe the Islamic prophet Muhammad (AD 570–632) took during a single night around the year AD 621 (1 BH– 0 BH) … miʿraj means rising, or going up to a high place. – Wikipedia. To paraphrase, in the Miraj, Muhammad “ascends to heaven” whilst still alive.
One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it. However, metrology of feet and types of feet can hide the elegance of a design.
I received Michael Glickman’s Crop Circles: The Bones of God at the weekend and each chapter is a nicely written and paced introduction to a given years worth of crop circles generally in the noughties. The above is the second in proximity to Stonehenge reminding keen croppers of an earlier one. This cicle preceeded the late-season (August) circle at Crooked Soley that I have an analysis of soon to be posted, drawing on Allan Brown’s small book on it.
Glickman’s chapter 10 : Stonehenge Ribbons and Crooked Soley provided a tentative analysis of the Ribbons as having the ends of the ribbons measuring 58 feet. The design was observed as making use of a single half circle building block for most of the emergent six arms emerging from the center. Michael suggested that there were 13 equal units of 58 feet across the structure.
Figure 10.4 Showing thirteen divisions of one of the three diameters of ribbons. photo: Steve Alexander.
From this I was able to observe that clearly the divisions were not equal in size and the white ones were clearly smaller as was the central circle’s diameter. Scanning the picture and placing it in my Visio program, so that a rectangle of 58mm was equal to the diameter of the right hand ribbon end, it was possible to determine that the ratio between these lengths was 5 to 4, or 5/4, from which the shorter white length must be 46.4 feet and that the diameter can be seen as 9 units across, that is 104.4 feet. The unit is 104.4 feet divided by 9 which equals 11.6 feet, which is 10 feet of 1.16 feet, the root reciprocal of the Russian foot of 7/6 feet, that is 7/6 feet divided by 175/176 (= 1.16). Going down the “Russian” root led to the diagram below.
My analysis of Michael Glickman’s figure reveals a span of 580 Russian Feet.
There are parallax errors so I have had to show the ideal designed shortened across the left-hand of the design, but the design has many numerical aspects where each arm is 27 units so that two arms are 54 which, plus the center, gives 58 times 10 equaling 580 Russian feet. But then I noted that 58 feet, divided by 5, gave the unit as 11.6 English feet while 58 feet divides into the 58 unit diameter across the crop circle.
Now we see a set of multiples of 29 are there as numbers {29 58 87 116 145 174 203 232 261 … }. The reciprocal Russian at 1.16 feet and the unit of 11.6 feet are decimal echoes of the number 29. The formula of the Proto Megalithic yard is 87/32 feet and 261/8 inches.
To be continued
One sees most clearly how a single concrete measure such as 58 feet can take the meaning of the design into the numbers required to create it.
