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).

Notes

  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 academia.edu) 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.

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.

  1. The day marker returns to the center and,
  2. 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.

Design of the Taj Mahal: its Façade

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

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. 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.
  3. Heath, Richard. Sacred Geometry: Language of the Angels. Vermont: Inner Traditions 2022.
  4. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  5. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  6. —-. 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.
  7. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  8. —-. Ancient Metrology, Vol. 3, The Worldwide Diffusion – Ancient Egyptian, and American Metrology.  The Squeeze Press: 2024.
  9. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.

Finding the Perfect Ruler, part 1

Written between 2002 and 2004, this article was evoked by my initial contacts with John Michell’s ancient model of the world. I discovered for myself the power of prime numbers in the ancient world view. Metrology was an early form of numeracy which developed through astronomy. We can see even more today.

above: Catching birds on the Nile Delta compared with the catching of different prime numbers by measuring phenomena. (from The Temple in Man by Schwaller de Lubitz, illustration by Lucy Lamy.)

Plato expresses the highest form of government as being by philosopher kings, whilst his preferred form of philosophy is Pythagorean, based upon pure number. Such a philosophy discovers the characters different numbers have within the definite field of number itself. This seems out of character with real power because we do not know of such a form a government and we appear to have lost the form of philosophy upon which it can be based. By a seeming miracle, this philosophy appears to be reconstituting itself again.

Recent discoveries about Plato demonstrate that once the ancient world knew the power of number, as a philosophy, the notion arose that a high form of government was possible through ordering the human world as the cosmic world had been. This was done by choosing units of measure that (a) showed the Earth (and Moon) to be a numerical artefact by (b) bringing out important numerical coincidences present within the Earth’s dimensions.

The Perfect Ruler was placed within the dimensions of the Earth by using the relevant units in ancient monuments that repeated the pattern, some having survived. To understand their message required inspiration, and the central core required the persistence of the John Michell, a traditionalist who in his Ancient Metrology sketches out its basic scheme, his Dimensions of Paradise showing how this applies to ancient buildings (see bibliography below).

But to understand the majesty of ancient metrological thought, one needs to focus on what numbers are and their uniqueness relative to each other. Thus, one needs to work with prime numbers, since they are the roots of the numerical field.

Working with Prime Numbers

Any number with limited “significant digits” can be and should be expressed as a product of positive and negative powers of the prime numbers that make it up. For example, 23.413 and 234130 can both be expressed as an integer, 23413, multiplied or divided by powers of ten.

Primes are unique and any number must be prime itself or be the product of more than one prime.

The first three primes are those most commonly encountered: 2, 3 and 5. The products of 2 and 3 give 6, 12 and the perfect “sexidecimals” like 60, 360 when combined with 2 and 5, i.e. 10. The ten based arithmetic we use implicitly uses 2 and 5, with negative powers applying to fractional parts. The primes {2 3 5} are called harmonic because the intervals of western music use them.

To analyse a number for its primal identity, simply remove the decimal place by multiplying by powers of ten (10 being 2 times 5, of base-10, the decimal system. We should note that, in general, metrological measures have a limited number of non-repeating significant digits and that the complexity of their fractional parts is entirely due to the hidden action of prime numbers seen within a decimal, base 10, system of notation. (Note also that, in later books, I increasingly revert to rational fractions, with integer top and bottom, since early ancients did not have base-10 or position notation, or zero, since call came from ONE)

Since metrology is our subject, and since an example is definitely required, we will analyse the tables of Greek Measure given in Michell’s Ancient Metrology, in both their Northern and Tropical Values.

Primal Therapy for Numbers

Whilst spreadsheets and programs can increase productivity, it is useful with smaller primes to follow the modern calculator method.

  1. Remove Decimals: Use the reciprocal powers of 10, e.g. 1.008 becoming 1008/ 1000
  2. Divide by Successive Primes: Start with the lowest primes, and when the result yields a fractional part, go back and move onto the next prime in order, as in 2, 3, 5, 7, 11, 13, 17, etc [see Appendix A posting for list of primes and web references to more]

The 1.008 becomes 1008 over 1000

Prime01234
divide by 21008 >>>504 >>>252 >>>126 >>>63 v
divide by 363 >>>21 >>>7A prime ! 
1008 =24.32.7
1000 =23.53 (103)

Therefore, the “shorter, tropical, or southern) Greek Foot is uniquely:

1008 over
which is
2.32.7 (126) over
100053 (125)
The resulting rational fraction for 1.008

It is soon noticed that when there is a decimal fraction, the numerator has powers of 2 that will simply cancel out with the denominator. Thus the numerator integer is long because of doubling invoked by the decimal system itself. The same is happening with positive powers of ten too, so that our base 10 system of notation is making the metrological values appear ludicrously accurate in their number of significant places, 1/7 giving a recurring “.142857”. However, it is only the prime powers that really count and are, in every case, simple. We can hazard a guess that the ancients used prime notation and certainly that any future metrology will benefit, as I have, from seeing numbers from their prime factors.

In the next part, the relationship of the English foot as standing at the root of ancient metrological measures. This was discovered by John Neal through realizing that Michell’s southern and northern measures had a different relationship to pure fractions of the foot, these fractions being the root for the variation of each module, just as the foot is the root for the fractional root feet which define each module.

Books about Ancient Metrology

  1. Berriman, A. E. Historical Metrology. London: J. M. Dent and Sons, 1953.
  2. 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.
  3. Heath, Richard. Sacred Geometry: Language of the Angels. Vermont: Inner Traditions 2022.
  4. Michell, John. Ancient Metrology. Bristol, England: Pentacle Press, 1981.
  5. Neal, John. All Done with Mirrors. London: Secret Academy, 2000.
  6. —-. 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.
  7. —-. Ancient Metrology. Vol. 2, The Geographic Correlation—Arabian, Egyptian, and Chinese Metrology. Glastonbury, England: Squeeze, 2017.
  8. —-. Ancient Metrology, Vol. 3, The Worldwide Diffusion – Ancient Egyptian, and American Metrology.  The Squeeze Press: 2024.
  9. Petri, W. M. Flinders. Inductive Metrology. 1877. Reprint, Cambridge: Cambridge University Press, 2013.