The Norton Disney Archaeology Group found an example of a “Gallo Roman Dodecahedron”. One of archaeology’s great enigmas,
there are now about 33 known examples in what was Roman occupied Britain.

An Interpretation of its Height

The opposed flat pentagons of a regular duodecagon gives us its height, in this case measured to be 70 mm. Dividing 0.070 meters by 0.3048 gives 0.22965 feet and, times 4, gives a possible type of foot as 0.91864 or 11/12 feet**.

** Where possible, one should seek the rational fraction of the foot, here 11/12, over the decimal measurement which assumed base-10 arithmetic and loses the integer factors at work within the system of ancient foot-based metrology.

Plan of Avebury showing the stone arrangement of the henge. Source: The Avebury Cycle Michael Dames (1977).

The principle of finding anniversaries appears promising when three solar years contain just over 37 (37.1) lunar months while three lunar years contain 36 lunar months and, if one then looks for a better anniversary, then one can move to the 8 year period which has two key features.

The sun will appear on the horizon where it did 8 solar years ago because of the quarter day every solar year.

The moon will be in the same phase (relative to the sun) after 99 lunar months.

This appears useful: by dividing the days in eight years (~ 2922 days) by 99 (having counted to 99 months by eight years) the resulting estimate for the lunar month is 29.514 days, out by just 23 minutes of our time.

Eight solar years was therefore an early calendar in which the solar year could be somewhat integrated by the lunar year. However, the lunar year was entrenched as a sacred calendar, for example in Archaic Greece. And it may be that when the Neolithic reached England in the Bronze Age that 99 stones were placed around the massive henge of Avebury so that eight solar years could be tracked in a seasonal calendar alongside 99 lunar months, 96 months constituting eight lunar years.

The three lunar months left over must then, divided by 8, give the solar excess over the lunar year as 3/8 = 0.375, whereas the actual excess is 0.368 lunar months or 5 hours less. In the previous post, two months the stone age could have been counted as 59 days, here 8 solar years could have been counted as 99 lunar months at Avebury. Through this, one would be homing in on knowing the solar excess per year (10.875 days) and the length of the lunar month, to more accuracy.

It is obvious that counting using whole months has not got enough resolution to catch an accurate result and so in the next post we must revert to counting days in inches, as was done at Le Manio around 4000 BC, over the 36/37 month anniversary at three solar years. It is important to grasp that while we have great functional mathematics, we are here using it to find out what the numeracy 3000-4000 BC could have intended or achieved within counts monumentalized geometrically as a stone monument that can store information.

The oral world of early numeracy was rather like number theory, where numbers can be observed as being related to the geometries of square, triangle and hexagon. The Islamic world of the Sufis appears to have continued this form of numeracy.

A recent book about possible Platonic numeracy in the Quran, Plato and the Quran, suggests the numbers 3 to 9 were stated as a puzzle inviting both the addition and multiplication for seven consecutive numbers, to generate two significant numbers, 33 and 20160, where 33 reminds us of the solar hero period of 33 years and 20160 is twice 10080, the diameter of the equal perimeter model of the Earth and the Moon.

Many centuries later, an early poem of Sufi master Ahmad Yasavi, in present day Khazakhstan, expressed a similar additive formula; that one should add the numbers 4 to 8 together and, when done, this generates the number 22. Twenty two was important in the ancient world and was seen to form the geometry of the equal perimeter square side 11 and circle diameter 14, which, can represent the relative sizes of the Earth and Moon. The geometry is a manifestation of a useful approximation to pi, as 22/7 = 3 + 1/7 or 3.142857, instead of the transcendent number 3.14159 … .

If one looks at the sequence, there are four numbers starting with four and so part of 22 is here 4 x 4 = 16, a square number. In addition there are the added ones of enumeration.: 4 + 1 = 5 + 1 = 6 + 1 = 7. These add up to 1 + 2 +3 = 6, a triangular number which one famously sees in the Tetractys of 1 + 2 + 3 + 4, then usually expanding downwards from 1, and this then adding to 6 + 4 = 10.

The lesser triangle of 6 can sit on top of the square of 16 to equal 22 while looking like a house roof for the square. The whole structure is seven units tall and I am looking at calling this a house number, but perhaps it is known somewhere in the literature – please let me know.

The first house number must be 5, a single 1 above 4 = 2 x 2.

The second house must be 12, a triangle of 3 above 9 = 3 x 3.

The fourth is 22.

The fifth is 35, a triangle of 10 above the square of 25 = 5 x 5.

The sixth is 51 , a triangle of 15 above the square of 36 = 6 x 6.

In each case, the triangle’s bottom row can be seen to share the top row of the house’s square and the triangular roof is most simply equilateral.

I wish happy celebration to my worldwide visitors, between the solstice and new calendar year; inviting you to see this “house number” as a “room” with a celestial “roof”.

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.