The Megalithic Numberspace

L9 222

above: counting 37 lunar months six times to reach 222,
one month short of 223: the strong Saros eclipse period.

There is an interesting relationship between the multiple interpretations of a number as to its meaning, and the modern concept of namespace. In a namespace, one declares a space in which no two names will be identical and therefore each name is unique and this has to be so that, in computer namespaces such as web domain names, the routes to a domain can be variable but the destination needs to be a unique URL.

If sacred numbers had unique meanings then they would be like a namespace. Instead, being far more limited in variety, sacred numbers have more meanings, or interpretations, just as one might say that London has many linkages to other cities. In an ordinal number set, there are many relationships of a number to all the other numbers. This means whilst their are infinite numbers in the set of positive whole numbers, there are more than an infinity of relationships between the members of that set, such as shared number factors or squares, cubes, etc. of a number.

The mathematician Georg Cantor saw “doubly infinite” sets. Sets of relationships between members of an already infinite set, must themselves be more than infinite. He called infinite sets as aleph-zero and the sets of relationships within an infinite set (worlds of networking), he called aleph-one.

Originally, Cantor’s theory of transfinite numbers was regarded as counter-intuitive – even shocking.

Wikipedia

However, in the world of sacred numbers, although there can be large numbers, in the megalithic the numbers were quite small; partly due to the difficulty that numbers-as-lengths were physically real while later numeracy abstracted numbers into symbols and, using powers of ten, modern integers are a series of place ordered numbers (not factors) in base 10, as with 12,960,000 – possible for the ancient Babylonians but, I believe, not expected for the early megalithic.

Another aspect of megalithic numbers is that they didn’t just come from counting astronomical time but were often revealed by the synthetic metrological/geometrical methods, these used to represent, compare or process the numbers. The ultimate factors of a number-as-a-length are the prime numbers that make a number up and, in practice, convenient combinations of prime numbers could transform one number measurement into another number of units by using the fractional feet of metrology, such as 32/35 (see next).

945 days is a good example since its factoring is 5 x 7 x 27 where 27 = 3 x 3 x 3, three cubed. In this time period, there are exactly 32 lunar months (32.0007 in fact) and 32 lunar months is 944.97888, 945 to one part in 44,743: effectively exact! (This was explored in these posts.) Out of this combination of numbers arose a unit of measure called the Iberian foot of 32/35 feet and an aggregate measure of 27 feet which could be used to represent the lunar month because 27 feet in Iberian feet is 27 x 35/32 = 29.53125 feet.

This anniversary of 32 lunar months in 945 days allowed the megalithic at Carnac, by 4000 BC, to factor the lunar month as a simple cube of 3 = 27 in days-per-Iberian-feet. This allowed days and months to be directly compresent within a monument exploiting this factorization, which can be found at Crucuno between the Dolmen and the Rectangle and also in Scotland at Clava Cairns and other sites .

In factorization, the megalithic were able to reduce numbers to their primes, or to make proximal pairs of fractions of say pi, so as to apply a number of multiplications and divisions by changing units and so, for example, achieving a rational (that is integer) result. but this is only visible if the modern investigator not only uses feet but also understands how rational fractions of a foot were carefully employed.

The methods of Alexander Thom had a very limited view of metrology, limited to the use of feet, and the megalithic yard and its aggregates and subdivisions, partly because historical geometry was firmly not thought to be a prehistoric phenomenon.

Another problem is that the ancient metrology of John Neal probably belongs to 3000 BC or later; it is therefore already too complex in its variations to resolve the relative simplicity of 27 x 35/32 = 29.53 Iberian feet.

In any case archaeologists will also strongly contest, by peer review, Neal’s proposed metrology and they themselves use meters rather than feet in site plans, due to the metrification of scientific units of measure called MKS. Therefore there would be more possibility of finding significant numbers of feet at ancient sites if archaeologists (a) used meters and feet, and (b) measured dimensions within a site as perhaps intentional instead of creating site plans as a mere record, with a scale in meters.

Returning to the megalithic “numberspace”, it is clear that this had to be simple integers (of the ordinal set) and involved factorization in order to find common factors, to transform their measurements into a simpler form where complex picture could be reduced to its essence, a sacred number. It must not have gone unnoticed that the factor 27 resembles the 27 plus days of the lunar orbit or that three lunar orbits were 82 day-inches long or that 8 megalithic yards (of 261/8 feet) equaled 261 inches or 9 x 29, having then removed the denominator 8 through a number of units.

Without any expectations about what they were dealing with, the megalithic were stumbling into a numberspace created by the earth, sun, and moon, as an integrated system in which time periods divided into other time periods in an intelligible way. Such a system is of a higher state of order than is encountered anywhere else of the earth’s surface, where the laws of physics do not allow the lossless recurrences of large gravitational attractors orbiting around one another in a vacuum. That is perhaps why the term heaven was originally coined for the sky, where things are less random yet repetitive in a chaotic way when seen from the earth.