November 2018 – Page 2 – Numbers of a Living Planet

Distribution of Prime Numbers in the Tone Circle

first published 13 February 2018

The ancient notion of tuning matrices, intuited by Ernest G. McClain in the 1970s, was based on the cross-multiples of the powers of prime numbers three and five, placed in an table where the two primes define two dimensions, where the powers are ordinal (0,1,2,3,4, etc…) and the dimension for prime number 5, an upward diagonal over a horizontal extent of the powers of prime number 3. Whilst harmonic numbers have been found in the ancient world as cuneiform lists (e.g. the Nippur List circa 2,200 BCE), these “regular” numbers would have been known to only have factors of the first three prime numbers 2, 3 and 5 (amenable to their base-60 arithmetic). Furthermore, the prime number two would have been seen as not instrumental in placing where, on such harmonic matrices, each harmonic number can be seen on a harmonic matrix (in religious terms perhaps a holy mountain), as

“right” according to its powers of 3.
“above” according to its powers of 5.

The role of odd primes within octaves

An inherent duality of perspective was established, between seeing each regular number as a whole integer number and seeing it as made up of powers of the two odd two prime numbers, their harmonic composition of the powers of 3 and 5 (see figure 1). It was obvious then as now that regular numbers were the product of three different prime numbers, each raised to different powers of itself, and that the primes 3 and 5 had the special power of both (a) creating musical intervals within octaves between numerical tones and (b) uniquely locating each numerical tone upon a mountain of numerical powers of 3 and 5.

*Figure 1 Viewing the harmonic primes 3 and 5 as a mountain of their products, seen as integer numers or as to these harmonic primes*

Erdeven Alignment’s counting of Metonic and Saros Periods

The word Alignment is used in France to describe its stone rows. Their interpretation has been various, from being an army turned to stone (a local myth) to their use, like graph paper, for extrapolation of values (Thom). That stone rows were alignments to horizon events gives a partial but useful explanation, since menhirs (or standing stones) do form a web of horizon alignments to solstice sun and to the moon’s extreme rising and setting event, at maximum and minimum standstill. At Carnac the solstice sun was aligned to the diagonal of the 4 by 3 rectangle and maximum and minimum standstill moon aligned to the diagonal of a single or double square, respectively.

It seems quite clear today that stone rows at least represented the counting of important astronomical time periods. We have seen at Crocuno that eclipse periods, exceeding the solar year, are accompanied by some rectalinear structures (Le Manio, Crucuno, Kerzerho) which embody counting in miniature, as if to record it, and it has been observed that cromlechs (or large stone kerb monuments) were built at the ends of the long stone rows of Carnac and Erdeven. Sometimes, a cromlech initiated a longer count,with or without stone rows, that ended with a rectangle (Crucuno). The focus on counting time naturally reveals a vernacular quite unique to this region and epoch. We have seen that the Kerzerho alignments were at least a 4 by 3 rectangle which recorded the 235 lunar months in feet along its diagonal to midsummer solstice sunset. After that rectangle there follows a massive Alignment of stone rows to the east,ending after 2.3 km having gradually changed their bearing to 15 degrees south of east. Just above the alignments lies a hillock with multiple dolmens and a north-south stone row (Mané Braz) whilst below its eastern extremity lies the tumulus and dolmen,”T-shaped passage-grave” (Burl. Megalithic Brittany. 196) called Mané Groh.

*Figure 1 The intermittent extent of the Erdevan Alignments, and associated dolmens*

Kerherzo Rectangle near Erdeven & Crucuno

first published in March 2018

In 1973, Alexander Thom found the Crucuno rectangle to have been “accurately placed east and west” by its megalithic builders, and “built round a rectangle 30 MY [megalithic yards] by 40 MY” and that “only at the latitude of Crucuno could the diagonals of a 3, 4, 5 rectangle indicate at both solstices the azimuth of the sun rising and setting when it appears to rest on the horizon.” In a recent article I found metrology was used between the Crucuno dolmen (within Crucuno) and the rectangle in the east to count 47 lunar months, since this closely approximates 4 eclipse years (of 346.62 days) which is the shortest eclipse prediction period available to early astronomers.

*Figure 1 Two key features of Crucuno’s Rectangle*

About 1.22 miles northwest lie the alignments sometimes called Erdeven, on the present D781 before the hamlet Kerzerho – after which hamlet they were named by Archaeology. These stone rows are a major complex monument but here we consider only the section beside the road to the east. Unlike the Le Manec Kermario and Kerlestan alignments which start north of Carnac, Erdevan’s alignments are, like the Crucuno rectangle accurately placed east and west.

*Figure 2 Two stones, angled to the diagonal of a 3-4-5 triangle 235 feet from north west stone and setting sun at summer solstice*

Harmonic Astronomy within Seascale Flattened Circle

first published in July 2018

Only two type-D stone circles (see figure 3) are known to exist, called Roughtor (in Cornwall) and Seascale (in Cumbria). Seascale is assessed below, for the potential this type of flattened circle had to provide megalithic astronomers with a calendrical observatory. Seascale could also have modelled the harmonic ratios of the visible outer planets relative to the lunar year. Flattened to the north, Seascale now faces Sellafield nuclear reprocessing plant (figure 1).

Figure 1 Seascale type-D flattened circle and neighbouring nuclear facility.
photo: Barry Teague

Stone Age astronomical monuments went through a series of evolutionary phases: in Britain c. 3000 BC, stone circles became widespread until the Late Bronze Age c. 1500 BC. These stone circles manifest aspects of Late Stone Age art (10,000 – 4500 BC) seen in some of its geometrical and symbolic forms, in particular as calendrical day tallies scored on bones. In pre-literate societies, visual art takes on an objective technical function, especially when focussed upon time and the cyclic phenomena observed within time. The precedent for Britain’s stone circle culture is that of Brittany, around Carnac in the south, from where Megalithic Ireland, England and Wales probably got their own megalithic culture.

The role of odd primes within octaves

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