Books and other occasional writings
For further details of the book look at the growing Publisher pages for it at Inner Traditions.
The egg-shaped stone circles of the megalithic, in Brittany by c. 4000 BC and in Britain by 2500 BC, seem to express two different astronomical time lengths, beside each other as (a) a circumference and then (b) a longer, egg-shaped extension of that circle. It was Alexander Thom who analysed stone circles in the 20th century as a hobby, surveying most of the surviving stone circles in Britain and finding geometrical patterns within irregular circles. He speculated the egg-shaped and flattened circles were manipulating pi so as to equal three (not 3.1416) between an initial radius and subsequent perimeter, so making them commensurate in integer units. For example, the irregular circle would have perimeter 12 and a radius of 4 (a flattened circle).
However, when the forming circle and perimeter are compared, these can compare the two lengths of a right-triangle while adding a recurring nature: where the end is a new beginning. Each cycle is a new beginning because the whole geocentric sky is rotational and the planetary system orbital. The counting of time periods was more than symbolic since the two astronomical time periods became, by artifice, related to one another as two integer perimeters that is, commensurate to one another, as is seen at St Pierre (fig.3).
Continue reading “St Pierre 1: Jupiter and the Moon”The fields of ancient Greece were organised in a familiar way: strips of land in which a plough could prepare land for arable planting. Known in various languages as furlong https://en.wikipedia.org/wiki/Furlong, runrig, journel, machen etc, in Greece there was a nominal length for arable strips which came to be associated with the metrological unit of 600 feet called a stadia. The length of foot used was systematically varied from the foot we use today, using highly disciplined variations (called modules); each module a numeric ratio of the Greek module, whose root foot was the English foot [Neal, 2000]. These modules are found employed throughout the ancient world, lengthening or reducing lengths such as the stadia, to suit geometrical problems; such as the division of land into fields (figure 1).
The traditional way to express the Harmony of the Spheres is geometrically, despite the fact that geometrical knowledge of the heliocentric planetary system was not available to Pythagoras who, for the West, first established this whole idea – that the planets were part of a system expressing harmony.
The opening picture is from Kepler’s Harmonices Mundi :
from a scan made of the Smithsonian’s copy,
made available on Wikipedia as in the public domain.
In my own work, on the type of ancient astronomy based upon time and not space, I find it to be the outer planets in particular which express harmony in their geocentric synods relative to the lunar year. This applies to Jupiter, Saturn and Uranus but Neptune expresses a rational fraction of 28/27 involving prime numbers {2 3 7} whilst the other three planets only involve ratios involving primes {2 3 5}. The harmony of the outer planets has been a strong source for the sacred numbers found in ancient texts, as with Jupiter 1080 – considered a lunar number perhaps because the Moon is resonant to Jupiter – who is shown by figure 1 to be geocentrically resonant to the other planets and the Moon.
Continue reading “Further Ratios of the Outer Planets to the Lunar Year”The Fibonacci series is an ideal pattern, widely found within living systems, in which the present magnitude or location of something is the product of two previous magnitudes or locations of it. The next magnitude will again be the sum of the last two magnitudes in what is, an algorithmic pattern producing approximation to the Golden Mean (designated by the Greek letter φ,’phi’). As the series gets larger, the ratio (or proportion) between successive magnitudes will better approximate the irrational value of φ = 1.618033 … – which has an unlimited fractional part whilst the virtue of the Fibonacci numbers within the Series is that they are integers forming rational fractions.
Soil resistance work (“geophys”), by archaeologists from the University of Leicester, of the land inside the southern stone circle of Avebury Henge, has revealed more about the Obelisk and lines of standing stones, which appear to have formed a near-square rectangle. Information can be hard to obtain when work is yet to be published but a press release to the Guardian and others many months ago (December 27th 2019) enabled figures from a media set to be viewed with public access. This has enabled me to so some site interpretation, using the (as-yet damned) numerical technique called ancient metrology. My results are fascinating and build upon the megalithic use of counting time as length to track important time-cycles such as the Nodal Period of 6800 days, between lunar maxima and minima, and the Metonic period of both 19 years and 235 lunar months, within which all of the varied orientations of Sun Moon and Sky are recycled.
