In my academia.edu paper on lunar simulators, based upon the surviving part of a circular structure at Le Manio (Carnac, Brittany), a very simple but poor approximation to PI could be assumed, of 82/26 (3.154) since there seem to have been 82 stones in the circle and the diameter was 26 of the inter-stone distance of 17 inches. The number 82 is significant to simulation of the moon’s orbit since that orbit is very nearly 27 and one third days long (actually 27.32166 days). In three orbits therefore, there are almost exactly 82 days and in day-inch counting that is 82 day-inches. Also of interest is the fact that in three orbits, the exact figure would be 81.965 day-inches which approaches the megalithic rod of 2.5 MY as 6.8 feet.

Continue reading “82: A Natural Accurate Pi related to Megalithic Yard”## Form implied by the Kaaba’s Walls

The Kaaba appears to express a geometrical progression of adjacent odd numbers starting with one and three. This differs from the super-particular ratios found within the right triangles of astronomical time periods formed by the Megalithic, in which the ratio pairs separated by only one rather than by two, between only odd numbers. However, the multiple-square rectangles used by the megalithic to approximation celestial ratios, made use of the three-square rectangle. In one of the smallest of these rectangles, it simultaneously approximates two pairs of ratios: The eclipse year (346.62 days) to the solar year (365.2422 days) and the solar year to the thirteen lunar month year (384 days).

Continue reading “Form implied by the Kaaba’s Walls”## The Golden Mean compared to PI

In reviewing some ancient notes of mine, I came across an interesting comparison between the Golden Mean (Phi) and PI. They are more interesting in reverse:

A phi square (area: 2.618, side: 1.618) has grown in area relative to a unit square by the amount (area: 0.618) plus the rectangle (area:1 ). This reveals the role of phi’s reciprocal square (area: 0.384) in being the reciprocal of the reciprocal so that in product they return the unity (area: 1).

Continue reading “The Golden Mean compared to PI”## Astronomical Time within Clava Cairns

In North East Scotland, near Inverness, lies Balnuaran of Clava, a group of three cairns with a unique and distinctive style, called Clava cairns; of which evidence of 80 examples have been found in that region. They are round, having an inner and outer kerb of upright stones between which are an infill of stones. They may or may not have a passageway from the outer to the inner kerb, into the round chamber within. At Balnuaran, two have passages on a shared alignment to the midwinter solstice. In contrast, the **central ring cairn** has no passage and it is staggered *west *of that shared axis.

This off-axis ring cairn could have been located to be illuminated by the **midsummer sunrise** from the **NE Cairn**, complementing the midwinter sunset to the south of the two passageways of the other cairns. Yet the primary and obvious focus for the Balnuaran complex is the midwinter sunset down the aligned passages. In fact, the ring cairn is more credibly aligned to the lunar minimum standstill of the moon to the south – an alignment which dominates the complex since, in that direction the horizon is nearly flat whilst the topography of the site otherwise suffers from raised horizons.

## Use of foot ratios in Megalithic Astronomy

The ratios of ancient metrology emerged from the Megalithic innovations of count&compare: counting time as length and comparing lengths as the longest sides of right triangles. To compare two lengths in this way, one can take a longer rope length and lay it out (say East-West), starting at the beginning of the shorter rope length, using a stake in the ground to fix those ends together.

The longer rope end is then moved to form an angle to the shorter, on the ground, whilst keeping the longer rope straight. The Right triangle will be formed when the longer rope’s end points exactly to the North of the shorter rope end. But to do that one needs to be able to form a right angle at the shorter rope’s end. The classic proposal (from Robin Heath) is to form the simplest Pythagorean triangle with sides {3 4 5} at the rope’s end. One tool for this could then have been the romantic knotted belt of a Druid, whose 13 equally spaced knots could define 12 equal intervals. Holding the 5th knot, 8th knot and the starting and ending knots together automatically generates that triangle sides{3 4 5}.

Continue reading “Use of foot ratios in Megalithic Astronomy”## A Lecture introducing Sacred Number and the Lords of Time

… given as the John Michell Memorial Lecture for

at Megalithomania 2015 in Glastonbury

- The overhead slides can be found at Academia.org.
- A flyer for the book launched by the lecture, here.
- The publisher’s page for the book is at InnerTraditions.com.

- A flyer for the book launched by the lecture, here.

## Thornborough Henge as Moon’s Maximum Standstill

The three henges appear to align to the three notable manifestations to the north west of the northerly moon setting at maximum standstill. The distance between northern and southern henge entrances could count 3400 days, each 5/8th of a foot (7.5 inches), enabling a “there and back again” counting of the 6800 days (18.618 solar years/ 19.618 eclipse years) between lunar maximum standstills.

Continue reading “Thornborough Henge as Moon’s Maximum Standstill”## Number Symbolism at Table des Marchands

Table des Marchands, a dolmen at Lochmariaquer, can explain how the Megalithic came to factorise 945 days as 32 lunar months by looking at the properties of the numbers three, four and five. At that latitude, the solstice angle of the sun on the horizon shone along the 5-side of a 3-4-5 triangle to east and west, seen clearly at the Crucuno Rectangle "Lunar Counting from Crucuno Dolmen to its Rectangle".

Before numbers were individually notated (as with our 3, 4 and 5
rather than |||, |||| and |||||) and given positional notation (like our
decimal seen in 945 and 27), numbers were lengths or marks and, when marks are
compared to accurately measured lengths measured out in inches, feet, yards,
etc. then *each vertical mark would naturally
have represented a single unit of length*. This has not been appreciated
as having been behind marks like the cuneiform for ONE; that it probably meant
“one unit of length”.

## Earth and Moon within Westminster’s Coronation Pavement

Our modern globes are based upon political boundaries and geographical topography yet they have geometrical predecessors, which described the world as an image, diagram or schemata. The original idea for the form of the world was summarised within a simple two dimensional geometry, like an eastern mandala or yantra.

Such a diagram was built into the Cosmati pavement at Westminster Abbey, built by Henry III and dedicated to the Saxon King and Saint Edward the Confessor. This exotic pavement became the focus for the Coronations of subsequent English then British monarchs.

Continue reading “Earth and Moon within Westminster’s Coronation Pavement”## Musical Tones of the Outer Planets

My crucial entré to planetary harmony came when I noticed musical ratios in the synodic time periods of Jupiter and Saturn relative to the lunar year. This approach differs from the norms for “harmonies of the spheres” (a.k.a. Musica Universalis) which are geometrical and spatial, rather than temporally harmonic.

The planetary harmony I found within synodic periods became the subject of my new book *The Harmonic Origins of the World (pub. *2018). These synodic ratios have been parts of my work from c. 2000, then expressed as “matrix diagrams” (*Matrix of Creation, *figure 2 below). In my new book, I show how **ancient tuning theory** seems to have presented the same information, in a different type of matrix (see figure 4).

Below I connect the outer planets using two additional (and useful) kinds of diagram, the right-angled triangle (figure 1) and the Pentad (figure 5), the latter developed in the 20th century within a discipline called *Systematics. *

## Eleven Questions on Sacred Numbers

In 2011, *Sacred Number and the Origins of the Universe* was nicely re-published in Portuguese by Publisher **Pensamento **in Brazil. Their press agent contacted my publisher for an email interview from a journalist who posed eleven questions about sacred number.

## Interview:

1) Is the universe a mathematical equation?

*If the universe is a creation then it needs to have organizing principles governing its structure. I believe that this structure is governed by what we call sacred numbers. Numbers relative to each other form proportions that in sound are perceived as musical intervals. The universe is more like a set of musical possibilities, making it more dramatic and open-ended than an equation.*

## The Roof Axe as Circumpolar Device

This article explores the use of axe motifs within a form of carved schematic art unique to the megalithic monuments near Carnac, southern Brittany, France. First published in February 2014.

A diagram found on the underside of the capstone
of a chambered dolmen called Kercado (see figure 1) appears to hold
metrological and astronomical meanings. Classified as a type of AXE, local axe
motifs are said to have three distinct forms (a) triangular blades, (b) hafted
axes and (c) the *Mane Ruthual* type [Twohig, 1981[1]].

Types b and c are often found in the singular on
the undersides to roof slabs and in the case of form (b), the hafted axe, I
have attributed its display below the roof slab of *Table des Marchands* at Locmariaquer (inset right) as being used to
represent the north pole between 5000 and 4000 BC, at a time when there was no
star near to the pole itself. The abstract point of the north pole, the
rotational axis of the earth, is shown as a loop attached to the base of the axe
haft, whilst the axe head then represented a chosen circumpolar star, as this
rotates counter-clockwise in the northern sky, at the fixed distance of the
haft from the pole itself. Note how compatible this idea of an axe ploughing
the northern skies is to our own circumpolar constellation, The Plough. Note
also that the eastern horizon moves through the equatorial stars at the same
angular rate as the marker star moves around the north pole.

## Sacred Latitudes of the West 1.

first published on Sunday, 19 September 2010 10:35

## Adventures in Geodetic Imagination

At the heart of *Sacred Number and the Origins of Civilization* lay the story of the *Secret Men of the North,* which followed the west-to-east path of a European Michael line, in the sense of the original invasion of the Indo-Europeans of the Baltic into the Mediterranean and as the later axis this provided for the Normans to orchestrate the Crusades; ostensibly to re-take Jerusalem from the world of Islam, that was also competing over Europe, from Spain, Sicily and Levant.

Whilst working on a continuation of such a geodetic story, the concept of Sacred Latitudes emerged in which parallels of latitude might have some psycho-historical relevance, based on the original insight that, in the last century, “manifestations of Mary” have emerged, first in Garabandal in Spain and recently in Medjugorje, in Bosnia, that are on exactly the same line of latitude, 43 degrees and 12 minutes. (brought to my attention by the late John D. Kirby’s studies of “Mary places”.)

Continue reading “Sacred Latitudes of the West 1.”