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).


Figure 1 The three-square approximations in a triple series of astronomical periods. Note that the diagonals relative to the base are the result of having three squares in a rectangle then one high and three along – and two different. Two such rectangles geometrically sum (their angles) to give that of the (First Pythagorean) 3-4-5 triangle, 36.8 degrees.
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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).

On the right, the phi squared square showing how the reciprocal of phi and its square uniquely sum to unity (area: 1), a property that is scale invariant between structures who share the same units and grow according to the Golden Mean.
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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”.)

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Iceland’s Model of the Earth’s Meridian

Einar Palsson [1, at end] saw that the myths of foundation for Iceland’s settlement in 930 had Pythagorean roots. Since then Petur Halldorsson has identified patterns that could not have been influenced by Pythagoras (c. 600 BC) and Pythagoras was known to have adapted the existing number sciences found (according to his myth) from Egypt to China.

Such patterns, called Cosmic Images by Halldorsson [3], seek to establish a geometric connection between places on the landscape and on the horizon, here in the south-western region near Reykjavik, the only Icelandic city. The spirit of a region or island was integrated through organising space in this way, according to centers (Things) of circles and their radius and diameter as numbers of paces, circles punctuated with places and alignments to other places, horizon events or cardinal directions. John Michell provided a guide to some of the techniques in his books [2, at end].


Figure 1 The Cosmic Image east of Reykjavik proposed by Palsson
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Palsson’s Sacred Image in Iceland

Extracted from The Structure of Metrology, its Classification and Application (2006) by John Neal and notes by Richard Heath for Bibal Group, a member of which, Petur Halldorsson, has taken this idea further with more similar patterns on the landscape, in Europe and beyond. Petur thinks Palsson’s enthusiasm for Pythagorean ideas competed with what was probably done to create this landform, as he quotes “Every pioneer has a pet theory that needs to be altered through dialogue.” Specifically, he “disputes the Pythagorean triangle in Einar’s theories. I doubt it appeared in the Icelandic C.I. [Cosmic Image] by design.” Caveat Emptor. So below is an example of what metrology might say about the design of this circular landform.


Figure 1 of Palsson’s (1993) Sacred Geometry in Pagan Iceland
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John Michell’s Perpetual Choirs

15 April 2017 Views: 10450

In 1972  John Michell inferred an enormous ten-sided form nearly sixty three miles across, in which important historical and neolithic sites had been intended as ten vertices around an ancient centre, signified by a Whiteleafed Oak.

Figure 1 The Decagon of Perpetual Choirs, anchored upon Stonehenge, the Solstice sunrise in summer and set in winter

Michell had previously [1991] developed the idea of the enchantment of the land as an actual practice; land areas were enchanted by using a geometrical pattern integrated with myths and ritual calendars, enacted within that framework. This  was long before, around 930, such a pattern was being established of thing-places in Iceland. The idea of thing places is still find-able in English names such as Goring, the centre northeast of Stonehenge, where the summer solstice sun arose.

“Perpetual choirs were a Celtic institution, from pagan into early Christian times. In Iola Morganwg’s Triads of Britain, translated from Welsh, it is stated that ‘in each of these three choirs there were 24,000 saints; that is,
there were a hundred for every hour of the day and the night in rotation, perpetuating the praise and service of God without rest or intermission.’ ”  – The Measure of Albion

“Three of the choirs were located at Stonehenge, at Glastonbury, and near Llantwit Major in Wales. Others appear to have been at Goring-on- Thames and at Croft Hill in Leicestershire, a traditional site of ritual,  legal, and popular assemblies.” The Dimensions of Paradise


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