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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Venus: Planet of Harmony: part 1

Venus has played a strong role in mankind’s imagination, being a bright object in the sky in the evening sky and then the morning sky, whilst also viewed as the primary female goddess of the Ancient Near East. To recent astronomers, she is covered in impenetrable clouds, whilst the invention of radar revealed a rocky sister planet to Earth but with no life as we know it. It is perennially associated with the pentagon, because its synodic periods draw out a pentagon within the zodiac in 8 solar years. The reasons it does so are intriguing to say the least, and we explore the unusual numerical characteristics of Venus seen from Earth.

(adapted from a 1994 text, using 2020 hindsight)

The Venus cycle of eight years in which a morning or evening star has five manifestations, dividing the zodiac into a pentagram (Figure 1.6 Sacred Number and the Origins of Civilization)

Part 1: A Nearly Golden Mean

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Politics of Number part 2

The YouTube talk below, from 2012, discusses how numbers are more significant in understanding past and present societies, through the medium of a museum reproduction I made of an object to be seen in the Heraklion Museum. It records a Saturnian calendar that must have existed in the matriarchal societies of the Minoans in Crete and might be a sort of tyranny of time which Zeus-Jupiter (son of Cronos i.e. Saturn) deposed, relegating his father to a golden cave on a smaller island.

This story of Hesiod’s Theogony exactly pollows the harmonic truth that Saturn has a synodic period 16/15 (a semitone) of the lunar year whilst Jupiter’s synod is 9/8 (a whole tone) relative to the lunar year – to very high accuracy. The politics in this is the advent of Indo-Europeans from the North whose patriarchal social structures largely displaced matriarchal structures of the eastern Mediterranean.

Whilst ancient cultures were rooted in stories where numbers were structural rather than merely descriptive, connected to the sky and time as a spiritual superstructure for life on earth, the recent material culture has lost touch with this meaning given to time and numbers as archetypal.

REVIEW of The Harmonic Origins of the World

During the latter part of the twentieth century, three divergent speculative perspectives opened up on the ancients’ cosmology: astronomical, musical, and metrological. The astronomical perspective found its classic expression in von Dechend and de Santillana’s Hamlet’s Mill. The musical perspective was spelled out, almost single-handedly, by Ernest McClain, beginning with his work The Myth of Invariance. The metrological perspective diverged into the practical (descending from Alexander Thom’s surveying in the nineteenth century), and the more theoretical work associated perhaps most famously with John Michell’s View Over Atlantis.  

These three perspectives shared an awareness that number was an indispensable guide. Number is invariant; three is always three, and always one plus two. Mathematics is a realm of order, and recurrent patterns like the seasons or the harmonic scale call for mathematical descriptions precisely because such descriptions find stability in change. 

As scoffers and skeptics like to point out, however, where there is pattern-finding, there is also often unconscious wishful human ingenuity. Moreover, because the astronomical, musical, and metrological perspectives were carried on sometimes in isolation from one another, their results diverged, and an apparent incommensurability emerged: how could they all be true? This gave scoffers an argument that was, on the face of it, difficult to answer: why not none of them instead? Perhaps the real answer was the skeptical shrug: the ancient myth-tellers and builders of stone circles were acting more or less haphazardly or moved by very terrestrial, local, and historical concerns. Was this not the simplest explanation?

Richard Heath for a quarter of a century has been building towards a case diametrically opposed to this.  From the beginning he worked with Thom’s practical metrological results, bringing them into dialogue with Michell and John Neal; then later with a further expansion of astronomical results that far outpaced von Dechend and de Santillana’s speculations on the precession of equinoxes. In The Harmonic Origins of the World, Heath goes a further step, bringing McClain’s results into dialogue with his previous work. Heath provides ample demonstration that the results of these various perspectives can clearly be seen to not diverge from one another. Suddenly it is very plausible that they might indeed “all be true,” because they were never, for the ancients, separate at all. 

According to Heath, there exists in our solar system a harmony of extraordinary beauty among planetary cycles. This harmony was observed by ancient astronomers, and enshrined in megalithic monuments; it was transmitted in oral and literary culture via a musical grammar of proportion, easily reproducible across various cultures, which informs scripture and speculation (in McClain’s phrase) “from the Rg Veda to Plato.”  These assertions are of course controversial and deserve scrutiny. But they give the lie to any facile dismissal of ancient cosmological sophistication on the grounds that reconstructions are inconsistent. Astronomy, metrology (practical and theoretical), and music are all comprehensible under a single analogical system. They hang together in a coherent, living dialogue.

This book is the most recent chapter and the most comprehensive introduction to a vital adventure in ideas. It is a detailed account of how human beings on the ground could make sense of the sky by way of the octave. In it, rigor and common sense meet wonder and awe. 

Harmonic Earth Measures

The Size of the Earth’s Meridian

It appears the ancient world had unreasonably accurate knowledge of the size of the earth and its shape: Analysis of ancient monuments reveals an exact estimate for the circumference of the mean Earth, a spherical version of the Earth, un-deformed by it spinning once a day. Half of this circumference, the north-south meridian, was known to be about 12960 miles (5000 geographical Greek feet of 1.01376 ft), a number which (in those Greek units) is then 60^5 = 777,600,000 geographical Greek inches. One has to ask, how such numbers are to be found very accurately within a planet formed accidentally during the early solar system?


Figure 1 The Earth as a circular Equator and a spherical Mean Earth, whose half circumference approximates the non-circular distance between north and south poles

John Michell’s booklet on Jerusalem found (in its Addendum) that the walls of the Temple Mount, extended for the rebuilding of the Temple of Solomon, was a scaled down model of the mean-earth Meridian in its length. These walls are still 5068.8 feet long, which is the length of a Greek geographical mile. This unit of measure divides the meridian into 12960 parts, each a geographical Greek mile.

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God of Harmony Osiris in Egyptian Mice Tomb

Recently an “early Ptolomaic” tomb was discovered similar in themes to the famous Egyptian Books of the Dead (Middle Kingdom). Normally written on papyrus, they feature multiple tableau of Osiris judging the dead and other scenes. Osiris is a long lasting and perhaps supreme god whose cult was present throughout 3000 years of Dynastic history. I have previously interpreted his throne through drawings but, in the new tomb, he is painted on the walls at least twice and the design of his throne looks like layers of “eggs”. Below is one of the press pictures taken from the Guardian, and the headline is Mummified mice found in ‘beautiful, colourful’ Egyptian tomb.

Osiris could have been seen as a/the god of Harmony and below I explain why harmony may have been thought technically significant at the dawn of our earliest texts, then found in Sumeria 900 miles to the East. The reason I believe musical ratios were significant at the dawn of history because they had naturally emerged from measuring the lunar and solar year and comparing these with the time between loops of the outer planets Jupiter and Saturn.

Wallis Budge drawing in Osiris Judge of the Dead. We can see the lines but no detail and the bottom right is a vertical root 2 rectangle rather than a near square.
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