Use of Ad-Quadratum at Angkor Wat

The large temple complex of Angkor Wat ( photo: Chris Junker at flickr, CC BY-NC-ND 2.0 )

Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root
of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).

The diagonal of a square of unit size is sqrt(2), When a square is nested to just touch a larger square’s opposite sides, one can know the squares differ by sqrt(2)
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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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On the Harmonic Origins of the World

Sacred Number at the Heart of the World (an article in New Dawn 168)

After the ice receded, late Stone Age people developed the farming crucial to the development of cities in the Ancient Near East (ANE). On the Atlantic coast of Europe, they also developed a now-unfamiliar science involving horizon astronomy. Megalithic monuments were the tools they used for this, some still seen in the coastal regions of present day Spain, France, Britain and Ireland. Megalithic astronomy was an exact science and this conflicts with our main myth about our science: that ours is the only true science, founded through many historical prerequisites such as arithmetic and writing in the ancient near east (3000- 1200 BC) and theory-based reasoning in Classical Greece (circa 400-250 BC), to name but two. Unbeknownst to us, the first “historical period” in the near east was seeded by the exact sciences of the megalithic, such as the accurate measurement of counted lengths of time, developed by the prehistoric astronomers. With the megalithic methods came knowledge and discoveries, and one discovery was of the harmonic ratios between the planets and the Moon.

The idea that the planets were gods had been born before the ancient world, through the data of megalithic astronomy and this megalithic idea was the basis for the religious ideas of the East. Megalithic astronomy and Near Eastern religious and harmonic ideas have both been written out of our history of civilization, leaving us with enigmatic monuments and ill-defined religious mysteries. How this slighting of our real history happened is perhaps less important than our discovering again the purpose of the megalithic monuments and of those religious ideas that sprang from the discovery that the planets were harmonically related to life on Earth.

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