Counting astronomical time led to a key megalithic discovery; that our world and its skies reflect the structural properties of whole and transcendent numbers.

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- Recent PostsThe current theme is search: Golden Rectangles which led to finding them in search: St Peter’s Basilica in Rome and in the Umayyid Mosque in Damascus. But the Olmec heads have come to mind after a TV documentary, so that work from 2017 was completed, suggesting “what they mean”. I have started a theme on Music, part one giving overview of how music derived originally from an ancient world where pure … Continue reading “Sacred Numbers of a Living Planet”
- Origins of the Olmec/Maya Number SciencesABOVE: Stela C from Tres Zapotes roughly rebuilt by Ludovic Celle and based on a drawing by Miguel Covarrubias. Introduction The policy of archaeology regarding the Maya and their root progenitor the Olmec (1500 BCE onwards) is that its cultural innovations were made within Mexico alongside an agrarian revolution of the three sisters, namely squash, maize (“corn”), and climbing beans. This relationship of agriculture to civilizing skills then reads like the Neolithic revolution in … Continue reading “Origins of the Olmec/Maya Number Sciences”
- Developmental Roots below 6Square roots turn out to have a strange relationship to the fundaments of the world. The square root of 2, found as the diagonal of a unit square, and the square root of 3 of the diametric across a cube; these are the simplest expressions of two and three dimensions, in area and volume. This can be shown graphically as:
- Music, part 1: Ancient and ModernWe would know nothing of music were it not that somewhere, between the ear and our perceptions, what we actually hear (the differences between different frequencies of sound, that is, different tones) is heard as equivalent musical intervals (such as fifths, thirds, tones, semitones, etc), of the same size, even when the pitch range of the tones are different. This is not how musical strings work, where intervals of the same … Continue reading “Music, part 1: Ancient and Modern”
- Music of the Olmec HeadsSeventeen colossal carved heads are known, each made out of large basalt boulders. The heads shown here, from the city of San Lorenzo [1200-900 BCE], are a distinctive feature of the Olmec civilization of ancient Mesoamerica. In the absence of any evidence, they are thought to be portraits of individual Olmec rulers but here I propose the heads represented musical ratios connected to the ancient Dorian heptachord, natural to tuning by perfect fifths and fourths. In … Continue reading “Music of the Olmec Heads”
- Umayyad Mosque: Golden Rectangles from Squaresphoto above of Umayyad Mosque, Damascus by Bernard Gagnon for Wikipedia CC BY-SA 3.0. In previous articles on double squares and then St Peter’s Basilica, it became clear that squares and double squares have been embodied, within sacred buildings and art, because circles can then spawn golden rectangles from them. A golden rectangleA rectangle whose sides are in the ratio of the Golden MeanThe Golden Mean is that unique ratio {1.618034}, relative to ONE {1}, in which its square and reciprocal share the same fractional part {.618034}. It is associated with the synodic period of the planet Venus, which is 8/5 {1.6} of the practical year {365 days}, by approximation. It is a key proportion found in Greco-Roman and later "classical" architecture, and commonly encountered in the forms living bodies take. (1.618034) or a Fibonacci approximation to the Golden … Continue reading “Umayyad Mosque: Golden Rectangles from Squares”
- St Peter’s Basilica: A Golden Rectangle Extension to a SquareHAPPY NEW YEAR above: The Basilica plan at some stage gained a front extension using a golden rectangleA rectangle whose sides are in the ratio of the Golden Mean (1.618034) or a Fibonacci approximation to the Golden Mean.. below: Later Plan for St. Peter’s 16th–17th century. Anonymous. Metropolitan Museum. The question is whether the extension from a square was related the previous square design. The original square seems quite reworked but … Continue reading “St Peter’s Basilica: A Golden RectangleA rectangle whose sides are in the ratio of the Golden Mean (1.618034) or a Fibonacci approximation to the Golden Mean. Extension to a Square”
- St Peter’s Basilica: Starcut & Equal PerimeterIn Malcolm Stewart’s book on Sacred Geometry, his starcut diagram was applied to Raphael’s painting The School of Athens to create radiants to the people standing around the Athenium Lyceum. “If the starcut was the central geometrical determinant for Raphael’s formal depiction of classical philosophy” it was a “known authoritative device” or framework for geometrical understanding. Stewart found a potential antecedent for such a technique Donato Brahmante’s plan for St Peter’s … Continue reading “St Peter’s Basilica: Starcut & Equal Perimeter”
- Starcut Diagram: geometry to define tuningThis is a re-posting of an article thought lost, deriving in part from Malcolm Stewart’s Starcut Diagram. The long awaited 2nd edition Sacred Geometry of the Starcut Diagram has now been published by Inner Traditions. Before this, Ernest McClainAmerican Cryptologist and Pythagorean Musicologist who decoded Plato’s cryptic numerical ciphers in The Pythagorean Plato. The Myth of Invariance showed limiting numbers had been an ancient way of defining the onset of key … Continue reading “Starcut Diagram: geometry to define tuning”
- Recent PostsI am just EXPORING unit rectangles (also called multiple squares) ===>LOOK AHEAD: SEARCH “4-square” OR “triple-square” ===>LONG READ: “The Broch that Modelled the Earth” (see below) ===> SEARCH on “pi” (and so on) ===> BROWSE MENU “Tuning Theory” ===>READ SERIES on The Great Giza Pyramid _by clicking on links.
- Double squares: Venus and the Golden MeanThe humble square, with side length equal to one unit, is like the number one. It’s area is one square unit and, when we add another identical square to one side, the double squareA unit rectangle of 1 by 2, with important use for alignment (CarnacAn extensive megalithic complex in southern Brittany, western France, predating the British megalithic.), cosmology (Egypt) and tuning theory (Honnecourt Man). appears. Above right the Egyptian Djed column is shown within a double squareA unit rectangle of 1 by 2, with important use for alignment (Carnac), cosmology (Egypt) and tuning theory (Honnecourt Man).. The Djed is the rotating … Continue reading “Double squares: Venus and the Golden Mean”
- Double Square and the Golden Rectangleabove: Dan Palmateer wrote of this, “it just hit me that the conjunction of the circle to the golden rectangleA rectangle whose sides are in the ratio of the Golden Mean (1.618034) or a Fibonacci approximation to the Golden Mean. existed.” Here we will continue in the mode of a lesson in Geometry where what is grasped intuitively has to have reason for it to be true. It occurred to me … Continue reading “Double Square and the Golden Rectangle”
- Hounds & Jackals as Venus CounterThe Petrie Museum has a game called Hounds & Jackals or 58 holes, from Egypt’s Middle Kingdom and widely found elsewhere, in the ancient world. Two players had a set of sharp ended sticks with animal heads, which sat in each of the 29 + 29 = 58 holes. The top hole is larger (as with the Cretan 34-hole circular kernos, at Malia in Crete). Cretan 34-hole Kernos One can see … Continue reading “Hounds & Jackals as Venus Counter”
- Eleven Questions on Sacred NumbersIn 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 … Continue reading “Eleven Questions on Sacred Numbers”
- Musing Mystical Review: Language of the AngelsI came across a very good review of my book Sacred Geometry: Language of the Angels in which the reviewer found the experience of reading over a month. She also told me how I might improve my handling of numbers. Many thanks for that since I will soon be entering the production phase of a further book out late 23, early 24. Reading this book has made me grapple with concepts … Continue reading “Musing Mystical Review: Language of the Angels”
- Story of Three Similar Trianglesfirst published on 24 May 2012, Figure 1 Robin Heath’s original set of three right angled triangles that exploited the 3:2 points to make intermediate hypotenuses so as to achieve numerically accurate time lengths in units of lunar or solar months and lunar orbits. Interpreting Lochmariaquer in 2012, an early discovery was of a near-Pythagorean triangle with sides 18, 19 and 6. This year (2018) I found that triangle as between the … Continue reading “Story of Three Similar Triangles”
- On the Harmonic Origins of the WorldDoes the solar system function as a musical instrument giving rise to intelligent life, civilization and culture on our planet? This 2018 article in New Dawn introduced readers to the lost science of the megalithic – how our ancestors discovered the special ratios and musical harmony in the sky which gave birth to religion and cosmology. The musical harmonies were the subject of my book released that year, called The Harmonic … Continue reading “On the Harmonic Origins of the World”
- Parthenon as a New Model of the MeridianThis was published as The GeodeticUnits of measures and monumental measurements relating to the numerical definition of the shape of the Earth by the late megalithic. And Musicological Significance Of The Shorter Side Length Of The Parthenon As Hekatompedon Or ‘Hundred-Footer’ in Music and Deep Memory: Speculations in ancient mathematics, tuning, and tradition, in memoriam Ernest G. McClain. Edited by Bryan Carr and Richard Dumbrill. pub: Lulu. photo: Steve Swayne for … Continue reading “Parthenon as a New Model of the Meridian”
- The Approximation of π on Earthπ is a transcendental ratio existing between a diameter/ radius and circumference of a circle. A circle is an expression of eternity in that the circumference, if travelled upon, repeats eternally. The earths shape would be circular if the planet did not spin. Only the equator is now circular and enlarged, whilst the north and south poles have a shrunken radius and, in pre-history, the shape of the earth’s Meridian between … Continue reading “The Approximation of π on Earth”
- π and the Megalithic YardThe surveyor of megalithic monuments in Britain, Alexander ThomScottish engineer 1894-1985. Discovered, through surveying, that Britain’s megalithic circles expressed astronomy using exact measures, geometrical forms and, where possible, whole numbers. (1894 – 1985), thought the builders had a single measure called the Megalithic YardAny unit of length 2.7-2.73 feet long, after Alexander ThomScottish engineer 1894-1985. Discovered, through surveying, that Britain's megalithic circles expressed astronomy using exact measures, geometrical forms and, where possible, whole numbers. discovered 2.72 ft and 2.722 ft as units within the geometry within the megalithic monuments of Britain and … Continue reading “π and the Megalithic Yard”

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