Chartres 1: the cosmic coding of its towers in height

The lunar crescent atop the “moon” tower’s cross.

Chartres, in north-west France, is a very special version of the Gothic transcept cathedral design. Having burnt down more than once, due to wooden ceilings, its reconstruction over many building seasons and different masonic teams, as funds permitted, would have needed strong organizing ideas to inform the work (as per Master Masons of Chartres by John James).

As shown below, Chartres main towers are unequal in height and the “western” facade itself does not align to east-west, as normal Christian churches do. The left tower is also higher than the right tower and, it has been said, the left represents the Sun and the right the Moon. The height of the left tower, to its globe below its cross, is indeed the solar year of 365 days in feet. But the height of the shorter right tower, to its own globe, is not the 354.367 days of the lunar year (of 12 months); rather, it is the top of its cross, sporting a crescent moon suggesting it is a moon tower, that is 354 and a third feet high.

The cosmic time coding of the two towers as solar year->lunar year between the globe’s height (on left in red) and the top of the cross (on right in blue). But the left tower also indicates the Saturn synod of 378 days to the top of its cross. The for-square rectangle, geometrically relating the solar (diagonal) and lunar years, is shown.

That is, the height of the lunar year in feet, from the same starting point as the solar tower’s height as the solar year, the lunar year would be to the top of the lunar cross, where the crescent is attached, and not to its globe. There is then a reasonable connection between the solar and lunar years and the two towers. However, it is also interesting to see the number of days, as feet, of the left tower to its own cross. It is exactly 378 feet, the synodic period of Saturn in days. Readers of my books and this site will remember that the ratio between the lunar year and Saturn synod is exactly 16/15: a musical semitone within the ancient tuning system called Just intonation.

This arrangement suggests Chartres was built to be a time-factored monument, which may be why the cathedral was aligned to midsummer sunrise (which was a megalithic norm) rather than being aligned east-west. Built on top of a solitary promontory, horizon events would have been clear across the flat fertile plains.

NEXT: the harmony in its towers

Interpreting Chartres
  1. the cosmic coding of its towers in height
  2. the harmony in its towers
  3. design of the west façade

Yet to come: the design of the Rose Window.

Astronomy 4: The Planetary Matrix

The re-discovery of the ancient planetary matrix, seen through three my three books: Matrix of Creation, Harmonic Origins of the World and Sacred Geometry: Language of the Angels.

Harmonic Origins of the World inserted the astronomical observations of my previous books into an ancient harmonic matrix, alluded to using the sacred numbers found in many religious stories and the works of Plato, who might have been the savior of what Pythagoras had garnered from ancient mystery centers circa. 600 BC. According to the late Ernest G. McClain*, Plato’s harmonic technology had been widely practiced in the Ancient Near East so that, to the initiated, the stories were technical whilst, to the general population, they were entertaining and uplifting stories, set within eternity. Ancient prose narratives and poetic allusions conserved the ancient knowledge. Before the invention of phonetic writing in Classical Greece, spoken (oral) stories were performed in public venues. Archaic stories such as those attributed to Homer and Hesiod, gave rise to the Greek theatres and stepped agoras of towns. Special people called rhapsodes animated epic stories of all sorts and some have survived through their being written down. At the same time, alongside this transition to genuine literacy, new types of sacred buildings and spaces emerged, these also carrying the sacred numbers and measures of the megalithic to Classical Greece, Rome, Byzantium and elsewhere, including India and China.

* American musicologist and writer, in the 1970s, of The Pythagorean Plato and The Myth of Invariance. website

Work towards a full harmonic matrix for the planets

In my first book (Matrix of Creation,) I had not yet assimilated McClain’s books, but had identified the musical intervals between the lunar year and the geocentric periodicities of the outer planets. To understand what was behind the multiple numerical relationships within the geocentric world, I started to draw out networks of those periods (matrix diagrams) looking at all the relationships (or interval ratios) between them. This revealed common denominators and multiples which linked the time periods through small whole numbers. For example, the 9/8 relationship of Jupiter’s synod to the lunar year could be more easily grasped in a diagram to reveal a structural picture, visualized as a “matrix diagram” (see figure 1).

Figure 1 Matrix Diagram of Jupiter and the Moon. figure 9.5 of Matrix of Creation, p117.

One can see the common unit of 1.5 lunar months, at the base of the diagram, and a symmetrical period at the apex lasting 108 lunar months (9 lunar years referencing the Maya supplemental glyphs). I re-discovered the Lambda diagram of Plato (figure 8.7), and even stumbled upon the higher register (figure 2) of the Mexican Quetzalcoatl (figure 8.1) made up of {Mercury, the eclipse year, Tzolkin, Mars, Venus}, Venus also being called the feathered serpent. These periodicities are of adjacent musical fifths (ratio 3/2), which would eventually be shown as connected to that of the outer planets, using McClain’s harmonic technology, in my 5th book, Harmonic Origins of the World (see figure 3).

Figure 2 Incomplete discovery of the Maya Quetzalcoatl, in fig. 8.1 of Matrix of Creation. I had not noticed that 390 days, times 2, is 780 which is the synod of Mars! This is in fact 41.8949 Node Days, which might be significant.

Also called the flying serpent in Pharaonic Egypt, this set of musical fifths, apparently undocumented in the near east, was part of the Mexican mysteries of the Olmec and Maya civilizations (1500 BC to 800 AD). The serpent is flying harmonically, 125/128 above the inner planets – for example, the eclipse season is 125/128 above the lunar year: 354.367 days × 125/128 = 346 days, requiring McClain’s harmonic matrices to integrate these two serpents, in Harmonic Origins of the World (figure 9.3).

Figure 3 The two harmonic serpents of “Heaven” and “Earth”

By my 6th book, Sacred Geometry: Language of the Angels, I had realized that the numerical design surrounding our “living planet” sits, is a secondary creation – created after the solar system, yet it was discovered first, before the heliocentric, exactly because the megalithic observed the planets from the Earth. I therefore propose an alternative timeline for the ancient mysteries. Instead of proposing a progenitor civilization such as Atlantis, as per Plato’s Timaeus: of an island destroyed by vulcanism. https://en.wikipedia.org/wiki/Timaeus_(dialogue)

My working hypothesis is that Atlantis and similar precursor solutions, simply “kick the can down the road” into an as-yet-poorly-charted prehistory for which there is no strong evidence. In contrast, the sky astronomy and earth measures found in use by the megalithic can only be the product of that singular megalithic culture. There is clear evidence of megalithic monuments recording an understanding of the cosmos then found in the ancient mysteries. Megalithic evidence can show the geocentric world view as being their achievement, based upon the numbers they found using geocentric observations, counting lengths of time, using horizon events and the mathematical properties of simple geometries.

Geocentrism was the current world view until it was superceded, by the Copernican heliocentric view. The new solar system, held soon found to be held together by naturals gravitational forces between the large masses, forces discovered by Isaac Newton. The subsequent primacy of heliocentrism, which started 500 years ago, caused humanity to lose contact with the geocentric model of the world, which had the planets in the same order relating the two serpents of outer and inner planets. All references to an older and original form of astronomy, based upon numerical time and forged by the megalithic, was dislocated and obscured by the heliocentric physical science and astronomy of the modern day – which still knows nothing of the geocentrically order that surrounds us.

Figure 4 The Geocentric Model by 1660

The geocentric model entered Greek astronomy and philosophy at an early point; it can be found in pre-Socratic philosophy … In the 4th century BC, two influential Greek philosophers, Plato and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere, stationary at the center of the universe.

Wikipedia: “Geocentric model” https://en.wikipedia.org/wiki/Geocentric_model

Primacy of low whole numbers

  1. Preface
  2. Primacy of low whole numbers
  3. Why numbers manifest living planets
  4. Numbers, Constants and Phenomenology
  5. Phenomenology as an Act of Will

Please enjoy the text below which is ©2023 Richard Heath: all rights reserved.

What we call numbers start from one, and from this beginning all that is to follow in larger numbers is prefigured in each larger number. And yet, this prefigurement, in the extensive sense {1 2 3 4 5 6 7 etc.}, is completely invisible to our customary modern usage for numbers, as functional representations of quantity. That is, as the numbers are created one after another, from one {1}, a qualitative side of number is revealed that is structural in the sense of how one, or any later number, can be divided by another number to form a ratio. The early Egyptian approach was to add a series of unitary ratios to make up a vulgar* but rational fraction. This was, for them, already a religious observance of all numbers emerging from unity {1}.  The number zero {0} in current use represents the absence of a number which is a circle boundary with nothing inside. The circle manifesting {2} from a center {1} becomes the many {3 4 5 6 7 …}.

The number one manifests geometrically as the point (Skt “bindu”) but in potential it is the cosmological centre of later geometries, the unit from which all is measured and, in particular, the circle at infinity.

Two: Potential spaces

From one {1} springs two {2}, to which we owe all forms of doubling as reproduction without sexual division, called “barren” by Plato, yet giving the possibilities of complex worlds of different scale, in terms of their limiting number. This is the first true number of Creation which gives the quality of polarity between the two halves of (as yet) nothing, halves of a world that will create the beginnings of an everything. Super dense, as an initial Form of forms, all things will come to rotate around this Axis of axes*. (Axes, when pronounced with a long e, is the plural form of the word axis, meaning imaginary lines that run through the middles of things. The word axe is derived from the Old English word æces, the axe which divides into two. ) This is the birth of duality, as with the centre and circumference of a circle or positive and negative (opposite) charge, and the medium of the wave or vibration, which gave birth to dynamic systems, such as planetary rotation of an axis or an orbit.

When number was incarnated in our own planetary creation, it was Saturn who visibly delimited the outer limits of the visible planets. His name is close to Seth and Satan (as the necessary adversary of the heroic Horus) and he was seen as limiting unbounded growth within existence. Saturn expresses 5 synods of the planet Saturn in 64 {26} lunar months (but this is to jump in numbers, though not too far, to the planetary double octave {24 48 96} lunar months. Sixty-four governs the “eye of Horus”: a government deriving from the mythical conflict between the god Horus with his rival Set; in the context of two eyes, here the right eye was torn out but then restored, to then see the role of two within the creation, in the “afterlife”.

Figure 1 The Egyptian icon of the Eye of Horus as the components used to represent vulgar fraction as a series of powers of two.

https://en.wikipedia.org/wiki/Eye_of_Horus: It derives from the mythical conflict between the god Horus with his rival Set, in which Set tore out or destroyed one or both of Horus’s eyes and the eye was subsequently healed or returned to Horus with the assistance of another deity, such as Thoth.

The Moon finds an exact reunion with the earth day after exactly 945 days, which equal 32 lunar months of 945/32 (29. 53125) days, very close to the actual lunar month of 29.53059, being effectively exact as 57 seconds different.

While the number two can, in being divided, create new areas of interaction (including cosmic octaves), its mere extension {2 4 8 16 32 64 128 …) forms only a backbone of potentialities, these then (see later page) borrowed by higher limiting numbers such as 720, a number containing favourable numerical factors for the creation an ideal “family” of limits, metaphorically presented by Adam and the Patriarchs of the Bible.

Figure 2 The vision of the Godhead asleep on a pre-creational ocean (of his sweat) attended by the Goddess until he awakes for a new creation.

The number {2} as dyad manifests as the geometry of the line. The line {2} from a center {1} as a rotational vector becomes the geometry of the circle.

Three and four: Actualization

The actual creation has a different planetary symbol, the equilateral triangle with three sides, seen also as the capital Greek delta, whose value is 4 because the planetary system is an Activity involving forces. These numbers are reconciled as 3 x 4 which equals 12, the number of Autocracy * and balanced action. We are told in myth that Jupiter’s twelvefold nature was “the receiving of the measures” from Saturn, as 4. Jupiter is the planetary demiurge which Plato describes carving out the World Soul “octave” {6 8 9 12}, using ratios involving Three, the cubit and its reciprocal {3/2 4/3} * (Timaeus). Only when we reach the lunar octave {24 27 30 32 36 40 45 48} will the diatonic scale of eight notes emerge, the first and last being the same note, doubled.

The first true doubling {2 3 4}, between 2 and its square, holds the first type of penetration of the octave, by Three {3}. With three, the Demiurge forms his World Soul using intervals involving only Two and Three {3/2 4/3}, which can create the fifth and fourth notes (“dominant and subdominant”) of an octave.

The number {3} gives form to the first geometry of area, manifest in the triangle which, given a right angle, becomes trigonometrical, as the functional mediation between the line and the circle.

The number four connects the relatedness of the Triad (3) with the existentially actual to provide an engine in which Form can become Substance through an intermediate pair of terms that fulfill the gap {2} between form and the actual situation. One could say this is the first instance of filling the octave with tones {8}, intermediate between 2 and 8. Four is the first square number which in geometry is called square as an area equal to 4 has sides equal to 2

Five: Vitality and Life

Coming next, Five {5} will also be able to divide the coming “octave” {3 4 5 6} in a superior way than three and two can alone, by redefining a new tone {10/9} for Just intonation and a corresponding semitone {16/15}, these cancelling the excessive powers of three produced by tuning only with three {3}, called the cycle of fifths, which used successive fifths and its inverse{3/2 4/3} because the ear can best define the larger musical intervals. The octave between three and six defines the framework of Just intonation where three intervals span the octave {4/3 5/4 6/5}, summing to doubling {2}.*

*This was probably referred to as “the three strides of Vishnu”, Trivikrama (‘having three steps’) being one of his 1,000 names.

The planet Venus brings a new type of harmony, which is also the sixth note {8/5 (= 1.6)} of a diatonic octave (see this page) since her synod of 584 days is 8/5 of the practical year of 365 days. The Fibonacci series allows whole number approximation to the Golden Mean {φ} between adjacent members obtained as being the sum of the two preceding numbers {0 1 1 2 3 5 8 13 21 34 55 …} unlike the ordinal set {1 2 3 4 5 6 7 8 9 …}, the latter instead obtained by more simply adding one more unit {1} to the preceding number. Unlike the musical tone and semitone of Jupiter and Saturn relative to the lunar year, Venus is resonant with the Earth’s orbital period of 365 whole days, and this type of orbital resonance, with each other, is mutually attractive, providing the lowest and most stable energy between the two planets. The inner orbital diameter (semi major axis) divided by the difference in orbital diameters, equals 2.618, or phi squared {φ2}*. (See later page for more on their orbits) Structures of growth, based upon Fibonacci ratios, are commonly found within living bodies, which must achieve this algorithm in which their present size added to their digestion of previously eaten food results in the sum of the two.

Figure The Fibonacci series in two dimensions are common forms of living growth.

The Venus synod will be seen to fit inside the octaves of the Moon because 20 lunar months is 590.6 days which is less than the synodic comma {81/80} of her 583.92 day synod*.

*The synodic comma is the exact ratio connecting Pythagorean and Just versions of the same note. One of the Indian temple designs is a nine-by-nine square grid which makes the number of equal-sized sub-squares {81) divided by the count where the central square is not counted gives the ratio of the synodic comma {81/80}.

Music: Child of the First Six Numbers

The larger intervals of numerically larger octave doublings are in this way foreordained in the first six numbers {1 2 3 4 5 6} and their relative size to each other, are five musical intervals {2/1 3/2 4/3 5/4 6/5}.  Doubling has led to the pillars of Plato’s world soul {3/2 4/3} and three when doubled {3 4 5 6} has led to the three strides {4/3 5/4 6/5}, both sets summing to Two {2}.

The first six numbers, creating all the large tones of musical harmony, punctuated by Seven.

Between the five musical intervals, the tones and semitones of Just intonation are to be found {9/8 10/9 16/15} so that, as a tuning system, the Just system leads automatically to the tones and semitone of the seven modal scales, in both melodic and polyphonic harmony.

When the World Soul {6 8 9 12} is twice doubled {24 48} and doubled again {48 96}, the two octaves express the world numbers of Gurdjieff {24 48 96}, but now these numbers correspond to lunar months and, as with music when heard, all of the possible intervals are compresent in the instrument, the Moon illuminated by the Sun, since one can count from any lunar month, over any number of lunar months, to achieve any of the larger and smaller intervals between these octaves. And it is now true that the three principle planets of Jupiter, Saturn and Venus are present at the second, fourth and sixth notes, each of these relevant to Gurdjieff’s theory of octaves as stated by him in Russia, and his cosmic epic Beelzebub’s Tales. And J G Bennett continued to build on what Gurdjieff had expressed, without knowledge of the astronomical references, to populate his own Dramatic Universe, in 4 volumes and many compendia (see Bibliography). Of particular importance is how human beings figure within the cosmic vision, without which a planetary cosmos involving consciousness and creativity would be meaningless. If one resists the modern functional view of cosmogenesis: music, or other forms of harmony, can be seen to redeem the creation of a world like ours, through the short cuts numerical systems naturally provide for us, through a gravitational environment that can provide these.

Coming soon: Why numbers manifest living planets

Numbers of a Living Planet: Preface

The image above is Kurma avatara of Vishnu, below Mount Mandara, with Vasuki wrapped around it, during Samudra Manthana, the churning of the ocean of milk. ca 1870. Wikipedia.

  1. Preface
  2. Primacy of low whole numbers
  3. Why numbers manifest living planets
  4. Numbers, Constants and Phenomenology
  5. Phenomenology as an Act of Will

Please enjoy the text below which is ©2023 Richard Heath: all rights reserved.

It is impossible to talk of a creation outside of the time and space of Existence, though from it, other dimensions can be inferred such as an “Eternity” visible in the invariances of numbers and structures. It is this higher dimensionality that leads to

  1. The recurrence of celestial time periods,
  2. The mental powers to recognise manifested patterns,
  3. The use of spatial geometries of alignment,
  4. The numerate counting of time,
  5. A phenomenology which is neither factual nor imaginary.

The quantification and qualification of Existence, adequately conducted, reveals harmonious structures within time and space, especially in the spacetime of our planetary system, when this system is as seen from our planet. The harmonious nature of our planetary system helped the late stone age to develop a large numerical and geometrical model of the world through counting astronomical recurrences. This model, which shaped ancient texts, implies that solar systems may have an inherent intelligence which makes them harmonious.

Harmony in a planetary system must therefore employ invariances already present in the number field, by exploiting the recurrent orbital interactions between planets and large Moons, this in a connected set of three-body problems. Before our exact sciences and instruments, prehistoric naked-eye astronomers could understand the planetary world by counting the duration of planetary time cycles: the subject my books explore. Through counted lengths of time, the megalithic age came to understand the invariances of the number field and so evolve an early and distinct type of numeracy. This numeracy lived on as the basis for the ancient Mysteries of the early civilizations, embodied in their Temples and in the Pythagorean approach to ordinal numbers and geometries, expressing the “number field” in two or three dimensions, areas and volumes. (see Sacred Geometry: Language of the Angels for an introduction to this)

That is, this early human numeracy naturally manifests within the maths governing rotational systems, this involving key transcendental* constants such as π, these regulating what is actually possible, mathematically, within dynamic planetary systems that are gravitational attractors of each other: these constants include pi {π}, √-1 {i}, e, and phi {φ}.  The first three { π, √-1, e} are surprisingly well-organized rotational frameworks making the behaviour of vectors relatively simple using geometry. For example, the lunar year of twelve lunar months has become strongly resonant with the two outer gas giants, Jupiter and Saturn. The Golden Mean (or Phi {φ})1 can be approximated by orbital ratios between planets through exploiting the Fibonacci number series2, most visibly in the orbital recurrence of Venus and the Earth, seen in the 8/5 {1.6} relationship of its synod* to the solar year. Phi φ is also expressed in living forms of growth, since growth is often based upon the present size of a living body and what it has previously eaten.  Fibonacci ratios are ideally suited to creating the “strange attractors” which can create stable patterns out of otherwise chaotic orbital interactions.

1 My use of curly braces is borrowed from a stricter world of set notation. It offers an ability to place groups of numbers, symbols and other non-grammatical element next to their grammatical context.

2 The series reinvented by Fibonacci uses addition of two previous number to create the next number. His version of that algorithm is {0 1 1 2 3 5 8 13 21 34 55 and so on}. These numbers are found within natural form of life, where such numbers can be generated from two previous states or when two counter rotating spirals of seeds will fill the surface of an egg shape with maximum packing. More on this later.

Through universal mathematical laws and constants, rotational and recurrent systems will effectively provide numerical shortcuts* (J.G. Bennett’s null-vectors) expressing Musical or Fibonacci ratios, and without those ratios being available, relationships within existence would be more complex, less synchronous, and truly accidental. Harmonic shortcuts have therefore given the planetary world a simplified mathematics when viewed from the surface of the earth, within the geocentric pattern of time. This synchronicity provided the stone age with a path towards a direct numerical understanding of time through phenomena (that is, a direct visual and countable phenomenology).

In this way, the megalithic cultures of prehistory found that the geocentric planetary system expressed numerical invariances (these already within the number field itself) thus making the time world of the sky unusually harmonious and intelligible. This contrasts with the now-popular modern notion that, while the solar system is a large and impressive structure, its origins come only from the mathematical laws of physics, these forever operating in a mechanical way. That is, the modern way-of-seeing planetary time is heliocentric and causal and this has hidden an ancient view, gained through the megalithic study of the phenomena in the sky using megaliths as large instruments with sightlines to the horizon events of sun and moon, to simply count of time-as-length and, evolve a very basic numeracy based upon numerical lengths (a metrology) and triangular geometries to compare lengths.

Megalithic methods employed the properties of circles, ellipses, squares, rectangles, and right triangles before the analytical geometry of Euclid, Greek math, or ancient near-eastern arithmetic. This was only possible because key parts of the mathematics of complex numbers, for example, are directly visible in the form of the right triangle and unit circle; as the natural form of two vectors: a length at a given angle (or direction) and another length at different angle gives access to ratios. A right triangle can therefore express two vectors of different length and differential angle, and this applies to a pair of average angular rates in the sky, without knowing the math or physics behind it all. If the two vectors are day-counts of time, then the right triangle can study their relationship in a very exact way. Such a triangle may also have been seen as the rectangle that encloses it, making the diagonal (vector), the hypotenuse of the triangular view.

The properties of the imaginary constant i (√-1) represents, through its properties, the rotation of a vector through 90 degrees. It is this that gives the right-angled triangle its trigonometric capacity to represent the relativity of two vector lengths. My early schoolroom discoveries concerning vectors in applied math classes, that right triangles can represent vectors of speed for example, was without any knowledge of the mathematical theory of vectors. This geometry enabled prehistorical astronomy to study the average planetary periods as vectors. That is, rotational vectors enabled the sky to be directly “read”, from the surface of the third planet, through simple day-counting, comparing counts with right triangles, and forming circular geometries of alignment to astronomical events found on the horizon; all without any of our later astronomical instrumentation, maths, or knowledge of physics.

Physics has not yet explained how the time constants between the planets came into a harmonious configuration, because it is unaware that this is the case. The mathematization of Nature, since the Renaissance, has hidden the harmonious view of geocentric planets and all preceding myths, cosmologies and beliefs were swept aside by the heliocentric world view (see Tragic Loss of Geocentric Arts and Sciences, also C.S. Lewis’s The Discarded Image).

The modern approach then emerged, of blind forces, physical laws and dynamic calculations. That is, while the simplifying power of universal constants is fully recognized by modern science (these having made maths simpler) the idea that these simplifications came to be directly reflected in the sky implies some kind of design and hence an intelligence associated with planetary formation.

Furthermore, modern way of seeing things cannot imagine that the megalithic could conducted an astronomy of vectors (using geometrical methods while not understanding why they worked) and that this empowered a simple but effective type of astronomy, without our mathematical or technical knowledge. This is an anachronistic procedural heresy for the history of Science and also for the present model of history, where science for us is the only science possible, evolving out of near-eastern civilization after the stone age ended.

Foundational myths of modern civilization are threatened by the notion that the world is somewhat designed by a higher intelligence. Until these subconscious conflicts of interest are overcome, prehistory will remain the prisoner of modernity where mysteries remain mysteries because we don’t wish to understand.

2. Primacy of low Whole Numbers

Tragic Loss of the Geocentric Arts and Sciences

This was an article for New Dawn.

The geocentric planetary model on the left was displaced by a visually simple heliocentric model, of how the solar system would look from a distance rather than from the Earth.

About 400 years ago, the move to the Heliocentric Model of the “solar system” swept away the worldview upon which human spirituality had been based for at least 5000 years. We can say that all spiritual literature was based upon the previous cosmological norms of the Geocentric Model. It is generally not realized that the Koran, New Testament, Buddhist, Tibetan, Hindu, Pythagorean, Platonic, yogic, shamanistic, and many other primary and secondary texts including Shakespeare, alluded to the details of a geocentric cosmology: a foundational framework often debunked as inaccurate yet, the geocentric was a valid ordering of the planetary cosmos. The religious values within the model were overtaken by the new scientific norm, which was inherently materialistic in its study of physical laws and processes, these universal throughout an ever-expanding vision of the universe, through observations and experiments in physics and chemistry deducing new types of knowledge. And mankind would soon use these new laws and discoveries to exploit the universe itself.

This transition from geocentrism to heliocentrism came against a backdrop of Islamic and Christian suppression of scientific discoveries, which represented a growing desire since Classical times for human reason to escape the shackles of the oral and then bookish traditions, which broadcast their own messages as if final, to be obeyed on pain of death or at least social exclusion. In this war between religious theocracies and an emerging modern science no quarter was given to the geocentric model, even though all previous traditional thought the world over relied on it. A cleric called Copernicus suggested that everything must revolve around the Sun and not the Earth. the geocentric past was soon ditched, like the baby with the bathwater and the whole of spiritual literature lost much of its foundational imagery. Science had displaced the ancient mythologies due to its own struggle to understand the physical world. The “natural philosophers” eliminated any mysterious causes for why things happened by discovering physical causes for all phenomena, these natural and real through physical laws without any gods or spirits being involved.

Pride before a Fall

Modern science might well have reminded monotheistic clerics of Adam, the Bible’s first man eating from the forbidden fruit, plucked by Eve from the tree of the knowledge of good and evil, which grew at the centre of a geocentric Eden. Like Adam, the scientists would then have the “knowledge of good and evil” and become themselves “as gods”, and this has become true for technology. The improving standards of living for many people in the West is taken to mean the clerics were wrong to suppress science, yet humanity has fulfilled the biblical prophecy concerning Adam: the scientists, industrialists and financiers have exactly become like gods, to “know good and evil”. The spiritual locale was further abstracted from being in the heavens, by removing its foundational geocentric model; simultaneously giving science an over-realised view of a purely physical earth and cosmos.

Science gave humanity powers over the natural world, leading to explosion in the world population based upon an industrial revolution that exploited the planet, its habitats and resources, on an ever-growing rate and scale. In the Iron Age, such a tyranny could only operate on a regional scale, but science-led societies now developed a global reach and an infinite franchise, with business models whose scope was the whole globe, to advertise and consume resources as products and services. In this sense then, the clerics were right: for though the clerics might have themselves behaved like repressive iron age tyrants towards science, they lacked the technologies that could ruin the Biosphere. Science now recognises the exploitation of the Earth, its biosphere, and its people to be a major problem, forecast to grow worse before better, and already more than bad enough. But economic growth is inherently unsustainable and so, what kind of a society will it be that does not depend upon growth to fix its debts? A geocentric society?

The ancient world could and did warn what sort of an archetypal trajectory the scientists would initiate for, like Icarus, the technologists would take humanity too close to the Sun. The wax fixing the wings of wide-bodied multinationals would melt and they would suffer the fate also of Phaethon, son of Helios the Sun, whose chariot he recklessly drove for a day. Losing control, Phaethan caused havoc in the skies and on the earth, his erratic pathway being visible as the deviation of the galaxy from the sun’s path. The Earth goddess Gaia made urgent appeal to Jupiter, who hurled his thunderbolt upon the precocious lad who fell into the eternal river Eridanus.

The Origins of Geocentrism

About twenty years ago, I found simple numbers between planetary periods seen from Earth. This caused me to drop some modern assumptions about which present the ancient view of the cosmos as inferior. For example, modern history is a linear view of the past with a fixed beginning in the earliest middle eastern cities such as Sumer and Babylon (3000 to 2000 BCE). Cities make a happy starting point since we live in cities ourselves and writing arose with the early cities, providing historical records.

In 2002, Matrix of Creation published a different, cyclic view of time, where the complexity of the modern sun-centred system became simple. Looked at without modern bias and, using a scientific calculator, a geocentric astronomy of average periods identified two unexpected baselines: the practical year of 365 days (the Earth) and the lunar year of 354.375 days (the Moon). It was this geocentric simplicity that had made astronomy possible for the late Stone Age (or “neolithic”). On the western seaboard of Europe, the megalith astronomers developed the first geocentric worldview which, I believe, was then inherited by the civilizations of the ancient near eastern cities.

Several astronomical innovations were required to carry out this form of horizon astronomy. For example, without modern numeracy they had to store day counts as lengths, one inch to the day[1]. The primary innovations were,

  1. Long sightlines were established to key celestial events on the horizon, such as the sun or moon, rising or setting.
  2. The number of days were counted between horizon events, to quantify each periodicity as a measured length between points or as a rope.
  3. Different celestial periods could then be compared employing simple geometries like the triangle, circle and square, revealing the ratios between celestial periods.[2]

Musical Ratios and the Giant Planets

The lunar year of 354 ⅝ days manifests the principle of musical harmony between itself and the outer planets. At 398.88 days, the synod of Jupiter is 9/8 of the lunar year, Saturn (at 378.09 days) is 16/15 of the lunar year, while Uranus (at 369.66 days) is 25/24 of the lunar year. In the pure-tone music of the ancient world, these are the three fundamental intervals called the Pythagorean whole tone, the Just semitone, and the chromatic semitone: intervals essential to the formation of musical scales.

In 2018, Harmonic Origins of the World was able to locate these outer planetary ratios within an ancient style of harmonic matrix, implied by some of Plato’s least understood dialogues. Centuries before, Pythagoras would have learnt of such harmonic matrices, from the ancient mystery centres of his day. Harmonic matrices and tables of numbers appear to have been used by initiates of the Ancient Near East[3] to give the stories of ancient texts such as the Bible a deeper subtext beneath. Set within eternity, stories could be entertaining and uplifting while those initiated in the mysteries, could find knowledge relating to harmonic tuning and the planetary world: Tuning theory and its special numbers had come to inhabit ancient texts because the outer planets, surrounding Earth expressed the three most fundamental musical ratios, the tones and semitones found within octave scales.

Geocentric knowledge can be found conserved within ancient narratives because, before writing arose, there was an oral tradition which had to be remembered until eventually written down. The ancient mysteries arose to connect the human world of Existence to the cosmic world of Eternity, visible from the Earth. Myths of gods, heros and mortals were but a natural reflection of the harmonic worlds of the heavens into the cultural life of the people, like the moon reflected in a lake.

Sacred Geometry: Language of the Angels illustrates how new types of sacred building and space emerged, still carrying the geocentric model, its numbers and measures into Classical Greece, Rome, Byzantium and elsewhere, including India, China and the Americas. For example, the Parthenon design (figure 1) incorporates the harmony of the outer planets with the lunar year and Athena (the patriarchal moon goddess) had the same root of 45 as Adam did in the Bible’s creation story written about three centuries before.

Figure 1. The Parthenon as a musical instrument model of the Moon (960) and the outer planets (Jupiter is 1080 and Saturn is 1024.) [figure 5.16 of Sacred Geometry: Language of the Angels where many further examples are to be found.]

Fibonacci Ratios and the Terrestrial Planets

The inner planets exploit the special properties of Fibonacci numbers as approximations to the Golden Mean. The practical year of 365 days can be divided into 5 parts of 73 days, and the synodic period of Venus is then 8 parts of 73 days or 584 days. The two numbers 5 and 8 are part of the Fibonacci series {0 1 1 2 3 5 8 13 21 34 etc. } in which the next number is the sum of the two previous numbers. 8/5 is 1.6 in our notation and 73 days x 1.6 equals 116.8 days (584/5 days)[4]. This reveals the inner solar system to be a realm in which, proximity to the Sun leads to numerical relationships informed by the Fibonacci numbers – when seen from the Earth.

The synod of Mars (Ares), the outer terrestrial planet, also relates to the practical year as two semitones of 16/15, a harmonic ratio perhaps because of his proximity to the gas giant Jupiter (Zeus), who is his mythological father.

Figure 2 (left) The geocentric pentacle of 5 successive Venus synods in 8 years of 365 days, within the Zodiac and (right) the ubiquity of the golden mean within the geometry of the pentacle. Such geometrical ratios would become emblematic and sacred to the sky.

The golden mean (1.618034…) is a unique but natural short-circuit within the fractional number field: its reciprocal (equal to 0.618) is equivalent to subtraction by one while its square (equal to 2.618) is equivalent to addition by one. The Fibonacci numbers, in successively approximating the golden mean, enable planetary orbits near the Sun to express the golden mean. For example, the Venus synod is 8/5 (1.6) practical years whilst its orbital period is 8/13 (0.625) practical years, because its orbit divides the practical year as the number 1. The synod of Venus is therefore a function of that orbital period and the practical year in a practical application of discrete mathematics. This sort of resonance is found in moons close to massive planets like Jupiter and so, the inner planets are like moons of the Sun, seen from Earth – exactly as Tacho Brahe’s geoheliocentric model eventually did, after Copernicus just before gravitation was discovered.

Figure 3 The Geocentric Model as (left) a Staff and
(right) Nine Concentric Rings or “spheres”

The Geocentric Inheritance of Greece

The medieval geocentric model had its origins in ancient Greece, due to Pythagoras. This was discarded by 1600, when Copernicus showed that many of the difficulties in understanding the form of the planetary orbits were due to the placing of the Earth and Moon at the centre or bottom, and the Sun as third planet out (figure 3). If the Sun, Mercury and Venus are swapped with Earth and Moon, the heliocentric system results – ordered according to its relative gravitational masses and orbital radii.

Figure 4 The Geocentric order (left) can be expanded to show
the Harmonic and Fibonacci ordering principles (right)

When accompanied by the set of simple time periods shown in figure 4, the geocentric model may have functioned as a focal aide memoire accompanying explicit oral or written explanations. The synodic planetary periods to either the lunar year or the practical year would be easily learnt by counting time as days between celestial manifestations. This might be the reason the ancient near east did not repeat the astronomy of the megalithic monuments. Instead, temples symbolised time and space, using a canon of sacred numbers in the name of the god or god-king. Astrology became a special form of divination within which long counts could arrive at the general state of the cosmos, correctable using instrumental or naked-eye observations. All such matters were associated with the state, and its specialists, including astrologers and scribes and the geocentric planetary system was a talisman for the ancient mysteries, astronomical and harmonic.

Poetry as the Language of Geocentricity

The primordial light initiating the Bible’s old testament creation story became the Word (in Greek: “Logos”)[5], of the New Testament. The logos was a proposed structure of meaning which held the world together within the human mind, if you could receive it. The second part of the creation story is therefore to understand the original creative process as a human creative process. Language has given human perception of the world a largesse of worldviews in the making. The geocentric world view became a particularly large corpus, through the texts of the religious centres but also through a poetic tradition seeking to locate its voice within a remarkably specific, consistent, and well-mapped-out topography, with geocentrism and its astronomical numbers at its heart. If there has been any major spiritual vision within human history it was geocentric and never heliocentric, even though the Sun is prime suspect for being the creative origin of the solar system and its extra-special geocentric planet, Earth.

By my 6th book, Sacred Geometry: Language of the Angels, I realized that the numerical design within which our “living planet” sits is a secondary creation – created after the solar system. Yet the geocentric was discovered before the heliocentric creation of the solar system because the megalithic had observed the planets from the Earth. So, although the solar system was created first in time, this creation continued onwards to produce a more sophisticated planet than the rest, where the other planets had the supporting roles, which the geocentric tradition had mythically alluded to, in a stable topography of places and mythic narratives; of gods, heroes, demons, events, and humans actors, serving as the sacred texts of the ancient world. Later writers both adopted and innovated this tradition:

In its use of images and symbols as in its use of ideas, poetry seeks the typical and enduring. That is one reason why throughout the history of poetry the basis for organising the imagery of the physical world has been the natural cycle. Northrop Frye, 1960.

Using literary criticism, Northrop Frye saw past the habitual assumption that high poets were artfully but merely remarking upon the sensory life and its everyday recurrences. Instead, he realised that living cycles were often employed as “similarities to the already arisen”, as Gurdjieff put it[6], meaning that the planetary world was being expressed by proxy through the natural cycles within poetry. And Life does depend upon the eternal cycles within which it sits: The spin and obliquity of the Earth and the orbit of its large moon. These two bodies are profoundly connected numerically to the rest of the planets according to the vision of the geocentric model, involving both Fibonacci and harmonic cycles. Frye first became aware of link between cosmology and poetry when analysing the works of William Blake, the poet who appeared to “make up” his own original yet geocentric cosmology and language; causing Frye to state “poetry is the language of cosmology”. Long after the heliocentric had suspended any belief in the geocentric, its language and metaphors still formed a stable tradition amongst poets, through the influences of a classical education.

The geocentric topography is quite standardized among its world-wide variation in imagery, over thousands of years, all quite agreeable with that used by Dante in The Divine Comedy, summarised by Frye in his essay New Directions from Old[7] as follows.

…For poets, the physical world has usually been not only a cyclical world but a “middle earth,” situated between an upper and a lower world. These two worlds reflect in their form the heavens and hells of the religions contemporary with the poet, and are normally thought of as abodes of unchanging being, not as cyclical. The upper world is reached by some form of ascent and is a world of gods or happy souls. The most frequent images of ascent are the mountain, the tower, the winding staircase or ladder, or a tree of cosmological dimensions. The upper world is often symbolized by the heavenly bodies, of which the one nearest to us is the moon. The lower world, reached by descent through a cave or under water, is more oracular and sinister, and as a rule is or includes a place of torment and punishment. It follows that there would be two points of particular significance in poetic symbolism. One is the point, usually at the top of a mountain just below the moon, where the upper world and this one come into alignment, where we look up to the heavenly world and down on the turning cycle of nature.[8]

By the time of the medieval, the image of the geocentric world had sprouted a sublunary gap between the Earth and the Moon with a rudimentary physics of the four elements – which are the four states of matter: solid earth, liquid water, gaseous air and a transformative fire; ideas from the pre-Socratic philosophers. With this palette, the storyteller or poet could allude to an invariant world view based upon megalithic astronomy, but now held as a diagram, made familiar through ever-new expressions or as an oral then written text.

A Simplified Model of Prehistory

The simplest explanation for which there is good evidence finds Atlantis to have probably been an Egyptian myth about the megalith builders on the Atlantic seaboard of Europe, whose astronomical knowledge became enshrined in the ancient mysteries. These mysteries have been made doubly mysterious since the modern age replaced the world view upon which those mysteries were based by the Copernican heliocentric view. This new solar system was soon discovered to be held together, not by the divine world, but by invisible gravitational forces between the large planetary masses and an even more massive Sun, forces elucidated by Sir Isaac Newton. The primacy of heliocentrism caused modern humanity to further lose contact with the geocentric model of the world and its two serpents, of the inner and outer planets (figure 4), a literary tradition that had lasted since at least 3000 BC.

If one but swapped the sun and moon-earth system, the geocentric planetary order became the heliocentric planetary order. The Copernican revolution seemed to be a minor tweak of a less useful model but tragically, the geocentric references to an original form of astronomy, based upon numerical time and forged by the megalithic, were lost and invisible to heliocentric astronomy. Science came to know nothing of the geocentric order surrounding the Earth and blind to the significance of the mythic worlds that animated the geocentric model.

You can find many additional articles at sacred.numbersciences.org


[1] It is remarkable that the inch was one of the first units of length used by the megalithic in Carnac to count days.

[2] These matters are fully explained, most in Sacred Geometry: Language of the Angels.

[3] According to the late Ernest G. McClain (https://ernestmcclain.net/), American musicologist and writer, in the 1970s, of The Pythagorean Plato and The Myth of Invariance.

[4] one fifth of the Venus synod is therefore close to the synod of Mercury (115.88 days).

[5] John X:Y

[6] “… the [whole] presence of every kind of three-brained being … is an exact similitude of everything in the Universe.” Beelzebub’s Tales to his Grandson. G.I.Gurdjieff. 345. Similar to the Pythagorean tradition of the human being a microcosm of the macrocosm.

[7] found in Myth and Mythmaking ed: H.A. Murray, Wesleyan University Press.115-131. 1959.

[8] ibid. 123.

Dun Torcuill: The Broch that Modelled the World

image above courtesy Marc Calhoun


Script

This video introduces an article on a Scottish iron-age stone tower or brock which encoded the size of the Earth. 

You can view the full article on sacred dot number sciences dot org, searching for BROCK, spelt B R O C H.

In the picture above [1] the inner profile of the thick-walled Iron-Age broch of Dun Torceill is the only elliptical example, almost every other broch having a circular inner court.

Torceill’s essential data was reported by Euan MacKie in 1977 [2]: The inner chamber of the broch is an ellipse with axes nearly 23:25 (and not 14:15 as proposed by Mackie).

The actual ratio directly generates a metrological difference, between the major and minor axis lengths, of 63/20 feet. When multiplied by the broch’s 40-foot major axis, this π-like yard creates a length of 126 feet which, multiplied again by π as 22/7, the simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods., generates 396 feet. If each of these feet represented ten miles, this number is an accurate approximation to the mean radius of the Earth, were it a sphere.

If we take the size of the moon in that model, as being 3/11 of 396 feet this would give a circle radius 108 feet and one can see that, using the moon, the outer perimeter of the brock was probably elliptical too.

Thank you for watching.