We have seen that the early numbers define the world of musical harmony but other important patterns arise within the ordinal numbers such as,
the Fibonacci approximations to the Golden Mean (phi = 1.618),
the Exponential constant (e = 2.718, the megalithic yard), from which trigonometry of the circle arises naturally,
the radial geometrical constant, (pi = 3.1416) as approximated by rational fractions {π = 22/7 25/8 63/20 864/275} and
the triangular progressions of square roots, as another development of the early numbers (in space) as geometry, also approximated by rational* numbers (rational meaning “integer numbers that can form mundane ratios”).
The transcendent (or irrational) ratio constants * (first mentioned in the Preface) are the visible after-effects of the creation of time and space. They must be part of the framework conditions for Existence, these also creating harmonicphenomenon that are not transcendent; these relying instead (as stated) on the distance functions of ordinal numbers: their distance from one and their relative distance from each other, lying beneath the surface of the ordinal numbers. Ordinality, to modern thought a universal algorithm for such distances, explains or defines what is harmonious in the physical world and in what way. Significant distance relations, such as those found in the early ordinal numbers, must then be repeated at ever greater doubling, tripling and so on {1 2 3 4 5 6} => {45 90 135 180 225 270}, where units can be scaled up by any number to become the larger structures, within any greater micro-cosmos. This is especially seen within ancient number science and its primary context of octave doubling, where what lies within octaves vis-à-vis scales and octaves within octaves, requires the right amount of up-scaling, as in the cosmology of Will (and not of Being), presented by G.I. Gurdjieff from 1917 onwards.
The illusion of number is that one can never penetrate the ubiquitous unitary distance of 1, the unity which becomes the ordinals which are so many exact assemblies of one; and of their ratios, so that one is not a number nor a transcendent ratio but rather is Number is the primordial Thing: a transcendent wholeness, found in every unit that causes relatedness through intermediate distance, or proximity. One is like Leibnitz’s Monads applied to the cosmic enterprise of universe building, as a fully quantified Whole and its Parts.
“The Absolute, that is, the state of things when the All constitutes one Whole, is, as it were, the primordial state of things, out of which, by division and differentiation, arises the diversity of the phenomena observed by us.”
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.
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
The recurrence of celestial time periods,
The mental powers to recognise manifested patterns,
The use of spatial geometries of alignment,
The numerate counting of time,
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 anastronomy 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.
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,
Long sightlines were established to key celestial events on the horizon, such as the sun or moon, rising or setting.
The number of days were counted between horizon events, to quantify each periodicity as a measured length between points or as a rope.
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 TheDivine 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).
[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.
The 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 square appears. Above right the Egyptian Djed column is shown within a double square. The Djed is the rotating earth which the gods and demons have a tug of war over. This is also a key story in the Indian tradition, called The Churning of the Oceans, where the churning creates both the food of the gods (soma) and every wonderful thing that emerges upon the Earth. In this, the double square symbolized the northern and southern hemispheres of the Earth. The anthropomorphic form Djed shown above has elbows indicative of the Double square.
Figure 1 The churning of the ocean (Samudra Manthan in Sanskrit)
The Djed appears to be the general principle of rotation of, and apparent motion around, the earth.
The god Isis is (as a planet) Venus and is shown (fig.2) offering up the sun disk: another Djed is below, with her Ankh symbol of Life atop the Djed, now having female arms . This sun most probably points to the practical year as 365 days which is 5/8 of the Venus synod of 584 days. (This ratio of 1.6 is the sixth note of the octave 1 to 2.)
In figure 2, two female attendants provide the duality which one might take to be her two famous manifestations of (firstly) the brightest Evening Star, as the sun goes down, and then (after that) the brightest Morning Star before the sun rises. Above there is duality again with three baboons either side of the sun, perhaps representing the six visible planets: Moon, Venus and Mercury: Jupiter, Saturn, Mars and their “tug of war”.
Figure 2 The creation of Horus-Ra from out of an ankh with female arms atop a djed. from Budge 1899, also fig. 7.8 of Richard Heath, The Harmonic Origins of the World.
The numbers 5 and 8 are Fibonacci approximations {1 2 3 5 8 13 21 34 …} to the golden mean, a transcendent number {1.618034…} which rational numbers can only approximate. Venus and the Earth have clearly settled into orbits around the sun resonant with Fibonacci ratios since the Venus orbital period (224.701 days) is 8/13 of the solar year. And it is this fact that eventuates in what we see on Earth, namely the manifestations of Venus every 8/5 of a practical year. of 365 days.
Figure 3 The double square, its in-circle and out-circle manifesting golden rectangles around itself.
In this post, I developed a result sent to me, that a square drawn within the upper hemisphere of a circle must define a golden mean rectangle either side from its height of 1 and the remaining radius of 0.618034… and so it can be seen that the divine principle of the Golden Mean emanates from the double square, either side of each square, when the double square is embraced by a circle drawn from its center. Obviously, on Earth and between orbits (of Venus and Earth), the Golden Mean (also called Phi) has to be approximated by whole number ratios but the principle is present within the geometry and its out-circle. Schwaller de Lubicz thought the dynastic Egyptians held the Golden Mean to be “the fundamental scisson” (literally “scissor cut”) in the range one to two and, its reciprocal can be seen to share the portion over 1 (figure 3).
One can see that geometry and the early numbers would have been seen as two aspects of what we call space and time, in which “things” are separate from each other in Existence but somehow conjoined within Eternity. What we call order is in fact an achievement of harmony made possible by the arranging and fitting of parts to form a coherent whole. It is this insight which gave meaning to their study of geometry and numbers from the prehistoric onwards, into the recorded history of early civilizations. The meaning for Life on Earth became encoded within ancient and prehistoric symbols, whose geometrical and numerical language of expression went to the heart of phenomena.
Sheikh Lotfollah Mosque is one of the masterpieces of Iranian architecture that was built during the Safavid Empire, standing on the eastern side of Naqsh-i Jahan Square, Esfahan, Iran. Construction of the mosque started in 1603 and was finished in 1619. for Wikipedia by Phillip Maiwald
The Golden Mean (1.618034) or Phi (Greek letter) is renowned for the behavior of it’s reciprocal and square which are 0.618034 and 2.618034 respectively; that is, the fractional part stays the same. Phi is a unique singularity in number. While irrational, shown here to only 6 figures, it is its infinite fractional part which is responsible for Phi’s special properties.
The Fibonacci series: Found in sacred buildings (above), it is also present in the way living forms develop. Many other series of initial number pairs tend towards generating better and better approximations to Phi. This was most famously the Fibonacci series of 0 1 1 2 3 5 8 13 21 34 55 89 … (each right hand result is the simple sum of the two preceding numbers (0+0 = 1, 1+1=2, etc.
Rex Bear talked to me by Zoom on the 11th March; about the extensive background of my new book Sacred Geometry: Language of the Angels. Below is embedded from the Leak Project YouTube channel.
