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

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Gurdjieff, Octave Worlds & Tuning Theory (2019)

This is a paper I suggested for the All and Everything conference in Cumbria, but it was not selected. It developed a number of strands, which I offer here as a snapshot of my thinking and research around 2019. This text was modified to become appendix 3 of my Sacred Number and the Language of the Angels (2021).


The first part presents what has only recently become known about ancient musical theory, to better understand the All and Everything of Gurdjieff’s intellectual output. This must include In Search of the Miraculous (Search, 1916-18) Beelzebub’s Tales (Tales, 1949) and Meetings with Remarkable Men (Meetings, 1963). In part 2 ancient monuments are shown to record a ‘lateral octave’ connecting humanity to the planetary world, 24. Part 3 explores the significance of the Moon in Gurdjieff’s lectures and writing. An appendix reviews the conventional virtues of the Moon as accepted by modern science, stabilising earth, enabling life and beings such as we, to evolve into appropriate habitats.


Abstract 1
Introduction. 3
Part 1: Ideas relating to a ‘science of vibrations’
The Role of Octaves
LikelySources of Gurdjieff’s Harmonic ‘Ideas’
Did Gurdjieff understand Numerical Tuning Theory?
Was Gurdjieff a Pythagorean?
Pythagorean Tuning
Greek versus Chinese Tuning?

Part 2: Where are the Lateral Octaves?
Part 3: The Significance of the Moon
Appendix 1: A Moon that created Life?
Appendix 2: Reference Charts from Search
Appendix 3: Index of the Moon in Search & Tales
Moon in Search
Moon in Tales


Publications about Gurdjieff’s ideas appeared after he and Ouspensky had died. The main works of Gurdjieff’s words are Search, Tales and Meetings. Beyond these lie autobiographical books and compendia of Gurdjieff’s ideas, by his students. Some of his students also looked into traditional sources such as Sufism and Vedanta, and followed up on new scholarship relating to cosmological ideas such as world mythology (Hamlet’s Mill, The Greek Myths); the number sciences of Pythagorean schools and Plato (Source books); ancient buildings (Megalithic Sites in Britain, Ancient Metrology, The Temple of Man); and musical tuning theory (The Myth of Invariance, Music and the Power of Sound).

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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

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Gurdjieff’s Diagram of Everything Living

first created: 28 October 2017

Gurdjieff first presented his ideas to groups in pre-revolutionary Russia. Amongst his carefully chosen students it was the habit to reconstruct talks and diagrams as much as possible, an endeavour that gave us a textbook of Gurdjieff’s ideas called In Search of the Miraculous (P.D. Ouspensky, 1950). This early form of the teaching was radically revised and extended by Gurdjieff, now as an author, during the 1920s, producing All and Everything whose part one was Beelzebub’sTales to his Grandson (G.I. Gurdjieff, 1950). Prior to drawing this diagram just after February 1917, Gurdjieff had been presenting ideas about transformation of energies, human and cosmic, using the musical theory surrounding the octave of eight notes. The Diagram of Everything Living was “still another system of classification… in an altogether different ratio of octaves… [that] leads us beyond the limits of what we call ‘living beings’ both higher [and lower] than living beings. It deals not with individuals but with classes in a very wide sense.”

Figure 1 The Diagram of Everything Living
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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)

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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.

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[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 (, 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.