The Geocentric Orbit of Venus

It is helpful to visually complete the movement of Venus over her synodic period (of 1.6 years) seen by an observer on the Earth.

figure 3.13 (left) of Sacred Goddess in Ancient Goddess Cultures
version 3 (c) 2024 Richard Heath

In the heliocentric world view all planets orbit the sun, yet we view them from the Earth and so, until the 16th century astronomy had a different world view where the planets either orbited the sun (in the inner solar system) which like the outer planets orbited the earth, this view called geocentric. The discovery of gravity confirmed the heliocentric view but the geocentric view is still that seen from the Earth.

The geocentric was then assumed to be wholly superseded, but there are many aspects of it that appear to have given our ancestors their various religious views and, I believe, the megalithic monuments express most clearly a form of astronomy based upon numbers rather than on laws, numbers embedded in the structure of Time seen from the Earth, and hence showing the geocentric view had more to it than the medieval view discarded by modern science.

Venus was once considered one part of the triple goddess and the picture above shows her complete circuit both in the heavens and in front of and behind the sun. The shape of this forms two horns, firstly in the West at evening after sunset. Then she rushes in front of the sun to reemerge in the East to form a symmetrical other horn after which she travels behind the sun to eventually re-emerge in the West in a circuit lasting 1.6 years of 365 days, more precisely in 583.92 days – her synodic period.

In my latest book, Sacred Geometry in Ancient Goddess Cultures, the young goddess of our Venus/Aphrodite is most clear in the matriarchal civilization of the Minoans, centered on the Greek island of Crete between 2000 and 1300 BCE. The famous “horns of consecration” resemble the horns of Venus in the sky, then used to bracket the rising sun and moon, on the horizon, from sanctuaries on mountain peaks or east facing “palaces”.

figure 5.5 of Sacred Geometry in Ancient Goddess Cultures (left rhyton of Kato Zagros, (center, detail of tripartite shrine and courtyard featuring three altars (c) Olaf Tausch, (right) the likely appearance of the whole sanctuary on a gold ring.

The extremes of the sun at Solstices and its mean, directly east at Equinox are three locations and the minimum and maximum moon, to north and south add up to seven locations seen in adjacent horns within sun or moon will rise at those key moments over a solar year and over the moon’s nodal period of 18.618 solar years. In the book the inter-palace distance between Knossos and Malia is found to be, in miles, the 18.618 years taken for the lunar nodes to traverse the Ecliptic

Phenomenology as an Act of Will

“Philosophizing consists of inverting the usual direction of the work of thought.” – HENRI BERGSON

  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.

Contemporary beings see the world in ever more functional and descriptive ways, where a form of words, or a mathematization of the world, overlays the actual sensory experience of it. This has made our task, of interpreting previous Ages, and their big ideas, prone to errors, pitfalls and presumptions. And the notion of there being a Universal Will of some sort seems, since the medieval period, highly optimistic: for why should humans be able to know more than our scientific instruments can tell us or be able to know the universe as a single whole, still connected to Everything. For myself, applying the phenomena of numbers found within the counted periodicities of celestial motions seem to give the key to an alternative world, hidden from modern science.

The European schools of Phenomenology, ably summarized by the late Henri Bortoft in his Taking Appearances Seriously (2012), pushed back against the reductionist functionalism of the modern descriptive mind (which Gurdjieff called man’s formatory apparatus) by returning attention to what is actually present in the sensory world, internalizing it in a way developed by Goethe, through using our inherent and still-operational powers of imagination: a serious type of day-dreaming.

Normally, several things (or parts of something) are aggregated into a whole generic average, as with the names for the parts of a plant: pistil, stamen, petals, vegetative leaves. Bortoft tells us that, in the late 18th Century, Goethe was able to see that each part of a plant was created by a common cell to be found in vegetative leaves and differentiated from there. His proposal prefigured the modern discovery of the stem cell, revealed only recently due to DNA research. But Goethe’s method showed us another approach to understanding, that the wholeness of a plant’s organization of its parts could be grasped through non-instrumental observation, in a process he termed “exact sensorial fantasy”. In a sense, the action of the plant was being assimilated into the psyche, rather than facts and evidence being placed in the linguistic mind.

Henri Bortoft describes how, when struggling to explain the situation, he was standing on a bridge near Sherbourne, worrying how to explain Phenomenology. He saw the verbal-descriptive world was like a river, seen from the bridge upon which he was standing flowing downhill, representing the descriptive path based upon an existing way-of-seeing. He turned around to look upstream.

Such an experience seems esoteric unless experienced for oneself, the structure of the situation reveals how close meaning may lie within phenomena.

Another example, for the history of science, is given where Galileo viewed the Moon using an early telescope. He initially saw (like his contemporaries with such telescopes) that there were many circles upon the Moon’s face. But one day, these circles were suddenly transformed into a landscape, as one might find upon the Earth, a landscape of craters. His new way-of-seeing the Moon was as a planet like our own having a landscape. Galileo had needed to keep looking and struggling to see beyond the circles, until he looked as if at a landscpe on earth which changed his organising idea to the moon as a planet; something no-one had yet done, despite having telescopes.

However Galileo’s discoveries (and subsequently those of Newton), fell back into the ancient Greek atomistic ideas, due in large part to a recently re-discovered Greek text on Atomism, an organizing idea which led to the new type of view, that nature was inherently mathematical. This way-of-seeing we now call Physics. It can now describe the whole physical universe (within the limits of modern instruments and mathematical mappings of world laws such as gravitation), and only rarely do the normal senses “accidentally notice” the appearance of something in a new way.

Therefore, in turning around Henri Bortoft saw that if one turns away from the path of description (verbal or mathematical), one can see with fresh eyes the wholeness and connectedness of phenomena outside of reductionist descriptive environment. The first looks into phenomena to find its meaning as an appearance of meaning within the the direct appearance of the phenomenon, and not assuming that we know what is there. This is surely to be recommended as the birth right of a human being, to understand the world directly and not through mathematics or hearsay. And it is very possible that the conceptual-mathematical way-of-seeing itself developed, from discoveries made in ancient times through the phenomenological approach, because it is visibly true that, in time, the planets are numerically encoded one to another, in a simple way.

Numbers, Constants and Phenomenology

  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.

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 harmonic phenomenon 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.”

Gurdjieff. In Search of the Miraculous page 76.

In Search of the Miraculous* had an 11-fold “Diagram of Everything Living” (shown above), in which the Universal Will for the universe was represented by an equilateral triangle within a circle (top left). The triangle expresses the equal division of the circle into three parts, and it is only through seeing the parts of Gurdjieff’s cosmology, in that book of lectures and (differently) in his later writings (and other sources) that one can arrive at a simple explanation for this triangle inside a circle (see section X), which also figures in his famous Enneagram (see below). The two circles demonstrate doubling in size, using the triangle which expresses division of both circles into three parts, which in Just intonation are three large intervals {4/3 5/4 6/5} which together equal 2. The important point here is that all the notes of an octave are related by the rational distances between the numerators and denominators of ratios, thus automatically increasing the relatedness of an octave’s parts, at whatever scale. This is what the ordinal numbers achieve from the very outset, of their seemingly primitive ordinality {1 2 3 4 5 6}, which leads to an intense and well-behaved type of relatedness. By the number 24, the octave of eight notes appears and, within this octave and the next {24 48 96}, seven modal scales emerge, from each interval of the major diatonic, in order (section 2.8).

In recent centuries, alternative voices to science have been talking about this sort of phenomenology. The European School of philosophers, pursued phenomenology rather than rational introspection. From Wolfgang Goethe (1749 – 1832) onwards, they wee discovering that science was not, in principle, a participation of the human senses in understanding the world but rather had become the application of instrumentality instead of the natural senses (next section). Moments of scientific genius, discovering new mathematical laws of nature, are remarkably not focused on how they were achieved, but on what they revealed within the physical world (as a technology to create a human “good”, exploiting new understandings of nature to explain then control nature). This change of focus had collapsed the original genius of a participatory moment, in which the fundamental process of understanding for its own sake, is a part of the world understanding the world. The problem was dramatized in Goethe’s Sorcerer’s Apprentice, where an apprentice magically tinkered disastrously with the world of his Master.  Phenomenology lacks the apparent usefulness that science provides since it seeks to understands the world rather than control it. In seeking to control the world, the world soon comes to control what the human world is like and what humans, now a world, want to do.

The failure to understand the world in the right way, on an individual level, suppresses the human destiny for which nature and the whole universe was probably created. It is easily done, to revert to a life where the world no longer participates within us but we benefit from the exploitation of parts of the physical world. The meaning of the world becomes our description of it, rather than the world’s meaningful action through human beings. It is therefore true to say that today we use numbers but don’t understand them* (in their pychoactive role of expressing meaning in the world) as the manifestation of the Universal Will for this universe. Holding to this is useful when wishing to understand the ancient number sciences, as they must have originally got their insights by looking towards the being of numbers as the native framework of the Universe. Numbers are, for example, made up of prime numbers, just as we think atoms are made of subatomic particles such as protons, neutrons and electrons.

Numbers can be explained as a tool for the universe-creating Will. The will of numbers is that, within the creation, “even God cannot beat an ace with a deuce [that is, a two]”

<EN> I do not remember which of us was first to remember a well-known, though not very respectful school story, in which we at once saw an illustration of this law. The story is about an over-aged student of a seminary who, at a final examination, does not understand the idea of God’s omnipotence.

‘Well, give me an example of something that the Lord cannot do,” said the examining bishop. “It won’t take long to do that, your Eminence,” answered the seminarist. “Everyone knows that even the Lord himself cannot beat the ace of trumps with the ordinary deuce.” Nothing could be more clear.

Ouspensky, In Search of the Miraculous, page 95

That is, numbers are a foundational set of rules based upon their distances from each other, in a single dimension or rather, in any direction away from one. This is perhaps why the strings of string theory are numerical and, in manifestation, how long chains of DNA proteins determine living forms. Numbers must be obeyed for the universe to be actual. Our world appears as we think it is and, the facticity behind material causes lurks within phenomena as more than a cause-and-effect “explanation” using physical laws. One can return to the notion that nature has provided, through numbers, shortcuts between numbers which, in the physical world, can connect things of a similar sort together, in a special way that means that the connection of the whole to the parts remains intact within phenomena.

The question is, how could numbers have created the context for a Living Planet and be knowable to human beings without an instrumentality other than the sensorium made up of senses + intelligence.

Phenomenology as an Act of Will

Why numbers manifest living planets

above: The human essence class related to four other classes in J.G. Bennett’s Gurdjieff: Making a New World. Appendix II. page 290. This systematics presents the human essence class which eats the germinal essence of Life, but is “eaten” by cosmic individuality, the purpose of the universe. The range of human potential is from living like an animal to living like an angel or demiurge, then helping the cosmic process.

  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.

The human essence class is a new type of participation within the universe where the creation can form its own creative Will, in harmony with the will that creates the universe. The higher intelligences have a different relationship to the creation than human intelligence. It is based upon this Universal Will (to create the universe) which has manifested a world we can only experience from outside of it. And the creative tip of creation* is the universal life principle that led to the human world where it is possible to participate in the intelligence behind the world, through a  transformation into an Individuality, creative according their own pattern while harmonious with the universal will.

*creative tip: The evolving part of organic life is humanity. Humanity also has its evolving part but we will speak of this later; in the meantime we will take humanity as a whole. If humanity does not evolve it means that the evolution of organic life will stop and this in its turn will cause the growth of the ray of creation to stop. At the same time if humanity ceases to evolve it becomes useless from the point of view of the aims for which it was created and as such it may be destroyed. In this way the cessation of evolution may mean the destruction of humanity.

In Search of the Miraculous. P.D. Ouspensky. 306.

Will is not something one does. Rather, it is a participation of one’s being with Will. This creates a transformational action of Will within a human that is receptive to it (rather than merely assertive on their own account). We are born able, through our unique pattern, to participate in our own understanding of the meaning that is this world. In this, numbers are more than data: they form structures of will which do not rely on complexity and are therefore directly intelligible for an intelligent lifeform, enabling what to do, by seeing more deeply what is in the present moment. For example, number is the foundation of that universal invariance: the Present Moment of selfhood*.

The myth of a philosopher’s stone presents a challenge, to find the “stone” itself, which we shall see is probably the numerically favourable environment upon the earth. The stone has been rendered invisible to modern humans by our functional science of infinite complexity, also called instrumental determinism. This has downgraded human expectations to being a walk-on part, an unintentional result of evolution, by natural selection, of intelligent life. To think otherwise it is necessary to see what is not complex about the sky, which is a designed phenomenon related to Life on Earth. Once-upon-a-time, the stone age understood the sky in this right way, the way it had been designed to be read by us, corresponding with the way intelligent life was intended to be, on a habitable planet with a large moon.

1.1 Geocentric Numbers in the Sky

Our pre-digested meanings are those of modern science. Whilst accurate they cannot be trusted in the spiritual sense, if one is to continue looking at phenomena rather than at their preformed conceptual wrapper. Numbers in themselves are these days largely ignored except by mathematicians who, loving puzzles, have yet largely failed to query the megaliths** but, if or when anyone might say the megaliths had a technical purpose, this has annoyed most archaeologists, who live by the spade and not by the ancient number sciences or astronomy.

**Fred Hoyle, Hawkins, Alexander Thom, Merritt and others all found something new in Stonehenge but still failed to explore stone age numeracy as well as the numeracy of metrology. Rather, they assumed measures unlike our own were used, yet the megaliths would continue to have no meaning “above ground”, except as vaguely ritualistic venues in loose synchronization with a primitive calendar.

Numbers are not abstract once incarnated within Existence. In their manifestations as measurements, they have today become abstracted due to our notation and how we transform them using arithmetic, using a positional notation based upon powers of two and five {10}, called the decimal system* (https://en.wikipedia.org/wiki/Decimal). The so-called ordinal numbers {1 2 3 4 5 6 7 8 9 10 …etc.} are then no longer visually ordinal due to the form in which they are written, number-by-number, from right-to-left {ones, tens, hundreds, thousands …} * (the reversal of the left-to-right of western languages). Positional notation awaited the invention of zero, standing for no powers of ten, as in 10 (one ten plus no units). But zero is not a number or, for that matter, a starting point in the development of number and, with the declaring of zero, to occupy the inevitable spaces in base-10 notation, there came a loss of ordinality as being the distance from one.

Before the advance of decimal notation, groups within the ancient world had seen that everything came from one. By 3000BC, the Sumerian then Old Babylonian civilization, saw the number 60 perfect as a positional base since 60 has so many harmonious numbers as its factors {3 4 5}, the numbers of the first Pythagorean triangle’s side lengths. Sixty was the god Anu, of the “middle path”, who formed a trinity with Fifty {50}, Enlil* (who would flood humanity to destroy it) and Forty {40} who was Ea-Enki, the god of the waters. Anu presided over the Equatorial stars, Enlil over those of the North and Ea-Enki over those of the South. In their positional notation, the Sumerians might leave a space instead of a zero, calling Sixty, “the Big One”, a sort of reciprocal meaning of 60 parts as with 360 degrees in a circle from its center. So the Sumerians were resisting the concept of zero as a number and instead left a space. And because 60 was seen as also being ONE, 60 was seen as the most harmonious division of ONE using only the first three prime numbers {3 4 5}.

 These days we are encouraged to think that everything comes from zero in the form of a big bang, and the zeros in our decimal notation have the unfortunate implication that nothing is a number, “raining on the parade” of ordinal numbers, Nothing usurping One {1} as the start of the world of number. The Big Bang, vacuum energy, background temperature, and so on, see the physical world springing from a quantum mechanical nothingness or from inconceivable prior situations where, perhaps two strings (within string theory) briefly touched each other. However, it is observations that distinguish meaning.

In what follows we will nevertheless need to use decimal numbers in their position notation, to express ordinal numbers while remembering they have no positional order apart from their algorithmic order as an infinite series in which each number is an increment, by one, from the previous number; a process starting with one and leading to the birth of two, the first number.

Whole (or integer) numbers are only seen clearly when defined by

  • (a) their distance from One (their numerical value) and
  • (b) their distance from one another (their difference).

In the Will that manifested the Universe, zero did not exist and numerical meaning was to be a function of distances between numbers!

Zero is part of one and the first true number is 2, of doubling; Two’s distance from one is one and in the definition of doubling and the octave, the distance from a smaller number doubled to a number double it, is the distance of the smaller number from One. This “strange type of arithmetic” *(Ernest G McClain email) is seen in the behavior of a musical string as, in that kind of resonator, half of the string merely provides the basis for the subsequent numerical division of its second half, to make musical notes – as in a guitar where the whole string provides low do and the frets when pressed then define higher notes up to high do (half way) and beyond, through shortening the string.

This suggests that a tonal framework was given to the creation by Gurdjieff’s Universal Will, within which many inner and outer connections can then most easily arise within octaves, to

  1. overcome the mere functionality of complexity,
  2. enable Will to come into Being,
  3. equip the venue of Life with musical harmony and
  4. make the transformation of Life more likely.

Harmony is most explicit as musical harmony, in which vibrations arise through the ratios between wavelengths which are the very same distance functions of ordinal numbers, separated by a common unit 1.

Take the number three, which is 3/2 larger than two. Like all ordinal numbers, succeeding and preceding numbers differ by plus or minus one respectively, and the most basic musical tuning emerges from the very earliest six numbers to form Just intonation, whose scales within melodic music result as a sequence of three small intervals {9/8 10/9 16/15}, two tones and a semitone.  Between one and those numbers {8 9 10 15 16} are the first six numbers {1 2 3 4 5 6}* (note absence of seven between these sets), whose five ratios {1/2 2/3 3/4 4/5 5/6} provide any octave doubling with a superstructure for the melodic tone-semitone sequences; their combined interdivision, directly realizes (in their wake) the tones and semitones of modal music.

We will see that the medium for such a music of the spheres was both the relationship of the sun and planets to the Moon and Earth, and this manifested quite literally in the lunar months and years, when counted. But Gurdjieff’s octaves cannot be understood without disengaging modern numerical thinking, procedures and assumptions. It is always the whole being divided and not a line of numbers being extended, though it is easier to look within wholes by expressing their boundary as a large number: Hence the large numbers of gods, cities, time and so on. For example, creating life on earth requires a lot of stuff: perhaps the whole solar nebula has been necessary for that alone and billions of our years. Were you worth it?

Phenomenology as a Native Skill

Counting the Moon: 32 in 945 days

One could ask “if I make a times table of 29.53059 days, what numbers of lunar months give a nearly whole number of days?”. In practice, the near anniversary of 37 lunar months and three solar years contains the number 32 which gives 945 days on a metrological photo study I made of Le Manio’s southern curb (kerb in UK) stones, where 32 lunar months in day-inches could be seen to be 944.97888 inches from the center of the sun gate. This finding would have allowed the lunar month to be approximated to high accuracy in the megalithic of 4000 BC as being 945/32 = 29.53125 days.

Silhouette of day-inch photo survey after 2010 Spring Equinox Quantification of the Quadrilateral.

One can see above that the stone numbered 32 from the Sun Gate is exactly 32/36 of the three lunar years of day-inch counting found indexed in the southern curb to the east (point X). The flat top of stone 36 hosts the end of 36 lunar months (point Q) while the end of stone 37 locates the end of three solar years (point Q’). If that point is the end of a rope fixed at point P, then arcing that point Q’ to the north will strike the dressed edge of point R, thus forming Robin Heath’s proposed Lunation Triangle within the quadrilateral as,

points P – Q – R !

In this way, the numerical signage of the Southern Curb matches the use of day-inch counting over three years while providing the geometrical form of the lunation triangle which is itself half of the simpler geometry of a 4 by 1 rectangle.

The key additional result shows that 32 lunar months were found to be, by the builders (and then myself), equal to 945 days (try searching this site for 945 and 32 to find more about this key discovery). Many important numerical results flow from this.

Counting the Moon: 99 equals 8 years

Plan of Avebury showing the stone arrangement of the henge. 
Source: The Avebury Cycle Michael Dames (1977).

The principle of finding anniversaries appears promising when three solar years contain just over 37 (37.1) lunar months while three lunar years contain 36 lunar months and, if one then looks for a better anniversary, then one can move to the 8 year period which has two key features.

  1. The sun will appear on the horizon where it did 8 solar years ago because of the quarter day every solar year.
  2. The moon will be in the same phase (relative to the sun) after 99 lunar months.

This appears useful: by dividing the days in eight years (~ 2922 days) by 99 (having counted to 99 months by eight years) the resulting estimate for the lunar month is 29.514 days, out by just 23 minutes of our time.

Eight solar years was therefore an early calendar in which the solar year could be somewhat integrated by the lunar year. However, the lunar year was entrenched as a sacred calendar, for example in Archaic Greece. And it may be that when the Neolithic reached England in the Bronze Age that 99 stones were placed around the massive henge of Avebury so that eight solar years could be tracked in a seasonal calendar alongside 99 lunar months, 96 months constituting eight lunar years.

The three lunar months left over must then, divided by 8, give the solar excess over the lunar year as 3/8 = 0.375, whereas the actual excess is 0.368 lunar months or 5 hours less. In the previous post, two months the stone age could have been counted as 59 days, here 8 solar years could have been counted as 99 lunar months at Avebury. Through this, one would be homing in on knowing the solar excess per year (10.875 days) and the length of the lunar month, to more accuracy.

It is obvious that counting using whole months has not got enough resolution to catch an accurate result and so in the next post we must revert to counting days in inches, as was done at Le Manio around 4000 BC, over the 36/37 month anniversary at three solar years. It is important to grasp that while we have great functional mathematics, we are here using it to find out what the numeracy 3000-4000 BC could have intended or achieved within counts monumentalized geometrically as a stone monument that can store information.