My first book interprets the planetary system through pure number. The numbers involved in this interpretation are surprisingly simple and will be accessible to anyone holding a basic arithmetic education. From this approach we have gained substantial new insights into the realm of mythology, religious thought and what have become known as the Traditional Arts. We show that the solar system evolved from pure number and can no longer be thought of as an accident of nature.
It is also no coincidence that this work lies poised between the realm of mathematics and the world before numeracy. In the ancient world, numbers assumed god-like powers that were continually creating the world through stable numerical relationships. The core of this ancient science developed such a view naturally through simple astronomical observations, by counting events and regular movements in the night sky. This science was then articulated as mythological stories, calendars, sacred geometry, musical theory and monumental architecture, such as the Great Pyramid and Stonehenge.
These artefacts, found in all ancient cultures, have remained obscure to the modern world because modern science has become too sophisticated to see the simple celestial relationships which demonstrate that the planetary system, including the Sun and Moon, hold to a particular design.
Figure 1 The five Trilithons of Stonehenge 3, highlighted in yellow within the Sarsen ring to express the five evening and morning star couplets which occur in eight practical years of 365 days. Plan from Megalithic Remains in Britain and Brittany, Oxford U.P. Central portion is fig.3, upside down to match the horseshoe of trilithons..
Inside the Sarsen ring of Stonehenge, there once stood a group of five trilithons, each made up of two uprights and a lintel stone, repeating the unique style of building found in the Sarsen ring. However the Trilithons were higher than the sarsens, punctuating an elliptical cup shape towards the midsummer sunrise, the axis of Stonehenge and its solstice-marking “heel” stone.
The Horns of Venus
The symbolism therefore involved (a) the Sun, (b) the number five of the trilithons while (c) expressed something involving close pairs. The dominant astronomical significance of the number 5 comes through the brightest planetary phenomenon of all, in which the planet Venus approaches the Earth, as Venus approaches from the east, preceding the Sun in the evening sky. It is often therefore called the Evening Star. Venus then shoots past the sun and reappears in the morning sky, again growing in brightness as the Morning Star.
Figure 2 The Horns of Venus when the evening and morning “stars” are visualised over an extended present moment of the Venus synodic period of 1.6 (⅝) practical years of 365 days. Fig. 2.2 of my Matrix of Creation, Inner Traditions, 2004 . (Drawn by Robin Heath.)
The original astronomers of the megalithic only saw the planetary system from the Earth and not (conceptually) from the Sun, as we do today. That is, they were naturally geocentric whilst the present worldview is heliocentric.
The astronomers could study cosmic time periods without arithmetic, through counting days, using a constant unit length to mark each single day adding up to a fixed length of days. Through such counting they would see 365 whole days between the solstices and (more reliably) between the equinoxes (when the Sun moves most rapidly on the horizon). It was also quite obvious that the horns of Venus were bracketing the Sun, just as the elliptical cup of the trilithons they erected at Stonehenge bracketed the solstitial sun, a sun which travels every day from east to west.
Five-ness in the Zodiac
If the earth was their viewpoint then the Zodiac of the sun’s path over the year could, like the Sarsen Circle, be seen as a circle of 365 days, and when the time between evening or morning stars was counted, the result was 584 days between the horn-like and brilliant manifestations of Venus. 584 days is 219 days more than 365 days. The sun has therefore moved 3/5th of a year forward and hence it became noticeable, as stated above, that 1/5th of the practical year is 73 days, the practical year 5 units of 73 days long whilst the Venus synod is 8 units of 73 days long. The Venus synod therefore has exactly 1.6 (8/5) practical years between its phenomena.
Figure 3 The Horns of evening (E) and morning (M) stars shown upon the circle of the Zodiac, each successive pair 3/5ths advanced within the solar year. [from Joachim Schultz, Movement and Rhythms of the Stars, Floris, 1986, fig 88]
The form of Venus upon the Zodiac therefore describes a 5-fold pentacle star. This would later make the number 5 and all of its properties, sacred by association to the planet Venus who became the leading goddess of the Ancient Near East. The Golden Proportion or Mean (1.618034…), often seen in Classical and Neoclassical architecture, has the number 5 as its root. Also, many living bodies share forms derived from the number 5, or of the Fibonacci approximations to the Golden Mean.
The Fibonacci series (of 1, 1, 2, 3 ,5 ,8 ,13 ,21, …) has successive numbers that sum to give the next number, and each new ratio, between successive numbers in the series, yields an ever-better approximation to the Golden Mean: (2, 1.5, 1.6, 1.6, 1.617, …).
Harmonic Origins of the World inserted the astronomical observations of my previous books into an ancient harmonic matrix, alluded to through the harmonic numbers found in many religious stories, and also through the cryptic works of Plato. Around 355 BC, Plato’s dialogues probably preserved what Pythagoras had learnt from ancient mystery centers of his day, circa. 600 BC.
According to the late Ernest G. McClain*, Plato’s harmonic matrices had been widely practiced by initiates of the Ancient Near East so that, to the general population, they were entertaining and uplifting stories set within eternity while, to the initiated, the stories were a textbook in harmonic tuning. The reason harmonic tuning theory should have infiltrated cosmological or theological ideas was the fact that, the planets surrounding Earth express the most fundamental musical ratios, the tones and semitones found within octave scales.
* American musicologist and writer, in the 1970s, of The Pythagorean Plato and The Myth of Invariance.
Ancient prose narratives and poetic allusions were often conserving ancient knowledge of this planetary harmony; significant because these ratios connect human existence to the world of Eternity. In this sense the myths of gods, heros and mortals had been a natural reflection of harmonic worlds in heaven, into the life of the people.
In the Greece before the invention of phonetic writing, oral or spoken stories such as those attributed to Homer and Hesiod were performed in public venues giving rise to the amphitheaters and stepped agoras of Greek towns. Special performers or rhapsodes animated epic stories of all sorts and some have survived through their being written down.
At the same time, alongside this journey towards 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.
Work towards a fuller harmonic matrix for the planets
In my first book, called Matrix of Creation, I had not yet assimilated McClain’s books, but had identified the musical intervals between the lunar year and the geocentric periodicities of the outer planets. To understand what was behind the multiple numerical relationships within the geocentric world of time, I started drawing out networks of those periods and, as I looked at all the relationships (or interval ratios) between them, I could see common denominators and multiples linking the celestial time periods through small intermediary and whole numbers: numbers which became sacred for later civilizations. For example, the 9/8 relationship between the Jupiter synod and the lunar year could be more easily grasped in a diagram revealing a larger structural network, visualized as a “matrix diagram” (see figure 1).
Figure 1 Matrix Diagram of Jupiter and the Moon. figure 9.5 of Matrix of Creation, p117.
One can see the common unit of 1.5 lunar months, at the base of the diagram, and a symmetrical period at the apex lasting 108 lunar months or 9 lunar years (referencing the Maya supplemental glyphs). In due course, I re-discovered the use of the Lambda diagram of Plato (figure 8.7), and even stumbled upon the higher register of five tones (figure 2) belonging to the Mexican flying serpent, Quetzalcoatl (as figure 8.1), made up of [Mercury, the eclipse year, the Tzolkin, Mars and Venus], Venus also being called Quetzalcoatl.
Figure 2 My near discovery of Quetzalcoatl, in fig. 8.1 of Matrix of Creation
These periodicities are of adjacent musical fifths (ratio 3/2), which would eventually be shown as connected to the corresponding register of the outer planets, using McClain’s harmonic technology in my 5th book Harmonic Origins of the World (see figure 3).
Probably called the flying serpent by dynastic Egypt, Quetzalcoatl’s set of musical fifths was part of the Mexican mysteries of the Olmec and Maya civilizations (1500 BC to 800 AD). This serpent flies 125/128 above the inner planets – for example, the eclipse season is 125/128 above the lunar year: 354.367 days × 125/128 = 346 days, requiring I integrate the two serpents within McClain’s harmonic matrices in Harmonic Origins of the World (as figure 9.3).
Uranus is above Saturn
The eclipse year is above the lunar year
the Tzolkin of 260 days is above the 9 lunar months of Adam
Figure 3 The two harmonic serpents of “Heaven” and “Earth”
By my 6th book, Sacred Geometry: Language of the Angels, I had realized that the numerical design within which our “living planet” sits is a secondary creation – created after the solar system, yet it was discovered before the heliocentric creation of the solar system, exactly because the megalithic observed the planets from the Earth. Instead of proposing the existence of a progenitor civilization with high knowledge** I instead proposed, as more likely, that the megalithic was the source of the ancient mysteries. Such mysteries then only seem mysterious because; a kind of geocentric science before our own heliocentric one seems anachronistic.
**such as Atlantis as per Plato’s Timaeus: an island destroyed by vulcanism, Atlantis and similar solutions have simply “kicked the can down the road” into an as-yet-poorly-charted prehistory before 5000 BC, for which less evidence exists because there never was any. In contrast, the sky astronomy and earth measures of the megalithic are to be found referenced in later monuments and ancient textual references. That is, megalithic monuments recorded an understanding of the cosmos then found in the ancient mysteries. A geocentric world view was a naturally result of the megalithic, achieved using the numbers they found through geocentric observations, counting lengths of time, using horizon events and the mathematical properties of simple geometries.
Geo-centrism was the current world view until superseded by the Copernican heliocentric view. This new solar system was soon found by 1680 to be held together by natural gravitational forces between large planetary masses, forces discovered by Sir Isaac Newton. The subsequent primacy of heliocentrism, which started 500 years ago, caused humanity to lose contact with the geocentric model of the world: though figure 4 has the planets in the correct order for the the two serpents, of inner and outer planets, this is also (largely) the heliocentric order, if one but swaps the sun and the moon-earth system.
All references to an older and original form of astronomy, based upon numerical time and forged by the megalithic, was thus dislocated and obscured by our heliocentric physical science and astronomy of the modern day – which still knows nothing of the geocentric order that surrounds us.
Figure 4 The Geocentric Model by 1660
The geocentric model entered Greek astronomy and philosophy at an early point; it can be found in pre-Socratic philosophy … In the 4th century BC, two influential Greek philosophers, Plato and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere, stationary at the center of the universe.
above: a 21-petal object in the Heraklion Museum which could represent the 21 seven-day weeks in the 399 days of the Jupiter synod. [2004, Richard Heath]
One of the unfortunate aspects of adopting the number 360 for calibrating the Ecliptic in degrees is that the megalithic counted time in days and instead saw the ecliptic as divided by the 365¼ days. In transferring to the number 360, with all of its easy factors, 8 x 9 x 5, moderns cannot exploit a key advantage of 365¼ days.
If the lunar orbit takes 27.32166 days then each day the moon moves by 1/27.32166 of the ecliptic every day. For this reason, after 27.32166 days the orbit completes because the Moon’s “year” then equals one as the angular motion has been 27.32166/ 27.32166 = 1.
The same is true of the lunar nodes, which retrograde to the east along the ecliptic in 18.618 years. For this reason one can say, the lunar nodes move by 1/18.618 DAYS (in angle) every day and to travel one DAY in angle, the nodes take 18.618 DAYS per day (needing the new term “node day” equal the 18.618 days.*** A solar year takes 19.618 node days (since 365¼ equals 18.618 x 19.618) and an eclipse year takes 18.618 x 18.618 – 346.62 days
*** These are average figures since the moon comes under variable gravitational influences that are episodic.
A general rule emerges in which the larger, whole cycles, lead to reciprocals which can be numerically characterized by knowing the number of the days in the larger period.
What really happens when Earth turns? The rotation of Earth describes periods that are measured in days. The solar year is 365.242 days long, the lunation period 29.53 days long, and so forth.
Extracted from Matrix of Creation, page 42.
Earth orbits the Sun and, from Earth, the Sun appears to move through the stars. But the stars are lost in the brightness of the daytime skies and this obscures the Sun’s progress from human view. However, through observation of the inexorable seasonal changes in the positions of the constellations, the Sun’s motion can be determined.
The sidereal day is defined by the rotation of Earth relative to the stars. But this is different from what we commonly call a day, the full title of which is a tropical day. Our day includes extra time for Earth to catch up with the Sun before another sunrise. Our clocks are synchronized to this tropical day of twenty-four hours (1,440 minutes).
The traditional way to express the Harmony of the Spheres is geometrically, despite the fact that geometrical knowledge of the heliocentric planetary system was not available to Pythagoras who, for the West, first established this whole idea – that the planets were part of a system expressing harmony.
The opening picture is from Kepler’s Harmonices Mundi : from a scan made of the Smithsonian’s copy, made available on Wikipedia as in the public domain.
In my own work, on the type of ancient astronomy based upon time and not space, I find it to be the outer planets in particular which express harmony in their geocentric synods relative to the lunar year. This applies to Jupiter, Saturn and Uranus but Neptune expresses a rational fraction of 28/27 involving prime numbers {2 3 7} whilst the other three planets only involve ratios involving primes {2 3 5}. The harmony of the outer planets has been a strong source for the sacred numbers found in ancient texts, as with Jupiter 1080 – considered a lunar number perhaps because the Moon is resonant to Jupiter – who is shown by figure 1 to be geocentrically resonant to the other planets and the Moon.
