The Petrie Museum has a game from the Egyptian Middle Kingdom which is also widely found in the ancient world, called Hounds & Jackals or 58 holes. Two players had a set of sharp sticks which can sit in each of the 29 + 29 = 58 holes. The top hole is large (like the Cretan 34 hole circular stone at Malia in Crete) and therefore one can see possibilities in such artifacts for storing objective numerical information as well as being kept within the cultural life of the people through having a values second purpose (rather like the 52 playing cards).

Cretan 34-hole Kernos

This was exactly how Gurdjieff suggested that, at a meeting of wise men in Babylon, it was seen that ancient knowledge would be forgotten were it not that art, games, buildings, dances, music and so on were designed to incorporate the knowledge until such time that human would be able, once again, to understand what they meant. In Beelzebub’s Tales such artifacts were termed logominisms.

Sacred numbers arose from ancient man’s observation of the heavens, and represent the secrets of cosmic proportion and alignment. The ancients understood that the ripeness of the natural world is the perfection of ratio and that the planetary system–and time itself–is a creation of number. We have forgotten what our ancestors once knew: that numbers and their properties create the forms of the world.

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.

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.

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).

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.

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 5^{th} 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

By my 6^{th} 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.

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.

For instance, Jupiter has a synodic excess over the solar year of 398.88 days and this means its angular motion is 1/ 398.88 DAYS per day while Saturn’s synod is 378.09 days and its angular motion is 1/ 378.09 DAYS per day. These synods are, by definition, differential to the Sun at 1/ 365.2422 DAYS per day.

Without seeing astronomy as calibrated to day and year cycles, one is robbed of much chance to appreciate the megalithic view of time and the time-factored buildings that came to be built in pursuit of quite advanced knowledge.

Looking from the relatively large cycles to the extremely small, daily angular changes of celestial bodies seen from Earth, reveals a further obscuration created, in this case, by the heliocentric view of the solar system, rather than the geocentric view which is obviously founded on days and years seen from the surface of the planet.

The largest cycle the megalithic could see using their techniques, reverses the direction from large-to-small to small-to-large since the precessional cycle (of the equinoctal nodes of the earth’s obliquity) is around 25,800 ± 100 years long. A star or constellation on the ecliptic appears to move east, like the lunar nodes, and using the angular measure of DAYS, it is possible to estimate that the equinoctal points move by a single DAY, in a given epoch, something like 71 years. The precessional cycle is therefore 71 years multiplied by the 365.2422 DAYS of the whole ecliptic.

The most important benefit of using DAY angles is that knowledge of a few celestial periods opens up a realm in which different scales of time can be derived from first principles. And added to that, the celestial periods appear related to one another so that so-called sacred numbers emerge such as the seven day week which divides into both the Saturn synod (54 weeks), Jupiter synod (57 weeks), the 364 day saturnian year (52 weeks) and others.

To understand the full scope of megalithic astronomy requires a geocentric calibration of the ecliptic as having 365¼ angular DAYS.