As such therefore, Pan’s death is another marker of transition at the beginning of fuller historical record keeping. This keeping of history may indeed have spelt an end to the dominance of mythological thought by the increasing use of rationality to unlock the nature of the physical world whilst banishing the complex mental world of allusion. At the same time though, Pan was manifestly not dead as he had been absorbed into the pantheon of Rome via Greece. He was a goat god that helped the Olympians overwhelm the preceeding Titans (associated with Saturn), to impose Jupiter on the celestial throne. We have encountered this process in the gap between Minoan Crete and classical Greece where Zeus appeared. In fact, Cretans came to be called liars because they retained part of the ancient matriarchal principle of the male king who must die, like the year, after a year and a day.

The illustration on the right is by Bob Jefferson. It first appeared on the cover of Talks on Beelzebub's Tales by J.G. Bennett. These talks sought to make accessible the deliberately challenging master work of G.I. Gurdjieff especially for those coming to these ideas for the first time, and originally delivered in talks to the students of the Sherbourne Academy for Continuous Education.

The Cretans not only said that Zeus was born on Crete (as per Greek myth) but also that he died there. This was infuriating for the new male order which had created immortal male gods to displace the matriarchal practices of the Mediterranean. The Goddess Metis was effectively recycled through Zeus’ head, in a virgin birth and “with a shout, fully formed”, to be reborn as Athena thus disposing of any previous divine female history. In this way her Parthenon was so called because she was born without a second parent and was always a virgin herself with resonances for the Virgin Mary. Thus, the appearance of parts of the previous pantheon into the new Olympians represents the inevitable process of reshaping the past familiar forms.

The new mind of classical times gave birth to now-familiar disciplines such as logic. In logical analysis, the facts are deduced without mechanisms such as allusion, metaphor and simile. In logic there has to be cause and effect that can be proved. It means nothing that a river looks like a snake. However, in the latter, high-level and intuitive, description there is a strong poesis that can integrate water, erosion, headwaters, and flood plains into a holistic overview. It is a powerful communication of a subtle truth not accessible to analytical thought, but communicated these days by schematic diagrams.

Download PDF of the superceded chapter 10 of Sacred Number

Some of these can now be found in my books, Matrix of Creation and Sacred Number and others in those of Robin Heath (Sun, Moon and Stonehenge, and his subsequent wooden books such as Sun Moon and Earth) and John Martineau (Little Book of Coincidence). Such direct observations of cosmic order patterned by number are complemented by the indirect sources of ancient numerical knowledge, accessible in the many works of John Michell (The Dimensions of Paradise) and the recovery of Ancient Metrology with John Neal (All Done With Mirrors).

The connections between direct cosmic knowing and what we inherited from the ancient world has naturally defined, in the last 50-100 years, a new subject or “protoscience”, which some unfairly call a “pseudoscience”! I have sought to bring these streams together with the third possibility that the natural form of knowledge for human kind was numerically based and not technological. This reveals a drama with respect to history itself, almost to the extent that written history marks a watershed in the loss of the numerical knowledge.

One of the strongest manifestations of direct numerical structure in our planetary environment involves Jupiter, our Moon and the solar year (hence the Sun, the Earth and even its rotation). The main actors are the following time periods and constants:

• Jupiter's, synodic period of 398.88 days [J_syn] and sidereal orbit of (10.858 +1) years [J_sid]

• The Moon's lunation of 29.53059 days [LUN] and Metonic Period of 19 SY [MP], in which the configuration of Sun, Moon and stars are closely repeated.

• The Solar Year, of 365.2422 [SY] days and 12.368 lunations [SY / LUN]

• e, the exponential constant = 2.718, and its square e² = 7.389

The strange relationships implicit in these are:

1. J_syn x 4 x 19 = 83 SY

2. 4 x 19 [Metonic periods] = 76 SY

3. e² is very close to LUN/4 [e would then be 2.717]

4. J_sid = SY/33,638 [10.858] +1 and 10.858 = 4 x e [where e is 2.715]

These numerical relationships are held together as if by numerical artifice, based upon the clustering of certain relationships within the domain of number itself, that is by properties within the number field itself.

Obviously, 1 and 2 above mean that J_syn/SY = 83/76 to a very high accuracy, varying by just one part in 136,000. Since the Metonic repeats four times in 76 years, then J_syn must automatically be resonant with it as 83/76. But the Jupiter synod of 398.88 days would have “reason” to be (a) just and exactly 83/76, (b) an integer (rational) fraction and have (c) 19 within its denominator as a factor.

We can discover the relative motions of Sun and Jupiter from the fact that there are 365.2422 DAYS in angle within the full year circle whilst in a Jupiter synod, the planet has moved 33.637 days. As in 4 above then, the Jupiter sidereal period is the time taken for Jupiter to traverse the year circle, 365.2422/33.638 = 10.858 plus one because Jupiter has gone one extra orbit over those enacted by the Earth's orbit within the sidereal period of Jupiter.

If 10.858 is close to 4 times e, the exponential constant, we can also note that 33.638 = 12.358 times e so that:

4e = SY/(12.368 * e) and since SY/12.368 = LUN, then the relationship LUN/4 = e² results in close approximation.

From this we can deduce that the exponential constant e “rules” the relationship between Jupiter and the Moon through the mediation of the solar year as a common denominator. This was well expressed towards the end of Matrix of Creation as figure 9.5 (left), where Jupiter is shown to have “captured” the Moon within its harmonic behaviour involving a whole tone of 8:9.

Whilst you could argue that the actual numbers don't matter (only the proportions), this soon appears wrong. The 12.368 LUN per SY is closely 12 +7/19 LUN which allows the Metonic period to resolve itself in 19 years, 7/19 being close to e [as it is 2.714].

Of course (?), e is a crucial number within the cosmos which has special powers when raised to powers with the imaginary number, the square root of minus one. This is the base of imaginary numbers which have led to massive utility in understanding the primes within the number field [Riemann Hypothesis], but with e generate a fundamental mathematical model for all energy transforming systems. The fact that e appears at all means that this system of Jupiter, Moon etc, is somehow normalised to both e and 19.

The number 33.618 (close to 33.638) emerges when the intermediate hypotenuse of a Lunation triangle [see Robin Heath's work] that is 12.368 long at the 3:2 point is also 33.618 feet long if the triangle is built using the [astronomical] megalithic yard (19.008/7 or 2.7154 feet) to build the 12:13:5 triangle so as to represent one MY = one LUN.

Finally therefore, the ancient peoples of the Megalithic left us evidence (through the lunation triangle) of the relationship to e within the year and the Moon and that behind this lies Jupiter, later Zeus, the King of the Gods and hence ruler of the Earth and Moon - once Saturn-Chronos' numbers were relegated to the semitone of 15:16 and the vestigial seven day week.

Root three appears as a very important proportion in the Gothic style of building whilst many sacred cubes are noted in sacred building in general, the Temple of Solomon and Leto [Egypt], Hindu temples, the Delphic altar to Apollo, and the cube of the New Jerusalem.

In his third book, Meditations on the Koran, Earnest McClain suggests that the original prototype of the cube is the cube of 60, which was the base number of the Sumerian and then Babylonian civilisations. From this base, still in use today (within time and angular measure) McClain shows the ability of 60³ to generate a tone map that defines a hexagonal array of musical notes, all within a single octave but held between 216,000 [=60³] and 432,000, a very significant number in, for example, the Vedic tradition as being the length of the Kali Yuga or dark age.

McClain Yantra for 432,000. Only this yantra can yield a hexagonal region where tones and their reciprocals co-incide. The hexagon has 37 tones because 37 is a hexagonal number, viz chapter 10 and the cube of Metatron.
[from p 90 of  Meditations on the Koran by Earnest McClain, Nicolas-Hays, Ney York, 1981]

We need to remember that a hexagon is a cube seen from one corner (and projected upon a flat surface) and that, in McClain's world, all ancient texts were written with numerical tuning theory in mind as a key plot generator. This last point has not been acknowledged yet by the worlds of scholarship or religion because the implications are too profound, subversive to the traditional ideas behind religious texts as communications from God or gods (rather than intimations of the divine world).

Returning to the Ka'aba, McClain gives a splendid account of its possible origins, the background of Mohammed's re-purposing of the shrine and the meaning of its non-cubic design.

Its width, length and height were probably intended to be 10 by 12 by 16 and McClain points to these proportions as being similar to the temple of Poseidon in Plato's myth of Atlantis, namely "6:3 plethora (full)" meaning expressive of 6:5:4:3 in that 5:6 lies between width and length and 3:4 between length and height. These ratios are minor third and perfect fourth.

One should note that the proportion between the width and the height is 6/5 times 4/3 which equals 8/5 the synodic period of Venus [584 days] in terms of the "practical" year of 365 days. The variation of width, length and height can lead to a greater tonal achievement that may be significant.

Why then should the polar radius of the Earth be, according to the ancient model, 3456 royal miles (as I pointed out in Sacred Number)? 3456 is 12 cubed [1728] times 2 and "the doubling of a [cubic] altar" was considered a challenge for the ancients, proved theoretically impossible in modern times. New Jerusalem was declared in Revelations to be a cube of 12,000 per side and as I found, one royal mile [8/7 miles] equals 6000 Greek feet of 176/175 English feet. This makes 1728 royal miles equal to the volume of a cube side length 2 royal miles of 12,000 such feet. [This I found in potentio within the layout of Washington DC].

The volume of a relatively small cube of 12 royal miles, projected to form a hexagon upon the surface of the Earth, generates an allusional volume one half of the polar radius. This relates to both tuning theory and the doubling of the altar. Such a cube has only powers of 3 and 5 plus 2 that figure within 10 = 2 times 5, and 12 = 4 times 3. However, 2 royal miles is 1 over 1728 of the polar radius, that is 1 over 12³ of its length.

Taking up the "doubling of volume" for a 12 side cube, the result is a cube 12 times the cube root of two in side length. The latter is very nearly 1.26 [actually 1.25992105, one part in 16,000 different] and this raises some interesting "ancient metrological" considerations, for John Neal's Standard Canonical transform is 126/125 or 1.008 of a foot. We can then see that 1.25 is 5/4 [the major third] and that this multiplied by 126/125 yields a highly accurate ability to create a cube that has doubled in volume. 5/4 times 126/125 is 1.26 which then times a side length of 12 gives 15.12 for the double volume cube's sides.

It appears then that this metrological ratio happens to be a practical means to the "doubling of the cubic altar" problem.

A unit radius has been drawn so that, using a rational Pi of 22/7, one eighth of the perimeter is 11/14 in length. We know that a very good approximation to the square root of 2 is 140/99 and that the vertical shown must be the reciprocal. On can notice therefore that to transform 11/14 into 99/140 we have multiplied by 9/10, the minor wholetone ratio (lost in our equal temperament).

This is an interesting relationship because it employs the key ancient approximations of Pi and root two with a linkage straight out of ancient tuning theory - a tradition so well developed that it was arguably the coded source of most surviving mythic material such as the Old and New Testaments, Gilgamesh, etc. [Much of what remains is then absorbed in the massive ancient speculations about precession of the equinoxes].

The Biblical source of 99/140 concerns Abraham and circumcision. As Ernest McClain shows in Meditations on the Quran,  Abraham's decision to circumcise himself at the age of 100, and similarly Ishmael at age 13, uses circumcision as a code for removing a little bit from a known rational ratio, 10/14 by removing a hundredth part to obtain 99/140. The 13th fifth in music causes the Pythagorean comma, a musical sin that must be corrected, symbolised again by removing something small "like" a foreskin. More of Ernest at www.ernestmcclain.net.

In the diagram, a geometric arrangement has achieved the same as this rule of thumb but also shown a relationship between a circle and an inscribed square. Multiplying by 14/11, the sector becomes a unit length and the vertical just 9/10, the radius 14/11. It is ideal (as shown by Neal in the Scottish Brochs) that the radius have 7 in its length. Here there is 14 and we also see the 11 as "pre-removed" to obtain the unitary circumference (of 8 units long).

It is very unlikely that the diagram above was not known by  the specialists of the Megalithic and Middle Eastern cultures as it reveals rational order between two irrationals, linked to a harmonic ratio.

"The staggering figures on these tablets were originally ignored as the ramblings of weak-minded Sumerians obsessed with numbers.  Nevertheless, Chatelain saw that there could be a lot more to it — his attention was drawn to the number 195,955,200,000, and he explains in his book how this is the expression of 70 multiplied seven times by 60... this huge cycle came off of Sumerian clay tablets, which were found in the burned-down remains of the Library of King Assurbanipal in Nineveh."

from www.divinecosmos.com

You might guess this "constant" appears to be in seconds of time! Even today time [and angle] is as it was defined by the Sumerian notation of base-60, with sixty seconds in each of sixty minutes in each of twenty four hours of the day. The constant is said to miraculously encode a whole range of astronomical if not physical constants. With respect to Sacred Number and the Origins of Civilization chapter one [viz. Saturn and the seven day week], something immediately comes to light;

1. In seconds, the Nineveh Constant is exactly 60 times the Saturnian synod of 378 days², being 22680 days long.

• If we take the Brihaspati period (chapter 9), called Trigon in the West, in which three conjunctions of Saturn and Jupiter takes place, it is found to be 60 times the Barhaspatya samvantara of 361 days (19²) or 21660 days which would give the constant 187,142,400,000 seconds. (It takes 361 days for Jupiter to traverse a single sign of the zodiac.)
  

The significance might be that the Saturn round of 60 was somehow a "Lord of Measure" just as the Trigon Period of Saturn-Jupiter conjuctions came to be seen as a "passing of the Measure" from Saturn to Jupiter.

The period 378 days is the time Saturn takes to traverse 1/28th of the Zodiac rather than the 1/12th of a sign. This period is one origin for the Indian Nakshatras of which there were 28 or 27, perhaps because these became associated with the orbital period of the Moon [27.32166 days avg] with later emphasis on the sign in which the Moon lay [the Moon moving in a day a similar angle as Saturn moves in "a year"]. This was clear in my first book, Matrix of Creation, where the zodiac of the ancient world appears to have been associated with 28 and the number seven which Saturn rules [especially through the week and the pole of the Earth the seven-fold "hill of heaven"].

^1. John Neal's web site is www.secretacademy.com and to increase its availablility John's very significant, large and quite heavy master work on metrology All Done With Mirrors can be bought here or by cheque and post to the address on his website.

2. The "Saturnian synod of 378 days" is actually the 378.09 days [on average] that the Sun takes to manifest the same aspect to Saturn, the slowest of the planets and called the "god of time", "el pondorosa" [the slow one] associated with the metal lead and plumbing the depths. Saturn also maintains the pure ratio of 15:16, a musical semitone, to the lunar year whilst Jupiter maintains a whole tone of 8:9 to the lunar year. These and other relationships form a numerical matrix of meaning behind such traditional associations.

National Geographic photographer Martin Gray has visited and photographed more than 1000 sacred places in more than 100 countries. His new book Sacred Earth features 200 lovely color photographs of pilgrimage sites in 80 countries. Published by Sterling, Sacred Earth is the most significant photography book in the world this year.

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Instead of 0.618 being attached to N [N=18 giving 18.618], 7/19 is attached (that is 0.36842) to N=12 to give 12.36842 lunar months per solar year, so that this fraction will resolve over the Metonic period of 19 years (see last posting). This is also quite closely proximate to 1/e (0.367879...), the reciprocal this time of the exponential constant 2.718281828...  rather than the golden mean.

19/7 is 2.7142857..., which whilst making it amenable to the Metonic also closely approximates the Megalithic yard of less than 2.72 - a unit of length recognised by Alexander Thom through statistical analysis of survey plans. One can see a relationship to the royal foot of 8/7 feet, its cubit of 12/7 feet and thence to a strange step of 19/7 feet rather than 20/7 [ a step usually being 2.5 feet). It must be the Astronomical Megalithic Yard that interests us here, a relevant formula for it being 19.008/7 feet, equally 19008/7000 which allows 19008 to provide prime number 11 in the numerator, and thence 11/7 making this a very fine Polar measure - it divides into the polar radius of the Earth, according to the ancient model of the Earth.

It was my brother's re-discovery of the Lunation Triangle with base 12, hypotenuse 13 and height 5 (the second Pythagorean triangle after 3-4-5), that revealed the ancient mechanism for harmonising the Sun and the Moon through an intermediate hypotenuse found at 3 high on the third side. Its length is the square root of 12² + 3² = 144 + 9 = 153 (fishes in a square root net, cast on the "right" side) 12.36931688... just slightly more than the 7/19 required for the Metonic.

This is the number of lunations in a solar year. It is close to but significantly not one third. The close thing gives you the rule of thumb, 37 lunations in three years, and interestingly 37 is a hexagonal number, 19 + 18. The number should be 365.242/29.53059 which equals 12.36825949, the underline being the signature of 7/19. The proximity to 1/e to 0.368 leads to the use of the megalithic yard (= e feet) to build the Lunation Triangle, whereupon the 0.368 approximation in the hypotenuse of 12.369, cancels with the 2.715428 feet approximation to e in the megalithic yard to yield exactly one foot at the end of 12 megalithic yards. The foot actually produced by this procedure is a Greek foot, 441/440 greater than the English but within that module.

This early link between metrology and astronomy through number appears very unlikely but was clearly intended and very useful.  It enables prediction of lunar phases and hence also of potential eclipses near the lunar nodes, also trackable using triangles (see previous) or using the Aubrey Hole simulator pioneered by Fred Hoyle and by inference, available as an early "clock" for astronomical events (see Robin Heath's descriptions of this).

I can now quote from an unpublished 1996 manuscript of a book written by Robin and myself.

Twelve and Thirteen

As we have seen, there are irrationals and their equivalent integers at work in the Moon's behaviour and it appears that the year is poised between the numbers twelve and thirteen, seen graphically in the lunation triangle.

Let us take the situation where the new moon began the year and twelve lunations [or lunar months] have passed. The Moon has returned to the Sun's position but 0.368 lunations remain in the year. As a part of the year, this period is 10.867 days long and therefore the Sun is 10.867 DAYS (of angle) from the year end on the Year Circle.

The Moon will travel 145.27 DAYS in that 0.368 lunations but 10.867 DAYS is travelled, by the Moon, in less than 20 hours and therefore [because the Moon reached year end in less than a day], in practical terms there are 13 orbits in [the time ]required for] 12 lunations. [In fact 12 lunations equals 12.9703 lunar orbits on average]

If we multiply 0.666 [2/3] by 12 over 13 we get 0.615 and so the ratio 12:13 is equivalent to 0.615/0.666 and, we think, a further veil has dropped away from the lunar number system. We can, in retrospect, see how the ratios equate like this: 0.666 is (2 over 3) which is (8 over 12/0.615) which is then 8/13 [because 8/13 = 0.615, a Fibonacci]

[If 12/13 = 0.615/0.666 = 8/13 times 3/2]

 The denominators are the creative forces and 12 evidently belongs to 0.666 [= 8/12] and 13 to 0.615 [=8/13], but in their relative size [one real fraction to the other], the other's denominator becomes the number of units relative to the other: [a fact perfectly expressed in the Lunation Triangle and ] a magnificent reciprocity based upon the field of pure number and expressed in the Moon's behaviour.

*** 

The square brackets are my attempt to make it more clear than mud. This remains an interesting insight linking again to a role for the Golden Mean, through Fibonacci approximation, in achieving near rationality within these two lunar time periods of orbit and synodic month. I went on (in Matrix of Creation) to find the reciprocal Golden Mean fraction of the lunation period, exactly 18.25 days, synchronous with Venus and the Practical Year of 365 days to a very high accuracy. The miracle is that all of these exact and approximate relationships coexist to create a rational environment at all, but this does require one to know the extent of the numerical network involved as well as its more sensational highlights.

To be able to form a hypothesis is a rare skill these days and this is exactly what is required to make sense of such an extended network of relationships.

"Knowledge gives nothing to a man until he gives everything to it"
(a Sufi aphorism through Idries Shah)

Known to the (classical) Greeks as the Metonic period, in 19 solar years the Moon's phase and its location in the stars repeats to quite high accuracy. Since the Sun illuminates the Moon to generate its phase, then the Sun also must be in the same relative position to the Moon, nineteen years later.

Also known to the Greeks (but demonstrably known also in prehistory)  there is a period of just over 18 years in which an eclipse of a given sort will recur. Thus, after 18 years of an eclipse (solar or lunar) one can make an important prediction of another, similar one. This "just over 18 years" is in fact the time it takes for exactly 19 eclipse years - bringing 19 in again - a type of year (346.62 days long) mentioned in the previous article and associated with the movements of the lunar nodes - the crossing points at which all eclipses take place.

In the 1990's, probably 1993, an amazing "fact" arose for me. If one builds an 18:19 right angled triangle, the third side is almost 6 in length. Conversely, if 19 and 6 are used then the base becomes 18.027 solar years long and the Saros period is 18.030 years long. It seemed to me that this near-Pythagorean triangle of 18:19:6 had been incorporated in the relative lengths of the solar and eclipse year and hence in 19 times these.

The Near Pythagorean Triangle that occurs with 18:19 when the third side is whole,
to accurately approximate the Saros Period of 18.030 years or 19 eclipse years.

The simplest thing to realise about the Saros is that 223 (a prime) lunations occur within it and that in 19 years, 235 lunations complete the Metonic. The difference is 5 + 7 = 12 lunations, the length of the lunar year. This is true because such cycles exhaust their variety in a symmetrical fashion, so that there is, in a sense, a lunar year (of 12 lunar months) at both the beginning and the end of the Metonic. An eclipse one lunar year (12 lunations) into the 19 years will result in an eclipse at the end - and the whole thing is continuous whilst, for the sake of understanding, we must measure starting points. In reality, continuously, the Moon's position is a repetition of where it was 19 years ago as well as where it will be in 19 years.

The actual triangle has the Saros period as 223 lunations and the Metonic as 235 lunations long giving an 18.030 year Saros period. The "unit" becomes 12 lunations and the third side 6 times 12 = 72. 235 divided by 19 is, of course, 12 and 7/19ths of a lunation or 12.36842105 rather than the actual of 12.36826623 lunations per solar year, yet accurate to 99.998748% which is why the Metonic is an accurate 19 year synchronicity.

The Paradigm of Number Field as Cosmic Generative Principle

Something needs to change about how we view co-incidences between such a triangle and the reality found in time. The geometry represents a property found within the number field itself and this is the credible explanation for such a geometry "being used", that the number field can do very special things when these special relationships between numbers can be embodied within dynamical systems. Rather like the strange attractors of chaos theory, such arrangements allow far simpler time relationships to occur that seem mystical to us but are in fact artifices of number.

I am not saying that this is a physical explanation (yet) for how the Moon could have come to have such relationships based around 19. Rather, that these relationships do work in the same sense that a machine allows things to be achieved that are otherwise impossible. Were such work associated with the number field, just as harmony is, then such structures in time echo to the fundamental structure of the universe prior to any Big Bang. In this sense, they might function like natural laws based on number rather than on physics, as in gravitation and the like.

The Golden Mean is already a perfect example of such an edifice since, it is the only real number proportion to one where the reciprocal and the square have the same fractional part (0.6180 = the reciprocal and 2.6180... the square). This artifice is found broadly in life but astronomically in the orbit of Venus through the Fibonacci series (see Matrix of Creation and Sacred Number on this).  Venus manifests phi just as the Moon manifests the properties of the number field relating to 19. Jupiter and Saturn manifest 18:19 in their synodic periods to give us the seven day week.

Mystifying numerical relationships, that appear regressive to modern science, probably belong to the number field, a field that few study in depth or with practical application. If these relationships are found, as I and others have shown, in the practical dynamics of the Earth's environment; then the association with prehistorical knowledge and then later mysticism has given a false impression of superstitious thinking when the facts speak for themselves - of a valid numerical not physical knowledge.

How this works can be shown using the triangle of the previous entry involving 18.618 and 19.618:

 The third side is quite interesting, apparently physically meaningless*, being just over 10 times the reciprocal of phi. I would like to work out an intermediate hypotenuse that is 19 long - the Metonic in years whilst the Draconic is 18.618 years (year of the lunar nodes) which period is 19.618 eclipse years long.

*The actual length of the third side is 6.1835265 which was rounded up in the diagram to 6.184. However, the number of lunations in half a year is 6.18413, two numbers within 99.99% of each other. There are 6800.076 days in a Draconic period of 18.618 solar years and 19.618 eclipse years in the same period making the form of the triangle correspond to the same period and the division of it by different units, the solar and eclipse years.

19² - (18.618)² = 361 - 346.62 = 14.38 and the sqrt is 3.792. If we divide the third side above (6.1835) by this the result is 1.631. This is nearly 1.618 as if, with N:N+1 and N=N.618, the whole number hypotenuse is found near the golden mean point on the third side, as below:

 In nature, such a working fact could generate an integer relationship where it would otherwise be highly unlikely.

1. Kneading the crust when the Moon formed orbiting only tens of thousands of miles above its surface.
2. Tilting the Earth to create our familiar phenomena of weather, seasons and large temperate zones.
   
3. Stabilising the tilt which otherwise would have oscillated wildly.
4. Continuing to regulate seismic and volcanic activity.
5. Protecting Earth from many bombardments, as does Jupiter.
6. Producing tidal influences in more recent times that evolve shorelines and large tidal environments.

During its existence the Moon's orbit has receded and the orbital period has therefore lengthened, as the energy from tidal interactions has slowed the rotation of the Earth, transferring energy to the Moon. The current orbit is on average 27.32166 days and the month 29.53059 days, the time it takes the Moon to again catch up with the Sun.

It's orbit is about 5.1 degrees relative to the plane of the solar system, effectively to the Sun's path through the year. The Sun's path, because of the tilt of the earth, is tilted and about 23 degrees to the celestial equator, which is the Equator of the Earth projected up into the sphere of the fixed stars.

This all means that the Moon does not follow the same path as the Sun in the sky. It travels above and below this path and only crosses at two points, an ascending node and a descending node where the Moon moves to the north of the Sun and to the south of the Sun respectively.

The positions of these nodes is moving, in the opposite sense to the movement of the Sun. Also, where these nodes are, the Moon can come in front of the Sun to cause some sort of solar eclipse, or the Moon can be opposite to the Sun in which case a lunar eclipse of the Moon by the Earth's shadow can occur.

Currently, the Moon is in such an orbit that it can just completely cover the Sun in part of its orbit (a total solar eclipse) though in other parts it is further away and smaller (causing an annular eclipse).

Many people think that the phenomenon of totality in solar eclipses represents an unlikely fact, indicative of some possibility that the Moon seems designed to do this. Certainly the likelihood of a technical civilisation co-inciding with this condition is theoretically an unlikely natural event.

However, the deeper one looks into the time periods associated with the Moon, the larger a network of co-incidences emerge and here I am going to take one area and show how ridiculously unlikely it seems. The subject here is the movement of the Moon's nodes relative to the year and the nodal or Draconic year of 18.618 years. (Other information can be found in Matrix of Creation or Sun, Moon and Earth by Robin Heath)

Because the Sun moves along the ecliptic in the opposite direction to the lunar nodes, the Sun will cross a node where the Moon might be in less than half a year. The Sun will recross a node after less than a year, in fact in 346.62 days on average, a time period called the Eclipse Year.

If 346.62 is subtracted from 365.242, the solar year, then the difference is 18.622 days. The square of 18.622 is 346.779 days, very similar to the length of the eclipse year. The square root of 364.62 is in fact 18.618 days and if this is divided into the solar year, then 365.242/18.618 = 19.618. That is, the eclipse year and the solar year appear to have a natural divisor, the period of which is 18.618 days long.

Using the Megalithic technology of right angled triangles, the two years can be represented as an N:N+1 triangle as below. A right angled triangle can always be represented in this form, where the difference between the hypotenuse and the base is divided into each of these to normalise the triangle. Technically this is called a superparticular triangle and it represents the essence of the triangle and the relationship between the two longer sides.

 The logic of this triangle is quite clear once you can read it. The base line of 18.618 must be one less than the hypotenuse of 19.618 (units of 18.618 days) because the sun moves 18.618 DAYS on the ecliptic "year circle" whilst the lunar nodes move away from the Sun just one DAY. In moving away from the Sun, a node is moving towards an earlier reunion with the Sun, around the far side of the year circle.

In the micro world, the creator of the relationship is the relative motions of the Sun and the Nodes. If this was a different ratio than 18.618 to 1, then another N:N+1 triangle would emerge but, because all right angled triangles can be normalised in this way, another interesting numerical relation would be available. However this triangle is special because the unit underlying it of 18.618 days also figures in the N of the N:N+1 triangle, making the eclipse year the unit squared.

Were the unit larger, what would happen? If the nodes moved more quickly then the triangle will get steeper with N reducing in size. This means that the excess of the solar year over the eclipse year is becoming a larger proportion of the solar year, i.e more than 18.618 days. Thus, the units of the triangle and the N implicit within its N:N+1 form diverge at any value other than they are.

Only in the present relative motions of the lunar nodes, and solar motion on the ecliptic, can the triangle be normalised. This is extraordinary enough. However, it is also true that the length of a day further divides up the excess of 18.618 days into the number 18.618 that also belongs to the N:N+1 essence of the triangle. This cannot be possible unless the rotation of the Earth is, by design, perfectly in time with this relationship.

Finally, in the macro world, the 19.618 of the hypotenuse represents also the number of eclipse years in the Draconic period of 18.618 years, the latter being the meaning of the base of 18.618 years. In that time the nodes have completed one complete revolution of the ecliptic, represented here by the number 1, which is how this normalisation of triangles manifests outside the "surface" of the solar year - all beyond the year is the reciprocal of all found within the year. This is a natural consequence of recurrence since each divisor of a period also manifests in longer periodicities that are numerically self-similar but reciprocal.

Every day, we can say, that the Moon's nodes move 1/18.618 of a DAY [on average] on the ecliptic

The above relationship is very hard to explain and since 1994, when it began to become clearer to Robin [Heath] and myself, it has remained a curiosity awaiting and explanation that would reach an audience. Within lies just one of the great co-incidences outside of science that the Moon provides. [In Sacred Number I use a John Michell anomoly relating the Earth, Moon, Great Pyramid and Pi of 22/7.]