Sacred Number

My brother sent me a copy of a recent Wooden Book on the Golden Section, a.k.a. golden mean, golden proportion, golden ratio, golden cut and often the greek letter "phi". It is a miraculous but necessary number within the number field for there has to be a fractional part (0.618034*) that when reciprocated, i.e. as 1/0.618, gives a number with exactly the same fractional part, 1.618.  Not only that but....

The golden mean is not just an irrational number (impossible fractional ratio), it is one of a few key ones that are like cosmic constants, in this case connected to the number 5 and the five fold geometry of the pentagon and pentacle star. All this is discussed in Sacred Number and the Origins of Civilization, including how five is associated with the astronomical period of Venus relative to the Earth. The relationship to five is clear in the simple method for generating phi which is to form a right angled triangle with side lengths 1 and 2, so that the hypotenuse is the square root of five (root 1² plus 2² by Pythagoras' theorum). Add one to this hypotenuse and divide the full length by 2 and the golden mean/ section results....

The Solstice having passed, the New Year is cosmically with us. We expect the heroic Sun to make "the turn" and within four days, on the birthday of the solar hero, the Sun can be seen to have headed North again to repeat the mythic journey of the year.

Gargan - Goddess - Maiden: This is an interesting triad inferred within Sacred Number.

The most pithy introduction to the Gargantuan I have read is in the pamphlet The Michael-Apollo Axis by Lucien Richer. It is worth quoting here and copies can be had here.

"We would first make clear that the Gargantua of the legend is quite different from the literary character created by Rabelais who has appreciably distorted his nature. In all the popular tales the giant Gargantua appears essentially to be linked with the movements of the Earth's crust [Fr: sol = earth, ground, soil]*, raising up mountains, carving out lakes or the beds of rivers which he also at times causes to disappear. Although with less tumult, his activity is akin to that of the Giants of Greek mythology and we think that, like them, he symbolises the energies [Fr: forces] of the Earth, his favourite places being the bowels of the earth and the summits. He thus possesses the character of a chthonian deity and, furthermore, in the Middle Ages was often considered to be an incarnation of Satan (Dontenville, ref 4c).

From an etymological point of view, it may be thought that the name derives from the Pre-Indo-European root KAR/GAR = stone. Another like-wise very ancient root might also be found in it: GANDA, meaning: a piece of rocky ground caused by a mountain landslide (16). Finally it is worth noting that the first of these radicals [in the sense of `root'] has doubtless supplied us with the Breton root GAL = pebble (from which comes the French word galet [meaning `a pebble']) and that in Brittany the word galgal is used to describe the heap of stones covering a tomb of the megalithic era. It has, however, also been supposed that the name Gargantua corresponded rather more to the idea of gorge [with the meaning of the `throat' or `gullet'], on account of the character's consuming thirst. Truth to tell, there is no hard and fast contradiction here as one might then take the word gorge according to its first sense which relates to the earth, the Latin gurges meaning: gulf, abyss, [gorge]. This thirst of the giant, like his discharges of liquid, seem to tally well with the activity of the energies [Fr: forces] of the Earth throughout its hydrographic network.
So it seems to us that Gargantua, like the Giants of Greek mythology, could be considered as a projection into the living world of a primitive deity of the earth: Gargan.
This name, Gargan, is borne by numerous place names but it is some-times found modified, especially into Galgan and Gargas. It is nearly always hill-tops or underground sites whose names are linked in this way with this chthonian deity; in France, for example: Mount Gargan in the Limousin and the one near Rouen; Mounts Gargan, Galgan and Gargas in the Alps; the grottoes of Gargas, prehistoric sites in the Pyrenees (4c). In Italy, Monte Gargano, with which we are concerned here, is doubtless the most important site to which the name is attached; Henri Dontenville has shown that this archaic deity very likely had a sanctuary there (4c).
As far as Mont Saint–Michel is concerned, it is its very origin that legend attributes to the giants: according to that legend the parents of Gargantua, Grantgosier and Galamelle, put down in that place two rocks which became Mont Saint–Michel and the little Island of Tombelaine. Furthermore, in the Middle Ages, the Norman mount was sometimes likewise called Mount Gargan.
But how can we explain the link which, in these two sacred sites, is now becoming apparent between Gargan/Gargantua and Saint Michael?
We must first of all remember that all religious historians recognise the specificity of sacred spaces (1, 5, 13, 17). Human beings have not of them-selves chosen the sites for the sanctuaries, they could only discover the `numinous' places (to use again the word adapted after R. Otto, from numen = divinity, in Latin) where the divine made itself manifest. This explains the permanence of sacred places in predetermined sites, which have served a succession of religions.
It is to Greece now that we must go. We know that Apollo, a sun god, was born in the Island of Delos at the same time as his twin sister Artemis. The site of Delphi was, in those days, the seat of the oracle of Gaia, the Earth, whom the serpent Python, the son of Gaia, was entrusted with guarding. Shortly after his birth, Apollo, having chosen to establish his sanctuary at Delphi, could only enter into possession of it after having killed the Python, a crime for which he sought purification at Thessaly, in the valley of Tempe.
This victory of the sun god is that of the heavenly powers over the forces of the Earth and it is this confrontation which truly constitutes the basis of Greek Mythology. ...

Lucien Richer, The St Michael-Apollo 'Axis',

trans Francesca Greene, Gatekeeper Trust 1998*comments in [ ] by the translator.

 When Athene sprang so impatient and fully formed from her father's head, it was as a new goddess for a new age. The waves of invaders from the north had brought with them to Greece a race of sky-gods to overwhelm the timelessly ancient reign of the mother-goddess. Or, to put it another way, it was already the Age of Iron, in which we still live. The Golden Age of Cronus, when humans lived like gods, free from worry and fatigue, was long past; now his son Zeus reigned, having vanquished his father as Cronus had himself overcome his father Uranus, the starry sky, son and consort of Mother Earth herself.
So now the gods lived high and far away on Mount Olympus, their golden apartments shrouded by clouds from human gaze, dividing up between the twelve of them the tasks of deity that Mother Earth had once encompassed alone. Yet father Zeus still had his work well cut out. As Joseph Campbell puts it, `wherever the Greeks came, in every valley, every isle and every cove, there was a local manifestation of the mother-goddess of the world whom he, as the great god of the patriarchal order, had to master in a patriarchal way'. And so he set out on his `long career of theological assault by marriage'.[from The Masks of God] It was from this policy that his daughter Athene was born, yet with her he had gone one better. No need for that dazzling array of disguises to cajole, overwhelm or force the woman into submission this time, no need for showers of gold or transformations into animal or bird to give expression to the inexpressible coming of a god. This time he did all by himself this brain-child was his own idea!

Ann Shearer, from ATHENE, IMAGE AND ENERGY, Penguin, 1998, p2 

 Note here also the reference to Amber and the Baltic, the golden apples of Atlas, and a completely congruent set of repreating patterns.  McHardy shows nine women on an island or secluded place, to be endemic within the place names and traditions of Scotland and much of Europe. They are linked to the "year and a day" tradition, leaving the island for one day to go feasting. The three by three magic square is called after Saturn, that is having nine cells. Even when satanised, these traditions continue on to re-emerge if someone takes an interest.

These nine women are often mentioned as poor maidens that are eaten by a dragon. This dragon is slain by a hero who usually rescues at least one maiden, a story carried through into castles and princesses held in a spell, and so on, a story familiar in triplicate to anyone who has participated in our present day culture.

To conclude, the Dragon and the Gargan are hard to dismiss as different or non-related to women and, almost certainly, a Goddess culture from the Stone Age.   

When I first researched Earth-based astronomy it was based upon the properties of right angled triangles, first of all related just to the periodicity of the Sun and Moon seen from Earth. These properties make right angled triangles, proportional calculators of a remarkable and simple kind. Let me explain since this naturally extends the capability of ancient peoples to perform complex mathematical tasks once they had mastered counting within astronomical cycles. It also led on naturally to the use of triangulation and the measurement of angles in such a way that advanced results could be achieved within a non-scientific (in our sense) culture. 

 Let me show a simple but very sophisticated example. First of all, suppose we have an English foot and want to make the Persian Foot. This can be done using a right angled triangle as per:

Our first requirement is to make a right angle using the simplest pythagorean triangle of 3 by 4 by 5 feet long, the perimeter being 12 feet or, conceivably, 13 knots in a rope with three stakes. More difficult then is to measure a base of 20 feet and an hypotenuse of 21 feet that touches a vertical formed by the extension of the 4 side of the 3:4:5 triangle.

Each of the 20 feet on the base now projects similarly onto the hypotenuse to define a length equal to one root Persian foot of 21/20 feet.  In the same way, assuming you can do it, all the other ancient measures in the ancient metrologists toolbag can be reconstituted from a single standard.

 Given that the ancient builders were known to work to one part in 1000 or better, and that measures were consistent, then as Neal and Michell propose their technology for maintaining measures must have been as accurate. However, Neal and Michell do not suggest how these root measures might then have been varied according to two ratios, 441/440 and 176/175. Instead of explaining these again here, the main point for us is that these are very small differences, 441/440 being just 1.002273 feet in the English module. How could this be achieved?

It so happens (see Sacred Number) that 441/440 can be decomposed, and one way is into 21/20 times 21/22. Since we have the Persian foot of 21/20 we can now repeat the process only making the triangle in Persian not English feet and forming the base out of 21 of these and making the hypotenuse 22 Persian feet long.

Once you decide you need a lot of one kind of foot, you have the option of generating over a much larger distance the exact length you want using triangulation over the landscape.  I will provide the complementary triangle that is one way to geometrically generate 176/175. Lying behind it all is a practical skill and facility with numbers that is only now being revealed by trying to explain the extraordinary capabilities of prehistoric cultures.

 Here the root Roman foot can be employed to fulfill the decomposition of the ratio 176/175 as 24/25 times 22/21. The Roman foot is  going to be enlarged by 22/21 by reading from the base to the hypotenuse.