When we say the Sun’s motion is just less than a degree, what do we mean. The first evidence of the degree appears historically in the remains of the Babylonian tradition, a tradition very focussed on astronomy. Whilst these ancient astronomers divided up these astronomical wholes, it is the objects of their study that truly divide up the whole sky with their relative motions.

The Babylonians evolved a system of number with a base 60, which is six times larger than the base we use today. In dividing up the whole circle, they used 360 degrees, that is ten times their base and this is because the year is just over 365 days long and this has a close relationship to 360, which is the nearest number that divides perfectly by 60 and thence divides perfectly by the first three prime numbers 2, 3, and 5. Instead the 365 days of the actual year divides by 5, but this yields the prime number 73, inconvenient for calculations.

We know therefore that division of the whole using 360 degrees entered the historical record through Babylonian science and also that the Egyptians used decans of 10 degrees within their own astronomical observances. This evolution of degrees has been combined with numerous other innovations emerging from the near east at the end of the Neolithic age, innovations that were thought to have diffused into Europe to form the cultural components of Classical Greece and the “history of the west”.

The degree is now so ensconced now in the cultural mind that, even though the base of 60 was superseded by the decimal base, we still divide degrees by 60 to form minutes of a degree and divide minutes similarly to form seconds of a minute of a degree, which are 1/3600 of a degree or 1/ 60 squared. However, as we see in the chapter on number bases, maintaining a base system requires an arithmetic combined with a notational system. The Babylonians had these but it remains an open question as to what any preceeding or contemporaneous cultures might have used to achieve the division of the whole circle. It seems unlikely that The Megalithic culture would have used it

The Babylonian use of a base with 2, 3 and 5 made their system very useful for the expression of musical harmony and indeed their own precursor civilisation, the Sumerians, had considerable knowledge of all the facts of musical harmony since their major gods had numbers associated with their role that in turn formed musical intervals within the early numbers (c.f. 40 = Enki , 50= Enlil and 60 = Anu, the three great gods of the Babylonian pantheon viz. Ernest McClain's work).

Therefore, since the megalith builders were also very accomplished in astronomical observation, and in surveying the land also, building circles, large alignments and so on, then there is a question mark over their means for achieving their results. We know, for instance, that they built these stone circles and had access to an extremely full corpus of sacred geometrical knowledge. We also know now that they used a system of ancient metrology to measure their constructions in various symbolic and practical ways whilst also making their work correspond with celestial events, especially on the horizon.

A circle was approximated in most ancient cultures as having the relationship between its diameter and circumference of 22/7 which is blah compared to blah. This has almost certainly led to a deep symbolism that surrounds the number 7 as sacred and polar and the number 11 as operational and representing the meridian of the Earth. The natural way of dividing up a whole circle could then also be seen as requiring the number 11 to be used, especially when one is engaged in physically realising circles, as the megalith builders were.

This is the clue to the inheritance, quite subliminal, from the ancient world of their system of weights and measures, particularly measures involving length. These measures formed an ancient metrology, or science of measuring and designing physical structures and we know that it was highly disciplined.

One primary discipline was not to use any prime number greater than 11 within their measures. The reason was that they wanted to be able to use measures, not only for pure harmonical ideas like the Babylonians, but also for achieving work in being able to translate between circular measure and linear measure.

This activity of relating the sky to the earth has both sacred meanings and practical outcomes. On the one hand one can believe, and there is clear evidence that they believed, that the cosmos has given rise to the earthly world. Still to this day, religion pins God somehow to heaven and science pins life on earth to the creation of a fortunate universe where life could arise.

On the other hand, any ancient astronomical finesse has to have a set of tools to achieve outcomes such as exact alignments and knowledge of long term periodicities in the heavens.

The ancient measures of length have one fundamental characteristic. They are all rational fractions of the English foot, but why? The reason is almost certainly so that the English foot represented one, the whole, and that all the variations of it such as 8/7 or 24/25, had some primordial character and function in dividing one in a unique way.

This range of measures are however linear measures, whilst the measures of the sky are angular, divisions of a circle. How the two relate requires a fresh look at the nature of the circle itself and the tasks that measuring angles imposes within it.

Most people see the circle as being made up of four sectors, each covering 90 degrees. There are strong reasons for this, emerging from the nature of trigonometrical reality and the application of two dimensions of measurement.  Using the east-west as one dimension and north-south as the other, as one walks around the circumference from the west, towards the north, one moves rapidly north whilst moving very little to the east. However, the easterly progress increases whilst the northerly slowly tapers down and this relationship between what we call W and N leads to the function Tangent(angle) = N/W.

From a modern perspective, circular functions are looked up in a standard trigonometrical table of angle versus tangent, sine and cosine. The tangent is just the sine over cosine ratio, that is the N/W above. Such tables have been found on Babylonian clay tablets. However alongside these are also found compendia of triangles, especially Pythagorean triangles with whole number sides, and these imply that using triangles to represent angles was also a known technique, perhaps an older one.

Knowing the tangent triangle for an angle can be as good as having the angle itself, in practice. Thus, with metrology and a science of triangles, one can do work without having 360 degrees to measure and therefore without any trigonometry. (see later chapter on such as science)

If, for one moment, we can possibly slip into a primitive perception where (a) numbers are significant cosmological factors and (b) the low primes 11 and below are required to measure things involving angular measure, then; how would one wish to view the circle. I would propose that the most significant aspect of any phenomenon is that which does not repeat the same behaviour all over again. Using this criterion therefore, we can say that a circle should be divided into 8 in order to define the essence of its circular variation in linear terms. That is, the reality of the two sides of a triangle, apart from the radial hypotenuse, find complete expression in the range of triangle from zero to 45 degrees in our parlance of degrees.

 

What I am responding to is the contradiction between a megalithic culture that had mastered measurement of both length and angle and the likely fact that they did not have the new Babylonian tool for doing this, that is trigonometry. This makes my approach conform to the modern cultural norm of not expecting the prehistoric mind to have developed abstract algebra and geometry until the very dawn of history, and the factual written evidence that we have of this development. Whatever came before, if it achieved a monumental and astronomical competence, this must have been through an alternative way of achieving similar works.

If we assume that the Stone Age had evolved the means to build what it did by its megalithic stage, then some completely new way of looking at angles and measure but be implicit in ancient metrology.

This new way of looking is to see the circle as divided up into a repeating eightfold cycle in which the growth of one dimension of the tangent triangle relative to the reduction in the other dimension is a repeated phenomena.

Having developed a metrology based upon fractions of a foot, in which only the first five primes were necessary, the 45 degree triangle becomes the representative of the number one and hence symbolic of the English foot. The hypotenuse is 1/ root 2 (equals the radius of a circle) and here we see that in two dimensions it is the root of two that is operative, as in the square and the circle drawn upon a two dimensional surface.

At this point an anomaly can be mentioned in that the latitude of Silbury Hill is accurately “360/7 degrees”[Heath, Robin, 1998]. If we translate this as being a fraction of 45 degrees; 360 divided by 45 is 8 and so it is that the latitude of Silbury Hill is actually 8/7 of the latitude 45 degrees. Of course, latitude is an angle and not a measure, but 8/7 is also the royal foot of the Egyptians, and a ratio considered representative of the difference in height, in sacred art, between the semi-divine ruler and the ordinary man.

As we shall see later, the latitude for the “manifestations of Mary” (and of much else besides) is 43.2 degrees and this is 24/25 of 45 degrees, in linear measure the Roman Foot of 24/25 feet. It was this fact that alerted me to the connection between angular measure, 45 degrees, and linear measure.

Suppose that the practical measure evolved within ancient metrology had an angular equivalent. This could have been seen as a natural cosmological consequence for the way things naturally divide up on the Earth a primordial and cosmic system employed in the creation of the Earth and this a “master plan” for the organisation of experience. This might have caused a significant monument to be erected at Silbury Hill, to monumentalise “sacred latitude”. Today a similar thing would be that Catholics are pressing to elevate the Virgin Mary as co-redemptrix of the Church, with Jesus, a movement reinforced by these manifestation of Mary at a sacred latitude today. It could be that places where interactions with higher worlds tend to become monumentalised as very significant to human life and culture and so, eventually, we must address whether such sacred latitudes exist.

Here we are groping towards the possibility that late Stone Age peoples read angles through tangent triangles, measured with a metrology that was based upon the same primordial ratios as these sacred latitudes “as if” the cosmic itself used prime numbers to divide wholes. Their use of linear ratios, limited by the nature of circles modelled by 22/7, had a divine precedent in the angular world.

Any angle can be measured by building a right angled triangle where the sightline is along the hypotenuse. However, by building a large circle, it is also true that if the circumference is made to be rational over 45 degrees of the circumference, then the tangent triangle for any rational fraction of 45 degrees can be constructed. This makes the construction of circles with a controlled circumference in different whole numbers of rational feet would also a system of angles to be evolved that, like the ancient measures of length, expressed ratios containing only the first five prime numbers. Of these primes the larger two, 7 and 11, are exactly those utilised by megalithic builders to represent Pi, the key ratio controlling the relationship between radius and diameter of a circle.

This technique of employing circles, ancient measures and rational fractions would thwen form a simple and coherent toolkit for being able to operate a scheme of angles and lengths that had great symbolic meaning. This symbolism would then emerge identically in the realm of both angular and linear measure and latitudes would then become associated with rational fractions of 45 degrees. It takes just one more symbolic act to evolve the idea of sacredness to these rational angles and that is to suppose their precedence or significance within the cosmic scheme itself.

We cannot know what the experiences were of the Stone Age people but, given that the manifestations of Mary appear, at three sites (Garabandal, Lourdes and Medjugorje), then it is possible that direct experiences were noted at certain latitudes. Of course, one has to ask, what are such experiences made of and are they truly of an objective nature. However, there are problems in our definitions such as objective and subjective when dealing with the spiritual world because these dichotomies appear to collapse exactly because, in the spiritual world, they are not separate. This will be gone into further in a later chapter, but it is reasonable to say that we should not expect the spiritual world to be structured in the same way our experiences within existence are. If existence is a created condition, then  that which precedes it will have differences else why the need to create it?

One example of the contradictory nature of the spiritual world is that it can contain multiple, equally valid, alternative realities whilst the existing world has to settle for one condition at a given time, it cannot support more than a single actuality. It is in fact for this reasons that what people bring back from the spiritual world can be so powerful a force for change but also how confusing the different versions of the spiritual world can be, as manifest in the differing yet absolute visions embodied in Judaism, Christianity, and Islam, to name but a few. The oneness of all religions is not a practicality today despite any attempts to increase tolerance.

We can certainly recognise that the idea of sacred sites is not a pathetic fallacy or just an arbitrary production upon the landscape. There appears to be an objective (and subjective) action recognised by all religions and also monumentalised deeper into prehistory. We see the Benedictines in particular and the Church in general overlaying the earlier pagan sites. We see Jerusalem, Mecca, and other holy cities seen as centres of the world.

However, we also have an impossibility that the earth itself could be sacred and be manifesting geologically according to some spiritual scheme. It is because we consider the surface of the Earth to be merely substantial, only caused by geologic forces, that we cannot see a mechanism any more whereby the earth could connect to the heavens or rather the heavens to connect to the Earth.

The Earth is a moving target, which means that the sky of stars moves continually above us. However, two things are fairly constant.

The poles are of course, therefore, a sacred latitude of 90 degrees north and south and at this, the parallel has reduced to a point.

If one were looking for some pattern overlaying the earth, then the idea of sacred latitudes is a natural one. If, in addition, one comes to such a concept from the point of view that low prime numbers within ratios are a cosmic principle, then having the sacred latitudes organised in this way becomes a natural organising principle.

If there is evidence, now more rare, of human contact with spiritual forces at these latitudes, then the definition of sacred latitudes by humans in the megalithic could meet their natural employment within the cosmic scheme. This could be a true harmonisation of above and below within a framework that transcends the causality that rules the existing world on the surface of the planet. Just as an aircrafts wing is modelled on the nature of air and aerodynamics, so also a megalithic focus upon a scheme including sacred latitudes would model the nature of the spiritual world in its necessary and possible points of contact with the material world.

A culture that had established this level of contact with the spiritual would be able to mediate for the spiritual. However, a culture without this would not be able to relate consciously with the spiritual worlds except through their subconscious minds. This is exactly the story of the present time and when looking at these latitudes one finds a mixture of spiritual and catastrophic events occurring along them, as if the failure to mediate causes human history of tragic kind, with many deaths and acts of atrocity co-incidental to these latitudes.