Sacred Number

In chapter 2 the seven traditional arts (aka Liberal Arts) are introduced. These existed in medieval times and were in some way descended from the original arts of Sacred Number responsible for the ancient model of the size of the Earth and the monuments that made reference to this model through their dimensions.

Three of these "arts" are explicitly numerical, involving

1. a knowledge of Number (often called arithmetic but more concerned with the properties of number)
2. a knowledge of Harmony, seen in music but available within harmonious proportions
3. a knowledge of Geometry, especially the properties of geometrical forms in transforming number

Three of the arts were linguistic, being called the Trivium from which our word trivial derives, to be mastered before studying the greater, numerical arts or Quadrivium. They involved,

1. Grammar, the structure of language itself
   
2. Dialectic, logic and the analysis and comparison of arguments
   
3. Rhetoric, the stating of arguments or, more likely this was Poetry
   

The seventh art was of Astronomy, sometimes called the royal art. We show in Sacred Number and the Origins of Civilization (Chapter One) that Astronomy is the likely teacher of the domain of number itself to ancient peoples. However, it became clear that there must have been other traditional arts, since three more emerge as essential:

1. Mythology, which lay at the heart of the oral traditions before the widespread use of writing
2. Metrology, which was used within monuments and was derived from the size of the Earth
3. Cosmology, which makes up the world views found in all religious thought and also within modern science

This creates a list of arts at least ten long. I created a graphic to illustrate this before other important ideas came along at the end of Sacred Number:

 They are organised here as a Tetractys - one systematic way of organizing ten elements. Metrology is here put in the centre but the arrangement is not the only interesting one.  Astronomy has gained two partners, Mythology and Cosmology, that are all "whole grasping", that is holistic arts used to build the ancient worldview. They form a triple with the numerical and linguistic arts in the other two corners, with metrology then forming the tenth art, in the middle and between, like the Pole itself.

Avebury is directly North of Stonehenge, a monument made up to two types of stone, sandstone "sarsens" and granite "bluestones". The bluestones were found in west Wales, in the Preseli mountains and, as Robin Heath has shown, their source defines a Pythagorean triangle relative to Stonehenge, having side lengths 12:13:5. Thus the bluestones appear to have been consciously sourced since this triangle's 12 side is 12 units of 9 Royal miles (see my own Sacred Number and Robin's Stonehenge wooden book, Sun, Moon and Stonehenge and other works).

I recently obtained Fred Hoyle's On Stonehenge, and he shows R.J.C. Atkinson's "likely source for the bluestones from southwest Wales" [Stonehenge 1956] and then the "likely route for the transportation of Sarsen Stones" (shown below) which are thought to have come from near Avebury, which monument used many such stones.

The route also follows a significant triangle that was defined between Avebury and Stonehenge - giving a scaled version of three lengths found in the ubiquitous ancient model of the Earth (Chapter 3), the radius of the Pole, the Mean Earth and of the Equator - which is introduced in Sacred Number but first described by John Michell in The Measure of Albion (now reprinted as The Lost Science of Measuring the Earth: Discovering the Sacred Geometry of the Ancients by Robin Heath and John Michell).

My own figure 4-14 is shown to the right from Chapter 4 - Ancient Theme Parks. The point here is that the two types of stones, their sources within megalithic Britain and the two triangles form a single concept with Stonehenge at the centre. The monuments are all scaled in accordance with the Avebury-Stonehenge triangle using ancient metrology within exactly a quarter degree of latitude. This latitude of southern Britain, between 50 and 51 degrees, happens to express the length that every degree would have on the mean (spherical) Earth.

All of this being expressed more fully in Sacred Number except for this level of symbolic congruence regarding the stones themselves.  

Our present day grid overlaying the Earth is of lines of Latitude (north-south) and Longitude (east-west). This system based upon the number 360 as degrees in a complete rotation (in direction) is as old, at least, as the Egyptians and Babylonians. 360 is a perfect number, having only harmonic primes as its formula is 2³ x 3² x 5. A similar grid, of Declination and Right Ascension is used to "grid" the sky and it is very possible that this sky grid came first in the pursuit of astronomy.

As geometry, the latitude/ longitude grid is simple, with two dimensions at right angles it is Cartesian and rectangular. It is not surprising therefore that there are alternatives and a number of them that try to describe the Earth and Sky in ways that correspond to Sacred Geometry and in particular the Platonic solids (see picture above). This was developed as early as the Pythagorean school of Plato and it takes the points and lines between points of a perfect form and lays them on the near spherical form of the Earth's surface. This idea comes with a lot of associated mental baggage such as that the Earth is an ideal form that has deviated somewhat from that form due to the nature of the material world. Within Aristotle's tetrad of four causes, such an Earth geometry is the final cause, just as the plan of a table is a final cause of a given table (chapter 9).

The use of ideal geometrical forms to describe the Earth has to have some kind of perceived benefit and this comes from finding meaning in the organisation of features upon the Earth. In this sense, this Pythagorean theory of the Earth is like theories such as Continental Drift, that require some phenomena that support their proposed mechanism. In this article you will find a useful review of the grid theory where the shape of the continents themselves appear to support the geometry proposed. Another "proof" is the significance of places at a nexus of lines or the alignment of places on a line or lines connecting two points.

A major proponent of the earth grid is Beth Haagen, whose web site includes instructions for using Google Earth as a mechanism for investigating her Becker-Haagen Earth Grid.  (One of her "neutral" lines follows the road in front of my house, on its way to a major node in NW Scotland.)

The Apollo / Michael lines are also leylines but differ from those of the world grid. Those lines produced by Platonic solid grids are parts of great circles whilst the Apollo lines are, characteristically, lines of constant bearing or rhumb lines. Thus, by Chapter 9 of Sacred Number, I am proposing that these lines are in fact the result of non-Euclidian geometrical forms that act as a formal cause for the shape of the Earth as an (oblate) spheroid. This, to my mind, reveals the problem with the Platonic grid model - it requires some kind of reason why the Earth should have a Platonic shape in the first place, for something needs to make this happen, a mechanism or a mind, nature or nurture.

It is not enough to just agree with Plato that the divine world should operate through pure geometrical form. It is mainly in the crystal world that one sees a propensity for perfect geometrical forms.  Therefore, it has sometimes said that "the Earth is like a great crystal" -  "in some way or other" . But surely a gravitationally achieved spheroid is beyond the realm of localised crystaline formation, for solid crystals are a feature of the crust. As an alternative to natural crystallinity, one otherwise must invent some nurture: a super mind that "in some way" maintains the crystal sphere in some higher dimension. One is thereby locked into inventing a supernatural being such as a planetary god because, whilst Platonic solids might apply to the Harmony of the Spheres (planetary orbits as per Kepler's diagram below) they do not seem naturally applicable to the Earth's rotating sphere.

It seemed to me that the 30 degree signature of Apollo-Michael lines must hold a clue to a natural generative mechanism. This angle is also involved in the ad triangulum, hexagon, vesica pisces and other root-three geometries that form a major numerical theme within history within Sacred Number.  The only possibility lay with the path curve geometry pioneered by Lawrence Edwards, written up in his Vortex of Life [Floris, Edinburgh, 1993], and explained here by Nick Thomas who supplied figure 9.5 from which I derived figure 9.4. 

So it seems that path curves would provide a valid mechanism for the existence of 30 degree rhumb lines like those of Apollo and Michael. Whilst modern science makes little use of such "projective geometry", it is always better to have a mechanism, rather than a mind, within a theory. Once invented as necessary such a cosmic mind would make our minds somewhat redundant and phenomena fickle; no longer susceptible to direct interpretation. It is an important virtue of the world that it is subject to fairly consistent laws. Without this, theories and worldviews would probably be impossible to achieve.

The Resulting Path Curve Grid