Sacred Number

Rectangles have a number of uses and, from the classical age until now, they have become the preferred floor plan for buildings. Numerically, we tend to see them as either a proportion or as an area.

As a proportion a rectangle can represent the ratio of the length to the width, as at,

1. Carnac, the Crucuno rectangle that embodies both two 3,4,5 triangles (the ratio of 3:4) or a rational version of Pi, in that case 25/8 (see previous post, ratio 32:25).
2. Stonehenge, the Station Stone rectangle that embodies two 12,13,5 triangles, ratio 12:5
   
3. Chartres, that manifests the nested ratios of one to the square root of three, the basis of the Gothic style, ratio 1:1.732, almost exactly 56:97.

As an area, a rectangle can embody a special number as the product of the two sides as at,

1. The Giza Pyramid in which the height times the south side can, in feet, yield a rectangle with an area the length of a degree of latitude (see Sacred Number, chapter 4).
2. The Parthenon that, as a rectangular Hekatompedon, has an area 100 times 100 or 10,000 square units (see Parthenon page)
   

In metrology, any reference length can also symbolise one of the key dimensions of the Earth itself according to the ancient model of the Earth, and so a rectangle's side can then divide into the Earth itself.

What is less known is that, in studying astronomical periods, a rectangle can help visualise the numerical interdivision of time periods such as those of the Moon, the solar year, Venus and so on. The same is true of triangles, which would have allowed ancient peoples to know, for example, the sidereal period of a planet from a knowledge of its synodic period, the latter being easily determined via counting on Earth.

To break out of this deadlock, I will (in the next weeks) present a series of examples, of "things that worked for me" to demonstrate that, simple as these techniques often are, the conclusions they lead to can often be extraordinary, bringing fresh insight to astronomy and ancient monumental architecture.

A very simple example involves the synodic period of Venus, a very important "star" in the ancient world, in fact a goddess and Aphrodite for the Greeks. In Matrix of Creation I discovered that the slight inexactitude of 8 solar years of 365.242 days equal to 5 Venus synods disappeared if the "practical year" of exactly 365 days was taken. 365 divides by five to yield a natural division of the year into five periods. (one calandar the Egyptians used was of 360 days plus five Neters. )

A very simple rectangle emerges with sides in this proportion, five by eight units of 73 days.

By looking at the two periods along the sides the way in which they both generate a common long period can be studied. Therefore, a rectangle can be used to analyse synchronicity of celestial time periods. Venus is the tidiest example of this but I will show that as an analytical tool the rectangle can show both the overall pattern of relationship and the building blocks out of which that relationship is built.

On the left is the "matrix" view  of the same Venus cycle. It demonstrates that there are two ways of multiplying 5 and 8 to get 40, and that these two ways (like the sides of the rectangle) are time periods belonging to Earth and Venus, whilst 73 days "belongs" to both as the common denominator.

 Another way of expressing 8 and 5 is as polygonal structures. Whilst today, the octagon is associated with Islamic architecture and perhaps from thence, as a norm of the Knights Templars, Charlemagne built the beautiful octagonal Palatine Chapel (lit. "Palace Chapel") when he became the first Holy Roman Emperor, three hundred years before the First Crusade.

One hundred years before this, the octagonal Dome of the Rock  had been built in Jerusalem. [The star at the focus of the crescent moon in the Islamic flag is Venus, a proximity that always occurs as the lunar crescent grows from the west.]

Whilst the U.S. military chose a Pentagon motif, this is only practical with larger buildings and the pentagonal star has instead become a powerful emblem and symbol of power or has to be incorporated within the golden rectangles of classical architecture.

The octagon is also a polygon most like a circle, and expresses balance of eight directions. Eight is (2² x 2) whilst Twelve, the basis of the Zodiac and classical geomancy, is (2² x 3), is useful for King Arthur's knights as a table and incorporates the square root of three within its geometries. Interestingly, within the octagon on the right there are the "knight's move"  of two units by one unit between every other corner, and this has the length of the square root of five, the same root behind the golden mean and pentagon. Five and Eight really are connected.

Megalithic monuments are sites of learning when one understands the Traditional Arts, especially Astronomy, Geometry, Arithmetic (number) and Metrology. The area around Carnac, Brittany is one of the foremost megalithic complexes and this hence has a lot to teach us.

The 3,4,5 triangle is the “first” whole number or “Pythagorean” triangle, that is the one with the lowest numbers. As with the Station Stone rectangle at Stonehenge, which is based on the second 12,13,5 triangle, two triangles can form a rectangle three units by four units.

Alexander Thom’s site survey for Crucuno, showing the rectangle created by two 3,4,5 triangles

Alexander Thom noted that one of the rectangular stone rings at Carnac, called Crucuno, forms such a rectangle 30 by 40 megalithic yards long. This year, visitors will be encouraged to view the solsticial sun across its diameter since the stone rectangle is aligned east-west, as if to mark the special nature of the latitude of Carnac.

More recently, John Neal has found a second relationship built into this stone ring. The southern extent of the rectangle can show the important relationship in sacred geometry of “squaring the circle”. In this case the height of the rectangle is slightly longer, 31.25 megalithic yards instead of 30, in which a circle with diameter equal to the width of 40 megalithic yards, has the same perimeter as a square of side length 31.25 megalithic yards.

John Neal’s Squaring of the Circle interpretation of Crucuno, after All Done with Mirrors

Neal’s relationship is based on one of the whole number approximations to Pi equal to 25/8 which is 3.125 in decimal rather than around 3.1416. Whilst this may dismay the modern sensibility, there is consistent evidence that approximations to Pi were often used within the ancient science as in the ancient model of the Size of the Earth, where 22/7 and 63/10 are both deployed (see Sacred Number).

Raising the Squared Circle to Stone 23 defines the height of the Rectangle of Crucuno

megalithic yards and the resulting relationship is exactly determined by the use of Pi at 25/8.

Chapter Five of Sacred Number shows how a number of archaic divinities have a common set of symbols, especially St Michael and Mithras, even though one kills a dragon and the other a bull. One of the startling images in the Mithraic artifacts (they left no literature being a secret society) is that of a Lion with a man's body, entwined in a snake.

This Mithras has wings which makes him a type of angel, a concept likely originating with the Persians. Whilst some say that Mithraism should not be confused with Mazdaism, there is reason that it did derive from Persia, arriving historically in Cilicia, Turkey, where there was a Perseus cult - note the similarity Perseus and Persia. The most famous city in Cilicia is Tarsus, from which Paul of Tarsus came, major founder of non-Jewish Christianity.

It is a wonder that Mithraism did not become the official religion of Rome since many legionaires were members and indeed it very much appears that components of many other religions and practices of the time were imported to official Christianity, including the iconography of Mithras as can be seen below in a photo I found on a dutch web board.

First off, you could be forgiven for thinking this is St Micheal or at least an angel if not an archangel. The lion has been sublimated (as was the Gorgon's head with Athena) onto the chest. The first picture stands on an explicit sphere, cruder versions of Mithras are of a torso emerging from a rock. This sphere is the emblem of the Earth.

In Chapter Five I introduce Michael and "His" Lines which run at 30 relative to east-west across Europe and in Chapter Nine I show how these could be naturally derived from the formal description of a sphere according to path curves and projective geometry. If one wanted an iconography to present this, it would be hard to beat this one since the lines are exactly described as serpents and are associated with the dragon as well. Were the encircling serpent to be interpreted as lines upon the Earth, then the man or lion encircled is in some way a God of the Earth who has become known as the archangel Michael.