Monday, January 23, 2012

40 Some SACRED GEOMETRY: the Crucuno quadrilateral and the orientation of megaliths

The Crucuno quadrilateral is situated in a field called “parc vein glass” (the field of the blue stone) in Plouharnel, Brittany, France. The rectangle measures 30x40 megalithic yards and its diagonal measures 50. It consists of two Pythagorean triangles of 3-4-5 proportions determined by the diagonal, forming a 3-4 rectangle. This is quite amazing, because it shows that the “Pythagorean” triangle was already known in the Neolithic period.
Another particularity of the 3-4-5 Crucuno rectangle: it is perfectly oriented east-west and its corners point at the sunrise and sunset of the solstices. Theoretically, a 3x4 rectangle should have a latitude of 47°31’ at Crucuno to show the solstice sunrises and sunsets at its corners (taking into account the obliquity of the ecliptic around 1800 BC). The latitude of Crucuno is 47°37’5’’, which is close.

This same orientation principle can be found in cathedrals, churches and chapels until the end of the middle ages. A good example is the Templar chapel in Laon, France, built around 1180:

Most megalithic monuments have a N-E or S-E orientation, which means: the direction of the sunrise on the summer solstice and the winter solstice. The majority is oriented towards the winter solstice, which marks the end of the shortest days, and the returning of light. The orientations aren’t rigid at all. The topographical situation has to be taken into account, like hills obscuring the horizon. And our ancestors weren’t trying to be “scientifically” accurate, it seems to have been a more symbolical expression, an approximation. The figure below shows that many dolmen have a N-E orientation (summer solstice) between 90° and 100°, and that the largest group has a N-S orientation (winter solstice) between 120° and 180°. Nevertheless, some megaliths show an astonishing perfect orientation. Like the chambered mound of Newgrange in Ireland, known for the illumination of its passage and chamber by the winter solstice sun, the sun fertilizing the womb of the earth as it were.

Prehistoric solstice cults were sometimes taken over by the church. An example is the St Peter and St Guidon church in Anderlecht, Brussels. According to tradition, in the second half of the 11th century, a horse ran up against a stone on the top of a hillock. This stone proved to be a dolmen that was surrounded by a hedge, because it couldn’t be moved. The remains are in the crypt of the church. On the winter solstice, a sunbeam falls through the opposite window to lighten the space under the stone. Pilgrims used to crawl under the stone in the direction of the light beam.
Saint Guidon crypt, Brussels

The Crucuno Dolmen, not far from the quadrilateral

Sunday, January 15, 2012


Squaring the circle is a problem proposed by ancient geometers, and has a symbolic meaning. It means constructing a square with the same area as a given circle with square and compass. The exact squaring of the circle is impossible because π =  3,141592653… is a transcendental irrational number, which means that the figure cannot be constructed with a compass and a ruler (pi cannot be expressed in finite whole numbers by which we measure squares). Only approximations can be made.
The ancient Egyptians used whole numbers to approximate the squaring of the circle (like the example above). A circle with a diameter of nine unities has almost the same surface as a square with a side of eight unities.
The squaring of the circle represents an attempt to unite two opposites which can’t be united: spirit and matter, sky and earth, body and soul (in the sense of conscience). Both circle and square represent a closed cycle. The square, symbol of the quaternity, is a representation of the four elements, the materialization of the circle so to speak. Both circle and square express harmony, but on a different level. They’re also a sort of prison, a closed circuit. That’s the real meaning of the cross (which is another representation of the quaternity): man at the center of the material world.

Figure 1

Figure 1 shows the squaring of the circle following an old masonic method. The circle, the triangle and the square have practically the same surface. The same idea can be found in some portals of medieval churches, like Notre-Dame-du-Port, Clermont-Ferrand, France, and Saint-Gilles-du-Gard, France (below).

The floor plan of St Paul’s cathedral in London consists of a squared circle at the center and seven concentric circles:


Sunday, January 1, 2012


The ten fingers symbolize the totality of the universe. Counting on ten fingers makes it "natural" to use a counting system based upon tens. The first letter in the Greek word "deca" (ten) is formed like a triangle (Δ δελτα). The Pythagoreans used pebbles to form their sacred symbol of the tetraktys (1+2+3+4=10): ten pebbles were arranged in a perfect triangle to form four levels: 1, 2, 3 and 4. The Greek word for pebbles,” kalkuli”, is the origin of the word "calculate".
Ten means completeness of order, matter in harmony (4+6). It’s also the start of a new cycle of numbers consisting of two digits (10=1+0=1 / 11=1+1=2 / 12=1+2=3 / 13=1+3=4 …). Ten includes in its digits the created (1), the non-created (0) and the return to unity.

Ten and the Kabbalistic Tree

Kabbalah (from the root KBL, Kof-Beit-Lamed) means “ to receive” within the ancient Hebrew oral tradition. The Kabbalah teaches that the manifest universe arose as a series of emanations or principles from the Ain Soph Aur, the "limitless light” (comparable with the big bang): the ten Sephiroth (enumerations). The first three Sephiroth represent the monad (1- point), the dyad (2 - line) and the triad (3 - triangle), from which the other seven archetypes of creation emerge. The Tree of Life with its ten Sephiroth is the map of Jewish mysticism. The Ten Sephiroth include both masculine and feminine qualities. The Kabbalah pays a great deal of attention to the feminine aspects.
1.    Kether (Crown)
The monad, the origin of all numbers and of creation. Also called the Primordial Point, the Point within a Circle. The essence of Kether can’t be comprehended by the human mind, because it isn’t part of a duality. The human mind can only “think” in dualities. Without dualities, thinking is impossible. Kether is so transcendent that it cannot be described.
2.    Chokmah (Wisdom)
The result of the first ”swirlings” of the Monad, the masculine-active force, the extension of the point into space, like a phallus. The dynamic force of the universe, the father, Abba.
3.    Binah (Understanding)
The feminine-passive potency, the mother, Mara, the great sea. The womb fertilized by Chokmah. Chokmah and Bina are the first polarities of manifestation. They can be compared with the proton and the electron, the building blocks of matter, and with time and space. Like Kether, the origin and reason of the first duality is beyond human understanding. We can merely hypothesize by applying the esoteric law: “so above, so below”. They are transpersonal.
4.    Chesed (Mercy)
The “child” of the first polarity, the concretion of the abstract concepts of Kether, Chokmah and Binah, the first Sephira that might be conceived by the human mind, represents love, the reflection of the former three in the world of manifestation.
5.    Geburah (Strength)
Represents power and the will.
6.    Tiphareth (Beauty)
The self.
7.    Netzach (Victory)
Represents feelings, instincts, emotions.
8.    Hod (Glory)
The mind, rational thoughts, intellectual abilities.
9.    Yesod (Foundation)
The unconscious and intuition.
10. Malkuth (Kingdom)
Represents the body, the senses and the material world.
This is of course a very brief introduction to the Kabbalistic Tree. The Sephiroth have a lot more properties than the ones mentioned. They can be expanded by any analog concept.

We all know the first sentence of the Bible: ”In the beginning God created the heaven and the earth.” This translation is not quite correct. First of all, there is no such word as “God” in the Bible. But let’s concentrate on the first word Berashit (Brasyt)  formed (right to left) by the letters Beth, Resh, Aleph, Shin, Yod and Tav. “In the beginning”, the translation of the word Brasyt, is based on a misinterpretation of the original Hebrew text. Every Hebrew letter symbolizes a number and an idea or concept. So each word is a combination of both numbers and ideas, which makes them difficult to translate in other languages. This means that a lot of information in the Bible is coded, disguised as stories.
Beth:  the physical support of all that is, anything that “contains”, all dwellings; the cosmic energy projected into actual manifestation.
Resh: the archetype of cosmic containers, the totality of the universe, all existence.
Aleph: the abstract principle that representing all that is as a pulsation of duality, unimaginable by the human mind.
Shin: the movement, impulse, breath behind everything.
Yod: continuity, the manifested existence in time of Aleph.
Tav: the archetype of cosmic existence, in its capacity to resist the life-death duality.
So, instead of “in the beginning”, Brasyt can be translated thus:
“The movement of ‘what cannot be imagined nor understood’, brought into continuous expression the dual principle of life and death, ‘the life-death' pulsation of all existence, by containing it in an infinite array of manifestations.”

Cross-section of human DNA, forming a beautiful ten pointed star

Tile, Iran, 15th century

Mayan numbers

Magic square of 10

If nine is one, ten is none, here is all the mystery (Goethe)