34 Some SACRED GEOMETRY (7)

Six and the hexagon symbolize perfection, stability, harmony, structure and efficiency. The hexagram, the six-pointed star, the Seal of Salomon, is made of two intertwined equilateral triangles, one pointing up, one pointing down, symbolizing the fusion of water and fire, and the symbols of the other elements and their properties (fire: warm and dry / air: warm and humid / water: humid and cold / earth: cold and dry). It’s Tiphareth, the sixth Sephiroth of the Kabbalah, meaning “beauty”. Six is “perfect” because it’s both the sum (1 + 2 + 3) and the product (1 x 2 x 3) of the first three numbers. So six is rooted in the triad.

In nature, hexagons are omnipresent. Natural forms are energy made visible. Six sided plants and animals use the hexagon because it’s the most efficient way to combine structure and function. In the human body, cells cluster together into a dense six angled structure. And there are of course the honeycombs, used by the bees because a hexagonal structure uses the least material to create a lattice of cells within a given volume, a nice example of efficiency. And many crystals show six sides.

Ice crystalls, basalt rocks, honeycomb

Lincoln and Reims cathedral

Saint Peter church, Caen, France

19th century Tibetan mandala Naropa tradition (Vajrayogini)

Milan cathedral

Six on the Qabalistic Tree

Alet-les-Bains, France

Saint Martin’s church, Laon, France

33 A Tarot intermezzo (1)

I have always been intrigued by the Tarot, the card deck consisting of 78 cards, 22 major Arcanas and 56 minor Arcanas, without knowing why. But since Arcana means “mystery” … I think that the minor Arcanas are the “playing cards” of the Tarot, while the major Arcanas are the survival of an archetypical old “wisdom” about life and conscience. The most ancient complete Tarot of “Marseille” is the tarot of Jean Noblet, preserved at the National Library of Paris, and dates from around 1650.

The contemplation of a major Arcana card is done by the interpretation of various symbolisms inside the cards, like space, the body, clothing, the colors and the numbers, among others. The details are not arbitrary.

This old song of the French Compagnons du Devoir (the Companions of Duty) is supposed to inform us a little on the colors: white, the tears of Maître Jacques / black, the earth which bore him / red, the blood he shed / Blue, the blows he suffered / yellow, perseverance / green, hope.

The symbolism of space: a figure sitting or looking at us often expresses the “static”, turned towards the left it expresses “the materiality”, turned towards the right interiorisation, and upright it expresses dynamism and activity.

The body: the head symbolizes thought, the neck affectivity, the abdomen the instincts, a beard virility.

Clothing: the belt is the domination of the instincts, a necklace means dependence.

This varies from deck to deck.

The 22 cards of the major Arcana are in a medieval style (I speak here about the Tarot of Marseille, mother of all modern Tarot decks). Since they are composed of 21 numbered cards + The fool without number, we can see seven ternaries (7x3) and three septenaries (3x7). And 22 is the number of the letters of the Hebrew alphabet. Each ternary expresses a kind of trinity. The law of three: + = and -, two polarities and their balance. For example: father-child-mother, spirit-heart-body etc…

One finds the same symbolism in the three septenaries: the cards I to VII symbolize the spirit, cards VIII to the XIIII the soul, XV to the XXI the body. It is really necessary to have the cards at hand to see it. Since The Fool has no number, it’s a free card.

The Fool, a kind of vagrant, is dressed like the buffoon of the king, who can say everything without consequences, as if he didn’t exist. Pushed by the dog, The Fool is like the wandering Jew, without stopping or stabilizing himself. The fool represents man directed by external circumstances, without the will to tackle them. He symbolizes the zero and potentiality. He is also the principle of the endless new beginnings.

Traditionally, The Magician symbolizes reason, will, activity and initiative. Man who masters in a logical way the material world he lives in. This implies also his “swindler”side, materialistic superficiality and action without morality . The cards have always  a “positive” and a “negative” side. The accessories on the table represent  the tools and talents he has at his disposal.

The Popess represents intuition, receptivity and passivity (in the sense of patience and discretion). The veil suggests Isis: the Popess raises the vail to show the interior side of things, the esoterism if you want. While The magician represents spirit and consciousness, the animus of Jung, The Popess represents the soul and the unconscious, the anima. The first three cards already tell us much about ourselves, and it is interesting to observe how their properties work in our lives of every day.

The Empress, the third card of the first ternary of the Tarot, is the female side of “power”. She symbolizes comprehension, wisdom and intelligence, or reason supported by intuition.

After the presentation of the first four cards, one can wonder: so what? Well, the goal is: to learn to know yourself. And there is much to know… And it should be seen as a game, not too seriously. One can for example observe oneself consciously from time to time (emotions, reactions, reasoning) to see when one is on the level of The Fool, The Magician, The Popess or The Empress, in simple daily situations…

0 The Fool  • directed by external circumstances • potentiality.

I The Magician • reason • will • activity and initiative (Spirit).

II The Popess• intuition • receptivity • passivity and patience (Soul).

III The Empress • comprehension • wisdom • creative intelligence (Body).

Jean Noblet Tarot

 Crowley-Harris Tarot

Dio Raman Tarot

32 Some SACRED GEOMETRY (6)

Five is the number of man in action in the world: five fingers on each hand, five senses (touch, taste, smell, hearing and sight), five members (two arms, two legs and the head), the “five pointed star” or pentagram inscribed in a pentagon by connecting its angles, man as the microcosm. One can be seen as the child in the womb, undifferentiated; two as birth, the child coming into the world, the first differentiation; three as the relation with the mother in the new environment; four as the relation with the father, the mother and the environment; five as the first development of the four functions of the psyche.

Kore and her apple

To Pythagorean mystics the pentagram was the symbol of spirit over matter, showing the ‘accomplished’ adult, able to balance his four elements: sensations, thoughts, feelings and intuitions. The pentagram appears in the earliest writings of Mesopotamia around 3000 BCE. Some authors think that the pentagram originated as a symbol of the goddess Kore. Her sacred fruit is the apple, and indeed, when an apple is cut through horizontally, both halves show a pentagram shape at the core, with each point containing a seed. Kore represents the female spirit of the universe. 

The geometric proportions of the pentagram are those of the Golden Ratio (F Phi, 1.618) or Golden Mean. This ratio also forms the foundation of the Fibonacci series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144..., where each number is formed by adding the previous two numbers. The Golden Ratio and the Fibonacci series are found everywhere in nature, from the human body to the spiral of our galaxy, and in everything in between. It seems to be the ratio of creation. It’s inside us, in our minds and bodies, and outside us, in everything existing.

Construction and proportion of the golden ratio

The golden ratio is also the most pleasing proportion to the eye. Shapes that resemble the golden ratio facilitate the scanning of images and their transmission through the vision organs to the brain. When we see the proportions in the golden ratio, we feel ‘pleasure’, and we call it beauty. No wonder the proportion is called 'sacred' and 'golden'. Man uses it in all the places and buildings where he celebrates his unity with the rest of the universe.

The stone circle on Borrowston Rig, Lauder, Scotland, consists of two intertwined circles of different sizes, as measured by Alexander Thom. He concluded that geometry has been used in the design of most megalithic sites. The overall area encompassed by the Borrowston Rig is some 48m x 41m. There are around 30 stones, none of them reaches more than 0.60m high. The Golden Section, the ratio 1.618, can be clearly seen in the lines A-B and B-C.

The ground plan of the church of the little village of Méolans, Haute Provence, France, shows the golden rectangle, golden triangles, the square and the equilateral triangle.

A few ‘golden ratio lines’ on the western façade of the Notre-Dame de Paris cathedral.

Northern rose window of Amiens cathedral

Laon cathedral 'analyzed'

Golden ratio inside a sunflower

31 Some SACRED GEOMETRY (5)

Four, the square and the cube are the fundamental units of manifestation. In the glyph 4 we see the four arms of the cross and the four cardinal points, the four seasons and the four moon phases. Four stands for materia, matter, and the four worlds: mineral, vegetal, animal and human. But also infancy, youth, maturity and old age. In the Kabbalistic interpretation, four is the Tetra-Grammaton יהוה (yod-he-vau-he) and also represents the four Kabbalistic worlds (Atzilut, Beriah, Yetzirah, Asiyah). Also: Yod (man), He (lion), Vau (bull), He (eagle), or the four evangelists Matthew, Mark, Luke and John.

Four is also the beginning of a new cycle, combining the circle (one), the line (two) and the triangle (three) to start an endless expression of patterns and forms as expressed by the Pythagorean Tetraktys. It’s also the quaternity of the four psychic functions: sensing, thinking, feeling and intuiting. And there are four elements in Alchemy: Earth, Water, Air and Fire, the four states of matter in a literal sense (solid, liquid, gas, and plasma). So four symbolizes the tangible whole of creation.

In nature, there are four types of chemical reactions, a law of four so to speak:
-       synthesis reactions (the combination of two elements to form a more complex molecule)
-       decomposition reactions (a molecule is broken down to smaller molecules)
-       exchange reactions (two molecules exchange parts)
-       reversible reactions (molecules can synthesize from other molecules).
There are also four general types of crystalline solid. The mineral pyrite can form real cubes and squares. Sodium chloride (salt) has the tendency to form cubic crystals.

In the past, many buildings (religious and others) used a plan based on the square (ad quadratum) or the equilateral triangle (ad triangulum) to form a rectangle, a rooted rectangle or a square. A good example is the pyramid, the simplest three dimensional form based on the square. 

The four elements of Alchemy

Masonic Tarot, card four

Pyramids

Pyrite crystal

Pythagorian Tetraktys

Ad quadratum

Ad triangulum

Rooted rectangles

Map Avioth based on a square and a root 2 rectangle

Marseille Tarot: earth, fire, air, water

30 Some SACRED GEOMETRY (4)

All good things go by three. The Egyptian triangle (the so called Pythagorean 3:4:5 triangle) represented the universal nature of Father (Osiris) + Mother (Isis) = Child (Horus), the trinity of creation, the recipe for the continuity of life. To construct the sacred triangle, the Egyptians used a rope with 13 knots, also used by the cathedral builders. The Shekinah in Judaism is thought to be Yahweh’s feminine aspect, forming about the same trinity together with the son. Brahma (the creator) - Vishnu (the sustainer) - Shiva (the destroyer) form the trinity in Hinduism, reflecting the essential ‘law of three’. It also brings to mind the three worlds of the Druids, the Celtic knot or Triquetra and the Triskele. One, two and three are the base of almost every spiritual system, because they show how the three separate essences are interconnected.

While the circle stands for harmony -  wholeness - eternity - the cosmos - the all in one - the unknowable drive behind life - the infinite cycle - the sun and the moon; the triangle represents the threefold nature of creation - the union of polarities - the three essential elements in alchemy (mercury, sulfur, salt) - the threefold nature of man (mind, body, spirit). Also: past, present, future - creation, preservation, destruction - thought, feeling, emotion - sun, earth, moon -  birth, life, death… The list is almost endless.

In the human mind, three-ness expresses the tendency of polarities to unite by balancing each other, the relation between two opposites. In the field of emotions and feelings we find the dualities: pleasure-pain, excitement-depression, confidence-fear, attraction-repulsion, love-hate. Balancing of polarities can be done by: creation of a new being (or a new reality) or adjustment of the opposite poles by means of an "intermediary", a principle higher than both. Two becomes three. Some examples of “trinities”: sympathy - antipathy - indifference, optimism - pessimism - realism, excitement - depression - apathetic calm. True balance is never achieved, it would mean a complete standstill, there’s a constant tension between the two.

In the physical world, the most commonly polarities are magnetic fields and the positive and negative poles in electricity. These polarities are the basis of the constitution of matter. Helium, the second atom, is the first element consisting of three parts: a nucleus of charge surrounded by two electrons. Sexual polarity in nature, the union of two physical elements, has a creative effect: the fusion brings about the birth of a new being, which is the big mystery of procreation.

The knotted rope

Reims cathedral: one big rose window, two towers, three entrances

Reconstruction of the Medieval trilobe

The Triquetra: three Mandorlas interwined.

Osiris, Isis, Horus

Circle divided in three equal parts starting from the Mandorla

The unity of the three

Alchemy

29 Some SACRED GEOMETRY (3)

When you throw two stones into the water you get the above pattern. It’s the circle mirroring itself, the birth of the ‘twoness’, the Dyad. In biology, it’s called “cell division”. In chemistry, it’s the hydrogen atom, the first element, and the only element consisting of two parts, a positive proton, and a negative electron.

Twoness means separation into a complementary duality, which means the two poles are mutually interdependent. Polarity is the building principle of all matter. It’s also the origin of consciousness and language, our mind interacting with the world. Our consciousness was created by the cycle of dark and light, night and day, the main duality on which all life on earth depends. In languages, duality is crucial for making meaning, like cell division is crucial for generating new life.

Where the two circles merge in the above image, a Vesica Pisces (fish bladder) or Mandorla is formed, a western version of the Yoni in Hinduism. From this Vesica Pisces, all other geometrical forms can be derived, it’s like the gate of geometrical forms. It’s often found on cathedrals, with Christ in the middle. Both the Gothic arch and the Islamic arch are often based on the Vesica Pisces.

Cell division

The life giving star

Viseca Pisces, Chartres cathedral

Gothic Arch

Vesica Pisces: the Matrix