37 Some SACRED GEOMETRY (10)

As the saying goes: “a cat has nine lives.” Nine is the number of the extreme. It is the highest number consisting of one digit. Nine (3 triads) announces the end of a cycle and the beginning of a new one. The human embryo needs nine months of growth before birth. The Egyptian, Celtic and Greek myths have an ennead of nine gods and goddesses, representing the entire archetypal range of principles, nine being the number of perfection.

The original hopscotch game consists of nine steps, the ninth one representing heaven. There are nine symbolic aspects of the universe divided into 3 triads: the night, the sky and time; the ether, the light and the stars; the sun, the moon and nature.

The Norse God Odin, ruler of the 9 Norse worlds, hung 9 days on the world axis or Yggdrasil tree before finding wisdom. The city of Troy was besieged for 9 years, while Odysseus wandered for 9 more years in trying to return home. The list is almost endless…

The enneagon was seldom used in sacred architecture, although the number nine has a rich symbolism. The enneagon is obtained by rotating the equilateral triangle and is mostly used to decorate domes, and in some (recent) rose windows.
  

The nine principles in ancient Egypt:

Atum (Creation)

Schu (Air) - Tefenut (Water)

Geb (Earth) - Nut (Sky)

Isis - Osiris - Seth – Nebthut.

 

Some calculations by Elisabeth Haich:          

0 x 9 + 1 = 1                                 

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

  

Some other mathematical properties of nine:

2x9=18 / 1+8=9

3x9=27 / 2+7=9

4x9=36 / 3+6=9                                      

5x9=45 / 4+5=9

6x9=54 / 5+4=9

7x9=63 / 6+3=9

8x9=72 / 7+2=9

9x9=81 / 8+1=9

 

Hopscotch

Motive on prehistoric pottery

The labyrinth

The 9 magic square is revered by Islam, by the Jains of India, in Tibetan Buddhism, by the Celts, and in Jewish  mysticism.

The four elements

The Hermit is the ninth card of the Tarot, representing spiritual accomplishment

The nine steps of the ladder in Freemasonry

36 Some SACRED GEOMETRY (9)

Eight is the first cubic number (2x2x2) and the number of cosmic order, equilibrium, perfection, infinity (in mathematics represented by a laid down eight), regeneration, renewal and rebirth (hence the octagonal form of baptismal fonts). In Buddhism, the number eight represents the eightfold path to overcome suffering: 1. right knowledge, 2. right aspiration, 3. right speech, 4. right behavior, 5. right livelihood, 6. right effort, 7. right mindfulness, 8. right absorption (the eight spoke Dharma wheel). In the east, eight also represents the eight forms of Shiva and the eightfold path of Taoism. In ancient Egypt, eight was the number of cosmic order. The Celtic wheel of the year has also eight divisions, representing the solstices, the equinoxes and the beginning of the four seasons. And the Medieval wheel of fortune has also eight spokes.

In early Gothic architecture, the octagon is mostly used in rose windows, pillars and baptismal fonts, rarely in the ground plan. But before and after the Gothic period, the list of octagonal buildings is impressive: the Dome of the Rock in Jerusalem, the Tower of the Winds in Athens, the palatine chapel in Aachen, the basilica of San Vitale in Ravenna Italy, the Liaodi pagoda in China, the octagonal Lamp Tower in India, the Laon Templar chapel in France, the abbey church of Trizay in France, Ely cathedral in England, to name only a few.

 Buddhist Dharma wheel

 Celtic wheel of the year

 The eight Moon phases

 Wheel of correspondences by Leibniz

 Abbey church Trizay, France

 Ceiling Ely cathedral, England

 Labyrinth Amiens cathedral

 San Vitale, Ravenna, Italy

 Tower of the Winds, Athens

 Laon Templar chapel, France

35 Some SACRED GEOMETRY (8)

A week has seven days, and folklore divides life in periods of seven years. Seven is the age of reason, 2x7 the end of childhood, 3x7 the end of adolescence, et cetera… Seven is the sum of 3 and 4, the spiritual and the material. In Alchemy, seven metals are associated with the seven classical planets, symbolizing the seven stages of transformation (calcination, dissolution, separation, conjunction, fermentation, distillation, coagulation). There are seven notes in the diatonic musical scale (Dominus - lord, REgina coeli - queen of heaven, MIcrokosmos - small universe, Fata - fate, SOL -sun, LActea - milky way, Sider - star). And seven directions (left, right, up, down, forward, back and center). The rainbow has seven colors, and Snow White has seven dwarfs (representing the temperaments inside us ). The Pleiades and the Big Dipper have both seven main stars.

The heptagon is the smallest regular polygon which can’t be constructed correctly with a compass and a ruler, only approximately, like the one above. Within the numbers 1 to 10, seven can only be divided by itself and one, that’s why the ancients called it the “virgin number”. The birth of the Greek goddess of wisdom Athena was explained by means of the heptagon. The sum of the letters of her temple, the Parthenon (meaning virgin) is 515. The angle of the regular heptagon is  51.412…°. Seven is the only number of the decade which can’t divide 360° without  a remainder. The “virgin” seven can’t be divided by a “lover” number of the decade.

The number seven was one of the most significant numbers in ancient times, and one of the most sacred number in religions. It means abundance and totality (seven heavens), the end of the first complete cycle, before starting a new one. Seven is also the number of the seven chakras (meaning wheel, vortex, whirlpool) of Kundalini Yoga and Tantric Buddhism. There is a resemblance between the seven chakras, the seven stages in alchemy, the Qabalistic tree, and the properties of the seven planets.

1. Root Chakra (Muladhara), the base of the spine (element earth, square, color gold-yellow, libido, lingam and yoni, plexus sacralis, mantra LAM). 

2. Sacral Chakra (Svadisthana), the lower abdomen, about 2 inches below the navel (element water, color white, crescent moon, inner sexual organs, plexus prevertebralis, mantra VAM).

3. Solar Plexus Chakra (Manipura), the upper abdomen, in the stomach area (element fire, color red, triangle, nutritive system, plexus solaris, mantra RAM).

4. Heart Chakra (Anahata), the center of the chest just above the heart (element air, color blue-gray, six-pointed star, heart and blood vessels, cardiac plexus, mantra YAM).

5. Throat Chakra (Visuddha), the throat (element aether, color white, circle, respiratory system, plexus cervicus, mantra HAM).

6. Third Eye Chakra (Anja), the forehead between the eyes (autonomic nervous system, medulla oblongata, mantra A).

7. Crown Chakra (Sahasrara), the top of the head (lotus, the brain, epiphysis cerebri, mantra OM).

Most authors describe the chakras as not physical, but as aspects of consciousness or as manifestations of psychic energy. But each of the chakras can be associated with one of the seven endocrine glands, and with different groups of nerves. There is certainly a link with the physical body, and with the hormones and their levels. Hormone levels are maintained in the body via feedback loops that tell the body when to make more of a specific hormone and when to make less of it. Blockages within this feedback system work to inhibit the proper flow of the endocrine system. It is interesting that “blockages and flow” can be used when describing the processes of the endocrine system, as well as when describing the work of chakra balancing. The frequency and sound vibration of the  Mantras could play a role here…

The seven stages in Alchemy offer us a similar system.

1. CALCINATION involves heating a substance in a crucible or over an open flame until it is reduced to ashes. Psychologically, this is the destruction of the attachments of the ego.

2. DISSOLUTION is (chemically) the dissolving of the ashes from Calcination in water. Psychologically, this represents a further breaking down of the artificial structures of the psyche by total immersion in the unconscious, non-rational, feminine or rejected part of our mind.

 3. SEPARATION is the isolation of the components of Dissolution by filtration and discarding any material. Psychologically, this process is the rediscovery of our essence and the reclaiming of what was previously rejected by the masculine, rational part of our mind.

4. CONJUNCTION is the recombination of the saved elements from Separation into a new substance. Psychologically, it is the union of both the masculine and feminine sides of our personalities into a new belief system or an intuitive state of consciousness.

5. FERMENTATION is a two-stepped process that begins with the Putrefaction of the hermaphroditic "child" from the Conjunction resulting in its death and resurrection to a new level of being. Psychologically, the Fermentation process is the inspiration of spiritual power from “the transpersonal” that energizes, and enlightens. Fermentation can be achieved through desire for mystical union, breakdown of the personality, transpersonal therapy and deep meditation.

 6. DISTILLATION is the boiling and condensation of the fermented solution to increase its purity. Psychologically, Distillation is the sublimation of psychic forces necessary to ensure that no impurities from the inflated ego are incorporated into the final stage.

7. COAGULATION is the sublimation of the purified ferment from Distillation. Psychologically, Coagulation is a new confidence that is beyond all things, a permanent vehicle of consciousness, the highest evolution of mind.

Systems and techniques like Tantra and spiritual Alchemy can be seen as maps showing the path of possible evolution of consciousness. Throughout history, man has always looked for transcendence to explain the mystery of life and his relation with the rest of the universe. Most of these teachings are “compatible”, the human brain is about the same everywhere, and ultimately, reaches the same conclusions everywhere.

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