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

28 Some SACRED GEOMETRY (2)

The simplest and most perfect of forms, the circle, the two-dimensional representation of the sphere, seen in the sun disk and the full moon, is the expression of unity, the Monad, the undivided ‘one’. Paraphrasing Empedocles (490-430 BC) we could say: the universe is a circle of which the center is everywhere and the circumference is nowhere. The circle is also the symbol of infinity, because it has no beginning and no end. In a philosophical sense, the circle represents a completeness which encompasses all space and time. Some words related to the circle: cosmos, navel, wheel, time, me, eye, center, cycle, enlightenment …

Nature making circles

Life seems like a circle - Vincent van Gogh

The Ouroboros, the tail-eater, the symbol of the constant re-creation, the circular nature of all cycles.

Shiva