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In this article we will discuss the preeminent symbol of the Tetrad: the square.  It is the numeric and geometric qualities of three-ness (triangulation) and four-ness (the square) that provides a foundational organization in both space and time, form and substance.

Quadrilaterals

A quadrilateral is any figure composed of four straight lines as its sides.

Examples include:

Parallelogram – both pairs of opposite sides are parallel

Rectangle – all four angles are right angles; adjacent sides are different lengths

Square – four right angles and all four sides are equal in length

Trapezoid – one pair of opposite sides are parallel; these parallel sides are called the base

Trapezium – no sides are parallel

Rhombus – two adjacent sides are equal; therefore, all sides are equal; no right angles

The Square (Tetragon) – 360º

A square has four equal straight sides joined at right angles.  The square is the perfect form of four-ness.  Four provides a bonding pattern of two pairs having oppositional, as well as complementary characteristics.

Robert Lawlor comments: “As all sides, edges, angles and dimensions are diametrically opposed and equally complementary, the square holds a unique integration of perhaps the most fundamental of universal polarities, that of the concept of an “Absolute Unity” or Oneness with an infinite, incalculable ‘Multiplicity’ or Two-ness.”  This Multiplicity within Unity is perfectly symbolized by the √2 ratio between the length of the side of the square (1) to the diagonal (√2).  See Article 37 for detailed information on this very important ratio.

Sum of angles = 360º

360 hertz = F#

That is, the sound of a square is F #. This is a perfect octave up from the triangle at 180 Hz (F#).

Area of a Square: A = a² where a = side length

The square is the fact that any number, when multiplied by itself, is a square.

Squares are formed by two pairs of perfectly equal yet oppositional linear elements, graphically fulfilling the description of universal Nature found in Taoist and other philosophies. Four-ness manifests the first level of attainment in the qualities of complete symmetry, balance and uniformity of structure.

(The reciprocal aspects of space/time and time/space; or matter and consciousness.)

Squares are associated with equality, reliability, fairness, firmness, and solidity.

Take these sayings into account:

• “square deal”
• “square meal”
• “fair and square”
• “facing problems square on”
• “back to square one”
• “square our accounts”…etc.

The circle is the symbol of unmanifest Unity.

The square represents Unity poised for manifestation.

The square thus converts the irrational circle into a measurable form.

There are many ways to construct a square.

Reference Construction Lesson #32: Squares.

The Square as Representation for the Material World

“The most primary polygon, the triangle (in red), arose from the intersection of the first two arcs in the east-west orientation procedure [the Vesica]…next, the square (in blue) stabilized and fixed the site within the solar system by giving exact north, south, east and west positions, the four cardinal directions.”1

The Triad represents the metaphysical reality – the source of consciousness. The Tetrad represents the physical reality – the creation from consciousness.

Keith Critchlow wrote, “When matter [the Tetrad] emerged, principle [the Triad] was already there. Otherwise no order could have ensued. This is a principle shared by the traditional wisdoms of humankind.”

“Four was cardinal for it represented the polarization of universal nature into the active qualities of heat and cold and the passive qualities of moisture and dryness.”2

In terms of the solar system the Tetrad represents the winter and summer solstices, longest night and longest day; and spring and autumn equinoxes, when day and night are of equal length.

The Square and Fourness as Earth and Nature – “The World Mother”

The Tetrad and Square are associated with Earth, solid ground, matter, and mass.

They also represent:

• Four cardinal directions – north, south, east, west

• Four elements – fire, air, water, earth

“The form of the square is particularly laden with the conceptual dualities (air/fire, earth/water) and self-reproductive drives that provide the “spin” to the great wheel of Mother Time,” writes Robert Lawlor.  It is these four fundamental elements that come together in various geometric resonances that form the entire Periodic Table of Elements: the mineral realm of our reality.

• Four steps of becoming – point, line, plane, solid

• Four states of matter – solid, liquid, gas, plasma
  • These unfold in a certain way, from most dense to least dense.
  • Fill a jar with water, soil and air and shake it up.
  • The natural layering as it settles will show the layer of the elements.
  • Earth – most dense
  • Water – 2^nd dense
  • Air – 3^rd dense
  • Light – most ephemeral of all
  

• Four perspectives of viewing any subject: the material level, the social-psychological level, the cultural-mythological level and the inspirational level
• Four types of knowledge: illusion (eikasia), belief (pistis), intelligence (dianoia), and understanding (noesis)

• Four rules – addition, subtraction, multiplication and division

• Four fundamental Forces – electromagnetic, strong, weak, gravitational
• Four traditional winds
• Four corners of the Earth
• Four seasons – spring, summer, autumn, winter

• Solstices and Equinoxes quarter the year
• Four nucleotide nitrogen base types in DNA – adenine, guanine, cytosine, thymine

• Four types of living beings in the universe (Plato): the heavenly gods (formed mostly of fire/light), winged creates that travel through the air, those that live in water, those that go on foot on dry land.

• Earthbound animals walk upon four legs

• All insects with wings except flies have four wings

• Four blood types – A, B, AB, O
• Four chambers of the human heart

• Four Humors – Sanguine, Choleric, Phlegmatic, Melancholic
• Four stages of transformation in the scarab beetle and butterfly – egg, larva, pupa, adult

• Four-cornered cracks of inelastic materials such as: old paint, tree bark, porcelain, tiles, glazed ceramic mugs…

The Tetrad and Mother Nature

The square is an ancient symbol for Earth Mother Goddess or “Mother Nature”.  The square represents the nourishing aspects of the Earth Mother Goddess: She gives birth, clothes her creation with material substance, and encourages their growth equally and unconditionally.

‘Nature’ comes from the Latin for ‘birth’ or ‘that which is born’.

Nature in Navajo means ‘Changing Woman’

Summer in Navajo means ‘Changing Woman’s Happiness’

‘Mater’ in Latin means ‘Mother’. Mater gives rise to ‘Matter’.  Mater is related to meter (measure) and matrix.

‘Pater’ in Latin gives rise to ‘Patron’ and ‘Pattern’.  “The very word ‘pattern’ is the origin of recognition. Without pattern we cannot make sense of anything; so pattern is the great reminder. Pattern is synonymous with recognition and the power of consciousness.”3

“Thus, natural forms can be seen as coming from both a mother and father, the mating of matter and pattern.”4   “Great is the mystery of marriage,” says the Gospel of Philip, “for by it the world is created.”

“All birth into nature requires a crossing of opposites. So the square came to represent the earth, and as such symbolized the conscious experience of finite existence, of what is born into Nature.”5

The Square as a Symbol for Material Boundary

There are square-cornered sports fields. These represent arenas of earthly action, material conquest and physical interplay.

The square chessboard represents material interplay in the world. Chess is the “Royal Game of Life”.

There are squares on sidewalks which represent the earth they cover.

There are many square-grid street patterns and right-angled architecture and square or rectangle houses.

Chain-link fences with tilted squares represent symbolic walls of earth.

Beds, tables, chairs, and thrones are miniature models of the earth itself.

A Buddhist analogy of the ‘squareness’ of life is said to go like this: “Time is like a necklace of square beads of tangible objects, or moments or events, and to be absorbed by this succession of limited frames is maya or illusion, whereas only the inner thread of the necklace, the unimaginable continuum, is reality.”

The square beads represent every action in physical reality. These events and experiences are real, but there is more to reality beneath them, unseen. If we get completely absorbed or distracted with the beads, we forget what lies beneath them, holding them together, and holding us connected to all else in reality. Our physical lives and bodies may die, but in the grand scheme we are divine creatures, unlimited by physical reality, eternal in our souls, and timeless in our natures.

The Tetrad (4) & The Human Tetrachord

“Since the whole earth was symbolized by the human microcosm, it is we who are referred to as the “four corners of the globe” containing the “seven seas” (chakras), as well as the four stages of a spiritual journey and four levels of a temple or society.”6

Earth Nature

This is the most dense and slowest to change.

It represents the Body Area of the Pelvis.

Its Action is Digestion.

Water Nature

The Body Area symbolized by water is the Belly.

Its Actions are Emotions. Emotions are mood’s like the movement of water: surging, rising and falling, turbulent, stormy, calm, sometimes a laughing mountain stream, sometimes a ferocious torrent.

Like water, emotions take the form of their container.

They are shaped by our worldview, traditions, beliefs, opinions and thoughts.

Emotions always follow beliefs, not the other way around.

Air Nature

The Body Area represented by Air is the Chest.

Its Action is our Thoughts.

Like clouds and wind, they are a pollinating source, spreading ideas over our inner landscape.

Fire Nature

The Body Area represented by Fire is the Head.

Its Action is our Intuitions.

Fire (like intuition) is the most ephemeral, the most electric, least dense and most difficult to discern.

Fire is a symbol of purpose.  No other element as fire possesses such a power and rapidity of transformation, purification and destruction.

The Four Elements of Transformation

1. “If you can think so deeply that you can rediscover the spiritual roots of thought, if you can recognize thoughts as living, spiritual beings …(Thoughts)
2. If you can develop a strong enough sense of your own individuality that you can become aware of your interaction with the Thought-Beings that weave in and out of yourself, yet not be overwhelmed by this reality …(Emotions)
3. If you can recreate the ancient sense of wonder and use this sense of wonder to help awaken the willpower that lies sleeping in your deep, dark recesses …(Will Power)
4. If the fire of love for your fellow human beings rises from your heart and causes you to weep tears of compassion …(Love/Compassion)

… Then you have been working on the Four Elements. You have begun the process of their transformation.”7

Water & Fire

Water represents the yin principle – the source of health, fertility and inspiration.

Fire represents the yang principle – the source of action and will power.

John Michell writes, “On the mental plane [these elements] are located in the depths of the unconscious mind, from which they may rise up to overwhelm the order of sanity, or inner temple, constructed by each individual. This is the periodic destruction by water that, according to the old philosophers, alternates with the fiery cataclysm invoked by excessive predominance of the intellect. At the point where the two forces meet is the citadel of the mind, the seat of judgment, where in daily life their rival claims are assessed and balanced, the success with which that is done depending on the quality of one’s overall mental pattern and its adequacy in reflecting the essential reality of things.”8

1. Critchlow, Keith, Time Stands Still, Brecourt Academic, 2^nd edition, 2007
2. ibid.
3. Critchlow, Keith, The Hidden Geometry of Flowers: Living Rhythms, Form and Number, Floris Books, 2011
4. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
5. Lawlor, Robert, Sacred Geometry: Philosophy & Practice, Thames & Hudson, 1982
6. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994
7. Booth, Mark, The Secret History of the World, The Overlook Press, 2010
8. Michell, John, The Dimensions of Paradise, Inner Traditions, 2^nd edition, 2008