In this article we will continue our discussion of creation myths, this time focusing on mathematical and numerical creation myths.
As you read, compare these ideas to the ideas in the religious creation myths from Article 86.
Pythagorean Mathematical Creation Myth
To begin we will review the ancient Greek/Pythagorean view of the Cosmic Archetypes 1-10.
Micheal Schneider writes, “The structure and patterns of arithmetic and geometry reenact the creating processes found all through nature. Numbers and their associated shapes represent stages in the process of becoming. These number principles do not only unfold sequentially but interpenetrate the universe simultaneously in a cosmic symphony.”
Alexander Polyhistor (1st century BC) gives Diogenes Laertius the mathematical cosmology of Pythagoras in Successions of Philosophers:
“The principle of all things is the monad or unit; arising from this monad the undefined dyad or two serves as material substratum to the monad, which is cause; from the monad and the undefined dyad springs numbers; from numbers, points; from points, lines; from lines, plane figures; from plane figures, solid figures; from solid figures, sensible bodies, the elements of which are four: fire, water, earth and air; these elements interchanged and turn into one another completely, and combine to produce a universe animated, intelligent, spherical.”
Stefan Stenudd writes, “Pythagoras replaced mythological ingredients with principles of higher purity and precision, numbers and their relations rather than anthropomorphic creatures.”1
One could think this system of belief is atheistic, yet it does not have to be. “There is a very long tradition, far older than Christianity and going back far beyond Plato, that identifies God with ultimate reality and truth”2 and not with a person or anthropomorphic figure.
The Decad – Cosmic Archetypes of Creation
The Monad – 1 – The Circle
The Monad is all about ‘Oneness’. Its shape is a circle, sphere, or an invisible central point. It represents Absolute Unity; Infinity; Timelessness; Equal Expansion in all directions (Equality) and the Cyclic nature of reality.
It is often used as a symbolic representation of God, the All-Including One, or as Plato put it, the “Whole of Wholes.”
It represents the undifferentiated, realm of infinite potential. It is timeless and has both zero dimensions and infinite dimensions. It is the Source of the physical reality.
The Monad in Christianity is ‘without form and void…the darkness over the face of the deep’.
To the Cabbalists it is the ‘Supernal Light…[that] filled all existence’, the ‘Endless Light of Will’ or ‘Absolute All.’
In Sufism it is the ‘Light of One’ and the ‘hidden Treasure’.
It is the infinite eternal becoming of the Buddhists and ‘The Way’ to the Taoists.
To the ancient Egyptians it is the ‘Nun, or Cosmic Ocean – the source of all.’
Every culture throughout the world understands the archetype of the Monad as the Source of all reality. It had many names, but meant one thing – The One Infinite Source of creation, the True Nature of All.
The Dyad – 2 – The Vesica Piscis and the Line
The Dyad is about “Twoness”. Its principles include Polarity, Duality, Action, the Power of multiplicity, and Love/Gravity because love and gravity are the same force – the force of action that draws the separated to re-unite.
As Bucky Fuller put it, “Love is metaphysical gravity.”
As the Monad is the father, so the Dyad is the mother. All subsequent numbers are considered children, or offspring, of the parents, the Monad and Dyad.
The dyad represents how the One becomes the Many. The Dyad is about Separation. It is represented by the Vesica Piscis – the eye shaped space between two equally sized, intersecting circles.
The Dyad is the result of the One – the Monad – casting a reflection of itself. This reflection fractalized out and is still fractalizing out in infinite ways to create the infinite variety of matter and life.
The Line is birthed from the womb of the Vesica. The line forms between the two centers of the circles. Two points define a line. The line represents action, movement and focused will power.
Mark Booth tells us, “In the ancient world sperm was understood to be an expression of the cosmic will, the hidden generative power in things; the ordering principle of all life.”
The line is the sperm that impregnates the divine womb. In other words, the line, the dyad, is the action of the will upon the infinite potential of the monad (the cosmic womb) that creates new life or that creates a new direction in life.
The Dyad represents the Divine Will or Light of Will in religious creation myths. It represents the first day of creation and the desire of the One to know itself. It represents the first movements of consciousness – that which created light, the photon, while simultaneously creating gravity.
The photon is the gift of individuality. Gravity is the gift of the return – the way back to Unity.
John Michell remarks, “The dyad was the symbol of the first active stage in creation, its equivocal nature arises from the conflicting desires of its two parts to react against each other and to seek reunion.”
This is a key point: the dyad is the force that separates and the tie that binds. Polar forces are not actually opposites, but merging tendencies, yearning to be reunited and balanced in unity.
The Triad – 3 – The Triangle
The Triad is about “Threeness”. It is represented by a triangle. Its principles include: harmony; balance; stability and the trinity.
The triangle represents the principle of creation – forming the passage between the transcendent and the manifest realms, the unseen metaphysical reality and the seen physical reality.
The Triad represents the separation of the physical from the metaphysical and the creation of individualized consciousness as the balance between the two.
The sacredness of the Triad and its symbol, the triangle, is derived from the fact that it is made up of the monad and dyad, and represents the linking force between the metaphysical realm (heavens) and the physical realm (Earth). That linking force is human consciousness.
The Tetrad – 4 – The Tetrad
The Tetrad is about “Fourness”. It represents physical matter; materialization, the ‘first born thing’ in the world of Nature; and the Four Elements. Four is esteemed as the primogenial number, the root of all things and the fountain of Nature. It represents the materialization of light forming the Four elements: Earth, Water, Air, and Fire and the formation of the mineral world from which life springs.
The Pentad – 5 – The Pentagon
The Pentad is about “Fiveness” or “Phi-ness”. It is intrinsically linked to the golden ratio, phi, the Fibonacci sequence and the property of fractal self-similarity. The phi ratio is embedded in the pentagon, the shape of the Pentad.
Its principles include: life, regeneration, health and humanity.
The Pentad symbolizes the fifth element – Aether – because it is free from the disturbances of the four lower elements. The dodecahedron, the 3D representation of the pentad, is also the element of Aether – the fifth element of Spirit.
The Pentad represents the formation of life from the material world. The mineral elements of the Tetrad are ensouled with life – the Pentad – to come together to form the single-celled organisms, plants, insects, animals and humans.
The Hexad – 6 – The Hexad
The Hexad is about “Sixness”. It is represented by the hexagon.
The principles of the hexad are efficient structure, function and order. “The numbers 6 and 12 frame the proportions of the heavenly bodies, divide up the circle, and measure the periods of solar time.”3
It represents the formation of the cycles of time in the physical realm.
The hexad also represents physical form. The four elements (the Tetrad) are combined with the Spirit (the Pentad) to create the various forms or bodies of everything we see in physical reality. The Hexad represents the container, vessel or boundary of each life form.
The Heptad – 7 – The Heptagon
The Heptad is about “Sevenness”. It is represented by the heptagon. The heptad is a symbol of eternal rather than created things and entails a seven-step process of transformation.
The Heptad represents the return to the Source through a seven-step process of transformation. These seven steps are the 7 notes of the diatonic musical scale, the 7 colors of the visible light spectrum, and the 7 chakras of the spiritual energy system. The seven-steps create the entire process.
The eighth step, the octad, represents the return, or the process repeated again, but on a higher octave or raised to a higher power.
The Octad – 8 – The Octagon
The Octad is about “Eightness” or “The Octave”. It is represented by the octagon. The principles of the octad are tied up within the idea of the octave – that is periodic renewal, self-renewal, limitless growth, and ‘same but different’.
This all refers to the principle of the octave – that is the eighth step is the same as the first step, but at a higher level. The perfect example of this is seen in music. There are seven notes in the diatonic scale (the white keys of the piano). The eighth note is the same as the first note, but at a higher octave – a higher level. Implied in this principle is the presence of limitless growth of spiraling octaves – octaves within octaves within octaves…to infinity – the eternal process of becoming.
The Ennead – 9 – The Nonagon
The Ennead is about “Nineness”. It is represented by the nonagon. Nine terminates the series of single digit integers, which begins again with ten. Because of this, the principles of the ennead include completion, highest attainment and the horizon.
The Decad – 10 – The Decagon
The Decad is about “Tenness”. It is represented by the decagon and symbolizes a journey into limitlessness. The Decad is ‘Beyond Number’ as it is beyond the nine single-digit integers. Yet it is also the ‘greatest of numbers’, not only because it is the tetractys (the 10 dots) but because it comprehends all arithmetic and harmonic proportions.
Pythagoras said that 10 is the nature of number, because all nations reckon to it and when they arrive at it they return to the Monad. Hence, ten is a lower form of the Monad, representing the created universe – the manifest creation from the unmanifest Infinite Source of the Monad.
Plato’s Numerical Creation Myth of Timaeus
In the Timaeus, Plato describes the birth of the world, the nature of the cosmos and the world-soul, among other things. He explains how a ‘craftsman god’ imposes order on a pre-existing chaos using mathematics and geometry in the construction of the cosmos.
Renowned Platonist scholar Robin Waterfield tells us that “Timaeus offers the first thoroughgoing teleological account of the world, with order being imposed on chaos by an external deity.
Why does Plato feel that he requires this teleology? There can be no doubt that Plato wants to link his account of the natural world to ethics and politics. In particular, the heavens stand as an exemplar of well-ordered motion. Just as the cosmos is well ordered, we, individually and collectively, should order our lives well. There is a good, that good exists independently of us, and we should aspire to that good…We hear that we should try to bring the wanderings of our mind into order to match the unwandering motions of the heavens.”
It is important to note that Plato’s demiurge, or creator god, is entirely good and free from jealousy. This is unique in the canon of mainstream religion.
However, “Timaeus is not really a religious work, at least in the sense that it does not say that we should worship god, nor does it lay down how god should be worshiped, nor give any structure for the organization of a religion. Rather, it tells us how we can embark on a program of intellectual improvement, based on an analysis of the relation between the cosmos and god. We should strive to become like god.”
The following text is an account of Plato’s numerical and geometric Creation Myth from the Timaeus explained by John Michell in The Dimensions of Paradise. Note the similarity between the Pythagorean view of the Decad and the religious creation myths from Article 86.
“The story is told simultaneously in two forms, mathematical and mythical, the first appearing to reason and intellect, the second supplying imagery and humor.
The traditional cosmology transcends and does not conflict with the proofs of modern physics. The best reason one can find for the creation of the universe, says Plato, is that the eternal God who experiences constant perfection wished out of kindness to share his state as widely as possible.
This first creation was a perfect sphere. This universal globe contained everything within itself and there was nothing and nowhere beyond it. It revolved on its axis but was otherwise motionless in the void.
The ineffable God of the universe did not directly fashion the various types of creatures within it. That was the task of a hierarchy of lesser gods or creative powers, divinely appointed to create and maintain order.
His Creator proceeded in the same way as the God in the Apocrypha (Wisdom 11:20), of whom it is said, “Thou hast ordered all things in number and measure and weight.” As the first stage in his plan to make all things as like himself as possible, he reduced primeval chaos to order by setting numerical proportions between its elements. These were symbolically named earth, water, air and fire.
In bringing order to the universe, the Creator gave geometric forms to the atoms of which the four elements are separately composed. These being the tetrahedron (fire); the cube (earth); the octahedron (air); the icosahedron (water). The dodecahedron is spirit or Aether, or as Plato said, “was used by God for arranging the constellations on the whole heaven.”
A model of the physical universe, as Plato described it, would be a perfect, all-inclusive sphere, containing every type of proportion as represented by the five regular figures of solid geometry.
The universe, however, is no mere mechanism but a living organism by virtue of its soul.
The difference between the created universe and the perfect pattern on which it was designed is the difference between an original and a copy. One of the basic tenets of Plato’s philosophy was that a copy is bound to be inferior to its model. Thus God’s creation was necessarily less perfect that the state of eternity that it imitated. It is subject to Time, and all its parts are transient, “continually being about to exist, existing, and having existed.” Plato summed up the universe in one phrase, as a “moving image of eternity.”
Spinoza’s Mathematical View of God
The last example of a numerical creation we will discuss comes from the philosopher Benedictus de Spinoza (1632-1677), discussed by WT Jones in A History of Western Philosophy: Hobbes to Hume.
Portrait of a man thought to be Baruch de Spinoza by Barend Gratt, 1666
Spinoza worked off of Pythagoras’s idea calling God, “a being absolutely infinite – that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality…”
Jones writes, “To hold that God wills, that He acts for ends as men do, that He is limited as men are by an external environment, is not only the baldest anthropomorphism; it also ignores the fact, which Spinoza believed himself to have proved, that God is perfect and so lacks nothing, that God is the totality of everything that is and so could not work within an environment that limits Him. It follows that God has not created the universe (God is the universe, perhaps), and that He is not a loving and providential Father. According to Spinoza, all the attributes with which Christian piety has endowed God are illusions, projections of our own ignorance and insecurity.”
“He believed that he had discovered what ultimate reality is – a system of implicatorily related truths – and he held that he had conclusively demolished the arguments purporting to show that ultimate reality is a Person.”
“But from the Christian point of view the religious function of God is far more important than His metaphysical and epistemological functions. Can one worship a system of truths?”
Yet Spinoza did have reverence, faith and devotion to his system of truths.
“Doubtless, for the ordinary man, the Spinozistic system of truths would be a cold abstraction; the strongest appeal of Christianity rests precisely on those personal qualities that Spinoza rejected.”
“It is unfortunate if the truth fails to satisfy the ordinary man’s religious needs, but that cannot be helped. Metaphysics is the attempt to ascertain the truth about reality. It is not designed to comfort the ignorant or to assuage the fears of the superstitious, and it should not be judged by such emotional criteria.”
Pythagoras, Plato, and Spinoza did not see God as an anthropomorphic figure, but as higher principles and processes that were infinite and timeless. They were attempting to get to the root of the situation and did so through the use of geometry and number.
This is not to denigrate any one person or religious belief system that chooses to symbolize these eternal principles in other ways. These principles can take any form one wishes and not lose their potency. For instance, divine love can be represented in any number of ways, and each of these ways will hold power and beauty and reverence for those in that particular belief system. Buddha can represent Divine Love. Jesus Christ can represent Divine Love. Two intersecting circles can represent Divine Love. The symbol is not as important as the principle. Far more important than displaying or worshiping a particular symbol is living the principle it is supposed to symbolize. That is all that matters.
At Cosmic Core we encourage each person to view reality, divinity and infinity in any way that holds meaning to them. No one is wrong. Everyone is right.
The only danger comes when a person or group of people refuse to respect another’s choice and demand they see it their way, and only their way, going so far as to damn another to a tortuous eternal hell – or worse, torture or murder another – if they refuse to worship the same symbol they do.
Pythagoras, Plato and Spinoza tried to prevent this from happening. Of course it didn’t work, at least not for the masses of human history, but they tried.
We can try too.
- WT Jones, Robert J. Fogelin, A History of Western Philosophy, Hobbes to Hume, Harcourt Brace Jovanovich College Publishers, 2nd edition, 1969
- Michell, John, The Dimensions of Paradise, Inner Traditions, 2nd edition, 2008