Sacred Numbers and Mathematical Mysticism: Pythagorean Principles of Universal Order
The projective, the form and the force, thesis and antithesis, etc.
| Scale | 1 | 2 |
|---|---|---|
| Father | Mother | |
| Sun | Moon | |
| Creative | Generative | |
| Force | Form | |
| Projective | Receptive | |
| Grace | Rigor | |
| Illumination | Purification | |
| Spirit | Soul |
Differentiation allows the possibility of movement, dynamics, change, impulse, generation, but also separation. It is therefore associated with the idea of purification, but also of generation.
The law of generation is governed by the number two: Man and Woman, the masculine and feminine that sages call the Sun and the Moon. The two that differentiates from one is divisible.
One is polarizable and when it is polarized it manifests two. The $1$ expresses the internal unity of numbers and no number can ever deny it because all numbers always come from $1$ and are therefore united in this relationship. The one polarizing within itself becomes two, thus giving origin to tension and movement.
In this sense $2 = 1 + 1$, suggests the $2$ as coming from two distinct aspects or two polarizations of $1$.
The Number 3
"The number 3: $1+1+1$, symbol of the Holy Trinity, of the Eternal, the Creator God of Heaven and Earth. The triple relationship with the Absolute, $3$ times Holy, Faith which is $3 \times 3 = 9$. This number 3 is recalled by Matthew 22:37; the triple principle of life: 'You shall love the Lord your God with all your heart, with all your soul and with all your mind'. The number 3, proper to the absolute characteristic of Almighty God, is the three that appears everywhere as a fundamental category of psychic life and thought and therefore also of the relative and autonomous completeness of the human being."
The Divine Being chose Number 3 to manifest His absolute characteristics. On this we can do nothing but observe the reality of this decision. The $3 = 1 + 1 + 1$ is the symbol of the Holy Trinity, thus highlighting the equal divine essence of His Three Persons.
The triple relationship with the Absolute, Three times Holy, is a relationship of Power, Wisdom and Love. Since Man is made in the divine image and likeness, Number 3 appears as a fundamental category of human psychic life. For example, the human psyche can be distinguished into Will, Intellect and Feeling: Being, Essence and Energy that are expressed as Power, Wisdom and Love.
| Scale | 1 | 2 | 3 |
|---|---|---|---|
| God | Almighty | All-knowing | Omnipresent |
| Virtue | Hope | Faith | Charity |
| Color | Red | Blue | Green |
| Being | Power | Wisdom | Love |
| Priesthood | King | Prophet | Priest |
| Ministry | Govern | Teach | Sanctify |
| Principle | Spirit | Soul | Eros |
The dynamic law governed by number 3 is called Ternary. When considered in the Kingdom of Nature, there are three "ternaries":
$3 = 1 + 2$, $3 = 2 + 1$, $3 = 1 + 1 + 1$.
In the first ternary $3 = 1 + 2$, the hierarchical superiority of one element, the One $1$ over the other two elements, the Two $2$, is evident.
In the second ternary $3 = 2 + 1$, the joint action of two elements, the Two $2$, in generating the One $1$ is evident.
In the third ternary $3 = 1 + 1 + 1$, ternary symmetry and hierarchical equivalence of the three elements is evident.
The $3 = 1 + 2$ and $3 = 2 + 1$ govern the two laws of polarization and generation.
$3 = 1 + 2$
The first ternary $3 = 1 + 2$ is the ternary of the Three Forces: two antagonistic and antithetical forces in dialectical alternation on the same plane of manifestation and a third force, balancing or neutralizing, on a plane orthogonal to the first two.
A numerical example of this phenomenon is given by the cyclic group of three elements $\mathbb{Z}_3 = (\{-1, 0, 1\}, +)$. In this abelian group, the One $1$ finds its inverse in the opposite polarity, namely $-1$, while Zero $0$ is the neutral or neutralizing element.
For example, atomic physics is synthetically governed by the ternary $3 = 1 + 2$ as positive, negative and neutral charges give rise to much of the mechanism that governs protons, electrons and neutrons. Subatomic physics is synthetically governed by the ternary $3 = 1 + 1 + 1$ through the ternary symmetry of the color force of quarks.
$3 = 1 + 1 + 1$
Three realities of the same substance contemplate each other dynamically in a harmonious way, interpenetrating.
$3 = 2 + 1$
In this formula we have hidden the Law of generation: the two, Male and Female, unite to generate the One $1$. The purpose, or end of generation is also its hidden cause: the Son.
The Number 4
Number 4 has been called since antiquity the Guardian of the keys of nature, but added to 3 becomes 7, the most harmonious and perfect number. The square well suits 4, and its Hebrew letter is Dalet.
In the Apocalypse and in the Bible this figure represents the idea of universality: the four living beings, together in the world of light of all living beings (they have many eyes). There are also the four horsemen bringing the four most serious scourges. There are also four colors of horses, colors that correspond to the four cardinal points and the day that have the function of indicating universality in time and space: white corresponding to the East and dawn; red, the South and noon; glaucous the West and twilight; black the North and night.
"4: It is the 'Guardian of the Keys of Nature' because without the four there would be no ordering of the universe. It corresponds to an Idea of Universality. Under its influence nature is arranged and here in fact we have that every natural manifestation is divided into 4 aspects: in fact here that everything relative to the universe follows the law of 4: the 4 seasons, the 4 aspects of the sun, the 4 cardinal points, the 4 elements. Whoever accesses number 4 accesses the very keys of Nature."
These first 4 numbers, considered as a whole, were called by the Pythagoreans Tetraktys, source that contains the roots of "Inexhaustible nature".
In the moral world Four $4$ are the Cardinal Virtues: Prudence, Justice, Fortitude and Temperance. Prudence is Wisdom or the reception of Wisdom applied to the discernment of good and the means to achieve it. Justice is the constant will to love God and neighbor according to what is due to them. Fortitude is resistance in perseverance and courage in pursuing Virtue. Temperance consists in the dominion of Will over inferior realities.
The theological virtues are Hope, Faith, Charity and Gnosis.
Spiritual life is structured on the basis of 4 Universal Powers, which manifest in the 4 elements and then in Society as in the individual.
All biological life is structured from four elements: Hydrogen, Oxygen, Nitrogen and Carbon; with respectively 1, 2, 3 and 4 valence electrons.
DNA nucleotides are formed on four nitrogenous bases: Adenine (A), Thymine (T), Guanine (G) and Cytosine (C).
The ordering of the Universe is governed by the Name of 4 letters.
In the Zodiac governs the heart of the fixed signs that regulate the Zodiacal Eras: the 15º of Leo, the 15º of Taurus, the 15º of Aquarius, from 15º of Aquarius and the 15º of Scorpio.
Using number 9 we generate the primary decompositions of 4:
$4 + 9 = 13 \rightarrow 4 = 1 + 3$
$13 + 9 = 22 \rightarrow 4 = 2 + 2$
$22 + 9 = 31 \rightarrow 4 = 3 + 1$
$31 + 9 = 40 \rightarrow 4 = 4$
$4 = 2 + 2 = 2 \times 2$
All elementary chemistry is based on a double dualism: the antagonistic polarity of electrons and protons (±) that seeks to be balanced and the spin of electrons (↑↓) that allows the formation of covalent bonds between various atoms. In this context, the tetrahedron emerges as the most stable and symmetrical architecture, embodying the dynamic balance between opposing forces and allowing maximum spatial separation between electron pairs, foundation of many molecular structures and the chemistry of life.
$4 = 3 + 1$
The Number 5
Number 5 is the sum of the first even number and the first odd number, that is $2 + 3 = 5$. For the Pythagoreans it was considered a nuptial or union number, of balance and harmony.