Sacred Numbers and Pythagorean Symbolism: From Unity to Cosmic Order
There was not only a great distinction between geometry and arithmetic, but even within certain limits there was actually an identity. Indeed, as I was saying, there is a close relationship between geometric figures or visualized numbers, arithmetic numbers conceived in a symbolic sense, and philosophical-metaphysical concepts. In fact, the geometric unit (the point) corresponds to the numerical unit in a symbolic sense (the $1$) which corresponds to the philosophical monad. Euclid's definition of a geometric point is "that which has no parts," which can be taken as a definition of numerical unity understood in a symbolic sense, as well as of the philosophical monad. Since in Platonic geometry, arithmetic, and metaphysics everything derives respectively from these concepts, it is always possible to translate a philosophical or ascetic doctrine into a numerical expression or into a geometric figure - in short, to pass from one to the other, as we shall see.
The number $1$ is not deducible from anything else. The number $1$ is God's number. This is its main characteristic; indeed, the Pythagoreans called it "simplicity" (clearly simplicity in the idea of indivisibility), meaning that which cannot be divided. On another plane, the Pythagoreans called it "Intelligence" because it reunites all things in itself, "being," "cause of truth," "model," or even "ship" or "chariot" because it is "that which hosts everything." They called it "friend," "life," and "happiness," but also "obscurity," "mixture," and "darkness" because in the one all numbers are present but are not yet explicated, not yet specified, remaining in a still undifferentiated state. This is a theologically important discourse: all numbers come from the number $1$, all numbers are contained in it, and no other number will ever deny the Unity of all numbers represented by $1$.
This is an important point that kept the Pythagoreans in check for years: how does $1$ become $2$? How can there be another $1$ that is not the $1$, where is it? "Someone might object that $1$ by addition of another $1$ is no longer $1$, but becomes $2$, while suffering nothing: he is wrong, since $1$ does not become $2$, neither the one to which it is added, nor the one added itself, but both remain $1$ as before; $2$ is predicated of their totality." (Plotinus, Enneads V,6,13-14)
What does this mean? 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 among themselves by this relationship. The one, polarizing within itself, becomes two, thus giving rise to tension and movement.
Indeed, $2$ was called "Mother of Zeus" as well as "movement," "generation," "change," "impulse," "nature." This tension and movement provoked by dualism is reconciled thanks to three - the synthesis that reunites thesis and antithesis.
"Friendship," "peace," "concord," "harmony," but also the "indomitable" because it can never be divided into two equal parts. In Christian context, it is associated with the Divine Trinity. So if we have $1$ as the symbol of God expressing the Essential Unity of Divinity, we have $3$ which instead represents the triple divine aspect. The number three appears as a fundamental category of psychic life and thought; for example, the human psyche can be distinguished into Will, Intellect, and Feeling.
It is the "Guardian of the Keys of Nature" because without four there would be no ordering of the universe. It corresponds to an Idea of Universality. Under its influence nature is arranged, and indeed we have that every natural manifestation is divided into $4$ aspects: 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 the number $4$ accesses the very keys of Nature. These first $4$ numbers, considered as a whole, were called by the Pythagoreans Tetraktys, the source that contains the roots of "Inexhaustible nature."
It is the number of "marriages," of the earthly principle with the celestial one. "Alteration," "light," "absence of strife," "ether," "quintessence," "marriage" as the union of the first even number and the first odd number, and also "androgyny" and "demigod," furthermore "cardiac" because it resembles the heart which in beings is placed at the center. It is the symbol of individual man in relation to Universal Man. And it is the symbol of all World Esotericism, from China to India, to Egypt, to Greece up to Christianity of the Modern Era. Therefore, world esotericism is under the protection and moves according to the influence of the number $5$, a number that corresponds to the light of intellect and also to perfect man.
To give you an example of how one can proceed in the meditation of a number, the number $5$ can be conceived as $1+4$, that is, the number $1$, man's will that dominates $4$, the $4$ elements and arranges them by illuminating them. Conversely, meditating on $5$ as $4+1$ means meditating on the elements, matter that dominates the one, the will, and thus leads to the individual's slavery to matter. For this reason, the number $5$ was also called "twin" as well as "nemesis" because it distributes both celestial and natural gifts according to its orientation. Therefore, when speaking of symbolic operations, the operations do not commute: writing $1+4$ is not like writing $4+1$ because in the first case it is the $1$ that dominates the $4$ and in the second it is the $4$ that dominates the $1$ (clearly here we are not making a discourse of writing but of the meditator's intention).
Being composed of three plus three, it was called "loving union," "peace," as well as "cosmos." Symbol of the entire universe. It was also called "health" or "panacea," as well as "harmony of the soul." Six is also the number of creation according to Judeo-Christian symbolism, being $6$ the days of creation. It is the advanced man. Saint Augustine specifies that God creates in $6$ days because the number $6$ is perfect.
Hippocrates: "the number $7$ through its hidden virtues maintains all things in being, dispenses life and movement, $7$ influences even..."