Sacred Numbers and Mathematical Reality

There exists therefore a fundamental difference between Number and cipher, just as there exists between real or transcendent Mathematics and human mathematics, which is a partial description of the former operated by Man. The mathematician by profession studies the properties of mathematical realities, and describes what he has intuited or discovered through conventional language that he sometimes must invent and present in a logical and orderly manner to other mathematical colleagues. The process is similar to that of a writer who describes a landscape spread out before his eyes. The landscape is real and independent of the writer, but the features of it that are captured and the words the writer uses depend on the personality of the observer, the language he chooses, and his descriptive ability. Having clarified what common sense tells us about Number, we come to a more advanced aspect of this: the qualitative aspect of Number. Those who have reflected profoundly on the essence of Number will have understood that one of its fundamental properties is the capacity for distinction. Only Number is capable of distinguishing. Specifically, distinction is not possible without dualism, that is, without the Number Two $2$, i.e., $1 + 1 = 2$. What is less known is that number distinguishes both in quantity and in quality. The first is an action of distinction in the multiple, the second a distinction in unity. Let me explain better. Outside of us, in the multiple, there exist many distinct units to whose ensemble we assign a number capable of identifying their quantity: for example, I can say that in front of me I have $1$ shelf with $5$ books, one of which is made up of $72$ pages, etc. Therefore, in this case I use a number that identifies a specific quantity of objects all united by the same quality: there was one unique $1$ shelf, the $5$ were all books and $72$ were all pages of the same book. This is not the only use of Number. In fact, if we fix the quantity instead of the quality and, for example, look within ourselves, that is, in the unity of our Ego, we can distinguish different qualities that we ourselves possess. These qualities can be identified and distinguished by Numbers: I can say that in me I have the One or $1$ to identify the ordering and creative principle of the Ego, the $5$ to indicate the Will capable of dominating the psyche, the $72$ to indicate the ascending capacity of the Spirit in harmony with the hierarchical structure of the Cosmos. Number therefore externally reveals quantity, while internally hides quality. All Numbers are linked to each other because they all derive from Unity $1$. It is therefore always possible to make explicit the bond that exists between one or more Numbers in the form of arithmetic formulas or geometric operations. The three fundamental binary operations are addition, multiplication and exponential, while the unitary ones are reduction, triangular and decomposition into prime factors. Without going too much into technical details, we can say that the two classic operations of addition and subtraction can be traced back to the single operation of addition which, in effect, has two motions: the first, that properly of addition, which is a motion of polarization and therefore differentiation; the second, associated with subtraction, which corresponds to a motion of discharge and therefore reabsorption. To be more explicit let's give an example. We consider Unity $1$ and in it we polarize two states: one active and one receptive. Then we can identify this operation of Unity in itself through addition, i.e., $1 + 1 = 2$. Conversely, we discharge the tension given by these two states, letting a current flow from the active or positive pole, flows toward the negative or receptive pole. After a certain necessary time, called transition time, we will find a new equilibrium dictated by a single undistinct state. This discharge operation can be identified by subtraction, i.e., $2 - 1 = 1$. Similarly, multiplication and division can be traced back to two phases of the same motion which for multiplication is one of scission and development, while for division it is one of reunion or synthesis. To be concrete, let's take as an example a Quaternary development of the Ternary, i.e., $3 \times 4 = 12$. The Three $3$ in this case declines in Four $4$ distinct modalities forming a single complete cycle. Therefore the Twelve $12$ is, in this sense, a complete development of Number $3$. Similarly, dividing Twelve $12$ by Number Four $4$, i.e., $12 : 4 = 3$, we return to the original Number, the Ternary.