The Spiritual Nature of Numbers: Three Levels of Mathematical Reality

To embrace such a spiritual conception of Number, one must cross a spiritual threshold that enables a being to experience within themselves the qualitative aspects of Number. Operating with them according to truth has more the aspect of a sublime calculation or the perfect execution of an initiatic ritual than of a discussion among scholars. The Number expressed by the digit $5$, at certain levels of reality, will not only indicate the quantity associable with five objects, but will also govern the Life of the Spirit as universal person, ordering Logos, or allow the symbolization of the Quintessence, as well as regulate the domain of Will over Force. To truly know how to control one of these meanings, however, is not the product of executing a mechanical procedure but is the result of the degree of awakening actually realized. To the conception of Number recalled above is often associated another, which we consider gravely erroneous, insofar as it is vitiated by a confusion of levels that reveals its true origin; the latter tends to consider numbers as pieces of a secret code or as representations of mechanical forces, devoid of intelligence and life. We, on the contrary, refer to Numbers according to a point of view that illuminates their nature as living beings, as ultra-empirical roots of formal manifestation, as ultra-ideal roots of informal manifestation, as absolute roots of non-manifestation. Absolute Numbers are metaphysical Reality in the eternal instant in which the latter differentiates into non-manifestation and possibility of manifestation. For this reason, numbers are, from the point of view of substance, cause of themselves and, from the point of view of essence, regulative principles to which manifestation must be traced back. Numbers are independent of any conception, of any cognitive act aimed at founding them or justifying their existence. They explain themselves. We can ascend toward them, for example by experiencing their action in manifestation, insofar as they are its structuring Principles; it is also in view of this ascent that the entire enterprise of Science can assume a spiritual value. We can free ourselves from illusions by unifying, through Number, what belongs to a state with what has always, in the unmanifested, governed it, founded it, preceded it, explained it. It is opportune, for greater expository clarity, to distinguish at least three degrees of reality of Numbers: 1. **Absolute Numbers**: they are the Principles of the world of non-manifestation. They are unknowable by the intellect in its human state. They are placed beyond the world of informal manifestation. They are true roots above all things. 2. **Ideal Numbers**: they are the foundations of the possibilities of formal manifestation. They are conceivable with the intellect, but only in an intuitive way because they live in the world of informal manifestation. They precede the created order. 3. **Numbers of common mathematics**: they are the manifestation of Ideal Numbers in the world of form. They are conceivable with the human intellect and usable in a rational way. In their most elementary use they allow to register and compare positive measures of quantity. In truth, these three degrees of reality of Numbers are simultaneously realized in the constitution of that unique being which, in the integrality of its states, is called Universal Man and of which there is clear indication in Saint Paul in his well-known tripartition of the constitution of the human being into Spirit, Soul and Body. From what we have asserted it becomes conceivable that it is possible to perform mathematical operations on three distinct (but not disjoined) levels: 1. according to a **Real Mathematics** that refers to absolute realities and where every operation is in simultaneous unity with all others; 2. according to an **Ideal Mathematics** that refers uniquely to ideas and which is qualitative in nature when directed toward the unmanifested, symbolic in type when directed toward the manifested world; 3. according to a **Natural Mathematics** or of things: which also refers to the world of natural realities. We insist in affirming that the tripartition we have outlined concerns Real Mathematics, independent, for example, from the cognitive activity of a being in human form. Indeed, with the activation of its normal cognitive faculties, eventually...