Traditional Mathematics and Pythagorean Number Philosophy

Unconscious of the unity of Mathematics, a being in human form normally follows cognitive paths of individual nature. In this sense we can speak of a human mathematics, of its history and of its discoveries or inventions (which must be so denominated, insofar as they are sometimes obtained having as the only conscious source of inspiration the relationship that human senses have with gross corporeal reality). The mathematics that we have defined as human is connected with the ideal and even with the absolute, even when such human or natural mathematics is clothed in a formalism of purely human nature, which is often the cause of subtle misunderstandings. Indeed, according to the paradigm of modern mathematics, every set of propositions deducible by means of the laws of formal logic from any axiomatic system constructed in an appropriate formalized language constitutes a mathematical theory, whose legitimacy is given solely by its internal coherence. Internal coherence would guarantee the existence of a model that would sanction its rightful belonging to Mathematics. It is important to affirm here that, instead, simple coherence, whether internal or conditional, does not necessarily ensure the presence of a model in each of the degrees—absolute, ideal, natural—that we have recalled previously. In absolute Mathematics not everything that is logically presentable and formally deducible from axioms is real in that degree. Formal logic consists of a set of rules that allow the transmission of a truth value from one proposition to another; Logic, in a superior sense, consists in the effective and total realization of the entire degree of Truth of Mathematics of that degree. The Truth of ideal Mathematics, for example, presides over and permits the incarnation of the Johannine Logos in the degree of total Being. Absolute Mathematics, moreover, does not necessarily have to be clothed in the form of a formal system such as those required by our human way, quite limited and limiting, of seeing or understanding. We conclude these brief notes by recalling that the deepest aspect of Number is given by its nature as an acting principle and not as a formal construct, and that it is from this acting nature that it is possible to explain the otherwise inexplicable efficacy of Number in understanding the laws of Nature and their reproducibility even within a laboratory. The qualities that are interested by this active aspect of Number allow us to conceive, in accordance with Tradition, Numbers not so much as something, but as Someone. The existence of this point of view is witnessed, for example, by the names that the Pythagoreans assigned to Numbers. They referred to Numbers as beings endowed with life. For example, the number Three was called "the Indomitable," "the Tireless." The number Four was understood as the Guardian of the Keys of Nature; the number Two as Mother of Zeus, the Five as Light. The Six was called the Cosmos or Loving Union. The Seven was Wisdom or Destiny. The One was called Friend or also Chariot, while the Ten was called Sun or also Eternity. In the traditional conception, Number is not a concept obtained by abstraction nor merely a useful instrument for recording empirical measurements. Absolute Numbers are Superior Unknowns that give form to the world and with which human intelligence can enter into harmonic resonance. To facilitate the recognition of this attunement with Numbers, the following disciplines can also be used: Metaphysics, useful for being able to conceive the life of the world of qualities, and Theology, which enables us to see, through ideal Numbers, qualities in action. Therefore, as a reflection of Metaphysics appears Arithmetic, that is, the science of the properties of numbers, and, as a reflection of Theology appears Geometry, that is, the science of the form and action of numbers. From Geometry can therefore begin the ascent to the Idea and from this to Numbers, by virtue of the reflection of their action on the world and on us. Research in Freemasonry (Pentadecade): Unreservedly beautiful is the love of truth: it carries far, and it is difficult to reach the end of the journey. More difficult, however, is the way back, when one wants to tell the truth. Giorgio Colli, Nature loves to hide. The verb "to search," as well as the word "search" are semantically connected to circum, to the circle. The word "research" and the verb "to research" evoke a double movement, essentially circular, with a return movement suggested by the prefix "re." It does not therefore appear arbitrary to connect to the semantic field evoked by the word "research" that act or that presentiment connected to having seen, to...