Sacred Mathematics: From Theodoro's Spiral to Organic Systems Evolution
that has not yet been made explicit. The work "Theodoro's Spiral, Irrational Numbers and $\pi$" shows that through the arrangement of quadratic irrational radical numbers in a spiral planar construction, one not only arrives at seeing an approximation of the transcendent irrational number $\pi$ through quadratic radical numbers alone, but also how an obscure passage from Plato's Theaetetus can be well illuminated. In the work "The Cosmic Numbers 5, 6, and 8," Niko continues the symbolic exposition of the first 12 numbers; here we note the distinction between the expression $5=1+4$, in which the 1 symbolizes the will of Man who dominates the elemental quaternary, and the expression $4+1=5$, in which fatality, that is the 4, imposes itself on the will of Man. The article by Ur "Infinite and Indefinite" provides a first doctrinal clarification that allows us to ascend through the way of the heart to that inescapable distinction between what is the ultimate goal of every initiatic journey and those that are stages erroneously experienced as intermediate, perhaps gathered in a single degree of existence, extendable even indefinitely, exactly as the series of natural numbers is obtainable by passage from a number $n$ to its successor $n+1$. However, it is in the act of closing a series, even indefinite, of gestures that the transcendent and superordinate nature of the Infinite shines. Mathesis proposes in the work by Radice and Tabit, "Symbolism of Divergent Series," the symbolic-mathematical bases for overcoming the quantitative notion of number and being able to embrace the generative essence of the same. Knowing how to understand, for example, that the sum of the series of squares of positive integers is zero, or makes zero, and giving reason for the procedures that authorize such results, constitutes for us a support for meditation of inestimable value. Radice and Tabit masterfully succeed in showing how such processes have nothing arbitrary or deviant but, conversely, show the symbolic possibilities inherent in Sacred Mathematics. Leovir and Zadik in "Gematria and Geometry" continue in the presentation of Kabbalistic symbolism. Gematria is that traditional technique of deep reading of the biblical text based on the comparison of phrases through the numerical equivalence of the terms that compose them. It is a technique focused, precisely, on the numerical value of Hebrew letters, which are numbers in all effects. The table with the gematric values of the 22 individual letters of the Hebrew alphabet and, for example, the gematric meditations proposed on the name of the 72 Angels, constitute an aid for our interior edification, which we wanted to point out in advance to the Reader. Finally, the work by Apotegma, "The Module of San Galgano Abbey," constitutes, especially for those who are connected to an initiatic way that places architecture as its operative base, an instrument for harmonizing initiatically and not in an exterior and merely aesthetic-profane way, with one of the masterpieces of sacred architecture on Italian soil. Apotegma wonderfully links the interior realizing knowledge necessary for the edification of San Galgano Abbey, with a field analysis that alone constitutes a realizing practice of exemplary importance, for those who frequent lodges which claim to excavate dark and deep prisons for vice and to raise temples to virtue. With this we leave you to reading and invite anyone interested in collaborating on this project to contact us at our email address. Mathesis@MatematicaIniziatic a.it The evolution of mechanical systems and organic systems (Alkes) An article by Pentadecade, present in this number of Mathesis, touches on a Gordian knot of Classical Mechanics reviewed in geometric key, that is the Flow Theorem. This seminal work allows us to address a theme more Physico-philosophical than Mathematical-theological relative to the dynamic evolution of organic systems and that of mechanical systems. What an organic system and a mechanical system are we will go on to define shortly. For the moment let us content ourselves with the common definitions that each of us can imagine and note how Physics of recent centuries has dedicated itself to defining instruments perfectly suited to describe the evolution of mechanical dynamic systems (such as objects in free fall, a spinning top, mechanisms of any type) and has not dedicated nor found instruments to treat in a satisfactory way the evolution of organic systems (a plant, an animal) except when the high number of individual elements did not allow neglecting individual consciousness and allowed mechanical modeling. According to us such situation is of contingent origin, in other words: we believe that there exist mathematical instruments that allow the study to understand the evolution of systems