Fig. 1: Section of the central nave. Reims Cathedral. Harmonic layout “Ad Pentagonum” (Drawing: © Josep Gonzàlez). “... there was a time in the so-called Middle Ages when human beings knew themselves capable of emulating the grandeur of Creation, and that was possible because a few enlightened ones found the harmony of proportion thanks to a simple mathematical relation which they called the number of God.” The Number of God José Luis Corral In the history of Ideas, as in that of Art, the search for harmony and for the geometric patterns that govern the Beautiful has been, and remains, the “Leitmotiv” of a great part of artistic speculation. It is an ontological concern that drives man to seek and discover the complex fabric that builds and constitutes the “World”. For generations, ever since the primordial offspring emerged from the caves, man has counted, gathered and serialized, consciously and unconsciously, the rhythms of nature. And, emulating the Gods, he has built, in his own image and likeness, evocations of the Logos. He has raised Architectures which, before being made of stone, were manifestations of that ancient, saturnine pulse that governs the universal order of things. Hence, throughout the ages, humanity has discovered physical and metaphysical tools, such as mathematics and number. And through them it developed the powerful divine acquiescence of Geometry, also called the language of God. For what is the divine if not Geometry? And it is through this speculation on the invisible order that nature generates that the architecture of the “beautiful” is materialized. “The Beautiful is the splendor of the True,” Plato tells us, and he asserts that the substance that generates all things speaks to us in the language of geometry, and we might infer, of “Reason”. For it is through “proportion”, which is ratio and analogy between numbers, that the intelligible manifests itself to us as a transcendent moral beauty: “…we confer upon the mathematical sciences the dialectical power to ascend from the cave to the light, from the visible to the intelligible, from the senses to the essence by means of intelligence. By these arts the best part of the soul can be raised to the contemplation of the best of beings: the Good.” Likewise for Aristotle, beauty, which is the manifestation of a moral and transcendent good, consisted of magnitude (μέγεθος) and order (τάξις). And this order, or “Taxis”, is what governs form, which is the appearance of things and in which perfect proportions are found, through just measure and symmetry, or rather, analogy: “...The supreme forms of Beauty, for their part, are order, proportion and magnitude, which the mathematical sciences display to a high degree...” . That is, Harmony, which is the universal relation between the parts and the Whole. And as Plato reminds us: “...it is impossible to combine two things without a third; a relation (Ratio) between them is needed to join them together. The best bond for this relation is the Whole.” And the relation par excellence that speaks to us of the Whole is the “Golden Section” or “Divine Proportion”. A sublime relation whose quotient was given precisely the name Tomé, that is, Section (τομή), whence its first letter was the τ or Greek Tau, which curiously uses a sign identical to the Egyptian ideogram reserved for the concept of sky, or roof, represented by a lintel supported by a T-shaped pillar. Thus, that divine number, numerically undesignable because it is irrational, which had the cherished property of harmonizing the parts of things with one another and of keeping the same proportion between them and the Whole, was recognized basically by its geometric description and by its sublime properties of homothetic and infinite growth. This is the number that, at the beginning of the 20th century, the mathematician Mark Barr would rename Phi, φ, in honor of Phidias, the distinguished author of the sculptures of the Parthenon, and which most of us know by the name given to it by the Franciscan sage, friend of Leonardo da Vinci, Luca Pacioli: “the Divine Proportion” . This proportion has countless epithets and qualifiers that describe it throughout history as that ineffable feat, the fruit of mathematics and pure symbolism. Its strength lies in its inexhaustible will to grow, in its self-morphic generation, exact and beautiful unto itself, capable of always evoking proportions full of immaterial and infinite beauty.