Sacred Geometry and Divine Beauty: Philosophical Insights on Geometric Forms and Spiritual Symbolism

From a philosophical point of view, force is an essential characteristic of beings: everything that exists has its own force and its own action through which it relates to the external world. In this philosophical framework, space is that principle which unites force centers among themselves, which comprehends the forces within itself and gives them the possibility to unfold. The result of this unfolding and interaction between force centers is a geometric form that corresponds to them. The resulting geometric form can therefore be a material form, when the action of these force centers manifests on matter, shaping it as in the case of earth and gravitational force. Or the geometric form will be a mental form when the action reverberates on thoughts, organizing and arranging them as happens with philosophical systems. Without modifying our definition in any way, we can consider as geometric also a psychic form when these forces reverberate on the soul, as in the case of vices and virtues and so on. In synthesis, the geometric form is the symbol or sign of an acting force. The goal of geometry is declaredly the realization of beauty. But what is meant by the beauty of a mathematical formula? Regarding this question, many definitions have been proposed. One of these, and which is most akin to the way we have presented the concepts, is that a mathematical formula is beautiful to the extent that it represents an idea. The beauty of a formula is evidently connected to the idea it expresses. If, in fact, the formula expresses no idea, or if this idea is not received, it becomes only a series of letters or glyphs without meaning and suddenly loses all beauty. Not only, therefore, does the beauty of a formula reside in its capacity to express an idea, but the more profound this idea is, that is, the greater its specific content or meaning, the more beautiful the external formula appears. Euler's identity, for example, is often cited as one of the most beautiful formulas of all time. It links together three radically distinct numbers coming from approaches far from each other. It in fact relates among themselves: e, Napier's number, typically coming from the combinatorial or analysis field; i, that is the imaginary unit, typically coming from the algebraic or arithmetic environment; and π, pi, typically coming from the geometric environment. These three numbers are then united in a single, simple formula: e^(iπ) + 1 = 0. What makes the formula beautiful is clearly not a purely graphic factor, but the idea it manifests. In particular, what makes this formula beautiful is its capacity to manifest the union of these three distinct elements in a simple and evident way. From the point of view of the philosophical approach we are using, beauty is the incarnation of an idea. The beauty of forms and geometric constructions that we will present will therefore reside not simply in a constructive symmetry or harmony but principally in the capacity of these images to incarnate transcendent concepts and ideas. In the philosophical system we have presented, we have distinguished in every being three fundamental aspects: concerning its freedom or autonomy, the fullness of its content or meaning, and its expression through action and form. In this perspective, we have said that beauty is the idea or content made perceptible to the being. Considered prevalently in its interior absoluteness, as the absolutely desirable or wanted, the idea is the good; considered in the fullness of the particular determinations it embraces, as content thought by the intellect, the idea is truth; considered in the perfection or completeness of its incarnation, as really perceptible to the sensible being, the idea is beauty. Let us consider, for example, a diamond with its infinite chromatic games and try to trace the origin of its beauty. Certainly the origin of its beauty does not reside in the chemical composition of matter. In fact, chemically, the diamond is nothing other than carbon. Likewise, the beauty in question is not to be attributed exclusively to the light or transparency of the material with respect to the light ray. In fact, a simple transparent glass allows light to pass entirely without any diffraction and certainly cannot be defined as beautiful as the diamond. The beauty of the diamond evidently results from the fact that neither the luminous principle nor the dark matter prevails unilaterally, but they interpenetrate each other, uniting in a single indissoluble reality of transfigured matter and incarnate light, of illuminated carbon and petrified rainbow. Its beauty derives from a transfiguration of matter through the incarnation in it of a different, trans-material principle. Light penetrating the diamond diffracts, acquiring its particular characteristics and qualities, without however ever losing the essential unity and chromatic harmony. Each of the colors acts in full freedom, without however damaging the perfect unity of the whole. The diamond, therefore, with its polychromatic games, becomes the symbol of perfection and uni-total life. Even if it is not understood, however it is perceived through the perception of the diamond. The object in question therefore ceases to be pure matter and reveals an idea, makes it sensible, incarnates it, and the more perfect this incarnation is, the more the object that incarnates it appears to us as beautiful. The geometric symbol is therefore an epiphanic symbol, a symbol, that is, which makes truth sensible, provides it with a body. It in a certain way realizes the truth and therefore manifests beauty. In this perspective, the great intellect that distinguished the philosopher Plato affirmed that God Geometrizes. This affirmation, simple as it is profound, identifies divine action with a principally geometric action, that is, of hierarchization or disposition. Since the most remote antiquity, geometric figures, for their inherent characteristics, have been associated with a divine or theurgical action and considered as ideal in representing the communion between celestial realities and terrestrial ones. If on one hand, in fact, geometric forms, for their abstractness, suggest to consciousness a spiritual plane far from the corruption of matter, on the other hand their formal representation necessarily leads back to a corporeal and therefore in some way terrestrial aspect. Geometric figures thus appear as a first corporification of spirit and their use in the worship of divinity is found transversally in all cultures. The religious use of geometry is in fact testified by the essential and geometric lines of the Egyptian pyramids, as by the spherical domes of Buddhist stupas, or by the cultic dodecahedra of the Etruscans as by the cubic altars of countless cultures. All this without considering the use of lines and geometric realities testified by the mandalas of Indo-Tibetan gnosis, by the geometric pentacles of the Greek and Hebrew tradition as by the numerous icons of the Christian iconographic tradition. Although operating in completely different cultural and cultic contexts, the sense of the use of geometry in these representations is always the same, that is, to represent a force in a pure state, that is, deprived of any contamination, and which, under certain conditions, can explicate itself and act on consciousness, teaching it the way of reintegration. At the base of every ritual worship of divinity there is the law of analogies or correspondences that allows communion between a reality of divine uncreated character and the reality of nature of creaturaly character. The principles on which the law of analogies or correspondences is based are, in fact, synthesized in three fundamental points: 1. the unity of the World, in all its parts; 2. the analogical identity of the Divine Archetypal Plane and of the material Universe, the second created in the image of the first and its reflection, inferior and imperfect; 3. a permanent relationship between the two, for the analogical identity and which can be expressed by the Science of Symbols. Geometric forms, purest and most abstract entities, have the scope of symbolizing the archetypal realities of divine character, perfect, thus reconstituting in the place where they are used a cosmogram immune from sin, preserved from every disintegrating or demonic force. In the mandala, as in the icon, as in the Christian, Islamic, Buddhist or Hindu temple, an image of the perfect cosmos is created, in which the arcane game of forces can be assimilated by consciousness, thus accomplishing the process of spiritual transmutation. Eloquent in this sense are the words of the great sinologist and orientalist Giuseppe Tucci in the description of the ritual use of mandalas: "The mandala outlines the consecrated surface and preserves it from the invasion of disintegrating forces symbolized in demonic cycles. But it is much more than a simple consecrated surface to be kept pure for ritual and liturgical purposes. It is in fact a cosmogram, it is the entire universe in its essential scheme [...] The same principle naturally regulates the construction of temples: every temple is a mandala. Entry into the temple is not only entry into the consecrated place, but entry into the mysterium magnum. [...] The mandala then is no longer just a cosmogram but a psychogram, the scheme [...] of reintegration from the many to the one, to that absolute, whole, luminous consciousness, which yoga makes shine again at the bottom of our being." Since antiquity, therefore, geometric figures were found ideal for adorning temples and places of worship, pentacles or sacred icons to solicit consciousness to the transforming process and help it enter into ecstasy and contact with spiritual worlds. Geometric figures constituted the first instrument for manifesting the force and action of number because geometric form does not refer only intellectually to the evoked concept, but sensibly disposes to it. Precise geometric figures, like an imperious octagonal structure, support consciousness to obtain an interior disposition, a sensibility that can be intensified thanks to the use of sacred music and which resolves in a beneficent reception of spiritual forces. Therefore circular, triangular, square, pentagonal, hexagonal and octagonal figures have been used for the architecture of sacred temples, as for the fabrication of worship instruments, with the aim of condensing in a material object the force of number, so that, under certain special conditions, it could again exteriorize itself in the free and pure state, beneficially investing the entire individual and modeling it under its action to conform it to the life of the Spirit. Man has always needed artificial means to awaken the potencies of his psyche and with this enter into harmony with the intellectual world. To facilitate this harmony he has often resorted to symbols, diagrams, geometric figures that helped him identify with their ideal content and produced in the interiority a decisive influence, that is, a transformation of consciousness. The symbolic images are therefore, in the Christian tradition, guides to educate the will and intellect by means of imagination. The figure, the form, the sensible impressions, educate the will and intellective faculties by directing them toward spiritual realities to which they are akin, thus disciplining the forces of the soul. To sublime terrestrial love and direct it toward spiritual realities in such a way as to allow the soul to dispose of its own potencies, Christian iconographers have therefore represented with various forms the essences and celestial realities. Each image synthesizes a force or virtue expressed by the celestial essence that the Christian ascetic must incise in his own soul. Sometimes the iconographers have taken inspiration from natural forms, as Dionysius the Areopagite testifies: "The experts of divine things resort to FIRE to represent celestial essences, and thus put in light their tendency to resemble God and imitate him as much as possible. They also represent them in the form of MAN since man possesses intelligence, a visual faculty oriented toward the high, a straight and erect form and the natural aptitude for command and guidance; [...] As regards the semblance of LION, one must consider that it indicates dominion, strength, indomitability and similarity, within the limits of the possible, to the arcane of ineffable divinity [...] The aspect of OX indicates strength, flowering age, the capacity to open furrows of intelligence to the reception of celestial and fecundating rains, while the horns symbolize their protective function and their invincibility [...] The aspect of EAGLE is indicative of their regality, of their capacity to elevate themselves and fly swiftly, of promptness, vigilance, speed and dexterity with which they grasp fortifying nourishment and of contemplation free from obstacles, direct and indefectible." Other times instead the same forces and spiritual realities have been represented by means of geometric symbols, numbers, squares uniting them with letters of the Hebrew alphabet. The use of geometric representations as symbols of realities and celestial essences is then evident in Renaissance Neoplatonic theurgy. In this context geometric forms constitute a fundamental element for the fabrication of emblems and pentacles capable of resonating with determined spiritual influences and of condensing the magical will of the operator. In the same way, as we will see, geometric figures are used in Oriental and Occidental iconography as support for meditation on the centers of consciousness, in order to purify these centers and attune them to the spiritual virtues corresponding to them. The sense of the use of geometric symbolism in this context is expressed clearly by Saint Bonaventure, in his Journey of the Mind to God: "Since number is most evident to all and very near to God, it conducts us, as through seven gradual differences, easily to him." Number, particularly in its geometric visualization, is most evident to all. It is naturally and universally understood and its force, its beauty and its evocative power require no specific cultural structure to act on consciousness. Likewise it is evident that the geometric figure encloses an idealization of natural reality and therefore transcends it. The visualized number, therefore, for its being most evident to all and very near to God, represents the principal instrument for sublimating the forces of imagination, attention and concentration. The geometric figure in fact provides consciousness with a material support but at the same time indicates to it an absolutely pure idea with which it must enter into contact. The purpose of geometric figures in ascetic practice is therefore, according to what we have seen previously, to fill the exterior and interior senses in order to channel them toward specific virtues through a subtle game of resonances. Consciousness, entirely polarized in the object of meditation, thus saturates itself with this sensible current and, in so doing, tears the fabric of natural reality to open itself to the purely spiritual one. In this process two elements play a fundamental role: the first is that of involving all the attention of the meditator by saturating his senses and the second is that of coordinating these senses harmonically together according to a law of correspondences that assures their resonance with the idea to be meditated. In fact the first aspect assures force in meditation by conveying all the energies of the ascetic, while the second assures precision in the objective. In this sense are to be understood the numerous symbolic associations and correspondences made between divine names and geometric forms which therefore represent true and proper symbolic keys for placing consciousness in contact with the invisible potencies of the cosmos. At the bottom of this book we will examine in more detailed way some approaches coming from the Hebrew and Indian tradition that will allow forming a clearer idea on the subject. When in fact a geometric form contains a divine name, this acquires a character and a particular force in relation to the name contained. The divine names of the Hebrew tradition, as also the mantras of the Indian tradition, are in fact true and proper words of force, endowed with their own dynamism and capable of awakening consciousness to determined states and placing it in the presence of precise spiritual realities. These divine names are also called words of power because "they not only reveal something regarding the essence of who bears them, but enclose at least in part the power." A logodynamo concealing in itself the divine presence and permitting its communication is therefore "a symbol word that opens the doors of Eternity." A logodynamo is therefore a sacrament, possible vehicle of divine presence which inserted in a geometric form makes it assume a markedly transcendent character. Geometric forms in fact have multiple planes of belonging and correspondence, but when these are polarized thanks to the inscription of a divine name, these inevitably acquire a supernatural character relative to the sphere and divine action. The geometric form acts therefore as an envelope in which is inserted a specific and transcendent content represented by the divine name.