FORMATIVE SACRED GEOMETRY & THE EGYPTIAN NETERS Myth dramatizes cosmic laws, principles, processes, relationships and functions which may in turn be defined and described by number and the interplay between numbers. The relationship between proportion and progression is a key to Sacred Geometry. Everything which is manifest, whether in the physical world or the world of mental concepts, belongs to the realm of continuous change. The only constant are the generative principles. The creation of three sacred roots within the vesica pisces The Square roots of 2, 3, and 5 are all the root relationships necessary for the formation of the five regular platonic solids. These roots are a trinity of form generating principles the Law of Three in a geometric demonstration. Transformation can be described by the processes of generation, formation, and regeneration. Also, the only numbers required to divide the octave into musical scales are 2, 3, and 5. All these irrational roots are symbols of pure archetypal processes, whereas fixed whole numbers are the structures which emerge to build upon these principles of process. THE GENERATIVE PROCESS: NUIT is the square root of 2 Any square whose side length is the length of Unity (1), will have the square root of two as its diagonal. The simple act of drawing the diagonal has given rise to 2. This is not because the square has been divided in half, but because 2 is implied: the diagonal of square 1 is the root of square 2, and square 2 is exactly double in area to square 1: Our body belongs to the earth, the square. Our soul belongs to the spirit, the triangle. Spirit is immortal because the triangle existed before and independently of the square. Yet spirit cannot operate in the physical world without a material body (but it can operate in other worlds and dimensions). Within a square, there are two diagonals which form a cross. Symbolism of 2's and of dualities always accompany the cross and the earthly generative square. When one becomes two, there is automatically an endless multiplicity through progression. The square root of 2 simultaneously symbolizes the principle of unity and the principle of multiplicity extending towards unlimited expansion. The square root of 2 is an irrational function which is a special class of number which cannot be expressed as a fraction or an integar. As such, it is symbollic of the archetypal realm. Nuit is the matrix of creation. Not only number, but form proliferates from the division of Unity. Nuit is the archetypal expression of the assimilative, generating, transformative function, the active power of nature. She is the mother of the Sun God RA. THE FORMATIVE PROCESS: RA is the square root of 3 The formative character of RA as the square root of three may be expressed in two major geometric configurations. The primary one is formed by drawing 2 equal circles, so that the center of each lies on the circumference of the other. The resulting shape is known as the Vesica Piscis. The hieroglyphic sign known as the "mouth of RA" is similar in shape and denotes unity. The Vesica Piscis is a balancing consciousness between two complementary pairs of opposites. The Eye of RA There is no synthetic symbolization of Unity which does not evoke all of the major principles. The roots of 2 and 5 can also be derived from this cosmogram of the Vesica. The second geometric configuration, in which the square root of three appears, is that of a cube cut by its diagonal. While the square root of 2 divides the surface of a square, the square root of three divides the volume of a cube. Everything in the created universe is a volume. Since the formation of any volume structurally requires triangulation, trinity is the creative basis of all form. The cube is the most elementary symbol of the manifest world. RA acts as a form generator: form creating flow. Ra is the number three, the reconciling force between two opposites. RA is the essence of divinity: unity in diversity. The RA function, as taught by the Henemmet in Heliopolis, is the nature and action of light (the Sun) and the source of creativity. Nuit swallows the sun in the evening and gives birth to him again in the morning. THE REGENERATIVE PROCESS: SEKHMET is the square root of 5 and PTAH is its related function, Phi, the Golden Mean The square root of five transverses two worlds, indicated by the upper and lower squares: the world of spirit and the world of body. Five stands for mediation, understanding and judgment. The ancients represented the world by the number 5 ( the four elements plus spirit). Sekhmet/Hathor is primordial femininity in both its facets: destroyer and matrix. The Golden Section (phi) arises out of the double square through its square root of five rectangle The double square, divided by a single diagonal, forms two right triangles, each having a base of 1 and a height of 2. Derivation of the sacred 3, 4, 5 triangle comes from the square root of 5 over 2 and demonstrates the relationship in Sacred Geometry between process and structure. Philosophical idea behind Golden Section: In the beginning was the word And the word was within God And the word was God A is to B as B is to ( A + B ) Word is to God as God is to (Word + God) The Golden Section describes a 2-term proportion demonstrating a one to one identity between God and matter showing a continuing identity. The key to phi is proportion, the relationship of equivalency between two ratios. The smaller term is to the larger term in the same way as the larger term is to the smaller plus the larger. It is the Three that are Two that are One. The Golden Division is the only continuous proportion that yields this progression. The terms representing the external universe are an exact, continuous proportional reflection of the internal progression. It is evolution guided from within, the creative dream of God. The manifest is an image of the Divine. The Golden Proportion represents indisputable proportional evidence of the possibility of a conscious evolution as well as of an evolution of consciousness. Phi also represents a coinciding of the processes of addition and multiplication. If addition is growth, multiplication represents accelerated growth. The so-called Divine Proportion, the Golden Section, or phi ratio is one of the most ubiquitous ratios found in living forms. It controls the spacing of seeds on a sunflower, the distribution of leaves on plants, various forms of natural spirals, and the ratios of the human form. It is generally associated with the principle of gnomic growth. Mathematically speaking, it is defined as the square root of five plus one divided by two (which is roughly equal to 1.618034...) This is the controlling ratio of the pentagon and is also asssociated with the double square. A well-known property of phi is in relation to the proportions of the human body. While the height of the body is divided in half by the genitals, the position of the navel indicates the phi division. Ptah is phi, creator and animator of form. He is fire fallen to earth, the creative aspect of RA. Ptah is always pictured bound in swaddling clothes, with only head, hands, and feet free. Even so, he functions as the master builder. |