What is this triangle that becomes a solid, this golden ternary that holds the single eye, this pattern for the unfolding foundations of divine formulation? What process of manifestation inspires the lines of thought which trace along geometric superfices bringing one to dwell upon the properties of solid form? Why then do we think in depth, as though through matrices of matter, and come to ponder the limestone edifices of the world's great pyramids? Perhaps the very mystery of this process is echoed in the piles of stone that recede into heaven above the plains of Egypt or Mexico, for men have always been spellbound by them as though they contained a key to the unfolding mystery of themselves.
In the shadow of the Great Pyramid in Egypt, Napoleon, sensing the presence of an ageless enigma, addressed his men: "Soldiers, from the summit of yonder pyramids forty centuries look down upon you." Intently wishing to penetrate its secrets, he located the passage leading to the 'King's Chamber' where he requested to be left alone for some time. It is said that when he emerged he was very pale and visibly impressed. He asked that the incident not be mentioned again and only hinted later, after he had become emperor, that he had received a compelling presage of his destiny. At St. Helena, just before his death, he was on the point of confiding to Las Cases, but instead he shook his head saying, "No. What's the use. You would never believe me."
While modern archaeologists think that the building of actual pyramids on earth was the result of centuries of gradual development and experimentation, Mayans of Yucatan tell of titanic builders who came with the very dawn of human enlightenment and left behind them the pyramidal edifices of Central America. Ancient Sabean records tell of the pyramid tombs of Agathodaemon and Hermes constructed during the infancy of the human race when gods openly walked upon the earth. Next to the numerous classical references to the enormous antiquity of various pyramids, the estimates of present-day scientists seem modest indeed. It is, for example, thought by contemporary scholars that the Great Pyramid of Giza was planned only around four thousand six hundred years ago and that the true pyramid was anticipated by step pyramids such as the magnificent mastaba at Saqqara built for King Zoser by the Master-Architect Imhotep. Several pyramids originally had dazzling white casings, richly covered with brilliant hieroglyphs. They were surrounded by a complex of structures, usually including a stone enclosure, mortuary temple to the east, chapel to the north, small ritual pyramid to the south, with rock-cut, boat-shaped pits all around. Ramps connected the pyramid enclosure with the valley temple at the edge of cultivated lands. There are seventy known pyramids in Egypt alone, together with the remnants of their complexes. How many lie buried beneath the relentlessly shifting desert cannot even be guessed.
The Egyptian cult of the sun which flourished during the Archaic Period seems to link the pyramid with the phoenix, depicted perched upon a ben-ben, an object of pyramidal shape resembling the sun's rays. The earliest pyramid may have been a colossal ben-ben constructed to enable the king within to rise phoenix-like along the converging rays to the sun's heavenly abode. The building of pyramids was of intimate concern to the reigning kings of Egypt whose highest priests were charged with overseeing their construction. Kings endowed their pyramids with large estates hoping to ensure their maintenance indefinitely. Indeed, the priests for Sneferu, Khufu, Rededef and Khafre still officiated in the ruins of their respective pyramid temples in Ptolemaic times. Many secular officials were employed including scribes who were 'masters of secrets' or secretaries, as well as farmers who supplied provisions for offerings and for the staff. The priest-architects were leading men among the masons and often members of the royal family itself.
Egyptologists, looking at the scattered evidence in the rubble surrounding the existing pyramids, have tried to reconstruct the method used to erect these awesome structures. It is believed that the Egyptians built the substructure and the descending passages first, then the granite 'burial chambers' and next the ramps of rubble which increased in height as they worked on the walls of the pyramid itself. The Great Pyramid covers thirteen acres and it is made of two and a half million blocks, each weighing two to seventy tons - more stone than has been used in all the cathedrals, churches and chapels built in England since the time of Christ. The facing blocks were fitted with optical precision. When he visited Egypt, Herodotus was told that the Great Pyramid required eighty years in construction, employing one hundred thousand men in work shifts that were changed every three months. The factual details concerning size, number and weight are so staggering that one is struck with the thought that either there was an unprecedented religious and political stability, as well as a remarkably enduring common will among Egyptian people, in order to sustain the building effort, or the mighty structures were indeed built by titans of another age. Without doubt a great mystery surrounds the legendary builder Imhotep. Described by ancients as a 'self-made man,' he is believed to have been born in Gebelein, the burial place of Asclepius. Manetho states that the Greeks considered him actually to be Asclepius because of his skill as a physician. Besides being a healer and architect, he was a high priest of Heliopolis and later in the Middle and New Kingdom he was revered as a god. This strongly echoes the teaching that the pupils of the Rishis and Devas of the Third Race handed down to the Egyptians and Greeks the canons of proportion and harmony of line and form as well as of soul and body. As The Secret Doctrine says, "It is owing to the divine perfection of those architectural proportions that the ancients could build those wonders of all the subsequent ages."
The proportions of the Great Pyramid embody some remarkable properties which modern science in its slow, laborious way is beginning to rediscover. There is a "definite relation between the shape of the space inside the pyramid and the physical, chemical and biological process going on inside that space." Decay is prevented, and worn down crystal structures return to their original forms, suggesting to some that the pyramidal shape accumulates electromagnetic waves, cosmic rays or some unknown energy. After all, forms can be understood through Fourier analysis as being combinations of various frequencies which act as different types of resonators for energy in the cosmos. Perhaps the pyramid is an enormous lens for the focusing of an unknown energy.
The mathematical properties of the Great Pyramid have rich implications from the purely symbolic level to the realm of structural engineering. The ratio between the circumference of its base and its axis is equal to π, while the 'King's Chamber' incorporates π and the sacred 3, 4 and 5 triangle of Pythagoras. Exactly one billion pyramids, placed top to bottom, would reach to a height of ninety-two million miles, or the distance to the sun, while the sum of the diagonals of the pyramid shows an approximate proportionality to the twenty-six thousand year sidereal year. The entrance on the north face is at an angle in relation to the apex, so that the line between them delineates the tilt of the earth's axis in relation to its orbit around the sun. The whole of the complex is built on a decimal system, as Napoleon understood, and its interior and exterior dimensions and angles are so precise that they can be linked with a wealth of astronomical, geographical and geodetic factors. Indeed, data of such extreme exactitude could be monitored so as to suggest overwhelmingly that the pyramid was, among other things, a colossal astro-physical tool. It indicates clearly by its placement a true meridian on earth from which the ancients could project a celestial meridian. The descending passage was dug on the north-south meridian line at a twenty-six degree angle. The ascending passage is also at twenty-six degrees and connects with the 'Grand Gallery' which acted as a transit circle, having an open slit on the meridian allowing observation of celestial movements. The precession of the equinox could be readily tabulated at the rate of one degree of arc in seventy-two years, allowing twenty-six thousand years for the full precession. The measurement of the summer and winter solstice, the moment of noon, and the length of the solar year could all be ascertained by the exact dimension of the shadow on the perfectly level floor which stretched flawlessly out from the north side of the pyramid.
The ancient Egyptian system of counting was governed by geometric factors. The circle in the square, quartered by the cross, enabled them to inscribe the pentagon within, which produced the Golden Section or the Φ proportion. "The side of a pentagon inscribed in a circle whose circumference is equal to the perimeter of the pyramid will be equal to the apothem, or slant height of the pyramid which will be the value of Φ." Φ was not considered by the Egyptians to be a number, but a symbol of creative function, of reproduction in an endless series. It is the application of Φ in the Fibonacci series which represents "the Fire of life, the male action of sperm, the Logos of the Gospel of St. John."
π is the unchanging value which links a straight diameter to a curved circumference. In the case of the Great Pyramid, its base is a square whose perimeter is equal to the circumference of a circle, the radius of which is equivalent to the height of the Pyramid. This acquires additional symbolic meaning when it is considered that the apex of the pyramid can be thought of as the pole and the perimeter as the equator. Each side is equal to a spherical quadrant of ninety degrees and the area of each face is equal to the square of its height, while the slope angle gives the π relation between height and base. Thus it was that the ancient priest-geometrizers of Egypt accomplished the squaring of the circle.
The triangle, being the first geometrical figure after the circle, is the predecessor of the pyramid which is the first solid. Its square base, having four sides, symbolizes the earth - the number four being the mean between monad and heptad. According to the Kabbalah, it is thus that "the two principles of temporal things, the pyramis and the cube, (form and matter) flow from one fountain; the tetragon on earth, the monad in heaven." The Pythagorean decade, symbolizing the plenum, embodies this process whereby the monad first becomes the two or duality, symbolized by the line; then gives birth to the three, or the triangle; and in finally becoming a solid, converts to four or a cube. By this inherent process of substantiation the One becomes the many, or the solid which is matter.
If the overall form of the pyramid has powerful metaphysical and physical qualities, its inner rooms are also deeply significant, symbolically and functionally. Within the 'King's Chamber' of the Great Pyramid there is a steady supply of fresh air which keeps the temperature at an even sixty-eight degrees. This seems an unnecessary luxury for a supposed burial chamber, and indeed no traces of any burial have ever been found there, though the unfounded idea of it being a tomb persists. The actual properties of the chamber are profoundly intriguing and point to its having a more important function. It has been considered by mystics down through the ages as the 'Holy of Holies,' the double womb which contains the creative process of nature. The dimension of the chamber is that of two perfect squares forming a rectangle. The square is a symbolic glyph for the female principle while the triangle is that of the male. Together they form the pyramid - the 3 and the 4, or the perfected androgynous man. The two squares or the double womb of the 'King's Chamber' indicate the duality involved in the creative process (as above - so below). Swinging an arc with radius equal to the side of a square from the midpoint of the side of one square, along the long side of the rectangle, one locates exactly the Golden Section of the rectangle. This process of proportional division can go on indefinitely, fully symbolizing the repetitive series depicted as 'the Fire of life.' In The Book of the Dead there is a very interesting illustration showing a mummy with phallus erect, the position of which, when measured relative to the length of the mummy, denotes the point of the Golden Section - the font of an endlessly unfolding series, the original element and seed of life. H. P. Blavatsky quotes a remarkable manuscript describing the 'King's Chamber' wherein the author states that if to these organs, treated as symbols of creative cosmic agencies, the idea of time periods can be attached, then in the construction of sacred temples, that place designated as the 'Holy of Holies' should borrow its title from "the recognized sacredness of the generative organs considered as symbols of measures as well as of creative causes."
Within this stark, rectangular room lies a lidless 'sarcophagus' fashioned from a solid block of extremely hard, dark brown granite, found nowhere in Egypt but fabled to come from Atlantis or America. In its inner measurements it forms a perfect 'astronomical atlas' revealing a precise knowledge of the solar parallax. Like the Ark of the Covenant, the sarcophagus may be some sort of 'energy accumulator.' This is significant for it was within this symbolic tomb that the Initiate waited during the three days prior to his resurrection from the realm of the dead. It was here that the worthy candidates awoke to new life and "rose toward the gods while the gods descended toward men." In the very act of initiation the candidate, representing the solar god, re-enacted and re-experienced the giving of the flame of divine knowledge to the earth - his uninitiated self. He descended into the female womb of the ark-like sarcophagus in order to receive and to transmit the penetrating ray of the energizing fire of the sun. It is profoundly fitting that his rebirth took place within that marvelous structure which symbolizes fire and its manifestation on earth.
In the Timaeus Plato describes the pyramid as representative of fire in that it is the form which has the fewest bases and is the "acutest and most penetrating in every way." All the other elements are cut by the sharpness of the angles and sides of fire. The earth, meeting with fire, will not be consumed by it but must continually be 'cut' and penetrated by its sharpness in order to maintain life. Like spirit, it is the nature of the particles of fire to penetrate, and though matter remains relatively inert in a manifested world, the fiery process of metempsychosis can render it vibrantly alive to a higher dimension in nature.
As undying witnesses of this holy flame and higher dimension, great Initiates have entered the arena of human turmoil throughout the millennia. Plato knew this and saw in the pyramid a symbol of the glorious descending hierarchy of manifesting spirit. The apex of the pyramid represented dynasties of gods which became eventually dynasties of demi-gods, the heroes all people celebrate in myth and legend. Finally, as the triangle became the cube, the dynasties became those of men who were called Rajarishis or Divine Kings by people whose memories were impressed by the archetypal pattern of a previous age. The Turin papyrus deciphered by Champollion lists dynasties "embracing the furthest mythoic times, or the REIGN OF GODS AND HEROES," and even in recent times the Divine Kings of the world were thought to represent the people in their relationship to cosmic and spiritual forces.
While kings may have ceased to be divine in a profane age, the pupils of the Rishis and Devas are the SERPENTS of WISDOM whose caverns are under the pyramids, the "triangular stones at the four corners of the world." They live today in the idea of the triangle, the golden ternary that holds the single eye, the pattern for the fully manifest pyramid of Divine Fire.
Hermes, July 1976