|Meditation on the Sacred Geometry||| Print ||
Meditation on the Sacred Geometry
The other day, my son called me. We talk for probably an hour or so a year. His formal education stopped with a High School GED, but he is an omnivorous reader and a splendid artist. Probably the last of the hippies. He asked me what I was up to and I told him I was preparing a paper on the Sacred Geometry.
He came back with a very erudite discussion of M and the Golden Mean. How it is the perfect proportion and can be found in entities as diverse as the human body and the chambered nautilus. I was quite taken aback. He may know more of the Sacred Geometry than I do! When I was a youngster, I asked the occasional Mason I met what the “G” stood for in his symbol. Invariably the answer, with no further amplification was “Geometry.” Now, of course, it is no secret that it also stands for God, the Great Architect, or the Great Geometrician. Around the world, there are other symbols inside the square and compasses. The Hebrew “Yod,” for instance, symbolic of God. I’ve been in countries where there is nothing displayed inside the compasses, which is also appropriate as it, too, indicates the Great Mystery.
The study of the Sacred Geometry goes back at least to ancient Egypt, and possibly back to Akkadian and Chaldean times at the dawn of recorded history. The Sacred Geometry was used to lay out the great pyramids, to align them with the heavenly bodies, and to assure their regular shape. It was also used to lay out fields after the annual inundation of the Nile. A loop of cord, knotted with twelve equidistant knots could be set out into a three-four-five triangle, guaranteeing a right angle for a land survey, or squaring the corner of a building. There is still more about the proportions of the great pyramid, but many books have been written on the subject.
Many of these ancient objects apparently have the facility to be a sort of calculator for the heavenly bodies. Stonehenge, for instance is laid out in such a way that one can determine the solstices, and apparently predict eclipses.
Many of the ancient sages who have contributed so greatly to our knowledge base were Geometers. Archimedes of Syracuse, for instance. (He, by the way, was the one who ran naked down the street crying “Eureka! Eureka!” for he had discovered how to measure mass through displacement while in his bath.) He was engaged in following out an idea when the Romans finally took the city. A Roman soldier entered his study, where he was engaged in a new thought. Compasses in hand and concentrating on the circles drawn in the sand before him, he held up his other hand, motioning back the soldier. “Please do not disturb my circles,” he said, whereupon the soldier promptly cut him down; an early exercise in the futility of “might makes right,” and another fine mind was destroyed.
Pythagoras, who studied in Egypt, and with whom Masons have a passing acquaintance, was a geometer. His philosophy of life and his religious beliefs were all interconnected with geometry and mathematics. Eratosthenes of Alexandria measured the circumference of the earth with remarkable accuracy using geometry. (He knew that a well in a particular city had the sun directly above it at noon on the Summer Solstice, casting no shadow. The distance between the city and his home was known. On the solstice, he measured the angle of the sun and the shadow it cast on the earth and constructed the same thing using the baseline of the distance between the cities. It was almost two thousand years before anyone bettered his calculations. With more accurate measuring devices, he would have been spot on.
Lawlor tells us:
And do you not know that they [the geometers] make use of the visible forms and talk about them, though they are not of them but of those things of which they are a likeness, pursuing their inquiry for the sake of the square as such and the diagonal as such, and not for the sake of the image of it which they draw? And so on in all cases...What they really seek is to get sight of those realities which can be seen only by the mind. Plato, Republic, VII, 510 d,e The Platonist sees our geometrical knowledge as innate in us, having been acquired before birth when our souls were in contact with the realm of ideal being. Plato demonstrates this in the Meno where he has an untutored servant boy solve by intuition the geometric problem of the doubling of the square.1
Geometry, (Greek for earth measurement) was considered a sacred art for thousands of years. It can even be found in the Bible: Wisdom put forth her voice; "When he established the heavens I was there: when he set a compass upon the face of the deep:" Proverbs, 8: 27.
Many don’t realize it, but by using the compasses alone, you can construct a square, then generate as second square using the diagonal of the original square. If the sides of the first square equal 1, then the diagonal is the square root of 2. The expansion of the square is exactly twice the area of the first square and its diagonal is the square root of 4, This can be expanded infinitely and the ratio remains proportionate. You can expand or diminish these squares from the infinite to the infinitesimal.
The ancient geometers dealt with ratios and proportions rather than decimals and irrational numbers. It was not until the modern standardization of materials that building design ceased to be geometric and proportional, and became mathematical. Hence the modern cereal box school of architecture. “We will build you a box to accommodate your needs, and divide it up into standardized boxes to use as rooms, or add boxes for expansion. Here is the material list and the cost.” The result of this can be seen today in any city, or any subdivision.
Those of you who have read the Dan Brown novel The Da Vinci Code will remember the discussion of the Fibonacci Series and M the Golden Mean. This is a ratio which works out in mathematics to (1+ o5)/2 and equals approximately 1.6080339.... In the Sacred Geometry, relationships are displayed in ratios and fractions, or are drawn with compasses and straight edge. The Golden Mean develops spirals which are found duplicated, for instance, in the curve of a chambered nautilus shell and the growth pattern in an abalone shell, the helixes of the seeds on a sunflower’s face, and the curves of a galaxy’s arms. The proportions of the Golden Mean are also echoed in the proportions of the human body. If you follow the proportions of the Vitruvian man we are almost constructed from M the Golden Mean and the Fibonacci series measurements. These are all things which were discovered long before the advent of modern decimal mathematics. The beauty of the Parthenon comes from use of the sacred geometry in every aspect of the building, from its basic proportions to the slight convexity of the columns and their slightly curved layout on the ground plan. The soaring cathedrals, built to the Glory of God, were designed using the Sacred Geometry.
The Sacred Geometry also is used to determine music and harmony, delineating the frequency of the sound with the respective length of the vibrating strings and also showing the chording by stopping the strings at certain points. All of these ratios and relationships can be demonstrated visibly by using the compasses, a straight edge, and a piece of paper (more easily seen using grid paper) Matila Ghyka, after going through the development of the various forms, in Chapter 7 “The Transmission of Geometrical Symbols and Plans, ” writes: Having discovered that there is a “Geometry of Life” correlated to what we called the Theory or Science of Space (and showing characteristic differences from the geometry of ordered inorganic systems like crystals), we shall now proceed to find out if there is also a “Geometry of Art,” and the connections, if any, between it and the Geometry of Life. The answer to the first question, if we consider the case of Architecture, is obviously in the affirmative, and it is in this realm that our research will start; we will later say that other “visual” arts, Painting, Sculpture, specially Decorative Art (any craft in fact where design is useful or necessary) have to take the “Science of Space” into consideration. We can even state that Geometry, and especially the concept of Proportion, thoroughly worked out by the followers of Pythagoras and Plato on the lines presented in Chapter 1, are the foundation of the whole development of European or Western Architecture, leading through the Vitruvian concepts of analogy and “symmetry” to a “Eurythmic,” symphonic attitude to Art in general.
The Golden mean mentioned above also describes the patterns of leaves on a stem to receive the greatest amount of sunlight and is also found in the spirals of DNA, the building blocks of all living things. One begins to see the Sacred Geometry manifesting itself everywhere we look. As Shakespeare makes Hamlet say, “There are more things in Heaven and earth than are dreamt of in your philosophy, Horatio.”
As always in a limited paper of this sort, with a ten or twelve minute time limit, we do not have time to do more than touch upon the subject, I’ve not even been able to mention the Vesica Pisces and its importance in both art and iconography, or the generation of the platonic solids. It is frustrating, I know, but I do hope that I have perhaps instilled a bit of curiosity that will lead to a study of the Sacred Geometry on your own account, as it is closely linked with both Freemasonry and the Hermetic philosophy. I have also found that one can find himself in an interesting and rather profound meditative state by doing the exercises that are in the workbooks showing how these forms are developed.
If you Google “Sacred Geometry,” There are about 164,000 hits, amongst which are some very