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The Geometry of Art and Life

October 30, 2007 Leave a comment Go to comments

My friend Dave Edman joined Friendship Lodge some years before I did; he struck up a conversation with the owner of a local antiques shop, and remembering that his grandfather was in the Craft, became interested in joining a lodge in Southington. He spent the next few years telling me that it was a great bunch of guys and that I should join. Let’s not consider that to be recruiting; rather, it’s more that as a long-time friend he thought it would be something that I’d enjoy.

Anyway, Dave, always interested in esoterica, wrote a paper shortly after joining that was posted on the old lodge website. We were talking about it during the Statewide Open House (an event in which WB Dave was heavily involved, including being the pointman for the article in the Hartford Advocate), and he wondered if some of my readers might be interested. I figured that even though there’s nothing in here about konspiracies, black helicopters, the Denver Airport, or Zeta-Reticulans, perhaps some people might enjoy it anyway.

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The Geometry of Art and Life

Whereas Freemasonry has little documented evidence of its origins prior to the early 18th century, there is a skein of proof in stone, that put to the test of logic, indicates that the fraternity could indeed have origins back to the time of Egypt.

Logical premises must be acknowledged to outline the limits of the argument. First, that ancient architectural wisdom found to be economically useful would be jealously guarded, and that its prevailing use and dissemination would be determined by the limits of wealth and commerce. The Art of Architecture would therefore be secret to a degree and would only burgeon at times of economic prosperity when an organized system of government generated the excess capital necessary for great public works. Western culture has a continuous line of empire echoing back, from the Gothic-Christian era to the Greco-Roman and finally the Phoenician-Egyptian. So it is certainly possible that a body of growing architectural knowledge could have accumulated and been passed on. Therefore, the geometric symmetry in design must resonate in harmonic analysis of the great monuments in all these eras. In other words, the designs of some of these buildings must have common blueprints and shared themes. This indeed proves to be the case.

The Great Pyramid and the tomb of Rameses show a sublime proportioning theme. Oriented due north and south, as was commonly determined by the “arpedonapts,” the ritual land surveyors, with controlling circle, pole and minimum shadow, the magnificent structure is still considered one of the great wonders of the ancient world. The mathematical and geometrical proportion known as “the golden section” is strongly projected in its construction. Known as “phi” and equal to 1.618, called simply “the section” by the Greeks as reported by Proclus in “On Euclid” and considered by Kepler, in “Mystericum Cosmographicum” in the 16th century, “a gem; one of the 2 treasures of geometry,” Pythagoras’ theorem being the other. The golden section is within the pentagram, geometrically found in every line with its intersects, and was therefore employed as a secret sign of brotherhood by the Pythagoreans, as Lucian writes in “On Slips of Greeting.” Along with the Monad, 1, from which all springs, the decad, Yod, 10, transcribed as “G” in the Roman, 5 the pentad was most sacred. The Great Pyramid triangle, with 1, being base edge to base center, phi being the hypotenuse with angle of 51º50′, and square of phi, apex capstone to base center, is the only right triangle, or triangle of equity, whose sides are in geometric progression. The Tomb of Rameses includes Phi within its geometric plan, using the golden rectangle, another extension of the phi theme. At any rate, suffice it to say that the Egyptians utilized the section phi. We know that Pythagoras traveled there in his search of philosophy and may have been an initiate long before the Alexandrian school brought together learned men from all over the civilized west.

The Pythagorean viewpoint of reality naturally led to number mysticism which could easily have been transmitted mouth to ear through the cabala, in operative and speculative masonry, and Christian mysticism. So closely were the geometric secrets of the pentagram held and the constructions derived from it, that it is written by Iamblicus in his “Life of Pythagoras” that Hippasus, a Pythagorean, upon publishing the construction of the sphere of 12 pentagons, the dodecahedron, perished by shipwreck for his impiety, was given credit for its discovery, whereas it really belonged to Pythagoras. Founded in Sicily and Calabria around 500 BC the brotherhood and school with its several degrees had great influence throughout Magna Graecia, to such extent that many of the Greek philosophers such as Plato were said to be initiates. Even Greek vases often have phi as a governing design principle. The Parthenon is a virtual study in design using the golden section.

Plato articulated the esoteric schools creeds, in Timaeus he writes, that “It was then that all these kinds of things thus established received their shapes from the Ordering One, through the action of ideas and numbers. “That the vision that the universe is a harmoniously ordered whole, that analogy and symmetry, proportion and ratio govern the cosmos or order is much worked out by Plato and the Pythagoreans. The whole development of European and western Architecture with theme, “as above, so below,” micro and macro cosmos with temple and savior perhaps linking the two, is borne out in the geometry of the so called divine proportion phi.

On to the Roman empire, reaching even into England with its language, commerce and grand planned cities. The practical secrets of building were transmitted by the corporations of stonemasons from the Roman “Collegia Opificum” through the monastic architectural shops of the Benedictine Carolingians, to the secular guild craftsmen of the Gothic age. Adding cement to the secrets of design , new heights in building were achieved. The Pantheon of Rome again resounds with the use of phi in its construction.

Gothic designers added the cruciform theme, which of course speaks to the sacrifice of the Anointed One. The predominant leitmotif of dividing a circle into 5, 10, or 20 parts automatically introduces the Pythagorean secret of the golden section. In Gothic plans especially the majority of standard church or cathedrals can be set within the fundamental Master diagram. An explosion of building occurred with great experimentation, Moslem closed arches and new techniques of ribbing and groining literally raised the roofs. The stonemasons guild halls flourished with libraries for teaching apprentices, journeymen and fellows rising to the level of their potential, some becoming design Masters. The Lodges at Strassbourg and elsewhere gave out marks to second degree companions at the end of their probationary period, which remained for life their password; and they had to be able to prove the mark with underlying lattice when questioned at other lodges. These master marks and their proof never shows the pentagram, pentagon or decagon, and were not secret; and yet their proof was supposed to be close held. These marks did in fact get full use throughout cathedrals in Europe on keystones.

The oldest Masonic documents from England suggest that King Athelstan established the first guild of Masons at York. The Cooke manuscript in the British Museum (a copy circa 1430 of an earlier document) quotes Pythagoras and Hermes as having revealed the secrets of Euclidean Geometry to the human race and the same document obliges the mason to silence regarding the secrets of his craft. So it does appears that our friend Peter Gower was indeed Pythagoras as suggested in Mack’s Encyclopedia. It seems that the secrets of the sacred geometry kept winking in and out of view throughout the long western history, and this was logical too, as given the tumultuous times, groups of craftsman scholars, and monastic brotherhoods bound to silence would have largely been out of the struggles of power and public attention. These closed lodges would have been a magnet for people who desired the privileges afforded the journeyman stonemason. Throughout the 19th century architects and archaeologists tried to find the keys for the beautiful proportions of the Greek and Gothic monuments, to find builder rules and canons of proportion. The secret of the Greek symmetry and Gothic harmonic composition resides in the Pythagorean pentagram and belies the import of the decad which denominates the golden section which we find way back in the Great Pyramid and in nature from the logarithms of the sea shell to the proportions of the human body. Take a measure from your feet to your belly , then a measure to the head. By means and extremes compare this to the numbers 1 and 1.618. Look at the joints of the fingers, see the divine proportion, a ratio found only in organic growth.

 

If you care to learn more about this, acquire the book “The Geometry of Art and Life” by Matila Ghyka, from which this article is largely taken.

Bro. Dave Edman
2/14/00

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  1. April 24, 2008 at 6:09 am

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  2. November 9, 2008 at 6:27 pm

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    Best Regards,

    Vincent

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