Archive for the ‘Geometry’ Category

The All-Seeing -i-

January 7, 2011 Leave a comment

First of all, I’m excited that Charles Tirrell of Masonic Renaissance has found the time and inclination to get back into blogging. Charles was my counterpart District Grand Lecturer in the New Haven part of the state, then moved on to be an Associate Grand Marshall, and I now see that in April he will be the District Deputy in that area. I extend my heartfelt congratulations, and I know that he’ll do an excellent job.

I like Charles; he’s young and progressive minded, and he’s the kind of person I have in mind whenever I hear the (sadly clichéed) expression “The future of Masonry.” Charles has consistently pushed for our Grand Lodge to adopt new technologies in order to reach — and be relevant to — the newer members of our fraternity. He’s bright, and well-spoken, and modest about his achievements.

And he prefers Apple computer products.

Apparently, I have so little going on in my own life right now that I have taken to ribbing friends about their choice of technology, much in the way many people poke fun at one’s favorite sports team, choice of automobile, or taste in literature. This ribbing is further driven by the fact that for the last year, my office and home networks have been plagued by more computer problems than I’ve ever seen; obviously I’m envious of anyone who is actually happy with their computer, and confess to some distrust at anyone who doesn’t have some anger, annoyance, or irritation with their gadgets.

To his credit, Charles has refused to take the troll bait; although for that matter, I don’t particularly think about Apple products except when I hear from him or a few other similarly inclined friends.

Until yesterday, that is.

Some of you may remember that last year I wrote a post that made light of the similarities between Freemasonry and the GNU/Linux community. I should have remembered that satire is based in reality.

Yesterday, while reading Lifehacker, I ran across a couple of articles about how Apple is introducing a new way to get software, entitled respectively, Why the Mac App Store Sucks, and Why You Might Really Like the Mac App Store In The Long Run. And suddenly, the pictures jumped out at me. Why?

Here’s the logo for the Mac App Store:

There's something oddly familiar about this design...

Umm… does this look familiar to you?

For reference, here’s a couple of random images from a Google image search.

A Past Master’s symbol from some areas of the world.

An older, lesser known version

I mean, of all the possible combinations that the graphic artists could come up with, they riff on the Square and Compasses?

Coincidence? I think not.

Although I’ve long explored the twisted logic of the conspiracy theorists, I don’t have any background with regard to the twisted logic of Apple users. I believe, however, that this bears looking into.

The District FC Degree

April 6, 2008 Leave a comment

Well, we pulled it off.

On Saturday, March 29, a dozen and half officers from the eight different lodges of District 5 managed to put together a very nice FC degree in the auditorium of the Masonic Health Care Center in Wallingford.

Anyone who has ever seen the bedlam which accompanies a normal degree rehearsal can only imagine what our single rehearsal was like the week before the degree. Well, that’s not fair – since half the people didn’t show up, the confusion in the temple wasn’t anything like it could have been, I’m sure.

On Saturday morning, several of the brothers met at Friendship and piled the officer’s stations, jewels, aprons, and the movable set of stairs into RWB Gary Arseneau’s and Senior Steward Kyle Charette’s pickup trucks. WB Ted Hasty, the poor guy who coordinated this event was already at the auditorium, moving the chairs and rearranging the room. By 10:45 am, everything was in position.

Which was perfect timing for my arrival at 10:55.

Apparently, WB Ted was a bit antsy about the event, and got there very early just to make sure that things were going to work out. He’s obviously my Bizarro world twin: he shows up as early as I tend to show up late. Oh, and I think that Ted has a reaction to the red kryptonite.

After the room was set up we were treated to lunch in the MHA cafeteria. I declined, owing to a traumatic lunchroom incident in my childhood involving spaghetti, soy meatloaf, and canned wildebeest – the details of which are best left to the imagination. But shortly afterwards, several of us took a small tour of the Ashlar Village facility, just up the hill from the hospital. Ashlar Village is a small community having a mixture of independent and assisted living buildings. We took a look into the newly remodeled main building. “Newly remodeled” is perhaps not the best term, and for the last several years it seems to be under a new plan called “constant remodeling.” I think that the facility changes every month. One of the highlights, though, was the small lodge room that has been built on one of the basement areas. It hasn’t been used for any official purpose, however as you can see from the pictures it’s had some unofficial uses.

By the time we got back, other people started showing up: officers from other lodges, several interested onlookers, and eventually, a few brothers from the hospital itself. Personally, I was a little disappointed at the turnout – only eight brothers from the hospital and nearby Ashlar Village ended up visiting. But that disappointment was mitigated by learning that one brother had not been to a lodge in over 40 years, and another had been hoping to see a degree for several years, but had no way to travel. Four of our guests were in wheelchairs, one had a walker, and another had a cane. One brother happened to pass by me heading down the hall and called out “What part are you doing, sonny?” I slowed down to talk to him and keep him company on the walk down. After assuring him that I really did not need to borrow his ritual book (why do some of the old timers read the books while following the degree? Self-appointed quality control inspectors?) he told me not to walk with him because he was shuffling along rather slowly and he didn’t want to hold me up. “I’m pretty sure I’ll make it by one-thirty!” he called after me as he inched along the hallway.

Click here to see the rest of the photos

The degree itself was a pleasant affair, made interesting because we had one candidate from Sequin-Level and one from Unity. Being a Fellowcraft degree, Friendship brought along their stairs. Yes, we have a set of spiral stairs that appear to have been built in the 50s; they disassemble for storage, so we were able to fit them into the back of a pickup and haul them down. Some of the visitors who had never been to Friendship spent some time testing them for strength; but we’ve never had a problem. I fear, however, that we’ll need to make some minor repairs, simply because age and knocking around in a closet every few months is taking it’s toll on them.

The officers performed admirably and the candidates had a very nice degree, made even more memorable by the fact that parts were done by officers from eight different lodges. Even the “Staircase Lecture” was broken up into several parts to allow the lodges to take a more active role.

On the way home, most of us wondered why we didn’t do this kind of thing every year. By the time several of us had driven back to Friendship to help unload the furniture, we’d resolved to have another District degree for the residents of the hospital for next year.

The Geometry of Art and Life

October 30, 2007 2 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

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