SQUARING-THE-CIRCLE

The building of a cathedral is a testament to a total knowledge; not its final goal, but a means by which the spirit of the pilgrim can be purified, quickened, perfected and lifted up toward sublimity. It offers an unparalleled relief; to feel again the well-spring of the divine that can be forgotten in the humdrum. The human body can perform a similar function.

It is March 12^th, 2010. The sun is blazing through a baby blue sky over Nova Scotia. It is cold and the resolution is flawless even as the Earth quakes and trembles as if in the midst of the labor of rebirth. All creatures must commiserate together even if only unconsciously – the magnitude of the labor is so great. As I attempt to penetrate the secrets of what makes cathedrals masterpieces of holism, and our bodies masterpieces of expression, it becomes increasingly urgent world-wide to transform our differences into a source of creative energy capable of protecting and enhancing the world’s highly interconnected web of resources. We cannot master these differences if we cannot master ourselves. Knowledge can inspire and guide. But it must reach down to the very depths of our shared humanity, a humanity that includes every creeping, peeping sentient creature here under the sky.

I have had occasion to reread sections of Louis Charpentier’s book on Chartres Cathedral and find it even more impressive than I remember back in 1985. It reminds me of the mountain of work that still lies before me. How do I contain the cornucopia? How do I represent the legacy? What do I choose to leave out, given that most people are already overstuffed with information? Charpentier invokes for me an inextinguishable path of transpersonal inspiration. You must not give up no matter how stony the path may get; no matter how many thorns may block your way. Belief guides your aching feet. The Sun lifts you. The basics do not abandon you.

The 2:1 Table can be given many names. From it arise all the contents of the cornucopia. We ourselves are that cornucopia. We ourselves arise from the 2:1. We ourselves are the Grail and its content and have the potential for some sort of qualitative leap, a ‘mutation’ of the soul if you like – even an improvement in our physical constitution. The spirit can heal an ailing vessel  from within. We ourselves are subject to the path of 3, three tables, three qualities bound by one essence. The 2:1 has been called the Mystical Table about which nothing can be said. But in my experience everything can be said about it. That’s the real problem: there isn’t anything that cannot be said about it! As the root of everything, the door through which phenomena enters the world and becomes square or round or square again, it is the parent(s) of everything. For this reason I will show two methods by which the 2:1 rectangle can ‘square-the-circle’. For several purposes at once, I will concentrate on equal perimeter for the time being. It has proven to have real relevance in this work. In this post I will show one method first. But we’ll take a short detour first. There is always a detour to make in the Labyrinth. But every path leads to the center and the center leads to the periphery.

The King’s Chamber Squares the Circle

For the sake of a legacy, that which is ancient, I will remind the reader again, that the King’s Chamber, 44 meters above ground in the Great Pyramid – built from 100 large blocks of granite, including 9 ceiling beams up to 29 feet long (50 tons each!) – is an exact 2:1 rectangular shape with a height that is ½ its own diagonal or 1.118 x Unity. I will also repeat that its dimensions, 5.236 x 10.472 meters, are derived from its perimeter which in meters names π, 31.416 meters. And this length that has become a 2:1 rectangular enclosure, comes from the difference between the square and circle with the same perimeter: the geometry that forms the basis of the Great Pyramid as a whole. Only ½ the configuration is above ground, so it is 280 cubits (radius) minus 220 cubits (square) leaving 60 cubits, which is 31.416 meters. Note that the basic configuration here above ground is based on a semi-circle around a 2:1 rectangle: JKPQ. The difference between semi-circle or radius and the 2:1 is TS, 60 cubits, or 31.416 meters. A 2:1 is 1/2 a square but also is itself a double square. Nature likes dimidiation.

In the previous post I showed the geometry of the ‘sba’ gate where the opening width is 10 and the height of the opening is 31.416. This is framed within an overall 2:1 construction. If the 31.416 height is turned into a circle, the width of the door will be its diameter. If that is turned into a 2:1 rectangle, it will be 5.236 x 10.472 in dimension (10 x 20 cubits) which we see in the illustration of the KC below.

The golden number squared is 2.618. 12 x 2.618 is 31.416. Recall the walk around the labyrinth at Chartres is about 261.8 meters or 500 cubits. The diameter of the labyrinth at Chartres is close to 13 meters. It’s possible that it was supposed to be 13.09 which is the Great Diagonal of the King’s Chamber (DG above). Here we can see that 13.09 meters measures the Labyrinth and the opening across the Royal Portal. It measures between the pillars of the Nave.

These numbers all appear together in a single Fibonacci-Series shown below. The depth and breadth of this series is one of the delights of this work. I have felt for some time that ancient sages have long known this series and had recourse to it. It strikes me that the Templars may very well have gotten their hands on the same series and were instructed as to how to use it. It is a unique play between the meter and the royal cubit. It starts simply as 1, 5, 6, 11… and then it also builds in the vertical plane with 2, 10, 12, 22, etc.; 3, 15, 18, 33, etc.; 4, 20, 24, 44, etc. Eventually it names the royal cubit (.5236, Line 4), the golden section (1.236, Line 4), the golden number (1.618, Line 2), 1.309 (Line 1) which is 1.618/1.236 and by Line 24 it names π as 31416. Note that the outside measure of the transepts at Chartres is 130.9 cubits (Line 1, Column XIV) or 68.54 meters that appears on Line 2, Column XVI. This Series E is a genuine cornucopia of number. Moreover, number and phenomena seem to arise together in an ineffable embrace

Series E is characterized by “5”, just as pentagonal geometry opens the golden proportion family. 1 is common to any Fibonacci series. It is as if this Series E represents a ‘leap’ of some kind: a qualitative transformation of the Prime Series which is 1, 1, 2, 3, 5, 8, 13, 21 … etc. When 5 and 1 are added together you get 6. 6/5 = 1.2 and 1.2 x 2.618 = 3.1416, an excellent version of pi that appears on Line 24, under the 1309 column. In any case 118, 309, 1309, all occur on Line 1 of this series. 382, 618, 1618, 2618, etc. all appear on Line 2. 5236 occurs on Line 4 and 10472 occurs on Line 8. 31416 occurs on Line 24.