Thursday, August 21, 2014

Sacred Geometry

Courtesy of Gary Callahan
Sacred Geometry, what an irksome name. Certainly, many atheists will find the descriptor 'sacred' troubling, the stain of an unacceptable supernatural patina. By contrast, the deeply religious are likely to reject the subject as potentially blasphemous, bordering on the occult. For the vast majority of us, it is probably the 'geometry' part that brings back bad memories of high school...wait, what's the difference again between a postulate and a theorem? As for me, Sacred Geometry is a subject I love to study and I very much enjoy teaching. It's just as well; one can not get far in the mastery of any traditional craft of architecture without it.

Of course there exists many sacred geometry traditions that developed independently around the world. However, it is interesting to discover how incredibly connected they all appear to be. This can largely be explained by the understanding that sacred geometry is an empirical study, the observed object being Nature, the observing subject, Man. I'll focus briefly on the Western tradition having its origins in Ancient Egypt and Greece, expanded upon by the Romans, Medieval Europe and Islam.

The Quadrivium

During the Medieval period the classical education was apportioned into seven 'artes liberales' the studies that would prepare a freeman to be a beneficial contributor to society. The first three, called the Trivium, were as follows:

Grammar - the mechanics of language

Logic/Dialectic - the mechanics of thought

Rhetoric - the use of grammar and logic to instruct or persuade

The Trivium were the lesser studies, 'trivial' is you prefer, that were to prepare one for the serious studies of the Quadrivium:

Arithmetic- number in concept

Geometry - number in space

Harmony - number in time or sequence

Cosmology - the dynamic study of number in time and space
In our modern, hyper-rational educational system a disproportionate emphasis is placed on the purely conceptual approach to number, the least instinctive and humanistic of the four and why most students dread math in my opinion (Polynomial long division anyone?) Sacred geometry encompasses all aspects of number in a balanced way. Where to begin in such a potentially all encompassing subject? Simply, at the beginning, by encompassing everything...

Oneness - Unity

The Universe, literally 'Uni' one, 'verso' turn of the divine compass that creates everything. It is the big bang, the pebble in the pond, the point of singularity that expands ever outward. It is also gravity that pulls us ever inward. Geometrically it is fundamentally represented by the point. Now a pencil 'point' really is, under a magnifying glass, a little mountain of graphite in three dimensional space. However, if you give it some thought, a true point does not physically exist. It is location without dimension, a metaphysical concept. It represents the center of the emanation, the outward manifestations of which are the circle and the sphere.

Twoness - Division

Significantly, for ancient peoples numbers were not just abstract 'integers' used for crunching numbers. Number was deeply imbued with meaning. For example, there certainly was a concept of twoness. Not just 'how much' was two but rather, what does two mean? If one already represents everything, two could not possibly be a multiple of oneness. Rather, the solution was that two represented a division of unity. Cell division is a clear example of the division of unity. For example, a fertilized human cell contains all the information needed to generate another human. 

Often this twoness manifests itself in difference, polar opposition. Light/darkness; heat/cold; good/evil. Yet duality has an inherent sense of incompleteness and tension, an underlying desire to return to Unity that generates attraction: positive/negative; body/mind; male/female. One of its geometrical representations is the line, the connection of two points, the concept of distance, a metaphysical separation from Unity, the source of the emanation.

Threeness - Multiplicity

Many ancient languages have a singular case, a dual case specifically referring to two people and a plural case to represent three or more. Essentially one, two...many. So it was that threeness was seen as a way to break through separation and duality that would lead to multiplicity. Father, mother...children. Interestingly, our English words for father and mother come directly from the Latin words pater and mater respectively. We likewise have inherited the words pattern and matter from the same roots and nature from natura, something born. Just as father and mother beget children so too pattern imposed upon matter gives birth to all of nature.

Three was also seen as the way through or a method to bind two polar opposites. This principle is embodied in our legal system. Where a conflict exists a plaintiff brings a complaint against a defendant. There is a provision of arbitration by a third party such as a judge or jury that allows for resolution. Geometrically, with three points we begin to conceptually enclose space. A triangle forms the metaphysical concept of the plane.

Fourness - Materialization

Finally we have moved from the conceptual to physical manifestation! With a location, length, breadth and height, volume is enclosed, a material object can exist in three dimensional space. The most efficient way to enclose three dimensional space is the tetrahedron or four-sided pyramid. This results in an extremely stable structure, the first of the Platonic solids, commonly found in nature as an organizing principle of extremely strong crystalline forms such as quartz or diamond. Likewise, associated with the square and the cube, fourness conveys a deep sense of stability and connection to the earth. Why geometry literally means metria, the measure of Gaia, mother earth! So that we divide and orient our land according to the four cardinal directions, traditionally forming quarters in our cities.

Assembling the tetrahedron and the other Platonic solids

So having journeyed from emanation to physical manifestation what could possibly be left? The most enigmatic of them all, worthy of its own consideration: Fiveness, the number of life, reproduction and regeneration.

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