“Make of man and woman a circle, from that a square, then a triangle, then another circle, and you will have a philosopher’s stone.

That tessellated mosaic pavement found in every lodge is a symbol that represents the seeming dualistic nature of the natural world. As humans, we may be inclined to believe that our actions, beliefs, and institutions are just as polarized as the black and white tiles of the pavement. However, as Freemasons, we are taught to always balance ourselves, trinitizing the polarities of negative and positive, male and female, of mercy and judgement. This transformation of a perspective of duality into one of trinity is a key component of many spiritual paths. Alchemy is one of those schools of thought that inculcates balance as an avenue of true spiritual growth.

The “geometrical depiction of the Pythagorean tetractys,” also known as the alchemical symbol of proportions has a distinct representation in the work of the Gentle Craft. It offers us metaphorical and mystical commentary related to not only duality, but unity and trinity as well. Firstly, it should be noted that this symbol is perfectly represented during the obligation of Blue Lodge Masonry. The large circle is represented by circumambulation. The triangle is represented by an action certain officers execute during the obligation. The square is symbolized by the position of the Craft at large during the same. The final and smaller circle is, naturally, depicted by the candidate. What then, does this symbol have to teach us?

Most ambiguous are the matching circles within and without the main elements of the diagram. This acknowledges the existence of the microcosm and macrocosm; that man has been made in the image of God. It also represents the inner and outer worlds of man. In one sense, the world at large is separate from the candidate. Yet, as depicted in the Kabbalistic Tree of Life, the Parmasayika, and other such cosmologies, other perspectives assert that the entire universe has its “just correspondence” within man itself. This arrangement is also referential to “a point within a circle” spoken of in the first degree lecture. The relationship of these two circles are indicative of that statement Freemasonry requires of its candidates: the confession of one’s belief in Deity. These dualistic elements of this diagram sets the metaphysical stage for transmutation by providing both the environment and the subject of the working.

The triangle is the next ubiquitous component of this alchemical equation. Deity being triune in nature has its correspondence in man as well. There are volumes that could be written about the idea of the trinity in relation to Masonry. For the purposes of translating this symbol to the profound physicality of Masonry, the triangle may allude to the “three distinct knocks” required of the candidate. The stations visited upon after reception may be represented in this Pythagorean shape as well. As stated before, the triangle itself is completely physically represented at that sublime moment of obligation- proof that this eternal symbol is an integral part of our work.

And then, the square, that structure that is formed by opposing lines, the intersection of duality itself!  In this configuration, that four sided figure has not one, but two sets of parallel lines. The vertical lines is the set described in our ritual. As the Craft take their proper place during the obligation, the candidate is supported by the sacred buttresses of the Saints John. These parallel lines represent the two polarities of duality.

It’s no coincidence that all of this occurs either upon or about the mosaic pavement of the lodge. The Craft in their position represent the bounds by which the laws of physics might operate. The Worshipful Master’s position represents that trinitization of opposites that creates the paradoxical nature of the human experience described in The Kybalion. Upon the mosaic pavement is the candidate tried, and by his advancement he perfects his ashlar. We may always be navigating the ideas of good and evil in our affairs, but the position of the Master admonishes us to always look to the East, to Deity, when we are in doubt of our motivations.

This alchemical symbol is enacted in a very physical way in Masonry. It leads the contemplative Mason to ponder upon the true nature of Geometry. If it is true that the Grand Architect of the Universe wrought this world by Geometry, what does it mean when we physically act out Geometry? What do the opposition or parallelism of certain lines indicate for us in our Great Work? The mystery of duality, explored via our study of Geometry, can be bring light to the true nature of our existence. The realizations of Geometry in form is the quintessential metaphysical mechanism of Masonry. Let us not forget that art and science that is foundation of our craft!