Freemasonry and Geometry: What are the Symbolic Meanings of the Most Basic Geometric Forms?

Freemasonry and Geometry: What are the Symbolic Meanings of the Most Basic Geometric Forms?

The more abstract a concept is, the more meaning that we can find in it. Is this because the meaning is all projected from within our minds, or because there is something objectively real there to be found? Plato or Pythagoras certainly believed the latter, as did Jung with his archetypes, and certainly the abstraction of mathematics has enabled much of our modern scientific grasp of the workings of the world around us.

In Freemasonry, we deal in symbols constantly. The Temple itself is a symbol, as are all the rituals which take place within, and there are layers of meaning which are only revealed as one progresses through the degrees. Geometry, in particular, is very significant to Freemasonry. This stems not only from the practical geometrical knowledge that was required to build grand cathedrals and other structures by operative masonry, but also from the Western wisdom teachings stemming from Pythagoras, Plato, and others, often referred to as Sacred Geometry, which sees a greater symbolic significance in geometrical forms.

While its common to find interpretations of more complex forms like the Flower of Life, or Metatron’s Cube, some of the geometric forms I find most fascinating are the simplest. This is because the simpler a form is, the more universal it is. In the simplest forms, I see the very foundations of all creation. So, what is the symbolic significance of a few of these simple geometric forms?

What follows are not in any sense “official” masonic interpretations of these forms, but merely one mason’s reflections on them. Books can and have been written to interpret these and other geometric forms, so here we will just be sampling a few.

The Point

pointThe point is the beginning of all forms, and all finite things. In that sense, it is the most abstract representation of finity, of a finite form. It does not even have definitions, specific boundaries, size, or dimensions, and therefore is the most abstract finite thing that can emerge from the formless infinity. It is also the beginning of duality, because in the point, you have one thing which is separated from everything else, the thing and its surrounding context, self and world. Yet, without a clear boundary, it still contains an element of infinity within it. The point can be viewed as infinitely small, or infinitely large. Without boundaries and other objects to be compared to, it has no reference.

In the point, we can see the fundamental essence of all finite entities, including each person: the Self, consciousness, existence.

The Line

HorizThe line is the first movement of the point, the first dimension of form. As such, it represents the most basic possible expression of time and motion. In the line, we can see the progression from moment to moment of what was first seen in the point. While the point is motionless and still, the line implies a trajectory, and a continuity. It is also the first impression of a space in which motion and change can take place. Yet, the line is only the simplest, most primal of forms with a boundary, and does not yet demonstrate a space in which objects may exist, although it begins to imply them.

In the line, we can see the fundamental essence of all motion and change, linearity, past progressing into future, and memory.

The Cross

sacred geometryThe cross is where two lines meet at a perfect right angle, and the simplest indication of the second dimension. In the cross, we can see the implied 2-dimensional plane stretching out in four directions. Also within the cross, we can see both the singular point, and the line doubled. Like every new form, it is the expansion of what came before it. The cross is where two intersect to become one; two planes, two people, two forces, and the point at which they meet is also their origin.

In the cross, we can see the fundamental essence of all duality, multiplicity, and complexity. It is the simplest possible mandala, and also represents the multiple dimensions of self, whether masculine/feminine, thinking/feeling, or ordered/chaotic, intersecting at the central point of consciousness or spirit.

The Circle

infinity circleThe circle is the perfect return of the trajectory of the point traveling in a line back to its origin. Simultaneously, it is an enlarged and expanded representation of the point, being equidistant in all directions from the center point. In the circle, the completeness and perfection of the process of the formless point expanding into form can be seen. Within the circle, we can fit any number of mandalic or sacred forms, such as the pantagram, the hexagram, the cross, or the equilateral triangle. It contains all of these in essence, and yet is beyond all of them.

In the circle, we can see the totality of form, the Ouroboros, the nearest form to infinity.

The Circumpunct

circumpunct freemasonryThe circumpunct is the completion of the journey from finite point to infinite circle. In the circumpunct, all of the dimensions of self which have progressed outward into form are in complete and total balance and alignment with their formless origin. In the mind, it is the personality in complete harmony with its essence and origin. It also represents the essential boundary of the self. While the point had a finite existence, it still had a certain infinite quality, in it’s lack of defined boundaries. In the circumpunct, we have both the boundary-less point of origin, and the boundary, with self on the inside, and world on the outside.

In the circumpunct, we can see the completion of all existence, the simultaneity of infinity and finite form, the perfection of self, world, and the relationship between the two.

Further Reflections

expanding dimensionsThe truth is that neither you nor I have ever really seen a point or a line, only things that are shaped like them, usually drawings on paper. But the truest sense in which a point and a line exist is in the abstract realm of ideas, yet they are clearly significant. We could not build anything without them, and this is true of mathematical abstractions, in general: they are ephemeral, yet essential. But can they be regarded as the true foundations of all creation, of reality itself?

What I am struck most by these simple forms is how each dimension, and the basic geometric form it represents, implies and transcends the next. The moment you create a point, it imples that that point could transcend the 0 dimension, and be a line, if only it moved beyond that 0 dimension. The moment you create a line, it implies that that line could move in a different direction, transcending that 1st dimensional existence, creating a plane. The moment you create a plane, it implies that that plane could be bent or folded, and that therefore a third dimension must exist. The moment you have a 3-dimensional object, it implies that that object can shift and change across time, thus implying a fourth dimension, transcendent from 3-dimensional space.

This seems to me to imply that the world in which we find ourselves is in fact a manifestation from the infinite 0 dimension, into the four dimensions where we currently find ourselves. Its almost as if a divine infinite mind, in similar manner to an architect, charted out and traced the fundamental principles of reality by which a creation could manifest.

But is that really where it ends? For us, the 4 dimensions are the extent of dimensionality we can see and understand, with even the 4th being somewhat mysterious to us. But what if this is merely because of our position along the spectrum of dimensions, and in actuality, this process of one dimension implying the next goes on infinitely, with the 4th implying and creating the 5th, the 5th the 6th, ad infinitum?

String theorists and various other kinds of physicists currently posit some number of dimensions, often 11 or higher, but what if there is no ceiling to the dimensional hierarchy extending into the unseen, unknown realms of possibility? In that case, we truly could be said to be dwelling in an infinite creation.

infinite dimensions

The Socratic Method: Does It Lead A Mason From Darkness To Light?

The Socratic Method: Does It Lead A Mason From Darkness To Light?

“I can’t teach anybody anything. I can only make them think.” 

So says Socrates, a great thinker of his time in Ancient Greece. He was known for educating his disciples by asking questions and thereby drawing out answers from them, called the Socratic method. The goal was to nudge people to examine their own beliefs, instead of unthinkingly inheriting opinions from others. The approach was a way for his students to find the truth of anything. Thinkers have venerated the method ever since. It really worked for the Greeks.

I have always had a fascination with Greek culture. I particularly enjoy studying Socrates, Plato, and Aristotle. I also admit to getting lost in Greek mythology at times, enjoying Greek food, and have always secretly wished that I could dance like a Greek goddess.

Given the above, it seems only reasonable I should find myself honing in on Socrates. Mind you, I am no authority on the great ones of the ancient past, other than being humbled by their wisdom and insight. Socrates is for me the most interesting of the three: a perspective I am sure many might agree and equally as many might disagree.

There are two statements that Socrates made that I found particularly thought-provoking. 

“To know, is to know that you know nothing. That is the meaning of true knowledge.”

“Let him that would move the world first move himself.”

The first quote that starts, “To know, is to know that you know nothing” is a paradox right off the bat. Yet, instinctively, somehow, I understand the entire point and it makes sense even while being a total paradox! And the second quote struck me as so linked and interrelated to the first one. One would be hard pressed to assert one carries more11873522964_9cb8eb5a44_b weight than the other or to even think about them separately. 

How can we know what we don’t know? Does the Socratic method offer us a technique to advance towards the light of true knowledge? 

Plato’s Dialogue: It’s About the Questioning

Socrates said: “It is the mark of an educated mind to be able to entertain a thought without accepting it.” In other words, question everything. I recently read the statistic that children through the ages 2-5 ask roughly 40,000 questions. I have wondered why, as we go through into adulthood, the number of questions we ask drops significantly. 

We know through the writings of Plato, the student of Socrates, that he was often quizzed by his teacher about deeper realities. Red Rose in the GardenIn “Plato’s Dialogues,” we can read short works in which Plato recreates various conversations Socrates had with another student. And thus, we get a really good idea of the Socratic method. 

The style of a Platonic dialogue may go something like this:

Q: “What color is the rose in the garden?”
A: “The rose in the garden is red.”
Q:”Is this rose still red to a blind person?”
A: No.
Q: “So you are saying the rose is red only to those who can see.”
A: Yes.
Q: “What color would it be to a blind person? Would it be pink or white or some other color?”
A: (No answer – student is bewildered).
Q: “So the rose is red only to those who can see.”
A: Yes.
Q: “If the rose in the garden is where no one can see it, is it still red?”
A: (No answer – further bewilderment).

And so on. The questioner might end up forcing a realization in the student of how color only exists in a person’s mind as a result of their perception; it isn’t actually a property of the rose. In other words, the rose is not red.

Socrates believed there were two ways to come to knowledge: through discovery and by being taught. To be taught presupposes that someone else has discovered the truth for you. He thought for his disciples to really know a subject, they should form their own beliefs and experience their own blind alleys and realizations.tunnel-2033983_960_720

How does this idea of discovery relate to the path of a Freemason? 

From Darkness to Light

Every Freemason is on a quest to discover his “true self.”  He is taught the importance of the Liberal Arts and Sciences, of which logic is one of them. The study of critical thinking and reasoning allows the Freemason to look beyond mere perception and dogma in the search for truth. In this way, it is possible to forge a path to moral, scientific, and philosophical enlightenment. “To know nothing” is leaning into the next moment, wondering what you are going to find. It is a form of being blindfolded or hoodwinked, waiting for more light. 

It was in Freemasonry that I really learned to embrace the journey from darkness to light, to become a friend of the Socratic method, and learn to be humble in what I don’t know. When I first joined, a poor blind candidate, I was asked probing questions about the First Degree. Questions like, “What does it mean to know thyself?” and “Is truth absolute or relative?” I was asked to explore the relationships among concepts and ideas. For example, I had to compare two types of symbols and to explain how they are similar, how they are different, or evaluate the meanings of each. 

Over the many masonic degrees, my mentors have pointed me in the direction of truth only to glorify the beauty of the group vision and the image of enlightenment. 

The Freemason W.L. Wilmshurst said:

“Truth, whether as expressed in Masonry or otherwise, is at all times an open secret, but is as a pillar of light to those able to receive and profit by it, and to all others but one of darkness and unintelligibility.”

I think he is saying that truth is a mysterious something that is sensed, even though the truthrational mind may try to discredit it. The ability to sense this invitation to truth, even when the path is dark and hidden, is perhaps the most important lesson to consider here. “The future I do not see. One step enough for me.” 

My takeaway from the Socratic method is this: Remember how little you know, question everything, and keep your mind open to other possibilities. If all goes well, truth is our travel companion from darkness to light.  What do you ask for? 

As Above, So Below: What Does it Mean to a Freemason?

As Above, So Below: What Does it Mean to a Freemason?

From the teachings of Hermes comes the well-known maxim, “as above, so below.” Those four words have become a sacred phrase, an adage of wisdom, an underlying principle, an ancient aphorism, and a mystic saying. The dramatic opening lines of the Emerald Tablet read as follows: 

“Tis true without lying, certain and most true. That which is below is like that which is above and that which is above is like that which is below to do the miracles of one only thing.”  – The Emerald Tablet (Isaac Newton Translation)

Over the centuries almost every organization and religion has loosely put their own spin on the formula. Many philosophical schools believe “as above, so below” is the same thing as the Principle of Correspondence. In other words, everything above (spiritual) corresponds to something material (below). Nothing exists in isolation. Matter contains spirit, and vice versa.

More often today, I think the phrase is carelessly bandied about. For some thinkers, the spiritual dimensions are dismissed as unverifiable or inadequate to explain how and what life is. Some say modern man’s understanding of the entire Hermetic chain has been flattened over time. I hope not.

Of interest to me, however, is how deeply and how widely that maxim is embedded into the teachings of freemasonry. 

How is the Hermetic principle applied to a Freemason? Or is it?

I may be mistaken, but “as above, so below” is not a masonic phrase, per say. If used in any way shape or form, it did not have its origins as words in ritual. I can only remember the phrase mentioned one time in conjunction with a lecture on astronomy. Even so, Freemasonry has some roots in the Hermetic tradition of Western occultism and so the philosophy is heavily embedded in the teachings. And it is here we begin the introspection and speculative discussion of the phrase itself.

The Masonic Ladder according to W.L. Wilmshurst

It is clear that a serious study of words and symbols can bring anyone quite far afieldJacob's labber blog into the poetic lens of metaphor. Sometimes, before venturing into my own fantasy land, I like to read what the masonic scholars say. 

There is one symbol in particular that W.L. Wilmshurst writes about in his book Masonic Initiations that struck me as a good example of the maxim “as above, so below.”

That symbol is Jacob’s Ladder. It is also called the Masonic Ladder and is said to reveal a connection between heaven and earth with God at the top of the ladder. Angels are seen ascending and descending. Some say the ladder shows a hierarchical ordering of the Universe, a great chain of being, a principle of correspondence.

Wilmshurst tells us:

“Indeed Life, and the ladder it climbs, are one and indissociable. The summit of both reaches to and disappears out of ken into the heavens; the base of both rests upon the earth; but these two terminals – that of spirit and that of matter – are but opposite poles of a single reality.”

If you think you can spot Plato in this, you are quite correct. Plato offered theories of knowledge that were also illustrated by ladders. Those who climb the ladder advance from one step to the next and build on the knowledge gained from the one below.

Now, there is something that Wilmshurst writes later on that I found interesting. He believes that this cosmological truth, the Principle of Correspondence, is one that Masons should all know. Yet, he claims that most Freemasons have “hazy notions on the subject.” And I quote: “The modern mason is not interested or treats the information as not credible.”

This line of thought left me with a question. Where does the modern Mason learn about cosmology?

The Great Chain of Being – Veiled in Allegory

Of course, there are always books and study papers to read to gain knowledge. But I am wondering if the true cosmological truths that Wilmshurst speaks of are kept alive in Allegory of Arithmeticthe masonic rituals and allegories. Each masonic ceremony speaks to the unconscious mind, slipping past the usual dogma and conscious defense mechanisms. 

If I can use a masonic metaphor for a moment; in the Mind of The Great Architect it has been written that there is a ritual taking place all the time. It is a divine drama with the building theme of making perfection out of imperfection. When, therefore, here upon earth, a ritual is enacted, symbolizing that eternal process, then some of the spiritual realms above are brought down to earth. It is this mysterious unity of thought, synchronizing above to below which gives Freemasonry its magic and eternal purpose.

In the book Spirit of Masonry, Foster Bailey writes:

“A symbol is an outer, visible, and tangible sign of an inner spiritual reality. If this is admitted, then behind all the outer forms of the Masonic work, latent in its rituals, and hidden behind the entire system of symbols, is some spiritual value and some definite and intended teaching which can be discovered by those whose vision can be awakened.”

Perhaps the “biggie” truth is this. The “inner spiritual reality” that Bailey writes about isHour Glass an inner state of being. For Freemasons, each of us is a builder, working with the hierarchical order of things, according to his ability. Each must not only contribute his work, he must also grow to be capable of greater work.

I believe that when the two realms of spirit and matter unite, the Lodge on High sends its spiritualizing forces of life to the humble lodge below. Yet, the idea is greater than just what can be experienced in a ceremony. I think Freemasonry is an exposition of Life itself – the creative life we all have to live. 

Certain and most true.

“Ascend with the greatest sagacity from earth to heaven and unite together the power of things inferior and superior; thus, you will possess the light of the whole world, and all obscurity will fly away from you. This thing has more fortitude than fortitude itself because it will overcome every subtle thing and penetrate every solid thing. By it the world was formed.”  – (H.P. Blavatsky Translation)