As far back as I can remember, I have had a fascination of mathematics. More particularly geometry and physics. A year and a half ago I was deeply immersed in an internet study of the orbit of Venus and it’s relation the Pentagram. Suddenly I became aware that the numerous pages I had open on my computer screen were Masonic. That lead me to a more diligent study of Feemasonry and before long, I was talking on the phone with our W.Bro. Secretary.
As my studies in Geometry specifically have become quite convoluted yet interconnected, I have not yet found a way to establish where to start with a sharing of its very enlightening aspects.
However, as I attempt to further penetrate the artistic veil of allegory guarding the studies of morality in Freemasonry, the more aware I become of the numbers that appear with astounding regularity in Masonic Ritual and within nature.
I hereby present to you the first of a few potential short lectures on some of the discoveries of my research. However, these interpretations of them may or may not be accurate. I ask you my Brethren that you only consider my comments a matter of personal opinion and that I request that any questions you may have regarding any of the topics I comment on, to be directed to a personal study of your own in order to determine your own opinions on this topic of;
Applications of Sacred Geometry to Masonic Symbolism
Numbers may be used to describe and even predict phenomena found in the physical universe which prompted the Pythagoreans to develop their system of Theosophical Numerology. It is believed that Freemasons later incorporated significant portions of this Theosophy into Masonic ritual and practice; thus it is no surprise that numbers are so prominent in the Craft.
Dealing with numbers sometimes requires an understanding of mathematics; however this understanding need not be advanced or even complex. This is true when examining our Rites and Symbols for evidence of hidden mathematical meaning.
The Devine Proportion, Fibonacci Series, The Masonic symbols of The Point Within the Circle, The 47th Proposition of Euclid and Vesica Pisces are important in the Craft as symbols of philosophical premise, and are fundamental in that capacity, to an understanding of Freemasonry and are intricately related from the standpoint of Geometry.
The Craft is rich in such symbolism, and yet we often fail to recognize that beyond the allegory there often resides greater light in the form of Geometry. The purpose of this series of talks is to expand the understanding that these symbols, which are in large part based upon regular geometric shapes and which may be constructed using the working tools of the craft.
It is my personal view that many of Freemasonry’s symbols may be used much like intermeshing gears or a chorus of singers, to arrive at implicit truths and illumination on a level of understanding which cannot be communicated using spoken or written language alone (very much like music).
It would be my hope that by sharing the features of these concepts, that future generations may achieve an understanding of Masonic principles and will inevitably will lead to more peaceful and harmonious relations among all men.
Here begins Part 1:
The Point Within a Circle.
Flip Chart: [DRAW A POINT]
The beginning of all geometrical matter is the point. A point has no length, breadth, or thickness. The creator can be described as a sphere with the center everywhere and circumference nowhere (i.e., a point within a circle). The point might be described as unity, the source, the unrealized beginning of all matter. In symbolic mathematics, “one” is omnipotent since “one” raised to any power (squared, cubed, etc.) is still one.
The whole essence of sacred geometry is based on undivided single pointedness, oneness, atonement, unity, idea.
A point of light representing the single consciousness that is within all of us.
Omnipresent, omnipotent unity.
….and it unfolds into “Duality” (see Vesica Pisces) and returns to unity.
[DRAW THE CIRCLE]
The circle having neither beginning nor end, is a symbol of eternity and it follows that the compasses have been valued as being a means by which that perfect figure may be drawn.
Through the ages, the circle has been credited with magical properties and in particular has been thought to protect from external evil everything enclosed within it. Folklore contains countless instances of people, houses, places, threshed corn, etc., being protected by the simple means of describing a circle around them. The innocent child could be placed within a circle, in which it was thought to be safe from any outside malevolent influence. The virtues of the circle were also attributed to the ring, the bracelet, the ankle and the necklace which have been worn from earlier times, not only as ornaments but as a means of protecting the wearer from evil influences.
The point within a circle has largely been regarded strictly as a metaphor within Freemasonry, and these metaphoric interpretations of the symbol are both powerful and poignant.
Ritualistically, it has been considered a symbol of control of conduct; a standard of right living.
“The Point Within A Circle” as a geometric construction provides the pathway for greater understanding of the Craft, and that it is an intricate part of the Craft symbolism which works in concert with other symbolism to advance understanding and provide more light.
The point within a Circle is a symbol of great importance in Freemasonry, and commands peculiar attention in this connection with the ancient symbolism of the universe and the solar orb.
The point indicating the sun, and the circle the universe, invigorated and fertilized by his generative rays. And in some of the Indian cave-temples, this allusion was made more manifest by the inscription of the signs of the zodiac on the circle.
It is the same thing, but under a different form, as the Master and Wardens of a lodge. The Master and Wardens are symbols of the sun, the lodge of the universe, or world, just as the point is the symbol of the same sun, and the surrounding circle of the universe.
Another interpretation of the “Point Within the Circle” may be included;
The “Point”, alluding to the individual brother. The “Circle”, the boundary line of his duty to God and to man, beyondwhich a man should not allow his passions and prejudices.
[DRAW 2 VERTICAL LINES]
The 2 vertical lines on either side of the Point Within a Circle symbol may represent the two Holy Saints John, namely John the Baptist, and John the Evangelist. The Feasts of the two Saint Johns are separated by six months time, and that the symbol of the Point Within a Circle is a sort of miniature ornery showing the path of the earth about the sun, with the feasts designating winter and summer solstices representative of the tropic of Cancer and the Tropic of Capricorn.
However the vertical lines date back before Solomon. (who lived nearly 1,000 years before John the Baptist was born). Early Egyptian monuments are carved with the Alpha and the Omega or symbol of God in the center of a circle embordered by two upright parallel perpendicular serpents, representing the power and wisdom of the Creator. The symbol apparently came into Masonry from an operative practice, known to but a few Master workmen on Cathedrals and great buildings.
[DRAW A DISECTING LINE THRU THE CIRCLE]
Drawing a straight line across the circle through its center…
[DRAW A RIGHT ANGLE TRIANGLE USING A STRAIGHT EDGE]
…and continuing by drawing a line starting at the point where the line through the circle center intersects the circle circumference (Point A in Figure 2), and to extend that line until it touches the circle at any point on its’ circumference. (Figure 2, Point C). . Connect the dot with the points at which the line through the center cuts the circle; the result is a perfect square.
This was the Operative Master’s great secret - knowing how to “try the square” It was by this that he tested the working tools of the Fellows of the Craft; did he do so often enough, it was impossible either for their tools or their work “to materially err”.
The square, the level and the plumb were made of wood - wood, cord, and weight for the plumb and level; wood alone for the square. Wood wears when used against stone. Wood warps when exposed to water or damp air. The metal used to fasten the two arms of the square together would rust and perhaps bend or break. Naturally, the squares would not indefinitely stay square. Squares had constantly to be checked for the right-angledness. Some standard had to be adopted by which a square could be compared, so that, when Operative Masons’ squares were tried by it they would not “materially err.”
Naturally, as a trade Secret this technique would have proven extremely valuable to the ancient Craft Masons, and could be used among other things, to check the squares of workmen to ensure that they were true.
How much greater becomes the meaning of the symbol when we see it as a direct descent from an Operative practice! Our ancient brethren used the point within a circle as a test for the rectitude of the tools by which they squared their work and built their temporal buildings.
In the Speculative sense, we used it as a test for the rectitude of our intentions and our conduct, by which we square our actions with the square of virtue….
Their point within a circle was Operative - our is Speculative! But through the two - point in a circle on the ground by which an Operative Master secretly tested the square of his fellows - point within a circle as a symbol by which each of us may test, secretly, the square of his virtue by which he erects an Inner Temple to the Most High - both are Masonic, both are beautiful.
The Vesica Piscis
[DRAW ANOTHER POINT WITHIN A CIRCLE OVERLAPPING]
The root of all sacred geometry.
The womb of the universe.
This symbol was used as a covert means of identification for Christians. The “Vesica Piscis” was used extensively during the middle ages, as may be evidenced by its incorporation in the Gothic architecture of Cathedrals of that era[x]. Many readers will recognize that the Geometry of the “Vesica Piscis” and its derivation, the Golden Rectangle play a prominent role in the layout of the lodge room.
This is intended illustrate the Geometric properties inherent in the construction of the symbol, and will show the “Vesica Piscis” in conjunction with the other symbols of Freemasonry already described to illustrate the close inter-relationship which they enjoy.
The “Vesica Piscis” may be constructed by overlapping two circles such that the center of each circle lies upon the circumference of the other. In Figure 1 I have produced the Vesica Pisces by overlapping two separate constructions of “The Point Within A Circle” The lozenge which forms the “Vesica Piscis” is highlighted for clarity in blue cross-hatch.
I leave you with this, as an introduction to the next part of this series, with more on the “Vesica Piscis” which will lead to a presentation on “The Devine Proportions”
Part 2. Vesica Piscis and The Genesis Pattern
Introduction
For the benefit of those Brethren attending this evening, who did not attend the first part of this session on this series, I would like to briefly state what lead me to a desire to share of this topic.
I have had a fascination and affinity for mathematics as far back as I can remember. In my studies of sacred geometry, I often found sources to be Masonic in origin. Which eventually lead me to my interest in joining the Craft.
I find not only that the studies of the Craft very enlightening, but the fellowship with Brethren I am getting to know, the most genuine I have ever experienced.
We are the leaders, and so we must be the ones to take the first step towards harmonious relationships among mankind.
I hereby present to you the second of a few short presentations on some of the discoveries of my research on this topic of the “Applications of Sacred Geometry to Masonic Symbolism”.
However, these interpretations of them may or may not be accurate. I ask you, my Brethren that you only consider my comments a matter of personal opinion and that I request that any questions you may have regarding any of the topics I comment on, to be directed to a personal study of your own in order to determine your own opinions on this topic of;
Applications of Sacred Geometry to Masonic Symbolism
In the last session, various concepts of the “Point Within the Circle” were introduced. A demonstration was performed using a square and compass, by drawing circles on a piece of paper. The images produced were simple two dimensional representations. Of course the universe is three dimensional. I now ask that you extend your imagination, to see those circles as spheres.