Showing posts with label geometry. Show all posts
Showing posts with label geometry. Show all posts

The Circumpunct

by Midnight Freemason Contributor
WB Darin A. Lahners


In the First Degree ritual, Freemasons are taught about the point within a circle or the circumpunct.  The uncyphered Illinois ritual states: "Lodges in ancient times were dedicated to King Solomon, he being our first Most Excellent Grand Master; in modern times to St. John the Baptist and St. John the Evangelist - two eminent Christian patrons of Freemasonry; and since their time there has been represented, in every regular and well furnished lodge, a certain point within a circle, embordered by two perpendicular parallel lines, representing St. John the Baptist and St. John the Evangelist.  On top of the circle rests the book of Holy Scriptures; the point represents an individual brother, the circle the boundary line of his duty. In going round this circle we necessarily touch on the two parallel lines, as well as on the book of Holy Scriptures; and while a Mason keeps himself circumscribed within their precepts, it is impossible that he should materially err."  What is not told to you, is that the point within the circle has further allusions.

The ancient alchemical symbol for gold was often represented by the point within the circle.  In Astrology, the Sun is also represented by the point within the circle. Pythagoras, who we are taught was the inventor of the 47th problem of Euclid, was "In his travels through Asia, Africa, and Europe, was initiated into several orders of Priesthood, and is said to have been raised to the sublime degree of Master Mason.  This wise philosopher enriched his mind abundantly in a general knowledge of things, more especially in geometry, or Masonry. On this subject he drew out many problems and theorems; and among the most distinguished he erected this, when, in the joy of his heart, he exclaimed, Eureka! signifying in the Grecian language, I have found it; and upon the discovery of which he is said to have sacrificed a hecatomb."  What we are not told is that Pythagoras used this symbol to represent the Monad.  

The Monad represented to Pythagoras the point of the beginning of creation, the Supreme Being, divinity or the totality of all things.  It symbolizes an idea of cosmic consciousness, a consciousness that experiences itself and learns from itself by observation and experience of the micro and macro, as well as the macro and micro.  The idea of the Monad parallels that which is above Kether, which is the topmost sephirot of the Tree of Life in Kabbalah.

Prior to Creation, there was only the infinite Or Ein Sof filling all existence. When it arose in G-d's Will to create worlds and emanate the emanated ... He contracted (in Hebrew "tzimtzum") Himself in the point at the center, in the very center of His light. He restricted that light, distancing it to the sides surrounding the central point, so that there remained a void, a hollow empty space, away from the central point ... After this tzimtzum ... He drew down from the Or Ein Sof a single straight line [of light] from His light surrounding [the void] from above to below [into the void], and it chained down descending into that void. ... In the space of that void He emanated, created, formed and made all the worlds.

-Etz Chaim, Arizal, Heichal A"K, anaf 2


The Zohar states that Kether is the most hidden of all things. According to Arthur Green in his work, Guide to the Zohar, it represents the primal stirrings of intent in the Ein Soph (Infinity) or the arousal of desire to come forth into the various states of being.  Kether is associated with the name that God gives to Moses, Ehyeh Asher Ehyeh which is commonly translated as "I am that I am" in Exodus 3:14 in the King James Version of the Old Testament. "And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you."  However, Ehyeh Asher Ehyeh can also be translated as: "I am who I am," "I will become what I choose to become," "I am what I am," "I will be what I will be," "I create what(ever) I create," or "I am the Existing One."  As Kether is the first emanation, the Zohar makes it clear that "the supernal crown (keter elyon) is the crown of kingdom (keter malchut)." Meaning that the first, highest emanation of the Divine- Kether is linked to the last Malchut, a concept which was summarized by Hermes Trismegistus:  "As above, so below; as below, so above."

It is probably not an accident that the name of God is revealed in Exodus 3:14.  Pi is defined as the ratio of a circle's circumference to its diameter.  It is most commonly rounded to 3.14, although its decimal representation never ends nor does it settle into a permanently repeating pattern.  As God is infinite and eternal, so is the numeric representation of Pi.  

To close, I will use a story that I ran across while researching this article (that had no attributable source) to illustrate my last point.  The story goes: 
I had a professor once who had asked the class to draw the best representation of God. There were some students who drew Christ, others an old man in a chair, and then there were some that drew the Hindu gods. In the end, all he did was draw a circle on the board with a dot in the center.“This is God, the circumpunct is perhaps the most perfect symbol to represent God. The circle,” His finger traced the circle on the board. “represents the all-encompassing power and infinite limitlessness of God. While the dot,” He pointed to the center of the circle “Represents our place within God, we are part of God. The circumpunct represents the perfect union of the divine and the created. The dot can represent anything within the omnipotent divinity of God.” He walked around the room in a circle then stood in the center. “Or it can also represent the self. The circle can mean the body, or the conscious self, while the dot can represent our subconscious or super-conscious.”

~DAL

WB Darin A. Lahners is our co-managing Editor.  He is a Past Master of St. Joseph Lodge No.970 in St. Joseph. He is also a plural member of Homer Lodge No. 199 (IL), where he is also a Past Master. He’s a member of the Scottish Rite Valley of Danville, a charter member of Illinois Royal Arch Chapter, Admiration Chapter No. 282 and is the current Secretary of the Illini High Twelve Club No. 768 in Champaign – Urbana (IL). You can reach him by email at darin.lahners@gmail.com. 

The Ashlar, The Circle, and The Quest for Perfection

by Midnight Freemason Guest Contributor
Bro. John Coggeshall

Recently I was presented with a mathematical dilemma that struck a particular cord with me as a Mason, and as I wrapped my mind around its mystery, mathematically I found myself discovering truths in its symbolism that are very relevant to every Mason and worthy of being shared. So what was the mathematical dilemma I was presented with? In short, it was a geometric construction that appeared to indicate that the infinite constant Pi was not 3.14159 as we all know, but rather simply 4. To begin, let’s imagine a circle with a diameter of 1, bounded by a square of width and height of 4 as shown to the right.


In this representation, the perimeter of the square as expected would be 4, and of course mathematics at least as old as our Fraternity tells us that the perimeter is that infinite sequence of numbers we know as Pi. As Masons we are taught to strive to perfect our ashlars, but what happens when the goal of our ashlar is the form of the circle? Attempting this is easy enough to attempt, simply “fold” the corners of our square again and again toward its respective edge of the circle as shown:



As we repeat this process again, and again, we soon can no longer distinguish the difference between our ashlar and the circle, and through this can claim that with enough effort our ashlar can indeed be sculpted into that perfect circle. The quandary however is that in this process, no matter how many times repeated, results in the perimeter of our circle not equaling the infinite Pi , but our original square’s perimeter of 4! 


How can this be so? Without getting into the Calculus behind the flaws of this experiment, what you need to know is that our process only yields Pi when the process is extended to infinity. How does this relate to us as Masons? To begin, let us consider the geometries we have employed in this allegorical example. From time immortal to today, philosophers and mystics have associated the circle with the Devine, infinite in its representation. Indeed the value of the circle can never be truly known, and as shown by Pi, is truly infinite in its perimeter. The square however is of a finite construction; unlike the circle its perimeter can be known and achieved. It is easy to understand in this light why the circle was regarded as Devine while the square was left to the material world -- the square is the work of men’s hands.

With this in mind, we know as Masons we are taught to perfect our ashlar, a task that can take a lifetime itself to achieve. However, like all endeavors, perfection of our ashlar should be planned if we are to achieve it – and herein lies the lesson taught by the allegory of the circle within a square. While our goal as Masons may be to perfect our ashlars, the definition of perfection we strive to achieve must be an imperfection itself to ever succeed. No matter how we try, we will never with our finite means be able to mold our ashlar into the perfection of the Architect’s circle, because it can only be fashioned by the infinite itself . Thus, it is important in our Masonic lives that we define the ashlars of our life within the bounds of what is capable of the fallible hands of man to achieve if we hope to ever to achieve it.

To put it another way, we are taught to exist within the bounds of our compass, but in truth it is equally important to only seek perfection within the means of the square. Seeking any true measure of perfection of our selves as man, just as our attempt to reproduce the perfection of the circle, is impossible. In fact, attempting it is a task with no end, and one that ironically will never produce even close to the correct result. The allegory demonstrates only the infinity of the GAOTU can achieve real perfection. As we as Masons draw our plans on our tressel boards, we must ensure the inherent imperfection of those plans is fully acknowledged and embraced in our own eye if the temple is ever to be completed, or achieve the perfection we do have the working tools to reach. 

~JC

Discovering His Wisdom, Power and Goodness

by Midnight Freemason Contributor
Steven L. Harrison, PM, FMLR


"Geometry, the first and noblest of sciences is the basis on which the superstructure of Freemasonry is erected.  By Geometry, we may curiously trace nature through her various windings to her most concealed recesses.  By it, we discover the wisdom, power and goodness of the Grand Architect of the Universe and view with delight the proportions which connect this vast machine.  By it we discover how the planets move in their respective orbits and demonstrate their various revolutions."

     I recall sitting in a science class in high school.  Our teacher, Mr. Mohr, dropped a chunk of sodium into a beaker of water.  The sodium instantly fizzed up and zooped around the beaker like an out of control power boat.  Then it burst into flames and finally exploded as the students oohed and aahed.  When the rumbling subsided, the diabolical Mr. Mohr called on an unfortunate student, "Henry, what made it do that?"

     Poor Henry was unprepared as usual; but since being unprepared was practically his trademark, he did not hesitate to answer:

"God."  

     The class thought it was funny.  Mr. Mohr, who had the sense of humor of a wounded gorilla, didn't. In his own gruff and unsympathetic way he explained that  just because we don't understand something doesn't mean it's a direct result of God's action.  

     True, but in fact the Masonic ritual teaches there is a relationship between God and the physical universe.  From that relationship, as we learn in the Second Degree lecture, we can not only observe the magnificence of the Creator, but also draw moral symbolism from metaphors we see in His physical creation.

     God and science are not at war.  They can't be.  It is we humans, who don't have all the answers when it comes to understanding either God or science, who somehow perceive there is a war.  As Henry discovered, it's a slippery slope to take something we don't understand, stop research, and conclude it's God's work; in that event, what happens when we discover the scientific principle behind it? Historically, many have taken the stance that the research is wrong in the face of overwhelming evidence that it is, in fact, right.

     In the 17th century, for example, humans did not understand the solar system.  It was taken as scientific and religious fact that the sun circled the earth ("He set the earth on its foundations; it can never be moved." ~Psalm 104:5, NIV).  When scientists proved the earth, in fact, did orbit the sun, rather than being inconsistent with God's design, it revealed it.  The church, however, still didn't warm up to the concept right away.  Today, scientists and virtually all religious establishments know it to be an incontrovertible fact.

     Today's hot buttons include evolution, the "Big Bang Theory" and a few more points of contention.    Regardless of your point of view on these issues, the facts for each are overwhelming; and with some religious groups challenging scientific evidence we are, on some level, back in the 17th century again.  Scientific discoveries are not political, not vindictive and not anti-God.  They are based on fact.  (Not, by the way, just on observation — any idiot can observe daily that the sun circles the earth).  These discoveries don't offer proof of God one way or the other.  They prove we have learned more about God's universe and, as we are admonished, should "view with delight" all such revelations.   (Do you recall the video game "Evolution?"  It allowed the player to create and evolve ecosystems based on certain parameters.  It enraged a few fundamentalists until some whiz kid pointed out the game didn't work without the intervention of the player... the creator.)

     What these scientific discoveries do prove is that God is bigger and more complex than we can ever comprehend.  So complex, in fact, that when asked to prove God exists, famed theologian and Freemason Peter Marshall responded, "You ask me to prove it?  How could my tiny mind prove God?  What kind of a God could my little mind prove?"

     The Reverend Marshall went further.  He turned the tables and asked his questioners to prove they existed.  Fact is, he was onto something.  Any legitimate, credible scientist today will tell you, your body is nothing but energy.  Your house, everything inside it, the trees outside, the very ground you walk on is nothing but energy.  This is not some kind of New Age folderol; it's scientific fact.  Sounds kind of spiritual, doesn't it? Or, as Dr. Wayne Dyer puts it, "You are not a body with a soul. You are a soul with a body" (also attributed to others).

     If what you personally believe about God seems inconsistent with scientific facts, consider this: scientists have already observed the world of relativity and the quantum world appear completely incompatible.  Yet, they coexist!  Can't God coexist along with them even with perceived inconsistencies?  And don't we know on some level all those inconsistencies have to iron themselves out, even if that process is beyond our human capability to figure out?

     So many concepts still baffle our best scientists: dark matter and dark energy; the nature of time and matter inside black holes — the "singularity"; a unified theory; the possibility of parallel universes; backwards time travel; dimensions beyond the three (four, if you count time) we live in; quantum entanglement, a phenomenon so strange and baffling that Einstein called it "spooky." To each of these, the best scientific minds around would say, "We just don't completely understand."  Or, perhaps more accurately, "We just don't have all the facts."  

     Many, even some scientists, think there may be spiritual elements to these mysteries.  The scientists, however, will not draw conclusions without proven facts — pesky hindrances that some outside the scientific community have the luxury of ignoring.  In our lifetimes, we will most likely solve some of these mysteries.  To many, those discoveries will not just reveal scientific facts.  They will also give us greater insight into the wisdom, power and goodness of the Grand Architect of the Universe.

     And I, for one, finding far more spirituality in science than science in spirituality, anticipate each new discovery with delight.


~SLH

Steve Harrison, 32° KCCH, is a Past Master of Liberty Lodge #31, Liberty, Missouri.  He is the editor of the Missouri Freemasonmagazine, author of the book Freemasonry Crosses the Mississippi, a Fellow of the Missouri Lodge of Research and also its Senior Warden.  He is a dual member of Kearney Lodge #311, St. Joseph Missouri Valley of the Scottish Rite, Liberty York Rite, Moila Shrine and is a member of the DeMolay Legion of Honor.