J.R.C. Evans Lecture 2009-2010
WHAT THE HECK IS A RIGHT-ANGLED PARALLELOPIPEDON?
Jake Mohns – 2009
I was much honored in May 2009 when the Deputy Grand Master, Right Worshipful Brother David Love asked me to participate as one of his JRC Evans lecturers during his upcoming year as the Grand Master of the Grand Lodge of Manitoba.
I consider this an incredible honor and am humbled to have this responsibility bestowed upon me. This honor allows me to address the men I admire most in life, my Masonic Brethren, and to share my personal observations, my suppositions and my personal conclusions on the topic of my own choice. I am truly humbled by this opportunity.
The lecture I have compiled is dedicated to the memory of Dr. John Robert Charles Evans, who was born in 1891, lived an exemplary and honorable life and ascended to the Grand Lodge Above in 1959. Most Worshipful Brother Evans was our Grand Master in 1954 to 1955.
In addition to being our Grand Master, Dr. Evans achieved numerous other Masonic titles, all of which he held dear to his heart. He was a great man, scholar, teacher, the Dean of Brandon University and a true Freemason.
It gives me a great pleasure to address the Brethren in his memory and I hope you will find this lecture informative, educational and uplifting.
I have chosen a topic with a geometrical content and physical theorem, based on philosophical contemplations, and their relationship to our everyday lives. I sometimes get a look of surprise when I announce the bases of my topic as geometry and physics, as they are not usually the first choice of men our age.
I do believe however, that you may find this a bit lighter and somewhat more entertaining and inspirational than most mathematical presentations you may have been forced to endure.
My paper is called, “What the Heck Is a Right Angled Parallelepipedon?” – I’m using this title for one especial reason – that’s exactly what Right Worshipful Brother Borgstrum, a dear friend of mine, asked me when he called me on the phone one day for some information.
Freemasonry is full of symbolism, each part being an important component in the pursuit of knowledge. To put it another way, with each symbolic meaning we gain from our various tools we have the opportunity to gain in our lives a better understanding of ourselves and those around us. Most of us have heard the term “Know thy Self.” I like to add “Understand those around us” to the phrase. Freemasonry offers the best for the best.
In this lecture I’ll try to present just one simple term or word and the philosophy surrounding it as it unfolds for us; that term is, “Right Angled Parallelepipedon.
When a candidate enters the Lodge room, for the first time wearing the apron of a Freemason, he is conducted to the Junior Warden, who then explains the Junior Warden’s Tracing Board. This is basically a presentation on the layout of the Lodge and is commonly referred to as The Junior Warden’s Lecture.
One of the first things the Candidate is told in this lecture is the following: “Let me first direct your attention to the form of the Lodge, which is a right angled parallelepipedon, in length from East to West, in breadth from North to South and in depth from the surface of the earth to its center, and even as high as the heavens. A Masonic Lodge is of this vast extent, to show the Universality of the Science.”
What I intend to do first in this presentation is to break this small portion of the Junior Warden’s lecture down a little bit and try to explain its important meaning. In doing so, I will start with a bit of history and lead up to the definition of a right angled parallelepipedon, then moving on to the applications and influences it has, not only in or Lodges, but in our everyday lives.
I will close off with a summation of my own personal thoughts and inspirations pertaining to the relationship of the importance of our teachings within this parallelepipedon and their relevance with respect to our membership goals and to the future integrity of our Order.
The concept “parallelepipedon” takes its origins from the ancient Greek mathematician, and philosophical physicist, Euclid, sometime around 300 BC. Today we have many types of physics: nuclear physics, quantum physics, thermodynamics, fluid mechanics, etc., but many scholars still practice philosophical studies as well.
In ancient Greek times, Euclidean geometry consisted primarily of philosophy and proposition – a lifetime’s worth of thought and theorems but not much practical experimentation.
An example of a proposition is displayed on the jewel worn by Past Masters. It is a powerful symbol as it contains the explanatory and descriptive architectural drawing of the 47th proposition of Euclid. This proposition was the foundation of the Pythagorean Theorem pertaining to right angled triangles and stands today as one of the important fundamentals in geometry.
Mathematically, it is explained in this manner; The square of the side opposite the right angle is equal to the sum of the squares on the sides containing the right angle: it follows then that if we make any triangle in which the square of one side is equal to both the squares of the two other sides, then the angle opposite that side must be a true right angle – the angle of a correct square.
The importance of this theorem can be illustrated thus: Suppose you wanted to find the distance to the moon. Two men can separate themselves by let’s say exactly 100 miles. Both men at the same instant in time accurately measure the angle the moon is at with respect to the other man’s position. The resultant is a value of the distance between them and two angles.
With these measurements and the use of the Pythagorean Theorem, the distance to the moon can easily be calculated. Variables, of course, such as the curvature of the earth must be taken into consideration, but this is only a crude example of the extensive use of this philosophical proposition.
Isn’t this triangular symbol somewhat similar in a way to our other Masonic tools? Such a small object with such a large application.
In later years, during the 16th and 17th century, classical physics, as found in the works of Galileo Galilei and Sir Isaac Newton took precedence in the world of mathematical study.
An example to show the comparison of the two, philosophical versus classical, would be if in one hand I had a 4 inch sphere made of iron, that was hollow, and in the other hand I had a 4 inch sphere of lead, which was solid, and I stretched my hands out and let them go to see which one would hit the ground first.
This is a very crude and inaccurate manner of measuring anything, but with effort, philosophical theories and small observations could be made. In actual fact, the same philosophical theories could probably be derived without actually performing the physical experiment at all.
With respect to all of the rumors of a test of a similar nature being conducted by dropping objects from the top of the Leaning Tower of Pisa, I really doubt it actually happened.
The point trying to be made here is, much more philosophy and contemplation needs to be applied in this example than is actually observed in the form of definitive measurement and actual mechanics.
Somewhat similar, in a way, to our Masonic studies, as Philosophy and contemplation are required to assist us in better understanding the teachings we receive within the Craft Lodge. Without this study, the symbolism is simply symbolism and is not understood or applied in our lives.
Now compare this same study to classical physics using a discipline referred to as Analytical Dynamics; the study of the relationship between the motion of objects and its causes. This is where an inclined plane many feet long would be built. The two spheres would be set on the top of the plane. When you release them, they travel down the plane and the potential energy transfers into kinetic energy along the way, at a measurable pace.
Along the plane, you can have markers or indicators showing distances, and what those markers or indicators imply is that timing devices such as a clock or a stopwatch could be used to measure the time factor involved and compare it to the distance traveled thus getting a much more accurate and meaningful measurement and allowing for accurate supposition and further discovery.
Experiments of this nature and the derivation of Calculus, lead to Newton’s famous and fundamental laws of motion. The basis of his second law of motion, Force = Mass x Acceleration, is the benchmark for modern Physics and is applied to many calculations, up to and especially including space travel.
Now, let’s get back to the word “parallelepipedon”: This word is from a translation by Sir Henry Billingsley, who in 1570 translated the works of Euclid from Greek into English. It is also the first known use of the word in the English language.
The derivation of the concept of a parallelepipedon is based on the 27th Proposition of Euclid. In a very basic summation, it is a six sided, eight cornered, three-dimensional geometrical object, which has opposing parallel surfaces.
The Oxford English Dictionary removed the word from their dictionary sometime between 1780 and 1800. Actually, it wasn’t removed as such, but was replaced with the word “parallelepiped,” which is defined mathematically, as “a polyhedron with six faces, each a parallelogram and each being parallel to the opposite face” …… basically the same thing, just a bit different name.
This word is also rapidly becoming obsolete, although no good word has emerged to replace it. The only place you will hear the word “parallelepipedon” today is within a Masonic Lodge while listening to the Junior Warden’s lecture.
So, what is a parallelepipedon? What does it look like if it’s got all these sides, corners and parallel things? Well, we’ve all seen one. Let me suggest a simple shoebox would be a good example.
Let me explain, by leaving the exact elements of Euclid’s geometry and calculation theorem out of the explanation.
A shoebox is a six sided, eight cornered, three-dimensional geometric object, with parallel faces. You have six sides and eight corners. The ends are the same size as each other, the same shape as each other and are parallel to each other. The top and bottom are the same size, same shape and parallel to each other and the two sides likewise, are the same size, same shape and parallel to each other.
Now if I bend it over, say by 30° or so and let’s assume the surfaces are elastic so they won’t fold or buckle, you would find that the ends are not square or rectangular in shape anymore, but are more of a diamond shape. Actually, in the shape of a parallelogram, but I’ll use the term diamond shaped for simplicity.
You will, however notice that these ends are each the same size, same shape and parallel to each other. Likewise, the top and bottom – same size, same shape and parallel and likewise again the two sides. This is what a standard parallelepipedon would look like, a folded shoe box. Please note, this is not yet a “Right-Angled” Parallelepipedon, but here starts the application it has in our lives:
The unique feature of a parallelepipedon is that it has prismatic properties. In other words, when light enters it, it will refract the light and break it up into its basic components – the true and fundamental colors that make up pure light.
Most of us have seen or played with triangular shaped prisms at one time or another and witnessed them refracting light. Well, a parallelepipedon has the same properties.
When the sun, the source of true light, enters a prism, it is refracted and we see the basic components of it in the form of the spectrum of fundamental colored lights produced=
Each of these components of the light can be identified and individualized. Although some of the spectrum is beyond the perception of the human eye, it is there and we must study and learn ways to theorize or recognize it.
One example is infra-red: Although we cannot see it, look at the important roll it plays in Thermography in today’s world of science and medicine.
Thus it can be readily concluded that without the inclusion of all of the elementary components of this spectrum, true light would not be possible.
The same effect takes place when light shines through on a rainy sky and a rainbow is formed. 1656 years after God created Adam and Eve on this earth; He destroyed it by flood. The rainbow was the sign God gave Noah after the great flood.
And God said, “This is the sign of the covenant I am making between me and you and every living creature with you, a covenant for all generations to come.” This was, and still is, the spectrum of true light, broken down for us.
In Freemasonry, we refer to knowledge as light. We are told the Lodge is in the form of a parallelepipedon. Therefore, we must conclude that light or knowledge is broken up into its true and fundamental components in our lodges, and it is. As the knowledge from the Great Architect of the Universe enters our Lodges, it must be concluded that it is also refracted,
Just as light is broken down into a spectrum of its basic parts, so is knowledge. In this spectrum we have the critical elements of true knowledge, those three Great Lights of Freemasonry; the Volume of the Sacred Law, the Square and Compasses
We also have all our Working Tools; with each one, when properly studied, teaching us separate meanings that we can moralize on and practice in life to become better people.
In a manner similar to the spectrum of light, some of the components of the spectrum of the knowledge are beyond the perception of the human eye. Upon initial presentation we do not recognize the entirety of the several parts and must use study, contemplation and philosophy to strengthen our knowledge.
Examples of these parts are the many symbolic items within our Lodges to moralize on: the Mosaic Pavement, the five noble orders of architecture, the seven liberal arts and sciences, and the diverse components and references explained or referred to in the various pieces of ritual Work given during the several degrees, to mention just a few.
Each contains vast teachings of life that are not readily visible or comprehensible without contemplation and philosophical study. Contemplations of life leading right up to death, and beyond, can and should be recognized with the aid of this spectrum of knowledge available.
We are reminded that in this life we may approach an approximation of truth, but probably will never attain it in perfection. We always will be searching, unable to comprehend the entire spectrum and will not receive it all until we pass on to “That House Not Made with Hands, Eternal in the Heavens.”
The light or knowledge is broken down into its fundamental parts. The components of true knowledge are exposed to us. And, as with light, if true knowledge is to be gained, it must contain each part of this spectrum of these elementary parts: an understanding of each of the components, especially considering not only its effect on you, but on all others around you. This is the key to wisdom.
By learning from the spectrum of fundamental knowledge contained in our Lodges and applying the results of this learning to our lives and characters, we add to our own knowledge and build wisdom.
When combined, knowledge and wisdom gives us one of the most powerful tools to work with in life. What we learn from the speculative spectrum within a Masonic Lodge are the deep seated principals of Moral Truth and Knowledge.
Just as light is broken down into its basic components in a prism, so knowledge is broken down into its basic components in a Masonic Lodge or parallelepipedon. All we have to do is learn from them. We can all do this through the teachings we receive and our own philosophical contemplation.
Also, we can study deeper into the Volume of the Sacred Law – Remember; this is the tool God has chosen to contain more of his Divine Will than in any other form and it is positioned in the center of our many Lodges – indicating its prime importance.
Now let’s take this parallelepipedon and straighten it back up to its original shape, as the shoebox originally was. Now enlarge it until it fills the entire volume of this Lodge room. It would still be a parallelepipedon but, at this point, it would be filling our Lodge room.
We could use one of the three Great Lights of Freemasonry, the Square, to measure or prove it. We would be able to measure the angles of the corners and they would prove to be 90 degrees and square or right angled, just as the term implies, it is now a “Right-Angled Parallelepipedon.”
Next we are told, by the Junior Warden, during his lecture, that this right angled parallelepipedon is in length from East to West, in breadth from North o South, and in depth from the surface of the earth to its center, and even as high as the heavens. “As high as the heavens” – that’s a vector quantity, not a scalar quantity. In other words, it does not define a limit. It intimates unlimited distance or length in one direction.
Nor do East and West or North and South have definitive distances. What this means is that the confines of a Masonic Lodge or more accurately, this right angled parallepipedon, does not stop 40 feet past the altar at the Master’s chair or at the wall behind him, or that wall over there, or the one over there. Nor does it end at the door leaving the Lodge or the edge of the Lodge property.
East is east and goes on until it meets the West. The same applies with North and South. The literal meaning of this phrase is that it extends in every direction indefinitely, or in other words, covering the entire planet earth.
The knowledge we learn, the Brotherly love, relief and truth that we teach and share in our Masonic Lodges goes with us everywhere. That’s what’s referred to in the Junior Warden’s lecture when he tells the Candidate that “a Masonic Lodge is of this vast extent to show the Universality of the Science.”
So in other words, if you’re downtown, enjoying a coffee break with an old friend, or whether you are on a vacation, playing with your children or grandchildren on a beach, or all stressed out at the local burger joint, trying to correct an error that took place with your meal, or even in the desert of Afghanistan, drinking bottled water and eating military rations, or anywhere else you may happen to find yourself, or any situation you may have to deal with in this world, you are still theoretically within the confines of a Masonic Lodge and should expect to conduct yourself as Freemasons.
Keep in mind that your gentle, compassionate actions reflect on the Masonic Fraternity directly. Always remember and practice, just as you would within your Lodge building, the moral teachings you have learned within the confines of the right angled parallelepipedon.
Now you know: “That’s what the heck a right angled parallelepipedon is.”