Triangles Everywhere

Triangles Everywhere

I was recently exploring the idea of the triangle – its form, function, stability, and meanings. In Freemasonry, as in many traditions, the triangle holds significant influence in symbolic meanings.

A triangle is a polygon with three sides and three vertices. There are many forms of triangles – right, equilateral, obtuse, acute, isosceles, and scalene. There are also oblique and degenerate triangles. Triangles may be multiple types. Triangles are generally believed to be two-dimensional objects whose interior angles, at least in Euclidean space, equal 180 degrees. They can be various shapes but the ones most often seen are right triangles and equilateral triangles.

Of the triangle knowledge from history, the famous philosophers Pythagoras, Plato, and Euclid are known best for theorems, ideas, and esoteric supposition surrounding the form. The form is so basic that it’s most likely older than written history. Ancient petroglyphs, such as those from Columbia, the Sierras in North America, and Mexico, show humans with bodies and heads in the form of triangles. This is a basic shape that mimicked the human form, with wide shoulders and narrow waist, or a wide head crown and narrow chin. There isn’t anything to indicate, in-depth, the symbolic meaning of the triangle other than it being incorporated into the human form.

The Egyptians used the triangle quite often, generally in the realignment of land plots after the Nile floods but also in architecture. In a 2000 thesis article regarding the “sacred triangle,” the author asserts that Egyptians knew and used, even in the Old Kingdom, the “sacred triangle” of 3:4:5. Indeed, the author goes on to state that using straight vertices, or a “simple, straight vertical pole,” to find location or identify specific time of day or days of the year. While this is a heavy-mathematics article, the reader might find some deeper, symbolic meanings in the geometry.

During the 6th C. B.C.E., the School of Pythagoras became known for its theorem regarding the formation of the ‘sacred triangle.’ Pythagoras left no mathematical writings of his own, while Euclid and Plato did. Thales of Miletus is really the creator of basic mathematics and geometry, and probably the first to give us theorems about the triangle. Pythagoras, who created the words philosophy and mathematics, is more well-known and did much to bring the form of the triangle into deeper meaning.

To Pythagoras, the number 10 was the holiest of numbers; the tetractys is a triangle form of 10 dots, created by interlinking the dots into nine triangles forming the 10th, larger triangle. It is used to symbolize the creative forces of the universe. From ancient-symbol.com, “In the figure, the first row has a single point that is representative of the Creator, the active principle, the divine power behind all creation and is associated with wisdom. The second row contains two points that represent the passive principle and are associated with friction, movement, impulse, strength, and courage. The third row with three points signifies the world coming out of the union of the above two, a union of physical and mental balance and is associated with harmony. The fourth row has four points that represent the four liberal arts & sciences that complete the world. These four points symbolize the four elements of earth, fire, air, and water.” This was, generally speaking, the first time that the philosophical meaning of a number, its holiness and perfection, being derived from pure mathematical reasoning rather than from inductive reasoning. It was more than the total of our fingers on our hands. Another interesting article on the triangle and tetractys, among other things, can be found here: http://www.projectawe.org/blog/2015/12/21/up-and-down-the-monochord-part-iii-triangle-trinity-unity. The author of this blog does a very good and thorough job of digging into these ideas, and I would highly encourage everyone interested in these subjects to read it.

In the alchemical writings of the Middle Ages, the classical elements of hermeticism were based off the form of the triangle, turned upward or down, with a line to denote the opposite or without to indicate the base elements. The conjoining of fire and water is indicative of balance and achieving perfection. The triangle is also seen in the “triangle of art” also known as Solomon’s Triangle. The circle in that triangle represents the space where spirits are called, with the triangle representative of the safe space from which the magician worked.

Triangles in astrology are seen as very positive, and a grand trine, or golden triangle, is seen as a creative, harmonious flow of energy in a person’s life; they generally are composed of the objects being in the same elements, in the form of an equilateral triangle.

Triangles are a form of stability, where two extremes are balanced by a third point. Triangles are everywhere in Freemasonry, overt and subtle, and have different stories surrounding each. These different stories speak to individuals differently even if the core remains the same; depending on the degree being worked and studied, the aspirant may find different aspects of the same truth. These truths are not much different than the ancient Egyptians and Greeks found and used in their daily lives. There are always extremes and balance is achieved by that third, divine point. One might also see that all emanates from the Divine, the single point, which may also turn into that point within a circle which is perfect balance. The perfect man may be the one who finds equilibrium during whatever storm shakes him. Taking this symbolism into our daily lives and applying it to our relationships with people is really the value of the study of symbol. We can work toward being the middle point between extremes, able to see both sides in equal measure. A more holistic view of those things that permeate our lives creates a better person.

Hidden Mysteries of Science

Hidden Mysteries of Science

Science is “the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment.” We all perform scientific acts each and every day. Being aware and present in our actual work, home life, educational pursuits, and leisure all encompass some aspect of “science,” as described above. Do we not learn relationship interaction through observation and experimentation? Of course we do! Do we study others and then experiment with things like cooking, clothing ourselves, cleaning the house, and raising children? Absolutely. Life is science.

And yet… there are the science doubters. The Washington Post did an article, in 2015, on science doubters. Entitled, “Why is Science so Hard to Believe?” the article goes on to discuss confirmation bias, the discipline of the scientific method, and why so many people would rather believe media hype or misinformation from friends rather than actual science. Media is not science and it is not gospel. We consume the media that’s easy to consume rather than do the work for ourselves. It’s easier to doubt than to verify.

Neil deGrasse Tyson has an interesting quote: “The good thing about science is that it’s true whether or not you believe in it.” He also said that “the universe is under no obligation to make sense to you.” Both of these quotes speak to the hubris of humans – we think we know much more about the word than we really do.

In a quote from an article on National Public Radio, the author quoted his friend, a professor of Jewish philosopher, as saying “science tries to make magic real.” The author goes on to specifically outline activities, now commonplace human activities, as ones that we once thought of as magical, for example, flying. We fly without a second thought; yet, 500 years ago, to say one flew was heresy, possibly leading to death. Other examples are the knowledge of “invisible” animals capable of making humans ill, or being able to see great distances into space (the past) through a telescope. The ability for our phones to “think” and talk with us would have been quite astounding to the medieval mind.

The author continues his journey with the main difference between science and magic: his belief is that the power of magic originates within us, where as science’s power originates outside of humans. Science is a set of immutable laws of the universe. Right?

Well, no. Science updates theories based on knowledge gained from further expressions of the scientific method, and then new theories are postulated. Science is evolving, a never-stagnant set of data that we are constantly testing and proving or disproving. Magic is generally seen as not obeying the laws of nature, being outside of those “rules” or “metaphysical,” as it were. Yet, we’ve all said it: couldn’t what we see as magic just be unexplained scientific laws that we do not understand quite yet?

Why are Freemasons charged to examine and study nature and science? Nature AND science? It seems that it might be because the world is made up of both the understood and the mystery. We have many questions to answer about nature and we use science to get there. Perhaps we could say we have many questions to answer about magic and science is the method. There’s no reason we can’t have wonder and reason hanging out together in our minds. We can appreciate the brilliant stars and the awe of an eclipse and still want to know how it happens. Knowledge does not take away wonder.

I want to believe that perhaps science and magic are part of the same evolutionary cycle – what starts out as magic becomes understood by science, which breeds questions within our curious minds, wonder at something unknown, triggering us to embrace the tools of science to explore. Freemasons get to play in both realms, being co-creators on the path of humanity.

How Do You Know?

How Do You Know?

Our modern times have brought us many great advancements. We find ourselves living longer, becoming more globally connected, and enjoying medical ingenuities, such as antibiotics, blood transfusions, and artificial organs. There are many amazing necessities and niceties that are enjoyed by the human race in varying degrees because of Science. Science has given us a lot to be thankful for. Or has it?

In recent years, there have been debates, and at times heated arguments, over the likes of genetically modified foods, vaccinations, and global warming. Even the effectivenessFlat Earth of Western medicine has cropped up in many personal conversations over the years. Ideas such as Flat Earth have come back to the scene in modern discussions and often with contention.

Once thought for certain by the general populace, many scientific concepts are met with skepticism. But before you believe this blog is about winning you over to one side or the other, I ask you read on, because it not. There is something greater underneath these debates, and it has everything to do with you.

When researching the Philosophy of Science the other day, I came upon a very intriguing
question: How do you know your knowledge is authentic?

What a wonderful question, and it has given me more than a pause. Now before we reduce this question to reducto adsurdum, and say how can we really ever know anything, let’s try to accept the question for what it is: an invitation to know ourselves a little bit better.

Knowledge. It is a formidable due to its ubiquitous nature. It is an invading species that finds life in the uninhabitable regions of our brain. It plants its roots and digs deep so it cannot be easily removed, often without our realizing it.

Thus, when we allow “knowledge” to pass our acceptance filters and impregnate itself in our world view, it becomes almost impossible to remove. Especially if it comes from an authority – like science, religion, or a person of a particular importance. But are these sources enough to make an idea become an organism of knowledge?

One of the greatest lessons science has taught me is that it is only at its best when it is being challenged, and I find that this true of human knowledge in general. Authenticity cannot exist if challenge is not present. Growth is a product of conflict, not peace. Knowledge that is real will survive and become stronger; the ideas that do not deserve to be uprooted and replaced with a more genuine concept.

How do you know your knowledge is real? We listen and we give the other side their due. This is a very Masonic and scientific principle. In doing so, the only danger we will face is the danger of becoming more authentic in what we know. That doesn’t sound so bad, does it?

 

When Did We Stop?

When Did We Stop?

It is easy for life to sweep us away on the current of self-importance. I don’t think we mean to; it just happens to be the way our culture works. Fast and busy and “me” centered. This way of life isn’t just an adult thing. We have shown our children how to do it. They, too, are pounded with the every day commitments we give them and allow. This way of living is like a fierce version of the Tango but at a pace it was never intended to be danced at.

This is my life as well; I made the same choice you did, to be a part of this me-speed machine.

Two events recently occurred that has made me slow my dance steps down and see those around me better: the launch of Falcon Heavy and a philosophical discussion on whether we should migrate to Mars.

The only word that I can give to the launching of Falcon Heavy is wonder. Watching the launch left my mouth open but with no words. There was something eerie when the sideFalcon Heavy boosters landed on Earth again. This shouldn’t be happening, I told myself. Side boosters don’t come back, they just don’t. Again, the wonderment had me re-watching several times over until the busy day I had, had dragged my eye lids closed.

Two weeks later the philosophical debate on whether humans should migrate to Mars coincidently dove-tailed with the SpaceX’s launch. The discussion was an interesting juxtaposition to my earlier experience of watching the Falcon Heavy launch. I entered the discussion, as I do monthly, with great enthusiasm about the topic. How could I not with this particular idea? We were going to talk about the possible expansion of our kind. To me, the feeling I had could be analogous to what people must have felt when travel to the New World seemed impossibly possible. The feeling was akin to infectious hope sprinkled with reservation. The New World, that is Mars, seems so alien, so inhospitable, could we ever truly make a life there?

It was after this debate that I have felt my mouth go dry with disappointment and my inner Tango stumble with the memory of a statement made earlier in the discussion, “What did schlepping to the Moon ever get us?” I shouldn’t judge I know… but I did. This question has forced me to understand the alternative purpose that Elon Musk had when he sent his Tesla roadster into space. He didn’t use his car solely as payload… he used it to get our attention.

I have to ask; I have to know. When did we stop looking up? When did we stop finding continual inspiration in the stars and unimaginable possibilities in worlds that seem saturns_shadowunreachable? I cannot help but to understand Elon Musk’s strategy. He needed to pull our eyes off the ground by wowing us with his fancy car whizzing around Earth’s orbit because a rocket that brings us one step literally closer to Mars, wasn’t and isn’t enough.

My hope has been temporarily dampened, but it still remains because it is possible to change the rhythm by which we live to include the stars. Space exploration isn’t about man schlepping through the cosmos; it is about us making a bigger place for ourselves in that inky black sky. And the possibility that we are closer than ever to doing just this gives oxygen to that small flicker of hope.

 

Astronomy and the Quadrivium

Astronomy and the Quadrivium

Perhaps your first thought, as was mine, is: “How can Astronomy be an ‘art?'” Furthermore, how can Astronomy be called a ‘liberal’ art? From a very interesting (and worth exploring) website called “Arts of Liberty,” we have a snippet for explanation:

“To call astronomy an ‘art’ can come as a shock to a modern reader… Perhaps without thinking much about it, we think of “science” as being a genuine and exact knowledge, whereas ‘art’ is more expressive, or touchy-feely.  But, that is not quite adequate, since medicine is also an ‘art,’ and it is anything but touchy-feely… And while ‘science’ and ‘art’ do not appear to be synonyms, it could very well be that the same discipline can be called both a ‘science’ and an ‘art,’ although for different reasons.

To understand this properly requires us to consider a sense of the word ‘science’ not in common use today.  The word ‘science’ comes from the Latin word scientia, which meant a very exact knowledge, a rigorous and sure knowledge of things deduced from self-evident truths.  The ancient Greeks would have called such knowledge epistémé...  

In the vocabulary of the ancients, an ‘art,’ like a science, meant a carefully reasoned-out knowledge, but more than that, it meant a knowledge of how to produce something.  Where there is no ‘product,’ there is no ‘art.’  So it is possible for a form of knowledge to be a ‘science’ but not an ‘art.’  For example, Aristotle considered the study of god to be a ‘science,’ a body of knowledge rigorously reasoned out from self-evident principles, but not an ‘art,’ because it did not teach us how to make gods, or how to do anything about god.”

Ptolemaicsystem-smallClaudius Ptolemy (100-170 CE) was a Greek mathematician living in Alexandria. His work The Amalgest was one of the most influential astronomical works until Galileo’s discoveries in the 17th C. The Amalgest documents many mathematical and astronomical treatises, including works by other mathematicians – works thought to be lost. The most significant piece of this Amalgest (total of 13 books), is the documentation of the geocentric model of the universe. Ptolemy’s work became the accepted theory of the structure of the planets and stars, with the Earth central to all.

This influenced not only astronomy and mathematics but also theology, philosophy, and fine art. Three centuries after it was written, Hypatia and her father Theon, genius mathematicians, added to the work with their own commentary, throwing in their thoughts of elliptical orbits, the procession of the equinoxes, revising Ptolemy’s Handy Tables, and introducing the sexigesimal calculation systems. It’s believed that this rendering of the Amalgest, with the Hypatia/Theon commentary, is the one that was used for the majority of the Middle Ages although no direct reference to Theon survives and Hypatia is mentioned only in a passing 10th C. reference.


And thus, the Quadrivium ends. I hope you’ve enjoyed my answer to the Bro.’s challenge of finding a significant event, work, or person who influenced each specific liberal art. The question was posed, should Freemason’s really learn the liberal arts? The answer, to me, should be obvious. Not only should we learn the liberal arts individually, but understand their context in the whole of being educated about the natural world. Human beings can be taught easily to survive; we cannot just “pick up” how to thrive, generate ideas, and create a better world.

An example of this “Freemasonic mindset” is James Madison, even though he was not a Freemason. In his early twenties, when the United States was in its infancy, he gave up much of his career and life to studying the histories and government of world cultures. He was relentless in his pursuit of the histories and knowledge of government administration, what worked, what didn’t; he studied philosophy, history, theology, art, classical literature, geography – the liberal arts and more. By the time he finished, and began his work in the new nation’s government, he was arguably the single biggest influencer in shaping the United States Constitution and the framework of our Democracy. By learning the past deeply, he was able to innovate and create a new world. To me, that is a main goal of the Service of Freemasons.

Geometry and the Quadrivium

Geometry and the Quadrivium

Whist sitting in school, slaving away with compasses and a ruler, one hardly remembers that geometry is the study of the measurement of the earth. Earth. The thing we sit on, utilize, and finally rest in when this is all over. The geometry in schools today looks nothing like the geometry of 3000 years ago. It is difficult to divorce geometry from the other liberal arts when we take into consideration the scale to while discoveries are interconnected. Geometry arose from the needs of agriculture, civilization, and war. For so much of this, we can thank Archimedes of Syracuse. A student of Euclid in the 3rd c. BCE, his advances in the field of geometry furthered irrigation (Archimedes’ Screw), astronomy (the first planetarium), and weights & measures (Archimedes’ Principle). The most interesting, to me, is The Method of Exhaustion (remember Dialectica) also known as “The Method” or “Archimedes’ Method.”

“…, to estimate the area of a circle, he constructed a larger polygon outside the circle and a smaller one inside it. He first enclosed the circle in a triangle, then in a square, pentagon, hexagon, etc, etc, each time approximating the area of the circle more closely. By this archimedes_circleso-called ‘method of exhaustion’ (or simply ‘Archimedes’ Method’), he effectively homed in on a value for one of the most important numbers in all of mathematics, π.” 1

Linked together with this Method is the “Method of Mechanical Theorems.” Proofs are everything to the mathematician, and in his Method of Mechanical Theorems, Archimedes had none that would be accepted. He set out using Eudoxus’ The Method of Exhaustion to prove what he knew to be true. In a letter to Eratosthenes, in manuscripts discovered in 1906, Archimedes outlines his thought processes. This document is known as the Archimedes Palimpsest.

Certain theorems first became clear to me by means of a mechanical method. Then, however, they had to be proved geometrically since the method provided no real proof. It is obviously easier to find a proof when we have already learned something about the question by means of the method than it is to find one without such advance knowledge.

The importance of these discoveries and the methods by which Archimedes came to them may be obvious – who doesn’t need π? However, it is also fascinating to peer inside the mathematician’s mind and view it with a Freemason’s perspective. Here was a man who could see the Plan, understand the Plan, and only needed to bring it to life: a divine spark of wisdom, the will to discover, and beauty in its presentation.

For an interesting and short expose on The Method and the “Archimedes Palmipsest,” whence this Method is documented, review  “The Illustrated Method of Archimedes” by  Andre Koch Torres Assis and Ceno Pietro Magnaghi. The PDF can be found here.

Additionally, the originally translated letter from Archimedes to Eratosthenes can be downloaded here. (Thank you, JSTOR.)


Just a note (1): The Story of Mathematics, Luke Mastin – http://www.storyofmathematics.com/hellenistic_archimedes.html – I’ve done my best to verify statements here, and so should you.

Mathematics and the Quadrivium

Mathematics and the Quadrivium

Personally, I struggled with Math in school. Faced with a math test, any math test, I froze, cried, banged my head against the desk, and ultimately gave up. I saw mathematics as an isolated “thing” to be conquered. You were either good at math, or you were not.

How little I knew, and how little I was taught, about true mathematics. More than numbers, factorials, and fractions, Mathematics is about relationships – of numbers: how they work with each other, work for us, against us, and can talk about any situation. There are mathematics of money, elections, government, science, music, agriculture, capitalism, socialism, any -ism. Math is language and structure: it is a bridge between all aspects of liberal art. Which leads us to the Bridges of Koenigsberg.

bridgesLeonhard Euler, a Swiss mathematician of the 18th Century solved, sort of, the problem of the Seven Bridges of Koenigsberg (Russia, at the time). Koenigsberg had two islands connected by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point (touching every edge only once). Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The bridges did not meet this condition and therefore, no solution could be found to the problem.

Yet, what this Eulerian circuit eventually did provide is the basis for modern topology , which has expanded into areas of quantum physics, cosmology, biology, computer eulernetworking, and computer programming. For example, the Eulerian cycle or path is used in CMOS circuit design to find an optimal logic gate layouts. For anyone wanting to read the paper outlining these paths in the original Latin, it can be found here.  English translations do exist. A good page on the history of topology is here.

Leonhard Euler was a fascinating individual in that he saw mathematics as something that infused all of life. Though his writings, he made applied mathematics accessible to the layman and his scholastic peers alike. An excellent and thorough biography, written by Walter Gautschi, can be downloaded in PDF form here. With a varied interest in all aspects of mathematics  (arithmetic, geometry, algebra, physics), music, anatomy, physiology, and astronomy, he truly was a man of the “Enlightenment.”  While he was not a Freemason from what I can tell, he seemed to hold much regard for the idea of true science, and creating a better world for his fellow man: a Freemason’s true ideals, to be sure.

The Quadrivium

The Quadrivium

What scholars call the “foundation of Liberal Arts” – the Trivium – is taught in order that one may expand to other subjects, building upon the skills learned. These subjects have been varied over time, based on the philosopher teaching them but they are now generally accepted as mathematics, geometry, music, and astronomy – the Quadrivium. While these subjects were taught by ancient philosophers (Pythagoras, Plato, Aristotle, etc.), they became “the Quadrivium” in the Middle Ages in Western Europe, after Boethius or Cassiodorus had a go at translation.

(Encyclopedia Britannica has an excellent article on Mathematics in the Middle Ages, which discusses the Quadrivium briefly.)

Anicius Manlius Severinus Boethius (usually known simply as Boethius) (c. 480 – 525) was a 6th Century Roman Christian philosopher of the late Roman period. Flavius Magnus Aurelius Cassiodorus Senator (c. 485 – c. 585), commonly known as Cassiodorus, was a Roman statesman and writer, serving in the administration of Theoderic the Great, king of the Ostrogoths.  The former, Boethius, did a great deal to translate most of the ancient philosophers from Greek to Latin. Many of his works on Aristotle were foundational learning in the Middle Ages. Cassiodorus made education his life’s passion, particularly the liberal arts, and worked diligently to ensure classical literature was at the heart of Medieval learning. Both men have been credited with coining the term “Quadrivium,” or “where four roads meet.” Adding to the mix of Medieval education “influencers” is Proclus Lycaeus, one of the last classical philosophers and an ardent translator of Plato. He is considered one of the founding “fathers” of neoplatonism and had a great influence on Medieval education as well. His translations of Plato are peppered with his own ideas of education and philosophy. One of his most interesting books, considered a major work, is “The Platonic Theology.”

sevenLA1For the serious student of the classics, all of these philosophers, in their original Greek or Latin (with English translations alongside the original) can be found in the Loeb Classical Library series. Many used book stores, especially near universities, carry these books and they can be had for about 10$ each. There are hundreds of books but all are quite good as original references (See NOTE below) Back to the Quadrivium…

While many see the Trivium and Quadrivium as “separate,” I think this is a manufacture of our modern educational system. The Trivium are the basics for communicating thought, generating ideas, and conveying those thoughts clearly; yet, like Freemasonry, I don’t know that you would have jumped completely away from your foundations. Plato, in The Republic, does note that the quadrivium subjects, as identified above, should be taught separately. The Pythagorean School divided the subjects up between quantity (mathematics and harmonics, or otherwise known as music) and magnitude (geometry, cosmology or astronomy.) Personally, I find it difficult to talk about music without first having at least fundamental mathematics and exploring both together makes sense. I have not delved into the curriculum of the universities of the Middle Ages in Europe but if someone else has, it would be interesting to hear about it. sevenliberalarts

What I find most fascinating about the art surrounding the Quadrivium (and the Trivium, for that matter) is that nearly all of the plates, pictures, or engravings represent the subject matter as female or feminine. Perhaps it has to do with the receptive qualities of studiousness, or the idea of fecundity or maybe gentleness; whatever the reason, many of the Medieval and Renaissance European depictions show all subjects with a feminine demeanor. Since nearly all scholars in the middle ages in Europe were men, perhaps it was simply a bleed-over of the Medieval ideal of women. I am sure this is another subject for another time.

On an additional side note, I searched for representations of the Quadrivium and Trivium in Islamic art, also knowing full well that Islam is aniconistic. Islam really had begun to gain ground at the last part of the classical period in North Africa & Europe and as such did not really experience the same type of “downfall” or Dark Ages, that Europe did. The schools of Islam continued to develop the subjects of the quadrivium and trivium uninterrupted until Europe “caught up.” In fact, many of the mathematics, geometry, and astronomy texts of the latter Middle Ages were translated from Greek to Syriac Aramaic or from Arabic to Latin, and later taught in Latin universities in Europe.  Suffice to say that Islam did have an impact of the learning of the West, probably much more than most people today are aware.

So, why would the Freemason study the Quadrivium? The answer, to me, is obvious. If the one of the primary studies we must take on is Geometry, we need to understand how number fits into this process. We need Mathematics to understand Geometry, and Music to understand relationship of numbers, working in harmony. Astronomy teaches us our place in universe, and allows us to expand our knowledge of our own earth toward the heavens. Geometry, or the study of the measurement of the earth, is far more than the squares and triangle theorems we all know…and love. It’s about how to apply these numbers to the world around us. As we will see in each of the subjects, they can be taken for their base modern “ideas” or we can expand and overlap them, apply them to the natural world, and thereby become better caretakers of not only the earth we live on but the beings who live on it with us. The idea of a Renaissance Man is one who is well-versed in these foundations and has ideas that expand the world around us. They make the world a better place to live in, now and for the future. The Freemason, to me, embodies this idea completely.

Next stop, the subjects of the Quadrivium. Thank you for joining me!


NOTE For those interested in more of the Loeb Classical Library, but limited access to purchase these books, Harvard University Press has been working to put them online. The link is here: http://www.hup.harvard.edu/features/loeb/digital.html.

Individuals can subscribe for a yearly cost, with subsequent years being cheaper, and non-profits can also subscribe for a reduced cost. If you are a serious researcher and you would like primary sources, this library is an excellent resource.

The Seven Liberal Arts – The Trivium

The Seven Liberal Arts – The Trivium

There is a real affinity for the goals of Freemasonry and the Seven Liberal Arts. From earliest teachings, we see that they are the foundation of many degree rites, the first of which is the FellowCraft Degree. To understand why this is, I think we must first understand the structure of the Seven Liberal Arts and what their history is.

The Liberal Arts have been, from antiquity, been the foundation stone upon which knowledge of the natural world rests. The seven liberal arts have been utilized since ancient Greece. Plato and Pythagoras were first in codifying their importance; the flowering of our western understanding of the liberal arts took place in medieval education systems, where they were categorized into the Trivium and the Quadrivium. Grammar, Logic, Rhetoric are the Trivium, and Arithmetic, Geometry, Music, and Astronomy are the Quadrivium. The Trivium combines the use of the senses with knowledge to lay the foundation for further study. The Quadrivium was considered to be the higher level education for the philosopher, and employed the use of the Trivium to be able to compose higher ideas and thereby, expand the knowledge of the human condition.

Freemasons the world over have expounded on the Seven Liberal Arts ad infinitum. All you need to do is search Freemasonry and Seven Liberal Arts, and you get a great deal of regurgitated drivel. That is not what I am striving to do in this next series. Here, my goal is to simply explain why the Seven Liberal Arts seem to have a kinship with Freemasonry, and perhaps provide small examples of each – withsevenliberalarts and without a Freemasonic connection. It’s up to you, the reader, to decide what you’d like to do with the information.

Plato’s Dialogues explain the curriculum outlined in detail and for any serious student of liberal arts, Plato is required reading. I, therefore, will not relate these concepts here. Suffice to say that the study of the Liberal Arts is more of a study of knowledge than it is of any specific actual data and information. As we may have learned by now, knowledge without application is dead and useless. Knowledge in the pursuit of higher ideals and higher ideas is more valuable than… than… well, you get the idea. Remember, one of the goals of Freemasonry is to better the human condition while standing up in defiance of falsehood, ignorance, and hatred. How do we do that if we are not searching to better our communication and knowledge, and the ways to bring both to life?

The Trivium is, as I said above, the foundation stone of the Seven Liberal Arts and really provides us the method and ability to communicate. It is composed of Grammar, Logic, and Rhetoric.

  • Grammar: Knowledge and Learning of Language
  • Logic: Reasoning, Questioning, and Thinking with Language
  • Rhetoric: Directing, moving, and Persuading using Language

While these all seem to be in relation to language, they are much more than language. They are the skills involved in achieving these ends. Therefore, the study of Grammar is also the study of history, geography, reading, and writing. It is basic, absolutely, but more encompassing than simply learning one’s ABCs and how to put pen on paper and write. Logic is about how we learn – we use our senses to experience, put our minds to thought, question, and experiment. We learn to ask the correct questions to achieve the answers we seek. They are not provided to us – we must seek them out and test for ourselves. Finally, rhetoric is the ability to take what we have learned with grammar and dialectic and put them firmly into the hands of an audience we are attempting to persuade. Rhetoric uses emotional discourse, thoughtfully created and properly applied, to communicate new ideas.

If it is not clear to the Freemason now why at least the Trivium is not important, one might want to question what they have actually learned while being a Freemason. Many may think that Freemasonry is all about enlightenment, walking in squares, or religious meanings. It might be those things to some but I think the true goals of Freemasonry are to provide a framework of how to be in the world, to make that world better for those that follow us but more importantly, for our own betterment. We cannot communicate lofty ideals via ritual alone – we need to be able to express what we have learned to a wider audience, to bring new thoughts to a wider world. To me, when we talk about service to the world, there is no greater service than being a hand-up to the betterment of the human condition and we do that by “teaching a man how to fish.” Study of the Liberal Arts is by one means to catch that “fish.”

Hortus_Deliciarum,_Die_Philosophie_mit_den_sieben_freien_Künsten

Understanding Chaos

Understanding Chaos
In this first 100 days of  2017, here in America and in some other countries, there has been a great deal of what we like to call chaos. Chaos is “complete disorder or disruption.” However, I’m going to challenge us all, especially Freemasons, to look at Chaos differently. We put “Order out of Chaos” but what does this mean? The challenge I have is to look at Chaos as something different and necessary to life and growth, or at least our ability to tell the difference.
 

Let me first start by saying this is not, emphasis on NOT, a political discussion. This is using an event in politics to illustrate a point. However you feel about the politics/events, right or wrong, is irrelevant to the content of this blog. What I want to do is illustrate how science and nature have a real place in our processes to affect change. Think differently. That said, here we go.

A recent event happened in politics in America – the Immigration Executive Order that Trump signed on January 27th. The executive order was, by mostly-credible accounts thus far, written by Steve Bannon, a self-designated fear monger. He stated, in a 2010 interview, “Fear is a good thing. Fear is going to lead you to take action.” He also stated that “I’m a Leninist,” [quoted as saying by a writer for The Daily Beast] He later said he did not recall the conversation. “Lenin wanted to destroy the stA30B258A-524B-4688-9D2F-EE9E6F4D5652ate, and that’s my goal, too,” the site quoted him as saying. “I want to bring everything crashing down, and destroy all of today’s establishment.”  Mr. Bannon told The Washington Post this year, “We call ourselves ‘the Fight Club.’ You don’t come to us for warm and fuzzy. We think of ourselves as virulently anti-establishment, particularly ‘anti-’ the permanent political class. We say Paul Ryan was grown in a petri dish at the Heritage Foundation.”

I do not think that Mr. Bannon is alone in
his thinking this way, especially across the current appointees and heads of various government agencies. I think Trump has a specific goal in mind: introduce chaos into the system to turn it on its head and change it. The difficulty that most people have is that it is chaos mixed with fear, hatred, and injustice – not Masonic values at all.

In a recent Facebook posting, historian Heather Cox Richardson explained this “shock event” in very succinct and clear terms – what it is, what the outcomes may be, and what we can do to overcome it. The full text can be found in this blog. I think that one of the best sentences in this piece, and one we should all take hold of is this: “But because shock events destabilize a society, they can also be used positively. We do not have to respond along old fault lines. We could just as easily reorganize into a different pattern that threatens the people who sparked the event.” Her point, in other words, is that we don’t have to react in ways we’ve always reacted – we can take our emotions and work differently. It takes consciousness, focus, and effort. It takes energy. Energy.

Here’s where I want to turn chaos on its head. In the world of science, specifically physics and thermodynamics, chaos equates to entropy. Entropy is not sitting on your couch, drinking a Coors, and watching the game. No. In physics, entropy is the lack of order or predictability; gradual decline into disorder. Simply stated, entropy is the spreading of energy until it is evenly spread. A great, in-depth, and head-expanding article on the second law of thermodynamics and entropy is here. I warn you, it’s long and even though it says “simple,” it takes focus to really follow the whole article. Bottom line: let’s just say, energy disperses.

If you look at our country, or any “related system” I will call it, we were founded by many humans with a great deal of energy for change. Events which upset the equilibrium – taxation, religious persecution, and the like – created energy, which in turn led people to expend their energy differently – fighting for and creating a new country and a new form of government. This energy, related to the creating of the United States of America, has over time, received influxes of upsets to its equilibrium; these are the events more remembered as shapers of the country. It is how we got to where we are today.

How does this relate to thermodynamics and physics? Hang with me, I’m getting there. There is new discussion about entropy and how physics can be applied to the biology of life. Another long article but with a very clear video about the thoughts and theories is found here. In essence, the article explains that in the end, thought (that is, intention, logic, and problem-solving) are the keys to fighting entropy and disorder. Another way of looking at this is that the destruction of forms happens because of entropy; the introduction of an upset to the equilibrium staves off entropy (chaos) and causes the current energy to reorganize and become a viable source for change. We can look at teleology as having a connection to thermodynamics rather than biology. Simply said, thought is energy.

Did I lose you? I might have lost myself. But, stay with me. Where I’m getting to is this: Freemasonry values nature and science – we need to look at both for the answers of how did we get here and where do we go next. Let’s take a step and connect biology, physics, and politics, weird as that may be, into a line and we can see how we got here. And, to Heather Cox Richardson’s point, how we get out. We need to take whatever energies we receive from the upset of the equilibrium and turn it into a thoughtful way to change our world.

Like the small discs of atoms the researchers used in their experiments in the above article, we too can use tools and socially organize into effective change advocates. We can create something new from the impetus we’ve been given. To me, Freemasonry has given me the balance to look at something like Chaos as see it as a blessing. I’m not talking about how that chaos is delivered, which may involve incredible emotional and physical upheaval. Pain, Fear, Hate, Ignorance – all of these continue. It is in our responses where we can affect the change. Until we think about our next moves, use the energy that we’ve been given to that plan of thought, and execute well, the shock event will actually create nothing new at all. I might even venture to say that what we might view as negative change can actually be what positive change needs to get going. All of these lessons are clear in nearly all degrees of Freemasonry. Sometimes, it takes chaos for us to see the value in what we’re learning. If we can take a breath and use our thought processes to absorb the disruption, we might be able to see the value in all sides of an event.