A Little Light Reading: The Arts and Freemasonry

A Little Light Reading: The Arts and Freemasonry

I have been asked often: “what are good books for people who are interested in Freemasonry?” Personally, I feel that any reading is good reading: it strengthens the mind, opens you up to diverse ideas, enhances your vocabulary, and makes you a far more interesting person for conversation. Regardless, there are a myriad of paths the aspirant’s reading may take, and still find they add substance and interest to the philosophies that make up your life. Nearly every genre has something to add, and I’ve personally found Masonic meaning in many non-“serious” readings. Masonry is everywhere, and for the ardent Freemason, it can be found in movies, science fiction writings, and even children’s books.

For those interested in Freemasonry, titles at The Masonic Publishing Company are robust places to start the journey. I’d highly recommend The Brother of the Third image-masonic-publishing-companyDegree, the Kybalion, and The Law. For those interested in Co-Masonry in general, On Holy Ground is a particularly engaging book on one organization’s foundation and history within the United States. There are really two aspects of reading in Freemasonry – about Freemasonry and about symbolismIf you’re interested in the symbolic nature of Freemasonry, The Secret Teaching of All Ages, by Manly P. Hall, is a fascinating romp through all kinds of studies and is a good foundation into alternative ways of looking at life, the universe, and everything.

Most late 19th century and early 20th century Masonic authors, like Leadbeater, J.F. Newton, Powell, and Wilmshurst, are also very good authors to explore some of the specifics of Freemasonry, without giving anything away. That is my caveat with anyone interested in becoming a Freemason: don’t read ahead. In fact, don’t read any ritual or about any degree you don’t have. Sure, you can find anything on the Internet; Freemasonry, however, is an experiential process and to truly find it work in yourself, it’s really a good idea to go in without expectations or knowledge. You might find you get in your own way. Books like The Science of the Sacraments, by Leadbeater, give one an idea of ritual work without speaking strictly to Freemasonic ritual.  The Golden Bough and The Magic of Freemasonry provide deeper insight into ritual and its importance in human life. Georges_de_La_Tour_-_Magdalen_of_Night_Light_-_WGA12337

As a Freemason, I see Freemasonry everywhere and find the concepts housed within almost every genre – fine arts (drama, oil paintings, etc.), science fiction, philosophy, fantasy writings, and many movies. Walking through an art museum, one may find the aspect of a ritual here, or a teaching there. Many Renaissance and Baroque painters styled their subjects in familiar Masonic situations. In writing, I find Freemasonry in Asimov, Le Guin,  Pullman, L’Engle, and Zelazny, as well as in various philosophies like Pythagoras, Plutarch, and Seneca. Reading autobiographies of people like the Founding Fathers (United States), provides some clarity in the type of “enlightened mind” that feeds a Freemasonic soul.

Movies are always fascinating to watch through a Masonic lens. Movies such as “The Adjustment Bureau,” “Inception,” The-Matrix“The Matrix,” and “I, Robot” capture the challenging questions of reality and what is the perfection of humanity.  In music, one can explore Mozart’s “Magic Flute” and Holst’s “The Planets” to find how music can be influenced by a Masonic mind. Any artistic medium that addresses the larger questions of life, why are we here, and how can we find meaning, speak to the Freemason who is seeking to add more to their Masonic work.

Beware of those authors who sensationalize Freemasonry. If it sounds too good to be true, it generally is. That is equally true of Freemasonry writings founded in speculation and falsehoods. There is much speculation without much fact, and while Freemasons are speculative, they are also rooted in truth, nature, and science.

That said, the arts are wonderful places to explore the concepts contained within Freemasonry and help broaden the minds of those seeking more of life. The secrets of Freemasonry are all around us and we have only to open our senses to find the way.

 

Know Thyself: The Ship of Thieves

Know Thyself: The Ship of Thieves

“I am not the person I was.” We hear that a lot, especially when it comes to growing older and, one hopes, wiser. Indeed, we’re not the same person we were. Over the course of time, our cells die, regenerate, add, delete, change, morph, and eventually we have all new cells. But we retain our name, our memories, our lives. Are we not the same person?

One would argue that of course we are. Or are we? Really?

We cling to our identities like dryer sheets to hot cotton shirts. In our minds, we are who we always have been. We are that twelve-year-old child who swam in the lake as well as that adult who had their first job in fast food. We remember events, creations, or possessions and claim them to be ours.

Conversely, we claim our “self” to exist because of those things. We do not change, or if we do, it is at a glacial pace. We affix our identity in time and space, and like an astronaut, place a flag on it and proclaim it to be ours, to be “true” identity: knowing who we are.Theseus_Helene_Staatliche_Antikensammlungen_2309_n2

In a recent conversation with a fellow Mason, I was discussing the Ship of Theseus. The paradox is quickly explained in this video: The Paradox of the Ship of Theseus. In essence, the question is this: at what point does the ship cease to become Theseus’ ship and become something else?

If we take one plank from the ship and replace it, we generally can agree that the ship is still Theseus’ ship. At what point, however, do you fix enough broken pieces that the ship becomes something else? My colleague was convinced that the ship remained and always remained Theseus’ ship. For him, the idea of identity stays with the generally recognized “thing” even if the sum of its parts is not original.

Conversely, the argument is this: if I am a thief, and I slowly steal the pieces of Theseus’ ship, replace them with identical parts,  take the original parts, and put them together in my backyard, who has the ship of Theseus? The original owner, or me?

My friend said that the original owner did. I disagree. If I take a painting from the Louvre, and replace it with an identical painting, and everyone recognizes it as the “painting,” who has the “real” painting? In my colleague’s eyes, then, have I really stolen anything?

identityI contend that I have, if nothing else, I have stolen the certainty of the Ship of Theseus. I have stolen, or potentially stolen, the idea of the ship. But these painful musings do have a purpose: they help us work out our identity – the answers to the question of: Who am I?

A brilliant article on this is found on Brainpickings. I would encourage you to watch the other short videos on this site: not only is the one on Who Am I thought-provoking, but there are links to life’s other huge questions. How do I know I exist? What is the Nature of Reality? But, I digress.

The question is, at what point is our self no longer “us?” Is it when all the cells in our body have replaced themselves? What about new neural pathways or brain cells? If we replace a leg or arm or heart, are we the same person? 

Freemasons live by an adage of “Know Thyself,” which also adorned the Oracle of Delphi  at the Temple of Apollo. We must first understand what it is that makes up our “self” and when does that “self” become something else. I think this is a life long exploration and, since the self is constantly undergoing change, are we always who we were? Perhaps not.

But then, where did “we” go? Does our identity persist? If it does so, how? What makes us, us?fingerprint

I asked my fellow Mason about clones, which sent us down an entirely different path, discussing identical twins, and the like. Does time make a difference? If a plank is rotten on Theseus’ ship, and it is replaced, does that make identity linger, as opposed to replacing a “new” plank? If I change my mind about how I feel about something, am I still the same person? What if I create new habits? What then?

We are ever seeking to understand our true natures; yet, our true nature is ever-changing. Freemasonry teaches us about the cycles of life, death, rebirth, nature. and science. It teaches us all of Life’s Mysteries. If stagnation is death and change is life, how can we ever be the same person moment to moment? Perhaps that is the mystery that we must ever follow: a constant, persistent discovery of who we are, and what we are doing.

Eritque Craticula Usque ad Tenebras

Eritque Craticula Usque ad Tenebras

The precipice of Winter. The hollow wind of Autumn. We humans are always on the edge of something. In this case, we are on the edge of seasonal change. As we slip from the warm days of Summer into the chillier nights of Autumn, we sense that change is imminent. We are on the edge, slipping from one day to the next, seasons rushing by in a flowing, ever changing stream. A stream, I must add, upon which we are always standing on the edge.

Nature teaches us a great deal of how to be in the world; most of the time, we just choose not to listen. Cement jungles are no place for the breath of the Green Man or the dance of a water nymph. Yet, Nature finds a way to express herself. In Traditional Chinese Medicine, this is expressed as Yin and Yang. A Taoist concept, everything contains Yin and Yang. Yin and Yang are two opposite yet complementary energies. Although they are opposite in their individual qualities and nature, they are interdependent. They are never separate and cannot exist without one another. The hard Yang of the cement contains in it air and space, Yin, in which it yields to the grass growing in its cracks. The meadow is dotted with hard boulders, unyielding and yet grounding to the lush, loamy soil.

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The traditional translation of Yin-Yang is Dark-Bright, which in turn translate to the traditional Chinese icon we see for it – two tear drops, intertwined, with a dot of the other deep in their bellies. Saying they are opposites is a faint allusion to their true natures. They are complex and rich for as simple as they appear. Both are archetypes and ideals, where simple human words are inadequate modifiers. They may be translated as “the shady side of the mountain (yin)” and “the sunny side of the mountain (yang).” Yin may also indicate the feminine, the moon, softness, passivity, sinister, darkness, overcast, or even treacherous. Yang, the “opposite” indicates masculine, the sun, hardness, assertiveness, open, overt, relief, light, and positivity.” There is always a bit of one in the other, a taste which makes them less opposite and more like polarities. Neither is good or bad, they just exist; intertwined for eternity in a dance of possession.

Chapter 42 of the Tao Te Ching (about 500 B.C.E. by Lao Tzu) is where the duality and Yin-Yang are found:

“The Way gave birth to unity,
Unity gave birth to duality,
Duality gave birth to trinity,
Trinity gave birth to the myriad creatures.
The myriad creatures bear yin on their backs and embrace yang in their bosoms.

They neutralize these vapors
and thereby achieve harmony.”

This may be interpreted that while the Way (Tao) gave birth to all of material life, it is contained within that life in the form of this duality. Thus, all matter, of animal, plant, or mineral contains yin and yang. All of Nature contains within it opposing truths, a constant tug of each end of the living spectrum. Being of Nature, we should be intimately at ease with the duality of our natures, right?

260px-Yin_yang.svg

Relative and absolute. We see absolute as our eternal goal – absolute truth. Is this not what the philosopher strives to attain? Is this not what the Freemason seeks? Absolute is the Truth which we hold as dearest, that which give us “rightness” of whatever we are understanding. Yet, relativity is important to our personal lives. We make judgments and choices about the relative Truths we perceive with our senses every day. How does that green shirt go with those pink pants? Does the omelet need more salt? Are we thirsty? These are truths, however small, in which we are always seeking answers and using our senses, our knowledge of duality, to provide answers. We are always on the edge, wondering if we are being deceived, somehow, by falsehood and ignorance. Curiosity is a sword to slay our own ignorance. Curiosity is not sheathed in ego.

The philosopher sees the duality in the people and situations around him. We recognize that there may be two sides to a situation: yours and mine, his and hers, etc. Without this sharing, we cannot see more Truth. We have to stand on the edge of reality, with another human being, and accept that this truth might fill in our blanks. Once we let judgement of Truth go, there is vast chasm in front of us. It is in recognizing duality that the pieces start to come together. Unity. We realize that we cannot have the whole picture. We may not ever have the absolute truth; yet, we may have relative truth to share. In heaps and bounds.

Thus, we are always on the edge of true understanding. Of knowledge. Of peace. Thus, perhaps we are always at an equinox within our natures. Halfway to Darkness. Halfway to Light. Eritque craticula usque ad lucem ac tenebras. A motto of change? A reminder of being on the edge? Perhaps we need not be so afraid of the darkness and the change, go out into nature, and learn what living really means. We can find Nature in everyone we meet, sharing in a brief bit of harmony by seeking to understand. Enjoy this Equinox, with balance and joy, understanding that the world will keep turning, seeking balance and yet, always on the edge. The Darkness is coming. So is the Light.

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Stoic about Time

Stoic about Time

“True happiness is to enjoy the present, without anxious dependence upon the future, not to amuse ourselves with either hopes or fears but to rest satisfied with what we have, which is sufficient, for he that is so wants nothing. The greatest blessings of mankind are within us and within our reach. A wise man is content with his lot, whatever it may be, without wishing for what he has not.”  – Seneca

In a recent Masonic Philosophical Society meeting, we discussed the likeness of Stoicism to Freemasonry. Seneca, Zeno, Epictetus, and Marcus Aurelius all took center stage. It was a lively discussion and the argument that Stoicism and Freemasonry are the same was extremely compelling. As I always do, I went on my own journey to rediscover what I had learned in school about the Stoics; with what I knew about Freemasonry, I felt that I was well armed to learn some new ways of looking at the Stoics.

I first went to TED Talks, where I always find a wealth of great ideas and food for further thought. There is an excellent animated video on the Stoics, by Massimo Pigliucci, entitled The Philosophy of Stoicism. It’s a very well done quick course on the Stoics. Another excellent TED talk on Stoicism is by Ted Ferriss, “Why you should define your fears and not your goals.” This is about 13 minutes long and is a very practical look at why Stoicism is beneficial and how you can use it in daily life.

What was very interesting was a single quite that Ferriss said helped him change his life: “We suffer more in imagination than in reality.”

Huh, I thought. Of course we do. But why? Another recent reading foray brought me to brain_opener_free_0another idea: time. We humans understand time only superficially, as it applies to us. Our brains are wired to understand and extrapolate possible futures, opportunities missed in the past, and move our lives to live in synchronicity.

There are factions of large people, including myself at one point, who thought that “living in the moment” was the key to being happy. I now don’t think we’re wired that way.

In a recent article in the New York Times, author and professor of psychology Martin E.P. Seligman agrees. “We Aren’t Built to Live in the Moment” examines how our minds work and why. He and his co-authors have outlined this process in their book, “Homo Prospectus.” The article, and the book, are really discussing the philosophy of Stoicism to make it through life.

time5

Time. We are subjects of Time. 

What really solidified this for me was listening to a recent Radiolab episode, which was a repeat of their first season, discussing “Time.” In it, the two podcasters discussed the idea of time and living in the moment. Robert Krulwich takes his co-host on a journey of reason.

Our mind does not process data at the time it is created. Smell, sound, and light – these are all generated by something and transmitted over some distance to our surroundings, where we pick it up via our senses, and whereupon it is interpreted by our brains. This distance travel take… time. It is not instantaneous. Our minds process – speed is only a matter of relativity. Ergo, we are never experiencing the moment. We are always processing memories. And memories are always subject to misinterpretation.

It’s no wonder we fear. We cannot live in the moment and must always interpret the past to create possible futures. Truly, like we never really touch anything, due to the molecular distance between surfaces, all that we have is an interpretation of our surroundings, received and processed in past, to guide us in our futures. Spending the time to put emotion into it grounds it even future in “memory.”

aurelius

To pull ourselves out of time is impossible, and thus, living in the moment is impossible. Ergo, we need a tool to bring us around to dealing with these memories in such a way as to not freeze us in our tracks. We are brought back to, again, the wisdom of the Stoics. “A bad feeling is a commotion of the mind repugnant to reason, and against nature,” stated Zeno of Citium.

Our modern psychologists agree:

“Homo prospectus is too pragmatic to obsess on death for the same reason that he doesn’t dwell on the past: There’s nothing he can do about it. He became Homo sapiens by learning to see and shape his future, and he is wise enough to keep looking straight ahead.”

– From Homo Prospectus, by Martin E. P. Seligman, Peter Railton, Roy F. Baumeister, and Chandra Sripada

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.

Music and the Quadrivium

Music and the Quadrivium

Music is delivered to us via our sense of hearing, which when young hears a wider range than when we are older. Our mind processes the complex mathematical formulas of sound waves, and that processing, can affect our mood, thoughts, feelings, and memories. Music is found in all cultures, at all human times – humming, hitting things together, singing, instruments. We have found a way, through music, to sounds and words much more integral to our lives than mere language.

There are so many aspects of music that it is impossible to scratch even the surface here. In a recent conversation, I asked a Brother, proficient in music theory, playing music, and song, what he felt the most important aspect of music was. Without hesitation he said, “The perfect fifth.” I asked him to explain.

M_Octave_Fourth_FifthThe human mind likes consonance, or harmony in its music. We find our minds like notes to be evenly spaced, and those that are not are “out of tune.” The perfect fifth is considered the most consonant of musical intervals. However, the musical scale cannot, mathematically, work with all perfect fifths, up octaves and down. There must be adjustment, otherwise it sounds “off.” This equal  interval spacing, what we’re familiar with today, is called equal temperament. There are several tuning methods, and several types of equal temperaments. These differences come from how the octave is divided mathematically.

This brings us to The Well-Tempered Clavier. The Well-Tempered Clavier is a collection of two series of Preludes and Fugues in all major and minor keys, composed for solo keyboard by Johann Sebastian Bach. It is sometimes assumed that by “well-tempered” Bach intended equal temperament, the standard modern keyboard tuning which became popular after Bach’s death, but modern scholars suggest instead a form of well temperament. There is debate whether Bach meant a range of similar temperaments, perhaps even altered slightly in practice from piece to piece, or a single specific “well-tempered” solution for all purposes. There are 24 pairs of preludes and fugues, in each book (48 total) each representing the entire set of musical keys.

Johann Sebastian Bach

Johann Sebastian Bach (1685 – 1750), German musician and composer playing the organ, circa 1725. From a print in the British Museum. (Photo by Rischgitz/Getty Images)

This set of music is significant for a few reasons. The first is that it is really Bach’s catalogue of the styles and techniques of Bach’s day. It inspired many composers and it can be seen, in some ways, as a type of “color card” for music – not unlike the paint chip cards you find in a hardware store. The music exploits tuning methods, temperaments, and construction that Bach would have used on any keyboard instrument.


Interesting book on humankind and music here: The Singing Neanderthals: the Origins of Music, Language, Mind and Body by Steven Mithen. London: Weidenfeld & Nicholson, 2005. ISBN 0-297-64317-7 374 pp.

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.

The History of the All Seeing Eye

The History of the All Seeing Eye

What people in the U.S.A. commonly referred to as the “All Seeing Eye” is more appropriately called the “Eye of Providence.” No, not Rhode Island. This would be the more divine providence – the big guy watching over all of us. Or gal. Or it. Whichever you prefer.

The Eye of Providence is the idea that some divine force is watching over us all, sees our deeds and actions, and judges accordingly. The Eye is associated with the Judgement card of the Tarot: Alchemical texts of the 17th Century and Egypt.

While the Eye of Providence, as noted above, has from the 18th Century C.E. onward been associated with Christianity, the idea of an “all-seeing God” has been around for Millenia. What is called “The Eye of Horus” originally was known as the Wadjet Eye, for the goddess Wadjet.

EyeofHorus

The Eye of Horus

Wadjet, as many can read on the Internet and in several Egyptian Mythology books, was one of the oldest deities in Egypt and dates from the pre-dynastic period. She is associated with Lower Egypt as well as the papyrus. Her name symbolizes the color of blue/green – the color of the papyrus plant. She is nearly always associated with a cobra and is considered the protector of pharaohs and the ruling classes of Egypt.

She’s seen as the Goddess, which represents time, heaven, and hell, and she is an ardent protector, especially of children. Over the millennia, she has been merged with many other goddesses, such as Bast and her sister, Nekhebet, Goddess of Upper Egypt, who is shown as a vulture. Wadjet has also been associated with Buto, the city which first revered her – originally named Per-Wadjet.

According to Herodotus, in his Histories ( Herodotus, The Histories, ii 55, and vii 134), “The Egyptians were also the first to introduce solemn assemblies, processions, and litanies to the gods; of all which the Greeks were taught the use by them. It seems to me a sufficient proof of this that in Egypt these practices have been established from remote antiquity, while in Greece they are only recently known.” There is note of a Temple to Wadjet in Buto (Per-Wadjet) that had an Oracle in it; it was considered that the Greek practice of using Oracles was co-opted from the Egyptians who, as Herodotus states, “taught them in their use.” 

The Eye of Wadget

The Eye of Wadget

Originally, oracles were used to be able to link the individual to the divine. A worshiper would travel to the oracle with a very specific and important question relevant to their lives. Kings would consult oracles to strategize on war or gain insight on divine events which would influence their people, like famine or floods. Using auguries drawn from various animals innards, smoke, visions, the flight of doves, or other “symbols,” the oracle would define the upcoming events based on intuition and divine inspiration. Oracles were eventually replaced by priests and religious figures as a way to connect the individual with their god or goddess, and in a way be a conduit for the divine.

We humans have always been looking for a way to have some kind of communion with the mind of our Divine source, whether it is through other individuals, hallucinogens, runes, tarot, channelling, or simply study. We look for some higher source to tell us what we ought to do, what will help us be successful, happy, healthy, or free. In this case, I find the idea of the Eye of Wadjet to be a symbol that connects us to a dusty, mythic past with some vague idea of what it really meant.

We’ve gone from the protection of a goddess to the protection of a country or our ideals, or maybe even our prosperity. I think this is the most interesting thing in this: the symbols we have in our daily lives are historical treasures that have been modified as our cultures modify them. They come to reflect what, and how we think about the world.

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.