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:

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.

Trivium: Rhetoric

Trivium: Rhetoric

We’re back with the third part of the Trivium: Rhetoric.

Rhetoric is the art of persuasion through communications, either written or spoken. There are always two components to rhetoric – the rhetoric and the audience. Rhetoric’s aim is to make comparisons, evoke emotions, censure rivals, and convince their audience to switch a point of view. Rhetoric takes the form of speech, debate, music, story, play, movie, poem; nearly anything that can be written or spoken may be a piece of rhetoric. In fact, it may be the rhetoric that makes the art.

In the poem, The Road Not Taken, by Robert Frost, the author provides a brief insight into life’s travels:

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.

The rhetorical line of this poem is: “I took the one less traveled by / And that has made all the difference.” Frost has set a scene for us of decision, or indecision, and given us a glimpse into his thoughts, which may be our thoughts at any given moment. His work is convincing us that in order to perhaps make a difference in our lives, we should tread whether others have infrequently traveled.

When we talk about skilled negotiators, people with “charisma” and “charm,” we are really talking about the art of rhetoric. We use rhetoric in our everyday lives when we create a job resume, negotiate to buy a car, when we debate politics, or even when we are convincing a teenager to clean their room. We may do it every day, but do we really understand the finer points of rhetoric? It seems to be the pinnacle of the Trivium and the highest goal we can work toward in order to communicate our ideas with one another effectively.

A nod to this blog for providing the Cornelis Cort images.

Beethoven’s Last Work – Ode to Joy

Beethoven’s Last Work – Ode to Joy

As a classically trained musician, I often frame the way I think about the mysteries of the universe in terms of music. I love the quote of Einstein where he says, “I live my daydreams in music. I see my life in terms of music.” A world without music would be lifeless, silent, and depressing. Almost every moment in a person’s life is continually underscored by music — from birth to death, at weddings and other celebrations. The ancients were convinced that music could become internalized by the individual; the music influencing, as it were, the manner of our thoughts, feelings, and actions.  

Beethoven’s Ninth Symphony and Ode to Joy 

The “Ode to Joy” in Beethoven’s Ninth Symphony, first performed on May 7, 1824, is one of those musical treasures that invites me to dream, to turn within and to contemplate my mortal coil. The chorus was the finale in the “last work” that Beethoven ever composed.

The idea for “Ode to Joy,” and the words for the chorus, came to Beethoven in his early 20’s.  The famous poet Friedrich Schiller had written in 1785 an excessively cheerful drinking song, and Beethoven was creatively impressed to set the poem to music. He was the first major composer to include a chorus and vocal soloists in the last movement of a symphony. In the chorus, we hear the joy of a man who, through suffering and compassion, embraced all.  

It is such a glorious moment. So shocking. So hopeful: even though we know the violence and burdens of the world are out there surrounding us, waiting for us. The joyful lyrics ring true the message of uniting all people in universal brotherhood. Beethoven’s little introduction to the poem also mentions not dwelling on sad things but being happy instead.

The last words direct themselves to heaven, and in some amazing m34481589172_8d767a068a_o 1usical craftsmanship, the movement ends with a sublime message:

Be embraced, ye millions!
For the universe, this kiss!
Brothers – above the canopy of stars
A loving Father surely dwells.

Millions, do you fall upon our knees?
Do you sense the Creator, world?
Seek him above the canopy of stars!
Surely he dwells above the stars!

Just imagine that Beethoven was fully deaf and writing about being happy!  He was acquainted with a deep compassion that swept through him for others in a destitute situation. He dearly loved mankind and his skill as a master musician provided the means to reveal to us the hidden nature of the world within us, touching our souls.  Could this message possibly be a metaphor in itself? Who is really hard of hearing — him or us?

Beethoven’s music has been said to awaken compassion and the desire for universal brotherhood.  Because of the feelings contained in Beethoven’s music, his works can stir crowds to higher levels of realization. One wonders what power graced Beethoven that he could write such music. His joyful message still has the ability to lift the souls of all who hear it. How does this piece or any music tend to shape and mold us?  I have wondered that so many times and questioned myself. I have tried to touch the heart of the composer; Tried to turn my life into an “Ode to Joy.”352228023_28f8dd197a_o

Ancient Philosophers and the Mysteries of Music

David Tame, in his excellent book on The Secret Power of Music describes how a select group of composers have been able to show us what the ancient philosophers knew about the mysteries of music:

Pythagoras’ understanding of music was far more than a merely materialistic, academic one, and such an understanding is lamentably rare today. Yet we discover something of this timeless flame of ageless wisdom preserved in that small minority of musicians who still today have combined academic knowledge and the practical experience of music with a genuine and earnest inner spiritual development.

A Modern Take on Immortal Beloved

I consider Beethoven to be among this elite group.  In the 90’s, there was a film that came out about Beethoven’s life called “Immortal Beloved.”  Critics disagree with much of the movie’s historical contents, but there is one scene that took my breath away. I have pondered the meaning of it ever since. 

It begins by showing Beethoven standing before the orchestra while he is conducting the finale of the Ninth Symphony. He finds himself thinking back to a childhood memory of running away from his abusive father. The film draws us in as this young boy runs through the woods to escape the awful beatings that have plagued him all his life. His journey leads him to a lake where he wades in to float on his back to look up at the stars. The whole scene is illumined by a radiant full moon. 

Suddenly, we are transported to a change of perspective as the camera pans back.  The lake becomes a reflection of the sky, making Beethoven look as if he is suspended amid the stars until eventually his young body has merged with the heavens. He finds himself in his own universe, yet above the pain and uncertainty of his troubled adolescence. From this, we are left to wonder if Beethoven was truly alone and if his immortal beloved was music: his music. 

An Ode to Joy and Freemasonry 

There are many times that I have given myself over to Beethoven’s “Ode to Joy” masterpiece.  I bathe in the sounds, leave the troubles of my world behind and allow the joy to slowly purify me.  Freemasonry is much like any beautiful well-crafted piece of music in that the ceremonies and rituals give inspiration and perspective.  While the millions of stars in the sky may make us feel small in comparison, Freemasonry teaches that we are capable of so much.  We are truly a significant part of this very same Universe, and we have within us capacity to behold a sacred moment of transcendent power.


Footnote:  Some say that Beethoven was a Freemason, although there is a lack of absolute evidence to that fact. Further exploration of this theory can be found in the article:

Trivium: Logic or Dialectica

Trivium: Logic or Dialectica

Today’s theme is Logic, or as seen the picture here, Dialectica. As the New Catholic Encyclopedia states, “Logic is the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness, consistency, and validity in those processes. The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference.”


Aristotle is generally considered the “Founder of Logic,” although many others before him put themselves to the task of thinking about how we think. One of these, Zeno of Elea, was considered to have developed reductio ad absurdum, or the method of indirect proof. If something cannot be both true and false, then an argument can be made from reducing the statement to the absurd.

For example, “The earth is round. The earth is not flat. If it were flat, people would fall off the edge.” Since the earth cannot be both round and flat, the statement is true.

Another good example, from Wikipedia (Yes, I know. Don’t judge.), reads:

xenophanes1The ‘reduction to the absurd’ technique is used throughout Greek philosophy, beginning with Presocratic philosophers. The earliest Greek example of a reductio argument is supposedly in fragments of a satirical poem attributed to Xenophanes of Colophon (c.570 – c.475 BC). Criticizing Homer’s attribution of human faults to the gods, he says that humans also believe that the gods’ bodies have human form. But if horses and oxen could draw, they would draw the gods with horse and oxen bodies. The gods can’t have both forms, so this is a contradiction. Therefore, the attribution of other human characteristics to the gods, such as human faults, is also false.

logic2Logic is mental training: once the words and language have been developed, we can think through situations, problems, and reason our way to clear conclusions that work in conjunction with the natural world. For example, if we seekers of Truth are to grow and understand how a symbol might be applied to our everyday lives, we need to understand not only what the symbol is, but how it works in the world around us, how nature employs it.

Logic utilizes the senses but the connection must be made in the mind to form usable conclusions. Logic is, to me, a fundamental aspect of any human being’s career, if one expects to progress through life and learn. We can learn Logic in the modern age via University, but this really teaches us about Logic, not how to employ our logical mind. It seems that only through discourse, or dialectica, are we able to truly develop logical thought processes and reasoning at a higher level. Masonic Philosophical Society, anyone?


As a side note, the Catholic Encyclopedia on has a very good article on Logic and its history. It’s concise and certainly doesn’t include manuscripts; I would encourage anyone with a keen interest in Logic or Dialectica to read Aristotle but also some of the pre-Socractic philosophers, whence a great deal of our modern ideas of logic come.