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

Whence Came You? Recent Scientific Challenges To The Big Bang Theory

Whence Came You? Recent Scientific Challenges To The Big Bang Theory

From time immemorial, the thinking man has pondered the origins of the Universe and his role in the cosmos. Scientists in the early 20th century brought forth The Big Bang Theory to explain the creation of the Universe. Recent scientific research, however, provides compelling evidence that the age of the Universe could be infinite. Was there a singular starting point of the Universe? What if the Universe has existed forever?

Understanding The Big Bang Theory

The Big Bang Theory postulates that our Universe did have a definite beginning. Prior to that, there was nothing. After that moment, there was something: our Universe. According to this theory, our Universe came into existence as a “singularity” approximately 13.7 billion years ago.

Singularities are thought to exist at the core of black holes, which are areas of intense gravitational pressure. The pressure inside a black hole is thought to be so intense that finite matter is actually smashed into infinite density. The Big Bang Theory argues that our known Universe began as an infinitely small, hot and dense singularity.

This is an illustration showing the cosmic epochs of the Universe.Then there was an explosion at which time the singularity inflated and then cooled. The Universe changed over millions of years from something tiny and very hot to the Universe’s current size and temperature. And the Universe has continued to expand and cool throughout history.  Thus, the Big Bang Theory provided a scientifically-based explanation of what happened at the very beginning of our universe continuing until our current time.  

Evidence for The Big Bang Theory

In the 1920s, Edwin Hubble studied distant spirals in the deep skies, measuring the individual stars within the spirals and HubbleandTelescopedetermining the brightness of each star. By combining these measurements with their movement and brightness, Hubble deduced that the Universe was expanding from a once compacted state.

If the Universe was smaller and denser in the past, The Big Bang Theory argues that the Universe expanded from a smaller state to reach its current point. In the 1940s George Gamow added to the theory by postulating that if the Universe was smaller it must also have been hotter. Defined by its wavelength, radiation’s energy and temperature stretch as the fabric of space expands. Thus, if the Universe were smaller, radiation wavelengths were condensed and created a higher temperature.

Extrapolating backwards, there is a point reached when radiation becomes too energetic to form neutral atoms. In the 1960s, Arno Penzias and Robert Woodrow Wilson experimented with the Holmdel Horn Antenna, built to detect radio waves bounced off Echo balloon satellites. When Penzias and Wilson reduced their data, they discovered a persistent low, steady and mysterious noise. Certain that the radiation they detected on a wavelength of 7.35 centimeters did not come from the Earth, the Sun, or the Milky Way Galaxy, they eventually postulated that it was the radiation left over from an explosion that filled the Universe at the beginning of its existence. They termed this remanent energy, Cosmic Microwave Background Radiation. Their work helped to cement the wide-scale acceptance of The Big Bang Theory.

Recent Scientific Challenges to The Big Bang Theory

Modern scientific research demonstrates compelling evidence against the concept of a singularity as the beginning of the Universe. Astrophysicist Ethan Siegel argues that instead of the singularity point, the Universe transitioned from a prior state, not filled with matter, antimatter, radiation, neutrinos, etc. Undergoing a period of Cosmic Inflation, this pre-Universe was filled with a form of energy inherent to space itself and expanded slowly without a change in energy or temperature. In the phase of Cosmic Inflation, there was an exponential expansion that stretched the Universe flat and wiped out any ultra-massive relic particles and topological defects. Ending approximately 13.8 billion years ago, Cosmic Inflation set up the conditions that lead to a Big Bang event, thus creating our known observable Universe. This theory adds the fascinating possibility that we may be living in a multiverse and our observable Universe is just one of many Universes.

In February of 2015, two physicists, Ahmed Farag Ali, Professor at Benha University in Egypt, and Saurya Das, Professor at University of Lethbridge in Alberta, Canada, pub440px-CMB_Timeline300_no_WMAPlished “Cosmology from Quantum Potential.” Their work proposes a “corrected” version of Einstein’s Theory of General Relativity and demonstrates inaccuracies in the current Big Bang Theory.  In the new formulation, the Universe did not originate from an infinitely dense singularity. In fact, the “theory suggests that the age of the universe could be infinite” according to the study co-author Saurya Das.

Moreover, Das and Ali’s research utilized Bohemian Mechanics to reconcile two of the most dominant theories in physics, Quantum Mechanics and General Relativity. Using this form of quantum theory, the researchers calculated a small correction term that could be included in Einstein’s Theory of General Relativity. In the new formulation, there is no zero-point singularity, and the Universe is infinitely old.

Destroying Ignorance

The Masonic Philosophical Society was established with the primary ambition to destroy ignorance. Which begs the question, “What is ignorance?” Perhaps ignorance is accepting what others tell you or what you have been taught without qucosmologyestioning. Instead of blindly accepting a concept like The Big Bang Theory as fact, Masonry teaches an individual to question why we believe something, to do our own research, and to consider other points of view. By questioning our preconceived notions, we open new doors of insight into how our world works and our role in the cosmos.