Saturday, July 23, 2022

What's a Liberal Art and Where Can I Buy One: The Quadrivium

                                            

The Quadrivium

This is part 2/2. Find Part One here.

Last week(ish) we discussed what a liberal art was and introduced the three liberal arts that make up the Trivium. These three arts, grammar, logic, and rhetoric, are the arts that concern the uniquely human powers of reason and speech. Today we'll look at the remaining four arts that make up a group called the Quadrivium. 

The four arts of the quadrivium are Arithmetic, Geometry, Music, and Astronomy. At first glance these may not seem like they're natural companions, well at the very least music seems to be an outlier, but it makes more sense when we understand that the arts of the quadrivium are the arts that combine human reason with number. These are my weakest subjects. I'm a poor student of them for many reasons, not the least of which are my own moral failings. I bring this up because, while I know what they are, they're a bit more difficult for me to explain than the arts of the trivium. 

The Four Arts

Arithmetic

So, let's get this over with: Arithmetic is the study of quantity (number) itself. It includes concepts as basic as even and odd, more and less, counting. It becomes more complex from there. Basically everything we do with quantity stems from the arithmetical art. Addition. subtraction, multiplication, division, fractions, decimals, variables, all of these and their relations are studied in arithmetic. Arithmetic can be as simple as counting and as complex as calculus. Arithmetic is usually considered to be the first and foundational member of the quadrivium as all the others use number as the foundations for their respective arts. 

Geometry


Next is Geometry. Geometry is the art that studies number in space, not the black void of space, but the


concept of space and spatial relations. This is the math with the shapes. Geometry is pretty abstract. It's interested in understanding figures. What are the different shapes? What are their parts? What rules govern their construction? Geometry was pretty set as a discipline for thousands of years. The Greek thinker Euclid literally wrote the book on the subject. There have been more recent developments in the field that I am absolutely unqualified to comment on given my one and only ever 'C' that I won in high school Geometry. However I do know that Descartes, the Renaissance thinker, wrote enough on Geometry that they named a branch after him (Cartesian Geometry aka analytic geometry), and apparently some mathematicians figured out how to break the rules set down by Euclid, so now non-Euclidian geometry is a thing. If anyone's interested in that.

Music

The third of the arts is Music! Wait, you say, these arts have been all about math. There's been numbers and rulers, what can music have to do with that? The way we think about music nowadays, as being very arty and about self-expression doesn't have a lot to do with how music actually works from a compositional standpoint. Music is the study of how number relates to time. Western music has seven notes in eight octaves. Music seeks to take these notes and, in varying combinations, at varying speeds, for varying lengths, create harmony, or sounds that are beautiful.

Astronomy

The last of these is Astronomy. This art is the study of number in both space and time. It looks at how the stars and planetary bodies move. It considers their relationship to one another and to the Earth.


Astronomy gives us our ability to create human notions of time (days, weeks, months, years). In the ancient and medieval world astronomy was studied for its own sake as much as it was studied for its uses in navigation and agriculture. Really until the Renaissance the realm of the stars and planets was considered a place of perfection. The Earth was fallen and broken, but the realm of the heavens was steady, unchanging, and uncorrupted. A lot of time was spent on astronomy rather than on the other sciences precisely because of this belief. Why would you study the mating habits of tree frogs when you could look at a glorious universe unmarred by sin? Of course with advancements in our ability to actually see the cosmos we've come to realize that some of our assumptions about its unchanging nature and indeed ats basic organization were fundamentally flawed. We've also come to realize that there's a great depth and beauty to be found by examining our own world. However, as humans we're still drawn to the stars.

Astronomy has become a difficult art for liberal arts enthusiasts to deal with. Some think that it should now be excluded. Others think that it should be taught with the other sciences like physics, biology, and chemistry. I think that I fall into the latter category, especially when it comes to physics. I think that quantum physics in particular has shown us more and more that the nature of the universe is more complex and potentially less material than we ever imagined. It may be true that the cosmos are not perfect and unchanging, that they cannot be understood in the mind alone, but as we learn more about just how much we don't know about the nature of reality I can't help but wonder if there was more wisdom than we realize in the old ways of thinking. 

Conclusion

The three arts of the Trivium are inherently linguistic arts. The Quadrivium seems to be their opposite in every way. They're incredibly abstract. They certainly have practical uses and applications, but at their core they exist in an ideal world and lose something when they're translated into material reality. The arts of the Trivium, on the other hand, are inherently concrete arts. Human language is a concrete thing. Grammar has to apply to an actual language for it to mean anything. Rhetoric must make use of the words that exist within a specific language and combine and play with them in ways that still make sense. The Trivium lives and dies in human minds and tongues. The arts in the Quadrivium can live in the mind (including the art of astronomy where men decided what the rules of the universe were in abstract and then tried to make what they saw fit their theory)

However, I think that the Trivium and the Quadrivium aren't really so different. I think at bottom they're both linguistic arts. The Trivium deals with human language. The Quadrivium deals with the language of the universe, the language of God, if you will. These arts seek a truth that is inherently more solid and objective than the arts of the Trivium. The Trivium, when used appropriately, tells the truth of what's in a human mind, a human heart, and this is a great and valuable thing. The arts of the Quadrivium tell the truth of what objective reality is. The Quadrivium take us outside of ourselves and show us something objective and solid. 

There's a lot that can be said about how the truths that the quadrivium reveal are more real when they're abstracted and not when we try to use them in our material reality. I'll just leave you with the thought that the realm of the spirit that can be reached by the human mind at the highest levels is a place of great order and perfection, and by peeking behind the curtain of the material world we can bring the lessons we learn there back to do great and wonderful things, even if they pale in comparison. 

Sources

If you're interested in learning more about the seven Liberal Arts and the Quadrivium in particular I recommend these sources.

  • The Marriage of Philology and Mercury by Martianus Capella. This is a fun resource because Capella explains what the arts are in an allegory. The character Philology, or the human intellectual life, marries the god Mercury. The seven Liberal Arts visit her on her wedding day to explain their gifts and to offer themselves to her as her handmaidens.
  • Institutions of Divine and Secular Learning and On The Soul by Cassiodorus. This one is nice because he provides pretty small descriptions that are easy to understand.
  • Etymologies by Isidore of Seville. This one is longer and more complex for those really interested in diving in. 

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