The Quadrivium
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.
Conclusion
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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