We didn’t get chickens, everything needed to slow down, so I put the brakes on a lot of the work I’m doing to rest. Winter is still holding on with some cold days, hopefully this week will be the end of it, I know the sun will reinvigorate me. The little princess is growing up fast, now able to roll over and starting solid food. Here is a photo of a tree in my woods, the marking start about 12 feet in the air, I don’t know if that’s wood peckers or high climbing beavers. My notes on the quadrivium also took a lot of energy, it felt more like studying where normally I’d describe what I do as interpreting.
Last week I mentioned Trivium and Quadrivium as an education in liberal arts, it began in Plato’s Republic where the Quadrivium was explained. I’ll be covering book seven in the Republic, verses 521 through 531. It is a conversation between Socrates and Glaucon, here and in the entire Republic they are discussing how to make a great city. The quadrivium, arithmetic, geometry, music, and astronomy are the subjects that should be taught in their fictional city to make people better. Note the term quadrivium was not used by Plato, but coined later.
We start by discussing the problem of ruling, solved because “we’ll be giving just orders to just people”, that leads into the problem of how to make just people. Socrates says, “turning a soul from a day that is a kind of night” is true philosophy. That is the perspective he will use when searching for subjects, how to lift up a soul. Education “mustn’t be useless to warlike men”. If people are spending all their time learning what has no utility, then an army will easily wipe them out and all that studying will be for not.
They had already discussed educating people on music and poetry since “it’s rhythms gave them a certain rhythmical quality: and it’s stories, whether fictional or nearer the truth cultivated other habits akin to these.” There’s an argument for reading fiction, but they’re looking for more, settling on “the inconsequential matter of distinguishing the one, the two, and the three,” number and calculation; what we call arithmetic. Since they’re using war as their standard, there is a story about a soldier in the Trojan war counting the enemy ships since no one had done it and that Agamemnon, leader of the Greeks, if he truly couldn’t count, didn’t even know how many feet he had. Being able to count would lead one to know if their army is bigger than another and how they should be positioned or maneuvered.
Socrates is fixated on ideas that summon us into being, saying, “if each is one, and both two, the soul will understand that the two are separate.” This may seem small to those who know how to count, but it is a different world to know you have two feet and can control each one. Alternatively the whole universe would be an amalgamation with no way to divide. Arithmetic is valuable as “It leads the soul forcibly upward and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies.”
The subject that comes after numbers is geometry, “insofar as it pertains to war, when it comes to setting up camp, occupying a region, concentrating troops, deploying them, or with regard to any of the other formations an army adopts in battle or on the march, it makes all the difference whether someone is a geometer or not.” I can attest to using geometry with maps, and being able to find an unknown location by calculating with geometric lessons. To quote Socrates, “geometry is knowledge of what always is. Then it draws the soul towards truth and produces philosophic thought by directing upwards what we now wrongly direct downwards.”
Since we have numbers and numbers on a plane make geometry, the next step would be the study of how these shapes move with astronomy. Movement is change of location over time, this would give better awareness of the seasons, months, and years. Appropriate for a farmer or navigator. “Astronomy compels the soul to look upwards and leads it from things here to things there.” This is a good metaphor for what I discuss on the show, we attempt to look up, for the good, distinguished from the lesser. For as Socrates said, “it’s very difficult to realize that in every soul there is an instrument that is purified and rekindled by such subjects when it has been blinded and destroyed by other ways of life.”
The final subject Plato gets into is harmonics, what we label music, for as the eyes fastens on astronomical motions, so the ear fastens on harmonic ones. The book discusses people attempting to find smaller intervals between notes, but they put ears before understanding. Harmonics is about numerical relationships. In an octave, the two notes next to each other don’t sound well together. The relation of notes might jump to a fifth, then down to the third before returning to the key being played. Different keys create relationships with different notes.
There is my explanation of Plato’s quadrivium.
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