The study of mathematics here at St. John’s begins with Euclid’s Elements, the wonderfully inventive book that takes us from the simplest beginnings of geometry to the highly complicated construction of five Platonic solids. Studying Euclid engages us in an activity that brings geometrical objects into being even as we recognize them for what they already are, eternal and unchanging, already possessing all the properties that will ever be revealed about them. When we repeat the steps of Euclid’s propositions, we take a journey of the imagination to reflect on the origin, nature, and elements of a line, a circle, a construction, a proof. The truth of each proposition comes to us (if it does) through the application of reason to our imagination.
This activity, trying to understand origins and elements, lies at the heart of all our discussions. Now it is true that we cannot always start at the beginning as Euclid did, with first principles and elements, building up our understanding from there. Nonetheless, once we have had this experience with Euclid, we imagine that we can work our way back from the appearances, from the phenomena, from the opinions of mankind, to the origins, principles, and elements that underlie what we are hearing, reading, and seeing with our senses, to uncover their origins, foundations, and elements. If we cannot start at the beginning, we must instead work to recover that beginning and uncover the elements of the object we are studying.
This is why we sometimes call our discussions “elemental” or “elementary:” not because what we seek to learn is simple or easy to grasp, but because we are always looking to uncover what lies beneath or behind what we think we are seeing. We are seeking to find a truth about the object of our study, just as we have come to see the truth of a Euclidian proposition through the application of intellect and imagination to the original, elementary building blocks. In all cases, we are searching out either the elements or the origins of the world in which we live.
Consider the kinds of elemental questions we might ask of one of the early classic texts: Homer’s Iliad.
Achilles rages. Why is he angry? What lies behind his rage? Is it natural or not? Is it justified? Can it be controlled? If in the end his anger is resolved and some sense of humanity restored, how did this happen and why?
“The will of Zeus was moving toward its end.” What has Zeus’s will got to do with Achilles’s wrath? Does that will control the fate of the warriors? Who are these gods and do they determine the outcomes of battle or do they serve as poetic metaphors for deathless forces we cannot control or comprehend?
In Plato’s Republic, Socrates builds a case for justice based upon a “noble lie.” Why does he do that? Why does he not speak of it as a truth? Or what keeps us from hearing a truth that it must come to us camouflaged? And later, he uses images, dramas, and myths, all metaphorical devices to help us understand. Are these helpful, and why? Why isn’t an appeal to reason sufficient? Why the invocation to the gods?
Why does Jesus speak in parables, for that matter? Or God from out of the whirlwind, when responding to Job?
What do these figures, human and divine, know about human nature that cause them to reach us in what appear to be such indirect ways?
We wish to understand what it means to be human, and we want to know about the world we inhabit. What are our origins? What was in the beginning? How do we live and grow? How do we satisfy our needs? How ought we to express our love and sympathy? How can we become better and wiser? How can we use our talents to make this a better world? How ought we to treat our planet and use the resources nature has provided?
We need to know something about ourselves and our world to answer these questions. We need to uncover a truth we can recognize for what it is—a helpful way-station and landing place on our path to a deeper truth. And on it goes, delving deeper into foundations, looking for the elements of the construction we call our world.
This quest for elements is the best way we humans have of getting to the roots of things, sorting out the world’s appearances, and making sense of our experience. And working at this together, in a community dedicated to learning, is one of the best services we can do, both for our own souls and for those of our fellow seekers.
This essay originally appeared on SignPosts for Liberal Education (February 2016) and is republished here with gracious permission.
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