With the resurgence of classical education, the disciplines of the trivium are commonly mentioned and discussed in articles, conferences, school literature, and curriculum. Less common, however, is discussion of the quadrivium and how it applies to education. Unfortunately, it has lagged behind despite the fact that together these seven disciplines make up the seven liberal arts that were intended to cultivate liberated or free people.
The word quadrivium literally means “the four ways” or the “meeting of four roads”—hence the name of this column: a meeting point for discussion of arithmetic, geometry, music (harmonia), and astronomy (cosmology) as liberal arts. We will seek to define disciplines, concepts, and terms, cover the history of the disciplines, and discuss resources and fascinating ideas. We will explore the quadrivium with the desire to inspire interest and interaction, cultivate understanding, and encourage practice.
From a Christian perspective, one reason to study the quadrivium concerns knowledge of the Most High God. Paul writes in Romans 1:20 that God has revealed himself through His creation. “For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made.” Arithmetic, geometry, harmonia, and cosmology help to explain concepts, relationships, and design in the created order thereby revealing aspects of the nature and character of God. More about that later.
In his Discourse Against the Pagans, 40, Athanasius says:
“It is right that creation should exist as he made it and as we see it happening, because this is his will, which no one would deny. For if the movement of the universe were irrational, and the world rolled on in random fashion, one would be justified is disbelieving what we may say. But if the world is founded on reason, wisdom and science, and is filled with orderly beauty, then it must owe its origin and order to none other than the Word of God.”
Orderly beauty fills creation from the movement of seasons, the physics of aerodynamics, the effect of glorious music, the virtue of a story, architecture, film, or design, and the interaction of seemingly disparate disciplines. As the Wisdom of Solomon asserts, “Thou hast ordered all things in measure and number and weight.” If the world works according to His pleasure because of the orderliness of creation and this order is a reflection of “His divine attributes,” then the quadrivium gives categories and a means to talk about not only creation but also her Creator.
The quadrivium gives categories and a means to talk about not only creation but also her Creator.
Arithmetic is not just formulas and numbers, but rather an exploration of the idea, concept, and meaning of number. What does “one” imply? What is a triangle number as compared to a square number? What are the unique attributes of numbers and the implications of them? When math becomes solely utilitarian or based on commerce, we lose the symbolic meaning of numbers.
Geometry is also not just formulas and shapes. Euclid’s Elements presents the ideas of figures, shapes and angles as a series of relationships and ratios. From the basics of numbers, Euclid moves to numbers in correlation to one another by teaching the concepts and reasons why those relationships work the way they do. This understanding becomes something that can be applied to moving an angle on a piece of paper or plotting out the foundations of a cathedral.
Harmonia, or music, is often relegated to music appreciation or theory or practice. However, the quadrivial approach is the Music of the Spheres—number in relationship in time. In essence, music is heard geometry. In addition, the basis of harmony is the recognition of right relationships, order, and shalom that can form beautiful music but also applies to the individual (balance and health), the home (marriage and parenting), organizations, society and culture, the very way that the earth is perfectly held in orbit and protected by the combined efforts of gravity, orbits, and other spheres.
Astronomy (Cosmology) is more than stars and planets, quasars and comets. To number and ratio and time, Cosmology adds the element of space and movement. Imagine the complexity of the earth spinning on its axis while orbiting a spinning sun that holds other planets in orbit while the entire solar system is itself orbiting around the center of the galaxy which is itself moving. And all of this is held together by the Word of His power. Christ sustains the complexity of cosmology.
In order to know any single thing comprehensively, one must know everything about everything. There is one Creator, one sustaining Word, and a wondrous plethora of ways that everything interconnects. There is great joy of discovery before us.