The Quadrivium

    There is a four year progression in Humanities (a modified “Great Books”), and there is a four year progression in the Quadrivium, in keeping with the founding essay of this website. The difference is that, in any given year, we will only offer one section of the Quadrivium (if a student has completed that section already, he will do independent study in a more focused area).
    The Quadrivium is the “motion” of the invisible Trivium. It is the investigation, not primarily of the empirical world (although this is to some degree implied), but of the “flesh” of the Logos Tomeus as it appears in the external world, as opposed to the internal world of the Trivium.
    The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied number (music).
    An example of how this would work for the Syllabus, concretely, is provided below. Keep in mind that for students of pronounced mathematical and scientific ability, they would be able to supplement these studies with intensive parallel study of their own. That is, we are not egalitarians here. The tutor does not pretend to a detailed mathematical knowledge beyond that of the educated person, and the student will have to tailor their own studies to suit their own abilities (guided by the parent). What we would do is to fit those independent studies within a certain framework, relating the part back to the whole. The tutor’s specialty is philosophy & religion, but he has a wide background in various subjects (including A&P, mathematics, and chemistry, along with several others) which allow him to oversee and guide this portion. The Quadrivium was meant to teach the student that the world is literally a “cathedral” built by invisible hands, and to provide a moral centering for exploring that cathedral. Since we all have bodies, and indeed, to a large extent, are that body, then the outer world must continue to interest the man of Western intellectual descent.
    Astronomy/Cosmology – this class centers around a Christian understanding of the Zodiac, God’s ancient revelation in the stars to the sons of men, proclaiming the Evangel. We use Witness of the Stars, as well as a book on the basis and association of Greek myths with the constellations (The Star Myths). The goal of this class is really to familiarize the student with the night sky in a historical and scientific sense, by focusing on the constellations. The companion text to this class is a source book on classical mythology, which functions like a “constellation map” that tells a story about the “God Who is There” (F. Schaeffer). This is in keeping with a very strong interpretation of Romans 1. And example of independent study in this area might be James Burnham’s celestial atlas.
    Arithmetic – A close reading of Iamblichus’ text on Numerology (Theology of Arithmetic), a history of mathematics using ET Bell’s Great Mathematicians, & a look at the liberal learning base of mathematics by John Allen Paulos (Beyond Numeracy). We also cover the book Quadrivium, which deals with the mathematical patterns in Nature. This course is designed to be an introduction to Mathematics, primarily for those who are specializing in the humanities, but also providing a modicum of mathematical proficiency, or as Paulos puts it, “numeracy”. We also read Morris Kline’s work in this class. There are brief excursions and introductions to Geometry, Calculus, and other advanced mathematics, but these are for the sake of demonstrating the humane side of the development of mathematics. Independent study in this course, or detailed “rabbit trails”, might be over statistics.
    Geometry – We work through portions of Euclid’s Elements. This is more suitable for advanced mathematical studies. However, we also supplement with game theory, including strategy and various other sports. The student will be introduced to Sun Tzu’s Art of War, along with various other essays on games and mathematics that study permutations, possibility theory, and also symbolic logic. In the Chinese tradition, the student would master a game, so discussions of game theory (including poker, chess, etc.) are appropriate to this course, which is why Sun Tzu is included to begin with. Game theory would constitute independent or detailed study in this class.
    Music – The student will choose a musical instrument of their choice, which they are learning to play, or can already play, or are simply interested in learning more about. Together, the instructor and the student will study music’s historical development, culminating in classical music, and how the instrument is part of that story. The student will focus on mastering at least the rudiments of playing the instrument. Painting or calligraphy would be an alternate mode of study chosen instead, and in the Chinese traditional Quadrivium, music is complemented by both. The tutor cannot teach subjects in which he is not of base proficiency, so the most that could be offered here (for some interested in the plastic arts), would be guidance to primary texts. Independent study in this area, for instance, might be in opera.

Because boys are generally slighted and neglected in the modern public school or even private school system (which heavily favors conformity of a specific type), the tutor will, makeup of the class permitting, allow independent study under the Number heading into strategy and the use of weapons such as quarterstaffs, etc. For those parents who made the mistake of not nurturing the moral imagination when the child was wrong, “I can’t put in what God left out”: you should have read them more Wind in the Willows. I follow John Milton’s advice in Aeropagita, in which it is recommended that half of boy’s time be spent in athletics. Since we can’t do that here, on-line, I modulate the curriculum to include (particularly for those inclined) a strong dose of military history, strategy, and game play. For instance, a student might be asked to present, for their tutorial final in Modern History, a review of The Seven Samurai. The core is classical in technique & content, whereas at the periphery of our modules, we will look at how the classical method can interpret and assimilate the modern experience of the melange d’sens.

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