Those who are bringing back classical education as an alternative to the deadends evident in John Dewey’s progressive education are familiar with the trivium: grammar, logic, and rhetoric, the three liberal arts that lead to a mastery of language. The other four liberal arts, the quadrivium, though, gets short shrift: arithmetic, geometry, music, and astronomy.
Many people think that the liberal arts is just another word for the humanities, forgetting the quadrivium completely. Dorothy L. Sayers, whose essay “On the Lost Tools of Learning” was a major catalyst for the revival of classical education, thought that the quadrivium represented “subjects” that would be learned after the trivium provided the tools for doing so. In this she was just wrong. The quadrivium are “arts”; that is, powers of the human mind. They are essentially mathematical, even in the way music was approached. Thus, classical education embraces the two spheres that educators recognize are necessary for education: language and mathematics.
Anyway, my daughter, who has been studying Boethius, the great systematizer of the quadrivium, explained to me the connections between the arts of the quadrivium, in a way that also helped me see the way mathematics really does provide a unifying model for the order and design that underlies all existence.
arithmetic = numbers
geometry = numbers in space
music = numbers in time
astronomy = numbers in space and time
Do you see why music is numbers in time? And why astronomy is numbers in space and time?
Now what we need is to bring mathematical education back from the dead–it’s telling that progressive education, for all its claim of being scientific and all, is failing most dramatically precisely in teaching science and mathematics–by coming up with a classical way of teaching it. Does anyone have any ideas? (And by this I don’t mean just teaching it more effectively or traditionally, such as Saxon Math. That and similar methods still lift numbers out of any context, which is not the classical way.)