Liberal Education in Harmonics in Philo of Alexandria

Abstract

This paper aims to analyze the passages of Philo of Alexandria on mathematical education in an attempt to reconstruct post-school mathematical education in the field of mathematical harmonics in the city of Alexandria in the first century CE. Present paper provides evidence that at that time some education in harmonics was received not only by professionals and scientists, but also by other free wealthy citizens. It is shown that the curriculum that became a part of later standard introductions to mathematical sciences, such as “Mathematics useful for reading Plato” by Theon of Smyrna and “Introduction to Harmonics” by Nicomachus of Gerasa, was already being practiced during Philo’s time. The topics that formed the basis of this course were the following: the physical causes of sounds, notes, strings, intervals, concords, ratios, separation of the canon, as well as Platonic and Pythagorean ideas about cosmic harmony. To master such a program, some knowledge of arithmetic and geometry was required. Thus, it is shown that to the time of Philo the quadrivium had already developed as an educational unity, where the topics logically followed one another, and the study of each subsequent subject of the quadrivium required basic knowledge from the previous one.