Definitions & Consolations

Having passed the midpoint of the England High School Summer Program and entering the second week, students rose this morning giddy and a little anxious. In hushed tones over breakfast, they discussed their excitement about today’s classes. In the morning session, they would be encountering Euclid’s Elements and approaching mathematics in a way that would be, for most, wholly different from what they had ever experienced before. And — also a likely a first — mathematics would be taught, like all classes at Thomas Aquinas College, via the Socratic seminar, rather than through lectures.

Primarily focused on definitions, common notions, and postulates, students broke ground into Euclid’s foundational principles. Some expected this conversation to be over in an instant — they’re definitions, what’s there to talk about?  

Turns out, there was no shortage of material! Euclid’s deceptively simple definitions usually spark intense debates, as students attempt to visualize the different shapes and concepts, while still holding true to the text and common experience. Some sections spent over a half an hour just discussing whether a line was made up of points or not — and that’s only the first definition! By the end of class, most students wanted more time to talk about Euclid’s first principles, and some sections went overtime by as long as 30 minutes.

Most students followed the first class with Mass in Our Mother of Perpetual Help Chapel, then resumed their discussions of Euclid over lunch. Before they knew it, though, it was time for the afternoon class —Boethius’s The Consolation of Philosophy. 

A well-respected and successful 5^th century Roman Christian, Boethius was falsely accused of conspiracy and sentenced to death. Understandably, as he awaited his sentence to befall him, he found himself confused and on the verge of despair. Rather than succumb, however, he put his mind to work and wrote his opus, the Consolation of Philosophy. In it, he and “Lady Philosophy” discuss evil, happiness, fortune, suffering, fate, and God — in short, many of the “big picture questions” the programmers have begun to consider over the last week. Students found their discussion of Boethius to be a highly engaging and worthy follow-up to the morning’s session on Euclid.

Later today, in addition to the afternoon recreation period, students will get to prepare for their first crack at demonstrating Euclidean propositions. We will have photos and more tomorrow morning, here on the Summer Program Blog!