Trivium & Quadrivium Homework

Image source: https://humanities.byu.edu/wp-content/uploads/7-liberal-arts.jpg

The first thing that struck me was that the study of liberal arts was required before the study of theology. I have taken a course on Religious Studies, and a few relating to Indian religions and I always found it interesting that in both Christianity and Hinduism, religion was something that was mostly studied by people who held religious titles, but that this was tied to their knowledge of a particular language. When religious texts were translated, they became accessible to the general public. I hadn't realized that, in the Christianity case at least, such high level of knowledge was required on top of knowledge of the language before a person was allowed to study theology. I wonder if studying theology used to be an intensive process and if that is why all these prerequisites were required or if it was something to do with creating separation between those who had access and those who did not (similar to a "free man" being allowed to study while a slave was not). 

The second thing that surprised me was that there was no controversy between algorists and abacists when Hindu-Arabic numbers were first starting to appear in Europe. I'd imagine this would have increased the difficulty in communicating math to each other, and I'm also surprised they didn't become defensive of the method they preferred. I think of Pythagoras and Hippasus and what types of change or suggested change are more offensive than others. For instance, I see a metaphor of language in the rise of algorists in Europe - it's essentially the introduction of a new "language" which expresses the same ideas as the native language but in a different format that the native language speaker may not understand. Languages don't always coexist either, depending on the politics of the area they are being introduced, but it has still been seen to happen. However, when Hippasus discovered irrational numbers, this went against what Pythagoras thought and he was sentenced to death for it. If the metaphor could be applied here, Hippasus was essentially put to death for discovering a new set of vocabulary in an existing language, which seems less extreme than speaking a different language. But maybe the metaphor doesn't quite work here. Or maybe there were some politics in play here. A professor once described math at the time of Pythagoras as a cult, using Hippasus as an example of what happened when someone strayed from what was accepted. I would be interested to look into when it stopped being cult-like and if there were other instances similar to Hippasus, but also other stories of coexistence because those would be helpful in validating students when they use different methods instead of pinning those who favour algebra against those who favour pictorial representations, for example.

Lastly, I thought it was funny that "extraordinary" math lectures were "diversions for holiday afternoons" at the University of Vienna, and interesting that this was one of the few places where math debates were held at the time. Going back to the "math as a cult" idea, it seems that, at least in universities like this, math became less absolute fact and more open for discussion around the 14th-15th century. I assume introduction of debates is what led to the decline in universal usage of Euclid's Elements in Europe (but it is still impressive that Euclid's books, although sometimes varying in emphasis, were a requirement for so long).