Assignment 2 Reflections

This assignment was the first time I found myself trying to ‘walk the talk’ as it relates to what I’ve perceived to be the goal of this course, namely to leverage history to provide context and make topics more engaging. Initially, when I chose explore this history of compass and straight-edge constructions, I had expected to primarily focus on the Greeks. While researching the Greeks, I was reminded of the deeply philosophical relationship they had with geometry – although there were practical applications of geometry, the Greeks were moved by the spiritual and sacred elements that they saw infused with these shapes. In attempting to better understand this motivation, I found a paper titled: “The Ritual Origin of Geometry”. The paper speculates that the first desire to create ‘perfect’ circles and squares was theological in nature. It also drew my attention to the importance of ‘peg and cord’ constructions, of which compass and straight-edge were mimicking.

This paper helped me realize (to a degree) how to really make this topic engaging. I posit many students would find the history of ancient rituals a more interesting entry point than history of the Greeks. I personally am much more excited by these ideas and can hopefully channel some of this excitement to my students. Additionally, having students actually execute peg and cord constructions is a highly collaborative activity. Much like the dancing of Euclidian proofs, students have the opportunity to embody the math which is so abstracted on the page.

Frankly, keeping in mind that the purpose of math history (for me) is to inspire students’ interest, I feel that typical chronological ‘reporting’ of history does not serve us. We care why these things happened, not when. Taken to an extreme, this leads me to consider the morality of embellishing history so as to make mathematics more interesting and engaging. Is it immoral to lie about the origins of the quadratic formula for the sake of learning the quadratic formula? It is a question worth asking, though it may be relatively unimportant. As someone still largely ignorant of the histories, it may be that all mathematical origins are fascinating and can serve to captivate students without embellishment. That being said, if it turns out they aren’t, I find myself without a clear answer to this question.  

Link for UBC Students to downloads a copy of "The Ritual Origin of Geometry". I HIGHLY recommend!

https://link.springer.com/article/10.1007/BF00327767

Was Pythagoras Chinese? - Reflection

As math teachers, we have the privilege of teaching knowledge which was discovered and proven, independently, by several ancient civilizations. This means that for many of the concepts we teach, there are multiple unique histories that can be used to provide meaningful context. With this in mind, how should we choose what to share? To answer this, I want to lean on what I believe is the purpose of including history in the first place:

Integrating the history of math into our math classes serves to inspire students by providing context which explains why the concepts were originally of interest.

 With this in mind, teachers trying to decide which histories to share should firstly consider the ethnicity of the students being taught. For example, a class of 2^nd and 3^rd generation Chinese immigrants (not uncommon in Vancouver) would likely find the Chinese history associated with Right Angle Theory much more relevant (and perhaps even understandable?) than the Greek equivalent. Similarly, if one is teaching to a class with primarily European Ancestry, the associated Greek history would make more sense to teach for the same reason.

Regardless of which history one focuses on, it is important to communicate to the students that other ancient civilizations also developed this knowledge in their own, unique ways. It would be extremely colonial to present exclusively one culture’s history, particularly in a subject (such as Math) where the knowledge being taught was discovered, independently, by many cultures around the world.

Lastly, in Math, Science, Humanities, and any other subject, I think naming concepts, constants, or ideas after the original inventor/discoverer is a bad idea. I have two reasons for this:

1. Often, the assumption is that the person who invents/discovers something is the FIRST invent/discover the relevant idea. As is the case with Pythagoras, this is not always true.

2. It is a missed opportunity to make ideas more accessible. I generally believe that it would be better to have self-describing names, particularly for ideas which have been shown to be fundamental to the universe. Instead of Boltzmann Constant, why not Gas Temperature Constant? Instead of Planck Length, why not simply Smallest Theoretical Length (STL)? I suggest these names with a healthy does of sarcasm (I don’t know how accurate the are) but I believe their advantage is clear. In particular, they would remove some mystery and gatekeeping from the academic world.   

Euclid and Beauty - Reflection

 This past week I found myself wanting to incorporate ‘ancient problems’ as I developed lecture resources, namely so I could demonstrate the ancient nature of what was being discussed (geometric sequences). After some digging, I found question 79 in the Rhind Papyrus which I adopted in a modern context. This new-found desire to leverage ancient problems inspires me to take the information in ancient books (such as ‘Elements’) much more seriously.

Although I’ve read about Euclid and his Elements before, I now find myself much more interested in this material than ever before. Although the study of these books is a daunting task, I suspect it would be well worth my time so that I might more easily know where to search for source material as I continue to develop resources.

My partner and I agree that ‘Beauty is in the eye of the beholder’. With this in mind, I suspect that many (if not all?) people who see the beauty in ‘Elements’ are those already deeply familiar with mathematics. It is a generally accepted notion that simplicity and generality are highly valued by mathematicians. As such, I can only speculate on the impact Elements must have had at the time of its release - to see the world of mathematics derived from such simple postulates would have been peak intellectual experience. In the years to follow, those who would have learned with Elements would come to appreciate its simplicity. It is only after this appreciation that any student would see Beauty in this place .

Beauty is subjective and (I suppose) relates to what the subject values. As a drummer, I value complex rhythms – those who have not invested time in understanding rhythms and patterns would likely fail to see beauty in the same places as me. In this way, I’d argue that beauty is a relationship between two subjective places, one of which is probably a human.