In deciding to write about a subject pertaining to mathematics, one of my biggest challenges is learning how to write for a large audience while commutating mathematical concepts without loss of understanding for the reader. This was one of the biggest criticisms I received in a group conference used to discuss research papers. In my latest draft I rearranged many paragraphs and spent a little bit longer describing quaternions and how they relate to three dimensional space. I have also tried to cut out some of the more complicated language. This is a difficult task in discussing quaternions and I have found this to be a good exercise for me. It has forced me to really think about how to be concise and simple.
My research for this paper has taken me places that I did not expect. I started out wanting to talk about the physical significance and or meaning of quaternions. In on reflective blog post I asked the questions, “Why did vector analysis win out of quaternion algebra? Does the quaternion algebra system represent some fundamental aspect of reality, or is it just a mathematical trick? Could reexamining quaternion algebra lead to a better understanding of a unified field theory? I feel that all of these questions pose similar problems of being two broad”. My research in the begging was focused more on recent theories in physics where quaternions were used. As I researched further, I became aware of a debate that had been going on for a long time of the use of quaternions. Thoughts about my research question turned to this debate. What it came time to post an entry on a primary research proposal, I posted this, “I plan to go through and analyzing the debate of the use of quaternions in math and physics in letters to Nature from the years 1880-1900. From the little of research I’ve done so far there seems to have been a heated debate that took place during these years concerning the use of quaternions. It is interesting to me that people feel so strongly one way or the other”. This process has been rather fun and interesting for me.