Update post (July 2019)

It seems that every time I return to write something on this blog, it’s about how infrequently I write (and that I’m awfully sorry, and I promise to write more, but it never happens). I see three main reasons for this:

  • I am now in a masters program in the School of Mathematics at the University of Sydney! My honours year went quite well overall, and my supervisor was happy to take me as a postgraduate research student.
  • Since March, I have also been working casually for Matrix Education, a private tutoring company that is well-known in particular for its HSC preparation courses.

From the two reasons listed above, you can appreciate that most of my time is spent doing mathematics in some way — reading articles and learning new theory for my research project, working on exercises from textbooks, or preparing tutorials and classes. The third reason is really a blend of two:

  • My own laziness coupled with a lack of direction about this blog.

This update post will explain this last point further.

calvinhobbes-peck

Writing about mathematics

For a while, I have been contemplating what kind of content to feature on this platform. The blog started essentially as a way of coping with my focal dystonia, as I was making a transition from studies in music to studies in mathematics. You will find that the earlier blogposts are mainly about my musical activities. However, at some point I decided to make the presence of mathematics more prominent, and ambitiously began a series titled “Diversions in Mathematics”. Currently, there are only two proper articles in that series (not counting the introductory Chapter 0), and it appears all but abandoned. This is only partially true: although nothing more for the series has yet been produced, I haven’t forgotten about it either. In fact, I am thinking all the time about writing mathematics! The problem is that I became indecisive about how to present the material — there was certainly no shortage of topics that I wanted to present. If you take a look at the current entries in the Diversions in Mathematics series, both contain formal definitions of mathematical concepts, and both attempt essentially to “teach” the reader some proper mathematics: the first piece deals with basic set theory, the second deals with countable infinities. While I am happy with the two existing pieces, I realised that the blogpost is simply not the right medium to “teach” mathematics, for the following simple reaon: I think that casually reading a blogpost isn’t a good way to learn mathematics in the first place! Hence I knew I had to change the direction of the mathematical part of my blog.

I am still committed to the goals set forth in Chapter 0: I intend to present mathematics in a way that combines the formal and the informal, and seek a balance between rigour and fun. As my current viewpoint stands, to present what is basically lecture material (as in the case of the extant Diversions) is not the way to achieve this. I have been planning the next installment of the series, and I believe it will be a blogpost of a very different kind than has so far been featured — please stay tuned if you are interested! Moreover, the mathematics and music have been rather separate entities on my blog, with a few exceptions (like the blogpost about mathematics and music exams). In the future, I will be more confident in letting the two worlds mix.

Writing music?

Unfortunately, I have devoted very little time to composing and arranging this year. Of course, I am always thinking about new music, and I play with little fragments of music in my mind constantly. But in order to write something coherent, even if it is only a short piece of 5 minutes or so, I find it necessary to make a consistent effort. However, doing so tends to disrupt my mathematical activity too much, which is not desirable at this time. Perhaps I will eventually develop a way to juggle these two demanding mental activities, but for now, it is very much the case that the activities of writing music and doing mathematics are mutually exclusive. I find that my listening habits have also changed. Although I have never lost my passion for music, these days I don’t listen to a lot of music, but rather choose very specific pieces when I feel like listening to something. It is possible that this is an effect of studying and teaching mathematics, which requires a focused, organised mind. When I was studying music, it was not uncommon for me to listen to a lot of very different music throughout the course of the day. Nowadays I often just have a single piece of chamber music by Haydn, Mozart or Beethoven, or a violin piece by Bach, which will persist in my mind for a few days, before getting replaced by another specific piece. But recently, I have also renewed my appreciation for Stravinsky and Ligeti — it is important to be connected to “newer” music too.

Perhaps I’m going about this the wrong way. If you look at my Variations for wind quintet (which is probably the piece I am most proud of, to date) you will see that I enjoy a certain amount of complexity in my music. However, I have also thought about writing some simple pieces — even tonal pieces! — for the sake of simply “keeping things going”. I know all too well that it is a mistake to wait for inspiration to strike. So it is likely that you will be hearing simpler compositions from me in the near future, for example, compositions that are suitable for younger students to play. I am certainly eager to try it out!

If you have reached this point, I want to thank you for taking the time to read my blog. I find that I express myself better in writing anyway, so you can imagine that the things I write on my blog are the things I would like to share with you in person, if only I had the conversational skill and lacked the social awkwardness to do so. It means a lot to me that a non-zero amount of people read the words I write!

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