End-of-semester reflections

Now that the semester is over I've had some time to rest and relax the past fortnight, and reflect on my experience this semester. And I think…I might enjoy teaching.

It's a question everyone's been asking me, but not a straightforward question for me to answer. The superposition of emotions that makes up how I feel about it refuses to yield to observation and collapse to a single, simple, state. Mostly, I don't feel anything – I don't dislike it, but I also don't feel any particular deep yearning towards it either. (Though in fairness this is also how I feel about programming, which I like well enough as a profession.)

The clearest indication came near the end of April, when I saw and applied for a software developer position in astronomy on this island. It was similar to positions I've held and enjoyed before, and had I applied last year I've have been quite excited for it – yet as I was applying, I felt an unexpected pang of…regret, I suppose, that I wouldn't be around to watch the students I've begun to get to know this year develop over the course of their undergraduate journey.

We'll see if it goes anywhere, of course. I'm on the schedule to teach several classes next semester so I have no idea how or if that would work if I got hired. I find myself thinking a dual arrangement might be nice, where I teach a few classes on the side going forward. But this is all speculation for now.

Another thing I've had time to reflect on was attending the graduation ceremony for UH Hilo the day before my birthday. I left in the middle of the semester when I finished up my Ph.D. at Swinburne, so my last time being part of a ceremony was my undergraduate commencement in 2012. This was also my first time attending as faculty, and I found it a profoundly different experience.

In some strange way, watching the doctoral students being awarded their hoods and degrees gave me a sense of closure. Back in 2021 I literally went from submitting my thesis Sunday afternoon to starting my job at Gemini the next morning, so I had zero time off in-between. That wasn't really the end of it, though, since I then spent most of the next six months turning my thesis into publishable papers, working on evenings and weekdays (with a small break in December for my thesis defense a few days before Christmas). I was pretty burnt out for a long time, and while that's probably representative of most grad students at some level I never really had much in the way of closure; my papers finally got published, and I just…didn't need to be spending most of the time I wasn't working thinking about the process anymore.

So I found it surprisingly emotional to be sitting among the other faculty at the graduation ceremony two weeks ago, watching my fellow newly-minted doctors receiving the rewards for their years of toil. Sitting with the faculty dressed in our formal regalia (wearing a borrowed finery in my case), I felt a connection to the scholars around the globe who for hundreds of years have sat in ceremonies like these, welcoming new learners to their ranks in fellowship. It was a really nice feeling being recognized by the chancellor, both for being a UHH alumnus and as part of the faculty. I try to stay humble and not let my accomplishments go to my head, but it's gratifying to have the many years of hard work I put in bettering myself be recognized.

So what's next for me? As mentioned I'm on the schedule to teach again in the fall, but I don't have anything officially going on over the summer. I have no lack of ideas for projects and things to try, however, so I hope to have ideas for posts before too long. After a little break I've started up on some woodworking projects, including constructing some jigs to make future projects easier. (One of the fun things I'm discovering about woodworking is the ability to simply make your own tools to accomplish things.) We'll see what I get up to, though! A hui hou!

Living my prime years

Another year, another birthday! And what a year it's been. Last year around my birthday I was working with NEON on the slopes of Mauna Loa (about which I gave a talk this week at the Hilo photography club meeting). This year I've just wrapped up finals weeks at UH Hilo after my first semester teaching, and attended the graduation ceremony yesterday. Attending graduation as faculty was an interesting experience and I have some thoughts about it, but they're still crystallizing so they'll come in a future post.

For today, I was thinking earlier that I'm celebrating my 37th birthday, and how that's back to being a prime number after 36. And then I thought about phrases like “being in one's prime,” or “being in the prime of life,” and started wondering: just how many years have I spent at a prime age?

Now, what does that very hastily-conceived notion mean? It's essentially just how many of your preceding years of life corresponded to prime numbers. We have to a little careful about birthdays, though; in essence, birthdays count years of age since the day of your birth, so your first birthday comes at the end of your first year of life. You are then “1 year old” during your second year of life until your second birthday. If we count the years which correspond to a prime number as “prime years”, we can compute, at each birthday, how many of your preceding years were “prime years” and what fraction that makes with your total number of years lived, as in this formula:

\[\text{prime years fraction}_{\text{at age }n}=\left.\frac{\text{prime years}}{\text{total years}}\right]_{\text{at age }n}\]

Confused yet? Let's start from your first birthday, which celebrates your first year outside the womb. One is not a prime number, so your total number of prime years lived to this point (out of a total of one) is zero; your prime years fraction is thus \(0/1=0\). At your second birthday, you have lived a total of two years; the first one is not prime, but your second year corresponds to two, which is prime, so you have one prime year out of two, or \(1/2=0.5\). At your third birthday, you have lived one non-prime year and two prime years (since two and three are prime), for a fraction of \(2/3=0.66\dots\)

And it's not hard to see that this is as good as it gets – at your fourth birthday you'll have lived two prime and two non-prime years so the fraction returns to 0.5, and since prime numbers only ever get farther apart your fraction of prime years begins a slow slide downwards. One interrupted by upwards jumps at each prime birthday, to be sure, but the overall trend is obvious. I found this sufficiently interesting to write up a quick Python program and plot what it would look like for ages 1–100, and here it is:

You can see the trend I've described: it starts at zero at your first birthday, shoots upwards the next two years, then begins a jagged descent. Since 37 is prime I've just jumped up to a prime fraction of 0.324, or, another way of putting it, just under one-third of my lived years have been prime (numbers).

The plot kind of reminds me of the nuclear binding energy curve in atomic physics, but I was also intrigued with where it seemed to be going. I thought it might be converging towards 0.2, but running it to 1000 dispelled that notion:

At this point I suspected it was converging towards zero at infinity, but my naïve implementation of prime-checking in my code was starting to take noticeably longer to run at higher upper limits. For a limit of ten thousand it still took under two seconds to run, but at a hundred thousand it took over four minutes:

I'm sure I could implement a more sophisticated method of prime-checking and push it to higher numbers*, but ultimately, checking whether a number is prime or not is a difficult problem (and one on which much of modern computer security depends). The overall trend is clear, mathematically, so for an idle musing like this I'm satisfied with what I got.

Anyway, I hope you found that at least a little interesting. We'll see where life takes me this year. Currently my summer is wide open (I've got a lot of ideas for things to do) and I'm on the schedule to teach again in the fall, but who knows where things might end up going. A hui hou!

*Edit: I certainly could, as I was checking all the way up to \(n/2\) instead of merely \(\sqrt{n}\).