I stepped outside tonight shortly after 8 p.m. to find it almost completely dark. I was surprised, as I am every change of season, at how rapidly the days have gotten darker, or so it feels. While seemingly endless summer days and long winter nights seem to linger long past their welcome, the pivot from summer into fall always feels stark. I remembered the nonchalant words of Mrs. Stob, my 11th grade math teacher, as she shrugged off this phenomenon:

“Sine wave.”

When I was 17, I understood sine waves about well enough to nab a B+ on the test and move on. More than a decade has passed, and my understanding certainly hasn’t gotten deeper, but I guess it works something like this: if you were to plot out the days of the year, with hours of daylight on the y-axis, and days on the x-axis, you would get a curve resembling a pattern called a sine wave. In other words, a curvy squiggle line (see above). Because it’s this and not a zig-zag shape, with pointed peaks and valleys, the slope of the curve is more gradual at the peaks and valleys, which mark the solstices, and more steep in the middle sections, which mark the equinoxes (or, if you really want some proper Latin, equinoctes). Something about circles and rotation. 

This is all a bit of a squiggly meandering to my point. It was in 11th grade, around this time of year, that a teacher of mine made an observation about something curious in the world and explained it with math. To my recollection, this was one of the only times I was led as a student to be curious about math in the natural world. And it stuck with me.

But by this point it was far too late. I had already self-selected as a “humanities person” who saved his true interest and academic curiosity for English, world languages, and social studies. It’s a shame, really, that we’re often led to do things like this. I think I had a couple of good English teachers early on, and I liked reading books, so I decided I must be an English person, and there you have it. Future writer for the post calvin, practically predestined from age 14. No one ever told me I could like English and math, or that I should.

Not to knock on my many math teachers over the years. I learned all the skills I needed, and through a couple clever mnemonic songs, I now have the quadratic formula and all my times tables written firmly into the deepest parts of my brain. Fun fact: you can do multiples of 9 to the tune of the Jeopardy! theme. Try it. 

It was functional, but it never made me curious. 

Maybe I’ve just been starting to notice more things lately, but I’m finally feeling more curious. I actually started watching Khan Academy videos earlier this week covering fifth-grade math skills. Partly because I wanted to know how to explain multiplication strategies to the students I work with if it came up. But partly also because I felt nostalgic for the sense of wonder I never had. 

You might sing a romantic melody about missing someone you never knew. But can you miss something you never learned?


  1. Avatar

    As you noted, it might not be too late. Can I recommend Zero by Charles Seife and How Not to Be Wrong by Jordan Ellenberg?

    • Alex Westenbroek

      Always love recommendations. Much appreciated.

  2. Avatar

    my brain is trying to figure out how to possibly put the multiples of 9 to Jeopardy! and it is painful. Any help for a fellow SLP & self-proclaimed humanities person with the interest and capability of doing math & “hard” science? 🙂

  3. Avatar

    LOVE this entry! I always marvel at the solstice and equinox. And it’s often said that Music and Math go hand in hand.

  4. Kyric Koning

    What a fun little piece. The cool thing about missing out on learning is that you can always try again. Or figure out something else. We never stop learning, unless we choose to.


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