Long Nights
Afternoon sun hangs low in the Southern New England sky, ready to plunge below the horizon just after 4pm. Today, the sun reaches only 24 degrees above the horizon. Compare to Summer Solstice, when the angular height is just above 70 degrees in my neighborhood. No need to measure. I feel the difference instinctively in the long, brancy shadows of trees that stretch across the cold December earth. I know the other side of our journey (or our planet) by sunburn blushing across bare shoulders in June.
Nature speaks to us in math.
On these darkest days of the year, I think of all things round and cyclic. Spherical bodies on elliptical paths, curving through space. The bright round sun sinking low and cool in the sky on its daily rounds. Waves, literal light racing through the emptiness of space to land on my dry winter cheek. Waves, symbolic now as I drag my chalk in an undulating path across my graph: daylight vs. time.
Once upon a time, on a tough day in precalculus, perhaps you consoled yourself: “After high school, I never have to think about this again.”
If you weren’t a science teacher, a physicist, a chemical engineer like me, perhaps you were right. A great many people get away with their personal campaigns to ignore trigonometry after high school.
But trig never went away, no matter how many people wish that it would. Trigonometry is the language nature whispers at solstice. Trig is the broad sweep my Northern home makes away from the sun. Trig is the opening of vast dark space, and the speckling of our winter nights with a cathedral of twinkling stars.
The math is all here for you when you’re ready to welcome it back.
Do you ever wonder why the night stays so long even after solstice has passed? Why the progress back into the light isn’t faster at this time of year?
There are many deep mathy layers to the answer. I made you a video to illuminate one layer, and a gif for those who are far too impatient for my miniature blackboard lesson. I felt inspired by the bright morning sun streaming steeply in my office window, and did my work in my pajamas, still sipping my tea. Why not? Math, on our terms, for the pure curiosity and wonder of it all, should be cozy.
