Hello and good morning.

I’m writing today’s blog post on my smartphone, because I walked to the train this morning.  That’s not quite the non sequitur it might seem to be.  Given the new train schedule, I arrived here only a few minutes before the 6:20 train is due to arrive, whereas on the old schedule, I would have just missed the 6:10 and sat down to wait for the 6:30.  Of course, I could simply let the 6:20 pass and wait for the 6:50 and pull out my laptop to write my post while I wait.  Perhaps, in the future, I will do that.  Today, though, I don’t want to push back my departure any further.

I’m now on (actually, in) the train, and I was surprised to find my preferred, relatively isolated seat on the older style car free.  Combined with the feeling of achievement from already having walked about five miles today, that’s pretty nice.

Today is the Winter Solstice, at least for those of us in the northern hemisphere, meaning it’s the day of longest night, if you will.  Going forward, now, the nights will become shorter, though the change will be hard to notice at first, since, near their maxima and minima, the derivative of sine and cosine curves (well, any smooth curve, really) is around zero, meaning the rate of change of the function is very small.  For one brief instant‒one infinitesimal moment of time‒during this 24-hour period, that rate of change will be exactly zero.

But, of course, the rate of change itself is constantly changing.  This isn’t true of all functions, obviously.  The rate of change in a linear function is a constant, and the rate of change of a constant is zero.  That’s why it’s called a “constant”.  And the rate of change of zero is still zero, no matter how many times you would like to take that derivative.

Sine waves, however, are cyclical, and their derivatives are also cyclical.  The derivative (i.e., the rate of change) of a sine is a cosine…and the derivative of a cosine is a sine (inverted, I think, if memory serves, but that changes nothing fundamental).  So, even the derivatives of such cyclical functions are eternally cyclical.  There’s something very pleasing about that, at least to me.

Oh, by the way, it is the Summer Solstice today for those who live in the southern hemisphere.  This has been a smaller number of people than live in the northern hemisphere for as long as human civilization has existed, I think, largely because there simply is more land in the northern hemisphere.  Nevertheless, there are now many millions of people south of the equator, and so there are oodles of those for whom Christmas and New Year’s are summer holidays.

Summer ought to be slightly warmer for those in the southern hemisphere than for those in the north, since technically the Earth is at its closest approach to the sun in January.  However, the Earth’s orbit is very nearly circular, so the difference between aphelion and perihelion is tiny, fortunately for us.  Also, there is much less land in the south, and land heats up much more rapidly and noticeably than water, so that may completely swamp the effects of slightly different nearness to the sun.  I’m not sure.  If anyone out there has that information, please let me know.

It’s a bit interesting to think of those people who have grown up in the southern hemisphere, seeing all the movies and shows (and before that, books and legends) that associate snow and cold and the like with Christmas time and New Year’s.  Of course, the reasons would not be a mystery, but it still might feel peculiar, just as it might feel rather alien for a northerner to hear of someone going to the beach to celebrate Christmas.

Instead of building a snowman, maybe such people might build a sandman.  Actually, given the old horror short story about the Sandman‒not to be mistaken for Neil Gaiman’s admittedly also quite dark creation‒it might not be great to make a sandman as part of a joyous celebration.

Although, being rather dark myself, I consider the notion somewhat amusing.  Maybe there could be a kids’ story called Gritty the Sandman, instead of Frosty the Snowman (Anakin Skywalker would hate that).  But Gritty would be much harder to destroy than Frosty.  It takes serious heat to cause sand to melt, and even then it just becomes glass.  Imagine that:  they try to kill Gritty with heat and fire, and he just turns into a misshapen blob of living glass, with razor sharp shards for fingers‒more deadly even than he was before!

Wait, that was supposed to be a kids’ story, wasn’t it?  Sorry, I got distracted.  Still it would be fun to hear a song with the lyric, “There must have been some madness in that old silk hat they found.  For when they placed it on his head, he began to…”

…who knows what?

Anyway, I’ve reached the office now.  My pedometer seems to have accidentally reset while I was on the train, as it’s only showing one mile of walking, which is the distance between the station and the office.  That’s a bit frustrating, but I know that the distance to the station from the house is almost exactly five miles, so I’ve walked six miles so far, and I’ve now reset the little bastard, so we’ll see what I’ll do for the rest of the day.  Maybe I’ll have the gumption to walk back to the house from the train in the evening.  I feel okay now, from my walk, but I don’t want to overdo things and set myself back.

I’ll sign off for the moment.  Have a lovely solstice if you can, be it your summer or your winter.  But if you’re in the south, and you make a sandman, try not to bring it to life.  Quite apart from it having the nefarious power to put you to sleep at will, remember that sand is basically just ground glass, and that can have dreadful effects on bare skin or on your mucus membranes.  And you certainly don’t want it in your eyes!

I think I’m imagining a new kind of horror story here, albeit a spoofy more than spooky one.  We’ll see what comes of it.

TTFN