“Oh, the weather outside is frightful…” Bad enough that it’s three degrees above zero as I write this (with the high today only four degrees). But there’s a winter storm warning in effect until 3:00 AM tomorrow morning. (Severity: Moderate; Possible threat to life or property.) We’ve had 2.3 inches of snow so far with another 7.2 inches expected.
But we’re Minnesotans, and we expect this stuff. Wouldn’t be a proper winter without a bunch of puffy frozen water covering everything. And people scraping various forms of it off their cars. The Minnesota Winter Ballet!
More importantly: Merry Winter Solstice! Less than two hours away as I write this…
And unless I manage to stay brief, who knows how long before you read this. No doubt some period of time after, so take heart that we’re on our way to longer days.
It’ll take a while for that to really kick, though, so hang in there. As explained in greater detail in this post, we’re going through a “trough” in the cyclic wave that traces the seasons. We crest that wave on the Summer Solstice. Both cases involve a change of direction, either from going down the slope into the trough and then starting back up, or from going up the slope over the crest and then back down.
Direction reversals necessarily involve a momentary full stop. That requires slowing down, coming to that stop, and then speeding up again (in a different direction). As such, both Solstices seem to “hang” briefly. The long days of summer seem to go on forever (alas, if only), but so do those brief cold days of winter. They kind of literally do.
In contrast, the equinoxes involve the slopes between crest and trough. Either sliding down (in the fall) or zipping up (in the spring). So those days pass by more quickly.
Which — considering the Earth makes a very nearly circular orbit — might seem strange. How can something pass slowly at two points in that orbit while passing quickly in two other parts? This business of two fast points divided by two slow points is more like how a pendulum swings. It pauses at the ends of its arc to slow down, stop, and change direction. And it’s fastest as it passes the bottom of that arc.
Exactly like the length of the days, but the Earth is on a wheel, not a pendulum, so huh?
The answer lies in how the Earth’s axial tilt and rotation interact with the circular orbit. Those combine to create the sine waves shown above. These virtual waves are emergent, since they depend on the length of the days (which depend on rotation and that axial tilt), but they exist from an experiential point of view (just like color images emerge from the red, green, and blue dots on our screens).
Anyway, I suspect it’s why Christmas is on the 25th rather than on the Solstice. Took a while for ancient humans to realize the days were, in fact, getting longer. So, party!
Because I’ve been reading (mathematician) Roger Penrose lately, and because he always spends considerable time in his books laying the mathematical foundation of his ideas, and because that usually involves teaching his reader the necessary advanced math, I’ve been thinking about fiber bundles over manifolds.
(Fiber bundles can be over all kinds of spaces, not just manifolds, but I’ve been thinking manifolds because they’re often more physical and intuitive than abstract spaces.)
Without overmuch detail (clock is ticking, Solstice about 80 minutes away), if we think of the year as a one-dimensional space of 365 days, each day has a one-dimensional fiber with the 86,400 seconds of the day. Think of a rod of days with 365 fibers hanging, one from each day. Each fiber is distinct, its own day, but definable cross-sections can run through the fibers. For instance, representing the sunrise or sunset times.
It’s an interesting theoretical maths way to look at it. It’s what I get for reading Penrose. I do sometimes wonder if he might be this era’s Einstein. Or in that class, anyway.
I thought I had a brief disappointment to mention, but a phone call I got while writing this (tick, tock, about an hour to go) put us back on Plan A. Which actually has a downside, but the downside of Plan B was worse.
See, I have a water leak in my long-unused guest bathroom — little more than a broom closet with a toilet and sink — I’ve seen bigger bathrooms on trains. I’ve been using it to store stuff (like two old PC CRT monitors and a recycle box for snail mail). I haven’t used it as a bathroom in, well, a decade or more.
The leak seems to be coming from the valve on the pipe that comes up from the floor and supplies the toilet tank. I’ve had that valve turned off all this time, but the leak is on the supply side. Drip, drip, drip.
Fortunately, slow at first, but the drip rate does seem to be increasing. Definitely isn’t decreasing.
Took me a while to get a plumber; I’m a private person, I hate having strangers in my house. And I know my housekeeping skills are awful and my furniture and furnishings pathetic. I don’t care, but I know other people kinda do, so it’s embarrassing.
Anyway, bit of phone tag, but finally set up an appointment for tomorrow morning at 7:00 AM. Then got a message earlier, distorted and static-y, about having to change to next Tuesday at 7:00 AM. Which, fine, whatever. Kind of a pain to go through Christmas weekend sopping up water with old towels (or turning it off when I can do without a water supply), but fine, whatever.
But while I was writing this post, he called back and said he’d worked it all out, and we’re back on for Plan A. Early tomorrow morning.
Which I prefer, but it means I have to be a little careful about celebrating the Solstice. I don’t want to be passed out in bed tomorrow at 7:00 AM when the plumber shows up. It won’t even be light out, yet! The hour isn’t the problem, I’m often up early (comes with age), but tomorrow morning was one I’d normally plan on sleeping in for.
I guess I’ll have to keep it to just one bottle of champagne…
Rather than try to beat the Solstice, it being far too late to advise anyone who doesn’t already know, I’m setting this to publish on moment. Have a great winter celebration, whatever it may be based on!
Stay sunward, my friends! Go forth and spread beauty and light.