I was going to start by saying that I had probably written all I could about Friday the 13th and the fact that there are 2 in a row when non-leap year Februaries have Fridays the 13th, and that a first glance might lead one to think this should happen roughly every 7 years on average*.  However, as I noted last time I discussed this, because the leap year day is in February, we will not have the two-in-a-row Fridays the 13th (February and March) as often as we might otherwise; it will not happen every 7 years on average.

Then, this morning, after recalling that today was Friday the 13th, I ran through the next years’ Fridays in my head in the shower, and it occurred to me that the next Friday the 13th in February‒which will be in 6 years, as I noted in the past‒will not be followed by a Friday the 13th in March!  2032 (six years from now) will be a leap year, so there will be 29 days in February, so there will be no Friday the 13th in that March.

The next paired ones, then, will be a further 5 years after that, in 2037 (not a leap year).  It would have been 6 years later, but there are two leap years in that interval, 2032 and 2036, so the next one comes a year sooner than it would otherwise.

It occurred to me that, because of the frequency of leap years, which is almost twice that of the cycles of days of the week, the frequency of those paired dates may well be once every 11 years rather than every 7.  At least those are both prime numbers.  I’m not going to work out some exact formula right now, though.  It’s not really important.

Of course, one could say that nothing is truly important, and I am persuadable along those lines.

There is a Doctor Who Christmas Special (the one from series 5) in which the antagonist/guest protagonist (played by Michael Gambon!) describes a woman in a cryo chamber as “nobody important”, and the Doctor characteristically responds by saying, “Nobody important?  Blimey, that’s amazing.  You know, in 900 years of time and space, I’ve never met anyone who wasn’t important before.”

This is typical Doctor, of course, but it raises the objection Dash (from The Incredibles) voiced when told that everyone is special:  Saying that everyone is important can be the same thing as saying no one is.

Of course, important is in the eye of the beholder.  But then again, the beholder is not important, either, except in its own subjective estimation and perhaps that of a few other, equally unimportant, owners of such eyes.

So, yeah, one could argue relative and subjective importance from local points of view, which is valid but more or less vacuous outside its small scale as far as I can see.  On a cosmic scale, it’s all just dust and shadows.  But you could also say that about the entirety of the cosmos itself.

I guess import has always been subjective, even though people are not inclined to see it that way.  But, of course, people are the products of their “local” forces, and they are not responsible for the laws of nature, nor for the things which have happened in the past that have affected them in the present (which could come under a certain interpretation of “the laws of nature” in and of itself).  I won’t get into all that now.

Going back to the shower, but on an entirely different subject, I was also thinking about the effects of diminishing amounts of shampoo in the bottle on the center of gravity of the bottle.  At the start, when it’s full, the center of gravity is roughly in the geometric center of volume of the whole thing.  But as one uses the shampoo, the center of gravity shifts lower and lower, since the air replacing shampoo in the upper part of the bottle is much less dense than the shampoo or the bottle.

But then, as one gets to the dregs, the smaller and smaller amount of shampoo in the bottle contributes less and less to the overall mass distribution of the bottle and its contents, and the center of mass begins to head back up.  Finally, when the bottle is “empty”, the center of gravity will have returned to almost the same place it was when the bottle was full.

All that’s fairly trivial, well-known stuff, I know.  But it got me to thinking about how much of the laws of physics, such as the laws of gravitation (Newtonian form), are solved using such concepts as the center of mass, which is really just a way of combining and averaging the effects of numerous tiny bits of gravitating material as if they were concentrated at one point.

Much of the mathematics of physics works this way, coarsely approximating the very fine details of reality in a way that provides reliable, reproducible guidelines and can produce testable predictions.

But the granularity of reality doesn’t actually ever go away, not at any level.  Even at the level of the quantum wavefunction of a single “particle”, the actual behavior of the thing as it interacts with things in the “larger” world is the summation of the effects of all the possible quantum states of the electron superposed upon each other and interacting with things‒everything‒which are also just collections of superpositions of quanta.  That superposition happening in a “space” that doesn’t directly coincide with the macroscopic space we experience, but whatever its dimensions are, they are real, because they have durable, reproducible effects.

Mathematics may be unreasonably effective in the physical sciences, as Eugene Wigner famously noted, but it seems not to be a refining of description but rather an averaging out, a glossing over, the inking of an underlying rough pencil drawing which nevertheless still constitutes the real, original picture.

It may be that, in a sense, all science is just various forms of statistical mechanics.  We know that, at larger scales, we definitely need the tools of probability and statistics to navigate as best we can the territory of reality.  And yet, we don’t teach this sort of stuff to most people, ever.  I wrote a post about this on Iterations of Zero, if I remember correctly.

I could go on about all this rather easily, I guess, but I am using my smartphone today, and my thumbs are getting sore.  That’s okay; yesterday’s post was probably way too long, anyway.

If I did a video of my thoughts on this I might be able to get into more detail, though it would probably be even more erratic and tangential than my writing.  Still, maybe it would be worth trying.

In the meantime, I’ll write at you again tomorrow.

*Go ahead, do a search on my blog page for Friday the 13th; I’m all but sure it will bring up the pertinent blog posts.