statistics

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You’re so vain, you probably think that nothing matters

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.

 

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You cataracts and hurricanoes, spout till you have drench’d our steeples, drown’d the blogs!

Hello and good morning.

I’m going in to the office today, since down my way, Hurricane Milton has not been very impressive so far.  This is not a surprise.  We were always going to be only on the periphery of the system, and on the leeward side of the state (so to speak).  There wasn’t even any rain of significance down by where I live; just a bit of relatively high wind.

We are going through a bit of rain as I ride in my Lyft to work, but for south Florida, it’s a piddling amount so far.  The wind is mildly interesting, but I’ve ridden a 650 cc scooter (basically a motorcycle with automatic transmission) through wind and rain much worse than this.  I don’t think that was a wise thing to do for anyone who cared about his or her life and health much, but for me, it was just fine.

I’m in a Lyft, by the way, because the train service is suspended today, as it was yesterday.  This was probably not absolutely necessary, but I respect the abundance of caution.

Traffic, at least, seems very light, which is also not surprising.  Most people in the area are not working today, I suspect.  We shall see how many people come to the office today.

I’ve been a bit frustrated lately, as an infection of some kind (possibly a few different ones) has afflicted quite a few people at the office, but I have not gotten sick.  Not only would such an illness give me the opportunity for rest for which I am able to excuse myself (and might even allow me to sleep, given the physiology of the immune response), but it’s also an opportunity potentially to develop some more severe, life-threatening superinfection*.

Apparently, some people used to call pneumonia “the old man’s friend”.  Well, I’m not that old (and I wouldn’t recommend my friendship to anyone, even a pulmonary infection) but apparently the average lifespan for people on the autism spectrum‒assuming that I am, which I give very high likelihood‒is somewhere in the mid-50s.  So, it wouldn’t be unreasonable for something to kill me sometime soon.

Of course, such averages are strongly affected by outliers.  People with the highest support needs are probably more likely to die at significantly younger ages, and that will tend to bring the average down.  It’s a bit like how the very high infant mortality rate strongly skewed the average lifespan in pre-modern times.  People who did reach adulthood probably didn’t live much shorter lives than we do now.

Actually, modern people in the west may be backsliding lifespan-wise, at least in America, as we eat more refined carbs and are less active and so are more prone to hyperinsulinemia, which brings with it not just increased risks of diabetes and elevated lipids, but even increased risks of high blood pressure, heart disease, stroke, and many cancers, as well as infections.

The infant mortality issue illustrates one way in which reported average lifespans and similar statistics can be misleading, at least for people who don’t understand what’s behind the numbers.  It reminds me of something I may have discussed here before:  people (rightly enough) make fun of the fact that (to make up a statistic that’s probably not too far from reality) ninety percent of people think they are above average drivers.

Now, it is almost certainly true that ninety percent of people are not above average drivers; it’s just that so-called neurotypical people tend to have overinflated (and undeserved) senses of self-esteem.  But the notion that seems to be implied in most discussions of such statistics is that it’s impossible for 90% of people to be above the average.  This is not the case, at least not if “average” refers to the arithmetic mean, as it usually does.

If ninety people out of a hundred each scored exactly 51 (out of a 100, say) on some test of driving ability, and the remaining ten only scored 1 point each, then the average score would be ((90 x 51) + (10 x 1))/100, which is 46.  So, ninety percent of people would not only all be above average, but would be five points above average.  It’s not a very impressive score, but it is true.

Now, if it were said that ninety percent of people think they are above the median, then that would be erroneous by definition, because of the meaning of the term “median”.

Most people don’t seem to understand these and other mathematical concepts, and yet those concepts and related ones of many and varied kinds can have significant impacts on the lives of billions.  I once wrote a blog post on Iterations of Zero recommending that probability and statistics be more aggressively emphasized in secondary school education, because I think understanding them would give people far greater insight and even agency in the world.

And yet, we see “humorous” memes such as the one below, of which there are numerous iterations and variations:

pythagorean meme

I say the fault for that lack of use lies with the individual, not with their education.  Just because they don’t use the Pythagorean Theorem doesn’t mean it isn’t and couldn’t be useful**, and even if the specific theorem wasn’t useful then the capacity to do it and other, related things, is useful.

I feel I may have mentioned it here recently, but even when one doesn’t use mathematics*** in one’s profession, working with them strengthens the mind and makes it more fit for many other purposes.  Usually, one doesn’t do push-ups to become really good at doing push-ups, and one doesn’t jog in order to become a really good jogger.  One exercises to become stronger and healthier, more capable.  The mind is even more responsive to exercise than is the body, and if there are limits to how strong it can become‒in whatever sense‒I don’t think anyone has come close to reaching them****.

That’s that for today.  I hope you’re all weathering your personal storms reasonably well.  The one down here hasn’t done much to me; I probably could have slept outside in the rear of the house last night without any trouble.  The wind might have been soothing.  It might even have helped me get a better sleep.  It’s not as though it could have been much worse.

TTFN

*By which I mean an infection that opportunistically occurs due to the body’s weakened defenses caused by an initial infection, not an infection with exceptional nature or virulence.

**Understanding geometry is so potentially useful in so many ways that it’s said that the only time in his life that Isaac Newton laughed was when someone asked him what the point was in studying Euclid.  Newton is universally reputed to have been quite arrogant, vindictive, and impatient, to say the least.  One can only imagine the sheer amount of vitriol and scorn that would have been conveyed by that solitary gelastic moment.

***Or philosophy, or physics, or chemistry, or biology, or history, or literature, etc.

****Not even Newton or Von Neumann.