numbers

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“Bright and early for the daily races, going nowhere, going nowhere…”

First of all, I would like to point out a bit of numerical fun we have regarding today’s day and date:  it’s November 11th, or 11-11.  That’s the case whether you’re using the US or the European date ordering system, since 11-11 is indistinguishable from 11-11.  It’s also Tuesday, and we have 2 of the same number with 2 of the same digits, which each add up to 2, so, two twos on Tuesday.  Fun!

Well, maybe things like that are only fun for me, but I have to try to entertain myself and find fun where I can; no one is gonna do it for me, that’s for sure.

Speaking of fun, what about this crazy weather?  I imagine it must be worse for the rest of the eastern US where this front or thing or what have you has had its effect, but it’s remarkable enough here in south Florida.

Yesterday, the high was 80F (I think that’s just under 27C‒or almost exactly 300K‒but I’m doing the figuring in my head while on the way to work, so I may be off), but now, this morning, it is 51F, and it is supposed to get lower before it starts warming up a little.  That’s a 29 degree drop (in Fahrenheit‒it’s roughly a 16 degree drop in Centigrade or Kelvin, which I guess would make the current temperature 11C or 284K) in about 12 hours.

This is one of the days I’m glad I’m not riding my “scooter”* anymore, because when you’re going over 70 on the highway and it’s 50ish degrees out, the effective wind chill is brutal.

For most of the US, especially up north, and for Canada, the weather down here is probably laughable.  Canadians would probably go swimming when it’s 50 degrees Fahrenheit (10C), and not in a heated pool, either, but in one of those cold Canadian lakes.  I grew up in Michigan, so I’m not far from that background, myself; I swam in cold lakes and rivers quite a few times in my youth.  But of course, I’ve now lived in Florida for quite some time‒more than 2 decades‒so I’ve gotten a bit soft.

Ugh.  I’m doing a blog post about the weather!  I was even about to talk about whether I prefer it hot or cold, and to give my reasons.  I’ll let you guess, if you’re so inclined, but I need to veer away from this subject.  It’s one thing to discuss the science of weather and climate‒those are interesting and very nifty and important subjects‒or the mathematics of weather prediction.  But merely to talk about the weather is just too sad.

I already expect it will be the “hot topic” (ha ha) at the office this morning.

There are, of course, good, sound, biological reasons for people to be concerned about the weather.  But that is not what I’ve been discussing, is it?  I’ve just been discussing it because it’s a little bit out of the ordinary, and it’s easy to talk about the weather.  That doesn’t make it particularly fun or engaging, though.  For instance, I never did quite grasp the opening lyrics to the Tears For Fears song, Head Over Heels:  “I wanted to be with you alone and talk about the weather.”

Presumably this is some manner of love song, and in it the protagonist wants to talk to someone‒I presume*** the object of his affections‒about the weather?  I’m almost sure there’s more to it; perhaps it’s an expression of how gripping the loved one’s company is, such that even talking about the weather with them is something worth seeking.  I have to think there was depth there (I don’t know the song well), because these are the guys who wrote Everybody Wants to Rule the World, and also Mad World (though my favorite version of that latter song is not theirs but the cover done for the movie Donnie Darko).

I guess in some ways I am too literal-minded, but I do try to catch myself at it and make it into a joke when I can, which often works very well.

Speaking of literal jokes, here’s a little one I posted on Threads and Facebook and the website formerly known as Twitter yesterday.

I made the joke up on Sunday, when I walked past a (now-abandoned) furniture store which still had a sign out front like the one in my joke.  If you know me, you’ll understand why this joke occurred to me at that time.

That’s enough gibberish for now, I guess.  I’m certainly past 701 words.  I hope you all have as good a day as you could hope to have (even if it’s not necessarily as good as you could wish to have).  Stay warm, my friends.

*I used “scare quotes”** because it was a 650cc scooter, so basically it was a full-on motorcycle, just with continuously variable transmission.

**It wasn’t strictly necessary, but I couldn’t resist putting scare quotes around the term “scare quotes”.

***Though one must be careful.  As we all know, when you presume, you make a pres out of u and me, and that’s not as good a thing as it might have been in the past.

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It’s a prime day for a (slightly) shorter blog post

Morning has broken!

Does anyone out there know a good, reasonably priced morning repair service or person?  I really don’t have the money or time to go pick out and buy a new morning.

Ha ha.

Sorry.  I know that’s quite a stupid joke.  Still, it should give you some idea just how tired I am.

I should have been able to get a decent sleep last night, but I did not.  That shouldn’t be anything new to me, but some days the effects of the insomnia seem to pile up far more than on some other days.  And today is one of those “pile up” days, it seems.

Thus, I intend to make this a relatively short blog post today if I can.  To that end, I’m setting my “target” number of words to be 701 instead of the usual 800*.  701 has the added advantage of being a prime number, which always makes things at least a little bit better from my point of view.

It’s funny how, as numbers get bigger, there seem to be fewer primes (they fall off as something like the natural log of the number range at which you’re looking, if memory serves).  And yet, there are an infinite number of them‒the same “countable infinity” as the natural numbers, “aleph nought”:

Also, we have the twin primes conjecture‒which apparently most mathematicians think is correct‒that there are an infinite number of primes that are with 2 of each other.

It has apparently been proven that there are an infinite number of primes separated by no more than about 500 or some such (it’s probably a lower separation now, but I haven’t looked into it in a while).  That may not seem like much of an accomplishment, but remember, we’re talking infinity here.  No matter how big the numbers get** you will never stop finding new sets of prime numbers that are no more than about 500 apart.

That’s not particularly useful to anyone but number theorists, I suppose, but it seems very interesting to me.

Incidentally, 701 is not part of a pair of twin primes, since 703 is not prime (it has four factors) and 699 is obviously divisible by 3.  And of course there is only one even prime (the number 2) because all other even numbers are divisible by 2.

Sorry, I know many people find these things boring, but I’m a fan of prime numbers.  In any case I’m trying not to be so negative in my blog posts, since I think it bothers a lot of people and may even be contagious at times.

It certainly doesn’t appear to do me any more good than does being a voice crying out in the wilderness, so to speak.  And despite the excellent biblical reference***, voices crying out in the wilderness usually are not heard or received by anyone or anything that can even understand them, let alone offer them any help.

I guess I can still talk about “imaginary” and complex numbers, because they just involve the square roots of negatives, but are not necessarily negative themselves****.  As long as I avoid multiplying them together, I should be able to steer relatively clear of negativity.

Ha ha, again.

I’m trying to try to avoid making other people miserable by expressing my own dark thoughts, so instead it seems I will make others miserable with my bad jokes.  You’re welcome.

Thinking about complex numbers makes me start feeling like I want to learn more about quaternions and spinors and so on, which seem truly fascinating, but about which I have only highly superficial knowledge.

It would be nice to learn more about them.  I probably will not, knowing me and my fatigued and distractible mind, but at least I can maybe be on the lookout for Numberphile videos about related subjects.  There’s at least one YouTube channel with a series on spinors.  Unfortunately, PBS Infinite Series stopped making new videos some time ago, but at least PBS Spacetime is still going strong, as are all of Brady Haran’s excellent channels.

And now, I’m over 701 (in the first draft), and so I’m done (for today at least).  I hope you all have a good day, and that your subsequent good days scale as the number of days, not as any logarithm thereof.

*I almost always go over my target, but at least it gives me a noteworthy place to decide it’s “time to wrap this up”.

**And there are described numbers so large that if you could memorize every digit of them, the information would be so concentrated as to turn your head into a black hole.

***It’s from the book of Isaiah.  John the Baptist supposedly quoted it and referred to himself as that voice, but then again, a lot of the writers of the “New Testament” shoehorned in references to supposed prophecy in the “Old Testament” to make the whole thing seem more sexy-cool (I guess).

****I just have to try to keep to the right upper quadrant of the complex plane.

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“The sun is the same in a relative way, but you’re older.”

Okay, well, here we are.  It’s Wednesday.  I don’t know what else there is to say about the day.  I guess…yeah, I don’t know.  It’s another day.  It’s a stretch of (roughly) 24 hours, the specifics depending on whether you’re using solar time or sidereal time or just the “self-contained” UTC time*.

UTC time is kept on a variety of clocks around the world and is based on the oscillations in the hyperfine transition frequency of the Caesium-133 atom.  That frequency has been defined as 9,192,631,770 Hz.  The international measuring community thing, whatever they call themselves, thereby agreed on defining the second as exactly 9,192,631,770 of those Caesium-133 oscillations.

Of course, oscillations of atoms, like all other processes that take time, slow down with increased spacetime curvature and with increasing speed relative to any given observer.  This is why the GPS satellites have to adjust their own time to account for both special and general relativity.  It’s pretty cool; you’re carrying proof of Einsteinian relativity in your smartphone.

You probably already knew that.

Then, of course, once they’ve decided on the precise value of a second‒knowing that the speed of light (or more precisely the speed of causality) is constant‒they then defined the meter as how far light travels (in a vacuum) in⁠ 1/299,792,458⁠ seconds (approximately 30 2/3 “vibrations” of a Caesium-133 atom).  Mind you, two observers moving relative to each other will see their meters as different each from the other, but c’est de la relativité.

It can be easy to imagine that definitions of units in science (and related fields) are not merely arbitrary but circular, almost tautological.  But really, given that these are attempts to codify specific attributes of reality itself, they would almost have to be self-referential with each other to be useful.

The length of a day is something that happens for real.  Thanks to the base 6 and 12 numbering system of the Babylonians, the day was long ago arbitrarily divided into 24 hours, each 60 minutes long, and each 60 seconds long, so a second was 1/(24 x 60 x 60) days or 1/86,400 of a day.

That worked well for a long time, especially since, before Galileo et al, humans couldn’t really measure time very precisely, anyway.  And then, until railroads allowed rapid travel between cities, it wasn’t necessary to worry too much about having the same time in different places.

But eventually that did become useful and necessary for many purposes, and eventually it was realized that a day wasn’t exactly what we were calling 24 hours, and indeed, that the length of a day varied slightly from day to day and year to year; also, a year isn’t a whole number of days long.  Also also, a day could be measured relative to the sun‒which is close enough that a day doesn’t end quite exactly after one full rotation since the Earth moves relative to the sun over the course of a day‒or with respect to distant stars, by which estimate a day comes closer to being exactly one complete rotation.

For most people most of the time, though, this precision, and that upon which it is based, are probably not merely irrelevant but unknown and unguessed.

Likewise, I don’t know how many people know about how Celsius made his temperature scale 100 degrees between the freezing and boiling of water at sea level pressure (a pretty reasonable choice, though I’m led to understand he initially had 100 assigned as the freezing point and 0 the boiling point!).

Then it was discovered that there existed a minimum possible temperature in principle, and they decided to set that scale, the Kelvin scale (named after William Thompson Scale**) using degrees of the same size as Celsius, but with zero defined as‒understandably enough‒absolute zero.

It’s all fairly interesting, if you’re in the right frame of mind.  But, alas, there’s every reason to suspect that all this information will be rendered moot and useless and perhaps even lost as the world winds down, or if life is replaced by artificial intelligence, or everything ends in some other way, as seems more than possible even in the relatively short term.

In any case, the laws of physics, as we know them, seem clearly to predict that the universe will tend toward ever-greater entropy and eventually all life, all structure will end.  Sometimes, I think it cannot happen soon enough for my taste.

Then again, there are cyclic universe proposals, such as Roger Penrose’s Conformal Cyclic Cosmology.  It bases its model on the fact that entropy, though always tending to increase, is not really an absolute quantity, not a substance, and that our universe’s “maximal” entropy may be the next universe’s low-entropy beginning, just on different scales; it doesn’t even require any “inflationary” burst of expansion to explain the uniformity of the CMB, I think.  I haven’t yet finished Penrose’s book about CCC, because though he is a stunningly brilliant mind, his writing can be a bit plodding and dry.

I guess it’s hard for any person to be good at everything, though Penrose has many strengths.  If memory serves, he invented a set of shapes which can be used to tile an infinite plane (in principle) with no gaps and no repeating patterns.  Supposedly this has been proven to the satisfaction of professional geometers, though I am not familiar with that proof.  Still, if it is a mathematical proof, then it is one of those rare things that we know to be certainly true, given its set of axioms.

It’s not necessarily useful in any practical sense, of course.  For instance, I think it’s probably true that any tiling system that can tile an infinite plane without repeating could not be used to tile a closed, finite, simple geometrically shaped portion of a plane‒such as a rectangular room.  I think you would always have to cut some of the tiles as they reach the wall, no matter how big the room is, as long as it is finite.  I do not know this for certain, that’s just my intuition.

Well, I guess I’ve wasted space and time enough here for now.  It’s no more wasteful than has been my entire existence, I guess, but also no less wasteful.  Or is it?  I don’t know.  In any case, for now I will stop wasting your time.

Please have a good day.

*Yes, it’s probably redundant to say “UTC time”, but the order of the acronym is sort of Yoda-esque‒it did not originate with an English term‒so I feel it’s tolerable to use it this way here.

**That’s a joke.  He was really William Thompson, the first Baron Scale***.

***I mean the 1st Baron Kelvin, of course, all joking aside.  A baron scale sounds like some long forgotten and unused (i.e., barren) bit of laboratory apparatus, left for eons, gathering dust in an abandoned world, like the broken statue of Ozymandius.  It’s very sad.

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The blog and baseness of our natures would conduct us to most prepost’rous conclusions

Hello and good morning.  It’s Thursday again, and I’m writing my Thursdaily blog post.  There’s not much more to say about it than that.  It’s terribly boring, isn’t it?  Honestly, I don’t know what I’m going on about, here or in the rest of my daily life.

I do, though, have one thing to ask out into the ether (not to be confused with the ethernet):  Does anyone know how to disable (permanently) the default “Aptos” font in the Microsoft Office applications?

I’m not asking merely to find out if there is such a person.  Presumably, someone at Microsoft will know how to disable that moronic and ugly font.  I’m more interested to know if someone among my readers can give me specific and clear instructions about how to do it.  Because if I never see Aptos again, that would be the only satisfying outcome with respect to that font for me.

Oh, also, can we find out how to disable their stupid AI “copilot” until someone asks for it, not make its irritating icon just pop up until you tell it “dismiss until next time I open this document” or whatever?  I don’t want it dismissed until next time.  I want it dismissed until sent for, which is unlikely to happen (but not impossible, which is why I say just to disable it until called for rather than, as with Aptos, permanently deleting it).

All that, noble readers*, is about as interesting as my life gets for the most part.  I am not walking/have not walked today, because I still feel worn out and terribly stiff and uncomfortable, and my left knee is still sore.  All of this does not help my chronic pain, either (other than helping it to persist and to become more prominent).  At least I have a tighter brace on my left knee today, as well as on the other knee (that would be my right knee, which hopefully is obvious).

I wear a brace on the right knee both to prophylax against it developing pain and to keep things even.  I’ve noticed that if I do that, I get fewer blisters on my right foot than if I walk with a brace only on my left, problematic knee.  This implies (to me) that the brace on the left knee shifts the way I walk overall enough to change the pressure points on my right foot when I’m stepping, and thus there develops increased abrasion in between my first two toes on that foot.

Exciting stuff, isn’t it?

I’m being facetious, of course, but maybe that isn’t clear.  Maybe this is all dull** and it’s hard even to tell when I’m not being serious.  I don’t know what to say, though.  Obviously.  But just as obviously, I will keeping saying things despite not having anything of merit to say.  I’ll even allow myself to use one-word sentence fragments for emphasis, because I suspect my subject matter is too dull to allow merely usual written language to keep the reader engaged, so I must resort to cheap rhetorical tricks of writing to imitate verbal communication in some ways.

I wish I had something more to discuss, some interesting subject, some curious conundrum—or even a conundrum that doesn’t have any interest in learning about anything.  Alas, as far as I can tell, I have no such thing.  I’m very frustrated by the pain that makes exercising so difficult, and by the fact that I have so much trouble with bicycles—though at least part of those difficulties would probably be better if I weighed less.

Okay, here’s a mildly interesting thing:  at the end of that last paragraph (1st draft only, I fear), I had written exactly 666 words.  Those of you embedded in a culture that has historically been influenced by Christian mysticism will know that number to be the one supposedly given by “St. John the Divine”*** as the number of “The Beast”, the so-called antichrist.

Now, Sinjun there made it clear he wasn’t writing blatantly and obviously but giving some kind of cryptic hint—I suppose it’s a good way to keep readers engaged and imagining silly things for at least a few millennia so far.  He wrote something along the lines of, “Here is wisdom.  Let him who hath understanding count the number of the beast, for it is the number of a man, and the number is six hundred, three-score, and six.”  (This is the English translation, of course.  It was apparently originally written in Greek, which I neither read nor speak.)

However, much to what ought to be the embarrassment of all those credulous bumpkins who have been frightened of that rather banal number for so long, it’s my understanding that in the oldest surviving version of the text of Synjon’s apocalypse****, the number of the beast was actually 616!

How did the beast manipulate the process of translation and get the scholars to mis-record the number as 666?

Okay, well, I don’t think any “beast” actually did that, but it’s a funny fact that so many people have it wrong, considering how susceptible people are to numerology.  At least I can have some sympathy for such a thing, for I love numbers in general, and 666 does have a nice symmetry and charm to it.  It’s not as symmetric as 888 or 000, but maybe that subtle lack of symmetry adds to its grip on the mind.

And, of course, “1 and 1 and 1 is three…got to be good lookin’, ‘cause he’s so hard to see”.

Come together?  Well, don’t do it over me.  And there’s no urgency, so feel free to do it right now or not.  Otherwise, try to have a good day.

TTFN

*I think reading is noble, if the what we call nobility matters at all and is based on anything of real worth.

**It’s a bit weird how “all” and “dull” are almost, but not quite, rhyming words.

***Not the author of the Gospel of John.  I guess “John” has just always been a common name.  Every Tom, Dick, and Harry is named either John or Robert, it seems.

****That’s just a synonym for “revelation”, by the way.  It doesn’t specifically mean the end of the world, it’s just become associated with the notion.  And Armageddon is named after a neighborhood near Jerusalem, I think:  Megiddo (I’ve probably misspelled it).  And “holocaust”, which apparently comes from middle English through French and Latin and Greek and even Hebrew, has a meaning that’s fairly plain when you break it down:  “holo-“, meaning everything, as in “hologram”, and “-caust”, relating to burning, as in “caustic”.  So, “burning everything”.  Nifty, huh?

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Only the truly continuous is infinitely divisible

Well, it’s Friday, the last day of another work week—the first full week of August (or Sexember, if you prefer) in 2025.  And here I am writing things that, so far, are not only trivial but banal.  Perhaps, as I go along, I will write something more interesting and surprising, but so far, I’m not impressed with myself.  I guess these things happen.

I did not end up riding my new bike back to the house last night, because there were thunderstorms in the area, particularly down by where I live.  I’m not too intimidated by riding a bike in the rain, but it’s a new bike, and its configuration is different than the type to which I am used, and it is slightly wobblier than my normal, so I felt it wasn’t a great idea to ride it five miles in the rain.  It turned out the rain was almost over by the time I got to my train stop, but it was nevertheless still quite wet and puddly, and I probably was wise-ish to avoid riding in it.

Still, it’s slightly frustrating.  Hopefully, today it won’t be an issue, because it would be a shame to miss the whole weekend with it by the house.  There are supposed to be thunderstorms today again, but they are expected earlier in the day than yesterday, and the weather is predicted to clear by early evening.  That should be fine, at least.

Of course, weather prediction is never perfectly precise—Chaos Theory being applicable and all that—but forecasts done for only twelve hours or so in the future are likely to be much more accurate than those for a day or a few days or a week ahead of time.  After about five days, trying to get too specific a forecast is a bit of a waste of effort, and it may always be.  One cannot, with finite computing power, calculate things to infinite precision, and without infinite precision, in the long term, Chaos makes one’s predictions ever more inaccurate.

Of course, that raises (not “begs”!) the question of whether reality is actually defined in any meaningful sense down to the level where limitless precision would apply.  In other words, are Real Numbers actually a thing that exists in reality?  That may seem a strange question, given that they are called “Real Numbers”, but that’s just a name, given by humans as a file heading if you will, a way to index the subject.  It doesn’t actually signify the reality of the real numbers, any more than those who call themselves “Conservative” in the current US are in any legitimate sense conservative by most agreed upon uses of that word.

Of course, all non-complex numbers are Real numbers, and all Real numbers can be considered complex numbers (just with a zero i component if they are only Real).  The counting numbers are still Real numbers, as are all the integers and fractions, and of course, all our best known “irrational”* numbers, like π and e.  But the vast majority of Real numbers cannot be specified by any reductive formula or algorithm, but have do be described digit by digit, forever—maximum information-type entropy.

So, to describe fully a “typical” specific Real number usually requires infinite information, with infinite precision.  But there’s a real (haha) question whether any portion of reality is defined so precisely, or whether that could even have any meaning.  As far as we currently know, the smallest distance that has physical meaning is the Planck Length (about 1.6×10−35 m), and the shortest time that makes physical sense is the Planck Time (about 5.4×10−44 s), and so on.  These are very tiny numbers, but they are finite, not infinitesimal, and are certainly not infinitely non-repeating decimals.

But does the Planck Length (and Time) apply to actual, bottom-level reality, or is that merely a limit within the constraints of our current understanding?  We don’t know, for instance, how such things apply to gravity when it becomes strong enough for such scales to apply.

It’s mind-boggling, or at least wildly stimulating of probably inexpressible thought, that reality may be only finitely defined at every given point in space (which “points” themselves would only be finitely packed, so to speak, such that below a certain scale, the distance between two points would have no meaning) or that it may in fact be infinitely defined, down to the fully expressed Real Number level, and that indeed it may be infinitely divisible in the same sense Real Numbers are—and thus there would be, between any two points in spacetime, as many points as there are in ALL of spacetime.

Either possibility is wildly cool and difficult to represent internally—indeed, impossible to represent perfectly internally, but difficult even to contemplate roughly at any very deep level.  Is it any wonder that people like Cantor and Gödel were mentally ill, given the kinds of things they contemplated and explored?  I’m not saying those things were the reason for their illness; that would be a cheesy sort of magical thinking, redolent of an H. P. Lovecraft story.  But the contemplation of infinities and complexity and chaos is both sobering and intoxicating at the same time.

What do you know, I drifted into less banal areas after all.  I guess that’s a decent way to end the work week of blog posts.  I hope you all have an interesting and good weekend, without too many utterly unpredictable events (unless they’re good ones for you).

*Just to remind you, this does not refer to numbers that are in some sense crazy, just that they cannot be expressed as a ratio of two integers, no matter how large the integers.  That’s the original meaning of the word irrational, but the very fact that there existed such numbers seemed so horrifying to the old Pythagoreans—or so I’ve heard—that it almost immediately acquired it’s secondary, now more common, usage.

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Try to remember the kind of Sexember…

Well, first of all:  TBIF (Thank Batman it’s Friday).  I’ve been feeling particularly poorly this week, with sleep that’s even worse than my usual, and that is not good to start with.  At least, on the weekend, I can knock myself out at night with Benadryl and not really care that I will be groggy the next day.

I’m basically going to call this week a loss.  I haven’t gotten much of anything done that I had intended to do, and that’s discouraging.  But it’s a new month now, so there may be some psychological* tendency to think of it as a potential new beginning of sorts.  Mind you, there’s really nothing special about this day relative to any other; the length of a month is related to the lunar cycle and the length of the year, but only roughly, and the specific divisions are fairly arbitrary.

Of course, we know that August is named for Augustus Caesar, née Octavian, who succeeded in taking control of Rome after the assassination of Julius Caesar (after whom July was renamed).  But it’s interesting, at least to me, to consider what it would have been named otherwise.  September, after all, is named after the fact that it was “originally” the seventh month, as October was the eighth, November the ninth, and December the tenth.

So, would August originally have been named Sexember (the sixth month)?  I think that would be the correct form, though Latin scholars among my readers should please correct me if I’ve used the wrong prefix**.  If I’m correct, I would like to propose a global change of name for this month back to the potential previous name.

“Sexember” sounds like a much more fun month than “August”, with its dog day connotations and so on.  Although, the prefix “sex-” referring to six has, as far as I know, nothing at all to do with the word “sex” relating to the reproductive divisions among animals, nor to the process involved, which‒for good, sound, biological reasons‒is something dwelt upon and enjoyed and even obsessed over by so many.  But I’m not worried about etymological purity here.

Imagine the antics on the various social media as oodles of young people of all ages geared up to celebrate “Sexember” and talked about how they planned to celebrate it.  Of course, I suspect most people would exaggerate their planned exploits, as people tend to do.  Social media is a supremely fertile ground for hyperbole and posturing and pretense and performative outrage, whether about political matters or just how “hot” one is and how perfect one’s life is.  I wrote a song about this topic a few years ago:  Like and Share.  Here, I’ll embed it in this post.

That brings up an issue raised by a very old*** and good friend of mine.  He noted that, since the company which published my songs put things on YouTube with disabled comments, there’s no direct way for people to give me feedback on them, good or bad.  Of course, the songs are also on Spotify and iTunes and supposedly on TikTok and all those others, but many of those don’t allow comments, either.

My works are also among the various available background songs that one can choose for “reels” on Instagram and on Facebook.  I enabled that last bit, and even used one once.  You all should feel free to use them, too.  In principle, I get paid when you do****.

Anyway, the thought I had was that maybe I should embed the songs here, on my blog, as posts.  Or maybe I could create a new page, like the one I have for “my books”.  I could call it “my songs” and could put the officially released ones there, as well as ones in progress, and I could even share some of my covers.  If I shared them as blog posts, at least, comments would be always available, and are almost always welcome.

Of course, that covers and the incomplete stuff are already on my YouTube channel, such as it is, and I even have a created playlist with all of them in it.  Those are already available for comment and response on YouTube.  I’m a long way away from having a monetized YouTube channel, though, and this blog isn’t monetized, either (though I sometimes think maybe I ought to monetize it, at least partially, or make a Patreon account or something).

I’m not sure what I’ll do.

In the meantime, hopefully today will be better than yesterday, which was a day on which I quite literally wished to be dead, because I felt miserable and in pain and alone, to say nothing of failing to achieve what I’ve wanted to achieve this week (or in this life).  The thing that most prevented me from taking action on that wish was that the effort involved would have been too great.

I feel less bad today, which‒given the nature of number lines and greater than/less than meanings and equivalences*****‒means I feel better than I did.  I still haven’t crossed the origin into positive territory, though, and I don’t know if I ever will again.  That’s the consideration that leads to contemplation of death:  if one’s present and expected future wellbeing function is always in the negative, then a return to zero is a net gain.  It’s analogous to a jokey thing I used to say:  The one who dies with the most debt wins.

Enough of this nonsense.  I’ll call this post and this work week to an end now.  I wish you all an excellent weekend, and of course, enjoy the first of Sexember!

*I made an interesting typo when I wrote this word, one which I don’t think I’ve made before, though it would seem a very easy one to make, given the layout of the QWERTY keyboard:  I wrote it as “paychological”.  That seems almost like something that could be a new slang term, with related terms “paychopathology” and “paychopath”.

**Perhaps “Hexember” would be at least as proper or more so (though we don’t have “Heptember”).  I’m not sure.  That would surely please some of the many Goth people I tend to follow online, but it doesn’t have as broad an appeal as “Sex-” does.

***By which I mean he has been my friend from way back (starting freshman year of college), not that he is very old.  He’s roughly the same age I am, and‒though I often feel as if I’ve been kept alive by one of the great rings for centuries or even millennia beyond my natural time‒my real age, in proper time, is 55 years, soon to be 56.  Of course, there is no actual quantum leap in age at the anniversary of one’s birth.  Time is continuous‒or, well, it is quantized, but at the scale of 10-43 seconds.  So for all foreseeable, practical purposes within our lifetimes, it is continuous.

****Though the pay rate is nearly as miniscule as the Planck time mentioned in the previous footnote.

*****A pet peeve of mine is when some people denigrate the notion of choosing “the lesser of two evils”, particularly during elections, expressing such sentiments as “the lesser of two evils is still evil”.  This may be true in a simple-minded sense, but it misses the point entirely and expresses woefully clunky thinking.  Such a person might be expected to feel that owing a debt of $10 was not any better than owing a debt of $100,000, since both are debts.  But when you think about with which debt you’d prefer to be saddled, the difference is clear.  Money has a way of sharpening people’s intuitions regarding numbers.  Indeed, there’s some evidence that “negative numbers” were first invented to deal with debts.

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Neither jot nor tittle, but just a title

It is Friday.  Friday it is.  I do not, though, plan to eat any green eggs and ham, nor do I intend to train Jedi.  I merely like to fiddle around with words.  I have also even been known to write and speak about cellos and violins and violas and basses‒wording around with fiddles, that is.

Anyway, this should be the end of the work week for me, so don’t expect a blog post tomorrow.  I’m not saying that there definitely won’t be one; it’s an outcome with a low probability, but it’s not zero.  In principle, the probability of any physically possible event happening is never zero.  But the odds can be so vanishingly small as to be zero for all practical purposes.

For instance, it’s physically possible for the entire Earth (the Moon included) to quantum tunnel to the Andromeda Galaxy, but I wouldn’t hold your breath.  I suspect that the odds of it happening are so low that the time scale between now and the evaporation of the largest black holes due to Hawking radiation (roughly a googol* years) would not even begin to make it likely to happen, even if it weren’t for the fact that the Earth and the Moon will have been so dead and so disintegrated by then that even the memory of their memory’s memories would have been long since lost to any mind that might still exist at that time…probably.

So, you can treat that Earth-Moon Andromeda tunneling as “impossible” for all practical purposes, but in principle, it could happen…

…right…

…NOW!

Okay, well, as far as I can tell, it hasn’t happened.  The sky is too hazy for me to see if the stars have changed, but I don’t think they have.  It would be quite something to experience the local stars of a different galaxy, but of course, if we tunneled into Andromeda, we might be in a relative star desert, or we might be in a place with too many stars for our long-term safety.  Also, if our solar system’s net momentum persisted, we would be unlikely to arrive in any kind of stable orbit of the center of that galaxy.

And, of course, I did not say the sun would come with us‒that would make the whole thing even more vanishingly unlikely‒so we’d all freeze in fairly short order, apart from organisms that use geothermal sources as the base of their food chains and energy cycles.  Those might survive for eons.

Anyway, it’s vastly more likely that I’ll work and write a blog post tomorrow than that we will quantum tunnel to Andromeda**, but it is still a very small likelihood***.  It may be less than one percent, I don’t know.  But it’s quite unlikely.

So, though it might be worth a quick glance to check in come the morning, especially if you were going to do that sort of thing anyway, I would not go out of your way, and I certainly wouldn’t recommend holding your breath.  I don’t think even a sperm whale could hold its breath that long, and I think they have the longest breath-holding record of any mammal (if anyone knows otherwise, please let me know).

In other news‒not that I’ve really given you any news so far‒my keyboard arrived safe and sound (so to speak) yesterday afternoon, so hopefully this morning I’ll be able to finalize the chords to Native Alien.  Then, maybe this weekend, I’ll record a little guitar-chord and voice demo so I don’t lose track of the song.

Then, next week, I can start working on a song based on the trigger “humility”.  I still have no clear conscious notion of an idea for such a song, but I’m not worried about that.  I know I can produce something (not the Beatles song).

I have to keep reminding myself that I don’t need to produce anything great as far as lyrics go‒I think the lyrics I have for Native Alien, which I shared the other day, are okay but not terrific‒I just need to get some words down.  I can always edit and alter things as the process evolves, just as the first draft of a story (or to a lesser degree a blog post) is just the beginning.

I’m also continuing with the circuit course on Brilliant, and I’m alternating reading that book Vector and The Lord of the Rings (yet again) and my own book, The Chasm and the Collision (also yet again, though LotR still holds the 2nd place record for my number of reads, well ahead of CatC and only bested in number of readings by The Chronicles of Thomas Covenant the Unbeliever).

All these are things that I can do alone, of course.  If there’s something to do that would require someone else’s participation, well, I’m shit out of luck.

I think that’s a phrase that applies fairly well to me, come to think of it.  And the word “alone” might as well have my picture next to it in the dictionary.  Though that might be confusing, since I can think of other words that would merit my picture even more than “alone” would‒words that would do their part to explicate just why I am alone, no doubt.

Batman knows I don’t want to hang around with me.

Anyway, I hope you all have a nice weekend, and if anything truly improbable happens to you, I hope it’s a very good improbable thing.

*That’s 10 to the 100th power, or a 1 followed by 100 zeros, in case you’ve forgotten whence the software company cribbed their name.

**Quantum tunneling is not rare on small enough scales, though.  It happens countless times every second in the heart of the sun, for instance.  If it did not, there would not be enough heat and pressure to overcome the coulomb barrier to fusion, and the sun would be some very large equivalent of a brown dwarf…or maybe it would contract more and get hot enough for fusion to take place without tunneling, but then I think the sun would be hotter and brighter and more short-lived, and I think it’s unlikely that the Earth would have produced any life, let alone humans.

***Think about it:  if you took something with odds of ten to the minus 120‒that’s 119 zeroes between the decimal point and the first non-zero digit‒and then made it a billion times more likely than it is, you’d still have odds of 10 to the negative 111th power, or 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001.  This is a good reminder that relative risk (or probability) is not the same as absolute risk (or probability).

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If I could write the beauty of your eyes and in fresh numbers number all your blogs

Hello and good morning, and welcome to another Thursday morning blog post.

I’m not sure how many of these I’ve written, but since I’ve done them nearly every Thursday, even when I was writing fiction on all other weekdays (and excusing the occasional sick day), we can guess that I wrote on the order of fifty such posts a year for about ten years.  Thus, there are on the order of five hundred such daily posts over the years, each one nearly a thousand words long (and some going beyond that).  So, overall, the number of words I’ve written in these Thursday blog posts alone is comparable to the number of words in my longest novel (Unanimity…so long I had to publish it as two separate books).

Of course, when we approach it from the point of view of actual information, à la Claude Shannon’s information theory and whatnot, I would have a hard time estimating how much actual information there is in such a post.  In the first draft of the preceding paragraph and a half, there were 174 words, which comprise 940-ish characters (counting spaces, which I think one should count, since a space or the lack thereof can matter quite a bit in English).

Now, each character in a typewritten document, not counting ”special” characters, can have one of 26 letters (not counting upper and lower case as separate things for my current purposes) ten numerals, and maybe a comparable number of punctuation marks.  So, each potential space in the writing would have a total of roughly 26 plus 10 plus, say, 8 other characters, so 44 possible characters.  Rounding up, that’s about six bits per character (26 = 64).  Rounding down would give five bits (which is only 32 possibilities), so it’s something closer to 6 bits than 5.

Assuming the ratio of characters to words in the average blog posts stays fairly consistent, that would be, for a 900 word post:  (900/174) x 940, which rounding here and there* gives about 810,000 divided by, say, 180.  This can be reduced first to 81,000 divided by 18, or 9,000 divided by 2, or 4,500 characters per post.  Checking the math on the calculator gets roughly the same amount.

So, 4,500 characters, times five and some fraction bits per character, gives us between 22,500 and 27,000 bits of information per blog post.  Let’s say 25,000 bits.

But when I look at the storage space of my average blog post, they are almost all between 17 and 20 K (which is actually as much as 160,000 bits) in size.

This mismatch shouldn’t be surprising, because while English is (like most written languages) a “redundant code”, storing a word processor document entails storing more than just the individual characters.

Returning to what we mean when we refer to the redundancy of written English, we mean that not every new character gives you as much information as is potentially available.  For instance, if one types the letter “q”, what follows will almost always** be a letter “u” in English, and so we would be quite justified, at least in this, in writing the word “quite” as “qite”.  But, of course, redundancy in any kind of code is useful for counteracting the problem of lost data in transmission, which was one of the things Claude Shannon was thinking about in founding information theory.

There are surely other ways in which the data in a given blog post is “compressed” during the process of saving, but I don’t know enough about the computer science of word processors to know the specifics of how that’s done off the top of my head.  And since, of course, I write these blog posts “off the top of my head” each morning, I’m not going to try to research that subject for now.  That would make writing my daily blog much less pleasant, and make the process quite (ha) a bit (ha ha) longer than it would otherwise be.

Now that I’ve thought about it and mentioned it, I’ll probably be on moderate alert for information regarding the process if I should happen to come across it, and if I do, I’ll be more likely to focus on it and add it to my model of reality than I would have otherwise.

And now I am rapidly approaching the 800 word mark for this post, a mark which I will no doubt pass before I have finished writing the first draft of this sentence.  And, indeed, I did.  So let’s draw this very peculiar post to its close, today.

I’m sure many of you*** are thinking something along the lines of, “Geez, I hope he goes back to just writing about depression and chronic pain and all that shit tomorrow…this post has been really boring.”  To those people, I can only apologize.  To anyone who shares my idiosyncratic interest in esoteric (but highly amateur in my case) things like information theory and whatnot, well—I hope at least you have enjoyed this.

TTFN

*It’s okay to do this since I’m not trying to be terribly precise, just to get “back of the envelope” numbers for fun, anyway.

**Not in this case, of course, since there is a quotation mark after that last “q”…and this one here, as well.  So, the “u” is not a completely redundant character, but it certainly doesn’t give anything like 5 more bits of information.

***If a fraction of my few dozen readers can really be called “many”; I’ll let myself get away with using it as at least a relative term.

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Is an “almost” pair o’ dice just one die?

Oooooh, it’s Friday the 13th!  It’s so spooky!

Not really, of course.  It’s just a day.  I like Friday the 13ths, mostly just because so many people seem to imagine they are unlucky, though I think that superstition may be less prevalent now that it was in the past.  Nowadays, the day is probably mostly associated with the slasher film “series” that uses that title.  Not that even the original movie’s story ever had much to do with the day.  It just was a catchy, well-known “scary” day, following in the footsteps of Halloween (although the latter at least had a theme that suited the day).

Of course, a major reason I like this day is that the number 13 is a prime number, and I like prime numbers.  I like 13 especially, because 13 is possibly the most feared and reviled of the primes, associated with bad luck in much the way that 7 is associated with good luck.

Hmm.  I know at least part of 7’s appeal probably has to do with the dice game “craps”.  7 is the most common total to achieve when rolling two six-sided dice, because there are more ways to get that total than any other number.  Meanwhile, of course, there is no way to get a 13 on two (normally numbered) six-sided dice, but it is only just out of reach.  It’s the first number that’s too high for such a pair o’ dice*.

Of course, you can’t roll a 1 on two six-sided dice either, but that feels more trivial.

I honestly don’t think the reason for 13’s association with bad luck probably has anything to do with dice; it wouldn’t make too much sense.  But someone out there, please correct me if I’m wrong.

It’s interesting to think about probability regarding dice, not least because the very field of probability theory was first created by a guy who wanted to optimize his chances of winning at dice.  According to what I’ve read, he succeeded, at least temporarily.

Nowadays, of course, that field has grown into a special subset of mathematics and physics and information theory and so on, affecting everything from thermodynamics and statistical mechanics to meteorology and quantum mechanics.  In a certain sense‒given that Schrodinger’s equation describes wave functions that have to be squared (in a complex conjugate way) to get literal probabilities that, based on Bell’s Theorem, cannot be further simplified, as far as we know‒probability may be something truly fundamental to the universe, not merely a tool for situations in which we don’t have access to information.  Based on Bell’s Theorem, which has been shown to apply in the Nobel Prize winning experiments of Aspect et al, it seems that, at root, as far as we can tell, the quantum mechanical operations are fundamentally indeterministic.

Of course, just because something is “random” at a lower level doesn’t imply that, at higher levels of organization, it can’t behave in ways that are very much deterministic in character.  Lots of little things behaving in a locally random manner can combine to create inevitable larger-scale behavior.  Perhaps the most straightforward and compelling such thing is the behavior of gases and the Ideal Gas Law***.  The motion of any given molecule of gas is unpredictable‒at the very least it is stochastic and has so many degrees of freedom as to be unpredictable in practice, but since quantum mechanics is involved in intermolecular collisions, it may truly be random in its specifics.

And yet, when oodles and oodles of molecules of a gas come together****, their collective behavior can be so utterly consistent‒with very little depending on even what kinds of molecules comprise the gas‒as to produce a highly accurate “law” with only 4 variables, one constant, and no exponents!

If that doesn’t seem remarkable to you, either you’re jaded because you’ve known it since secondary school or I haven’t explained it very well (or both, of course).

It’s interesting to think about the probabilities of dice games using more than two dice and/or dice with more or fewer than six sides.  Tabletop role-playing gamers will know that in addition to the 5 “perfect” Platonic solids*****, there are quite a few other symmetrical (but with sides not formed from “regular” polygons) solid shapes that can be turned into everything from ten-sided to thirty-sided dice.

But RPGs tend to involve rolling one die at a time, except when rolling up characters, at which time (in D and D and Gamma World, at least) one uses 3 six-sided dice (or 4 when applying a technique to yield better-than-average characters).

I wonder why there are no games of chance using more than 3 six-sided dice or using, say, multiple four-sided dice or eight- or twenty- or twelve-sided dice.  The probabilities would be more trouble to work out, but they would not be harder in principle.  If any of you out there either know of or want to invent a game of chance using more than 2 dice and/or other than six-sided dice, feel free to share below.

In the meantime, I’ll call this enough for today.  I am supposed to work tomorrow as far as I know, though that’s always subject to change.  If there’s no post here tomorrow, then it probably means I didn’t work.  I probably will work, though I couldn’t give you a rigorous working out of the mathematics involved in determining that particular probability.

Have a good day if you’re able.

*You can sometimes see them by the dashboard lights.

**Unless superdeterminism is correct.  However, this is a very hypothetical thing, and I’m not very familiar with what arguments are proposed to support it, so I won’t get into it.

***PV = nRT if memory serves. [Looks it up]  Yep, that’s right.  Four variables and one constant (R).

****Even if it’s not right now, over me.

*****These are, presumably, solids that really care about each other but in a non-romantic way.

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“It’s just the kind of day to leave myself behind”

Well, it’s Tuesday, isn’t it.

Note that I ended that sentence with a period, despite the fact that it seems to be in the form of a question.  That’s because I didn’t really mean it as a question; I had no desire to imply that I wasn’t sure what day of the week it was.  I’m reasonably certain that today is Tuesday.

I’m not absolutely certain, of course, because outside the realms of self-contained systems of mathematical or logical axioms and rigorously defined and applied operations, there can be no true certainty, only higher or lower credence.  Real-world probabilities never reach zero or one.

Mind you, some things are so likely as to be practically certain, and there’s not much point in worrying about whether they are true unless and until some completely new evidence and/or argument makes itself known.  Such is my conviction that today is Tuesday*.

No, I was expressing a sort of resignation about the fact that today is Tuesday.  I would have said it in a sardonic tone had I been speaking aloud.  It’s not that Tuesday is an especially bad day of the week necessarily, notwithstanding the Beatles telling us that Tuesday afternoon is never-ending.  No, it’s just that Tuesday is still practically the beginning of the week, but I am already tired from Monday, and it’s a long way until the weekend, especially if one works on Saturday, which I am going to do, as far as I know.

That last statement has a lower credence than I give to the fact that today is Tuesday, but it’s still well above a 50% chance.

I know, I know, why am I writing this inane nonsense?

It’s just stream of consciousness.  I’m not planning it out, except to the extent that something I’ve written already makes me think of something else I want to write next.  But I have no particular chosen topic today, obviously.  Not that this is atypical.  I almost never have any plan when I start writing blog posts; I just start writing.  Sometimes I’ll just start with an inane phrase, like I did today, and see where that takes me.

Oddly enough, I think when I do have a particular topic in mind—such as in my short-lived series My Heroes Have Always Been Villains—people don’t seem to enjoy my posts as much.  Or, at least, I don’t get as many “likes” or views.  Maybe some people read and “like” them via social media or something, but if so, whatever they’re doing doesn’t reach me as feedback.  I don’t really see comments or responses that aren’t done here on my page.

Of course, as you may already know, the initial purpose for this blog—in this incarnation—was to try to promote my fiction by interacting with potential readers.  Boy was that a dud of an idea!  [No question mark ==> rhetorical, but not really a question].

More people read and have read this blog than ever read any of my books, unfortunately.  It’s rather discouraging, and it’s a large part of why I haven’t been writing fiction for a while, and the last thing I wrote, Extra Body, I just published here.

While I always write the stories I want to write and that I will enjoy (or whatever one might call the process) there really is a rapidly diminishing marginal return as one writes books that almost no one is even aware of, let alone purchases, let alone reads.  And as you know, I have no stomach for self-promotion.  Sometimes I envy narcissists, at least for an instant; then I remember that I tend to find them disgusting (though just a smidge of narcissism can be endearing in the right circumstances).

I also am not very good at interacting with people who might help promote my work, let alone at asking for that help.  I’m pretty good at the creative stuff, or at least I’m tolerably good at it.  I can write, I can draw, I can do music (playing and singing) and other similar stuff.

I’m also pretty good at science and math, and not just in a rote learning sense; I’m pretty creative there, too.  I once invented my own “number” which I call a “gleeb”, the symbol for which was a combined cursive g and b:

The nature of a gleeb is that, if you multiply it by zero, you get one (in other words, a gleeb is the “forbidden” or “undefined” result of 1/0).  That may not seem to make sense, but while I was “up the road” I even worked out some of the algebra and properties of such a number, and it turned out—to my inexpert analysis—to be logically consistent, at least.

I’m not saying it’s useful.  As far as I can tell, it’s not.  But it was a bit of mental fun and exercise, perhaps the intellectual analogue of playing hacky sack.

I’ve also occasionally thought of ideas in physics and in medicine that I thought were interesting, and which later I discovered had actually become areas of research or therapy (the therapy bit is in medicine, not in physics…as far as I know, there are no therapies in physics, despite the fact that there is such a thing as physical therapy**).

But I am not good at putting myself forward or putting myself out there or calling attention to myself.

Okay, well, I guess that’s enough meandering nonsense for the moment, though such nonsense can sometimes be fun.  Hopefully, Tuesday afternoon will not become some bizarre event horizon in which we are stuck forever.

Of course, the person going through the event horizon doesn’t experience the process as eternal; only the distant observers “see****” them slowing and slowing and coming finally, asymptotically, to a complete standstill.  The person who goes through, if they are looking backward, might see the whole history of the universe playing out before them—at least until tidal forces spaghettify them—but they will not experience time stopping.  Think about it:  how could one experience time stopping?  The passage of time is inherent in the process of experience, certainly as we know it.

I hope you have a good day.

*And even if it weren’t, I could just call it Tuesday and say that I have my own way of naming the days of the week, and it would be no more arbitrary than the one in use here in the US and elsewhere.

**This is as opposed to psychotherapy, of course, but it also can lead one to imagine such things as ethereal therapy or conceptual therapy or metaphysical therapy.  What would that last one be***?

***See, I ended that sentence with a question mark; it really was a question, though mainly a rhetorical one.

****I put that in scare quotes because as a person (or whatever) gets closer and closer to an event horizon, any light or other signal leaving them, heading outward, gets red-shifted to longer and longer wavelengths, so it becomes harder and harder actually to see them.  In the end, we cannot truly observe them stuck there forever, because the wavelength of the light leaving them approaches infinity.