numbers

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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.

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O heavy lightness, serious vanity, misshapen chaos of well-seeming blogs

Hello and good morning.  It’s Thursday, of course‒thus the “traditional” opening salutation‒and here I am again, writing another in a line of hundreds of Thursday blog posts.

Have I said all that I could say, already?  Probably not.  The number of possible 800+ word strings of English writing is surely unfathomably vast.  If I were going to try to give some kind of upper boundary, we would consider that there are a few million words in the English language, and I could just try to solve for a few million to the 800th power.  That’s a huge number (104800). But most of those combinations‒all of them, effectively‒would be nonsense.

By “all of them” I mean that, if one applies the constraints of grammar, or even just of making tolerable sense to a potential reader, the number of strings of 800 coherent words is so much smaller than the number of possible strings of 800 words without care for sensibility that, if one were looking at some shape or field that represented the latter, the former would probably be too small to see, given the constraints on the resolving power of visible light.

It’s a bit like the possibilities implicit in DNA.  The human genome is on the order of a billion or so base pairs* long, if memory serves, and each “site” on the genome has 4 possible “letters”.  So, the potential number of sequences of DNA in that genome is on the order of 4 to the billionth power, which would be 2 to the 2 billionth power, which is about 10 to the 600 millionth power (10600,000,000).

That’s a huge number. Remember, a googol is merely 10100, and it is already a number that far exceeds the number of baryons in the (visible) universe (which is on the order of 1080).  And remember how exponentials work:  every time you add 1 to the exponent you multiply by the base number, in this case 10.  So, 10101 is ten times larger than 10100.

As you can see, the number of possible DNA sequences is beyond astronomical, at least unless we get into, say, the measures of entropy represented by an event horizon, as an indicator of the number of possible quantum states it could have “within”.  But distances and times and numbers of particles in the accessible universe are unnoticeably small compared to the number of possible sequences of DNA**.

However, the vast majority of those base-pair combinations would certainly not code for anything that we would consider human, or indeed any other living creature that’s ever existed on Earth.  Most are the analogue of throwing random words together to make a blog post.  They wouldn’t come close to coding for anything that would be a living creature.

Nevertheless, even ruling out all the nonsense, the number of possible viable human genomes is vast.  It may still be larger than the number of particles in the visible universe, but don’t quote me on that‒I haven’t checked those numbers.  In any case, it’s much larger than the number of humans who have ever lived, and probably larger than the number of humans who will ever live even if the species goes on to become cosmically significant.

What this all comes down to, I guess, is that I haven’t come close to writing all the possible blog posts I could write, even ruling out ones that wouldn’t make any sense and even ruling out ones that differ from others only by a word or two.  I guess this blog itself constitutes a case in point.

But boy, it can be a lot of work trying to write something new every day, and even more work trying to write something interesting.  That’s why I don’t bother with the latter criterion; I just write whatever comes out, which is usually something at least mildly interesting to me, and I figure it’ll reach kindred spirits if they happen upon it‒and if such people even exist.

Speaking of kindred spirits, I hope you all have a lovely day.  At least I hope it will be as good as it can possibly be‒which it will, since once it’s happened, it can’t have been otherwise than it was.

TTFN

*In case you don’t recall, DNA is a long chain molecule of polymerized “nitrogenous bases”, adenine, guanine, thymine, and cytosine.  Because each DNA base can pair up only with its complementary base (A with T, G with C) this allows for high fidelity copying, and thus reproduction.

**Now, if the universe is spatially infinite‒which it looks like it is, but may not be‒then of course the number of particles or quantum states or even planets with life would be infinite, and thus larger than any possible finite number, no matter how big you might choose.  Fun things happen when one deals with infinities.

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Year-long quanta and Planck exercises for your core

Well, it’s Monday again.  Huzzah.

I don’t have much new to say.  I still do not have my air conditioner, thanks to the frustratingly poor delivery logistics of FedEx®.  I also have to blame the seller, of course (though I find the concept of blame mostly valueless) since they were the ones who advertised the unit as arriving between the 28th and the 30th of May (this year), and they failed to ensure that it would in fact arrive within their predicted time range.

Hopefully it will arrive today, and hopefully by the time I get back to the house I will have the energy to set it up.  Usually at the end of the day I barely have the energy to change my clothes.

In other news, it was my sister’s birthday recently.  That’s a good thing, and I’m glad she’s doing well.  It would have been nice to spend it with her, but that wasn’t doable given my recent life events.  Of course, I’ve said before that it’s a bit funny that we think of a person as one year older on their birthday, as though time applied to human age in quanta the size of one Earth year.

At the Planck scale time may in fact be quantized, but that’s a very, very tiny scale‒if memory serves, it’s the time it takes light to travel one Planck length*‒and for ordinary experience, the flow of time is continuous, though it is variable thanks to Relativity.

That got me thinking what it might be like if time did apply to humans all at once, one day a year.  I think that would have some curious consequences.  For kids, of course, it might be quite a cool thing, and they might look forward to each birthday enthusiastically‒especially around the time of puberty.

But for adults past their twenties, say, birthdays might become a thing of fear, or at least anxiety, and more so every year.  Imagine that even the long-term consequences of illnesses and injuries only accrued on one’s birthday‒possibly at the exact anniversary of the time one was born.  If you knew you’d been injured that year, you’d surely be dreading the birthday on which the consequences of that injury first fully applied.

Or what if you knew you were predisposed to some chronic complaint, or had a risk for some form of cancer, or of dementia, but you wouldn’t know if anything had happened until the time of your birthday?  I imagine everyone would plan to go to the doctor the day after every birthday, at least once they had passed their twenties.

It’s an interesting idea for a story, perhaps.  You could see people having birthday parties and the like, partly to celebrate and partly to offer support for their friends who were aging.  There could be whole special rituals surrounding the process, especially as people got old enough to perhaps die when the year accrued.

And then there could be a weird, truly bizarre occurrence.  Maybe one person would be found who, after aging “normally” his whole life, suddenly got younger at one year’s birthday, and then again at subsequent birthdays, as if there were some type of glitch.

Heck, even a person who aged continuously would be a freak of nature in such a world.

Anyway, that’s what I found myself thinking about.  It seemed mildly amusing.  I’m not going to write such a story or anything.  At least I don’t expect to write it.

Indeed, I’m basically finished writing this for today.  I hope you have a good day and a good week.

*Which is on the order of ten to the negative 35th meters.  That means that there will be thirty-four zeros after the decimal point before there is any other numeral, so…a very small distance across which causality may act at the “speed of light”.  Since the Planck length is 1.6 x 10-35 meters and the speed of light is about 3 x 108 meters per second, the Planck time would be 1.6/3 times (10-35 over 108) or .5 x 10-43 or just 5 x 10-44 seconds**.  That’s way, way too small for us to measure.

**Or .00000000000000000000000000000000000000000005 seconds.

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Let him that hath understanding count the numbers of the words

It’s Friday, and I’ve already heard, from the boss’s own mouth, that we are not going to be open tomorrow.  I think everyone at the office (including the boss!) has been working quite hard this week, and they’ve been doing things they wouldn’t usually be doing in addition to their regular duties, which they’ve all (well, almost all) been doing quite well.  Everyone could use a break, and I am certainly no exception.

I’m planning to make this post pretty short, today, because I am under the influence of steadily accruing fatigue.  Of course, I’ve said such things before, haven’t I?  And then I often go on and on and make quite a long post.

I wonder how many words I’ve written on this (and my other) blog since I returned to the outskirts of this world in about 2015.  I can do a little “back of the envelope” calculating, I guess.  I’ll slightly overestimate the daily word count as an average of about 1000, then balance that by underestimating the number of days I write per week at just 5 even, so that would be 5000 words a week or 260,000 words in a given year if I were only writing the blog, not working on (or counting) fiction.  So, that would make probably something over a million words since I started blogging, probably more (there were long stretches when I only wrote one post a week).

Of course, just one of my fiction works was half a million words long (though I had to split it into Book 1 and Book 2 to be able to publish it).  I wish I could have kept writing fiction, but it gets so dispiriting just to fire your fiction out into the void, and I am not good at promoting myself.  I think if I had just one actual fan, someone who liked my stuff for its own sake and wanted to read more just because they like my writing (even though they don’t know me or owe me) then I would probably be motivated and keep writing fiction.

Speaking of fans and promotion and all that sort of stuff, there was a weird thing that happened on Wednesday.  WordPress gives you daily statistics bar graphs when you sign into the account, and normally, my blog gets in the high 20s or 30s of visitors every day, but on Wednesday there were over 900 views or visits or whatever they call them.  I have no idea how that happened or what it might signify.

Possibly it’s a glitch, or perhaps there’s some form of LLM searching through blog posts.  Who knows?  It’s curious, though.  So, if any of you has any ideas that seem plausible, I would be interested in hearing your thoughts; please leave a comment below.

Okay, well, I guess that’s about it.  This work week has not been as horrible as the last one, but it has not been easy.  I really look forward to being at least able to sedate myself with Benadryl and the like this weekend so I can try to recover as much as possible.  I wish the AC in my room were working, but at least I have a good quality, powerful floor fan.  Unfortunately, it’s not a fan of my fiction, ha ha, but it is good at what it does.  Still, I have to be careful, because there’s somewhat more of a risk for dehydration with a fan.  That’s okay.  I mean to keep myself aggressively hydrated.

I hope you all have a very good weekend, whether there are 900 of you or 90 or 9.  Heck, if there were 9 billion of you, I’d still want you all to have a good weekend.  Imagine that, if the entire human race (and then some) all had a very good weekend.

Maybe someday.

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The paragraph indentations below are not merely done on a whim

     Wow, okay, yesterday was one heckuva day, and not in a good sense for the most part; it was a real cluster-fudge*, so to speak.  This is not meant to imply that yesterday was all bad or anything; that would be absurd.  I may be a madman (without a box, alas), but I am not so irrational as to think that there were no positive things in any given twenty-four hour period, even if I restrict the universe being evaluated down to only things that happen to me.

     I have never been one of those depressed people who interprets himself or his life as “all bad”.  That would make things easier, probably‒I would either have destroyed myself long ago or I would have embraced my identity as a pure villain**.  But I am capable of nuance, an attribute that seems often to be missing in our political discourse.

     Mind you, that latter happens largely because it’s what people seem to want to consume, or at least what enough people want, and to which enough people respond, that it becomes a stable and often successful strategy for politicians to use.  So, at least some of the “blame” for the vacuity of news and politics is that humans tend to run toward misleading simplicities rather than dealing with a complex world in which even people with whom they disagree can have good points and do good things and have their own pain and loss and fear and love and memory and dreams.  And even people with whom they agree on most things can nevertheless sometimes behave like complete assholes.

     The world is complicated.  How could it not be?  Almost everything of which we are aware and of which our reality consists is constructed from incomprehensibly vast numbers of interactions between quantum fields on tiny, tiny scales, with causality propagating at the speed of light, with behaviors and properties requiring complex numbers*** to describe mathematically.  If you’re an electrical engineer, you might use complex numbers in real life, because they are very useful for modeling cyclical processes like alternating current, but most macroscopic, emergent processes don’t require complex numbers to describe.

     Or maybe they would be best described, mathematically at least, using complex numbers, but most macroscopic, emergent phenomena have too many things going on‒too many moving parts, if you will‒to be efficiently described by any remotely practical mathematical formalism.  Even computer algorithms might be inadequate to describe the functioning of large scale matters in sufficient detail.

     It may be that natural language really is the best tool for describing such aspects of reality, since it allows one to vary one’s level of intricacy and complexity to suit the needs of any given situation.  But of course, to do so requires one to be rigorous to the point of being a martinet about one’s language usage.  If a word or term can have more than one meaning, it is crucial to specify which meaning one intends so as to avoid apparent disagreements that actually just come down to semantic confusion.

     I don’t necessarily mind semantic discussions‒I like words and language and logic and poetry and puns and all that stuff‒but if one is trying to share an explanation for something, and really to share understanding, precise word meaning is going to be necessary.  You can’t use html to write a program that runs in Pascal.  Okay that’s not a great analogy.  Let’s say…you can’t win a game of Texas hold ’em poker by following the strategy you would use for euchre.  It’s not just that you won’t win; your moves won’t even make sense.

     Okay, well, that’s probably enough for today.  I’ve been trying not to be as negative as I was yesterday, and I think I’ve succeeded reasonably well.  I do this sort of back and forth thing so often that some people have said they wonder if I am literally bipolar with a rapid cycling rate.  I can only respond by saying that this possibility has been considered by me and by several different mental health professionals, and it is thought not to be the case.  Of course, I’ve never been tried on a course of, say, lithium****, nor really on any of the other, less tricky mood stabilizers (other than as would-be adjuncts for chronic pain treatment).  But if I were occasionally waxing manic, I would imagine that sometimes I would feel really good about myself, and I rarely do.  Also, antidepressants have never triggered a manic or hypomanic event for me, and I’ve taken many different ones at different times.

     All right, well, there was a whole paragraph after I’d already said I’d written enough.  My apologies.  I do go on, don’t I?  Have a good day, if you can.

*If no one has used that euphemism as the name of a brand of candy, I’ll be even more disappointed in humanity than I was already.

**Knowing me, I would probably accidentally do good for the world every time I tried to do evil.  At least it would be funny.

***Complex numbers are numbers with one “real” part, i.e., some number on the usual, continuous number line, and one “imaginary” part, which is a real number multiplied by i, the square root of -1, which is no more truly imaginary than is any other number.

****I like the song a lot, though.