Mathematics

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This tue, tue sullied (or solid) day

Tuesday or not Tuesday?  That is the question.  And the answer, for today at least, is that today is Tuesday.

I don’t know when you’re reading this, though.  Odds are, if you aren’t reading this on the day I publish it, that you are not reading it on a Tuesday.  In fact, once we get out past the rest of this week* there should only be a roughly 1 in 7 chance that you are reading this on a Tuesday.

That’s probably pretty obvious, huh?  Still, it can be useful to be in the habit of thinking in terms of probability and statistics, since that’s the way nature sorts itself out, right on down to the level of quantum mechanics, to the best of our understanding.  If people had a better understanding of the nature of probability, many things in the world would run far better, or so I suspect.

I have written at least one previous post (on Iterations of Zero) about how I think probability and statistics should be emphasized far more in general math education at the secondary school level (even for non-college-prep students).

Imagine a world in which most people had grown up learning about the nature of probability with reasonable rigor.  There would be fewer headline-based scares about things that are unlikely enough to be irrelevant‒e.g., plane crashes‒and more appropriate understanding about things like vaccination and disease prevention of various kinds, among numerous other matters.

Imagine if the people of the world really understood the difference between absolute risk and relative risk, and if they grasped the difference between sensitivity and specificity for medical tests.  Heck, imagine if the public at large had a decent elementary grasp of Bayesian probability.  Bayes’s Theorem is not really all that difficult, when you get right down to it.  Veritasium did a nice video about it**.

Of course, as I’ve said before, if wishes were horses, we’d all be neck deep in horse shit, whereas that’s only figuratively the case as it is.  But it would be nice if politicians and other people with undue influence had to deal with a general public that was savvy about the legitimate use of statistics and why (and how) they are fundamental to a thorough understanding of the world itself.  It’s not an accident nor a mistake that Jaynes named his book Probability Theory: The Logic of Science.

And science is not an esoteric thing.  It is not a high-falutin’ mode of thought that doesn’t pertain to the average person.  It comes from the Latin scire, meaning to know.  It is fundamental to the nature of our epistemology, to not just what we know about the world but how we come to know it, how complete and how incomplete is our understanding and what the nature of the world really is at deepest and broadest and finest and coarsest levels.

So, it’s fairly pertinent to everyone, really.  After all, if you want to win a game (or get your best score or whatever) you’re best off understanding the rules as well as you can.  A true novice is unlikely to win a game of chess, or of Go, or even of Mario Kart against someone who knows what they are doing.

Now, nature isn’t our adversary per se‒if it were, we would all be long gone‒but it “knows” its rules and always and only plays by those rules, by definition.  In fact, if you come upon a place where you think nature has broken its rules***, what’s really happened is that you’ve come to a place where you don’t understand the rules.  Nature cannot be “wrong”.  There is no such thing as the “supernatural” in reality, because anything that actually happens, that actually exists, is part of nature.

Even if you discovered that you were in a situation such as that described by Descartes or The Matrix, in which the reality you think you know is an illusion, that is simply a newly discovered fact about the nature of reality, and it raises**** the question of what is the nature of that illusion, what is behind it, and by what laws of physics do those entities operate?

So, anyway, it’s good to learn about how reality works if you want your best chance (never a guarantee) of doing what you want successfully and getting what you desire from life.  No one here gets out alive (at least it’s very unlikely) but you might as well make the game as rewarding as you can in the meantime.

*Which I suspect would be when most non-same-day readers would read this.

**He also did a really nice one about the logistic map and chaos and the Mandelbrot Set that will blow your mind if you haven’t thought about it before.

***I’m thinking of those stories with submoronic headlines such as “New discovery breaks physics!” which don’t make sense to anyone who knows anything, and which should embarrass those who write them.

****It does not beg the question.  To beg a question is not to raise the question, but rather to proceed as if it had already been asked and answered in a way that you’re presuming it to be answered.  It is a way of skirting fundamental issues and avoiding having to prove a case.  In other words, it is willfully or accidentally disingenuous.

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Progress and (good) regress reports

I’ll start with the good regress:  I’m feeling significantly closer to baseline pain levels today than I was the last few days‒at least so far, though the day has only just begun.  I suppose I could have just said that I feel “better” today, but I fear that could be construed as meaning that I feel “all better”, which is not true and hasn’t been true for many, many years.

Still, I would rather be at my current level of chronic pain than the pain I was in yesterday or the day before.  And it should probably go without saying that I would pick either state over the pain I had while my kidney stone was present (and the irritation from the ureteral stent over the subsequent two weeks was nearly as bad, largely because it persisted for those few weeks).

I didn’t get a lot of work done on Native Alien yesterday, though I did progress a little.  I also don’t have anything down regarding the new song-takeoff word “humility”.  I’m beginning to think that I should stick to a song every two weeks, because I just have too much else going on to be able to achieve a song a week.

I also think I may need to buy a new small keyboard (the piano kind, not the typing kind) to use at the office, because I really have a somewhat difficult time trying to work out chords for a tune when I’m trying to play the tune on the guitar and then to play the chords on the guitar and see how they sound together.  I can’t really do both at once on a guitar, but on a keyboard it’s a piece of piss (as Brits might say).  Also, singing while figuring out the chords is difficult because my pitch in singing can be influenced by the chord I’m playing, and I might mistakenly adjust the tune to the chords instead of the other way around, without realizing that I have done so.

So, we’ll see.  I may order a new, relatively small keyboard for the office.  It would need to be inexpensive, but that should be pretty doable*.

I have continued to do the Brilliant course on circuits, which remains quite basic.  It’s a far cry from when I started doing their course on linear algebra, which I had never formally studied.  Don’t get me wrong; that’s a very cool and good course, and it applies to things in which I’m very interested, such as General Relativity in particular, but I got distracted in the middle of it‒I think I should have started by reviewing the fundamentals first.

I am currently reading a book called Vector, which goes into the history and mathematical theory of vectors and tensors, via quaternions and so on, and that’s pretty cool.  I find that learning the history of science and mathematics really helps get the subjects into my head.

As for other matters, well, there’s not much else going on.  Today is payroll day at work, so it will be somewhat hectic, but there’s no holiday or anything to warp the schedule.  Hopefully that means everything will go pretty smoothly.  At least I won’t have to be in as much pain while doing it as I might be.

I’m trying very hard to get back into doing more regular exercise, but trying to avoid causing exacerbations to my chronic pain while doing so.  It’s a bit of a tightrope walk, so to speak.  If I screw up, while it doesn’t lead to me literally plummeting to my death, it can set me back and make me feel terribly discouraged.

I had intended to try to ride my bike to the train this morning, but starting yesterday afternoon it began to rain quite heavily all throughout the area, so I didn’t get a chance to pump up the tires and whatnot.  This morning it was not raining, but it is supposed to rain on and off throughout the day, so biking isn’t so attractive.  I guess I’ll just wait on that and do some extra walking if I can.

Sorry, I know this is probably really dull and uninspiring reading.  I don’t know what to say about that.  I just spew these blog posts out as they come, so I don’t claim much more responsibility for the quality of the content than you can claim while reading it.

I will keep you updated on progress on my song(s) and of course you will see my writing.  I suppose, if I should try to start writing fiction again, I’ll let you know about that, but I don’t think that’s likely to happen any time soon.  There’s too much other stuff going on, and I’d need to stop doing this blog every day but Thursday.  I doubt that anyone would actually feel bereft if I stopped writing, but I flatter and delude myself that maybe it would be so.

I hope once more that you all have a very good day, and I reiterate that, no matter what, you will have the best day you could possibly have.  Don’t let that stop you from trying to ensure that this particular best day is really a very, very good one.  You might as well try.

*Addendum:  I looked on Amazon and there was a well-rated, small “beginners'” keyboard by Yamaha that can be delivered by tomorrow and was quite inexpensive, so…reader, I ordered it.

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Chords in music and in time

It’s Monday again, the start of another work week‒that is, if your work week begins on Monday.  In the modern world‒and indeed, perhaps always‒there are many people whose work weeks start on days other than Monday.  I suspect, though, that the majority of people still work their week starting on Monday, at least in the West, though it may not be a large majority.  If anyone out there has easy access to any rigorous statistics on the matter, I would be interested to learn.  On the other hand, I’m not going to seek the information on my own, so it’s not a tragedy if no readers have it.  I like trivia, but this is definitely quite trivial, at least from my point of view.

I hope you all had a good weekend.  My own was not very interesting, and I felt tired, but then again, I did have a cold starting in the middle of last week, so I guess I was still recovering.  I feel as though that particular infirmity is reasonably well on its way.

I worked a little on the chords of last week’s song, Native Alien, though not very much.  At least at the house I have my keyboard, so I can play melody and chords at once to confirm which chords sound best to me.  Interestingly, it seems that the chord to start the song (at least the melody) will be a C major chord, which is the V chord of the key of F major (though if the song could be considered to be in D minor, it would be the VII chord).  This is not unusual, of course, nor particularly noteworthy.  It’s just interesting for me to recognize specific facts to which I didn’t pay attention when I wrote earlier songs, because I’ve thought more about music theory since then, probably because of the guitar.  It’s a curiosity for me.

Speaking of songs, today I plan to do another round of flipping coins to pick a basic topic, or subject, or trigger‒whatever might be the better term‒for another song (lyrics) for this week.  Of course, last week’s word, Earth, didn’t really become the subject of the song, just a takeoff point, but that’s fine.  The idea was just to give me some way to give myself a start.

In other news, I had a weird thought last night after watching one of Sabine Hossenfelder’s latest videos.  I wrote an email to myself about the thought so I wouldn’t forget it, and I’ll include that text here, so you‒yes, you‒can see what you think (I have edited this text for clarity and to correct typos):

“If the overall arrow of time is caused by the tendency toward increase in entropy from a lower to a higher entropy state (“Big Bang” to heat death, at the cosmic level), that could behave analogously to a current (like in the ocean, not a wire).  Meanwhile, locally*, we know that the laws of physics don’t appear to have any directionality time-wise.  So perhaps locally, matter and wave interferences in the sense of quantum wavefunctions can happen not just in space but in time itself and the future can feedback on the past, just not in such a large way that it would overwhelm the overall tendency (though maybe even that is not impossible).  The effect of such a temporally retrograde wave wouldn’t flow backwards so fast that it would override the current itself (probably).  However, that wave could still affect its predecessor, creating standing interference patterns in time and things along those lines that might be the source of so-called super determinism.  Think about this a little bit.”

That last injunction was intended for me, but if any of you want to think about it, you’re welcome to do so (it’s not as though I could stop you even if I wished to stop you, which I don’t).  Of course, if I’m going to really explore this notion, I’m going to need to bone up on my mathematical physics in a serious way, and it’s always hard to find the time.  That’s always been a bit of a weakness of mine:  I get very interested in something and develop skills in it because of my interest, then something else catches my attention, and soon all my energy goes there.  I don’t tend to forget the things I learned previously, at least, and sometimes when I return to them, I even find that I’m better than I was before (e.g., after not playing guitar for quite a while, when I picked it up again, certain songs or chords with which I had trouble before had become much easier).

Also, of course, the fact that I have to work for a living is another distraction.  I really do need some ultra-wealthy patron out there to provide me with living and intellectual resources so that I can devote my time to my wonderful pursuits without having to earn my living.  I also want world peace, world freedom…and a unicorn.

I guess in the meantime I should probably go back to using Brilliant dot org to spruce myself up in terms of mathematics and physics (and computer science in the meantime, why not?).  I have an annual subscription (supporting Sabine Hossenfelder, whom I mentioned earlier), so I might as well use it.  It’s a better use for my spare time than diddling around on social media.

Okay, well, I hope you all have a very good day, and that it is the beginning of a very good week for you.

*I’m using the colloquial meaning of “locally” her not the strict physics definition of locality.

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Had we but time enough, and space…

It’s the beginning of a new week but the end of an old month:  Monday, June 30, 2025, AD (or CE, if you prefer).  After tonight at midnight, we will be in the second half of this year, for whatever that’s worth.

Of course, one can debate whether Monday is really the beginning of the week or just the beginning of the work week.  Many consider Sunday to be the start of the week, at least here in this region of the “West”.

But, of course, since mainstream Christianity sees Sunday as the sabbath day, a day which is supposed to commemorate the day on which God rested after creating the world, seeing Sunday as the beginning of the week doesn’t make a lot of sense.  In the “original” observance of the sabbath—the Jewish one—Shabbat falls on Saturday (beginning Friday at nightfall), which makes more sense.  Then, Sunday really is the beginning of the week.

Not that any of this actually signifies anything real.  The start of the week or the start of a month or the start of a year are all just as arbitrary as one’s choice of the location of the origin and the x and y axes in setting up a system of coordinates in Euclidean space (or a plane, in this case).  As long as one is consistent in applying them, any calculations involved will turn out the same.  It is, in a way, a kind of symmetry, which would—in physics, anyway, if one were applying Noether’s Theorem to such as absurd situation—imply a conservation law of some variety.

I suppose there is a sort of conservation of days and months, in that one cannot by adding or subtracting days or months on a calendar change the length of a year or of a lunar cycle.  Although, with a big enough rocket or explosion or whatever, one could noticeably alter those things—it would be catastrophic for creatures on Earth, but this is science we’re talking about here, and if life on Earth must suffer for the advancement of science, then so much the worse for life on Earth!

I was kidding with that last bit there.  I am currently alive and on Earth—though at times I rue both facts—so I don’t actually want to treat life on Earth frivolously for my own curiosity’s sake.  Also, and more importantly, the people who matter most to me live on Earth*.

Anyway, over time the orbit of the moon is going to lengthen, as the moon very slowly draws farther and farther away from the Earth (which it is doing).  The length of a day and of a year both also slowly and subtly change over time.  Those time scales are long, though, and probably the sun will go red giant before either rate has changed enough to cause significant trouble, barring some large-scale asteroid collision or something similar.

This does, however, raise a point about the relationship of symmetry and conservation laws, à la Emmy Noether’s theorem.

It is the symmetry of translation—moving something from one place to another doesn’t change the laws of physics—that implies conservation of momentum.  And it is the symmetry of rotation—it doesn’t matter in what direction you’re oriented, the laws of physics are the same—that implies conservation of angular momentum.  And it is the symmetry of time—the laws of physics don’t change from one moment to the next—that implies the conservation of energy.

But here’s the rub:  on the largest of scales, the universe is not time symmetric; the past is significantly different than the present (and the future).  And so, on long time scales, the conservation of energy does not apply.  This is not merely a case in which I’m playing word games, by the way.  In this instance, I am speaking the truth about the nature of energy at the level of the cosmos according physics as it is understood today.

It’s an interesting question whether our local asymmetry in time—i.e., that the direction toward the “Big Bang” looks quite different from the other direction in time—is really just a local phenomenon.  That may seem strange, but perhaps it will be useful to consider an analogy with the various dimensions of space.

In space, in general, there is no directionality to the three dimensions.  One can go up and down, back and forth, and from side to side with equal ease, at least in space in general.  However, if you live on the surface of the Earth**, there is a very real difference between “up-down” and the other two sets of directions.

This apparent directionality to space is caused, of course, by the gravitational effect of the mass of the Earth itself.  It is an entirely local directionality, caused by a local phenomenon.  And similarly, the seeming directionality of time may be merely because we are “near” (in time) to a local, powerfully influential phenomenon:  whatever caused the Big Bang and produced a region in time of extremely low entropy and significant expansion, whether it is cosmic inflation or something else.

It seems pretty clear that, as entropy increases “over time”, the difference between past and future will become less and less noticeable, until eventually, there will be effectively no directionality to time***.  And so, in the “heat death” of the universe, the conservation of energy would steadily apply more and more, even at cosmic scales.

Not that there would be anyone to notice.

Of course, one can ask if there exists more than one time dimension.  I have asked this before, myself, I think on my other blog, Iterations of Zero.  But now there are some serious physicists entertaining the notion.  This sort of thing always makes me feel at least a little bit clever:  when I thought of something before the mainstream physics articles were published (or at least before I encountered them).

Anyway, that’s enough of that for now, this morning.  I hope you all have as good a week as you can.  Well, you will inevitably have as good a week as you can, but I hope it will subjectively be good  for you, too.

*I am not one of those people.

**As I suspect most of you do, at least physically.

***Very much in the way that, as one gets farther and farther away from the surface of some strongly gravitating body, like a planet, the difference between up and down becomes less and less prominent and finally vanishes into undetectability.

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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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Mind your vectors and terms of address

I’m writing this on my mini laptop computer again, because even though I find the extra weight of carrying it mildly annoying at the end of the day, at least sometimes the irritation of trying to write using my stupid smartphone is worse.

Although, since those two versions of me exist at different times, it’s hard to weigh their degrees of perceived irritation against each other.  In the morning, if I’m using my thumbs to try to type on a diminutive screen in a fashion that could be easily predicted to lead to some manner of repetitive stress injury, its all too natural for the “me” of that moment to hate the “me” of the previous evening who elected not to bring the laptop computer back with him.

But the “me” of the evening, when faced with the minor extra effort of the mini laptop, can feel very much overwhelmed and exhausted and think that the “me” of the following morning won’t find the process of writing using the smartphone particularly difficult.

The human consciousness clearly doesn’t have one, singular, constant terminal drive or goal as an imagined artificial general intelligence might.  I suppose one might think that the drive “to stay alive” would count as an ironically designated terminal goal, but that’s clearly not an accurate interpretation of the situation.

Not only are some people quite self-destructive and even actively suicidal—which you might credibly dismiss as dysfunction, not the lack of a dedicated system, though I think that would be imprecise—but there’s no good way to think that such a specific drive could evolve.  Evolution is blind to “death” as a concept or force, except as a failure, an accident, a lack, whatever you want to call it.

Before humans, as far as we can tell, no creature on Earth had a concept of “death” as the cessation of the biological processes of an individual organism.  Instead, there are proxies, such as the drive to avoid pain, and the related strong sensation of fear relating to danger and so on.

Similarly, there is no drive “to reproduce” in human (or other animal) minds.  Teens going through puberty don’t start feeling the literal desire to replicate their DNA in other bodies.  Instead, proxies for reproduction evolved, urges and drives that tended to lead to increased chances of reproduction, such as dominance hierarchy drives and displays in social primates such as humans, sexual attraction, and—of course—the pleasure of sex itself, with the reward-based drive to have it as often as feasible (with other inputs adjusting the strength of that drive and causing it to manifest differently in the two biological sexes and at different times and places).

The human brain—like probably all the other adequately complex brains on Earth—is a mélange of modules, with varying drives and processes that have evolved in parallel and sometimes independently, and also developed ways of interacting with each other.  Of course, at the root are the automatic drives that are all but undeniable—the respiratory drive, the thermoregulation drive, and so on.

There are even drives that are neurological in a broad sense, but that are so fundamental that they cannot be interdicted by the rest of the nervous system, only adjusted—I’m thinking here mainly of the heartbeat, the driver of which is in the sino-atrial* node and the Purkinje system of the heart, which is sort of a cross between muscle and nerve tissue.

The upshot is, if you ever feel that you’re “of two minds” on some particular subject, you’re probably not just speaking metaphorically, whether you know it or not.  Your final actions are produced by what I see as the final vector sum (and it can be quite small in the end or it can be huge in magnitude and surprising in direction) of all the drives or “pressures” in the brain that have any effect on decisions about behavior.  Then the action caused by the final behavior feeds back on the system**, changing the lengths and directions of some (perhaps sometimes all) of the contributing vectors, causing changes in the inputs and thus changes in the final vector sum of behavior.  Lather, rinse, repeat as needed, ad nauseam if not actually ad infinitum.

Please don’t imagine this as the sum of physical vectors in real spacetime.  The number of possible dimensions of such mental/neurological vectors is huge.  For all I know, there might even be spinors and tensors and matrices involved, but I don’t think those are necessary for my vague model.  “Simple” higher dimensional vectors probably do the trick.

What a curious set of things about which to write that was!  I had originally intended to start this post with some version of The Simpsons’ “Hi, everybody!”  “Hi, Dr. Nick!” exchanges, perhaps then noting that I could change “Dr. Nick” to “Dr. Robert” and thus reference both The Simpsons and the Beatles at the same time.

But then I might have noted that, although the Beatles song is so titled, “Dr. Robert” is not the way anyone has ever referred to me in actual practice.  It would be, honestly, a little weird for someone to refer to their physician as, for instance, “Dr. Joe” or “Dr. Judy” or whatever, certainly in our culture.

Mind you, there was that tendency for a while (it may still be prevalent) to have kids speak to adults such as teachers and daycare workers and people of that sort using their “title” and then their “given name”, such as “Miss Barbara” or “Mister Jimmy”.  I have always thought that was weird.  I mean, just imagine someone trying to address a certain prominent fictional character as “Dr. Hannibal”.

Alas, that all ended up being a discussion not worth having, except as an afterthought.  Though it’s debatable whether any discussion at all is actually worth having—including the discussion about whether any discussion is worth having.

You all can discuss that if you want; feel free to use the comments below, and to share this post to your social media platforms or what have you.  When you do discuss it, remember to define your terms ahead of time, and stick to them rigorously—i.e., the meaning of “discussion”, and of “worth”, and so on—so that you decrease your chances of getting involved in semantic games and misunderstandings and sophistry.

Whatever you choose to do, please try to have a good day.

*The “sino* in that term relates to its location in what’s called the sinus of the heart, and the “i” in it is a long “i”; it has nothing to do with China, though an identical prefix is sometimes used to mean “related to China”, but in this case with a sort of short “i” sound…or, really, a long “e” sound.

**And there are surely numerous other feedback loops all along the way affecting many, or perhaps all, of the vectors.

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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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Monday morning, wearing down

Well, it’s Monday again.  Time keeps marching on without respite, as it is apparently wont to do, “progressing” in the direction of increasing entropy, whether time is a fundamental aspect of the universe or an emergent phenomenon.  In either case, there doesn’t seem to be any sort of time stream or time vortex like in Doctor Who, but rather a process that simply is a linear dimension with some “entanglement” (not to be confused with quantum entanglement) with the dimensions of space, such that motion and acceleration in space changes one’s “motion” in time, in an updated version of the Pythagorean Theorem.

For those of you who like to share the joke about “Yet another day when I didn’t use a2 + b2 = c2” you’re really depriving yourself of a deep understanding of something that turns up in and governs a ridiculous number of the things and processes in the physical reality in which you live.  Consciousness—despite clever but tortured sophistry (in my opinion) by some prominent philosophers of mind—in no way appears fundamental to the universe*.  On the other hand, the Pythagorean Theorem, which was neither invented nor discovered by Pythagoras, applies in all levels of dimensions, however many you might conjure, and with the modification to make it reflect velocities, it applies to spacetime as well.

There can be no readily conceivable brains** in two spatial dimensions, but Pythagoras nevertheless applies.  In one dimension, it doesn’t really apply, but in one dimension there are no triangles of any kind, so it doesn’t make much difference.  It’s difficult to imagine how consciousness could possibly occur in one dimension (notwithstanding the seemingly one-dimensional paucity of ideas held by so many people, especially in politics).

Anyway, enough of this nonsense.  Well, it’s not nonsense, but it is rather pointless meandering of random thoughts that interest no one but me, and will probably lose me readers.  Weirdly enough, people seem to come and read more often when I write about my depression and self-hatred and anxiety and ASD and how there’s absolutely nothing going on in my life that makes it worth living.

Well, rest assured, all those things are still present and active and driving me toward an early grave, which in some senses will be a release, or at least an escape of sorts.

I keep trying to think of things to engage myself and my interests, but so far to no avail.  I think about asking my boss to give me back my black Strat to play at the office, or I consider bringing in another guitar, or maybe even getting a portable keyboard or something, but when I think of any of them, I cannot even imagine doing anything but sort of staring at them as if I don’t even know what their purpose is.  I don’t play my guitars or my keyboard at the house, either.

It’s likewise with even fiction, other than silly Japanese light novels that take a day or so to read (not continuous time).  I think I like them mainly because of the social interactions of the characters, many of the main ones of whom are somewhat socially awkward.  It can feel, however briefly, that I have a social group of some sort, as I read the stories.  Of course, that means that once I’m done reading there is a comparative let down, which sometimes makes me feel worse than I did before.

I tried to read some of Feynman’s Lectures on Physics, but I lost interest almost immediately, though he was a brilliant and engaging teacher.  I also tried to read some of Anthony Padilla’s Fantastic Numbers and Where to Find Them, which is also very good and fun; if you’re interested in who he is, you can check out the YouTube channel Sixty Symbols, and sometimes Numberphile.  He shows up in both places fairly often.  But in any case, though I like his book (I’ve read it before) it has not been able to grip me.

I’ve also tried to start reading Stephen King’s novella The Life of Chuck, since it’s now a movie and is getting positive reviews.  At least Stephen King is almost always an engaging read.  But I’m not sure I’m getting into the story.  Quite a while ago, I started the first story in If It Bleeds, the collection in which the above novella appears, but I couldn’t get into it at all.  When I can’t even get into reading Stephen King***, things are looking bleak.

I did watch the rest of the latest series of Doctor Who, and it was pretty good, and quite surprising at the end, but Batman only knows when the next series is going to happen, and there will only be a handful of episodes if it keeps up as it has been.  That’s too little too late for me to use as motivation for continued existence.

I don’t know what to do.  I really don’t know.  I feel very lost and, more importantly, very much without any internal impetus.  I can’t even listen to songs I like, let alone try to sing along (or play) without feeling like I’m going to cry, though I don’t understand why.  I’m at the end of my rope (I have two, and both are tied into nooses, just for “fun”).

Anyway, that’s enough.  Sorry to bother you with my crap again, but in my mind, you asked for it by complaining about my tedious math and science stuff.  I hope you have a good day.  Unless you’re lucky (or I am) I’m sure to be back again tomorrow with another blog post.

*The only reason I can discern why some people think consciousness is fundamental to the universe is that consciousness is fundamental to human experience—indeed, one could say that it is human experience—and of course, such people seem tacitly or implicitly to think humans are the measure of all things simply because that is what they are.

**The degree of interconnectivity is just too low.  Connections between 2D neurons would be terribly limited, as would room for such things.  I suppose that, since we can always map anything three-dimensional onto some two-dimensional surface, à la Bekenstein-Hawking black hole entropy and the holographic principle, we could construct a sort of brain in 2D, but that’s a tortuous process, and seems quite unlikely.  Of course, 4D would give us even more available connectivity than 3D—also there are no knots or tangles in 4 spatial dimensions—but there are other issues with 4 (macroscopic) spatial dimensions that would seem to get in the way of life as we know it, such as the nature of gravity (and other forces) and the rate of such forces’ diminishment.  For instance, the force of gravity (and electromagnetism, etc.) in four dimensions would fall off at a rate proportional to r3 rather than r2, and there are apparently no stable orbits in such situations.

***What’s worse, I cannot even get into reading Tolkien.  I’ve tried.  When neither Stephen King nor Tolkien, nor even well-written science books, can engage me, something indeed has happened.

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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.