Mathematics

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

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

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

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

You probably already knew that.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Please have a good day.

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

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

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

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Is it a sine of the (space)times that we are where we are in the week?

TBIF* or TDIF**, either way, it’s Friday.  It’s the last day of the work week.  I started writing “It’s the end of the work week” (emphasis added), but I realized that, since it is early in the morning, and I am just on my way to work, this time could not accurately be called the end of the work week.  One could, in fact, say that 20% of the work week yet remains; that can hardly be called an end, any more than a B minus can be considered a perfect score (unless one radically changes the grading system one is using).

Such are the random things that spring forth from my brain via my fingers when I am writing my blog posts in the mornings (in this case on my laptop computer, which is literally on my lap***).  I’m sure you’re well aware of that, if you’ve read this blog for any length of time.  I don’t really know ahead of time what I’m going to write, unless I have a specific subject to address.  Even then I often address subjects in ways that surprise me.  This is because when I write I am really “thinking out loud”, although in this case, “out loud” is figurative.

Do my thoughts meander like a restless wind inside a letter box?  Well, they’re probably more like a restless discarded Cheetos® wrapper in the wind of a nearby tornado; one should almost certainly use a junk food metaphor when describing the way my thoughts spontaneously arise.  Not that I think my thoughts are “junk”, no more so than anyone else’s are.  I just think it’s rather appropriate to consider many of them as having a bit of a temporary amusing effect, but without any real nutritional substance.  Junk food has its place****, after all.

I don’t know what else to write today, but I’ve only written about 450 words so far, including the first four footnotes below.  I would say that I don’t want to shortchange you, the reader, but you’re not actually paying for this in any sense other than spending your time.  And since time cannot be used as legal tender—when you “spend” it, I don’t receive any from you—I guess I shouldn’t consider it to be shortchanging you.

In any case, whether you spend your time reading my blog or doing something else, your time passes all the same.  You could slow it down relative the those around you by accelerating to relativistic speeds, but you would still require the same amount of your “proper time” to read a blog post.  And to those watching you pass at some substantial fraction of the speed of light, it would seem to take you longer than it would take us.

Remember, from a particular, mathematically precise, point of view, you’re always moving at the speed of light—it’s just that most of your motion is through time.  This is part of why you cannot ever reach the speed of light through space:  As you tilt your motion vector toward faster motion through space, less of your motion is through time, until it would stop for you completely.

It’s a bit analogous to moving (say, driving or flying) in particular compass directions.  Imagine your default motion is all northwards, so there is no east or west component to your momentum, but that your momentum vector is always the same length, i.e., you speed in your direction of travel is constant.  If you start to veer eastward a bit, going at that same fixed speed now in a north-northeast direction (for instance) the component of your motion that is northward is smaller than it was*****.

As you veer more through northeast toward east-northeast and beyond, staying at your same speed but in your new direction, the component of your motion that is northward becomes smaller and smaller.  Finally, of course, if you go due east, there is no longer any component of your motion in the northerly direction.

This is close to being the same thing that would happen if you could somehow achieve the speed of light through space, except that the geometry of spacetime is (if memory serves) hyperbolic.  This means “relating to or described by hyperbolas”, it doesn’t mean that the geometry of spacetime exaggerates things all the time.

In any case, though, an object or person traveling at the speed of light (through space, so to speak) would cease to experience any “proper time”.

And with that, I think we’ve come to the proper time to bring this week of blog posts to a close, even if the work week still has a fifth of its time remaining.  I hope you all have a good day (whatever day on which you may read this) and then a good weekend (whenever the next one is for you) and a good week and so on and so on and so on.

*Thank Batman it’s Friday.

**Thank Doom it’s Friday (I suppose one could use TDDIF, Thank Doctor Doom it’s Friday, but that would eliminate the parallel with the more traditional version of the acronym).

***Does the term “laptop computer” imply that there could be a “lapbottom computer”?  What would the bottom of a lap look like?  Would it just be the “bottom”, in which case it really has nothing to do with the lap, since your lap disappears when you stand up, but your ass doesn’t?  If there is no lapbottom (i.e., if laps are instead bottomless) then why use the term laptop?  Why not just call it a “lap computer”?  If people wanted a foreshortened version of that, they could just call it their lapcom.

****That place is 7-11™.

*****By how much?  Why, one only need apply the Pythagorean Theorem to the components of your momentum vector.  It’s dead simple.  If you prefer, you can use trigonometric functions, such as the cosine of the angle of your motion relative to full north, but mathematically there is no difference.

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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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You flocks, you shoals, you fine emergent things

Well, it’s Tuesday morning, and I’m feeling a bit beat up and wrung out from yesterday, which was an extremely bad day, pain wise.  I really felt quite stiff and sore all day, and I couldn’t help walking with a limp.  It’s quite frustrating.  I do have potential assistance of a kind coming today, and hopefully that might make a difference.  We shall see.  I’ll tell you more when I have more information.

As for anything else, well, there’s really nothing else going on in my life.  I still haven’t done any work on new song lyrics, nor have I played the guitar or keyboard at all, nor sang.  I don’t even know what kind of shape my voice might be in at this point, but it’s probably pretty rough.

I think maybe I should drink more coffee during the day.  I used to drink it regularly when I was up north, but I’ve fallen off a lot since coming to Florida.  A big part of that is just that coffee is a hot drink, and hot drinks in Florida can be quite unpleasant.

But also, if I can reevaluate my own internal workings and decision-making memory‒which I can‒I tried to cut back on caffeine because I feared it was a major contributor to my tension and hostility and anxiety.  Well, you’ve read my blogs before (unless this is your first time), so it should be fairly clear that that particular intervention was not fit for purpose.  And one thing coffee has always done for me has been to be something to put in my mouth and stomach other than food.  That’s certainly worth a lot in my case.

Anyway, in the new office we have two refrigerators‒the boss brought in one from his garage that was not being used much‒and though neither has an ice maker, ice trays are easy.  So I can make iced coffee to take the sting off coffee’s hot nature.  I can’t directly take the sting off Florida’s hot and muggy nature, of course, but it’s bearable most of the time.

And in the long run, who knows how Florida’s specific climate will alter as the world’s overall surface temperature increases?  One might assume it will just get hotter and more humid*, but it’s best not to jump to conclusions.  Weather patterns are the archetypal chaotic system, and though climate and weather are not synonyms, there is a relation.

Many things interact to maintain specific local climates.  For instance, the Gulf Stream keeps the British Isles much warmer than they would be otherwise, being so far north, but it is not a fixed pattern in the Atlantic, but a product of confluences of various forces and feedback loops (as well as probably feed-sideways paths).  It has not existed forever.  It just feels like it has because human lives are so short, and human minds tend to be woefully parochial and provincial.  This is a source of so many human problems, not least the failure to learn obvious lessons from history.

But I guess there’s not much point in moaning about that lamentable fact right now.  I try to do my little part by writing about what I think are occasionally interesting and thought-provoking ideas, and by trying to learn about all sorts of things myself, from history and philosophy to biology and physics and mathematics‒and, of course, I’m technically an expert on medicine.  It’s as if I hope that by increasing my own knowledge about as many things as I can, I’ll be able to bring up the average and perhaps have some magical diffusion effect.

I don’t actually think that, of course, nor is that really my motivation for learning about various things and stuff.  I just like to understand and know things, to the degree possible, and I enjoy the process of learning them.  Physics is the most interesting subject to me in many ways because it is the study of the workings out of physical reality.  Everything else that happens is “simply” chaotic, emergent murmurations that happen on the surface of the underlying processes.

There is a question whether mathematics is even more fundamental than physics or is rather an invention of humans to describe and work with the patterns that are happening that are not guided by mathematics, perhaps, but simply produce it as an epiphenomenon.

I think Stephen Wolfram proposed something along those lines, based on “cellular automata”**, but though I have his book A New Kind of Science, I have not read it, because I have the Kindle edition.  It’s not really formatted for Kindle, so it’s basically just a PDF of the original book, and that can make it very difficult to read on one’s smartphone.

Such thoughts are quite entertaining and they can sometimes be productive.  I often wish more people were interested in them rather than, for instance, what some particular celebrity did to some other celebrity, or whether some particular advertisement can, with tortured logic, be “judged” to be inherently offensive and even evil, or just how horrifically to punish someone who agrees with only 99% of the things you believe, but disagrees on 1%.

Okay, I need to avoid getting started on that train of thought.  So, I’ll draw today’s post to a close.  Hopefully, by tomorrow I will have some relatively better news than I’ve had recently.  If so, I will probably share it with you.  In the meantime, try your best to have a good day.

*Particularly if sea level rises enough for a lot of the state to become submarine‒now that would be high humidity.

**The most well-known case probably being John Conway’s Game of Life, which is a “game” on a 2-dimensional grid of squares, with particular, simple rules about what happens to any given square depending on whether its neighbors are empty or not.  Remarkable, self-sustaining, and even traveling patterns form from these basic notions, similar to the way the flocking*** behavior of birds can be described with a few basic rules followed by each bird individually, requiring no communications other than just seeing where one’s nearest neighborings are.

***That sound like an epithet, does it not?

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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.