Mathematics

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That was a weird tangent dot com?

Well, it’s Friday, the 30th of January.  We’re almost done with the first month of the year (2026).  Has it been an auspicious month?  Has it been inauspicious?  I suppose the answer to such questions will vary from person to person depending upon how their personal month has gone.  And I suppose that points toward the notion that actual auspices are certainly not any kind of reliable indicator of how the future might go, at least not without great care to separate true patterns from false ones.

On the other hand, it’s not entirely mad to try to draw some potential conclusions about the near future from what’s happening in the present and what has happened in the recent past.  That’s one of the useful skills that’s available to minds that have the capacity to note patterns‒one can try to anticipate the future based on patterns one has noticed over time, and potentially, one can try thereby to avoid outcomes that are undesirable.

Of course, humans do tend to notice patterns that aren’t actually there a lot more than ones that really are there*.  This is usually‒probably‒related to the notion of the differential detriments of different types of errors:  It’s usually more useful to see potential threats that aren’t there than it is not to see potential threats that are there.

I think anyone who stops to think about such things will recognize that the first type of organism will be somewhat more likely to live long enough to reproduce than the second type, though they may be much less comfortable and content in the meantime.  Jumping at shadows can certainly be maladaptive, and too much of it can have a net negative effect on general outcomes, but not jumping at hyenas and lions (for instance) tends to be a very short-lived habit.

This goes back to my frequent talking point that fear, the ability (and it is an ability) to become alarmed and unhappy but energized and driven to fight or flee is going to be present in nearly every lifeform capable of movement over time.  Variations who feel less fear, or none, will not tend to reproduce as much because they are more likely to be killed in any given finite stretch of time, so whatever genetic makeup they have that leads them to lack a fear response, or to be prone to lack it, will not tend to propagate down the generations.

“Genetic makeup”, the term I used in that last sentence (go look, it’s there), made me think of a possible future technology in which people use some CRISPR-style techniques to achieve the effects that hitherto require the use of cosmetics.  They could insert genes into the cells of their cheeks, for instance, to lead them to have more pinkish pigment, or perhaps to make local blood vessels dilate for a nice blushing look, instead of having to use rouge (which is what I think the stuff is called that one applies to make one’s cheeks look pinker).  Or one could generate actual pigments in the cells of one’s upper eyelids, or increase the thickness of one’s eyelashes, all that sort of stuff.

Of course, doing this might entail risks.  Presumably, altering the genes of a given population of cells, even at the local level, could increase the risk of developing cancers, because one cannot perfectly control where genes will insert (at least not so far), and there will always be a chance of mucking up genes that regulate cell division rates.

Once one cell becomes more rapidly reproducing than its companion cells, it will tend to overpower them, in numbers anyway, over time***.  And with rapid and persistently higher rates of reproduction, there come more chances for new mutations to happen.  Those mutations that kill their cells obviously just go away more or less immediately.  Even the ones that revert their cells’ division rates back to “normal” will be quickly locally overwhelmed by the faster growing ones.  But a mutation that encourages even faster division/reproduction will quickly take hold as the dominant cell type, ceteris paribus.

And then, of course, this even more rapidly dividing population of cells will have that many more chances to develop mutations.  And so, down the line, given the billions of cells present in just one’s face, we find the chance for skin cancers to develop, once a cell line becomes so prone to reproduce itself that it cannot be constrained by any local hormonal or immune processes.

That was a weird tangent, wasn’t it?  Although, frankly, I could change the title of my blog from “robertelessar.com” to “thatwasaweirdtangent.com” and it would not be inappropriate.

I’ll finish up today with just some basic housekeeping style stuff:

I will probably not work tomorrow, so I will probably not be writing a blog post.  But if I do write one, it will show up here.  I will certainly not be sleeping in the office tonight, but I did sleep here last night.  I had a terrible day yesterday, pain-wise, and after work I went to the train station but the train was badly crowded and there were no relatively comfortable seats available, so I gave up and trudged back to the office.

I just felt worn out, and I feared that if I did go back to the house, I might not come to the office today.  And today is payday, of course, and Sunday is the first of a new month, so rent is due (Wouldn’t it be nice if rent was dew?  Maybe not if you lived in the Atacama Desert.  Though a little dew might be very strong currency there, come to think of it, relative to most of the rest of the world). 

Hopefully today will be a better day than yesterday with respect to pain.  So far, at least, it doesn’t feel any worse.  The hard office floor can help a bit sometimes with my back pain.  That makes a certain amount of sense, or at least it may do so.  After all, our ancestral environment did not include mattresses.

Anyway, that’s what I’m up to, that’s my life.  I mean that seriously.  That’s pretty much all there is to my life:  Getting up and getting to work (while writing a blog post), doing office stuff while dealing with noise and people and tinnitus, not getting long enough breaks because people seem incapable of watching the time, being the last to leave the office, commuting back to the house, trying to get at least a bit of sleep, and then repeating.  There appears to be nothing more than that coming my way until I’m dead.  Which, I think you might be able to understand, becomes more attractive and less frightening as the tedious, exhausted, and painful days go by.

I hope you all have a good weekend.  As for me, I hope at least to be able to sedate myself enough to have a longer-than-usual sleep tonight.  It’s not ideal (pharmacologically induced sleep being generally and significantly less beneficial than natural sleep), but it’s what I have to use.

*Think of the constellations**.

**Won’t someone please think of the constellations!?!?

***It’s like the difference between exponential functions. ab will grow much more rapidly**** when b is 3, for instance, than when b is 2 or 1.5 or 1.1, and so on.

****Stop looking at the negative side of the number line, dammit.  Just stipulate that a is always a positive number.  Or make the function the absolute value of ab, in other words, |ab|.

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Really, Doctor Elessar, you must learn to govern your passions

I woke up this morning thinking‒or, well, feeling‒as though it were Saturday instead of Tuesday; I’m not at all sure why.  But it is Tuesday…isn’t it?  I suppose if I’m wrong I’ll find out soon enough.  But my smartphone and the laptop and the internet-connected clock all seem to support what I think, and what I thought when I woke up (as opposed to what I felt), which was that this is Tuesday, the 27th of January, 2026 (AD or CE).

It’s odd how emotions can be so bizarrely specific and yet incorrect.  I know that this is not merely the case with me.  We see the effects of people following their emotional inclinations over their reason all the time, even though those emotions were adapted to an ancestral environment that is wildly different from the one in which most of us now live.  It’s frustrating.

Though, of course, frustration itself is an emotion, isn’t it?  Still, it is simply an observable fact that emotions are unreliable guides to action.  We definitely could use more commitment to a Vulcan style philosophy in our world.  And by “Vulcan”, I mean the species from Star Trek™, Mr. Spock’s people, not anything related to the Roman god.

Of course, the specifics of the Vulcan philosophy as described in the series have some wrinkles and kinks that don’t quite work.  For instance, curiosity and the desire to be rational are emotions of a sort, as are all motivations, and the Vulcans do not avoid these.  Then again, in the Star Trek universe, Vulcans do have emotions, they just train themselves to repress them.

Still, the Vulcan ethos is not so terribly different from some aspects of Buddhism (and some of Taoism and also Stoicism), and the logic focus and internal self control are quite similar to the notion and practice of vipassana and other meditation types.  Perhaps metta can be part of that, too**.

Wouldn’t it be nice if everyone on this planet committed themselves to mindfulness and rationality*?  Perhaps it will happen someday, if we do not die as a species first.  It’s not impossible.

By the way, AI is not our hope for that future, specifically.  Just because AIs are run on GPUs that use good old digital logic (AND, OR, NOT, etc., i.e., logic gates) doesn’t mean that what they do is going to be logical or rational or reasonable.  We are creatures whose functions can be represented or emulated by circuit logic, but the functions‒the programs, if you will‒are not necessarily logical or rational or reasonable.

Humans’ (and humanoids’) minds are made up of numerous modules, interacting, feeding back (or forward) on each other, each with a sort of “terminal goal” of its own, to use AI/decision theory terminology.  They play a figurative tug-of-war with each other, the strengths of their “pulls” varying depending on the specific current state of that part of the brain.

I’ve spoken before of my notion of the brain/mind being representable as a vector addition in high-dimensional phase space, with the vector sum at any given moment producing the action(s) of the brain (and its associated body), which then feeds back on and alters the various other vectors, thus then changing the sum from moment to moment, which changes the feedback, which changes the sum, and so on.

The AIs we have now are at best analogous to individual modules in brains of creatures of all levels of braininess, doing specific tasks, like our brains’ language processing centers and spatial manipulation centers and memory centers and facial recognition centers and danger sensing centers and so on.  We know that these modules are not necessarily logical or rational in any serious sense, though all their processes can, in principle, be instantiated by algorithms.

If we imagine a fully fledged mind developed from some congregation of such AI modules, there is no reason to think that such a mind would be rational or reasonable or even logical, despite its being produced on logic circuits.  To think that AI must be reasonable (or even “good”) in character is to fall into a kind of essentialist, magical thinking‒a fairly ironic fact, when you think about it.

Okay, well, this has been a rather meandering post, I know (a curious phrase, “meandering post”‒it seems oxymoronic).  I didn’t plan it out, of course.  There is much more I could say on this subject or set of subjects, and I think it’s both interesting and important.  But I will hold off for now.

Perhaps I’ll return to it later.  I would love to receive lots of feedback on this in the meantime.  Also, I would still like to get feedback about yesterday’s post’s questions, such as those about Substack.  I won’t hold my breath, though.

Heavy sigh.  Have a good day.

*Not “logic” as they called it in Star Trek, because logic is not necessarily related to the real world, but can be entirely abstract.  Imagine if the logic to which Vulcans dedicate themselves were Boolean logic.  Of course, at some level, based on the Turing’s ideas, including the Church-Turing Thesis, all thought processes can be reduced to or represented by intricate Boolean logic.  But I don’t think that’s what the Vulcans are on about.  I’ve often wondered if perhaps the Vulcan word that translates as “logic” in English has more sophisticated connotations in Vulcan.  Maybe they don’t use “rationality” because they connect it to rational numbers, and maybe “reason” is too closely related in Vulcan to “cause”, which as I’ve noted before is not the same thing (“there are always causes for things that happen, but there are not necessarily reasons”).

**One can imagine a perverse sort of dukkha based meditation, in which a person focuses deliberately on feeling the unsatisfactoriness of life.  I doubt it would be very beneficial, but I can almost imagine ways in which it might be.  The very act of deliberately focusing on suffering and dissatisfaction might lead one to recognize the ephemerality and pointlessness of such feelings.  I don’t intend to try it, though.

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“Stupid is as stupid does, Mrs. Blue.”

Well, here I am again after all, writing another stupid blog post on another stupid day in a stupid life on a stupid planet.

Now, with respect to that last entry on my brief list, one might say, “Hang on.  Of all the planets we know, Earth is the only one with clear life, let alone intelligence.  Doesn’t that make it an exceptionally smart planet?”

I would agree that, yes, it is an exceptionally smart planet (so to speak).  But that’s not saying very much.  All the other planets in our solar system appear to be lifeless, so they are really neither smart nor stupid.  They are merely lumps.

You can’t (or shouldn’t) call a rock stupid nor should you expect it to be smart.  The concept of “smart” doesn’t apply.  It’s a bit like my term “unsane”, which does not mean the same thing as “insane” as I use it.  “Unsane” means that the concept of sanity (or its lack) does not even apply (it’s a good term to use in a cosmic horror setting).

To be stupid‒in the sense in which I am using it here, anyway‒one must have the capacity to be smart.  It’s an important distinction, I thinktion.  I recall hearing a guest* on Sam Harris’s podcast discussing the notions of smart versus stupid.  Basically, smart could be thought of (in this guest’s view) as doing something in a way that was faster or more efficient than randomness would provide.

I think this person used as an example the process of getting from one’s house to the nearest airport.  The nonintelligent way to go would be, for instance, just to make randomly chosen turns at each intersection.  Using that strategy, one would get to the airport eventually, though the time it takes would scale (I think) proportionally to the square root of the distance…or maybe it was the square or the log, I don’t remember off the top of my head how such drunken walks scale with distance.  I think it must be more like the square than the root.  If I had the energy, I would look that up for clarity, but I’m not up to it right now.

Anyway, the point is, random turns on finite roads will get you to the airport eventually**.  Whether or not life would still exist on Earth by the time you arrived is uncertain, but you would get there.

Any route that took you less time than the “average” random route could be considered relatively intelligent.  The most intelligent route(s) would be the one(s) that got you to the airport in the least amount of time (or by the shortest distance, depending on your preference, though the two often coincide).

On the other hand, going around and around the block on which you live would never get you to the airport.  That would be stupid.  As you can see, it’s worse than just being nonintelligent.

Actually, of course, it would still be stupid if someone chose to do the random walk method to get to the airport when maps, etc., are available (unless one were doing it as an experiment, though in that case one’s goal would not be to get to the airport as efficiently as possible).

My point is probably well hammered into the ground by now:  to be stupid (at least as I am using the word) one must have the capacity to be smart.

For instance, I am supposedly quite smart.  In principle, there are probably few strictly intellectual disciplines which I could not “master” if I had the will (and resources) to do so.  There are some things that require particular bodily or other configurations or capacities that make me incapable of doing them more or less at all‒I could not be a professional basketball player or an Olympic gymnast, for instance.  But when it comes to “mindy” things, things for which a skill can be learned, my attitude has always been more or less that if someone can do it, then I could do it given enough time and effort.  I’ve not encountered anything so far that’s disabused me of that judgment.

And yet, despite that, look at the state in which my life wallows (I do not refer to the state of Florida, though that’s evidence supporting my point).

If I were able actually to constrain and focus my mind on one (or a few at most) subject(s) and just work on that (them), I think I could honestly make a real, significant contribution.  Perhaps it would not be anything revolutionary or monumental, but it would be a difference.

Unfortunately, I cannot seem to remain focused on specific things just on my own.  This is part of why I have done best in preprogrammed curricula.  Medical school, for instance, was fairly easy (in terms of mental difficulty, not in terms of the amount of work).  But depression and insomnia and anxiety and what I now recognize as the effects of ASD, and possible other forms of “neurodivergence”, make it difficult for me to learn things straightforwardly‒to drive as quickly to the airport as possible, figuratively speaking.

So, what point was I trying to make, again?  Oh, yeah.  To be stupid, one has to have the capacity to be intelligent, at least in the sense in which I am using the word “stupid”.  Maybe it would be better to use variations of the word “idiot” such as idiocy, being idiotic, that sort of thing.  Even the Doctor openly admits to being an idiot, despite being arguably the smartest person in the Doctor Who universe.

I guess that could make me feel better about myself, in principle, since if even the Doctor is an idiot, it’s not too shameful if I am.  But Doctor Who is not reality, nor is any other work of fiction (unless one is invoking the broadest, most unfiltered concept of the multiverse***).  In the real world, my stupidity makes me in many ways far stupider than any annelid worm, for instance, because I ought to be smarter than I am, I ought to be more secure than I am, I ought to be more at ease than I am.

I certainly ought to be more successful than I am now and have been for a long time.  My living quarters and conditions and whole lifestyle now are significantly less posh and luxurious than conditions were in college (and that’s not even counting the fact that I was getting an education then).  Even prison seemed‒in some ways, at least‒healthier and more conducive to well-being than how I live now.  And I don’t see any sign, nor recognize any clear way, that I’m going to do anything but continue to go downhill from here.

And, alas, I fear that the hill I’m descending has no lowest level.  It just keeps on going down, down, without even a “rock lobster” to break up the wretched descent.

Enough.  I hope you have a good day.

*I checked; it was David Krakauer, in the Making Sense podcast number 40, unless I’m quite mistaken.

**Assuming unlimited fuel and an airport (and set of roads and a vehicle) that last long enough.

***See Brian Greene’s The Hidden Reality, and possibly Max Tegmark’s Our Mathematical Universe.

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Minding primes and priming minds

It’s Monday the 19th of January (in 2026 CA or AD).  19 is a nice prime number, but it’s one people don’t think about very often.  Stephen King turned it into an “evil” number in his extended universe, which is much less obvious and predictable than using the unjustly maligned number 13.  I’ve always* liked that he did that.  It was clearly chosen at least partly because it was (and remains, and always will be) a prime number.  But it’s not an obvious one.  So, nice job King-sensei (not that he needs my moral support, though I would welcome such support from him).

I occasionally think about mailing Stephen King a copy of one of my books just on the off chance that he might read it some day when he’s bored.  If I were to develop the chutzpah to do such a thing, what do those of you who have read my stories think would be the best one to send him?

Take your time, and don’t be shy.  I’d love to hear from all…what, one of you?  Two?

I don’t think there could be three, but I could be wrong.

Returning to the topic of prime numbers, I had a cool thing happen on Friday:  I bought some stuff at the local convenience store, and my total was $19.07.  I looked at it for a moment and thought that it was a cool-seeming number.  I know 19 and 7 are both prime, and the digits don’t add up to a multiple of 3, nor is the total number a multiple of 4 or 5, obviously.  I wondered if it might be prime.

Back in the day, I would have had to check that more or less manually, but nowadays, I was able just to type into the search bar “Is 1907 prime?”

It is!  Or so claims Google.  If necessary, I could check it myself, by hand, though that would be laborious.  I suppose it wouldn’t be hard to write a quick computer program to check all the possible factors (among numbers less than 954**).  I doubt that I will do either thing, though.  I’m pretty confident in Google on this point.

And now, having said that, I’m starting to feel uncertain.  Could Google be wrong about this?  Am I really going to have to check for myself?

I remember when I realized I had never seen the Pythagorean Theorem proven mathematically (I grew up in a declining school system, sorry).  So, I had to prove it to myself to my own satisfaction, which I did.  Thankfully, it’s easier to prove something like that when the answer (so to speak) is well known.

Okay, enough numeracy, or whatever the best term for the preceding matters might be.

I did not work on Saturday, which is why I didn’t write a blog post on Saturday.  The office was open, but my coworker was able to come in, and the boss specifically told me to take the day off.  Apparently, my exhaustion really was beginning to show, even to other people, which seems not to be the usual case.

Of course, having one day of actual rest doesn’t cure my situation, but it is a minor respite.  I have more fundamental issues than mere rest or lack thereof, but I am not sure there is any way to fix them, at least not in practice.

In principle, of course, it must be possible at least to improve the settings in my brain‒tweak this set of synapses and adjust sensitivity to this or that neurotransmitter, increase (or decrease) the blood flow to this and that region of the brain, etc.  That sort of thing, done precisely and judiciously, could in principle correct or adjust any parameter of brain function one might want, in whatever ways lie within the realm of the brain’s potential.

We’re a long way from being able to carry out such manipulations, and it’s by no means certain that we will exist long enough for neuroscience to achieve such things.  But there’s no principle of nature that precludes it.

Of course, people might be quite leery of even researching such things, even when we finally know enough to do so.  After all, if we can adjust the brain specifically and precisely to make it less depressed or less anxious or less forgetful, we can adjust it in other ways, too.  One could adjust someone’s brain to make them fall in love with a particular other person, like the mythical old magic love potion.  I think most people would rather not fall in love that way (though there’s no reason to think such love would be any less delightful to experience than ordinary, clumsy, stochastic love such as what we have now).

Indeed, one could adjust human minds to make them happy, no matter what the circumstances.  Of course, this could well be used to dominate whole populations of people; one could keep them under constant control because they would be happy, and you could keep them motivated and loyal and satisfied with whatever their lot might be.  I think most people would find that notion repugnant, but it is at least somewhat morally ambiguous, because such people would be as legitimately happy as anyone who becomes happy “on their own”.  Indeed, they might well be happier than any person had ever been before, and more “well-adjusted”, and more creative, and more psychologically healthy.

I get near some of these concerns in my book(s) Unanimity:  Book 1 and Unanimity:  Book 2.  I wouldn’t say those specific ideas figure centrally, though matters of mind and free will and the nature of a person’s character and how it can be changed by physical events are a big part of it.  Also, all sorts of horrible things happen, since it is a horror novel.  And there’s a lot of room for all of it, since it’s as long (total) as the unabridged The Stand and It, to bring us back to Stephen King.

With that, I guess I’ll draw today’s post to a close.  Hopefully, I won’t already be exhausted by tomorrow.  I hope you have a good day.  And if any of you know Stephen King, please ask him which of my books he might think he would want to read.  I’d really appreciate it.

*Well, not always.  I didn’t like it before it happened or before I knew about it.

**Incidentally, 953, which is the rounded-down answer to 1907 divided by 2, is also a prime number.  That’s kind of nice.

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There’s an infinity that shapes our ends, despite having no end itself

It’s Friday now.  It will in fact be Friday now until midnight tonight, local time.  Indeed, one could argue it will be Friday now until finally midnight strikes at the international date line, when this Friday will finally be gone from the entire Earth, forever.  So, though as a matter of physics there is no universal “now”, and even for individuals, the “now” is an evanescent thing, a constantly moving and infinitesimal single frame of the movie of one’s existence, nevertheless that “now”, for me and for most others on Earth, will still be Friday for some time.

How many such “nows” are there, even for one individual?  Well, that depends a bit.  If the Planck time (5.39 x 10-44) is just an artifact of our lack of complete knowledge or ability to calculate, and time is truly continuous, then there is an uncountable infinity of such “nows” in any given day, or indeed in any given hour, or in any given second, or in any given picosecond, or indeed, in any given Planck time*.

Such is the nature of the uncountable infinity, as in the case of the real numbers:  between any two numbers, no matter how arbitrarily close you want to make them (as long as they are not identical) there is an uncountable infinity of numbers, larger than the number of possible quantum states in the visible universe, larger than the “countably” infinite number of integers.  In fact, that uncountable infinity between any two such real numbers is as large as the uncountable infinity of the set of real numbers itself, of which it is a subset.

Infinities are weird.  You need to be careful with them.  I doubt that contemplating them has actually driven anyone to madness‒though it’s easy enough to imagine that it might exacerbate depression‒but maybe minds somewhat prone to madness are more likely than others to contemplate infinities in the first place.  In any case, contemplating them can put other things into perspective.  For instance, no matter how arbitrarily large a number you might pick, it is just as far from infinity‒even the boring old “aleph nought” infinity‒as is the number one.

An interesting thing to contemplate is that, if you could pick a truly random number from, say, all positive integers, you would almost certainly get some number far huger than any number ever named or contemplated by humans, larger than a googolplex, larger than Graham’s number, larger than TREE(3), larger than the time required for a Poincare recurrence of the cosmos.  Graham’s number (for example) is big; the information required to state it precisely, if contained within the space equivalent to a human brain, would cause that space to collapse into a black hole!  But Graham’s number is nevertheless finite, and so there is a finite number of positive integers lower than Graham’s number but an infinite number of them larger than it.

It’s interesting to note the related fact that the chance of you randomly picking any particular integer is mathematically equivalent to zero‒so I’m told‒and yet you will pick some number.  Let that bake your noodle for a bit.

By the way, when I earlier compared the moments between two points in a continuous time stream to the number of possible quantum states in the visible universe, I was being a bit contradictory.  After all, our designation of the maximum number of possible states in a given enclosed region of spacetime‒which is “equivalent” to the number of square Planck lengths (each such square being 1.6 x 10-35 meters, squared, or 2.6 x 10-70 square meters) in the surface area of a sphere surrounding such a region**‒is based on quantum mechanics, and thus implicitly entails time being only sensibly divisible down to the scale of the Planck time.  So comparing that to a continuous time is comparing two fundamentally incompatible realities.

Oh, incidentally, I’m writing this post on my smartphone today.  I just didn’t feel up to bringing the lapcom with me yesterday, and I didn’t expect to write any on The Dark Fairy and the Desperado today.  I did, however, have a bit of a thought, as I’m prone to do when conscious, whether I want to do it or not.

That thought was that, perhaps, I can try to write my blog posts in the evenings‒on the way back from work, say‒but set them up still to be published the following morning and work on fiction in the morning.  Writing fiction seems to give me a boost, mental health-wise, when I do it in the morning.  It’s quite ego syntonic, as they say, or at least it seems to be.  But I don’t really want to stop writing this blog.  Then I’d just be floating in the void all alone, writing fiction that I like but that almost no one else will ever read.  That is a discouraging thought.

In any case, I don’t think I’ll be writing a post (for) tomorrow, since I don’t think I’m going to be working tomorrow.  If I am, and if I cannot get out of it, I guess I will write a post, and it will likely be a grumpy one if it happens.  But I may start next week writing the following day’s blog post on the evening before and doing fiction in the morning.  One good aspect to writing fiction in the morning is that the initial writing and the editing process are separate.  I don’t have to edit what I write each day on that day, which I have to do with this blog.

We shall see what happens.

In closing, I leave you with this juxtaposition of two notions:

*If time is not sensibly divisible even in principle below the Planck time, then the maximum number of “nows” in a given day is just 24 hours divided by the Planck time, or about 1.6 x 1048 “nows”.

**See Bekenstein-Hawking black hole entropy calculations and the Holographic Principle.

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The moving finger writes, and having writ, now must edit

This is it:  my last blog post of 2025 (barring some truly unexpected circumstances).  I will probably be writing a post tomorrow, because I think we’re going to be working tomorrow, despite the fact that it will be New Year’s Day, and a stunningly large fraction of the people of the world will be hung over or otherwise exhausted from ringing in the New Year.

I suspect New Year’s Eve/Day is the most widely celebrated holiday in the world, far surpassing the numbers who celebrate any mere religious holiday.  Since the world in general uses the same “Gregorian”* calendar, it’s a rare commonality for the human race, and worth celebrating.

If only they could work on finding more things in common, since after all, they have almost everything actually in common with each other.  And yet, they focus on trivial cultural or superficial differences and battle viciously over them, as if they were fighting truly alien beings.  Talk about your narcissism of small differences.

Humans are so stupid.  The more of them there are, the stupider, somehow, as though the lowest common denominator tends always to dominate the dynamics.  It’s like Tommy Lee Jones’s character said in Men In Black:  a person is smart, but people are dumb, panicky, dangerous animals, and you know it.

That isn’t always the case, obviously.  Humans have accomplished great things in large groups, interacting with mutual exchange to mutual benefit (or not so mutual benefit), but that probably only happens in rarefied circumstances, discovered or arranged by luck or by the skill of one or a few who are cleverer than average, and sustained thanks to a form of natural selection.

Because of the sheer power of such organizations of people, those rare few types of interactions can endure for tremendous lengths of time and be astonishingly effective and broadly prevalent.  This can distract one from the fact that the ideas were so singular and ingenious.

Money, for instance, has been invented more than once, but it’s a relatively low-hanging and particularly nutritious fruit, allowing as it does for the far more efficient exchange of goods and services to (ideally) mutual benefit.  Of course, commerce can be cheated and can thereby become nonproductive or even counterproductive, especially if one or a few entities obtain disproportionate wealth and power.  This sort of selection for detrimental equilibria happens in the world of biology as well.

Imagine a football game in which, every time one team scores, that team gains an extra player and the other team loses one.  Once one side takes the lead, they’re likely to keep it and increase it, making them ever more likely to maintain their dominance.  It can make for a pretty boring and not very productive game.  Such a situation is worth avoiding, even if you happen to be on the winning team.

Written language is, of course, the single most important human invention‒more important than even the invention of language itself, though that was a necessary prerequisite, so the argument could be made that it is more important or at least more fundamental.  Thankfully, language is a different type of thing than money, so it’s not as easy to game it to secure an unreasonable advantage for any individual or group.

There is, of course, an often-used attempted strategy of discouraging or preventing literacy in some groups or one sex (always the same one, it seems) to keep them from gaining the power that written language can impart, but it can be harder to keep those systems in place than for a monopoly to maintain its economic advantage.

Still, even written language isn’t automatically self-protective.  It’s possible for misinformation and disinformation to spread and even prosper, at least for a time (such situations tend to self-destruct), and it can do terrible damage, much as mutations in somatic DNA can lead to cell dysfunction, cell death, and sometimes cancer.

Analogous things can happen to whole civilizations as well, and they have happened many times, but that’s no reason to blame language or learning.  One doesn’t prevent cancer by eliminating DNA itself or by killing the host organism (that does eliminate the cancer, but in an unsatisfying way).  Only better, more thorough thinking and language, the equivalent of DNA proofreading, can do that without catastrophe.

And I, by writing this post, try to contribute to the good language, the useful or at least interesting language, in the world.  I suspect I will continue to do so as the next year begins.  I hope you enjoy whatever celebrations you have in store.

*Though Pope Gregory the Whatever Number was merely the one who commissioned it.  Astronomers and mathematicians actually did the work.  We have some scientifically literate Popes nowadays, at least, and a Belgian priest was among the first to do rigorous mathematics using Einstein’s new field equations (though Friedman got there a little earlier, his work was apparently not as convincing) to demonstrate that the universe could not be static** based upon them.

**Leading Einstein to introduce Λ (lambda), the cosmological constant.  He later called this his biggest blunder (supposedly) but it turned out to be a useful and term and concept in describing the apparent evolution of the universe as we know it now.  Like Planck before him, even Einstein’s fudges*** were deeply insightful and useful.

***Speaking of Einstein, I recently got an email from my old med school alumni association with the subject line “You are responsible for Einstein’s success”.  To which I so wanted to reply, “I know, right?  But did he mention me in any of his papers or even throw me a word of thanks (in German or otherwise) in his acceptance speech when he got his Nobel Prize for demonstrating that light comes in ‘packets’ which we now call photons?  No!  Ungrateful bastard.”

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“For years and years I roamed.”

Well, I might as well stick to the same pattern, so…ahem.  It’s New Year’s Eve Eve today, which means tomorrow will be New Year’s Eve and Thursday will be New Year’s Day.  At that point, if we wanted, we could just start counting days down or up‒i.e., Day 1, Day 2…or Day 365, Day 364…and so on.

Of course, if we were going to do such numbering, I guess it would make sense to divide things up into months for easier “local” day-keeping, which is what we’ve done as a civilization.  But those months are irregular and rather haphazardly named.  This can occasionally be irritating, though of course I have a sentimental fondness for at least some of the month names.

Unfortunately for the goal of making months of uniform length, the number of days in the year isn’t evenly divisible by any number larger than 5, unless I’m mistaken…

Yes, I was correct, unless you want to divide the year into 5 groups of 73 days.  That might be kind of fun, since 73 is one of those overlooked prime numbers, and it has the slight extra fun that its digits add up to 10, the base of our usual number system.

Still, especially considering the necessity of leap years (with the convoluted adding of days, removing of seconds, not adding a day when it’s the turn of a century unless it’s also the turn of a millennium and so on) it seems cumbersome to divide the year evenly.

I rather like the solution of making 12 months that are each 30 days long and having the remaining 5 (or 6) days be a period of celebration.  It could be held around one of the equinoxes or the solstices, or it could even be split up between two of them.  I’m inclined to put them at the end of the year, when the Winter Solstice in the northern hemisphere happens, because it’s long been a holiday time anyway.

Of course, this all biases against those in the southern hemisphere, but there are significantly fewer people in the southern hemisphere, or at least there were the last time I looked into it…

Yes, I was correct again, it seems.  According to my quick and dirty check, there are on the order of about a billion people in the southern hemisphere, as opposed to the remaining roughly seven billion people in the northern hemisphere.  I guess that means the winter solstice would be a good time for those separate days.  And I’ve not heard many Aussies complain about being able to go to the beach on Christmas or New Year.

Mind you, one could do that down where I live anyway, if one were so inclined.  I am not.  The beaches on the east coast of Florida are mostly annoying, and the Atlantic is not much fun for swimming.  The west coast of Florida, where one swims in the Gulf of Mexico, is much more pleasant.

I’m not a very big beach person at the best of times (or the worst of times) but I have quite a few pleasant memories of being on one or another beach on the Gulf (of Mexico).  They all date back to at least 33 years ago, though, so maybe it was just due to the nature of youth that I enjoyed them.

Alas, I’m not truly young anymore by most standards; I’m 954 years old.

Ha ha, just kidding.  Or, wait, maybe not.  I know that exoplanets have been discovered that orbit very close to their stars, and so have orbits that can be as short as a few Earth days (possibly fewer).  So, if the universe is infinite in spatial extent, which it so far looks as though it is, and if there is no lower constraint due to the laws of physics on the length of possible “years”, then there exists, somewhere in spacetime, a planet by the years of which I would be 954 years old.

Actually, if spacetime is infinite, there should be an infinite number of such planets even if they happen only once within any cosmic horizon.  But let’s not get into that right now.

Let’s do the math; it’s simple and easy, so why not?  56 years old x 365.25 days in an Earth year makes me 20,454 days old, at least on my latest birthday.  Dividing that by 954, which is almost a thousand, should give a year length of roughly 20 days per year…okay, well, the “exact” number of 21 and 70/159 days per planetary year is what is required to make me 954 years old.

Actually, though, since the number of days in that hypothetical year is smaller than the time since my last Earthday birthday, I will have to adjust my days’ old age number to the precise one:  20,525 days, which if divided by 954 gives us a year length of 21 and 491/954 days, or 21.51 days (playing slightly free and loose with significant figures).  There will be a range of possibilities, of course, since I could be anywhere in the 21-ish day course of my 955th year and still be able to call myself 954 years old, if we go by similar conventions to those followed by humans on Earth.

Okay, well…that was sort of a weird digression.  I know, I’m weird, so maybe given that, a weird digression is, in a sense, not weird.  But given other considerations, it still is.

I am an odd person, I know (though I don’t know if I’m prime).  Sometimes‒rather often‒I think I’m losing my mind.  At other times, though, I think my mind is functioning within parameters, but it is contemplating things that are vast and potentially troubling to the feeble mortal ego if one does not drape oneself in the obscuring veil and cloak of delusion.  But my fabric sensitivity doesn’t allow me to tolerate such garments for long; you could say I lack PPE for such things.  Perhaps the secret is to destroy the ego (which may well just be an illusion, anyway), but that is more easily said than done.

Who knows?  Not I.

And yes, it’s “Not I” not “Not me”.  You wouldn’t say, “Me don’t know”, so you shouldn’t say “Not me” in response to the question “Who knows?”  Apologies to David Bowie and Nirvana‒but The Man Who Sold the World is a song, and so they are allowed poetic license.

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A very low magnitude happiness vector

It’s Friday now, for those of you who have been drinking heavily in the run-up to the big holidays and have lost track of the days.  I’m certainly working today, but I don’t know if the office will be open tomorrow, so I don’t know if I will write a blog post tomorrow.  If you’re interested, feel free to check this site in the morning.  Or, if you like, you can subscribe, and you’ll be sent emails for new posts.  But take that suggestion like a broken barometer:  no pressure.

That’s almost all that I feel I have to say.  Ordinarily, not having anything to say doesn’t mean I won’t write a post.  I’ll just blabber and blather for nearly a thousand words, just to see myself write*.  But there won’t be anything of substance.

Probably a good fraction‒perhaps even a significant majority‒of everything you can find on this blog is pointless nonsense.  Though, of course, I might contend that everything is pointless nonsense.  But here in this blog, you will sometimes find it concentrated, distilled, freeze-dried, and vacuum sealed.

No, I don’t know what some of those things might mean here, metaphorically, any more than you do.  I was just saying words that I thought seemed good.  I have curious tastes, though, so I’ve no idea what others might think of them.

Anyway, that’s me trying to act all silly and funny and whatnot, as if I might be even slightly happy, so that other people don’t have to worry about me.  Well, don’t worry about me.  I’m not happy at all, but it doesn’t matter in the slightest, because neither do I.  Maybe that’s just the way everything is, or maybe it’s just me.  Neither would particularly surprise me.

So, anyway, yeah, I’m not happy, not in any useful sense of the term.  John Galt said that happiness is a state of noncontradictory joy, and that’s always seemed to me like a pretty useful definition of the word, though it’s not the only useful one.  But I like how it separates joy from happiness.  Even people going to the gallows can sometimes joke and laugh, if only as a defense from fear, and in those moments of laughter they may feel joy.  But it is perforce transient, and it’s unlikely that they would be willing to say that they were happy**.

So, in that usage of the word happiness, joy would be necessary but not sufficient for actual happiness.  And both might be relatively orthogonal to a state of wellbeing (which is another word that has more than one interpretation).  Still, though the dot product of happiness and wellbeing may be surprisingly small***, I don’t think it could be zero.

Yes, I use vector multiplication as metaphors for such things, though honestly, it’s not really even so far separated as to be merely a metaphor.  Vectors can be useful for tremendous numbers of things that may seem far afield from each other, from computers and artificial intelligence to physics to biology to economics and ecology.

They can even be of use in psychology, though I don’t know how often they are used therein.  I haven’t dived into a lot of more formal psychology recently, though I like the popular works of Daniel Kahneman and of Jonathan Haidt.  And Paul Bloom is great fun.  But popular works of psychology rarely involve measuring aspects of mental functioning as vectors in a phase space.

Though, as you might have picked up if you’ve read a lot of what I’ve written here, I think it’s useful to think of human behavior and actions as the outcome of a vector sum of all the various “pressures” in the brain/mind, which end up with a resultant that determines what one’s actions will be in that moment.

But, of course, the action itself can feed back on the input vectors, altering them in various ways (maybe their angles, maybe their magnitudes, rarely but possibly their actual sign, which admittedly would just be equivalent to an angle change of 180 degrees, or 𝜋 radians).

Likewise, the state of many of those vectors can change with time.  For instance, one could imagine a vector associated with one’s degree of alertness.  Such a vector would tend to have greater magnitude in the daytime than late at night in most humans, so it waxes and wanes inherently (though even this is likely a result of input vectors delivered by various aspects of the sensory systems).

But the actions taken as a product of previous moments’ vector additions can affect this vector, too.  If a previous resultant led to one having a strong cup of coffee, that might increase the magnitude of the alertness vector, though there would be a delay.  Alternatively, if the previous outcome had led to one drinking a significant amount of Wild Turkey 151 on an empty stomach, the alertness vector might soon start decreasing in magnitude.

Okay, I’ve reached the point in the blog post where I’m using vectors to describe the effects of coffee versus whiskey.  I think it’s reasonable to bring things to a close now.  I hope you all have very good days, by any reasonable measure.  If I work tomorrow, I’ll write a post tomorrow.  I’ll leave figuring out what effect that will have on your own wellbeing for your consideration.

*Analogous to speaking to hear oneself talk.

**Though I can imagine possible situations in which one might be literally happy even on the way to the gallows.  It would be a very brief happiness, nonetheless.

***I doubt that it is, but I also doubt that it is the full, direct product of the magnitudes, as it would be if there were no angular difference at all.  Wellbeing, I think, is more complicated than happiness, which is itself by no means simple.

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“No need to get up-tighter”?

It’s Monday again, and though it is not raining down by me, I’m all but certain that it’s raining somewhere right now, so one could say “it’s raining again” without fear of being entirely wrong.  No matter how you might want to cut up spacetime based on “planes” of “simultaneity”, there is sure to be somewhere in the universe where it is raining now.

Actually, if the universe is infinite in spatial extent, one could probably prove that it is a mathematical certainty that it’s raining somewhere, since there are‒as far as we can tell‒only a finite number* of possible quantum states in any given region of spacetime, and some of these include rain.  Indeed, even if it were not raining on Earth, anywhere, in some given instant (an unlikely eventuality), the fact is that rain can happen in many places in many forms.  I’m led to understand that it sometimes rains neon in the atmosphere of Jupiter.

So, perhaps the song by Supertramp shouldn’t have been It’s Raining Again, but should have been It’s Raining Still.

I don’t know.  Maybe that wouldn’t suit the rhythm of the song.  Then again, it always was a song where the sentiments expressed in the lyrics didn’t quite match the upbeat character of the tune.  This was probably deliberate on the part of the band.

Oh, in case anyone was wondering, the reason there was no post on Saturday was that, indeed, we did not work in the office on Saturday.  We didn’t work out of the office, either, as far as I know.  Well, I know I didn’t work, so even if they worked, we did not work, so I guess I’m right there.

I did a fair amount of walking on Saturday, and nearly as much on Sunday, though Saturday’s walk was more interesting.  I walked in a “park” along a canal in south Florida, and found myself well down into Dade County before I found an exit from the park area that took me to a road on which I could get something to quench my thirst and a place to which to call an Uber (they have a hard time picking one up in a park alongside a canal).  I had walked about seven and a half miles, and I could tell I was getting a bit too much sun**, though my feet and ankles and knees seemed to be holding up okay.

On Sunday I went for another walk, during which I had enough sunscreen.  That was because on Sunday I took my walk solely for the sake of walking, unlike Saturday, on which I had a specific purpose, and my longer walk began on a whim after that purpose was achieved.

It wasn’t an interesting or noteworthy purpose, by the way.  I’m just not discussing it because it cannot have any bearing for anyone but me.

Let’s see, is there anything else going on that’s worth discussing?  Well, of course, there are things going on in the world, and in the universe, and so on, all the time, and probably many of them are worth discussing to someone, or would be, even if no one knows they are happening.  But, of course, pretty much anything that happens, no matter how locally momentous, is historically trivial, let alone cosmically trivial.

Probably there aren’t many things that aren’t cosmically trivial.  I suppose if inflationary cosmology is real and it started at some locus in spacetime, then that would not have been trivial.  But if there is eternal inflation, there’s a real question as to whether it started at all.

Of course, even then, with eternal inflation, the local drop of the inflaton field down to the vacuum state (or a pseudo-vacuum state) here in our bubble universe‒leading to the formation of our universe, all its matter and energy, and possibly the configuration of our natural laws and constants‒would seem to be significant.

But that would only be significant to us, the creatures in this bubble universe.  On the scale of the cosmos overall, it would be just one bubble universe formation in an endless sea of such bubble universes, each one no more striking than the cavitation bubbles that form and then collapse in water that’s starting to boil.  Indeed, if our universe is such that an eventual recollapse will happen, i.e., a “Big Crunch”***, then we really are a lot like a cavitation bubble.

I guess this has been a slightly odd way to start the week‒which is unfortunate, given that today’s date is an even number (24) not an odd one.  But I don’t think I’ve ever claimed not to be an odd person.  I think I’ve known that I was different and a bit peculiar‒perhaps more than “a bit”‒since I was very young.  That’s okay in and of itself.  If most people are “normal”, why the hell would anyone want to be normal?

With that, I wish you all an abnormally good day and week, and if you’re in the US, I hope you have a good holiday coming up, and that you are anticipating it with eagerness.

*It’s big, don’t be mistaken.  But the biggest finite number you can think of‒ever‒is no closer to infinity than is the number 1.  So, in a universe that’s infinite in spatial extent, all possible finite configurations will be instantiated somewhere‒indeed, they will be instantiated an infinite number of times.

**I hadn’t planned on such a long walk, so I was not prepared in that sense.

***Our best information right now seems to indicate that we are not going to recollapse, but that we will continue to expand, at an ever-increasing rate.  I suppose that would make us more akin to a bubble that fully forms and expands in boiling water, escaping from the liquid into the air above.  Such bubbles are no more important than the cavitation bubbles, though.  They’re merely different. 

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How now, you secret, black, and midnight blogs!

Hello.  Good morning.

It’s Thursday.  It is, in fact, the 2nd Thursday in November, which means that, from the point of view of Thursdays in November, we are halfway to Thanksgiving (which in the US is the 4th Thursday in November).

Of course, we are not precisely halfway to Thanksgiving from the point of view of the days of the month of November overall.  Thanksgiving falls on the 27th of November this year‒14 days from today, of course‒so we are not quite halfway there as far as the days of November are concerned, but we are close to it.  If the month had started on a Friday, the halfway point in days versus Thursdays would be the same.

I think that the maximum disjunction would happen if the month began on a Thursday.  The 8th would then be the 2nd Thursday, and Thanksgiving would fall on the 22nd, which is quite a bit larger than 2 x 8.

Mind you, all this depends on starting one’s count in November.  That is not too unreasonable, but one could just as sensibly start counting Thursdays right at or after January 1st (let’s see, this year that’s 46/48 Thursdays, or about 95.833%).  If we did that, we would already be practically at Thanksgiving.  If we counted all days, we might be even closer still, percentage-wise.  Let’s see, 317/331, or about 95.770%.  Whataya know?  I was wrong, the Thursday one is “closer”.  I suspect this varies from year to year, but I’m not interested enough to check.

We could also begin our count at the beginning of autumn, which sort of seems appropriate.  Or, perhaps most sensibly still, we could start right after the previous Thanksgiving, beginning our counting on “Black Friday”.

Jeez Louise, I think I’m losing my mind, here.  Why am I writing about such nonsense?  I mean, yes, it’s interesting to notice how arbitrary and artificial human ways of counting days and things and so on are, so I suppose it’s somewhat edifying, and even could be mildly interesting for a moment.  But I nevertheless feel bad for wasting my readers’ time.

Though, I suppose, in a certain sense, one could say that all time is wasted‒“Plans that either come to naught or half a page of scribbled lines” and all that.

“Where do we come from?  The dust.  Where do we go to?  The grave.”

Of course, that last quote was not meant to be a general description of the human condition, but refers to Ray Bradbury’s “October People” in Something Wicked This Way Comes.  I’ve always thought that I’m an October person, since I was born in October.  Like Macduff, in the play from which Bradbury’s title above is taken, I was a C-section, though it would be a hyperbolic* to say that I was “ripped untimely” from the womb.  (Still, does my manner of birth mean I could defeat Macbeth?)

October is over now, in any case, and who** knows if I shall see another.

I don’t know if anyone has ever written about “November People”, but they don’t sound particularly scary nor particularly inspiring.  This assessment is not meant to refer to people born in November!  Several of my favorite people were born in November.

In other news, I did receive my Principles of Neural Science yesterday.  I used my dollar coins to choose a section, and I read it in the afternoon:  it was about neural firing and muscular activation during locomotion, briefly comparing lamprey with vertebrate, especially mammalian, locomotion patterns.

It may seem trivial, and I didn’t learn much that I didn’t at least implicitly know before, but the specifics are new, and all information has the potential to be useful.  We cannot know for certain ahead of time what knowledge might be most beneficial, just as we cannot predict the specifics of progress and invention.

As I said, I chose the textbook page via my coin-flipping process, using my three Sacagawea coins.  I keep a few dollar coins with Susan B. Anthony and/or the aforementioned Sacagawea with me at all times.

I carry such coins not so much for decision-making but because I like to roll them across my fingers when I want to “stop my hands feeling busy”.  I guess it’s a form of “stimming”, and I’ve been doing that particular one since college.  I taught myself to do it after I saw Val Kilmer, as Chris Knight, doing it in the movie Real Genius, which was one of my favorite movies.

Well, this has been a lot of pointless nonsense today, hasn’t it?  I apologize, and I guess I can try to mitigate my offense by at least trying not to produce too much of nothing***.  So I will draw this post to a close now.  I hope you all have a good day.  I will very likely write a post tomorrow, so you can look forward to that, if it’s the sort of thing to which you look forward.

TTFN

*You know, like non-Euclidean geometry.

**The WHO does not know, though with a bit of background information they could probably make reasonable predictions.

***According to the song, that can make a man feel ill at ease.  It can also, according to the same song, make a man abuse a king, which seems like it would be quite a rare situation.