Mathematics

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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.

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“Though this be madness, yet there is method in’t”

Well, first let me apologize for yesterday’s blog that largely concerned the weather, and in a trivial sense at that.  It was rather lamentable, I know, with emphasis on the first four letters of that adjective.

On the other hand, I don’t apologize for having had my little bit of fun with the date.  That may have been even less interesting to most of you than my jabbering on about the weather, but I like it.  I fully expect that I will do such things again.  For instance, in a similar vein, today is a bit fun because it is 11-12*, so the numbers are in appropriate ordinal sequence with no gaps.

That’s not very fun.  More fun will be had (by me, anyway) on Friday, when it will be 11-14-25.  If you don’t immediately see the fun there, it may help that a similar fun date next month will be available on 12-13-25.  This fun also works with the European date order (but in both you have to leave out the digits that denote the century).  Also, there were no equivalently fun dates in any month before October.

This is the most fun I’ve had on any kind of date in at least 16 years, I would guess.  That’s an easy call, because I haven’t been on any date at all in at least that long.  See what I did there with the multiple meanings of the word “date”?  Of course you did.  What do I think you are, a moron?

No, I do not think that.  You are reading a blog post, so you are a reader, which gives you a serious leg-up, moronia-wise.  You draw from the well of that greatest of all human inventions:  written language.  Your taste in reading material may be somewhat questionable, but I cannot legitimately complain about that.

Wow, I feel like I ought to be almost done with this post, but I’ve barely passed 300 words.

On to other things.  I’m going to try to do a better job about science reading during my downtime in the office.  It’s not that I’m completely slacking; I’m reading Shape by mathematician Jordan Ellenberg, and I just read his earlier book How Not to Be Wrong.  I’ve read both before and/or listened to the audio books, but they are well worth rereading.  He’s a great math professor, and has a gift for explaining potentially abstract concepts.  I think he’s slightly better at this than Steven Strogatz, the author of The Joy of X and Infinite Powers, but they’re all good.

I also just yesterday gave in to an urge I’ve had for some time:  I ordered a textbook I liked in med school but which we didn’t really get into as deeply as I would like:  Principles of Neural Science, by Kandel et al.  The edition I had was by Kandel and Schwartz, if memory serves, but Dr. Schwartz is no longer involved, it seems.

It’s a textbook, so it’s pricey, even in paperback, but I discovered that I could put it on a payment plan through Amazon, so that’s what I did.  It arrives today.

I’ve also resolved, at least tentatively, to try to take the heat off my reading of my science books‒including the above newcomer‒by doing something I did when reviewing/studying in med school:  I would get a text that I was reviewing, and I would pick a section to read/review by flipping a coin.

Actually, it was a series of flips, each one dividing the “remaining” part of the book in half.  In other words, for the first flip, heads would mean I would look in the front half of the book, tails would mean the back half.  Then the next flip would decide to which half of that half I would narrow things down further.

Anyone who has spent any time dealing with computers and/or binary numbers can readily recognize that, with 10 flips of the coin, one could choose a specific page in a 1024 page book.  I guess every flip would count as a kind of “half-life” for the book’s pages.  If one wanted, one could even choose one’s pages not with a coin flip, which is not truly random, but with a quantum event that has a 50-50 chance, like measuring whether a given electron’s spin is up or down.

Of course, I don’t have a Stern-Gerlach gate, so I would have to “farm out” that process.  But I understand that there are apps that you can use that have their sources at labs where each decision is truly made by a quantum measurement.

It’s not terribly practical nor more useful for pickling book pages than is a coin flip, but if you’re a convinced advocate of the Everettian, “many worlds” version of quantum mechanics, it has the added “benefit” that each “flip” will divide the universe into two “worlds”, one where you choose from the earlier half, another where you choose from the latter.

Coin flips do not enact such splitting, not in anything but the trivial sense that every quantum level interaction potentially does so.  The experience will be the same for you, though, except whatever glee you might derive from splitting the universe to choose a section to read.

Anyway, I’ll be trying to read my books, random section by random section.  Believe it or not, this works for me.  I don’t have to learn things in order, usually, and this method avoids me feeling bored while trying to trudge through a text in order.

Perhaps I do have some aspects of ADHD up in there in my brain.

Well, I’ve now passed my target length for this post by some margin, so I’ll call this enough for today.  I expect to be writing another post tomorrow, but like everything else**, it is not absolutely certain.  I hope you have a very good day.

*Only in the American style Month-Day-Year format, though.  It is less fun in the European Day-Month-Year format.

**Yes, even death and taxes, in principle.

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Some Halloween-style pictures among unrelated words

First of all, Happy Halloween to everyone who celebrates this day in any fashion.  Even if you don’t celebrate it, you might as well have a good day.

I don’t discriminate based on Holiday celebrations.  How very admirable of me.

Once again, I mean to keep this post short by making my target 701 words to start with, because I’m very tired this morning.  It was difficult to get up at all, and I still feel as if I’m vaguely sedated.  Unfortunately, it doesn’t seem to have been one of those sedatives that’s associated with euphoria.  It would be nice if it were, right?  If they would agree, I would agree.

Unfortunately, I’m just groggy and weak and blurry.  By which I mean I feel that the world seems slightly blurry to me.  I don’t mean that I am blurry if you look at me.  I might imagine that I could be blurry (meaning as a function of me not just poor vision in the observer) but I have looked in a mirror already this morning, and while I am far from easy on the eyes, I seem to be in focus.

Thinking of atypical interpretations of things people say, I was listening to one of the guys on the phones in the office yesterday, and I heard him use the expression “qualified individual”.  Now, I know what he meant, and it’s a perfectly valid term when discussing a promotion with a customer.  But it occurred to me that one could use the term to refer to someone who is an individual…but only from a certain point of view.

For instance, Norman Bates could be thought of as a “qualified” individual.  Yes, he’s a single person in the sense that he is one organism*, but there is more than one distinct personality in his head.  You could also say that the narrator in Fight Club is a “qualified” individual, as is James McAvoy’s character (should that be “characters”?) in Split.

Oops, sorry, I guess I could have given a spoiler alert for those movies.  But if I had done that, it would have ruined the surprise!

Of course, from certain points of view, even your typical unqualified** individuals are not as monolithic or monotonic or monotropic or, well, monopersonic as one might imagine.  We know that in split brain patients, when the corpus callosum is severed to reduce the problem of, for instance, uncontrollable seizures, the two sides of the person’s brain can act and think in some ways like two separate people.  They act like two individuals in other words, though in such circumstances, that word is least applicable, since if anyone is “undivided”, it is not these people.

But they are only a special, more extreme version of that which is true of the rest of us.  Our minds are all divided into many separate modules and centers, often running largely in parallel with each other.  There is no one central, “terminal goal” region of the mind; there are separate and conflicting areas and aspects, and even they are not constant.  Many introspective practices, particularly those associated with Buddhism, recognize that the concept of an individual, homuncular “self” is nebulous at best and is never even close to being real.

It seems the term “individual” is just as incorrectly presumptuous for people as the term “atom”*** is for, well, atoms.  However, if we’re referring to more physical literality, then it’s still pretty accurate, certainly for everything more complex than a flatworm.  If you start splitting people (and other animals) in pieces, what you get, at best, is a creature with missing bits and lots of dead former body parts.  You don’t get more than one being.  Often you get no one, because you will have killed the person with whom you started.

In such a case, one divided by two might in a sense equal zero.

Of course, even in basic mathematics, if you divide one by ever larger numbers, you get closer and closer to zero (it’s the limit as the denominator goes to infinity).

Speaking of going to infinity, the value of 1 / (701 – x), where x is the number of words I’ve written, has now crossed the singularity at infinity and is asymptotically approaching the x-axis from below.  On the positive side of the x-axis, starting from the beginning of a post’s first draft, that number can never be smaller than 1/701, since even I cannot write a negative number of words****.  But once I’ve passed the 701 point, the numbers can become an infinitesimal negative fraction, in principle.

In practice, I’m practically finished here.  I hope you all have a good day.  I will probably write a post tomorrow.

*Not counting skin and intestinal flora and the like.  If we count those, then we can all, like Walt Whitman, truthfully say “I am large, I contain multitudes”.

**Again, this has nothing to do with the person’s skills or résumé or experience or innate abilities, it’s just saying that one wouldn’t normally feel the need to add any caveats when calling a person an individual.

***Which means, basically, “uncuttable”.  And what we call atoms can indeed be “cut”.

****A number of negative words, on the other hand…

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

Morning has broken!

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

Ha ha.

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

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

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

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

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

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

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

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

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

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

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

Ha ha, again.

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

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

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

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

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

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

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

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

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Bing-bing-bing! Ricochet Robert.

I’m in a rather unusually bad amount of pain this morning, even for me, so please excuse me if my thoughts are somewhat incoherent or distracted or grumpy-seeming.  Though I don’t know how you would be able to tell if I’m grumpier than usual.

It’s Monday yet again, and it’s only been two days since my last post, not three, because I worked on Saturday, and on that day, I also wrote a very angry blog post.  I think some people might have found the degree of malice I expressed on Saturday disquieting or at least just not good, which I can understand.  I tend to think of such terrible things a lot more often than most people do (though I share them only infrequently); it’s one of the reasons I find my own company unpleasant.

But, of course, I’ve tried to compensate for my dark tendencies by doing as much good in the world as I’ve been able to do, such as by becoming a doctor.  I’ve never actually acted on any of my darkest impulses and dreams, except when I write horror stories, or when I write non-horror stories with horrible elements in them.

I guess maybe that’s one of the things that’s been therapeutic for me about writing fiction.  Maybe the trouble is right now that I don’t have a good outlet for my terrible thoughts.

Of course, I know that the idea of thoughts and emotions as “substances”, as if some manner of fluids, which can build up and need release is not merely incorrect, but is not even a good analogy for how emotions and other neurological states work.  This is part of why meditation is far more effective against stress and tension than is, for instance, the often counterproductive notion of catharsis.

Of course, sometimes things that work well for neurotypicals don’t work nearly as well for those on the autism spectrum*.  For instance, there is apparently some reasonable evidence that cognitive behavioral therapy, which often works quite well for neurotypicals with depression, is not as effective and can even be counterproductive for autistic people; we already tend to over-self-evaluate our cognitions, and so the tricks and workarounds of CBT often are not merely redundant but miss the issues entirely.

Along a line of possibly similar nature, I’ve written before about how meditation often serves to reduce my anxiety but at the same time worsens my depression.

And yes, in case you’re wondering, I think it’s all a matter of neurological states‒or neurohumoral states if you want to be slightly more precise.  I’ve spent nearly my whole life interested in such things; still, I have found neither evidence nor argument that has so far persuaded me that there’s any significant credence to the notion that humans are anything but temporary patterns of matter/energy, “spontaneously” self-assembled like any termite mound/colony or beehive/swarm**.

Once that pattern breaks because it can no longer sustain itself, due to injury or age or what have you, there is nothing more to it; it’s a hurricane that has passed.  There can be records and traces of its passing, and the damage it has done can linger for a long time, but there is no “afterlife” for weather patterns.

People are more complicated than hurricanes, at least in some senses, I will admit that.  But more intricate complexity doesn’t tend to make things more durable; it makes them more fragile, ceteris paribus.

Of course, all else is almost never equal.  Nevertheless, it’s often useful to consider complex matters as partial differential equations in more than one variable***; one explores the equation by holding all but one variable constant and differentiating or integrating along only one variable at a time.  As long as one thinks carefully about such things and never forgets that one is holding the other variables constant‒and by not forgetting, hopefully avoiding the oversimplification of one’s model of reality‒one can penetrate a great deal by recognizing when powerful tendencies persist even given the fact that other variables can influence matters.

For instance, the metallicity**** of stars influences the size at which they undergo certain levels of fusion, which is why it is thought that the earliest stars had different lifespans and luminosities relative to mass than later stars (like our sun).  But they still, overall, behave like stars, and the bigger ones shine brighter and last a shorter time than the less massive ones.  They are more alike than unalike, the narcissism of small differences notwithstanding.

Well…that tangent, or series of tangents, sure took me down unexpected paths!  But I guess that’s the nature of tangents; in any nonlinear but continuous function (even one as simple as a circle), there are a functionally infinite number of possible tangents.

I think that’s the right mathematical metaphor; isn’t it?  I guess it doesn’t much matter.  I’m just expressing my highly stochastic thoughts (I doubt they’re truly random) as they come.  But they would probably follow different courses if I did not express them in this fashion.

I hope your own thoughts are less troublesome to you than mine are to me and that you are at least at some degree of peace with yourselves and with each other.  You might as well be, though I know that’s not enough to guarantee it.  Still, do what you can, okay?

*Which I am, as you may know; I have written at least in passing about my recent, quite late, diagnosis.

**I don’t mean “like” here as “the same as” but rather “in the same fashion as”.

***My terminology is a bit sloppy here, but I’m not trying to be mathematically rigorous, I’m just trying to get my thoughts across with some clarity and accuracy.

****To astronomers/astrophysicists, a “metal” is any other element but hydrogen and helium (this no doubt irks chemists).  The earliest stars would have been almost entirely hydrogen and helium, certainly to start off.  Mind you, even later generation stars like the sun are still by far mostly hydrogen, but seemingly small “contaminants” can have noticeable effects on big systems, as in the fact that water vapor and carbon dioxide markedly affect Earth’s atmosphere and surface temperature despite being present in tiny amounts compared to nitrogen and oxygen.