Mathematics

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For a minute there, I found myself

Wow, I’m really tired.  I had a terrible time falling asleep last night, even though, once again, I was tired and “shagged out” as if after a long squawk, in the words of Michael Palin’s pet shop owner from the dead parrot sketch.  And then, of course, when I finally did get to sleep, I didn’t even come close to sleeping through until my alarm‒though, rather amusingly, I fell back to sleep about half an hour before my alarm was due to go off, so I got to enjoy being awakened by it when I was thoroughly mired in unconsciousness and confusion.  Nevertheless, I did still get up and do three quick sets of (bad) pull-ups before taking my shower, getting dressed, and so on.  And here I am at the train station, waiting for the second train of the day.

I know all this must make for incredibly tedious reading, and for that I am truly sorry.  I’d prefer to write more about potential stories, and which ones, if any, my readers prefer, and about potential “podcasts”*, and all that stuff, with an eye to the future.  But when I revert to insomnia‒after an all-too-brief respite caused by a rather severe illness, the remnants of which are not even gone‒it’s just terribly discouraging.  It’s a special kind of teasing furlough, like getting a weekend off from being in prison, but having to go right back up the road after the weekend, for a sentence the length of which you don’t even know.  And there’s only one reliable way to escape.

It makes it hard to think about any future whatsoever.

Ah, well, it probably really doesn’t matter.  What do I want with a future, anyway?  I don’t have “a life” at all in any appreciable sense.  I can’t even read fiction‒including even comic books and manga for the most part‒anymore, and that’s long been one of the highlights of my life.

I’ve occasionally been able to watch some shows, most recently Wednesday, and I’ve even gotten through five episodes of The Rings of Power, the latter while I was sick.  And, of course, I’ve watched all of the episodes of the modern Doctor Who, most of them more than once, but these are the sorts of things that in the past I had always done with other people, with whom I could share the enjoyment, and even talk about the shows and so on.  It’s just not as much fun to do by myself, even when I watch some of the “reaction” videos of other people watching the shows for the first time, which is almost like watching with a friend, but not quite.

Even the prospects of getting healthier, sleeping better, trying to conquer dysthymia and to integrate into my self-understanding a probable diagnosis of Asperger’s all seem pretty unmotivating.  What’s the point, for instance, of seeking out an official, confirmatory diagnosis of the Syndrome Formerly Known As Asperger’s, at significant personal time and expense?  What, ultimately, would this even do for me?

What’s the point of trying to find a therapist with whom I can work, and that I can work into my schedule‒perhaps through BetterHelp or similar‒to try to mitigate my dysthymia/depression?  It feels better, so to speak, just to feel horrible constantly rather than to have brief respites of feeling a bit better, a bit more “normal”, only to have that feeling slip away again.

It’s even hard to pursue further learning in mathematics and physics, both of which I find deeply interesting.  I have tried to use Brilliant to work on my skills, but though their interactive, stepwise, animated approach is interesting, and I can see why it would appeal to many people, I find it boring after a very short time after I start to use it.  I think I just do better with textbooks, and with problem sets.  I even bought a copy of one of my old college calculus textbooks, the Thomas and Finney one, and started working through it to re-hone and improve my mathematics skills, with an eye toward moving to higher level mathematics after that.  But I haven’t gotten very far.

I also got a copy of Sean Carroll’s Spacetime and Geometry, and the huge tome Gravitation, by Misner, Thorne, Wheeler, et al, which not only is the bible of General Relativity, but is also an excellent demonstration of its own subject.  This is all in an attempt to improve my formal understanding, at the mathematical level, of General Relativity.  Special Relativity is pretty easy, and the mathematics to deal with it formally is/are rather straightforward.  But I don’t have a deep handle on tensors and matrices and higher dimensional geometries‒not at the mathematical level, anyway‒which I’d like to have to be able to approach the subject at a real, quasi-professional level.

I’d also like to be able to do the same thing for quantum mechanics, which is at some levels more straightforward than GR.  I got Susskind’s Theoretical Minimum book on that, but haven’t been able to sustain my attention for it.  That’s my fault, not the writers’.  Anyway, I really want more than the “minimum”; I want to get deeper into the subject, mathematically, because the concepts are all reasonably clear‒although often explained in rather wooly terms by many popularizers‒and I would like to be more formally and mathematically adept at the subject.

And I deeply regret not having done more in pursuit of furthering my pretty good initial exposure to computer science, both at the software and hardware levels.  Related to that, I would like to have done more in circuit theory and more general electrical engineering.

Of course, I did have a lot of my time and energy taken up by biology, chemistry, organic chemistry and the other subjects related to becoming a doctor.  And, of course, “helping” my now-ex-wife study (to the extent she needed help, which was, let’s face it, not very much) when she was in law school was quite fun.  But the time and effort put into both medicine and my marriage have turned out now to be moot and pointless, though they were worth the cost due to the fact that my children are here in the world now.

That fact would be worth almost anything.

Anyway, I don’t have any point** here with all this, and I’ve gone on long enough today.  I’m just tired, and if I can’t find a way to stop being so tired all the time, I really don’t see any good reason to try to keep slogging forward.  All the way up until my next birthday, my age and the two digit number for this year are both prime, and it’s sometimes better to leave while still in one’s prime than afterward, as I mentioned in a previous post.  Meanwhile, though, I’ll see if I can find any other answers.

Oh, P.S.:  Does anyone know off the top of your head how one checks the results (so far) of a poll one has arranged on WordPress?  I’m sure the answer is somewhere in the WordPress “help” functions, but it’s not amenable to a superficial and obvious search, and I’d rather not have to “chat” with one of their “happiness engineers”.  It doesn’t matter much, but if you know,  would you please leave a comment below?  Thanks.

*That’s one of those amazing terms that was a brand new thing based on an entirely new and revolutionary technology, but now that technology itself is already obsolete, but the term lives on.  I think the closest similar thing that readily comes to mind right now is the expression “running out of steam”, which I would guess arose from the era of steam engines, which are quite obsolete, but the expression remains common.

**Now there’s a pithy summary of a life 

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And “prime” rib doesn’t come from the 13th rib, even though cows have that many*****

Well, it’s Tuesday, the 27th of December (in 2022 AD or CE) and I’m writing this on my phone because I didn’t feel like carrying my laptop yesterday.  I have to say, now that I’m not writing fiction anymore, I find the portable laptop more and more just useless and even irritating.  It was handy on Friday night, when I was at the hotel‒“free” Wifi that comes with the room and all that‒but that sort of thing is unlikely to happen very often.  In any case, I brought it with me on Friday specifically with that thought in mind.  But for other purposes, it’s just mostly an unnecessary and often unpleasant burden, rather like its owner (me).

I think it’s interesting that, come 2023, I will be (indeed, I already am) 53, a prime number, in a year for which the last 2 digits (23) are a prime.  2023 is not a prime, though it looks like it might be at first glance.  But it has prime factors 7 and 17 apparently; a nice pair, but the number they produce (by multiplying 7 x 17 x 17) is by definition not prime.  Still, that’s not many prime factors, and again, they’re particularly pleasing primes, though 7 and 13 would have been more fun.  But 7 x 13 x 13 would be 1183, I think…yes, that’s right.  I just went and checked my mental arithmetic and it was correct.  Phew, that would have been embarrassing to make that sort of mistake in front of all my readers.

So, anyway, 1183 is nice, but it’s 840 years ago next year.  So I’m a little late for that one, I’m afraid.  It’s 839 years ago this year, and 839 is a prime number, but neither 2022 nor 22 are prime, so what’s the point in that?  I wouldn’t even have looked at the number if not for my previous digression.

All that stuff is beside the point I intended to make.  The point is, my age is a prime, and the last 2 digits of the year will be prime, so if I die before my next birthday (but on or after New Year’s Day, of course), I will, in a sense, die “in my prime”.  It’s slightly forced, but as Michael Palin said in the role of a pet shop owner, “It’s as near as dammit”.  He was trying to pass off a terrier as a cat for the customer, who said it wasn’t a “proper cat”.

Anyway, that’s all slightly encouraging about next year’s prospects for me.  It’s about all I have to look forward to (or, rather, “all I have to which to look forward”), so I have to take what I can get, even if it involves squeezing a bit of the potential prime number relationships.

When you think about it, the numbers for the years are more or less entirely arbitrary, and even Darth Ratzinger* has admitted that the historical Jesus (assuming he actually lived) was born in about 6 BC, according to our current date system.  Which is kind of funny, when you think about it‒Jesus was born six years before Christ.  But then, we know he wasn’t born on Christmas, either, as I’ve mentioned before.  Hey, it was 2000 or so years ago, how accurate do you want people to have been**?

The next subsequent chance I would possibly have to die “in my prime” would not be until 2029, when I’m 59!  Although, 2029 is actually a prime number, and so is 29.  So that’s a bit tempting.  But I don’t even really want to imagine waiting six more years!!  And what if I died by accident some year in between?  What a waste that would be.

All of this is silliness, of course.  I like the idea because it’s playing with prime numbers and playing with words at the same time, and they are both things that I like to do.  But I’m not in any way committed to any numerological notions in any magical thinking sense.  If I were, then the 2029, 59 thing would be much more convincing, particularly since 2029 is the year the asteroid Apophis‒named for an ancient Egyptian god of chaos and destruction‒will come within 19,000 kilometers of Earth on April 13th.   That will be a Friday the 13th, by the way!  And if the asteroid passes through a very tiny gravitational “keyhole” (extremely unlikely) it will have its orbit altered such that seven years later it will hit the Earth***.  If I were dogmatic, committed to some quasi-mystical notion of prime numbers and the magical powers of some words, that would all be quite convincing.

But I don’t believe in any mystical or magical things, and I don’t think I’m wrong not to want to believe in them.  I’m well acquainted with metaphorical notions of magic (and fictional ones, of course) and am well acquainted with awe and with the numinous and with the state of being moved profoundly by wondrous things, from the contemplation of the scope of space and time on up to the births of my children.  But these don’t require belief, in the sense of conviction without justifiable evidence and reason.  Faith of that kind is a bug, not a feature, of the minds in which it resides.

So, no, I’m not convinced by the prime number/prime of one’s life coincidence.  I’m just very tired, and have nothing of real, deep value in my life, nor am I myself of any real, deep value.  But I enjoy prime numbers and word games, so it would at least be mildly amusing and satisfying‒or so I imagine‒to die in a year in which my age is prime and so are the last 2 digits of the year.  There’s nothing deeper to it than that.

There probably is nothing deeper than that, come to think of it.

*That’s the Sith name of Pope Emeritus Benedict.  Is he even still alive?  Also, why does “Sith” get the red squiggly underline of an unrecognized word, but “Jedi” doesn’t?  It’s blatant bigotry and hypocrisy by the Jedi, as should come as no surprise to anyone.  Well, I’ve added Sith to my local dictionary, at least.

**Of course, presumably God could have ensured precision and accuracy, but probably an omniscient, omnipotent, infinite being would not think our arbitrary dating systems‒or indeed, we ourselves‒were important in any way whatsoever.

***Of course, there’s plenty of time before then for someone who has, for instance, a private space program to send up a rocket that will gently nudge the asteroid, just a little bit, so that it hits the Earth in 2029…or in 2036, if that’s easier to pull off.  It wouldn’t need to be anything as dramatic as NASA’s recent asteroid deflection test thing, but it would require careful simulation and then application of force on a local scale.  Are you listening, Elon?  It wouldn’t be a mass extinction event, nor even a civilization-ending event, but it would be a global catastrophe such as hasn’t been seen since civilization began.  It might shake humans out of their idiotic Woke vs. MAGA type tribal bickering and make them take seriously the fact that they need to spread out off this planet, to colonize the moon and Mars and so on.  Or…was that actually the purpose of the rocket you sent toward Mars with a Tesla in it?  Is that camouflage for a mission to nudge Apophis to make it hit the Earth?  That’s it, isn’t it?  Oh, I knew you were an evil genius after my own heart!****

****Speaking of evil geniuses, I’ve seen recent videos that show, for instance, what the Death Star’s weapon would look like if it were accurate to real lasers, or showing how impractical it would be to use such a powerful laser, and regarding the apparent rebound energy if one fired a laser powerful enough to destroy a planet.  But the Death Star weapon is no more a laser than are blasters or lightsabers (though lasers may be involved in the workings of the devices).  Blasters and lightsabers are packeted plasma weapons of some kind, with the plasma perhaps constrained in highly shaped electromagnetic fields.  And the Death Star weapon is similar but of a different fundamental type.  I suspect it to be a highly energetic and dense plasma, but composed of anti-matter, and when the plasma strikes the planet at relativistic speeds, the matter/antimatter annihilation is what provides the incredible destructive force.  Or perhaps, alternatively, it is some form of plasma of W and Z particles, which cause massive, rapid nuclear decay in the atoms of the planets they strike, causing hitherto unprecedented fission events on a planetary scale.  It might even be a quark-gluon plasma, but generating that on such a scale seems boggling even to my jaded science fantasy mind.  Anyway, that’s neither here nor there, it’s just a pet peeve.

*****It can come from the 7th rib, though, and I guess you could request that specially.

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Never seem to find the time…

It’s Tuesday now, and I’m writing this post on my smartphone, because I couldn’t be arsed to bring my laptop back from work with me last night.  Perhaps this entry will therefore be more concise than usual, but I wouldn’t lay heavy money on it.  It’s more likely than winning the $1.9 billion Powerball Con Game, but that’s not saying much.  Getting struck by lightning during a shark attack is probably more likely than that.

There’s a full lunar eclipse in progress as I write this, and the umbra has about halfway covered the moon.  I took a snap with my smartphone as I left the house and then more when I got here to the train platform.  I’ll share some of them below.  They are not of very good quality‒and the first one is just streaks of light, because apparently I was too excited to keep my phone still while taking the picture‒but then again, in the days before smartphones, I wouldn’t have been able to take such a picture at all.

The last time I recall watching a lunar eclipse with any degree of attention was back when I was in either junior high or high school, and I had a very cheap telescope on our back deck (This was quite a bit later than the reminiscence I described yesterday).  I have to say, the one happening now is quite a bit more impressive than the one I remember.  The shadowed portion of the moon is almost completely black, and the encroaching edge of the Earth’s shadow is quite, quite different than the usual arc of the moon’s own phases.  It’s fascinating.

I forgot again to work on editing my audio recording of thoughts about time yesterday.  I feel like I want to make some excuse, and there are surely reasons, or at least causes, but it doesn’t really matter what they are.  So, now I’m going to try to rehash those verbal thoughts to give you all either a preview or‒more likely‒a replacement for the posting of those spoken words.

I was triggered to talk about time when watching a science video in which someone pointed out, as people often do, that we are able to travel rather freely in any of the three dimensions of space, but that our direction in time seems entirely one dimensional, and we don’t seem able to choose our direction or speed through it.  But this is a slightly misleading characterization of the situation, I thought, and that thought is not entirely original nor unique to me, but this is my way of thinking about it.

It’s true that, if we were in deep space, especially in one of the gargantuan intergalactic voids (where light from all the surrounding galaxies would be too faint to be visible), there would literally be nothing to differentiate up from down, left from right, forward from backward, or indeed, any of these axes of motion from the others.  But that’s not the situation in which we find ourselves.  We are on the surface of a planet, in the presence of a rather strong gravity “well”, and that changes very much the way we experience the three dimensions of space.

Ignoring the facts of terrain, and thinking back to before we had modern technology, it’s clear that, while we are basically free to move forward and back and left and right‒and indeed, we can swap those axes out arbitrarily‒we are not free to move up and down at will.

Even birds and insects and bats cannot freely move through the up-down dimension, not in the way they can move along the curved plane of the surface of the Earth.  It requires great effort for them to change their height, and they are limited by that effort and by the density of the air through which they swim.  Because we are near a source of strong gravity, there is a clear directionality to one of the dimensions of space, and the only reason we don’t keep falling down is that there’s a planet in the way, but if it weren’t there would be nothing pulling us in one direction.

In a somewhat analogous sense, the only reason there seems to be a directionality to time is that we are near (in time) the presence of a region of very low entropy:  The Big Bang.  Since that time, about 13.8 billion years ago, entropy has been steadily increasing, as is its tendency, for fairly simple, mathematical reasons that make the 2nd law of thermodynamics among the most unassailable of all principles of physics.

All the processes that cause us to experience a directionality to time are driven by the tendency for entropy to increase, and that includes the clumping of matter under gravity, the growth of biological organisms, the accumulation of memory, and the development of technology.  Increasing entropy‒on the largest scales‒is all that allows temporary decreases of entropy locally.  Put poetically, it is only the inevitability of death that allows life to exist at all.

But of course, in the future, as entropy increases, life and local order will be no more possible than they would be in intergalactic space.  Once entropy increases enough‒and the vast majority of the existence of our universe will be in such a state, just as most of space is not near the surface of a planet‒there will be no way even to know which direction of time would have corresponded to what we now think of as past and future, because the laws of physics are locally time-reversible.  Time in that epoch would be no more uni-directional than space is in the vastness of an intergalactic void.

What’s more, it’s clear based on special and general relativity that time is not purely one dimensional.  Time and space bleed into each other depending on relative motion and local spacetime curvature.  That which can curve is not, strictly speaking, entirely one-dimensional in a Euclidean sense.

All this makes me wonder if, perhaps, the Big Bang era is not strictly a “plane” orthogonal to the time dimension, but might in fact be the surface of a sphere…or, well, some manner of hypersphere in space time, the surface of which is all at one “moment” just as the surface of a planet is all‒more or less‒the same distance from its center.

If so, then the Big Bang need not have happened merely in one direction in time.  Others have toyed with ideas like this*, with the thought that there might be a sort of mirror image universe to ours, extending the other direction in time from us, its future analogous to our past.  I’ve even occasionally wondered if the (very slight) relative abundance of matter over antimatter in our direction of time would be mirrored by a relative abundance of antimatter in that universe**.

But on further thought, I’m led to wonder if there need be merely two mirror universes, delineated by the Big Bang, heading in opposite directions.  Perhaps there is a continuum of such directions, just as there is a continuum of “up” directions from the surface of the Earth.  Perhaps our expanding universe has more in common with the expanding size of a sphere around the Earth’s center, which gets larger and larger as one moves away from it, and the Big Bang is not so much a beginning of time or the universe as it is a local area of low entropy in time, allowing the existence of phenomena‒including life‒near its surface that experience a difference locally between past and future only because they exist in an entropy gradient.

Perhaps, far out in the “future” of the universe, there might exist other local entropy minima, in any direction in time from us‒directly ahead or even at right angles in time to us, or any combination thereof.  Of course, “reaching” them would be harder than traveling out into intergalactic space, given that they would probably exist across unguessable gulfs of timeless “time”***.

How would we even measure or pass through time in a region in which entropy was near-maximal and time was without any inherent direction?  Perhaps if it were possible to accelerate continuously to near enough the speed of light that one’s personal time slowed ever more and more, one could survive to arrive at a place where entropy would begin to decrease.  But what would that even be like?  Would one enter such a realm as if a traveler from its future, moving‒to any local residents‒backward through time?

I could go on and on about these ideas, and maybe I’ll explore them more in future (ha) posts, but for now, I’ve taken enough time (ha ha).  This was certainly not a concise blog post, but I hope it was at least intriguing.  I’d be interested to hear your own thoughts on such matters.

In closing, I’ll just ask the following thoroughly fanciful question that just popped into my head:  What would happen to a werewolf during a lunar eclipse?

*For instance, The Janus Point by Julian Barbour, deals with some similar concepts.  I haven’t finished reading the book, but I thought of the ideas I’m discussing before I’d encountered it, and my ideas are somewhat different, though far less expert than his.

**Though they would surely switch the terms, calling our antimatter their matter.

***And reaching the portion of our universe that heads in the opposite direction in time would seem to require exceeding the speed of light, which appears to be impossible‒though perhaps wormholes might lead to such places, if they in fact exist.

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Fear no more the heat o’ th’ sun Nor the furious winters’ blogs

Hello and good morning.  You should know that it’s Thursday if I use some variant of that greeting.  I got started in that habit early in the course of writing my (then only Thursdays) blog, and got myself locked into the pattern mentally.  Now it would make me very tense and stressed if I were to write a Thursday blog post without that opening.  Likewise with the title being a slightly altered quote from Shakespeare.

I’m writing this on my laptop for the first time this week, because I decided to bring it back from the office yesterday.  It was our first decent business day this week, but I still felt thoroughly rotten, in the sense of being tired and in pain.  I’d been lying awake in “bed” during the night, looking at the clock, deciding when just to give up and get up.  I had seen the time getting to about 3:50 and started thinking about the various three digit numbers coming up.

I knew none of the even numbers were prime, and I knew 351 wasn’t prime, since the sum of its digits is a multiple of three*.  But 353 looked like it might be prime, so I started checking it in my head.  Obviously it wasn’t divisible by any even number, nor by 3, nor by any multiple of 5, so I started trying from 7, then 11, then 13, then 17, then 19, then 23, then 29…by that time I was getting suspicious.  The next prime was 31, and I tried that in my head, but it wasn’t divisible, because after you divide the first two digits by 31, you’re left with 43 remainder, which is clearly not going to be evenly divisible, so I stopped there with that.  And the next prime number was bigger than 35 (it’s 37), which started making it look like 353 might be prime.

I cheated then, turned to my computer and checked with Google if 353 was prime**, and it said it was.  That was good enough for me.  I decided to get up at 3:53, which by that point was about a minute and a half away.

Thus, I got on the first train, and luckily, there were no “trespasser strikes” or any other kind of delays, and my train arrived and left at the scheduled time.  I definitely am not going to kill myself by jumping in front of a commuter train (or probably any other train).  I don’t like hypocrisy, and to be worn out by delays only to cause them oneself would be petty and spiteful in a way that I would prefer not to be in my swansong.  I need to do something less intrusive.

That’s all unless, of course, I give up on trying to be polite and just act on some impulse that comes at the right time in the right place, and fuck all the humans if it causes them problems.

I’m sitting in a different seat on the train than I usually use, because I didn’t feel up to climbing to the top level.  I worry that I’m sitting in someone else’s usual seat, but it’s very non-crowded on the midway level of this train car, so I don’t think I’m causing anyone inconvenience.

It’s probably bothering me more than it would bother anyone else that I’m not in my usual seat, but I just didn’t feel like taking 8 more stairs up.  If it had been a prime number of steps, maybe I would have done it.  Probably not.  I only just now counted the stairs to see, but I hadn’t counted them before deciding I didn’t want to climb them.

It was eighty degrees out and quite muggy when I left the house this morning before five o’clock.  Don’t envy it.  It’s not as though people are going to the beaches or sitting out in the sun and sipping cocktails, or enjoying any other aspects of warm weather.  Everyone is scratching out their livings, going through their daily routines in a grimy, overcrowded urban environment.  One of the only visible effects of the warmth is that you’ll see people wearing things like basketball shorts to work—grownups who are not professional athletes wearing baggy, gaudily colored shorts in places of business.  How is one to take any of them seriously?

At least the people who run the Tri-rail trains all wear uniforms of one kind or another.  They are quite professional and serious—and pleasant and friendly to passengers***—and they do their jobs well and with enthusiasm.  There’s even a conductor who sometimes works in the evening on the train I catch leaving work who, as we approach my station (which is Hollywood) makes the announcement, “Now approaching Hollywood…Hollywood, California, now approaching Hollywood.”

I like this because it’s similar to my own usual thoughts when we approach the station, which is to recite the words of the man on the street in the beginning of the movie Pretty Woman, who calls out to no one in particular, “Welcome to Hollywood!  What’s your dream?” and so on.  That’s a moment or two before we see a young Hank Azaria in a bit part as a detective, investigating the murder of a prostitute, astonished that tourists are taking pictures of the crime scene.  It’s an unusually dark beginning to a classic romantic comedy.

Real romance rarely begins so darkly, though it often ends unpleasantly.  It does always end, eventually, even for those who stay together for the rest of their lives, because life is no more than 120 years (at the extreme maximum) for humans, and usually quite a bit less than that.

Sorry.  That’s dreary, even for me.  I’ll try to turn it around by taking a line from the…I think fifth series of modern Doctor Who, in which the Doctor describes a species of mayfly on some planet I can’t remember, saying that they live only twenty minutes, and they don’t even mate for life!

Time is relative in many senses.  I’ve had more than one day this week that seemed to last far longer than twenty-four hours.  The faster you think, the slower time will seem to pass for you, so it may be worth practicing that, if that appeals to you.  Users of psychedelics sometimes report their trips seeming to last for eons, and meditation and similar states can sometimes produce similar experiences.  We all know that dreams can give that impression.

So, as Tyrell says to Roy, “Revel in your time,” even if all those moments will be eventually be lost like tears in the rain.

TTFN

Hollywood_Amtrak_Tri-Rail smaller

*It’s actually also a multiple of 9, since its digits add to 9, but it’s 9 times 39 (9×40=360, take away a nine and you get 351), and 39 is 3 x 13, so we know that 351 is also 27×13.  The prime factors of 351 are 3x3x3x13.

**I do this sort of thing often enough that when I start typing, by the time I get to “Is 353…”, Google pops up the option (and the answer) for the question “Is 353 a prime number?”

***This is lost on me, I’m afraid, though I admire it.  When the driver waves out of his window toward passengers as he pulls in, I’ve never had the impression that he was waving at me until this morning when, for the first time, I thought it seemed like he might have turned a final wave in my direction after more obvious ones to other regulars—I always stand at the far end of the platform.  I just felt a bit frozen and stressed, like someone who’d been called on in class but hadn’t been paying attention to the lesson.  I tried not to look toward the window, but just kept kind of looking down-ish and toward my entrance to the train, and I felt like a fool.

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The borogroves sure are mimsy today, aren’t they?

It’s Friday again, and another weekend approaches.

Yippee.  Huzzah.  O frabjous day.

I think I don’t work tomorrow—at least, I’m not supposed to—so there probably won’t be any blog post then (which will be Saturday, unless some hitherto unimagined catastrophe literally throws the days of the week out of order).

I may be posting a new video on my YouTube channel this weekend, though.  I haven’t made one yet, so there’s no guarantee that something won’t stop me from doing so.  I’m unlikely to be lucky enough to be involved in an asteroid impact between now and tomorrow, but there’s a functionally limitless number of things that could, in principle, stop me from recording a video.

Nevertheless, it is my intention to make a video, so I probably will.  This is a different type of thing than fasting; no physiological processes and neurological feedback loops are likely to interfere with my commitment to making a video.  Evolution is, so far, utterly blind even to the existence of videos…though that could change.

I’m still not sure what topic I want to address in the video, unlike last time.  I may literally just start my timer, start my video, start to talk, and see what happens.  If that sounds like an inauspicious way to start a video, well, you’re reading the written equivalent of it right now.  If you enjoy this, you’re proof that it can work.  If you don’t enjoy it, that’s not proof that it cannot work, since your lack of enjoyment doesn’t preclude anyone else from enjoying it.

People do seem to have trouble understanding that others can like things that they themselves find disgusting.  I can sympathize with that, and fall prey to the failing myself, but that doesn’t make it reasonable.

It’s true that all mammals, let alone all humans, have more in common than they have differences, but nevertheless, the potential differences just within a given species, given sexual recombination of genes and the sheer number of genes each individual has, is well worthy of the adjective “astronomical”, so we shouldn’t be surprised that others like things we find repugnant.  In fact, given that the number of possible combinations of gene pairs in human DNA alone is vastly larger than the number of (for instance) light years the visible universe is across*, maybe we should switch our use of the terms “biological” and “astronomical” to describe very large numbers.  Unfortunately, I think most people wouldn’t catch onto the nuance of saying that something was “biologically large”.

Oh, well.  It was a brief dream, swiftly shattered by the one who dreamed it.  Typical.

Anyway, so, I’m back on food again, more’s the pity.  I’m tired of having all these biological urges and needs and drives.  They’re very irritating.

Also, I’m tired of how stressed and angry I get about things people do at work.  Don’t get me wrong—the specific things I’m thinking about are worthy of anger.  But the problem is that I get so stressed, and so angry, and it just makes me hate myself more and more all the time, without any evident upper bound to the process.

I wish it were true to say, “I can’t stand it anymore”, but unfortunately, I’m able in principle to continue standing things for who knows how long.  I wish I would just collapse into a heap, and literally, physically, not be able to go on.  It would take so much out of my hands and would be such a relief.  Unfortunately, there’s no clear sign of that happening, though I try to sabotage my own health as much as feasible without being Baker Acted.

And here is another maddening thing that just happened:  the trains this morning, it turns out, were all shifted to one side of the track, as was the case last week once.  But this wasn’t announced early, unlike last time, so I went to my usual spot to start writing this while waiting.  Then, when the “announcement” was made, it was just posted on the overhead light board; there was no verbal announcement, though they give recorded verbal reminders about such things usually—they’ve been informing us, ever since Labor Day, that the system will be running on a Sunday schedule on Thanksgiving, which is in November, for those of you who don’t know.  Labor Day was in the beginning of September.

I only failed to miss my train because I always start getting ready to board five minutes early, and I looked up from my writing to notice that there was no one on my side of the tracks.  Only then did I see the notice that trains were all boarding on the other side.  I was able to take the elevator up to the bridge, but I had to rush down the stairs on the other side because my train was approaching, and my knees and hips and ankle were miffed about that.

It would have been nice for one of the people who always gets on the same train I get on to have said something to me, rather than just letting me sit there typing on one side of the track by myself.  I’d like to think I would have said something to them, were the situation reversed.  Maybe I wouldn’t.  Maybe it’s an instance of the bystander effect.  Maybe it’s one of those rare circumstances in which my reticence to interact with strangers is obvious to everyone, and I seem so unpleasant that no one wants to interact with me even enough to say, “Hey, all the trains are boarding on the other side for some reason…better cross over.”

Better cross over.  That’s the best idea I’ve heard today, that’s for sure.

Okay, well, that’s it for today’s disjointed meandering.  I hope you’ve found some modicum of joy in it.  It would be nice to be able to do at least something positive for the world, even if it’s small.  It would be far better than what I usually do.

*Using the particle horizon as the measured “distance across”. **

**Actually, since there are four bases in human DNA (guanine, cytosine, adenine, and thymine), if they were assigned randomly, then even a string of 1000 base pairs has 1.15 x 10602 possible combinations.  If memory serves, this is larger than the String Theory landscape, which number is already so vast as to lead many physicists to say it can predict anything and therefore it can predict nothing.  And human DNA is on the order of a billion nucleotides long.  My computer calculator can’t deal with billionth powers of four, but a billion is a thousand times a thousand times a thousand, so 41000 cubed should be about 101806 unless I’m missing something.  The diameter of the visible universe in Planck lengths is only 5 x 1061, which is not even close to the same order of magnitude.  Of course, the maximal information within a horizon the size of the visible universe is larger still, but then again, that’s a measure of the maximum entropy possible within that region, so that’s almost a given.  I think it’s 210^123 or something along those lines.  I may be getting at least some of this wrong.

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Welcome to the October Country

Well, it’s October 1st, the beginning of a new month in 2022, a month initially meant to be the eighth month, based on its name.

I’m at the train station and, it being Saturday, the schedule is different than during the week.  There’s also some question of whether the trains are boarding on the usual side or not.  There’s a displayed “announcement” on the light boards that all trains are boarding on one side at this station until further notice, but it could be something left over from yesterday.  Also, the guard is not aware of anything regarding the change in sides.

Nevertheless, today was a day for ordering the monthly pass on the machines, and the ones on my usual side weren’t even working, so I’m on the other side for the moment, anyway.  I’m going to have to try to be vigilant as the time for my train approaches*.  If I miss one train, the next won’t come for another hour.

It’s hard to be vigilant, though.  I feel absolutely exhausted.  My brain feels like it’s barely running on one cylinder, metaphorically speaking**.  I’m just so very tired.

Thankfully, I can embed below my video, which I did end up posting on my YouTube channel yesterday afternoon, so that can provide some of the content and spare me a little writing today.  I might as well, since what I’ve written so far is about some of the most banal things imaginable.

Just a bit of clarification about the video, in case any is necessary:  Obviously I don’t mean to say there is literally no life in the universe, since that would be a contradiction (If there were literally no life, then I could not be speaking about the fact).

I just have always been irked by people who make the wide-eyed claims that it’s so amazing and quasi-mystical that the constants of nature are so perfectly designed to make life, and that must imply some sacred meaning or purpose to it.  That’s about as idiotic as looking at the location of a speck of dust in the corner of a school gym and saying how amazing it is that all the facts of nature conspired to bring that speck of dust right there at that point…it had to have been part of some greater purpose!  It’s drivel.  Only the case with life is even more unimpressive.

My biggest issue with this is that it leads to a kind of quiescence, an assumption that, if the universe was “designed” just so that life can exist, then life, and particularly intelligent life, must be important, and the universe will somehow arrange things to nurture us and protect us from extinction.  If you think that’s the case, then ask the dinosaurs, or better yet, any of the far greater numbers of life forms that went extinct in the Permian-Triassic “Great Dying”.

Oh, wait, you can’t.  They’re all extinct.

No, the universe is almost completely hostile to life, both in terms of its space and in terms of its time.  We are lucky beyond ordinary imagining, though I tried in the description of the video to give some notion of just how lucky in spatial terms, at least, by noting that life exists in roughly only 1.5 x 10-64 of the universe’s volume.

As far as time goes, well if you’re thinking of humanity alone, based on the time that has elapsed since the “Big Bang”, which may or may not be the literal beginning of our universe, the percentage is tiny enough, and others have demonstrated this handily, as in the “cosmic calendar” that Carl Sagan made famous in Cosmos.  But if you want to count all expected possible future time, well then our existence is some fraction of what could be infinity, which is pretty undefined, but might as well be called zero.  The limit certainly approaches zero as we extend the future further and further.

This is not necessarily a call for people just to give up and say “what the hell”, though you have that option, of course, and it is tempting.  I wanted to note that, if you would like for life to continue, and even to have some lasting, cosmic-scale impact, then you can’t take it for granted.  You need to work at it, and work hard, and work long.  The universe is not trying to kill us (contrary to Neil DeGrasse Tyson’s habitual way of putting it); if it were, we would be dead already.  But the universe is huge, and it does not even have the capacity to care what happens to life, except in the minds of that life itself.

All life is in the situation of a castaway on a desert island—there’s no preexisting infrastructure, there’s no one out there looking out for you or protecting you, or providing your light, your heat, your air-conditioning, your food, your clothes, your shelter, what have you.  If you want any of those things, you’re going to have to make and/or find them for yourself, and you’re going to have to keep doing it, for as long as you actually want them and want to survive.

Without much more ado, here’s the video***.  I forgot to ask when I made the video, but please give a “thumbs up” and subscribe and share if you are at all inclined to do so, for any colorable reason.  And feel free to check out the other stuff on my YouTube channel if it looks interesting to you.  If anyone finds this interesting at all, I’m hoping to make more such videos about topics that interest me, assuming the universe doesn’t eliminate me in the meantime (though it seems likely to do so).  Oh, and please let me know what you think, either in the comments below the video or here.

Thanks.  Here it is:

*Just a slightly later addendum:  They have announced overhead that my train is approaching in 10 minutes, and have confirmed that it is not on its usual side.  So I was right to be proactive.

**Of course, it’s a metaphor.  I don’t honestly think that any of you really believe that my brain is an internal combustion engine of some kind, except in the loosest of possible senses.  Apologies.

***I wore a mask and dark glasses in the video mainly because I don’t like how my face looks—it bears evidence of the many things that have happened to me in the last decade or so.  Maybe no one else can see it but me, but it is what it is.  Anyway, the glasses are awesome, I really like them, and the mask combined with them makes for a good look, I think.  Certainly better than my underlying face, anyway.

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Tangents of tangents of tangents, oh my!

It’s Wednesday, the middle of the week based on our usual reckoning of things.  Welcome.

Of course, the universe at large doesn’t give any preference to days of the week, or months, or whatever.  Days, per se, are more or less natural units of time, as are years.  Both are related to regular, physical phenomena in the solar system*.  Now, one could argue that since the moon’s orbit around the Earth is roughly twenty-eight days, that seven days in a week is a sort of natural division, since 28 divided by 4 is seven.  That’s not an unreasonable thought, but it is derivative, unlike the measure of a year or a day.

Of course, rather irritatingly, the days don’t evenly divide into the years, nor do the months (orbits of the moon, which itself isn’t quite an even number of days), which means we have to do all sorts of mucking about with the number of days in months to get a reasonable number of them per year, and only one of them has 28 days, but even that changes every 4 years, except every hundred years when it’s 28 again, except every thousand years when it’s 29 again, and so on.  And then, of course, we have to add and subtract “leap seconds” on an irregular basis to adjust things to keep them consistent, lest the seasons creep steadily in one direction or the other relative to the calendar as the years pass, even as the times of day and night also shift.

If the period of the moon’s orbit around the Earth divided evenly into the orbit of the Earth around the sun; and the length of days on Earth** also evenly divided into the orbit of the Earth around the sun; and if those divided evenly, say, into the orbits of the sun around the center of the Milky Way; and then if the second, as we decided it, turned out to be some round number of oscillations of a cesium atom being pumped by a particular wavelength of light—say 9 billion exactly, when measuring a previously decided interval of one sixtieth of one sixtieth of one twenty-fourth of a day…that would all be quite a collection of coincidences!  That would make me start wondering if the whole thing was designed by someone.  As it is, though, it looks very much like it just all kind of happened, with no inherent direction or purpose or goal.  Which makes more sense of most of human history and the natural world than the alternative does.

It would also be quite a coincidence if, for instance, pi turned out to be 3.141618110112114…or some other regular pattern alone those lines.  Especially if some similar pattern of interest showed up when it was measured using other number bases, like base 2, base 16, whatever.  That would be something.  Or imagine if pi were an exact integer.  Of course it’s hard even to imagine what it could possibly be that could make the ratio of a circle’s circumference to its diameter into an integer, how that could actually be achieved, since the number pi is something born of what appears to be fundamental geometry, constrained by internal logical and physical consistency.

Anyway, the universe looks very much like, as I said yesterday, a spontaneously self-assembled system.  For all we know, it’s just a collection of quantum building blocks of some kind that fall together in a bunch of spin-networks, if that was the right term, to form spacetime that acts like General Relativity when there are enough of them***.

And, maybe the other quantum fields are just emergent phenomena that develop as part of the properties of these conglomerated spin-networks, and the net result of their gross uniformity leads them to mutual repulsion, and then—rather like quarks being forcefully separated leading to formation of new quarks if you could do it, which you can’t—when spin-networks are stretched apart, they simply generate new, connecting networks in between, out of the energy from the tension of their repulsion.  Thus, spacetime can expand forever, generating new space-time as it does, and perhaps the other quantum fields, again, are mere epiphenomena that arise when enough spacetime exists.  And everything else, as we can already tell, is a bunch of epiphenomena overlying, or produced by, that.

Here’s a question that just occurred to me:  If spacetime can be continuously created by stretching of the preexisting network, in response to “dark energy” or “inflaton field” or whatever one might call it, popping little new nuggets of spin networks or whatever spacetime is made of into existence, can it, on the other end of things, be made to disappear?  Can quantum spacetime be unmade as readily as it is made?  I don’t think it would have to happen, say, in the “singularity” at the center of a black hole.  I can see that as potentially being a thin and narrow “tube” of spacetime stretching off and continuing to grow but only in one direction, like the function 1/|x| as it approaches zero, with a finite “volume” perhaps, but an infinite “surface area” that can keep growing indefinitely if spacetime really can just keep reforming itself.  Though maybe, if the chunks are of finite size, the tube can never narrow past some certain minimal “circumference”.  I wonder what the implications of that could be.

But can spacetime ever un-form?  Quarks that could be formed from, for instance, stretching the gluon field between two of them could, in principle, “un-form” if they encountered an anti-quark of the proper character.  They can even decay, I think.  But they wouldn’t simply disappear, they would convert into, presumably, some pair of high-energy photons, and maybe something else, too.  But spacetime itself doesn’t always obey the straightforward law of conservation of energy/mass, as GR has already shown.  Conservation of energy is a property of things within spacetime, and is born of the mathematical symmetry of time translation, as per Emmy Noether’s**** Theorem.  It doesn’t necessarily apply to spacetime itself.  So under what circumstances, if any, could it simply spontaneously disappear, and what affects would that have?

Well, that’s something I’m not going to figure out right here right now, I’m afraid.  But, boy, have I gone off on some tangents!  It’s rather like a moon or a planet suddenly released from the gravitational embrace of that which it orbits, to go off into eternity like a rock from a King David-style sling.  Or like the derivative of any continuous function, or the derivatives of derivative of derivatives, “most” of which end up settling out at some constant, if memory serves (but not the exponential function, ex!).

All this is, apparently, just what happens when one cannot stay asleep after three in the morning and so gets up very early and waits for the first train on Wednesday morning.  One thing leads to another, but with no inherent direction or purpose or goal.  Things just happen.

That sounds familiar.

*The rotation of the Earth and its orbit around the sun, in case you didn’t already know.

**Of course, there are different ways to define a day.  There’s a solar day, which—if memory serves—describes the time it takes for the Earth to turn until the same longitude line (so to speak) is facing the sun, which, because of the motion of the Earth in its orbit, is going to be slightly longer than a sidereal day, which—again, if memory serves—describes when the same longitude line returns to its place relative to the distant, “fixed” stars.  Of course, the stars themselves are not truly fixed, but their angular location changes so slowly that that’s an adjustment that doesn’t have to be made often.  I think there are other day measures, but they aren’t popping into my head right now.

***I realize that this is very loosely a description of loop quantum gravity, and that one prediction of one form of that model predicts that light speed even through a vacuum varies ever so slightly by frequency—and that our best measurements of light from distant quasars and the like seem to disconfirm that prediction.  But I don’t think the jury is completely in on that question.  And maybe that specific form of LQG is not quite correct, or the difference is smaller than expected.  I don’t know the subject well enough to opine.

****Look her up.  Einstein called her a mathematical genius.  Hilbert invited her to teach in the University of Göttingen (fighting against the powers that be that didn’t want a woman professor).  She should be a household name.  Her face should be on currency.  She should be bigger than every TikTok “influencer” combined.  That she is not should bring every human shame.

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You pick the space and I’ll choose the time, and I’ll climb the hole in my own way*

It’s Tuesday now, the day that Professor Coyne, aka PCC(E), over at Why Evolution Is True calls “the cruelest day”.  I’m not sure the origin of that expression; as far as I can recall, his website is the first place I encountered it, but I like it.

It’s not the beginning of the week, which has a certain hectic energy at least, with everyone in a kind of recovery from their—hopefully restful—weekend.  It’s not “hump day”, which many people call Wednesday, when things are starting to coast toward the end.  And, of course, it’s not its counterpart:  Thursday, which is a day on which anticipation of the coming weekend can energize one for the day’s work.  And, quite obviously, it’s not Friday, when those who are on a 5-day-a-week schedule are effectively already beginning their weekend**.  Tuesday is the day with the least to make it stand out.  Which, of course, makes it stand out.

Also, as the Beatles pointed out, and as I often note, Tuesday afternoon is never-ending.  And, if time were to be truly continuous and infinitely divisible, then one could effectively make Tuesday afternoon never-ending in a Zeno’s Paradox sort of way, just by subdividing the time in between each moment as each moment passed.

Or, of course, one could fall through the event horizon of a black hole.  To distant observers, that fall would indeed seem to be never-ending (though before too long the image of the faller would redshift into invisibility).  And for the person falling, the end would come rather quickly.  Assuming that person survived the gravitational tides, according to General Relativity, time literally comes to an end in the singularity of a black hole.

Though I always picture the heart of a black hole a bit more like one of those “Gabriel’s Horn” shapes in mathematics, which has an infinite surface area but a finite volume.  Of course, I don’t have the skills and expertise to work the equations of GR, but it feels to me that, if spacetime is endlessly flexible****, then there need never be a true “end” to time; it could just stretch longer and thinner always, infinite in “surface” but finite in “volume”.

I know that’s all a bit esoteric, and I’m sure my understanding is incomplete.  If there are any theoretical physicists specializing in GR reading this who can help me think more clearly about black holes and singularities and why it would be necessary for time to completely end if spacetime were continuous rather than simply to stretch—making a mathematical singularity, but not literally an end—then please do let me now.

I realize that there may be concepts that can only be dealt with rigorously using the mathematics, but on the other hand, clearly the mathematics is translatable into “ordinary language” at some level, or no one would ever be able to teach it or learn it.  And I have at least a bit of mathematical background, though I haven’t formally studied how to do the matrices and whatnot involved in GR.  Still, Einstein himself didn’t know how to do it when he came up with the initial ideas, so he had to learn it and then work with it, but he had the ideas first.

I don’t have his brilliance, obviously—which is certainly not an insult—but if there’s a way to demonstrate why time literally ends at a singularity***** rather than simply stretching out into an endless tube, with shrinking cross-section (in higher-dimensions) but ever-expanding “area” (again, in higher dimensions), I’d like to know.  I mean, according to the whole Dark Energy paradigm, the expansion of spacetime is accelerating now and there’s no theoretical limit to how much it can expand, which seems to mean, at some level, that it has infinite stretchability.

Or perhaps it would be more accurate to say that spacetime can continue to be created between any two points that are stretching apart, somewhat—but not quite—analogous to the way in which if you try to separate two bound quarks, all you do is create two new partner quarks with the energy you’ve put in to try to stretch them so now you’ve got two pairs of inseparable quarks.  Neener neener neener.

Anyway, I know that Penrose and Hawking developed their singularity theorems for black holes and those are accepted by physicists and mathematicians throughout the world.  They are/were brilliant people, there’s no doubt about that.  But does the theorem mean that spacetime literally vanishes at some literally infinitely dense point in the middle of a black hole—which strikes me as implausible given the stretchy-stretchy nature of spacetime—or is it a singularity more in the pure mathematical sense like the function 1/x as x approaches zero?

Enquiring minds want to know.

Wow, that wasn’t at all where I thought I was going when I started this post today, but those random, drunken walks can, at times, at least lead past interesting scenery.  No one would be likely to argue that a black hole doesn’t necessarily belong in a wasteland; in a sense, it is the ultimate wasteland, at least this side of the heat death of the universe.  But it is interesting, topographically (and topologically, to a novice such as I), and though it would be nice to be able to enjoy such scenery with company who would appreciate it in a similar fashion to the way I do, well…one has no “right” to such a thing and no good reason to expect it.  It’s lonely, but at least the wasteland has places of beauty.

And if one gets tired of walking, and/or one is curious enough to see where it leads, one can always just jump into that black hole.

*This is a slightly altered line from the Pink Floyd song Fearless, off their excellent album Meddle.

**Some of us work every other Saturday, of course, and when you have no life, like I have no life, a weekend is not something to which to look forward, except for the chance to rest one’s back.  I don’t really do anything for fun, have no friends with whom I spend time, no places that I go for entertainment or for shopping or whatever.  All such things are too tainted by memories of loss, and anxiety, and the feeling of not belonging on this planet.  My life is more or less a wasteland.  But I can’t see any way out of it (other than the obvious), and I can’t even really tell if I’m just walking in circles within it.  I think I’m walking in random patterns, like a “drunkard’s walk” (though I rarely drink).  And, of course, in a random walk or drunkard’s walk, one will eventually get arbitrarily far away from one’s origin point (though the average location will be the origin, interestingly), but the distance between one and the origin increases—I think, if memory serves—only logarithmically.  And I suspect that the exit from the wasteland is very far away, if it exists at all (other than, as I say, the obvious).  Oh, well.  Life promises one thing and one thing only; anything else is just luck***.

***A footnote within a footnote, just to note the mildly amusing fact that, so far, my footnote is longer than the main text of this post.

****A big “if”, of course.  It doesn’t seem to jibe with quantum mechanics, apparently, but we have no convincing theory of quantum gravity to settle the issue.  I’m so frustrated.

*****Again, according to General Relativity—I know it’s thought not to be the correct picture in such extreme circumstances, because of the uncertainty principle, among other things.

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O heaven! that one might read the blog of fate, and see the revolution of the times.

Hello and good morning.  It’s Thursday again, and so it’s time for what is, “historically”, my weekly blog post, though in fact it’s merely another iteration of my now-nearly-daily blog post.

It’s getting harder at times to think of what to write about.  I’m more or less committed to doing this whole thing stream-of-consciousness style, since I’m hoping that—just maybe—it might act at least as a form of “talk therapy”, though there are fewer questions and less feedback than one receives from real, usual therapy sessions.  Still, maybe just expressing my thoughts in this fashion will help me to organize them in some way.  I’m certainly not writing fiction or playing music, so I don’t have anything to speak about with respect to those subjects now.

It’s the first Thursday in August 2022, now that I think about it.  That doesn’t seem particularly noteworthy; I can’t think of any major holidays in August, though I suppose I could be forgetting about something.  August is one of those comparatively dull months, though it is a month of “pure” summer, in the sense that, in the northern hemisphere, it’s all in summer, like July, not split up into two seasons like June and September.

It is a bit curious that we don’t start our years at the winter solstice.  People have known about the solstice, about it being the “shortest” day of the year, for who knows how many thousands of years, and many festivals worldwide have been associated with celebrating this renewal of the length of days, dominated in the west of the modern world by Christmas and then New Years.  I think it’s mildly weird that we don’t simply begin the next year on the solstice, or the day after it.  We do start it thereabouts, but why not right on that day?

Maybe the issue is that the solstice changes subtly over time, and occasionally happens closer to one day than another?  I don’t know quite enough about it to say for sure.  If anyone out there does know to what degree the solstices change, feel free to comment about it below—not on Facebook or Twitter, unless you don’t care about the comment being seen for a while, anyway.  I don’t interact much via Facebook anymore; it’s too stressful and depressing, though I miss knowing what many of the people I used to know are doing, seeing pictures of them and their families and whatnot.

Twitter is slightly less stressful, largely because I don’t feel personally involved in any of its stupider aspects and don’t tend to follow people who are.  Twitter, to me, is a good place for sharing links to articles and videos and for one-liners and “What’s your favorite of the ________ movies?” types of questions and answers.  Even with the “enhanced” 240 character limit, it’s simply not a venue for expressing or discussing any deep or complex thoughts.  No wonder “discussions” on the site almost inevitably devolve into monkey-style feces flinging (metaphorically).

Speaking of days and equinoxes*, I read recently that the rate of the Earth’s rotation has speeded up, and indeed, that we recently had the “shortest” day recorded—that’s not shortest in the sense that the winter solstice is the shortest “day” of the year, but that the actual period of the Earth’s rotation has decreased.  It’s not by a lot, of course—I think it was on the order of a microsecond or so, though I may be misremembering that order of magnitude.

It’s certainly not something a person would notice, but the international group that manages the Universal Time standards and sidereal versus solar days and the like needs to pay attention and note such changes.  And if they adjust years—adding leap seconds for instance—that all has to be coordinated with things like GPS satellites and so on, which already have to be managed with respect to General Relativity and Special Relativity; their function depends on highly precise time-keeping, and time is different farther up in “space” and at higher speeds.

As for why the Earth is speeding up, well, I haven’t read any speculation, but at first glance it seems odd.  One might expect that, over time, if anything, the Earth’s rotation might slow down, and I believe that has been the overall trend over billions of years, with tides and the like very, very slowly dissipating angular momentum.  For a rotating body to begin to rotate faster requires—by conservation of angular momentum—that its overall mass distribution gets closer to the center of rotation, like the proverbial spinning ice-skater pulling his or her arms in closer to his or her torso and thereby speeding up.

spinning skater

I wonder if, perhaps, there is some change in the distribution of the Earth’s mass in the form of water from glaciers, such as in Greenland**, and mountain glaciers in other places, decreasing the amount of mass that was higher up and away from the center of the planet and bringing that mass down into the sea, which by default is as close as things like water can get, since liquid water “seeks” the lowest level.  Of course, general erosion of mountains and even adjustments of the planet’s crust due to plate tectonics could have effects on rates of spin, but it seems to me that they would be too slow in their effects to be so noticeable—so to speak.

I’m sure we’ll be hearing more about this phenomenon, particularly if it continues.  It’s unlikely to make a difference in our day to day lives that could possibly be noticeable to people who aren’t measuring with the most precise instruments science and technology can produce, but the information is a curiosity, and it could be at least a marker of the effects of climate change.  Or perhaps not.  There may be another explanation.

Maybe by sheer chance the Earth got hit with meteorites that, for this one small bit of time, happened to, on average, deliver their kinetic energy in the direction of the Earth’s rotation.  It’s not something that’s likely to be a trend, but it could, in principle, happen briefly just by chance.  It seems highly unlikely to happen in such a way as to cause a measurable change in the rotation rate, but what do I know?

Anyway, that’s about enough meandering thoughts for today.  I hope you are all having reasonably good days—even if they are shorter, and you have a microsecond or so less to get your daily chores done.  Please use that diminishing time by spending it with those you love and who love you, if you can.  Take advantage of the moments you have by doing things that are affirming for your relationships and families and so on.  Entropy is always increasing—that’s the 2nd Law of Thermodynamics, and it is as inexorable as any law we can imagine.

We could find someday that there are exceptions to the speed of causality (aka the speed of light), but no one who knows anything about thermodynamics thinks anything is ever going to overthrow the 2nd Law, since it’s based in the fundamental nature of mathematics and probability.  The universe might start again in a Poincaré recurrence, but that’s not going to be for another 10120 billion years or so, so don’t hold your breath.  Or do, if it pleases you; we’re all going to be long gone before any recurrent universe happens, anyway, even if nothing like the “big rip” makes such recurrence impossible.

As I said, don’t waste time.  Love your loved ones and spend time with them if you can—and if they want you around.  Don’t take such things for granted.

TTFN

whirling globe

*I was, you can go check for yourself.

**I feel that the ones in Antarctica might be less impressive in effect only because they are so much closer to the axis of rotation already.

by

Talk about digits, my blog’s got ‘em.

It’s Monday again, and it’s also the first day of August in 2022.  This makes it interesting, in a sense, but I always need to remind myself that, no, Monday being the first of the month does not mean that we’re going to have a Friday the 13th.  It’s when Sunday is the first day of the month that we have a Friday the 13th.

That’s not really important, of course—I have no superstitious beliefs about 13 or Friday the 13th.  In fact, 13 is one of my favorite numbers, so I rather like a Friday the 13th.  This is partly because some people think it’s an unlucky day, and partly because of the bad reputation 13 has with the public among the primes, especially when compared to 7, which is not even as interesting a prime, in my opinion, as 13.  Though, when added together, 13 and 7 do make 20.

This is not a big deal, though.  According to Goldbach’s Conjecture, every even number greater than 2 can be made from the sum of 2 prime numbers.  As far as I know this still hasn’t been proven in a rigorous mathematical sense, but I also don’t think they’ve been able to find any exceptions, and since they have supercomputers and the like with which to work these problems, they’ve gone pretty darn high.

Similarly, they’ve solved π (pi) to about 62 trillion digits or whatnot.  Think about that incredible number of digits.  By comparison, a googol—which is a number larger by far* than the number of elementary particles in the accessible universe—is only 100 digits long.  The Planck length itself is 1.6 x 10-35m.  So, it has 35 digits of significance, really, taking the most generous possible meaning of “significance”.  And that’s the fundamental, measurable minimum sensible distance quantum mechanics, in its current best form, says exists for reality**.

In other words, even if we had the greatest possible precision that is physically within the realm of reasonable speculation, we could not measure the radius and circumference of any instantiated circle precisely enough to come close to telling if it matched the current figured length of π.

Of course, no actual, physical circle is going to be a perfect, mathematical circle.  See above regarding the Planck length; that alone will screw up how perfect a circle can be.  Also, spacetime itself is not perfectly flat (although it can locally be extremely close to flat, and on the largest scales it appears to be flat).  Even the presence of the person doing the measuring would probably be enough of a spacetime distortion to make a circle’s ratio of circumference to diameter mismatch against π.

Don’t even start trying to compare the ratio of circumference to radius in a massive body like the Earth or the Sun.  Those ratios are measurably (in principle at least) below π because of spacetime distortion as described by General Relativity.  And, of course, a black hole’s radius, as measured from within, would be functionally infinite.  So, its local equivalent of π would go to zero.

But π is a mathematical constant, describing ratios of mathematical objects that are precisely defined in flat, Euclidian geometry, and as such, π is a real thing…indeed, a transcendental thing, you might say.  It is known to have an infinite number of non-repeating digits.  Which is not to say that there are no repeats at all, just that there is no repetitive pattern.  Obviously, in base ten we have only ten digits with which to work, so there are quite a lot of reuses of each digit—an infinite number of them, in fact.

In fact, I suspect—though I don’t know—that if you πcked any finite number of contiguous digits of π, you would eventually be able to find a recurrence of them somewhere down the line, though it might be far beyond what’s been calculated to date.  The reasoning, at least as I’m thinking about it, is similar to the reasoning that demonstrates that the “Level 1 Multiverse” is a real thing, if spacetime is infinite in spatial extent.  The best data we have now seem to indicate that either space really is infinite or at least it’s waaaaaaaaaaaaaaaaaaaaaaaaaaaay bigger than the 93 billion light-years-across visible universe.  This is part of that spacetime flatness I mentioned before.

To think about it from a more mundane point of view:  the Earth, locally, looks flat (ish), but if you start precisely measuring the angles of bigger and bigger triangles, you’ll find that they’re adding up to more and more above 180 degrees, showing—even if nothing else did show it***—that the Earth is not flat, and in fact has “positive” curvature in Riemannian geometry.  But if you kept on measuring the sums of the angles of bigger and bigger triangles and they all stayed at 180 degrees to the greatest precision you could possibly muster even at immense size, you’d come to the conclusion that, well, either the world on which you stand is flat, or if it’s a spheroid, it’s a really, really BIG spheroid.

The analogous measurements (in three spatial dimensions, obviously) have been done on the scale of the microwave background radiation, which is as far back (and thus as far away) as we can see with light (microwaves, specifically):  about 300,000 years after the Big Bang.  They are consistent with a flat spacetime.  So, as I said, the universe is either spatially infinite, or WAAAAY bigger than what we can see.

This infinity doesn’t really do us any good, of course.  We still couldn’t reach almost any of it, even if we were traveling at the speed of light, since the expansion of the universe appears to be accelerating, and thus distant regions are moving away from us faster than light.  But, since quantum mechanics appears to dictate that, within any closed region of space, there is a maximum number of possible configurations (defined, at its upper limit, by the event horizon of a black hole with that apparent volume, the number of possible states (or its entropy) of which is related to the surface area of the horizon expressed in Planck lengths squared…so, it is big, but it is finite), then if space is infinite, there will be regions of space “out there” that are precisely the same as any finite region you might choose to compare them to, from the size of a human to the size of the accessible universe.  Indeed, in a spatially infinite universe, there are an infinite number of them.

If it helps, you can think of decks of cards being shuffled.  There are 52! (read as “fifty-two factorial”****) ways for a deck of cards to be ordered if they are shuffled randomly…that’s about 8.06 x 1067 ways.  It’s a big number, and though it’s nowhere near the number of elementary particles in the visible universe, it’s so big that we can be mathematically all but certain that no two fairly shuffled decks of cards have ever in human history come out the same.

However, if we have an infinite number of decks being shuffled, not only will any given ordering be repeated, it will be repeated an infinite number of times, though there might be quite a large average distance between repeats.  So it will be with iterations of any person or planet or galaxy or locally causally connected “universe”.

Don’t worry about it too much.  Though in an infinite universe there are an infinite number of any given person (as well as every possible variation thereof), these doppelgängers will have no effect upon you, except perhaps to blow your mind, as your existence will blow theirs.

Well, I don’t want to keep going on forever (har!), so I’ll call it to a close now, by noting in passing that this month (August, see above) is named (as many know) for the first “official” Roman emperor, as July was named (also as many know) for the first “de facto” Roman emperor, and June was named (as very few know) for June Cleaver, the empress of late 1950’s to early 1960’s American television.

*How far?  About 10,000,000,000,000,000,000 or 100,000,000,000,000,000,000 times as big.

**That doesn’t mean there are no finer distances, necessarily—though it might—but unless quantum gravity or whatever changes things significantly, it sure seems to be a limit…a physical one, not a mathematical one.

***Other things do.  The Earth is round, and people have known this for thousands of years, contrary to popular belief.  2200 years ago, Eratosthenes figured out the Earth’s circumference by measuring shadow lengths at different latitudes and doing some basic trigonometry.  He got the right answer, too.

****Which is 52 x 51 x 50 x 49 x … x 3 x 2 x 1.  The 1 is a really superfluous, since anything times one is just the thing itself, but it’s there for completeness.