Mathematics

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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.

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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.

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Who is this Frigga person, and why is a day and a minced oath named after her?

Well, it’s Friday once again, despite all the odds against that happening*.  I’ve now been writing these quasi-daily posts for almost two weeks.  Really, I suppose, it’s closer to being a week and a half, but that’s a difficult measure to use, because half a week, of necessity, involves half a day in the middle, since weeks have an odd number of days, but days, and daily things, are whole numbers.

I’m told that the number of days in the week was originally related to the number of “non-fixed” celestial bodies that are visible to the naked eye:  the sun, the moon, Mercury, Venus, Mars, Jupiter, and Saturn.  Of course, our modern. English names for the days don’t completely match up with the names of the planets/moon/sun, but we do have a Sunday, a Moon Day, and a Saturn Day**.  That’s almost half a week worth of days…but, of course, since weeks are made up of an odd number of days, we can’t have a whole number of days equate to half a week, anyway, as I said before.

It’s good that the number of minutes, hours, and seconds in our standard time measurements are more sensible.  It’s my understanding that this comes from the Babylonians, who were not only good with hanging gardens*** but with highly divisible numbers, such as 24 and 60.  Just look at all the ways you can divide sixty evenly:  by 2, by 3, by 4, by 5, by 6, by 10, by 12, by 15, by 20, and by 30!  And 24 isn’t a slouch for being a smaller number; you can divide it by 2, by 3, by 4, by 6, by 8, and by 12.  Just imagine if the number of minutes in an hour, or seconds in a minute, or hours in a day, were odd numbers.  Imagine if they were prime numbers!  How cool would that be?

No, wait, I mean that would be highly inconvenient.  And it would be inconvenient.

Presumably there were other attempts to devise systems for measuring time during a day—I think I recall reading that sometime around the French Revolution and the creation of the Metric system****, there was an attempt to innovate a decimal clock of some variety.  You can sort of understand where they were coming from, if this story isn’t apocryphal.

But there appears to be a sort of natural selection with secondary inertia that applies to things like systems of time division, and it’s very difficult to knock out an entrenched one that functions reasonably well, and upon which many dependencies have evolved, without some truly catastrophic breakdown of the prior system.  Just look at the QWERTY keyboard layout!

None of the preceding was what I had “planned” on writing about this morning.  Well, I say “planned”, but it was just a vague notion, and I distracted myself right from the start with stochastic and tangential thoughts, which is almost always how these blog posts happen.  As it was written by the great Robert Burns—you know he’s great just from his first name—the best-laid plans of mice and men gang aft agley.  And my plans are rarely among the best laid; in fact, I don’t think my plans have gotten laid in more than ten years.  No, not even on Frigga’s Day, which you’d think would be good for such things.

I had thought about a post detailing a movie or story idea, about a person who wakes up one day to find, or perhaps discovers gradually, that he has become a zombie.  He’s not a philosophical zombie à la David Chalmers, but a horror-style zombie…of sorts.  He doesn’t start shambling about (much) and he certainly doesn’t have the urge to bite and/or eat living humans, except maybe when they’re being really annoying.  He’s just gradually rotting and falling apart and wearing away.  He has no vivacity, has low energy, and his face and body are steadily decaying and becoming disgusting.

But none of the people around him seem to realize what’s happening to him, even when he tries to call attention to it and see if anyone can help.  He’s gone to doctors and sought out zombie-therapy (it’s not a unique problem to him), and tried medications, and meditations, and supplements, and lifestyle changes and all that sort of stuff, but it doesn’t seem to help…or when it does, it only helps a little, or for a very short while.

I’m imagining his appearance degenerating sort of in the fashion of David’s friend, who was killed by a werewolf, then showed up more and more rotten every time while he urged David to break the bloodline of the wolf in An American Werewolf in London.

And our protagonist is unable to rest, because, well, rest doesn’t really help a zombie feel better.  It’s just immobility, after which, if anything, he’s stiffer and sorer than before.

A big part of the story would be him feeling tormented by the fact that the people around him don’t seem to realize that he’s got this problem, even when he tries to ask for help.  And he could really use some help, because—being a zombie—he’s unable to help himself.

Finally, he decides he just has to try to figure out what ways there are to destroy zombies reliably, and with reasonably little pain and mess, so he can end his torment.  Some versions of the zombie lore say its enough to “shoot them in the head” as in George Romero’s movies, but others say zombies will keep moving as long as any part of them remains intact.

He considers using fire, but that would be very difficult to force himself to use.  He still feels pain, you see.  Indeed, he feels it more than most, because his body is slowly falling apart, and his nervous system is fairly screaming at him that something is wrong, all the time.  So, if fire didn’t work, or if someone “rescued” him after he’d doused himself and lit the match, he’d be in that much more pain and his existence would be that much more horrific.  Similar issues arise with notions like walking into the depths of the ocean to be crushed or jumping from a very high cliff.  If he shot himself but didn’t aim perfectly, he’d be “alive” but with part of his brain destroyed, assuming destroying the brain even works on zombies.

And the people around him might still not realize that he had a problem.

I’m not sure how this story would end.  Is there ever going to be a way to cure this affliction?  It seems unlikely.  There are treatments that sometimes relieve symptoms (in the story world), but there is no known cure, because the cause is nebulous.  Zombie-ism is at least somewhat genetically influenced, since it tends to run in families, but no one is quite sure how, and it appears to be too thoroughly multifactorial even to conceive that there might be one single root cause.

It’s a bit ham-handed as stories-that-are-metaphors go, but if it were well done and well-acted, it could be decent.  If someone did it, I might watch it, or read it, seeing as I am a zombie myself.

Let me know, please, if someone makes that movie or writes that book.  Thanks!

*As far as I know, there was almost no chance that it wouldn’t happen, but it sounds more dramatic the other way.

**And you could sort of make the case that Wednesday, from Wotan’s Day, is a Jupiter Day, but that’s stretching things a bit.  I’m not sure that in Norse mythology Wotan or Odin was ever actually associated with the planet Jupiter.  And Friday is supposedly named after Frigg, or Frigga (played by Rene Russo in the MCU), a Norse goddess of fertility or some such, very loosely similar to Venus—and apparently, many languages (as in the Spanish “Viernes”) refer the name of this day of the week more directly to Venus.

***You’ve gotta be careful with hanging gardens, though.  If they fall, your former garden can become a dwelling place of demons, as in the line from Revelation 18.

****Which is quite a logical, internally consistent, and excellent system.

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Wednesday morning at five o’clock as the day begins…

It’s actually 5:03 am as I’m starting to write this, but it’s damn close to the time mentioned in the opening line of the Beatles song She’s Leaving Home, and that seemed too fine a coincidence not to note at least in the title of today’s post.

It’s not ironic, by the way, in case anyone out there thinks it is—though probably most of the readers here on WordPress know the difference between irony and coincidence.  But the public at large, unfortunately, at least in the USA, seem to think irony is simply any somewhat amusing or tragic coincidence.  Whereas (for instance) the only real irony in the Alanis Morissette song, Ironic, is that none of the examples she gives in the lyrics are really cases of irony*.  In that sense, the entire song, taken as a whole, is truly ironic…which is a rather delicious irony, if you ask me.  I sneak myself toward the suspicion that Ms. Morissette did that on purpose, and in fact, I would be delighted for her to confirm this fact.

If anyone reading knows her personally, could you ask her for me?  Thanks.

Today is July 13th, a date which has the slight fun of being a pair of prime numbers (7 and 13, in case anyone was unclear on that).  It has the added charm of being a combination of a supposedly lucky number (7) and a supposedly unlucky number (13), which combination is borderline ironic in a certain sense, but not really.  Of course, which numbers are deemed lucky, and which are deemed unlucky is deeply culturally dependent.  Apparently, for instance, the number four, in at least one of the ways it can be pronounced**, is considered unlucky in Japan, because it sounds like the word for “death”.

This is all good evidence that “lucky numbers” are not actual, natural, real things in the world, outside of human minds.  Cultures the world over figured out arrows and spears, and fire, and the fact that things fall when you drop them, and that pyramids are strong and stable structures.  The Mayans figured out the number 0 (zero) centuries before Europeans used it or came to the western hemisphere, but the people of India had figured it out, too, on the other side of the world.  When things are real and natural—at least when they’re also useful or pertinent—cultures across time and space will tend to arrive at the same conclusions about them.

Judge for yourself, based on this, whether the many and varied world religions have more in common with “the wheel” and “counting numbers” or if they are more like “lucky numbers” and local fashions of apparel.  Don’t worry about what I think; I’m not here to tell you what to decide.  I’m here to be judgmental if I disagree with you.

I’m kidding about that last sentence.

This will now be, if my figuring is correct, the eighth of my pseudo-daily blog posts since I decided to do this instead of writing fiction—which I cannot be arsed to do right now—or playing guitar—which I don’t enjoy much at the moment, and which is giving me some kind of repetitive stress inflammation in my right hand and wrist.  That soreness could be contributing to my lack of enjoyment, obviously, but I don’t think it’s the main thing.  I’ve just got rather severe (and worsening) anhedonia.

For example, I threw away a Dutch apple pie yesterday which I had accepted as an impromptu gift from someone who had it and didn’t want it, because when I began to eat a small piece, I realized I didn’t much like it.  This is very weird for me.  In my younger days, I was known to eat an entire mini-sized Dutch apple pie from the Publix bakery in a single sitting***.  It was one of my favorite things.

This is not the only one of my prior “comfort foods” or foods-of-indulgence that has lost its charm.  Almost all of them have.  You would think I would start to lose weight, since I’m not eating as much of the foods I like.  Maybe I am, but it’s too slow to notice.  Oh, well, whataya gonna do?

I don’t think I really have much more to talk about today.  It’s arguable, of course, that I haven’t had much to talk about on any of the previous days that I wrote blog posts, or when I wrote fiction for that matter, but that didn’t stop me from writing—which is fine in my view.  But today I just think I’m in the mood to peter out early, not just with writing but with everything else.  I wish I could take the day off work or something, but Wednesday is the day on which I do my most “crucial” work at the office.

Someday soon I’ve gotta just get them ready to take care of all this without me, because I really don’t know if I’m going to be around much longer.  Not because the job is bad—it’s not.  I like the people I work with well enough, and my boss is very nice, and positive, and my coworkers are for the most part good and well-meaning people****.  In fact, it’s safe and accurate to say that the only person at the office whom I really, deeply, do not like…is myself.

I need to get away from that asshole.

*If “Mr. Play-It-Safe” who was afraid to fly had refused to get on a plane but had instead taken a train, and then the train had derailed catastrophically, that would have been irony!

**“Shi” as opposed to “yon”.

***This wasn’t a good thing, per se—it’s certainly not a healthy habit, and was in its own way a desperate attempt to find some reliable source of positive feeling when I couldn’t seem to generate such things by other means.

****One of them came in late yesterday specifically because he wanted to be home to watch the revelation of the first scientific images from the James Webb Space Telescope, and I can’t argue with that decision or his priorities.  They were fine images indeed, though I’m more interested in the new science that can be learned through them.

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If Tuesday afternoon is never-ending, Wednesday morning ITSELF can never come.

It’s Tuesday again, just like it was last week on this day, and I’m still doing my “daily”* blog posts, since I don’t have any desire either to write fiction or even to play any guitar.  This is at least a quasi-productive way for me to use time that I would have used to write fiction, at least until the Second Law of Thermodynamics claims me at long last, and I rush—all oblivious—into its cold but comforting embrace…to poeticize idiotically a simple fact of physics and mathematics.

Tuesdays often make me think of the Beatles song, Lady Madonna, because for me, one of the most memorable lines of that song is “Tuesday afternoon is never-ending”.  This is particularly pertinent when things are slow at work in the afternoon, though I don’t think most other people regard dull days at the office in terms of songs, like I often do.  This being me, I tend to focus on dark and/or negative songs and lyrics, or at least melancholy** ones.

I rarely think of Thursdays in terms of my stockings needing mending, at least.

The notion that Tuesday afternoon is never-ending raises an almost Zeno’s Paradox type notion.  If Tuesday afternoon really were never-ending, then Wednesday would never arrive, so there would never be another day.  Although, despite it always being Tuesday afternoon, if people could nevertheless still move and act and do things, it would be useful to break time into manageable chunks for the purposes of scheduling, planning, working, sleeping, and so on.  Also, it’s never Tuesday afternoon everyplace on Earth at once, so if Tuesday afternoon in Britain were to be never-ending, then Tuesday morning in the US, Canada, Mexico, Brazil, etc. would be never-ending, and Tuesday evening for most of Europe, and of course, Tuesday night into Wednesday morning for places east of that, right up to the international date line.

And, of course, if the Earth had stopped spinning—assuming it had done so without the numerous catastrophic effects this would otherwise entail (watch this lovely video by Vsauce to see some of these discussed)—the weather patterns on Earth would be permanently changed and made horrific.

Depending on whether Earth became the equivalent of tidally locked on the sun, or if it had just stopped rotating, it would either have a permanent sun-facing side, or it would have a day as long as its year.  Then again, even a year-long day is not literally never-ending, so I guess it would be the “tidally locked” situation.  Before long, the Prime Meridian would become a very hot strip of Earth indeed!  And the International Date Line would become extremely cold.

It is tangentially interesting to think about—having mentioned Zeno’s Paradox earlier—the notion of continuously divisible time.  If time (or distance, as in Zeno’s original paradox) were infinitely divisible, à la the real number line, it would seem that one could never experience the passage of time because before you could get to Tuesday evening you would have to go halfway through Tuesday afternoon…and before you got halfway, you’d need to get a quarter of the way…and before that you’d need to get an eighth of the way…and so on.  If things are infinitely divisible, or so says the “paradox”, you should never be able to get anywhere, either in space or time, because no matter how arbitrarily close you choose two points in space to be, or two points in time, or two numbers on a number line, there are an uncountable infinity of points in between.

Calculus, of course, deals with this issue by means of taking limits as distances go to zero, and the like; it handles instantaneous and continuous rates of change quite nicely, thank you very much, while still rigorously defining functions in terms both accurate and useful.  As for reality itself, it seems to side-step the issue entirely by making space and time, in practice, not infinitely divisible at all.

The minimum distance that makes any physical sense is the Planck length, and the minimum time is the Planck time.  To say you’ve traveled half a Planck length, or that something lasted half a Planck time, is apparently saying something that has no meaning in the real world.

Of course, the Planck length and time are REALLY small:  1.6 x 10-35 meters and about 10-43 seconds.  So, we cannot directly measure either of them with current technology, anyway.  Not even close.  But they are real things, when it comes to quantum mechanics, with real, verifiable physical implications that have been tested and confirmed with tremendous accuracy and applicability.

One does tend to wonder, though, about spacetime itself.  According to General Relativity, gravity is not a force in the sense that electromagnetism and the strong and weak nuclear forces are forces but is instead a manifestation of the curvature of spacetime, leading objects in it to attempt to follow the closest thing to a straight line (a geodesic) in a curved, “flexible” four-dimensional structure, in the way one has to follow a great circle on the surface of the Earth to pick the “straightest” possible path between two points on the surface of a spheroid.  This really matters for airplanes, and even for ships.

But is space itself infinitely divisible?  GR*** treats it as such, but GR conflicts with Quantum Mechanics at places of small size and high mass, producing senseless results (so I’m told…I haven’t done the figuring myself, regrettably).  Spacetime certainly seems to be able to expand indefinitely, as it has done since at least what we call the Big Bang, and it continues to do so at an increasing rate even as we speak, so to speak.  That’s trivial to conceive of with things like continuous variables, real numbers, things with uncountable infinities between any two points.  Just multiply everything by two, say, and all the numbers are twice as big, and just as uncountably infinite.

But if space is discontinuous, in some sense, as implied by presumed quantum gravity, how does the expansion manifest?  Does more space pop into existence between two regions formerly separated by a mere Planck length?  We know that if you try to separate two quarks that are bound to each other, the strong force between them becomes so intense that new, formerly virtual, quarks pop into actual being between them****.  Is this what happens with spacetime itself?  As intervals get stretched, do new nuggets of spacetime appear?

We know that it’s possible to produce new, positive energy in spacetime, balanced by the “negative” energy of gravity, so there is no local violation of conservation principles*****.  Maybe spacetime spontaneously generates more spacetime, using the force of the cosmological constant, or its equivalent, to create these new bits of spacetime as it goes along.  It seems plausible, given what we know about the finite divisibility of things we’re able to confirm experimentally, and at least little bits of spacetime seem much less energetic on a per-unit basis than things like quarks or even electrons and neutrinos.

Infinite divisibility may work quite nicely in mathematics—indeed, it does—but it may not be plausible in the real, physical world.  Spacetime is real, and if it expands, then that expansion must happen at some level and be describable in principle.

None of which changes the fact that Lady Madonna is an awesome song.

*I put “scare” quotes around that, because technically, it’s not a true daily function, since even if I continue doing it for a long time, I don’t expect to write on Sundays, and probably roughly not every other Saturday, since I won’t be going to work, and I write this during my commute.

**“Melancholy” has become a rather soft kind of negativity in modern parlance, but I wonder how people would feel if they considered when using the word that it comes from the old concept of “black bile”, one of the supposed four “humours”.

***General Relativity.

****Not a violation of Conservation of Energy…they get their substance from the energy you applied trying to separate them.

*****Again, alas, I have not done the specific math myself, but the concept is straightforward and logical.  One can similarly create a new positive electric charge as long as one creates a balancing negative charge at the same time.  It happens in nuclear decay all time.

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Monday mornin’ couldn’t guarantee that Monday evenin’ you would still be here with me

It’s Monday, July 11th of 2022, and this is the first Monday blog post among the ones that I’ve begun writing every weekday morning, which only started last Tuesday (and that is why this is the first Monday post…as you probably guessed, or could have guessed, even if you didn’t already know).

The fact that the date is 7-11 (in the American system of writing dates, anyway) is rather pleasing, and not just because it consists of two consecutive prime numbers.  It calls to mind an interesting thought—to me, anyway—about cultural evolution*.  The store chain, 7-11, took its name originally, as I understand it, from the hours it stayed open.  That was from seven in the morning until eleven at night, not from seven until eleven am or pm.  That would have entailed a business open for only 4 hours a day (or eight, if it had been done in two shifts, which I guess could have been interesting to make into a store name).

At the time, or so I’m led to understand, having a store open from seven in the morning until eleven at night was exceptional enough that it was worth making into the name of your convenience store**.  But of course, free market economies having at least a little bit in common with biological evolution, it wasn’t long before competitors started showing up, since the resource laden niche of the long-hours convenience store had been shown to exist.  Eventually 7-11 extended itself to be a store worthy of the name 7-7…or 8-8, or 9-9, or any other string of times that loops around the clock and comes back to start again ad infinitum.  They could have just renamed it “24-7” if that had been a cultural meme at the time, but of course, by that time, “7-11” was already an evocative meme, and a highly recognized and popular brand, so there was no need to change.

But as is often the case with cultural evolution due to economic competition, once the store hours had been extended to 24 hours a day, every day, there was no credible way to scale back merely to 7-11, except perhaps in a few rarefied and “underserved” markets.  In most places, the chain would have lost market share to shops that had already sprung up in competition with it…even those that weren’t 24-hour stores, because their advantages were usually in the form of lower prices than 7-11 was able to charge.

Thus, 7-11’s 24-hour schedule, etc. became a sort of peacock’s tail or Irish elk’s antler of the retail economy.  Nothing short of a true and rather complete collapse of world retail seems likely to reset the norm of store hours…or of working hours, or of “at-will employment”, or of other similar configurations.  Because, though change can be brought about by politics, via laws and regulations, politicians—and their promises—are as subject to inadequate equilibria and peacock’s tails (and bird-of-paradise courtship displays) as anyone and anything else.

If the public at large were bright enough, and self-aware enough, to adapt rationally what they voted for, or how they made their purchases, or the hours they were willing to tolerate working, or the conditions under which they were willing to work, they probably wouldn’t ever have landed themselves in the first place in situations where the only ways to reset things are via catastrophic occurrences, deliberate or accidental.  And, unfortunately, since there is rarely any well-thought-out, scientifically planned or tested cultural adjustment done, revolutions and other catastrophes tend to be bloody and destructive and horrible, and to make things worse for everyone, until evolution has time to find another equilibrium that is at least a bit more efficient and tolerable.

But maybe I’m wrong about all that.

All this does bring me around to something that always irritates me:  the way politicians, or activists, or similar people, talk about wanting or seeking to make “change”.  That’s just simply too vague and useless a word to use, in my judgment.  Seeking and working to make “change” is not good enough, because though all improvement is necessarily change, not all change is improvement.  In fact, given the extremely high-dimensional vector space of all possible directions of cultural change, or societal change, or political change, or economic change, and given the comparatively narrow region of that vector space that most people would consider better than the space in which they already reside***, there are far more ways to make life more or less universally and objectively “worse” than there are places in the space of possibility which could be thought to be better.

Even in a one-dimensional space (so to speak), with a random change you’d have a 50-50 shot of either getting better or worse, and that’s as good as it can get even in principle with respect to random movement.  The higher the number of dimensions, the more ways things can potentially get worse (or get no better).  And reality is a very high-dimension vector space of possibilities indeed****.

So, don’t make change just for the sake of “change” without thinking very carefully about what you’re doing, because you’re more likely to make things worse than you are to make them better, by any reasonable definition of “better” you might care to choose.  And if you gain an advantage by keeping your store open longer than others, other people will eventually extend their hours to compete with you until finally, all relative advantage is squeezed down to being so tiny as not usually to be worth the effort.  And everyone will be stuck in a new, more exhausting equilibrium, like tall trees in a rain forest, competing for the otherwise ample sunlight and water, when they could have survived much more easily and efficiently if they could all just have agreed to stay short.  But they couldn’t do that, being trees.

Humans are not trees, of course.  But they don’t seem to be that much smarter.

Have a good week.

*Not to be confused with Cultural Revolution, which tends to be a very bad thing even when done deliberately and “planned” in advance.

**Though I’m not sure if even the term “convenience store” existed before 7-11 conjured it.

***The portion of the vector space in which we now exist clearly has going for it the fact that we can exist here, at least in the short term.  To take an analogy, imagine being on Earth and being given the opportunity to teleport instantly to some other random spot in the universe—or to some other, random planet in the galaxy, even.  What odds would you give yourself that you would survive more than an instant once you reached your destination?  The reason we’re alive here on Earth right now is because we can be.

****This has nothing to do with higher numbers of spatial dimensions, as in String Theory or M Theory or related proposed systems of physics.  Those entail literal, spatial dimensions, of the sort through which we regularly move, though with certain special characteristics, whereas I’m talking about dimensions of vector spaces, or “phase spaces”, the dimensions of which you can think of as being analogous to any of the axes on a set of graphs that map data relative to other data.