Author: Robert Elessar

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Complex clocks, misleading DNA, and signs (not sines) of support

Well, it’s Wednesday, which follows Tuesday, which follows Monday, which follows Sunday, which follows Saturday, which follows Friday, which follows Thursday, which follows…

…that’s right, it brings us right back to Wednesday again.  It’s a little bit reminiscent of the Doe, a Deer song from The Sound of Music.  Or, maybe you could say it’s a little like Rock Around the Clock.  All these cyclical things are amusing in that each member of the closed, recursive group both precedes and follows itself.

That gives me an interesting idea.  At least, it’s interesting to me.  I’ve seen clocks (dial style clocks obviously, not digital ones) that designate the hours with radians, such that in place of the 12, for instance, there would be π/2, since the whole circumference of any circle is 2 π radians.

Six o’clock is then 3 π/2, nine o’clock is then π, and three o’clock is just 0 (or 2π).  The order of these numbers uses the tradition of beginning counting radians (or degrees) at the 3 o’clock position as it were.  The other numbers (1, 2, 4, 5, etc.) are various ratios of π, using the trig functions that give us the results for what we would think of (typically) as 30 degrees, 60 degrees, and so on.

Well, why not do a novelty clock with the hour markings represented by complex numbers?  In engineering and in physics, they are very frequently used because they are excellent ways of calculating cyclical things, using a unit circle (in this case, a circle with radius 1, centered on the origin of the complex plane).  Using such an arrangement, multiplying any complex number by i results in a 90 degree rotation (counterclockwise).

In the case of a complex number clock, the 3 o’clock position is just 1 + 0i, 6 o’clock is 0 – i, 9 o’clock is -1 + 0i, and 12 o’clock is 0 + i.  I’ll work out the specific complex numbers for the other hours, and I’ll put them in a footnote* below, but I don’t think I can do it off the top of my head while commuting.  For one thing, I don’t recall the sine and cosine of 30 degrees…

Wait!  The sine of 30 degrees (aka pi over 6 radians) is just ½.  And since we can take that as a leg of a right triangle with hypotenuse length 1 (since it’s a unit circle) then the Pythagorean theorem tells us 1^2  = ½^2  plus the cosine^2 of 30 degrees, so the cosine equals the square root of 1 – ¼ or the square root of ¾, in other words √3/2.  So 2 o’clock would be √3/2 + (½)i.

One o’clock (or 60 degrees) just reverses the ordering of the parts of the complex number:  ½ + (√3/2)i.  Then 4 o’clock is √3/2 – i, five o’clock is ½ – (√3/2)i, 7 o’clock is -½ – (√3/2)i, 8 o’clock is -√3/2 – (½)i, 10 o’clock is then -√3/2 + (½)i, and and 11 o’clock is -½ + (√3/2)i.  Neat and tidy!

I’ll leave it as an exercise for the reader to work out the complex numbers for the various minutes of the clock face**.  And, of course, if I’ve made any errors above, please let me know.

But anyway, I think you can see that this might make for a novelty clock every bit as exciting as the ones that just show you the hours as radians.  It might be slightly more rarefied than the other, but then again, engineers might prefer it (though they tend to use j rather than i to represent √-1, because i already stands for electrical current****, if memory serves.

Wow, how’s that been for some weird digressing?

Is “digressing” a word?  Google Docs seems to “think” it is.

Hopefully those quotation marks don’t offend Google Docs if it really does actually think.  If it’s any consolation (and even if it isn’t), I would be inclined to use such “scare” quotes when referring to the hypothetical thought processes of many a human.

On to another digression:  I had a weird thought just now, while my mind briefly wandered to imagining a potential crime thriller, maybe about a serial killer.  What if the killer, anticipating the potential for DNA evidence to be used to try to catch him*****, makes it a habit to pick up strands of hair, discarded tissues, used Band-aids, and various other things from various places such as public (pubic?) restrooms, barber shops, and so on.  He then leaves them randomly chosen and scattered at his various crime scenes to throw off investigators.

Of course, he’d want to be careful to get his DNA samples from widely chosen and semi-random places, such as maybe rest areas on major highways.  Otherwise the very pattern of those sources might give investigators something with which to work.  The FBI, for instance, can be impressively clever about such things.  At least, well, they were under previous administrations.

Jeez Louise, I’m really losing my mind, am I not?  Certainly it seems to have slipped its leash.  My apologies for this chaotic brain sneezing; I hope you don’t catch any mental viruses from me.

With that, I’ll bring this to a close.  I hope I end up feeling better today than I did yesterday, though so far it doesn’t seem promising.  More importantly, as always, I hope all of you have very good days.

*Well, there’s no point in doing this in a footnote now; I worked it out in the main body of the post.  See above.

**Just kidding.  Seriously, please don’t feel obligated to do this***.  I’m not going to do it (or might I say, “i is not going to do it”?)

***On the other hand, if one of you feels compelled to do the figuring, please share your results with me.

****That could almost be like someone’s protest sign, perhaps one that is held up and shaken outside a courthouse:

*****The vast majority of serial killers are men.  It’s a travesty, this wild gender/sex disparity; it’s the last bastion of unrepentant, unapologetic misogyny!  We need social programs to try to get more women out there serial killing!  Maybe we should provide subsidized child care services, so single moms won’t have as hard a time getting into the field…or wherever they might want to dump the bodies of their victims.

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“…the emptiest of feelings…”

Ugh, boy, wow, do I feel wiped out this morning, which seems mildly peculiar after a night’s sleep, however inadequate.  I didn’t have the energy to do my usual morning pull-ups today, even, and that’s rare.  Well, I say “usual”, but I actually alternate:  on even days I do pull-ups in the morning, on odd days I do dips, and on Sundays and on those Saturdays on which I don’t work, I do neither.

<sarcasm> Isn’t that exciting to learn?  I know that I can barely contain myself; I can’t imagine how it must be for all of you! </sarcasm>

Anyway, I don’t know why I am so enervated this morning.  I mean, I slept an entirely inadequate amount, but that’s not atypical or unusual for me.

Yesterday was even a decent day as far as it went.  We only worked a half day at the office, but sales were nevertheless pretty good.  Then afterward, I had a discord call with my youngest and we watched two excellent episodes of Doctor Who.  This is their first time watching, and it’s nice to be able to introduce someone to the show, especially one of my two favorite people ever.  The show is being quite well-received.  This is not a surprise.

Of course, I went back to the house later than I would have if I had not watched the Doctor, but not as late as usual.  Then I went to bed pretty sensibly.  That doesn’t translate into a good night’s sleep‒not by a long way‒but I did what was within my power.

It’s not as though I can do anything that’s not within my power.

So, yeah, I don’t know why I feel so beat this morning.  I don’t feel like I am coming down with some infectious illness (unfortunately), and I don’t have the symptoms that would go along with some rather severe medical process that could cause acutely worsening fatigue, like a GI bleed or something.  There’s no faintness/lightheadedness, no rapid heart beat, nothing of that sort.  I also have no new pains that I have so far noticed, and as far as I can tell I am not jaundiced, so my liver is probably okay.

Well, whatever.  The point is I feel a lot like crap.  But, unfortunately, I don’t feel sick enough not to go to work (or to write this blog post).  And I am not allowed to take breaks of any kind unless I am legitimately incapacitated.

“Not allowed” you ask?  Not allowed by whom?

By me’m, is the answer, albeit a deliberately ungrammatical one.  I cannot seem to let myself stop trying to do shit unless I am actually ill enough that I cannot really do anything.

I have been like this for as long as I can remember.  Even back in my early grade school days, I remember fantasizing about getting seriously hurt so that I would be able just to lie about and rest for a bit.  Honestly.

When I had open heart surgery‒it was August 7th or 8th, 1988, 2 weeks before I was to go back to university‒it was quite unpleasant of course, and quite painful.  Indeed, I remember that my first thought upon beginning to regain consciousness was more or less “damn it, I survived”.

It’s not great when you’re 18 (or probably any other age) to get your chest sawed open and your blood artificially circulated and oxygenated for a while, then to wake up restrained and intubated and cortically blind (I didn’t put that last thing together completely until quite some time later).

But it was, nevertheless, freeing.  I didn’t feel the need always to be doing something, to be accomplishing something, because I couldn’t.  That was kind of amazing, and it felt so at the time.

I wasn’t even afraid when I was going to get my heart surgery (or the catheterization before that).  It’s not that I was brave; it was nothing like that.  I was just too intrigued by the whole process, which was admittedly pretty cool and amazing, and I was almost unconsciously looking forward to having everything taken out of my hands for a while, whether I liked it or not.

Of course, in a sense, everything is always mostly out of our hands.  Our own agency, such as it is, is something we don’t choose, and we don’t choose our nature and our “specs”* and our talents and capacities.  Even our will is something that starts as it is without our input, as does the universe itself.  The best you can do is try to surf on the chaos.

But I’ve always felt the need to do something whenever I’m conscious and able to act.  Even if the “something” is a fun thing, or just a distracting thing, there’s always a pressure to do it, and it’s been there for as long as I can remember.  And it’s just a relief to have it taken off line temporarily, to have it rendered moot for a while.

When I had my heart surgery, I knew that it might kill me.  I certainly knew it intellectually, just as I also knew that the odds were very small‒roughly one in a thousand according to the statistics my cardiologist had shared with me.  Even back then, I had a good enough intuitive grasp of probability and statistics to know that, though immensely higher than the chance of winning the lottery, these were odds about which it was not worth worrying.

But I also just wasn’t horrified by the prospect of dying.  Even then I didn’t really believe in any kind of afterlife.  And I experienced (or, rather, I did not experience) more or less as complete a simulacrum of death as it was possible to undergo, one far more closely approximating it than mere dreamless sleep:  deep general anesthesia including hypothermia and cardioplegia, and the non-pulsatile cerebral blood flow that heart-lung bypass entailed.

If I had died on the operating table, there would have been no experiential transition for me.  That’s rather fascinating.

Anyway, sorry to bother you with my fantasies about, and my missed opportunities for, a painless death (or just for the chance to rest because there was nothing I could do).  Maybe I’ll feel better by tomorrow.  Maybe I’ll feel deader by tomorrow.  I could even be wetter by tomorrow, this being Florida.

I hope all of you are feeling and doing better than I.  I mean, come on, it’s not a very high bar to clear.

*By which I mean “specifications”, as of a machine or process, not “spectacles”.

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It’s serious Labor just to get through each Day

Good day to you all.  It’s Monday, the 7th of September, and for those in the USA, it is Labor Day.  That’s sort of the government holiday antipode of Memorial Day.  The latter marks the unofficial beginning of summer, and the former marks the unofficial end of summer.  In south Florida, I can fairly and reasonably say about the supposed end of summer, “Would that it were.”

That’s because the weather in autumn‒late autumn, anyway‒is much more pleasant than it is in summer here.  This is a large part of the reason for the “snow bird” phenomenon:  people who live up north during the warmer half (roughly) of the year and then come down to Florida during the cooler half of the year.

I say “cooler” in the meteorological, thermodynamic sense, not the social sense.  Contrary to what many people here seem to believe, there are not many cool people per capita in Florida.  It just doesn’t tend to fit the regional identity in any sense; “The Florida Man” is not celebrated for his coolness.

Just to give you an idea of how bad it is:  I am probably only barely below the mean level of coolness in Florida, at least based on the usual criteria of greater society.  Even well-known people from Florida are rarely noted for being cool.

Not that it really matters, of course.  Coolness is an epiphenomenon that accreted like pipe scale on the surface of primate dominance and reproductive hierarchical behavior patterns; that’s all fairly obvious looking at humans from the outside as it were.  But it all becomes self-referential after a while, building on and/or reacting in support of or opposition to prior standards of “coolness”, until it’s long since become a sort of autoerotic death spiral, a precursor to AI slop.

That doesn’t mean I don’t sometimes appreciate cool things and people; I just recognize “coolness” as entirely parochial.  What octopuses think is cool and what spiders think is cool and what albatrosses think is cool are going to be very different from each other and from what humans think is cool*.

Speaking of coolness, I went to the movie theater (by myself) this weekend to see the new Spider-Man movie.  The movie was certainly reasonably cool as far as it went; I thought it was well made and well acted and fun and so on.  It was at a theater that has a full bar, which is also pretty cool, so while I waited I had a Jack and Coke (to help with some social anxiety).  It was tasty, but it made me need to use the restroom four times before the movie started.  That was annoying.  But I rarely drink alcohol, anyway, so it’s an effect I need not dread.

The popcorn was pretty good, I guess, and so on, and the seats were comfy, but by the end of the movie I just felt more alone than I had before, despite coming out and joining the throng (then going into Target for some cat food and then to Walgreens for some sparkling water before ordering an Uber back to the house).

It was an expensive day, though.  The concessions were even more expensive than the ticket (and that’s not counting the Jack and Coke).  And the Uber to and from the theater was not cheap, either.  So, I don’t think I’m going to be doing that very often.  I may not do it ever again, maybe not even for Doomsday.

Though, when it comes to money, it’s not as though I’m saving for retirement.  I don’t expect to retire.  As of right now, I just expect to keep moving until I fall apart and then just basically die.  I mean, in the end that’s what everyone does, but my situation is likely to have less bric-a-brac cluttering up the works than many.

Honestly, I wish I could skip to the end a lot of the time.  Which I guess I can, of course, but it requires gumption and willpower to do it, and I am generally low on spoons, as the metaphor goes nowadays; I’m not sure how that figure of speech became prominent, nor why, but it feels somehow apropos.

Many things that I am doing to try to improve my willpower and my mental reserves and so on are at least partly to try to build the will to overcome my instinctive but annoying resistance to self-destruction.  I’m getting there, I think.  I’m making progress.  Maybe I’ll get there soon.

Honestly, I don’t really even mind that much if I don’t get to see Avengers: Doomsday.  I’m just sick of all of this shit.

I hope you all are doing better than I am.

*Of course, the thought processes as such are likely only to be very roughly analogous to what humans think about coolness, especially for non-social species.  There may also be overlap; I imagine many humans might think certain examples of flying skill shown by an albatross are very cool, and so might another albatross.

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“I said he’ll flip ya…flip ya for real.”

It’s Friday today, and though I am not a believer (and, more or less as I say in the meme below, I don’t want to be one, since I’m not impressed by “belief”) I will thank anyone and everyone who might be responsible for the fact that this is the end of my work week this week.  So, thank God it’s Friday, thank Cat it’s Friday, thank Frigg it’s Friday (thank Tony for his “Friggin’ Friday” comment), thank Cthulhu it’s Friday, thank Doom it’s Friday, thank Eru it’s Friday, thank Brahma it’s Friday…

I suspect that you get the idea.

Anyway, I’m very tired and need some rest.  It’s not that it’s been a particularly onerous week; it hasn’t really been.  If anything, it is I who has been more onerous than usual this week even than I usually am.  But I don’t think I’ve been much more onerous than usual.

I suppose that it’s up to those around me to say how much of a burden I’ve been, but I know their answers would be inconsistent and pretty confabulated.  This is not intended to insult them; it’s just the nature of human accounts of things that have happened to them when they are asked without having been paying attention to those things (in particular) in the first place.

Nature didn’t create a brain that keeps a running measure of its mood in relation to each individual around them, like some endless EEG plot.  What would be the use of such a function in the natural world?  Even if useful, would the use be worth the inevitable cost?  And could the drunken walk of the blind idiot god Evolution ever stumble upon such a process even if it were useful?

Well, given infinite time, it probably could, but we haven’t had infinite time to explore the space of possible biological innovations, and we probably will not have it.

Anyway, the point is, as Louis C K pointed out, it’s not up to me whether I’m being an asshole, at least not according to the impressions of others.  And I guess it’s not up to me whether others feel I am onerous or not.

Then again, it’s not up to them whether I consider myself to be a burden or not.  And I have the only front-row seats to me.  I am the one (and only) who is with me all the time*.

And consider something else:  all my meandering oddness (oddity?) that is on display here is me when I am tired, slowed down by literal decades of insufficient sleep.  Imagine how irritating I might be if I were fully rested and energetic!

Don’t make the mistake of imagining that it would necessarily make me calmer and more sedate.  I knew me back in the years when I used to get much more adequate sleep (though I have always slept less than most anyone else in my family).  I was not particularly sedate or calm then.

In closing, I’ll mention a weird thought that occurred to me when I was looking in the mirror (another daily burden) after my shower.  In principle, if one were picked up out of 3D space into 4D space, rotated in the proper way while there, then set down in 3D space again, one would be physically mirror-reversed***.

This would be a big problem, and not just because other people would be freaked out in subtle ways.  Every chiral molecule in one’s body would also be flipped from ortho to sinister, left to right (and vice versa).  That means you would need to eat similarly flipped food****, because your biological molecules only work on one version of most molecules.

Also, your DNA (which has chirality in spades) would be rotated in the other direction, so you certainly couldn’t reproduce.  But you couldn’t build new cells anyway, because many of the requisite molecules in that process are chiral.

Even your neutrinos/W and Z particles would behave differently, because this is one force/process in nature that is not parity-symmetric.  Meaning there is in a sense a handedness to the way the weak force acts.

Of course, that’s also the case with electromagnetism, come to think of it.  There is the famous “right hand rule” for how magnetic fields occur in response to changing electric fields/moving currents, and how electric fields respond to changing magnetic fields (see Maxwell’s equations).

So, heck, if you were so flipped, you might not even be able to interact with the electroweak sector of the quantum fields of our universe, and you might fall apart immediately at the subatomic level.  It would depend very much on whether such constraints are carried along with the stuff of one’s body or if they are imposed (and reimposed) by the fields in the universe around it.

I don’t even know what would happen with electric charge or hypercharge or spin or whatnot.  It almost makes me want to write Changeling in a Shadow World.  But I doubt that will happen.

With that weird stream of consciousness, I will let you go for the week.  I won’t be writing any new posts before Monday, exclusis improvisis.

*At least I’m the only one with a nervous system.  I suppose my skin and gut flora are with me all the time, but as far as I know, they don’t think in any reasonable sense.  Also, can any of them really be said to be with me always?  Their dividing/reproducing rates are very high compared to a human (or humanoid) lifetime, after all.  I guess it depends upon whether I consider a bacterium that undergoes mitosis to be two new organisms or just one increased organism that is continuous**.  Both options are reasonable and plausible, and nature doesn’t appear to care, outside the minds of humans, how such things are considered.

**This implies, in a sense, that all life on Earth could honestly be considered one organism, since there appears to have been one ultimate common ancestor to us all.  Thus, Life would really be a (so far) immortal organism.  I think that’s actually a pretty reasonable way to look at things, and it’s very much a sort of larger-scale, fractally self-similar pattern to how a human body is initiated with one cell−the “ensouled zygote” as I once mockingly made a meme about, after deciding it would be a good name for a band.

***If this is difficult to imagine, consider it in lower-dimensions.  Imagine an asymmetrical trapezoid in Abbot’s Flatland, with one of its two “legs” different than the other.  If it were picked up into three dimensions, flipped over, and then put back down, its asymmetry would now be in the other direction, and other Flatlanders might no longer even recognize it.

****This is part of why the possibility of being eaten by aliens, or of them eating us, makes little sense.  If you tried to eat food from an alien ecosystem, it would at best just go through you unabsorbed, and at worst would give you potentially fatal indigestion.  All your digestive processes are honed to work on other biological substances that occur within the ecosystem that evolved on Earth.  And this entails many lock-and-key enzymes and molecules that digest depending on chirality.  This was part of the motivation behind creating left-handed sugar and left-handed fat, which might physically behave similarly and perhaps even smell or taste somewhat the same, but would not be absorbed.  But such products almost inevitably lead to digestive troubles at best.

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A jest’s prosperity lies in the ear of him that hears it, never in the blog of him that makes it

Hello and good morning.

It’s Thursday again and time for another of my traditional Thursday blog posts*, though nowadays that’s embedded among the blog posts I write on all the other work days.  I haven’t written fiction in quite a long time, and the original reason for this (Thursday) blog was to promote my fiction.

But heck, it’s been a couple of weeks since I’ve even so much as picked up a guitar‒though I keep looking online at these parlor style acoustics, because they look like they’d be a good size for convenience and such.  But it’s just a bit of a pipe dream and a distraction to look at them.

There is no lapcom involved in this post today.  I didn’t take it with me when I left the office last night, but there was no more “reason” for that decision than there had been for the fact that I brought it the day before.  There were causes, as there always are, but not reasons.

Although, now that I consider it, I did feel that yesterday’s post was a bit too long.  That didn’t consciously enter into my decision-making when I chose not to bring the lapcom, but I did think about it earlier in the day, after posting.  Most, if not all, of what happens in most decisions we make is unconscious, or subconscious**, or whatever word you might want to choose.  So I can’t rule out that there were actual reasons for me not bringing my lapcom last night, but whatever the facts of that matter might be, there were, and always are, causes.

In any case, yesterday I fell prey to my tendency to write quite a lot when typing on a lapcom or other regular keyboard, because it’s so fast and easy for me.  It’s faster than speaking for me, and it’s certainly faster than using the “smartphone”, even not counting all the typos that occur when using the latter***.

I continue to toy, from time to time, with trying to type a tome using Google Docs.  But its interfaces, while okay for writing blog posts, don’t feel quite right for writing fiction, at least not for me.  It’s probably a stupid notion anyway.  I don’t really expect ever to write any more fiction.  That’s not a good thing, but then again, very little is.

I’m actually getting irritated that my lapcoms and my desktop computer at work are beginning to show some signs of their ages, and I fear that they may need to be replaced soon.  Worse, my smartphone is getting a bit laggy, and I cannot upgrade it to the latest operating system so I can no longer use my banking app on it.

But I really don’t want to go through the hassle of getting and setting up a new phone (or computer).  It’s so irritating and so uninteresting.  I actually had the general, vague hope that I would not live long enough to need to upgrade my computer(s) or phone again.

Honestly, the constant displacement of entropy that comprises the process of staying alive at so many levels is just dreary and almost laughable.

Speaking of laughable, I’ve been thinking about trying a personal experiment:  I’ve been thinking about trying to go without laughing for a day or a week or something along those lines****.  I just wonder what effect that would have on my experiences.

I tend to overdo it with jokiness, and I tend to partake in a lot of comedy of various kinds, almost in a desperate way.  It could even be be considered an addiction, or at least like a substance abuse problem, including its own abstinence syndrome:  I used to have the experience that, after reading a Dave Barry book, I would crash and feel quite depressed and morose for a while, as if in withdrawal from laughing so much.

Perhaps laughter is one of my means to try to hide from reality, to hide from the present, to try to hide from me.  I haven’t committed to the idea, yet, but it does intrigue me.  Most of my literary heroes do not spend a lot of time laughing.  And I have few, if any, real world heroes, but such as I have, though far from agelastic, are not prone to joke about a lot or get giggly or silly, like I do.

Those facts may be irrelevant for me, of course.  I am a unique snowflake (just like all the other snowflakes), and I don’t necessarily have the same attributes as those I admire, especially fictional characters.   But it is intriguing as almost a kind of fast, but one in which I would abstain from laughing rather than from food or water.

I’ll keep you posted on my effort (probably).  If you want to give me your input, you’re welcome to do so.  In the meantime, I hope you have a very good day.  Don’t stop laughing on my account.

TTFN

[P.S., a thought just occurred to me, because the words of an old ABBA song (misheard, as I just realized) started going through my head:  If you think that there’s nothing you can’t do, that anything is possible, then all the troubles that continue in the world are implicitly your fault, because you could have solved them.  After all, there’s nothing you can’t do.  To be fair to them, ABBA was actually singing “there is nothing we can do”, which I had misheard and misremembered as “can’t” for decades.  Indeed, their song goes pretty well with parts of this post, especially the song’s first few lines.  Who would have guessed?]

*I almost said “my traditional Thursday podcast”.  How’s that for a weird mistake?  I’ve certainly toyed with the idea of a podcast at times, but that requires more time and editing and so on than my little five-minute or so snippets of audio.  But I do like to listen to podcasts, at least about topics that interest me.  Perhaps it was a Freudian slip.

**I accidentally typed “sunconscious” here, originally, and it seems like kind of a charming word, so it’s a shame it doesn’t really mean anything.  But one certainly doesn’t want a conscious sun, as the dubious Doctor Who episode “42” tried to warn us…or something like that.

***You might almost think that word means “one who lats”, but of course it’s not that kind of word and has close kinship with “later” and its ilk.

****I.e., a period of time.

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Infinite distractions have limited effectiveness

It’s Wednesday now, and I’m writing this post on my lapcom.  There’s no particular reason I’m doing so, though as always, a cause or causes surely exist(s).  I just felt the impulse to take the lapcom back to the house with me yesterday afternoon, and I saw no reason not to indulge that impulse.  That’s about it.

It’s the 2nd day of September, which should come as no surprise, since yesterday was the 1st day of September.  Numbers don’t necessarily have to be put in any given order—and indeed, one cannot properly order the Real numbers, because there is an uncountable infinity of them between any two points on the number line, however arbitrarily close you might want to choose them—but the ordinal numbers have an inherent order.  Thus the name.  Duh.

I often marvel at the cool facts about uncountable versus countable infinities.  Think about it.  The “natural” numbers represent a “countable” infinity because you can make progress counting them and, if you had infinite time, you could in principle count them all, though it can be a bit mind-bending to try to imagine what that could really mean.  But it is true, mathematically speaking.

It’s also true that this infinity, the so-called countable infinity (ℵ₀, or “aleph nought”), is matchable one-to-one with all other countable infinities.  You can assign a natural number to every integer, and to every even or odd number, and to every rational number (i.e. every fraction) and so on.  Therefore, they are the same “size” or “cardinality”.

In case anyone wonders why that point might matter, all one has to do is to try to list the Real numbers (designated with ℝ).  These are all numbers including the integers and the rational numbers, but also all irrational numbers, i.e., numbers that can’t be expressed as a ratio of any whole numbers or integers.  The latter set includes pi (π) and e (e) and phi (φ, the so-called Golden Ratio) and so on, but these are simply a taste of what’s available.  All of these numbers have a potentially infinite number of digits* after the decimal point, and those digits do not have any repeating pattern, for if they were consistently repeating, they would be rational numbers.

Cantor’s “diagonal proof” demonstrates that there are more Real numbers than there are integers (or any other aleph-nought level infinities of numbers).  I won’t get into it here—it’s not that difficult, and it’s very clever and rather wonderful, but it would take a bit of time, so I just put a link to it for anyone who is curious.

What’s more, once we realize that fact and think about it a little, we realize not only that the Real numbers are uncountably infinite, vastly more infinite than the integers of the natural numbers, but something even more mind-boggling:  Between any two numbers you can choose, however arbitrarily close you want to make them, there is an uncountable infinity of Real numbers.

You could pick two numbers that have eighty-thousand zeroes after the decimal place before you start getting non-zero digits—such numbers would be far closer together than any separation we could possibly physically measure using any sensible unit of measurement—and the number of Real numbers between them is much, much larger than the number of integers, and is indeed equal in size to the Real numbers.

You can kind of understand why some of the people who worked with notions such as these, like Cantor and Gödel and so on, got pretty loopy at times**, though it is not possible to say definitively whether the mental atypia were caused by too much contemplation of infinities or were the reasons why such people got into studying them, or were pure coincidence.

Of course, the above raises for me the question whether the infinity of the Complex numbers is larger than that of the Real numbers.  I don’t believe it is***; I’m not looking it up to confirm right now, but I am just going to think it through out loud, as it were.

A complex number is made of two “parts”:  the so-called Real part and the so-called Imaginary part.  But the Imaginary part is just i, the square root of negative one, multiplied by some Real number.  So, each complex number is made up of two Real numbers, but two real numbers can be expressed as one Real number in various ways.  So, the Complex numbers have a higher dimensionality than the Real numbers (2 versus 1), but they have the same cardinality, as the terms go.

There are higher versions of countable infinities used occasionally in mathematics.  I find them a bit more contrived than the preceding, but perhaps that’s just because I’ve never had the call to use them nor to play around with them.  These are your ω and ω +1 and so on.  The idea behind it is that you can arbitrarily say that, once you’ve counted all the natural numbers (for instance), whatever the hell that might mean****, you can go on and count some more, calling the next number after infinity ω (that’s a small-letter omega, the counterpart to Ω, which is kind of a cooler-looking symbol).

Anyway, that’s enough of me nattering on about matters that don’t really ever seem to interest anyone around me other than me—I guess I’m not really around me, so I didn’t really need to add to caveat—but about which people sometimes smile indulgently for a moment or two, since I sometimes get rather excited when mentioning them.

This doesn’t happen often, though.  By which I refer to occasions on which I get excited.

This is all just distraction, anyway, and that’s getting more difficult for me over time.  I don’t really feel that I’m going anywhere or getting anywhere.  I’m just killing time while waiting for something to kill me.  I hate the world (by which I mean the universe, and maybe even the Universe), I hate my life, and I hate myself.  This is not a mood (though it entails a mood at times); this is a judgment, this is my (provisional) conclusion, this is my strongly held opinion.  I need to stop running from it; I suck, and so does everything and nearly everyone else.

Present company is excluded, of course (not counting me).  Indeed, I wish all of my readers the very best possible of every possible thing for which things can be the best.

*Though it is interesting to contemplate whether one can take any arbitrarily large run of digits of, say, π and always be able to find the matching sequence in any other irrational number.  I don’t know the answer to that question, so if anyone does, please let me know.

**Poor Gödel became convinced—or at least afraid—that someone was trying to poison him, or might try to poison him, and so he would only ever eat food prepared by his wife.  There is something rather charming, almost romantic, to the notion that he distrusted other people, in principle all other people, and yet he believed in his wife completely.  I wonder if she was flattered.  It was tragic, though, because when she became ill, he stopped eating, and he eventually more or less starved to death.

***It isn’t.  I eventually looked it up just to confirm (or refute) my judgement.

****You can say this, in a way, because (for instance) you can count the integers by first counting the positive integers, to positive infinity, and only then starting to count the negative integers toward negative infinity.  This means you can continue counting after you’ve counted an infinite number, at least in a sense.

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Audio post about a new book I’m reading

This post relates somewhat to my regular post from earlier today.

Here is a link to the book I mentioned.

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Memento mori

Well, it’s the first day of a new month today.  September is that new month, of course, and despite its seven-related name, it is our ninth month, pushed back partly because of the egotism of two ancient dictators and those who revered them.

Not to say there weren’t things to admire about Julius Caesar or even Octavian (AKA Augustus, whose earlier name meant “eighth”, which at least suits the current month order).  But it is a fact that they are both just as dead as the veriest plebian or slave in their “empire”; their bodies are dust in the wind, if that.

Yes, we remember them‒a bit‒but that does them absolutely no good.  They returned to their initial state, as Mark Twain discussed at least once:  that he had been dead for millions of years before he was conceived, and it had not inconvenienced him in the slightest, so there was little to fear about returning to that state.

If you want to be remembered as a Roman Emperor (it’s probably too late for you to do that now, but let’s consider it for the sake of argument), be remembered like Marcus Aurelius, whose contributions to Stoic philosophy and the nature of a good life are still guiding and inspiring people today.  Aurelius continues actually to have effects even millennia after his death‒real ones, consequential ones, not just having people know the names of months that are named after him*.

Marcus Aurelius’s words continue to help stimulate thought and to help with psychological equanimity, and they do so in more logically defensible ways than those of most religious patriarchs (largely because the vast majority of religions are mere hodgepodges of various kinds of bullshit).

Of course, it’s almost certainly all futile.  All of it will be entirely effaced in all but the most theoretical sense (e.g., the law of conservation of quantum information) by the passage of time, as everything returns to the state mentioned by good ol’ Samuel Clemens, who is just as dead as Julius Caesar, himself.

I mean all this even if somehow “intelligent” life on Earth survives and advances long enough and successfully enough to become cosmically noticeable or even cosmically important (not a very high likelihood) and even if they discover or create ways to make the universe survive indefinitely or to make new universes or whatever.  There is still simply the matter of the signal and the noise.

This is the counter to the sometimes-heard claim that “the internet is forever”.  Well…maybe, but I doubt it.  Even if it is, though, your most embarrassing upload is already long-since unnoticeable amidst the cacophony.  You are merely one face in a crowd of billions, most of whom spend most of their time merely looking at themselves.

We live in troubled times, as the saying goes, and it is certainly true now.  But it has always been true, since the very origin of life itself.  Life is trouble, it has always been trouble, and I strongly suspect that it will always be trouble.  C’est la vie, c’est la guerre, c’est la mort.

The only state in which there is no suffering is death.  The state of Nevada may try to claim that spot, what with Las Vegas and Reno, legal gambling, legal prostitution, and whatnot, but just go wander out into the desert for a bit and see how it feels.  Don’t even get me started on California or New York or Florida as being states without suffering!

Okay, enough with the stupid, homonym-based jokes.

It is, whatever you call it, the beginning of the month in which, in the northern hemisphere, summer transitions into autumn (or fall).  Autumn is my favorite season, and not just because of the autumn people and Cooger and Dark’s Pandemonium Shadow Show**.

No, there are many things I like about autumn, aesthetically.  It has my favorite holiday, and it has my birthday, and up north it has the lovely changing of the leaves and so on.  In Florida, of course, the good things about autumn are strongly attenuated, but Florida has that effect on many of the pleasant things in life.  At least the weather begins to moderate in Florida in the autumn.

Of course, one of the two most important events in my life happened in September, shortly before the beginning of autumn.  And, less important, but still fun, September 22nd is the day Frodo set off on his journey in The Lord of the Rings.  It’s also his (and Bilbo’s birthday).

Frodo and Bilbo are fictional characters, of course.  Nevertheless, I strongly suspect that many millions of people know far more about them than they know about Julius Caesar or his nephew.  Those two imperators are at least as “fictional” now as entirely made-up characters.  Not much cop, this Roman Emperor lark, is it?

Well, have an enjoyable day if you can.  You might as well.

*I wonder how many people in the Western world even know where the names of August and July originate.  I would not be surprised if I learned that a higher percentage of Japanese people know about the etymology of those two fully summer months (or those two fully winter months in the southern hemisphere).  But what proportion of westerners know anything about Amaterasu or Tsukuyomi?  I’d bet it’s higher now than at any time in the past, but I’d also bet that it’s still mighty low.

**”We are the hungry ones.  We are drawn by your torments like dogs in the night, and we do feed…and feed well.”

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“He had gone often alone into the void places seeking the Imperishable Flame”

It’s the day of the moon today.  By which I am not referring to Doctor Who, series 6, episode 2 (the second part of a two-parter) which was called The Day of the Moon, if memory serves.  That was a good episode, and it tied into a long arc of a storyline that Stephen Moffat had put into motion in series 4, when he wasn’t even the show runner yet.  But it has nothing to do with my first sentence, today.

No, I am simply referring to the fact that this is Monday, the weekday named (in English and some other languages) for the moon.  It’s also the last day of August in 2026.

I occasionally wonder, what if Tsukino Usagi, AKA Sailor Moon, recognized that her name was associated with the first day of the work week (and of the school week).  I wonder this because Usagi is notoriously not fond of having to go to school.  She’s also something of a crybaby, and I can just imagine her lamenting the fact that her Sailor Senshi name is linked to the start of the work week.  I can also imagine her being jealous of Sailor Venus, since in Spanish at least, that is associated with Friday (Viernes).  Sailor Venus probably wouldn’t care.

And it also only just occurred to me to wonder what had happened to Sailor Pluto once Pluto was reclassified as a dwarf planet*.  I mean, if she’s really more associated with the God of the Underworld than with the now-dwarf planet, as does seem to be the case in the manga and anime, then I guess it’s fine.

Perhaps Sailor Pluto wryly smiled and shook her head indulgently upon learning that the humans had named a very small, very icy object among countless other similar objects, with a highly eccentric orbit that isn’t even in the same plane as that of the planets, after her namesake.  And she might indulgently shrug upon hearing of the more recent reclassification.  She probably didn’t care much, but she might well have known.  She was one of the Sailor Senshi who never seemed really to revert to a truly mortal form nor to have been reincarnated as a normal human.

Okay, well, that was a weird little discursion that handily demonstrates some aspects of my rather niche nerd status.  I went from Doctor Who right over to Sailor Moon (while making passing references to planetary astronomy).  That’s fine, though.  I really like both…series, sagas, stories?  I’m not sure the best word to use to encompass them both.  Perhaps “universes” is good.

It does annoy me that we now use the word “universe” when referring to things that might be merely one of many, of perhaps infinite, things, when “uni” means one**, with the implication that it is the only one.  I wish we could find a better term, so we could go back to using Universe, with the inherent capital “U”, to refer to whatever encompasses everything.

I had intended to use the term “metaverse” in my own stories, such as The Dark Fairy and the Desperado, that dealt with many planes and subsections of existence, but then Fuckerberg stole the term.  And I did start thinking about it and using it way before he arrogated it to his pathetic little virtual empire.  Then I had to switch to “Omniverse”, which may actually be a more accurate term than Metaverse, but it doesn’t sound as good in my opinion.

So, yeah, now (even in legitimate physics) there is the general use of (small u) universes, which is almost inherently contradictory.  Many Worlds may be better, but its a little nonspecific.  There are, many worlds, many worlds just in our solar system.

Maybe the term “polyverse” might work?  Perhaps “facets”?  I don’t know.  I suppose it doesn’t matter much.  It’s just me dwelling on and being bothered by things that don’t really even register to most other people.  Thoughts unlike those of my brethren, indeed.

I hope you have a great day.

*I was resistant to the notion when I first heard about it, from my kids as it turns out.  But I looked into it, and I heard the arguments‒perhaps most accessibly addressed by Neil DeGrasse Tyson‒and I was convinced.  It turns out that the international astronomical community doesn’t lightly go and change the designation of something, knowing there will be many pissed off Boomers and Gen-Xers (Hello!), but does so only with very well thought-out reasons.

**Though, to refer to cartoons again, Uni was also the name of the little unicorn on which the barbarian character doted in the cartoon Dungeons and Dragons from way back when.