Mathematics

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Blogger that I am, I am even poor in thanks; but I thank you

Hello and good morning.  It’s Thursday (obviously) and I am writing this on…my lapcom!!  That’s right, I’m pleased to say that after all my discussion yesterday about trying to give my thumb bases a break, I maintained the impetus into the evening to bring the mini lapcom back with me, and I am now using it to write this post.

I’ve probably already said more about this than was merited, but I’m rather pleased with myself.  That doesn’t happen all that often nowadays—me being pleased with myself, I mean—so I am trying to indulge it as much as I can, hopefully without overdoing it.

Let’s see, now, is there anything else to talk about today?  Hmm.  Nothing comes to mind right off the top of my head.  Perhaps I should just call it good and wish you all a good day and say “Ta ta for now” in abbreviated form.

But, no, I don’t think I’m going to do that.  Not having anything to say has rarely stopped me (or lots of other people, I suspect) from running off at the keyboard/mouth.  I don’t know if that’s healthy or good or not; probably there is no specific absolute “value” slot or slots in which to put that fact.

The goodness (or badness) of a thing is often largely dependent on that for which some particular person might use it, or the semi-arbitrary tastes of any given person.  But as for absolute goodness or badness, I’m not sure those concepts ever fully apply.

Even nuclear weapons can at least be argued to have had some modicum of benefit.  It’s an ill wind indeed, as they say, that blow no one any good.  There can be little doubt that the atomic bomb shortened the war in the Pacific in World War II, and that was good for Allied soldiers, though clearly not good for Japan, at least not in the short term.

Then, of course, there was the Cold War, which was terrifying and had the potential to send civilization back millennia or more.  Thankfully, it did not.  It’s a bet I wouldn’t encourage the world to make again—that the doctrine of Mutually Assured Destruction would prevent most conventional wars that might otherwise have led to the death of many millions and the immiseration of millions more, albeit without destroying civilization in the process—but we got away with it that time (so far).

So, yeah, good and evil are largely viewpoint dependent, though they are not absolutely subjective.  I suspect there are quite a few things in the world, or in the potential of human behavior, about which if you surveyed many hundreds of thousands of people, the very large majority would agree on whether they were generally good or generally evil.  Child sex trafficking comes to mind as one of those more or less universal evil things, I suspect.  On the other hand, saving innocent children from violence or disease or catastrophe would probably pretty generally be considered good.

But of course, all this is very anthropocentric (or anthropoidocentric, maybe).  If you were to canvas the opinions (if they existed) of various sexually transmitted viruses and bacteria and protozoa, they would probably be in favor of all forms of sex trafficking, and of indiscriminate, unprotected sex in general.  It might be their equivalent of clear-cutting the Amazon rain forest to make room for non-native crops.

Blowflies would surely be quite satisfied, at least in the short term, if humans had massive, bloody wars that left bodies strewn, unburied, in the streets.  But humans—selfish bastards that they are—are unlikely to do such a thing just because it would be nice for the flies.  They might do it for other—arguably no better—reasons, but not for the flies.

Shakespeare said (or, well, Hamlet said*), “there is nothing good or bad, but thinking makes it so.”  And, of course, in Paradise Lost, Milton’s Satan says, “The mind is its own place, and of itself, can make a Hell of Heaven, a Heaven of Hell”, though I may have left out some archaic contractions.

To be fair, we should expect Satan to say something like that, shouldn’t we?  And we should not give too much credence to his viewpoint.  Hamlet, on the other hand, is much more morally ambiguous than, say, the leader of the fallen angels, so it’s more convincing when he says his line during a semi-philosophical interaction with his two former friends.

Well, I feel that this has been a rather peculiar blog post, even for me.  I suppose one might expect that, if one normally wrote peculiar blog posts, one might expect that a “peculiar for me” blog post by such a person would be a “normal for someone else” blog post.  But that intuition is misleading and usually wrong.

There are many more ways to be “peculiar” than there are to be “normal” in most cases, so, like the phase space that can be used to diagram entropy, when things move from one spot semi-randomly to another, they are much more likely to become more peculiar than to revert to more normal.

The other way only works in strictly one-dimensional situations, though in those situations it is worth noting.  For it is a fact that, ceteris paribus, the lesser of two evils is the greater of the two goods, just as a less negative number is a more positive number, by mathematical definition.

On that, I’ll draw this lapcom blog post to a close, with a deep, sincere thank you for reading:

Thank you, deeply and sincerely, for reading.

TTFN

*You cannot assume that an author agrees with a point made by one of the characters in the author’s works.  This is true of many a celebrated quote.  The famous Oscar Wilde line “I can resist anything but temptation” is spoken by Dorian Gray, who is not a particularly good person, and probably does not represent Wilde’s considered ethical opinions.

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Reflecting on indirect, unconscious drawbacks and their impacts, and other weird thoughts

Well, there’s no lapcom here today, alas.  I just didn’t feel enough drive or urge or energy‒or perhaps impetus‒to bring it with me when I left the office.  Maybe I should say that the magnitude of the vector for taking the lapcom with me was overbalanced by the net vectors that summed up to pushing in the other direction in this (very) high dimensional phase space that is the description of the state of my nervous system and its effects on my activity.

You’ve heard of Hilbert Space*?  Well, you can call this “Robert Space” if you wish.

Anyway, so, yeah, I’m writing this on my smartphone today, and I’m already regretting it a bit.  The arthropathy in my thumbs is complaining rather vociferously (and quite metaphorically) just from the little writing I have so far undertaken.  So, hopefully, I will be able to keep this relatively short today.

That doesn’t always happen.  Like a lot of people, I suspect, sometimes when I get rolling in habitual behavior, I keep barreling through even when I can feel the negative effects already as I do it.

Conversely (or whatever the proper term is), it has occurred to me just in the last day or so**, that my thumb pain may be part of why I haven’t been playing guitar.  It’s not that, when I think of playing it, it occurs to me that my thumbs hurt and so I consciously choose not to do it after weighing the fun versus the pain.  If it were that conscious, I would (clearly) know it already.

But the thumb pain can make the process of playing less pleasant, and that can decrease the emotional reward and reinforcement I get from doing it, and so, in the fullness of time, make me less likely to do it in the future.  It’s sort of a very low-level application of the aversion training from A Clockwork Orange.

If so‒it’s strongly possible, but I cannot swear that it’s really, definitely the case‒that may mean that what I really ought to do to increase my playing is to try to increase the magnitude of that “take the lapcom home” vector.

But, of course, it’s not some axial vector, aligned along only one unit vector, with a cross-product (or outer product, I think, if memory serves) of zero.  And it’s not a fundamental vector, with only itself as its input, either.  It’s a vector that is, itself, the sum of many vector inputs (and heck, maybe some scalars, I don’t know, but I don’t think tensors would apply to this situation), some of which would probably surprise me.

Still, it might be worth a try.  It’s not as though the thumb arthropathy is something I like and want to keep.  So, if I can find ways to counter it, maybe I can see what effect that has on my tendency to play guitar, and thus, finally, on my tendency to sing.

I used to sing a lot, especially when I commuted by car and could play various CDs (but not treasury bonds, ba-dump-bump) and sing along but no one could hear me.

Even when driving my scooter*** to and from work, I had a Bluetooth enabled helmet, linked to my playlist on my phone.  When you sing inside a motorcycle helmet, in traffic, you don’t need to worry about being overheard.

Now I don’t commute that way, and since I have housemates, I don’t often feel comfortable just singing when I’m in my room.  But early morning in the office, when playing guitar, it can be good.  That is, as long as playing guitar is good, which is apparently not the case for now.

Oh, well, I guess I shouldn’t dwell on it.  Everything is futile, everything is imperfect, everything is chaotic, everything is entropic.  And to paraphrase the Stones, I’m neither waiting on a lady nor am I waiting on a friend.  I’m just waiting on the end.

Speaking of the end…

*Maybe you haven’t.  Let me know.

**You wouldn’t think it would take so long for this possibility to occur to me.  I mean, I’m reasonably bright, and the connection is not a distant or particularly occult one.  Unfortunately, you cannot choose to think of something before you have thought of it.  Likewise, you cannot choose not to think of something once you’re thinking it, but you can let such thoughts go and do your best not to identify with them.  Oh, and also, by the way, no one has ever been able to “unsee” anything, ever.  The expression is idiotic.  Also, there’s no hour (or other period of time) in your life that you’re going to get back.  Noting that fact about some specific, unpleasant hour just makes you sound semimoronic.

***I say “scooter” because I guess that’s the official term, but it was a 650 cc Honda Silverwing, so really it was a full-on motorcycle that just had continuously variable transmission.  I’ve always been clumsy with manual transmission vehicles.

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‘Tis not so deep as a well, nor so wide as a blog-door; but ’tis enough, ’twill serve.

Well, hello and good morning to you, too.  It’s Thursday, and so I have used a version of my “traditional” Thursday blog post opening, and I will use a traditional Thursday ending.  Further bulletins as events warrant.

I’m glad that at least some people liked my rather atypical* blog post yesterday, in which I basically just described what I had played (and sung) the morning before.  Somewhat ironically, I did not play, nor did I sing, yesterday morning, and I don’t expect that I will do so today.  This is mainly, or at least pivotally, due to my chronic pain.

I don’t tend to talk that much about my chronic pain anymore, or at least not as often as I think I used to talk about it.  I don’t know, maybe I talk about it roughly just as much as I have all along, at least in the time since this stopped being a Thursday-only blog.  Still, it feels to me that I’ve been discussing it less, because I fear it’s not only boring for people but also depressing, and I am depressing enough without talking about pain.

But my chronic pain has not diminished, though it is variable from day to day and moment to moment.  There are times when I feel that something I’m doing is making it improve, but it usually ends up just to have been a normal part of whatever complicated cycle the pain intensity and character undergoes.

There are cyclical and periodic phenomena at nearly all levels of the cosmos, it seems.  Biological processes, which often involve thermostat-style feedback controls, are far from being an exception.  So, chronic pain goes up and down‒in a complex pattern that has differing periods and amplitudes overlapping** each other‒in ways that can be particularly misleading if you’re also trying to reduce it by various means.  Also, the things you try, even if they don’t truly work, can nevertheless affect the periods and amplitudes of one’s pain cycles.

Anyway, so, yeah, I’ve been having a lot of pain over the last several days‒more than average, though I am almost never not in pain.  I have also been eating an unusual number of legal CBD/delta 9 gummies.  They don’t seem to make the pain go away, but they change how I respond to it a bit, decreasing the amount of spasm and disordered walking and posture and tension and grumpiness that I experience, at least a bit.

But they make me groggy, if that’s the right word.  They also make my time sense rather weird, though that’s rather interesting, since it calls attention to the subjectivity of the experience of time*** which I discussed the other day, I think.  They also engender some minor perceptual illusions, especially auditory ones, possibly because of my poor hearing, but that is also rather interesting.

So, they make my pain experience a bit less intense and maddening, and they make it feel less as though one or the other side of my body is being forcibly twisted and contorted as I move, which is often how this shit feels.  At least, they make that sensation less stressful, and they seem to decrease some of the muscle spasms.

They also make my mathematical figuring and other mental processes feel less reliable.  I already have a seemingly deficient sense of being right‒for instance, no matter how often my mental figuring of sales amounts and so on is shown to be correct, I never for a moment feel secure enough about it not to check a few times using the computer.

Even then, I feel somewhat worried and uncomfortable, but sooner or later, I have just to go on to the next thing, because I will never be able to convince myself that I am correct beyond even a reasonable doubt, let alone to mathematical certainty.  It’s like the classic OCD thing where one has to keep going back to the house to check that one hasn’t left the stove on even though one empirically knows they have, or things along those lines.

To be clear, the gummies don’t appear to affect the quality of my mental work‒as far as I can tell, I can do mental figuring and other, similar processes as quickly and as accurately with it as without it.  But it makes me feel less sure, if anything, than without it, though I guess it also makes me slightly less anxious about being wrong.

It also takes away some of my mental focus, and also generally makes me feel a bit less motivated.  Perhaps, if I were able fully to embrace that lack of motivation, I might eventually come out the other side of the phenomenon and have a new, purer kind of motivation, one not born of constant tension and anxiety (and even some paranoia).  But I don’t know how to accomplish that, and even if I did, my credence in the possibility of it working is not nearly high enough to make me willing to try it.

Anyway, so, these are some of my thoughts on why I didn’t play or sing yesterday, and why I almost certainly won’t play or sing today.  It’s also part of why I don’t write fiction or draw or paint, and also part of why I don’t finish teaching myself professional level general relativity and quantum mechanics.  Yes, my interests tend to go all over the place and get in each other’s way even when I am at my best.  But even I know that I could accomplish so much more, so many more interesting things, if I were not in significant pain every fucking day.

So, yeah.  I’m out of it more than usual, which I don’t like, since mental acuity is my primary strength, and the thing I like most about myself.  That may not be a high bar to clear, but still, it’s what I have.  And I’m enervated and discouraged, and I’m tired of bothering to do anything, but I can’t seem to convince myself that, no, the stove is not still on, it doesn’t need to keep being checked.

What a pain.

TTFN

*I’m not sure if there really is a typical blog post type for me, so maybe “atypical” isn’t a very useful adjective here.

**Fourier (I think he was the one) famously showed how any kind of waveform can be produced by the superposition of sine waves of various periods and amplitudes, and this insight has tremendous impact on the nature of quantum mechanics and its particular types of superpositions.  It’s also the deeper explanation of the Uncertainty Principle.

***This has no effect on actual time itself, of course, at least based on all the best information we have about such things.  It’s just a perfectly understandable product of the nature of a biological computer’s (multiple) means of keeping track of time and reporting on that process to the rest of that biological computer (i.e., the brain).  It’s simply not true that experience is reality.  One’s experience is part of reality, of course, and need not be treated dismissively, but while toilets are necessary in any office skyscraper, it would be absurd to say “toilets are skyscrapers”.  Unless, of course, one built a toilet 50 stories tall.  Even then, that’s just one edifice.  So one could say, “that toilet is a skyscraper” legitimately, but that doesn’t make it any more sensible to speak categorically about toilets being skyscrapers.

This is not about buildings and plumbing.

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Birthdays, Holidays, Mythology, Vectors, Maxwell, and a Beatles song…

It’s Friday again, the 25th of September.  There are only three more shopping months until Newtonmas.

Yes, I know that it isn’t strictly accurate to celebrate Newton’s birth on “Christmas”, because Newton was born on December 25th according to the Julian calendar.  The Gregorian calendar had been invented already; England just hadn’t adopted it (partly because it was a Catholic invention).

But Newton’s birthday was a lot closer to December 25th than Jeshua bin Josephus’s was.  According to what I’ve read and heard from scholars who specialize in such things, the Nazarene was born sometime in the summer.  Oh, and also, there was no census requiring men to return to their towns of birth ever promulgated by Caesar Augustus, not according to any single official record of any kind.  The author of that gospel just threw that in to provide an excuse to have Jesus born in Bethlehem, so that his birth could comply with certain messianic prophecies.

Yes, the so-called fulfillment of prophecies that is used as “evidence” that Jesus was the messiah was added after the fact, by people who never knew Jesus, writing decades (or longer) after his death.  This shouldn’t surprise anyone, really.  Religions in general don’t tend to be very coherent and consistent; they just sort of happen by a kind of memetic evolution, and they are made of various hodgepodges of prior myths and folklore and post-hoc shoe-horning into supposed prophecies.  They bear no hallmarks of having actually been created and/or delivered by supernatural entities of any kind, let alone omniscient ones.

I certainly don’t think any deity is responsible for the fact that today is Friday, so I will not be thanking one, whether God or Brahma or Amaterasu or Quetzalcoatl or Odin or Jupiter* or Whatever.  Also, I am scheduled to work tomorrow, so this is not the end of my work week, anyway.

I’m relatively pleased to inform you that I’ve been reading a decent book for the past few days (not continuously, ha ha).  It’s called Vector, and it’s about (oddly enough) vectors‒the mathematical entities that have magnitude and direction, among other things.

It follows the lives and insights and advances of people like Hamilton, who brought us quaternions (which are very cool) among other vector insights, and various other people who developed the mathematics and science of vectors (we will be getting to tensors and so on before long).

Currently I’m in the midst of the discussion of Maxwell and his astounding development of the principles of electrodynamics, including his recognitions that electricity and magnetism would, if oscillating, produce a self-propagating wave that would travel at precisely the “speed of light”, by which he deduced that light is in fact an electromagnetic wave.  (This accomplishment is one of the most impressive in the history of science, and it is a tragic injustice that Maxwell’s name is not as well-known as those of Newton and Darwin and Einstein and Schrodinger and so on.)

Indeed, the very invariance of the speed of light as revealed by Maxwell’s equations was one of the things that led Einstein to postulate that the speed of light is an absolute constant in all reference frames, leading to Special Relativity (and eventually, even more impressively, to General Relativity, which will make use of and extend the vectors and tensors and matrices to which we’re gradually being introduced).

It’s very exciting.  Honest, it is.

And, of course, there’s the very cool fact that quaternions ended up being useful for describing the curious properties of particle “spin”, including the fact that, for spin ½ particles (which are “fermions”), if you want to rotate it and get back to the state in which you started, you have to rotate 720 degrees, not 360.

If this seems counterintuitive, just think about a Mobius** strip.  Are you thinking about it?  Good.  That should distract you nicely from trying to grasp the nature of fermion spin.

Kidding!  It helps to show you how the notion is not something deeply bizarre or seemingly nonphysical.  With a simple Mobius strip, going around 360 degrees will land you on the opposite side*** of the paper from the place where you started; you need another full trip around 360 degrees to return to where you began.

I’ve occasionally thought that it would be fun to set up an art gallery or other kind of museum with a single “circular” corridor that crosses over itself (by going up or down a level gradually) and that requires visitors to go around twice to get back to the entrance.  It wouldn’t really be difficult to pull off, and it would be much better (I think) than the Guggenheim layout.  Unfortunately, I don’t have the resources to commission such a gallery, so I’ll leave that as an exercise for the reader.

Don’t let me down.

Okay, well, that’ll about do it for today.  I should be writing a post tomorrow, so if that’s something that pleases you, then you can safely and reasonably anticipate being pleased, exclusis improvisis.  In the meantime, I hope you have a good day.

*Though the planet Jupiter deserves some thanks for helping make life on Earth more possible and stable by sweeping up a lot of the stray space debris that might otherwise have slammed much more often, or much more persistently, into Earth.  But, being a planet, Jupiter doesn’t require thanks or praise to do what it does.  It just requires physics.

**He shows up in the book, too.

***Though the Mobius strip has only one side, really.  And a Klein bottle has a continuous, single surface encompassing its inner and outer aspects (i.e., the inside and outside are the same), and crosses through itself without breaking that surface.  At least, it does that in 4 spatial dimensions.  Our three dimensional Klein bottle models are shadows, if you will, of a true Klein bottle, much as a drawing of a Mobius strip is just a shadow of such a strip.

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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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“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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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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The title of this blog post is wrong

Well, to quote Emperor Palpatine (in Return of the Jedi), “Everything is proceeding as I have foreseen.”

Now, admittedly, I haven’t specifically foreseen very much, other than trivial things that are foreseen without any conscious thought.  But I did foresee (and did predict*) that I would go to the office today and that I would write a blog post today, which is what seems to be happening.  Hopefully, the Death Star will not be blown up around me.

Anyway, yeah, I’m going in to the office today.  Huzzah.

Okay, with reference to the preceding sentences:  Someone needs to tell all the word processor programs that just because we have a compound word “into” does not mean we cannot use the expression “in to” without it being a mistake!  The two things do not have precisely the same meaning, and the split words are in any case more fundamental than the compound word.

You’d think the editing software was worried that “in” and “to” were like neutrons or something, and that if you separate the compound words from each other they’ll just…decay with a half-life of about ten minutes, like free neutrons do.  Therefore, it’s got to keep them bound, because neutrons in a nucleus are really stable and can last until, I don’t know, the protons decay, if that even happens**.

Perhaps I’m overly impatient, but I get frustrated by the fact that a lot of the time, perhaps most of the time, when Google Docs gives me its grammatical suggestions, I have to choose the option “Suggestion is wrong”.

What bothers me about this‒one of the things‒is that I am pretty sure that I have more grammatical expertise than most people around me, and maybe more than most of the people who use Google Docs.  So, out there in the world where people are using it, mostly they are not correcting it, but are allowing it to correct them without even critically evaluating it.

And so, far from such grammar checkers improving people’s grammatical skill and knowledge, they weaken it.  One does not, simply by driving 26 miles every day, get in shape to run a marathon****.  If anything, one’s physical fitness tends to atrophy, and if one only gets around by motor vehicle, one tends to become far less fit, less healthy, weaker.

Of course, training too much can damage a person’s fitness as well.  Like the Laffer curve, we find our peak benefit somewhere in the middle of the arc.

Well, it looks like my footnotes today are even longer than the main body of this post.  I suspect that they are also somewhat more interesting than the main body of the post, but interestingness (interest?) is in the mind of the beholder, so only you can judge that.

I hope you all have a very good day today and a very good day tomorrow.  You should rest and prepare yourselves, because come Monday, I will be writing another blog post…as always, exclusis improvisis.

*It’s interesting that this word, which has a similar compound structure to “foresee”, is clearly of at least slightly different origin or evolution, linguistically.  Fore see:  to see before, to see ahead of time.  Pre dict:  to speak before, to speak the thing before it happens.  We pre dict but we don’t fore dict.  Likewise, we fore see, but we don’t pre see.  Curious.

**There are various theoretical reasons many physicists think protons should decay eventually, but that the half life is predicted to be something like 10 to the 35th or 10 to the 40th years or some such.  Now that’s a long half life, obviously.  But…there are a loooooot of protons.  There are so many protons (they’re everywhere, believe me, you just can’t seem to get away from them) that even if it will take 10 to the 40th years before half of them would decay, we should still be detecting some of them decaying now and then, if we look***.  But “we” have been looking for quite a while, and we haven’t been able to detect any instances of proton decay whatsoever so far.

***Think of it this way.  If there were a lottery in which to win you had to match 10 numbers, each of which could be between 1 and 100 (nonrepeating), the odds of matching one ticket would be roughly one in 6.28 times 10 to the 19th power, or one in 62,800,000,000,000,000,000 (sixty-two quintillion, 800 quadrillion).  Even so, if you had 10 to the 20th people (a hundred quintillion) playing it every week, you’d expect to have fairly frequent winners despite the long odds.  The chances of winning for one individual are so slight that they might almost as well be waiting to quantum tunnel through their front door, and yet the odds of there being no winner may be only about a coin flip in any given running of the lottery (I could work out the precise odds, but I don’t know that it’s worth the time and effort).  This is not a contradiction.  It’s a good reason to remind people not to be fooled by the fact that they may see on the news that someone often ends up winning the slightly more sane lotteries that we actually run.  Your own odds of winning are so close to zero that you’re almost certainly far more likely to die in a car accident on the way to buy your lottery ticket than you are to win the lottery, but when someone does win, it’s big news.  It’s somewhat analogous to the situation with airline crashes.

***Simply walking into Mordor, on the other hand, might be good for one’s fitness, if only there were not so many…environmental health risks.

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Migraines, after-effects, lesser evils, and greater goods

I’m a bit wiped out this morning, so I may only write briefly.  For those of you who may not know it, I developed a migraine headache yesterday.  It started with the surprisingly rapid onset of a “classic” migraine aura, which is to say a deficit in one’s visual field, marked by apparent, weirdly twinkling, almost rainbow-like lights.  It is not as lovely to see as one might suspect if one has not had it.  This first time it happened to me, way back in my early teens (while I was caddying), I worried maybe my retina had become detached.  Weirdly, this concern did not lead me to panic, nor to seek help, nor even to stop in the middle of that golf round‒work is work, after all.

The classic migraine, which is what this migraine with twinkling lights is called, seems to begin with a rapid, spreading depolarization of cells in the brain cortex, particularly (in this case) in the occipital lobe (thus the visual aura, because that is the region of the vision centers of the brain).  It spreads from there, and as part of its spread it seems to lead to vascular swelling and pressure in the meninges, which causes some of the pain.

The science has probably improved since the last time I studied it, so some of this description may be inaccurate.

In any case, as soon as I realized what was happening, I took steps to head things off.  Although I had taken a naproxen that morning, I popped three ibuprofen right away.  After a few minutes, as the aura progressed, I added two acetaminophen (extra strength) as well.  This was probably not ideal for my body‒kidneys, liver, and to a lesser extent, stomach come to mind‒but I didn’t really hesitate, because I have experience with migraines, and not just with treating them.  I also made sure to drink lots of water.

Anyway, I did get some dull pain (as well as just dull dullness) centering loosely on the left side of my head, but the Motrin™ and Tylenol® seemed to have done their work well, since I took them so quickly.  I did have pain, but it was not nearly as severe as it usually is, though I took one more ibuprofen a bit later when it seemed to be increasing.

With migraines, though, the pain is more an effect than a primary part of the process.  In a way‒and only in a way‒a migraine is a bit like a slow-moving seizure.  As such, it tends to cause quite a lot of fatigue in one’s central nervous system, and I certainly felt that yesterday and continue to feel the after-effects today.  For instance, I am making many more typos than I usually make right now.

I do seem to have slept slightly more than usual last night.  Tiring one’s nervous system by internally, directly causing the hyperactive discharge of whole populations of neurons seems to lead to slightly deeper sleep, no doubt because for the nervous system, it is something of an emergency and it must be cleaned up.  Trust me when I say, while the slightly longer sleep is nice as far as it goes, it is not worth it.

Even though I was able to prevent the worst of my migraine pain, the other effects were still quite palpable and unpleasant, and their after-effects remain.  They aren’t good.

This is not to say there aren’t many, many worse things in the world, and certainly when one has only two choices, one should choose the least bad of the two.  For instance, I would choose many migraines over a kidney stone.  The lesser of two evils is, mathematically, the greater of two goods.

If this fact is confusing‒I don’t know why it should be, but apparently it is, and that confusion has been consequential on large scales‒think of the old grade-school level number line, centered at zero.  If you have two negative numbers, such as negative two and negative twelve, you can certainly say that they are both negative.  But that’s a function of where you put the origin (where the zero is), which you can shift and put anywhere else, given the infinity of the number line and its inherent symmetry.

But even if you move the origin 100 places to the left, so that you now have 98 and 88 instead of -2 and -12, the distance between the two numbers, and their mutual relationship based on that, is unchanged.  One of the numbers is still less negative than the other.  And if that number measures the usefulness or the desirability of something, and if one has only the two choices, then one should pick the less negative one, which is by mathematical definition the more positive one.

A billion is less negative than a million.  And negative a million is less negative than negative a billion.

I’m not sure how I got from migraines to here, but that’s okay.  I’m sure it will make at least some sense during the edit.

Anyway, I hope that my mental fog will clear a bit today.  It would be nice to be able to sleep better without requiring general neurological, pathological exhaustion.  But then again, many things would be nice that are simply not so.  By which I mean they aren’t real, that they don’t exist, that they aren’t the case, not “many things would be nice that are simply not nice”, which wouldn’t make a lot of sense.

If wishes were horses, we’d all be drowning in horse shit.  And then we’d probably wish for it to go away, which would just produce more horse shit.  Alas.

I hope you all have a good day.

[PS:  I tried to do a brief audio recording on the way to the office from the train, while walking, because a thought had occurred to me and an occurrence had gotten me thinking, and I also wanted to “experiment” to see how well I’d be able to compensate for the noise of traffic and (to a lesser extent) wind.  It was unfortunately something of a disaster, and to correct it all would have required many hours of audio manipulation that may be beyond my skill.  So I just deleted it.  But I thought I would at least mention it.]

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Don’t regress if it’s just going to make you mean

Well, here we are again, starting another frikking work week.  It seems like only seven or eight days ago that we did this last time.  I don’t think there’s any more good that can be said about this occasion than on any of the previous occasions.  In some ways it is worse, for it merely continues the fruitless, pointless process it entails, without any clear increase in wisdom or knowledge or well-being.

There’s certainly been no gain in happiness‒for me, personally, or for the world at large.  Though probably there are some individuals who are better off this week than they were last week, by any criteria one might reasonably choose.  Gaussian curves tend to have outliers, after all; that’s the nature of the normal distribution.

Of course, there are negative outliers as well, down at the other end of the curve.  I feel for them.  Hopefully, their place in the lower percentiles is a fluke, a local, transient variation not produced by any particular process but merely by statistical fluctuations.  If so, they will almost certainly experience regression toward the mean next week:  when an exceptional occurrence in an iterated or longer term process is followed, almost always, by more average outcomes in whichever direction brings it toward the mean* of the curve.

That’s good.  It would be a shame if there were some process making it such that some individuals were persistently prone to be in the lower tail of the curve.

Of course, though I used the subjunctive just now, it’s not really a contrafactual situation; there really are plenty of people whose situation is such that each week for them tends to be worse in general than the weeks of the vast majority of other people.

This is almost certainly not by their own conscious choice.  It’s not easy to imagine a realistic situation in which someone deliberately chooses to be consistently worse off than most of their fellows.  Unconscious or subconscious urges, on the other hand, can lead to such things (presumably), as can bad habits that have taken hold.

Don’t look down on people who are stuck in bad habits that are clearly doing them harm.  The nervous system is built around habits, and does not change them lightly.  They are how people are able to do most of the things that they do.

If you had to decide de novo, without the grace of habits, what to do on any given occasion or in any given situation, odds are good that you would exhaust yourself rapidly, and you would screw things up at least as often as not.  There are good reasons why “System 1” takes care of most situations for most people**.

“System 2” requires much more time and effort and literal energy than “System 1” does.  And the brain already uses about 20% of a typical human’s calories.  So there, you see:  data centers have always been very energy-intensive, and they always will be.  There are good, sound thermodynamic and information theoretic reasons for this.

Okay, well, anyway, this has been a bizarre digression or series thereof.  It’s weird, and probably not terribly interesting to most people.  Such is the stuff of my thoughts; I can’t, in good conscience, recommend it to anyone.

Speaking of the stuff of my thoughts, I did a brief-ish audio recording yesterday afternoon, which I posted quite a bit later in the day.  I don’t know if it’s interesting or even coherent; I did not edit it for content, just sound quality and pause length.  You can listen to it if you want (obviously) and feel free to give me feedback on whether or not it is coherent.

Meanwhile, I hope that each and every one of you reading this feels better than I do right now.  If I could know that, I think it would make me feel slightly better.

*By mean, I mean (ha) the arithmetic mean, or what might be called the average in common parlance:  you add up the values of every “entry” and then divide by the number of entries.  This is not to be confused with the median, which is the value halfway from the worst to the best (or whatever) of a given particular listed and ordered data set.  It’s an important distinction, because confusing the two leads to some fairly common mental errors.  For instance, while by mathematical definition it is impossible for more than half of all comers to be above the median, it is entirely possible, if atypical, for more than half of people to be above average.  This just requires those who are below average to be significantly more below the average than the others are above it.  For instance, if you gave a test to 100 people, and 90 of them scored 50%, while 10 of them scored 0%, the mean would be 45, and so most people would be above the mean.

**There may be some evidence that people with ASD, for instance, tend to use System 2 far more often for far more things than neurotypicals do.  This may be part of why autistic people, even level 1 ones (which I am not, apparently, at least according to my official diagnosis), are so often just mentally exhausted, even by things that “ought” to be straightforward.