numbers

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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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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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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.

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Does the tread on a Mobius tire last twice as long?

“And it must follow as the night the day” that the second day of the work week (today) follows the first (yesterday).  This is what happens with ordinal numbers; they delineate (if that’s the word I want) the order of things.

Of course, as with numbers on the standard clock, or cycles of days of the week, or months of the year, the first day (or whatever) also follows the second day.  Indeed, in a small enough cycle, they can follow each other by exactly the same amount.  This is what happens in a binary cycle, like soldiers marching (or any biped walking).  The left foot starts off, and the right foot follows immediately after.  But then the left foot follows the right foot immediately after that.  And so on.

Of course, the weekdays have seven members, so that cycle may be more akin to the movement of the heptapods from Arrival.  And there are more months still, and more days in months than that, but the cycles still cycle.

Some cycles are surprising, of course.  For instance, if you go for one 360-degree turn around a Mobius strip, you’re not back where you started; you’re on the opposite side of the strip, “underneath” where you began.  To return to your starting point, you must take another 360 degree (or 2 pi radians, if you prefer) run around the strip.

This is a good analogy with (and a way of making some intuitive sense of) the spins of fermions, i.e., particles with half-integer spins, such as electrons and quarks.  When we say they have half-integer spins, we mean if you “rotate” one 360 degrees, it will end up in the opposite spin configuration to where it started; it requires another 360 degrees to return to its beginning.

That’s in contrast to the integer-spin bosons, which behave more “intuitively” in that they require 360 degrees to come back to where they started, like numbers on a clock.  Photons are probably the most obvious examples of spin-1 particles.

There is also a hypothetical spin-2 particle, the graviton (still a boson, because it has an integer spin).  This is easier to model in one’s head, because it “looks” the same after a 180 degree rotation.  It’s pretty easy to imagine 3-dimensional shapes to model that.  Think of football shapes, or even just rectangles.

Of course, it would be even easier to imagine “spin 3” or “spin 4” things:  think of equilateral triangles and of squares.  One can even quite easily imagine a spin-infinity object.  That’s just a circle; no matter how you spin it (maintaining its center point) it looks the same.

Of course, if you’re Archimedes (you’re not; I checked), you get closer and closer to finding out the value of pi (the ratio of the circumference of a circle to its diameter) by bounding a circle’s circumference between regular polygons that fit exactly within and exactly around the circle and taking their perimeters.  It’s hard to do that for a triangle, or at least it’s hard for me to do in my head, but a set of squares*, one nested in a unit circle**, the other in which is nested a unit circle, can be done.

The perimeter of a square in which is nested a unit circle is easy, because each side of the square is length 1, just like the diameter, so the perimeter is 4.  The interior square has diagonal length 1.  So any two sides make the legs of a right triangle, and a^2 + b^2 = c^2.  So side^2 plus side^2 equals 1^2.  Or, 2 times the side-length squared equals 1, or a single side squared is 1 over 2, and the length of a side is 1/√2 (we only use the positive root, since we’re talking about physically realizable lengths).  Thus, the perimeter of that square is 4 x (1/√2), or 4/√2, which is 2√2.  That ends up being around 2.8 ish.

So, it seems pi is between 2.8 and 4.  Which it is.  That doesn’t narrow it down much, but if you go from there to ever-increasing numbers of (equal) sides in nested/nesting figures, as Archimedes did, you can get arbitrarily close to the actual value of pi.

That’s all you can do, since pi is an irrational number.  There is an infinite amount of information encoded in the digits of pi, and indeed in any irrational number (making each irrational number its own version of the Library of Babel in a sense).  But pi is a fundamental geometrical number, so that fact hits home with it perhaps more than with any other specific number.

If the universe really is continuously divisible (this possibility is far from certain), then each spot in the universe contains a potential uncountable infinity of info.  If that is the case, nothing can truly, fully simulate the universe in detail.  But we can still make useful models.

I could get into the restrictions imposed by the Planck length and the Planck time and so on, but that’s a whole can of bees I don’t want to open just now.  Instead, I’ll call this to a close for today.  I hope you have a good one.

*A very crude starting point, but it’s good for demonstration.

**In this case I’m using that to mean a circle with diameter 1.  Sometimes one sees it used to refer to a radius-1 circle.  It doesn’t matter that much, but it’s very important to be clear which one you mean.  Just as it’s useful, even crucial, to define terms before beginning a discussion to avoid arguments over nonissues***.

***For instance, if you get two people to agree on what they mean by “sound” before you ask them, “If a tree falls in a forest and no one hears it does it make a sound?” then there is unlikely to be any disagreement, because the answer will be trivial (either way).  Thus, this is not actually a philosophical conundrum, despite its reputation; it is merely a demonstration of the folly of poor communication.

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Fictional birthdays, date misassignments, and the calendars of Caesar and the Pope

Hi, everybody.  It’s Wednesday, July 22nd, which means there are only two months left for you to buy something for Bilbo and Frodo’s birthday.  Though, actually, they’re pretty well-to-do hobbits, so it seems unlikely that you’ll be able to get them something they want that they don’t already have.

Oh, and also, hobbits give other people presents on their own birthdays, not the other way around.  This always struck me as odd, but kind of cool.  It’s almost like saying, “Here’s a little gift for you in celebration of my birth, just to remind you what a gift it is that I was born and that you know me.”

Well, at least that’s one way of looking at it.  Anyway, I don’t think you’re likely to receive a gift from Bilbo and/or Frodo, even on their birthday, apart from being able to read and/or watch The Hobbit and/or The Lord of the Rings.  That’s a lucky break for us all, when you think about it, and you don’t need to wait for September 22nd to partake of it.

I know, I know, why would one celebrate the birthday of a fictional character, anyway?  Well, it’s not as though mainstream culture doesn’t do it already, in oodles of major religious holidays.

Even if you’re convinced that Jesus really existed, biblical scholars agree (so I’m told) that he was not born on December 25th, but sometime in the summer, probably.  The later Church, never shy about playing free and loose with facts of reality (as religions tend to do), reset the date in order to appropriate the typical winter solstice-related festivals heavily celebrated by many cultures.  Such celebrations included Saturnalia (Roman culture‒you can tell because it’s got Saturn in it) and Yule (Norse, with the evergreens and mistletoe and holly and such like).  There were probably others.

The earlier Church cared more about Easter anyway, which makes a bit of internal sense.  That’s the purported miraculous day, when Jesus regenerated and flew to the heavens in his TARDIS.  Or whatever happened, if anything.

Of course, if we all wanted to avoid mislabeling Jeshua’s birthday, we could just celebrate Newtonmas on the previously celebrated day, since Isaac Newton was born on December 25th.  And he definitely did things that, while not literally miraculous, boggle the mind of nearly every mortal with knowledge enough to understand those contributions.

Mind you, he was, by all accounts, a serious dick and a born curmudgeon.  But he was effing smart, and his scientific accomplishments surely compensate for, say, his bloodthirsty reign as Warden of the Royal Mint, and even his really petty and childish vendettas against other scientists.

“‘A was a man.  Take him for all in all.  I shall not look upon his like again.”

Ah, but there’s a catch (or a rub, since we’re quoting Shakespeare):  Newton was born on December 25th according to the Julian calendar.  The Gregorian calendar* did already exist, but England did not adopt it until sometime after Newton’s birth.  They were sort of stubborn about going along with Catholic innovations, and it held them back.  I blame Oliver Cromwell.

Anyway, by the modern, “Gregorian” calendar, Newton would have been born sometime in about…January, something like the 7th, I think, but I’ll look it up (see below).

Why the disparity?  Well, as you may know, the Julian calendar does have leap years.  Earth’s trip around the sun takes 365 and about a quarter days, so the extra full day builds up and is added onto every 4th year.  Except…

…well, it’s not quite a full quarter of an extra day there in that orbital period.  So, over time, the Julian calendar gets ahead of the literal year a bit.  It’s a small bit, but it’s there, and it accumulates.  To correct for this, one of the things the Gregorian calendar does is to skip the leap day on any year divisible by 100**.  It also adds the leap day back on every year divisible by 1000, but I think that’s only applied once since the Gregorian calendar was created.

Anyway, by the time the Gregorian calendar was put in place in England, the Julian calendar had accumulated something like 11 extra leap days.  Maybe it was 12.  If January 7th was the Gregorian date of the 25th of December, Julian, that would be, let’s see…I think 14 days.  I suspect I’m off a bit in my recollection, so I’ll look it up and add a footnote***.

Wow, that was a weird, discursive post, wasn’t it?  I guess it’s probably more entertaining than hearing me talk about my problems with my mental health, at least.  Indeed, one might say that I am instead hereby demonstrating my problems with my mental health‒some of them, at least.  Anyway, I hope this was at least mildly entertaining and possibly informative.  It’s at least probably better than my previous two posts.  In any case, I hope you have a very good day.

*Named for Pope Gregory Peccary the Nocturnal Gregarious Wild Swine.

**I mean “evenly divisible”, of course.  Every number is divisible by 100.  Pi is divisible by 100:  ℼ/100.  “i” is divisible by 100:  i/100.  See?  But they don’t give integer quotients.

***Here goes:  Newton’s birthday would have been January 4th of the following year according to the Gregorian calendar.  This is ten days that needed to be skipped by the Gregorian calendar, or a thousand years worth of Julian calendar mismatch.  By now there would have been about five more extra days in the Julian calendar, so your birthday would be officially labelled as whatever day is 15 days before what it is, Gregorian Style.

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What do you call an infinite number of finite and separate beings? Maybe just “reality”.

I don’t really have much to say today.  Not that such a thing usually prevents me from running off at the keyboard (or the smartphone in this case) for stupid lengths on any given day.  But I think it may do so today, because my energy is flagging, and it’s only just very early in the morning.

I suppose today’s date is mildly entertaining:  it’s 7-7-2026, and that is the same in either the USian or the European way of ordering the day and the month.  But that’s pretty unremarkable.  Any day of a month in which the ordinal* number for the day is the same as the ordinal number for the month will produce this.  There are, thus, 12 such days every year, and they are the same days every year.  So, they are not very exciting.

I guess it would have been better back in 2007 (07-07-07), or even better, in 1977 (7-7-77).  But then it would only be fun if you drop the two digits for the century (i.e., 20… or 19…).  It’s not great, is it?

I don’t know.  What should I talk about, here with my shouting into the void and gazing into the abyss and jumping into the conclusion?

That latter expression almost sounds like a euphemism for dying, doesn’t it?  Is it like skipping to the end of a mystery novel?  Probably not, because I’m very close to being certain that, unlike the end of a mystery novel, nothing will be revealed when one dies.

By that, I don’t mean that the truth will be revealed and it will be that there is nothing.  It’s more subtle than that.  I mean nothing of any kind will be revealed to you, because that to which the revelation might occur is what will cease entirely‒in a way, that happens every moment, but not in quite the same way as it will (I suspect) at the time of death.

Of course, I could be wrong about this, in principle.  But I am not “agnostic” in the usual sense of simply not having any inkling one way or another about a question.  I think there are good, strong reasons‒based on all we know of physics and biology and mathematics, and on how many different mythologies there are about “life after death” and how much they stink of desperate human fear and wish-fulfillment, how anthropocentric they are, when clearly the universe is not anthropocentric‒to think that death is simply the dissolution of the four-dimensional pattern that was a person, a sort of re-annihilation of “virtual particles” back to the vacuum state of the quantum field.

In a spatially infinite universe (or in some other version of a multiverse) it seems to be that there will exist other versions of you, both identical ones and nearly-identical ones, as well as quite different ones, including ones that inexplicably have all the memories of being other versions of you.  But they will not literally have been you, and there will be a much higher proportion of “you” that will have random memories of every possible kind of nonsense.

Of course, none of these versions of you can violate the laws of physics**.

And they aren’t really you, are they?  If they were, you might be experiencing everything any version of you is experiencing now, and you are not.  There are strong impediments to such a simultaneous experience of infinite lives, not the least of which is the relativistic impossibility of information traveling at infinite speed, as well as the incoherence of the concept of “simultaneity” for objects with spatial separation (if this is not obvious, I encourage you to look into special relativity).

So, yeah.  You are the state of your being right now, and that state is always changing (not randomly, though a lot of it does seem to be stochastic).  There is not a much better description of “you” for accuracy, though there can be more precise and thorough descriptions of the details.

There could be a billion or a googol or Tree-3 number of “identical” copies of you, but each one would be just a separate “you”, no more a literal part of your being than would be your former womb-mate if you were one of a pair of identical twins.

Reality can be disappointing, though that’s really only if you think you have any right to expect it to be otherwise than it is.  And you don’t have any such right.

Have a good day if you can.

*I think it’s ordinal, not cardinal, in this case, but I’m not too sure.  I’ll look it up.

**I truly despise expressions, usually found in clickbait headlines, such as “this or that finding breaks physics” or “this shouldn’t happen, according to physics”.  No.  Nothing breaks physics.  Nothing that happens “should not” happen according to physics, because physics is what describes what is out there in reality.  If something seems to defy physics, that just shows that we don’t understand physics well enough.  Such things are not generally frightening or worrisome to physicists (and other scientists); these things get them motivated, for they reveal places where we can learn new things about the universe.  Scientists, ceteris paribus, love finding things no one understands.  Science knows it doesn’t know everything***, and what’s more, science kind of loves that it doesn’t know everything.  That’s part of the excitement, the challenge, the possibility of growth.

***If it thought it knew everything, it would cease.

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Drop and give me twenty! (The prime factors of twenty, I mean)

It’s another lapcom blog post today, for the second day in a row.  Huzzah!

That doesn’t really count as any kind of streak—though no doubt WordPress will send me an automatically-generated “You’re on a streak!” message, since that’s apparently something that encourages people to keep using the site regularly.

I guess it would be nice if I were going for some kind of personal record—if I were trying to write as many days in a row as possible, for instance—to be aware of how many I had done without having to keep track of it myself.  And, I guess, if you’re recording streaks, you have to start somewhere, and the smallest possible streak is two.  You don’t really want to count one as a streak, because then everything is a streak and it loses much of its meaning.

This is somewhat analogous to the reason that 1 is not considered a prime number, though you cannot deny (correctly, anyway) that it is divisible without reminder only by one and itself (which is also one).  But for mathematical purposes dealing with primes, this would be a rather useless add-on to the set.

It would also make deciding the number of prime factors of a number pointless, instead of being specific and fixed for each number.  As it is, without one counted as a prime, it is specific and fixed.  For instance, the prime factors of 36 are 2, 2, 3, 3.  But if 1 were considered a prime, you could have 1, 2, 2, 3, 3 or 1, 1, 1, 2, 2, 3, 3, with any arbitrary number of 1s, because every 1 would not change the final product of those primes.  You could have an endless string of ones if you wanted.  And so, the number of prime factors of any given number would be up for grabs, whereas right now it’s fixed.

I know, I know, it’s not terribly important in day to day life for you to think about such things.  Some people are disdainful of even learning about such things unless they have a direct impact on their lives in a clear and obvious and simpleminded way (emphasis on the “simpleminded” there).

There are people who make jokes about the fact that they learned the Pythagorean theorem and don’t use it, or that they know how to do square roots but don’t really need them, or learned the quadratic equation and haven’t used it since that class in high school (or college, maybe).

Such people perhaps think that the point of doing push-ups or bench presses or squats or lat pull-downs is to get really good at doing push-ups or bench presses or squats or lat pull-downs.  They may imagine that the reason to do toe touches is to get really good at touching your toes, and if you’re not going to try to do that, then don’t do toe-touches.  These people probably think that everyone who jogs regularly is doing it so they can get better and better at jogging.

I think you probably see my point, but I’ll make it explicitly.  The purpose for all that physical exercise is not to get good at doing calisthenics (or whatever), not for the vast majority of people.  It’s to be comes stronger, fitter, more flexible, to develop better endurance, so that you will have those capacities to bring to bear on any other task in life.  In many, many matters, being physically fit will make a person more effective.  Sometimes it can even save someone’s life.

Likewise for doing things like math.  Some people will go on to be mathematicians, of course, or to become physicists, who use mathematics regularly in their work.  But everyone can strengthen their brains (far more than they can strengthen their muscles, which have a hard ceiling on improvement).  They can improve their ability to think logically and systematically, to recognize patterns and to be able to manipulate them in their heads, by practicing and understanding mathematics.

Understanding percentages will make it immediately clear, for instance, that something cannot sensibly be reduced in price by 600%.  Understanding probabilities can help one recognize why one should not invest in the lottery (unless you’re the one running it, in which case, by all means—if it doesn’t trouble your conscience).  And one should not blindly trust the representations of, say, managers of mutual funds and the like.  Even though what they happen to tell you may be real data, omission can be just as misleading as straightforward lies.  You also need to know what they have left out.

If they tell you their fund increased in value ten days in a row, implying thereby that you should want to invest in it, you need to think about (for instance) just how many funds they have.  How many funds are they picking from and for how long?  If they have a thousand funds, assuming equal chances of gains or losses, you should expect on average for one of them to go up for ten days in a row in any ten day period.  But the next ten days, it would be a different, random one that goes up*.  Or, if you can pick any ten days out of a given year, you can probably find somewhere where there’s a ten-day streak, or nearly so, even if you only have a few funds.

I have not done the math to figure that last bit out specifically, but it directly relates to the probability that you will have a string of ten heads in a row somewhere if you flip a coin 365 times.  That goes back to basic probability.

It can serve you well to study some micro- and macroeconomics.  It can also do you good to study a bit of basic chemistry and biology; you wouldn’t even have to have any more advanced medical knowledge than high-school level to know that while injecting enough bleach will kill COVID, it will also kill you, and so will not be a much better therapy than setting yourself on fire or detonating yourself with TNT.

I made a meme about a similar idea that I sent to a friend who was all too easily persuaded by conspiracy theories about various “natural” substance being able to kill cancer but that “Big Pharma” didn’t want you to know about them.  Actual knowledge of how cancer works and how lab tests in vitro work would have protected him from such claims, but I took a slight shortcut to hammer the point home.  Here it is:

Anyway, that’s already a lot for today.  I tend to write faster with the lapcom, and so I tend to write more.  I hope it’s not too irritating.

I hope that about myself and the things I do quite often, but I’m afraid I still end up being irritating more often than not.  My apologies.  I also hope you have a good day.

*Again, all this assumes about a 50/50 chance of going up or down.  Considering how many regulatory and other factors are in place to encourage markets to go up, it’s probably skewed slightly toward gains**, and this will increase the chance of ten-day streaks of gains.

**As evidence, if one had invested in a simple index fund without any significant churning (I think that’s the term) over the last several decades, one would have made around about 10% a year.  That’s roughly twice the rate of inflation, so there is still a real, adjusted net gain.  Given compounding, if you invested $1 in, say, 1990 with that return, you would now have, let’s see…$30.91.  If you invested a million, you’d now have $30.9 million.  Higher rates of return than this will tend to involve higher risk.

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Your dates are numbered

Okay.  Well.  It’s Tuesday now, and it is the second day of June in 2026.  That’s a borderline almost mildly fun date to write out:  6-2-2026.  It has sixes and twos, mainly (though there is a zero in there, which I’m not sure my mind will let me discount despite its lack of any magnitude), and it is almost palindromically arranged when in the US format of date writing.  There are even three twos, which add up to six, and that might be cool…except for the fact that there are two sixes, so if we’re thinking that way, we would need six twos.  That would also be a more pleasing number of twos, given everything.  Unfortunately, I don’t know if there will ever be such a date.

Let’s see…2-22-2226 has six twos but only one 6, whereas 2-22-2266 has two sixes but only five twos.  I guess 2-22-22,266 will be good, but that is quite a long way in the future.  I doubt very much that I will be alive 20,000 plus years from now.  I’m not sure of 20,000 minutes!  Actually, again, let’s see…there are 24 x 60 minutes in a day, so that is 1440 minutes in a day, and so 20,000 minutes would be only around two weeks.  Okay, so I will probably still be alive in 20,000 minutes.

Let’s see (a third time)…20,000 hours would be about 833 days, so a bit over two years.  That’s quite a bit more doubtful than two weeks, but still not a crazy possibility.

As for 20,000 days, well that’s getting quite unlikely.  That’s just under 55 years, which would make me almost twice my current age.  Again, that’s quite unlikely, and I’m rather glad that it is.

20,000 weeks is not really worth considering.  If I were to live for centuries, it would only be because of astonishing medical advances* that presumably would have cured or at least ameliorated my many dysfunctions, so I would probably feel much happier than I do now or have felt for many, many years.

Speaking of many, many years, 20,000 months would obviously be well over a thousand years (20 being well over 12, as I’m sure is obvious).  If we’re going to consider that, then we have to invoke the same kinds of pseudo-miracles as we did for 20,000 weeks, we just need around four and a half times more of them, so to speak.

How the hell did I get onto this subject, or topic, or whatever it is?  Oh, right, I was noting the numerals in today’s date and how they came teasingly close to being fun, but don’t quite make it.

For those of you who might be puzzled by my use of the word “fun” when dealing with simply pointless patterns or lack thereof in things like dates, well…I like numbers.  It’s similar to the way I also like words.  I like words when they’re used to convey interesting information, and when they’re used to tell interesting stories, and when they’re combined and juxtaposed in beautiful and/or amusing ways to make poetry‒and I also sometimes like nonsensical wordplay and puns.

Also, of course, while “fun” may or may not have some manner of absolute scale, like temperature, nevertheless, as with temperature, our experience of fun is a relative one.  Tepid water can feel quite cool when you’re coming out of a sauna, but would feel nicely warm if you had just come inside to escape a bitter winter storm.

Fun can be similar.  So, if you’re used to having a goodly amount of fun in your life, then noting patterns and relations within ordinary “numbers”** can seem rather dull, even if you’re fond of numbers.

But if your life is as pathetic and irritating, on a day to day basis, as mine is, why then even simple, stupid, pointless things can seem somewhat positive.  The value of the function at that point is still well below the x-axis, but it’s not as far below, for that brief moment in which one notes an amusing numerical coincidence***.

That’s all theoretical today, though, because as I noted, today’s date doesn’t quite measure up.  It’s somewhat disappointing, but at least I was able to write an idiotic little blog post about it.

*I can, of course, think of various horror story scenarios in which someone could keep living for centuries and yet continue to deteriorate, but not be able to die.  These are probably quite a bit less likely even than the “medical advances” scenario.

**Why did I use the “scare quotes” there?  Because dates, even when expressed numerically, are not really numbers.  They are more of a code or a location marker, just a kind that uses numerals as its digits because they are memorable and at least correlate with some physical externalia.  “Phone numbers” are even less to be thought of as true numbers.  Their digits don’t even signify anything logically or arguably numerical.  “Phone address” would be a more accurate term.

***Yes, yes, I know, the specific placement of the x and y (and z, etc.) axes is arbitrary, so one can shift one’s target axis down‒lowering one’s expectations, perhaps‒and not need to change the shape of the function.  That may be true, but one does change the integral and the absolute value of the function, so it is not the same, unless one throws in a constant that exactly corrects for the shift in the axis.  In which case, what the hell are you doing wasting our time with this crap?

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When pigs fly and so do fried eggs, things are weird

Well, I did something rather unusual (for me) yesterday, and I’m doing something rather unusual (for me) now.  I bought tickets for the Powerball lottery yesterday.  And this morning I’m composing at least part of this blog post by using voice to text on my phone.

Apparently, when using voice to text. just saying the word “paragraph” doesn’t cause the text to begin a new paragraph.  This is in contrast to what happens when you use the names of ordinary punctuation, and the voice to text turns it into that punctuation, which is actually reasonably impressive.

Okay, well apparently you have to say “new paragraph” to get it to do a new paragraph, but that makes it challenging to describe in writing what you have to say to make it do that.

As for the Powerball ticket thing, well, yesterday we had a customer who didn’t seem to understand how their credit card worked, and we had difficulty getting their purchase to go through.  When they had spoken with their credit card company (supposedly) and told us that it should be clear (for the second time), as I was proceeding to run the card, I said aloud “if this goes through I’m going to buy a lottery ticket”.  It went through.

Then, later in the day, a similar thing happened, and one of my co-workers heard me say what I had said earlier. He said that he would be happy to go in with me on lottery tickets.  I said I don’t know how you even buy them*, but I want to get one of the big ones, the Powerball ticket.  So we said he would chip in $10 and I would chip in $10 and we would buy $20 worth of Powerball picks.

Then, as I was heading out, the boss asked what we were doing.  I told him, and he said he wanted to chip in 10.  So, I bought $30 worth of quick pick Powerball tickets for the drawing that apparently happened last night.  I did not bring them with me to the house, they are waiting at the office.  I do not by any stretch of the imagination expect to win.

Okay, well, to say by any stretch of the imagination is a bit of an exaggeration.  However, as I said to my co-worker, I am probably more likely to survive jumping off the Empire State building than I am to have one of these lottery tickets win.  As he replied, it’s not impossible, though.  He knew he was being silly, but it definitely was a “you go first” moment.

This was a one time thing, done both out of a sense of ennui and a sense of pointlessness; it was just a silly, frivolous thing to do.

Okay, enough with the voice to text stuff.  It’s irritating.  I won’t say that it doesn’t have its charms, but they are limited.  I also don’t like the way it auto-punctuates.  It also doesn’t even seem to know the word “ennui”, if you can stomach that fact (and even if you cannot).

In other news, or “olds” as the case may be, I continue to try to mitigate my chronic pain, with erratic (at best) results.  But I’m still trying.  It’s a profoundly unsatisfying thing to which to have to dedicate a substantial portion of one’s mind and life, but it’s very difficult to ignore or to take in stride.  Even Mr. Spock couldn’t just ignore his pain after he got infested by that flying fried egg thing.

Of course, that makes sense.  Biologically, as I’ve said possibly hundreds of times, it does not make sense for an organism to be able to ignore pain.  Oh, sure, it can be suppressed briefly in emergency situations, and we know that happens.  You can also squelch alarms of various kinds in the industrial world, as you can silence alarms on heart monitors (temporarily) when you know why it’s going off or you know that it’s an artifact.

But important alarms do not bear complete silencing or disconnection‒not without creating significant danger.  That is, unless the alarm is a holdover, a remnant of something that used to be relevant but no longer is so.

Imagine a carbon monoxide alarm, put into a house in the days when they had gas heat and cooking and so on.  This was a reasonable precaution.  But then imagine that it started going off because it detected CO, and in response, the homeowner replaced the gas heat and gas cooking with electric alternatives.  Now there are not even any connections to the gas supply, and as an extra precaution, the owner bought an electric car, so no danger exists of CO poisoning other than some deliberate chemical attack.

And yet…the carbon monoxide alarm keeps going off.  And it doesn’t just do so intermittently; it is constant, though the volume varies a bit.  And by design, it is intrinsic to the very structure and function of all else in the house, so to remove it is either impossible or would disable numerous other, still important systems and still relevant alarms.

That’s a bit like what chronic pain entails.  It ruins some things and taints all things.  After a while, it’s hard to remember what it was like not to be in pain.  And after it has helped drive away everyone important to one‒for no one wants to spend much time around a lost cause‒it can be very difficult to maintain even any semblance of optimism.  You just want to shut that bloody alarm off, even if you have to blow up the house to do it.

Oh, well.  Whataya gonna do?  Maybe if I have won the lottery, I’ll be able to find some newer answers.  I’ll look into that right after I catch the flying pig back from my celebratory skiing trip in Hell.

If I were to win the lottery, I don’t think I would stop working, at least not immediately, and I certainly would not reveal it here‒again, at least not immediately.  Possibly there would be ways to tell, but don’t spend too much effort thinking about them; the chances of winning are almost nanoscopic.

Actually, the chances are much higher of me choosing to jump off the Empire State Building than of winning the lottery.  And the chances of me choosing to jump from a much nearer tall building are higher still.  I even have a building chosen for the purpose, just in case.

Whatever.  It doesn’t matter.  I don’t matter, certainly not in any larger sense, and barely even to myself.

You all matter to me more than that, though, so I hope you do well and have a good day today and a consistently improving set of days hereafter.

*It turns out to be quite easy, of course.  When you’re trying to encourage people to give you their money for nothing, you don’t want to make the process too difficult.