Mathematics

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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.

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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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He reads the post with just his fist and still believes he gets the gist

Well, I said yesterday that there would be roughly a 50/50 chance whether today I would write on the lapcom or on the smartphone, and guess what:  today I am writing this either on the lapcom or on the smartphone!  How’s that for an accurate prediction?

But wait.  Which one am I using?  Can you tell just by reading this post?  Are you sure?

Of course, I know which one I’m using.  It would be most ‘passing strange if I did not know whether I am writing this on my lapcom or on my smartphone.

Is there a way for you, the reader, to tell?  Probably.  Almost certainly.

But do you know what that way is and how to apply it?  I doubt it very much.

That’s not an insult, by the way; I don’t know what it is or how to apply it, either.  I’m just pretty sure there is such a way.

Of course, from my own point of view, the metaphorical wavefunction has already collapsed, and there is only one possible remaining outcome, whereas before there were (at least) two.

I say “metaphorical wavefunction”, invoking the quantum mechanical notion of the collapse of previously superposed quantum states into one final state, but there are good reasons for us to doubt that notion’s accuracy even within quantum mechanics.  After all, it would be the only known physical process in the universe that is not time-reversible and which destroys information about prior states of reality.  That oughtta be a pretty big red flag for scientists.  It’s almost as bad as finding a process that seems to violate the 2nd Law of Thermodynamics*.

I find the Everettian approach to quantum foundations much more intuitive, personally.  That doesn’t necessarily mean it’s more likely to be correct, but I think, I suspect, that it is.

Anyway, in the macroscopic world, the seemingly superposed possibilities that present themselves as we come to the point of a decision are not actual superpositions.  They are merely models we render in our minds of possible outcomes to try to improve our decisions.  In fact, in almost every case, it’s likely that the choice we make was “determined” ahead of time‒by the laws of physics, not by us.

I would guess that it was that way when Bohr’s and Heisenberg’s “Copenhagen Interpretation” of quantum mechanics became so dominant despite its failings.  The problem is, Bohr and/or Heisenberg (I don’t recall which one) was by reputation exceptionally charismatic, and he was well able to ensure that his/their notion(s) became predominant, not because the ideas were more convincing, but because the people were (or the person was).

That’s not a good reason.

This is part of why I dislike the practice of public “debates” about controversial topics at pretty much any level.  When it becomes a contest in and of the moment, the “winner” of the debate is not necessarily the one with the best evidence and the most consistent and clear reasoning.  It is, often, the one more skilled at mere rhetoric, the better sophist, the one with the better ability to manipulate human cognitive biases, the one with the better speaking voice, the better looking one, the one who makes the best jokes (especially at the other’s expense).

This is not a good or reliable or useful way to measure empirical reality‒except that part of reality that tells us who is more superficially persuasive to Naked House Apes.

That’s part of why the court system in general is so bad:  the one who wins in court is not necessarily (or even probably) the one who is right, but rather the one who has the better lawyer with more resources.  This usually translates to “the one who happens to have more money.”  That’s not a good basis for any kind of system that refers to itself with the term “justice”.

Oh, well, what are you gonna do?

Well, it would be nice if you could do your part toward at least improving these things in whatever way you might be able, especially if you are in any kind of influential position.  This here, this writing, is me doing at least some of my part, for whatever it’s worth.

In the meantime, I’d be interested to get your feedback:  do you think this post was written on the lapcom or on the smartphone?  Why do you think that?  Are those your real reasons?  Or are they the reasons you create‒some might say confabulate‒to justify a decision you made for reasons that are not clear to your conscious mind?

Please let me know in the comments.  And talk amongst yourselves there, too, if you like.

Also, please have a good day.

*This is not to say that it is impossible for net entropy to go down in a closed system.  It’s not only possible, but if you wait long enough, it’s going to happen somewhere, for the 2nd Law is statistical in character.  But for anything but the simplest situations, you’re going to have a wait for such an outcome.  Even if you’re just flipping 13 coins until you get all heads or all tails (or any other specific, ordered pattern you might want), then it’ll take a little while.  Getting all heads in a row (say) on 13 coins is a one in 8192 chance, if my mental arithmetic is right.  It would take some time, but you could pretty readily flip those 13 coins more than 8000 times, especially if you flip all 13 at once each time.  But anything much more involved than that (and just 2 more coins would require four times as many flips) becomes rapidly and astonishingly more unlikely.  If you’re waiting for any sensible region of, say, the Earth to experience spontaneously decreasing entropy, you’re going to be waiting such a long time that probably the current time (about 13.7 billion years) since our Big Bang would seem like an unnoticeably tiny fraction of the blink of an eye.  And, of course, the Earth is not going to be around that long‒not more than about another 4 or 5 billion years at most.  If that seems like a long time to you, you need to adjust your perspective.

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I almost forgot to put a title here again

I’m writing this blog post on my smartphone, as I did yesterday’s post, and in contrast to the posts from Monday through Wednesday.  I haven’t yet received any direct feedback on whether there’s a difference for the reader or what it might be, but the numbers seem to indicate that the phone-written posts are more popular than the lapcom-written ones.

This could, however, be mere statistical fluctuation, having no relation to whether readers find one or the other type of post better.  Quite possibly, most readers wouldn’t be able to tell one from the other without being told, even if the lives of their dearest loved ones were on the line.

Such is the difficulty with finding truly dispositive evidence in ordinary life.  But that’s not to say it can’t be done.  One just has to try very hard to be clear-headed and objective.  And I don’t mean “try to try” to be clear-headed, not just to be able to say “I tried to be clear-headed”, but actually to act with the true intent to be clear-headed.

Of course, the human senses and human brains gather a tremendous amount of information every waking moment, checking it against their hitherto-built model of reality, seeing if things meet expectations according to that model, and trying to improve that model, that map, of reality.  Mind you, there’s way more info in most places than anyone can take in.  That’s okay, for the most part.  Most of that detailed information is irrelevant to the life and reproduction of a far-flung African ape*.

Speaking of updating one’s models of reality, I just yesterday came across a video/written course on tensors (for physicists and would-be physicists).  The professor’s approach seems like it’s going to be a good one, so I’m planning on trying to go through the course.

I want to learn well about tensors (about which my understanding is not yet fully clear, though I get the gist of the basics) not just for my own curiosity‒which drives me, in principle, to want to try to understand everything in the universe‒but also because I will need skill in using them and manipulating them if I am to solve my longstanding point of curiosity in Special/General Relativity.

I have a specific question about what the theories predict would happen in specific circumstances, and I have not been able to find anyone who reliably answers it.  Really, no one has answered it at all, which is not too surprising, since it is fairly esoteric.

We’ll see whether I can commit to the bit.  I have a hard time maintaining focus on things for too long at once.  I dearly love to learn about new things and to develop new skills, especially in the sciences‒well, also in the arts‒but it seems that after (far too short) a time I get distracted by another interesting thing.  Either that or I just get mentally fatigued and need to distract myself, usually either with music or something funny.

I suppose that’s not really that unusual.  But lordy, it’s frustrating.  I wish I could actually want to do what I want to want to do.  Maybe I will be able to do so someday.  Maybe I will be able to devise or find more direct control of the regions of my brain which govern attention, focus, and drive.

Of course, we do have some somewhat direct ways to affect those brain regions.  The most widely used of these ways is caffeine.  The majority of people in the world use some form of caffeine on a regular basis.  At least, that was so the last time I looked.

Of course, there are other such tools, some more powerful in some ways than caffeine, but they come with their own sets of difficulties:  these include the amphetamines and related compounds and cocaine.  They can be useful in certain circumstances, but are difficult to use well, without significantly detrimental overall outcomes.

It would be easier if we could directly stimulate (and suppress) specific areas and processes of our brains at will.  Of course, the technology to do such things exists, more or less, in raw form.  One can stimulate the brain with implanted electrodes, or one can manipulate it more indirectly via externally applied electric and magnetic fields.

This has been done, of course, if only fairly crudely.  The technology I describe in Unanimity is (mostly) very real.  Is that what makes it scaaaary?

Probably not.

Okay, that’s enough for today, and for this week as well, since I am not working tomorrow (barring the truly very much unforeseen).  I hope you all have a good day and a good weekend.  Have a good meal or two while you’re at it.  Though, possibly, that’s implicit in most concepts of good days and good weekends, come to think of it.

Oh, well.  Have good ones nevertheless.

*That refers to humans, in case it’s not clear.

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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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In nature’s infinite blog of secrecy a little I can read.

Hello and good morning.

I may be brief today*, because I am mentally fairly exhausted.  Yesterday was a bad day for me, pain-wise and mood-wise.  I’ve had large amounts of more than one kind of pain medicine on board, and I felt…well, I felt somewhat less pain in some places, but I’ve started to get some broader symptoms that I sometimes get when I’m taking too many NSAIDs for too long.

My thumbs and my knees and ankles and such are actually feeling wobbly and unstable as well as being generally a bit puffy and plenty sore.  This isn’t really like an inflammatory kind of swelling; that would indeed be a failure of the Non-Steroidal Anti-Inflammatory Drug(s) I take, would it not?  No, this feels more like a sense of having excess fluid in each joint, as well as in between them, and less tautness, less stability, and somewhat ironically, more pain, albeit of a slightly different character that usual.  It’s quite frustrating.

Also, my back and hips and shoulders don’t feel much, if any, better than usual.

I’ve been wondering lately if I might have some form of relatively mild hypermobility syndrome, which often goes along with ASD it seems (some of the causative genes are probably the same, or at least tend to travel together through the genome).

I have long had certain slightly atypical flexibility issues or attributes**.  For instance, I’ve always been able, with a bit of a pull, to put one or the other of my feet behind my head from a seated position.  I can also scratch pretty much any part of my own back, and I have always been able to do this, though I sometimes need to pull one arm a bit with the other.  Also, I have a hard time holding my head straight upright for very long at a time; it’s uncomfortable, and I need to lean it to one side or another pretty much constantly.  Maybe that’s just a weird habit, I don’t know.

Of course, hypermobility can be associated with various kinds of chronic pain, and can certainly make other things worse.  Unfortunately, it’s not something that can be cured, any more than autism can be cured (or any more than having a particular color of eyes or hair can be cured, though they can be masked, as by dyes or contact lenses).

I am far from sure about this tentative self-diagnosis, and I’m always leery of “second year med student syndrome”, but I think I am being reasonably objective here.  Genetic testing would be required to confirm something like Ehlers-Danlos Syndrome, but I don’t meet the criteria for full-blown EDS***, and less full-blown syndromes may not easily (nor cheaply) be testable, or testable at all.

I suppose it doesn’t really matter much.  I do not expect my baseline previous health to be recoverable in any reasonable sense.  This is one reason I’m not too terribly worried about things like heart disease and infections and so on.  Why would I want to live a longer life of the kind I now live?  It’s like asking someone if they want the massive street construction project on their block, that’s slowing traffic and making terrible noise all day and into most nights, to be extended‒not by the workers doing more improvement, but just by working more slowly and being less efficient.

At least yesterday, in between doing payroll, processing deals on an unusually busy day, and trying to discourage my body from committing war crimes against itself, I remembered and indulged in a resource I haven’t used in a while:  I got on bioarXiv and skimmed through the abstracts of some of the more recently uploaded papers in general biology, neuroscience, genetics, molecular biology, and such like.  It can be kind of fun.

I don’t enjoy it as much as I do going to the original arXiv (hosted at my alma mater), which deals in physics, mathematics, computer science and the like.  But the bio site requires less mental effort and is simpler in many ways.  This is at least partly due to the fact that I am an MD, and I got my degree from one of the more research-oriented medical schools (we were required to do a publishable medical science research project as part of our degree) so the terminology is more or less at my fingertips.  This probably would apply even more at medrXiv, at which I spend less time than the latter two.

ArXiv, the physics/maths/CS site, has oodles of interesting articles always up‒I have, for instance, downloaded a PDF of a paper by David Deutsch from there‒but most require more mental effort than on the other sites, because I don’t have as good a handle on some of the jargon, and I often need to review the mathematics involved, or more often try to absorb it for the first time.  Still, it’s very cool, though it’s a real embarrassment of riches; it’s like being in the biggest candy store in the world,  but having only three dollars to your name, and having to choose what to buy with it.

The potential opportunity costs are staggering, but I guess that’s a good problem to have.

Speaking of reviewing mathematics, I found a nice little YouTube channel by a woman from MIT who does good reviews of basic integration and more advanced techniques like integration by parts and trig substitutions and such like.  I find her stuff much less sleep-inducing than the videos on 3Blue1Brown, though Grant has oodles of great videos, well-produced and in-depth but clear, about many topics in mathematics.  Unfortunately, his voice is if anything too calm for me, and his animations, though superb, are if anything too smooth.

I think, also, that I learn better by seeing someone writing the stuff out‒possibly this engages my mirror neurons and thus makes more of my whole brain focused on what’s happening.

Incidentally, the lady mentioned above is not officially affiliated with MIT, she just went there.  But you can actually “attend” lecture courses in various subjects in Physics, in Mathematics, in Economics, in Computer Science, and so on, from MIT at their YouTube channel.  It’s truly remarkable, and if you’re just after learning the stuff but aren’t seeking an Official Piece of Paper™, it’s a tremendous resource!  Stanford also has similar online lecture courses, as I think does CalTech.

I’m pretty sure Harvard does this also, but there’s no need for any of you to go slumming there.  Why not just watch Baby Shark or something‒and Gangnam Style is actually pretty enjoyable.  I know, I know, Steven Pinker is at Harvard, and he’s one of the most enjoyable (and thought-provoking) public thinkers in the world, but I don’t think he gives any of their online lectures.

Although, given the notorious grade inflation known to be rampant at Harvard, you might just get an official “A” from them simply by clicking on one of their videos.

Okay, I’m at the stage of taking cheap shots at Harvard (they do not deserve such disrespect, even though there really is a problem with grade inflation), so I’ll call this post to a close.  I hope you’re all having a better week, year, decade, and life than I am having.  Though, really, if you’re not reading preprint scientific papers for free online, how good can your life be?

TTFN

*I was not.  Perhaps this is analogous to the situation that led to the famous quote about not having time enough to write a short letter‒only in this case, it is not time but mental energy that limits my concision.

**Some of these things are slightly curtailed now because I am too plump, but that’s a different issue.

***No, I do not refer to Ross Perot’s old company, Electronic Data Systems.

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We have met the cosmic horror, and…

Well, here I go again (on my own, like the song says) writing another blog post.  As for why I am doing so, well, there is surely a set of causes‒potentially tracing all the way back to the Big Bang, or at least the period just during and/or after inflation, assuming that happened, which seems more likely than not‒there may not be any good reason for it.

Oh, of course, I could come up with reasons.  I could “justify” myself.  Indeed, there is reason (har) to think that justification and persuasion to bolster one’s status and identity in a tribe against others with opposed motives may have been one of the driving forces behind the development of the human reasoning capacity.  This is apart from, and perhaps almost orthogonal to, the basic power of reasoning to understand and thus best navigate the territory of reality.

Once it got started, reasoning would have accelerated thanks to biological arms races between those competing for survival and reproduction, and then it would have turned out serendipitously to have been more broadly and powerfully useful than merely for securing status and food and mates.

Imagine if the peacock’s tail had turned out not only to be ostentatious and beautiful and sexy (to peahens, anyway) but tremendously useful and broadly powerful, especially once it reached a certain level.  Imagine if the peacock’s tail had allowed peacocks to build skyscrapers and boats and trains and planes and cars, if peacocks’ tails helped peacocks build a global civilization, quite apart from their ability to secure one’s status and acquire good mates.

That’s quite possibly more or less what happened with human brains.

Of course, like the peacock’s tail, the human brain is not without its drawbacks.  I suspect that things like depression and anxiety, and perhaps even neurodivergence, are simply potential (and statistically inevitable) outcomes for a brain that has grown powerful enough to assess the world deeply and uncover the almost Lovecraftian terror of our tiny little existence when placed against the scope and scale of the cosmos.

I say “Lovecraftian”, but even with Lovecraft, though the beings in the mythos are thoroughly inhuman and incomprehensible‒unsane, as I like to say‒they are still beings.  The true cosmic horror is surely that beings of any kind are almost nonexistent; indeed, to a very good approximation, they are nonexistent.

In some senses, this can at least be morally reassuring.  If we do go and spread out through the universe‒or even just the galaxy or even just our local family of stars‒and there are indeed no other life forms, then at least we need not worry about violating implicit rights.  Uninhabited asteroids (for instance) don’t have goals or wishes and, as far as we can tell, they cannot suffer.

Of course, we may have aesthetic concerns about such things, but aesthetics are not as urgent as ethics.  And, of course, we will still have moral/ethical concerns toward each other; that almost goes without saying.

Whether or not we will exist long enough for the ethics (or lack thereof) of changing the state of uninhabited other places in the galaxy to be pertinent is quite uncertain.  I see nothing in the laws of physics that makes it impossible, so in that sense, I am optimistic.  But I see nothing in the laws of physics, nor more specifically in human nature, that makes it certain or even likely that we will survive to spread out from our native planet to any significant degree.  And I see nothing in the laws of nature that seems to imply that, if we don’t succeed and spread through the cosmos, anyone else will do so, or indeed that anyone else even exists.

Don’t get me wrong; physics clearly and undeniably allows life to exist, and it allows (human-like) intelligence and civilization to exist.  But those are two different scales of allowance.

The molecules and principles of life as we know it, with long-chain molecules capable of carrying information and of replicating themselves, leading to “competition” and “improvement” and increasing complexity and so on, seem so straightforward as to be happening potentially (but far from certainly) in a good many places in the universe.  This is straightforward enough.  The equivalents of viruses and prokaryotes may exist in many regions.  It’s even possible that there may be such life in other places in our solar system (Europa and Enceladus being possible contenders).

But multicellular, “eukaryotic” life, seems likely to be much rarer.  Basic life started on Earth, as far as we can see, very shortly after the Earth formed and cooled enough for complex molecules to endure (nearly 4 billion years ago).  Eukaryotes, especially multicellular ones, didn’t really arrive until about 500 million years ago.  So, seven eighths into the time of life on Earth, it was basically just “bacteria” and some viruses.

Then, for significant, interpersonal, symbolic and technological intelligence to develop took another…well, basically another 500 million years.  And as far as we can tell, it’s only happened once.

That doesn’t give us a good, clear picture of how rare or common such a thing is‒one is a difficult number of experimental subjects from which to draw too many conclusions‒but it’s possible that the existence of technologically intelligent life is so rare as to occur only once per, on average, every chunk of spacetime as large as our visible universe.  It could even be rarer than that.

In an infinite cosmos, of course, even such exceedingly rare events would happen an infinite number of times (so to speak).  But that doesn’t necessarily make things less lonesome.  If you have an infinite number of decks of cards (with no jokers), all thoroughly shuffled together, there are literally just as many Aces of Spades as there are red-suited cards in total (ℵ₀, the “smallest” infinity).  Nevertheless, if you draw cards randomly, you will only get an Ace of Spades one twenty-sixth as often as you will get a red-suited card.

Similarly, there are as many whole multiples of a trillion as there are integers in general (again, ℵ₀), but if you pick a random integer, you’re still only going to pull such a multiple one out of a trillion times (on average).

So, maybe the takeaway is that the real cosmic horror may be that we are the only entities haunting the abyss, and there are no (other) mad idiot gods bubbling away at the center of celestial existence.  Maybe it’s just us.  And if our lights go out, then nobody is home.

It’s worth considering, not least because it has every chance of being true, whether literally or just practically.  For if the nearest other technological life form is in another galactic cluster, for instance, then we are, for all reasonable purposes, alone in the universe.

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It’s the end of the week, but weakness persists

It’s Friday again, at last, and this is indeed the final day of the work week for me.  I am not expected to work tomorrow, and I think that even if they decided they were going to hold the office open tomorrow, I would not go in.  I am too tired and dispirited to once again throw myself into the gears of the machine just because other people want me to do it*.  Honestly, I feel it’s more likely that I’ll throw myself into real machinery than that I will go to work tomorrow.

Speaking of such throwing, as I was leaving the train yesterday evening, I found myself looking under the engine, seeing where the wheels meet the tracks, and wondering if I would have the guts just to lay my head across the track‒my neck, really‒and let myself be run over.  It would be a quick death, I suspect.

I don’t think I have the guts, though, not right now.  Also, it would be rude to screw up people’s commutes.  But it does carry a weird kind of perverse attraction.

Nothing else of interest is happening, really.  Well, perhaps one might concede that there are many interesting things happening, in the sense of the old curse, “may you live in interesting times”.  Unfortunately, even those types of interesting things that are happening are so…well, almost so trite, so pathetic, so contemptible, so predictable, so “been done already”.  None of the weird, would-be interesting, things that are happening are impressive in any sense.

Okay, well, I’ll concede the relative interest and impressiveness of the Artemis II trip around the Moon recently.  It would be more interesting if it hadn’t been something we’d done literally before I was born (3 months before, to the date, for Apollo 11’s landing), using computer systems that were‒to use the most conservative definition‒28 iterations of Moore’s Law ago.  So, literally, by more (ha) than one measure of that “law”, we are at least 2 to the 28th times as advanced, computationally, as we were when we first went to the moon.  That’s conservative, because I’ve heard descriptions of Moore’s Law that put the doubling time at 18 months, in which case there would be about 37 doubling times since then.

For those of you for whom exponentials don’t carry quite the visceral impact they ought to carry, 2 to the 28th power is 268,435,456.  So, by more conservative, every-two-year characterizations of Moore’s Law, our current computational powers are more than 268 million times what they were in 1969.  By less conservative estimates they are 137,438,953,472 times, so more than 137 billion times as advanced.

To be fair, it’s just computer tech that has advanced like that.  The process of engineering rockets hasn’t improved to the same degree, because that’s a large-scale engineering thing, and is more constrained by the rate at which one can directly interrogate nature and build and test technology.  Still, we went from Kitty Hawk to the Moon in about two thirds of a century, but in the more than half a century since, we’ve certainly not extended that streak much.

Okay, to be fair, we got pretty good at sending out space probes and such.  Even then, though, our most distant and still most impressive probes were launched in the late seventies.  There have been some quite impressive things since, and I intend no shade to be thrown at them.  That Pluto thing was very impressive, as are almost all of the Mars missions and the probes sent to other planets (on the other hand, the ISS isn’t that much more impressive than Skylab was).

The things that have improved significantly have largely done so solely because the increased capacity of computers has assisted in modeling and, well, computing things.  So, rocket science has improved to the degree that computer science has improved, divided by the fraction of that improvement that cannot make a difference in how well rockets can be made.  Something like that, anyway.

Yeah, rocket science hasn’t advanced much in my lifetime.  Brain surgery has done a bit better, but not as much better as one might have reasonably expected.

Then again, we’ve certainly improved our ability to make memes and now AI images and videos to make fun of people and express our own loyalties or outrages.  Yes, in a real sense, many of our greatest advances in recent decades have been improvements in our ability to hurl feces at each other like the monkeys we all are.  We appear to be more engaged by such shit-flinging even then we are by sex, which seems mind-boggling.

I say “we” but that broad description does not apply to everyone.  Some people are still more interested in sex.  At first glance, that would seem to be the more evolutionarily stable of the approaches, but it’s an empirical question, so we can really just wait and see which, if either, of the two tendencies prevails in the long run.

To paraphrase Dave Barry, I myself plan to be dead.

Anyway, that’s about all I have to say for this week.  I don’t mean to make a post tomorrow, but of course, as always, that is barring the unforeseen.

I hope you have a good weekend.

*Okay, to be fair, that’s not really the reason.  I do it because I get paid.

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It’s not about me. It’s not about you. It’s not even about everyone.

It’s Friday today (as I write this, anyway‒it may be another day entirely as you read it), and I am in the process of heading to work.  I will also be working tomorrow, barring (as ever) the unforeseen.  And that doesn’t just include the foreseen unforeseen; the unforeseen unforeseen (especially that one) can also change what happens tomorrow, in ways that we do not expect, more or less by definition.

Of course, the Tao te Ching advises us to act without expectation, and I suppose that’s pretty good advice.  The universe doesn’t make special deals, such that if you do some particular thing, it will definitely turn out the way you hope.  The universe does what it has always done, and you are not the subject or the object of its action‒you are just one of the innumerable things the universe does.  It did not have to ask your permission, and it will not apologize.  It also does not make exceptions, not as far as anyone can see.

 

Since the beginning

not one unusual thing

has ever happened*.

 

You can imagine and draw a map that looks any way you want, that contains fairy lands and misty mountains and roads that are shorter in one direction than another**, but if your map doesn’t match the actual territory, it’s not going to be useful for traveling through that territory safely and successfully (by whatever reasonable criteria you might judge success).  Likewise, blank spots on the map don’t imply blank spots in the territory, and writing “here be dragons” does not somehow conjure dragons into existence (alas).

Reality is that which actually exists, whether or not anyone “believes” it or “believes in it”, whether or not anyone has been, is now, or ever will be aware of it.  Heck, if eternal inflation and a consequent inflationary multiverse following (for instance) the string landscape are true, then the vast majority of the stuff of reality will never, ever be known, because most of it‒the ever-expanding inflaton field and those bubble universes where local laws are such that complexity cannot exist, as well as those huge stretches of even our universe that precede (or follow) any existence of life‒will never be accessible to conscious experience.

That’s okay.  Man is not the measure (nor the measurer) of all things.  Man is the measure of almost nothing.  Man‒indeed, all life of which we know‒is a tiny little epiphenomenon that exists in a tiny little sphere of nonzero thickness on and around the surface of the Earth.  I’ll try to remember to do the math comparing that volume to the volume of the visible universe and put it in a footnote below.  If it’s not there, I didn’t do it***.

One sometimes hears people say‒often they seem to be trying to make excuses for themselves to believe in some deity or other‒that the universe is exquisitely tuned for life, such that it requires explanation by some “supernatural” means.

When I hear or read such things, my reaction is, “What universe are you looking at?!?”  Almost no place in the universe can be survived by life as we know it, let alone produce it.  The fraction is so close to nonexistent that it is zero to a good first approximation, and a good second approximation, and a good third, and so on.

It may seem that time could possibly give us a bit more comfort than space does, since life on Earth has existed between roughly a fourth and a third of the time since our Big Bang.  But the future of this universe gives every indication of being without end, whereas conditions for large scale matter to exist‒as far as we can tell‒will not last long (not compared to infinity, which to be fair, nothing is, not even TREE(3) or Graham’s number or any other huge but finite numbers).

By the time the last supermassive black holes finish evaporating due to Hawking radiation, which will be about a googol years, things will already have been impossible for any kind of life we would recognize for eons of eons.

Of course, it’s conceivable that life will grow to become cosmically important and able to engineer specific ways for the universe to avoid heat death (or whatever is coming), or to make new universes, or whatever.  But that’s a mightily narrow course for the future to thread.

And the time until a straightforward Poincaré recurrence of the current state of our universe makes a googol years seem unnoticeably teensy by comparison.

Anyway, the main point I’m making, if there is one, is that the universe neither promises nor owes you anything.  That doesn’t mean it’s not okay for things to be important to you.  You matter (on the scales we’ve been considering) nearly as much as the whole Andromeda galaxy.

It’s fine for you to try to make your life what you want it to be.  Why not?  There’s no one else who has any legitimate claim to it (not counting children, friends, etc., all of whom could be considered part of “what you want it to be”).  Just don’t expect other people, let alone the vastly bigger number of things that are not people, to be also trying to make your life the way you want it to be.

Okay, that’ll do, pig.  I’m tired (What else is new?).  I’ll most likely write a post tomorrow.  I hope you have a good day.

*I got this haiku from Eliezer Yudkowsky’s Rationality: From AI to Zombies, though I am not sure if it originated with him.

**Actually, I’m not sure how you would draw that.

***I did it, though I initially made a mistake in calculating the surface area of the Earth, as you can see below if you look closely (I forgot to square pi in the denominator).  Anyway, assuming that the depth-to-height range of life on Earth is about 20 km, then the volume for life as we know it is about 1 x 10^19 cubic meters.  The volume of the visible universe on the other hand is 2.6 x 10^81 cubic meters (if my calculations are correct).  That means that the fraction of the universe that is, to our knowledge, amenable to life is 3.8 x 10^(-63), or 0.0000000000000000000000000000000000000000000000000000000000000038 of the volume of the universe.  By comparison, the fraction of your volume represented by one of your tens of trillions of cells is roughly 10^(-12), or .000000000001.  You lose thousands of cells every proverbial time you scratch your nose.  How much do you notice them?  How much less would the universe notice if it scratched all life off?