philosophy

by

Only the truly continuous is infinitely divisible

Well, it’s Friday, the last day of another work week—the first full week of August (or Sexember, if you prefer) in 2025.  And here I am writing things that, so far, are not only trivial but banal.  Perhaps, as I go along, I will write something more interesting and surprising, but so far, I’m not impressed with myself.  I guess these things happen.

I did not end up riding my new bike back to the house last night, because there were thunderstorms in the area, particularly down by where I live.  I’m not too intimidated by riding a bike in the rain, but it’s a new bike, and its configuration is different than the type to which I am used, and it is slightly wobblier than my normal, so I felt it wasn’t a great idea to ride it five miles in the rain.  It turned out the rain was almost over by the time I got to my train stop, but it was nevertheless still quite wet and puddly, and I probably was wise-ish to avoid riding in it.

Still, it’s slightly frustrating.  Hopefully, today it won’t be an issue, because it would be a shame to miss the whole weekend with it by the house.  There are supposed to be thunderstorms today again, but they are expected earlier in the day than yesterday, and the weather is predicted to clear by early evening.  That should be fine, at least.

Of course, weather prediction is never perfectly precise—Chaos Theory being applicable and all that—but forecasts done for only twelve hours or so in the future are likely to be much more accurate than those for a day or a few days or a week ahead of time.  After about five days, trying to get too specific a forecast is a bit of a waste of effort, and it may always be.  One cannot, with finite computing power, calculate things to infinite precision, and without infinite precision, in the long term, Chaos makes one’s predictions ever more inaccurate.

Of course, that raises (not “begs”!) the question of whether reality is actually defined in any meaningful sense down to the level where limitless precision would apply.  In other words, are Real Numbers actually a thing that exists in reality?  That may seem a strange question, given that they are called “Real Numbers”, but that’s just a name, given by humans as a file heading if you will, a way to index the subject.  It doesn’t actually signify the reality of the real numbers, any more than those who call themselves “Conservative” in the current US are in any legitimate sense conservative by most agreed upon uses of that word.

Of course, all non-complex numbers are Real numbers, and all Real numbers can be considered complex numbers (just with a zero i component if they are only Real).  The counting numbers are still Real numbers, as are all the integers and fractions, and of course, all our best known “irrational”* numbers, like π and e.  But the vast majority of Real numbers cannot be specified by any reductive formula or algorithm, but have do be described digit by digit, forever—maximum information-type entropy.

So, to describe fully a “typical” specific Real number usually requires infinite information, with infinite precision.  But there’s a real (haha) question whether any portion of reality is defined so precisely, or whether that could even have any meaning.  As far as we currently know, the smallest distance that has physical meaning is the Planck Length (about 1.6×10−35 m), and the shortest time that makes physical sense is the Planck Time (about 5.4×10−44 s), and so on.  These are very tiny numbers, but they are finite, not infinitesimal, and are certainly not infinitely non-repeating decimals.

But does the Planck Length (and Time) apply to actual, bottom-level reality, or is that merely a limit within the constraints of our current understanding?  We don’t know, for instance, how such things apply to gravity when it becomes strong enough for such scales to apply.

It’s mind-boggling, or at least wildly stimulating of probably inexpressible thought, that reality may be only finitely defined at every given point in space (which “points” themselves would only be finitely packed, so to speak, such that below a certain scale, the distance between two points would have no meaning) or that it may in fact be infinitely defined, down to the fully expressed Real Number level, and that indeed it may be infinitely divisible in the same sense Real Numbers are—and thus there would be, between any two points in spacetime, as many points as there are in ALL of spacetime.

Either possibility is wildly cool and difficult to represent internally—indeed, impossible to represent perfectly internally, but difficult even to contemplate roughly at any very deep level.  Is it any wonder that people like Cantor and Gödel were mentally ill, given the kinds of things they contemplated and explored?  I’m not saying those things were the reason for their illness; that would be a cheesy sort of magical thinking, redolent of an H. P. Lovecraft story.  But the contemplation of infinities and complexity and chaos is both sobering and intoxicating at the same time.

What do you know, I drifted into less banal areas after all.  I guess that’s a decent way to end the work week of blog posts.  I hope you all have an interesting and good weekend, without too many utterly unpredictable events (unless they’re good ones for you).

*Just to remind you, this does not refer to numbers that are in some sense crazy, just that they cannot be expressed as a ratio of two integers, no matter how large the integers.  That’s the original meaning of the word irrational, but the very fact that there existed such numbers seemed so horrifying to the old Pythagoreans—or so I’ve heard—that it almost immediately acquired it’s secondary, now more common, usage.

by

This tue, tue sullied (or solid) day

Tuesday or not Tuesday?  That is the question.  And the answer, for today at least, is that today is Tuesday.

I don’t know when you’re reading this, though.  Odds are, if you aren’t reading this on the day I publish it, that you are not reading it on a Tuesday.  In fact, once we get out past the rest of this week* there should only be a roughly 1 in 7 chance that you are reading this on a Tuesday.

That’s probably pretty obvious, huh?  Still, it can be useful to be in the habit of thinking in terms of probability and statistics, since that’s the way nature sorts itself out, right on down to the level of quantum mechanics, to the best of our understanding.  If people had a better understanding of the nature of probability, many things in the world would run far better, or so I suspect.

I have written at least one previous post (on Iterations of Zero) about how I think probability and statistics should be emphasized far more in general math education at the secondary school level (even for non-college-prep students).

Imagine a world in which most people had grown up learning about the nature of probability with reasonable rigor.  There would be fewer headline-based scares about things that are unlikely enough to be irrelevant‒e.g., plane crashes‒and more appropriate understanding about things like vaccination and disease prevention of various kinds, among numerous other matters.

Imagine if the people of the world really understood the difference between absolute risk and relative risk, and if they grasped the difference between sensitivity and specificity for medical tests.  Heck, imagine if the public at large had a decent elementary grasp of Bayesian probability.  Bayes’s Theorem is not really all that difficult, when you get right down to it.  Veritasium did a nice video about it**.

Of course, as I’ve said before, if wishes were horses, we’d all be neck deep in horse shit, whereas that’s only figuratively the case as it is.  But it would be nice if politicians and other people with undue influence had to deal with a general public that was savvy about the legitimate use of statistics and why (and how) they are fundamental to a thorough understanding of the world itself.  It’s not an accident nor a mistake that Jaynes named his book Probability Theory: The Logic of Science.

And science is not an esoteric thing.  It is not a high-falutin’ mode of thought that doesn’t pertain to the average person.  It comes from the Latin scire, meaning to know.  It is fundamental to the nature of our epistemology, to not just what we know about the world but how we come to know it, how complete and how incomplete is our understanding and what the nature of the world really is at deepest and broadest and finest and coarsest levels.

So, it’s fairly pertinent to everyone, really.  After all, if you want to win a game (or get your best score or whatever) you’re best off understanding the rules as well as you can.  A true novice is unlikely to win a game of chess, or of Go, or even of Mario Kart against someone who knows what they are doing.

Now, nature isn’t our adversary per se‒if it were, we would all be long gone‒but it “knows” its rules and always and only plays by those rules, by definition.  In fact, if you come upon a place where you think nature has broken its rules***, what’s really happened is that you’ve come to a place where you don’t understand the rules.  Nature cannot be “wrong”.  There is no such thing as the “supernatural” in reality, because anything that actually happens, that actually exists, is part of nature.

Even if you discovered that you were in a situation such as that described by Descartes or The Matrix, in which the reality you think you know is an illusion, that is simply a newly discovered fact about the nature of reality, and it raises**** the question of what is the nature of that illusion, what is behind it, and by what laws of physics do those entities operate?

So, anyway, it’s good to learn about how reality works if you want your best chance (never a guarantee) of doing what you want successfully and getting what you desire from life.  No one here gets out alive (at least it’s very unlikely) but you might as well make the game as rewarding as you can in the meantime.

*Which I suspect would be when most non-same-day readers would read this.

**He also did a really nice one about the logistic map and chaos and the Mandelbrot Set that will blow your mind if you haven’t thought about it before.

***I’m thinking of those stories with submoronic headlines such as “New discovery breaks physics!” which don’t make sense to anyone who knows anything, and which should embarrass those who write them.

****It does not beg the question.  To beg a question is not to raise the question, but rather to proceed as if it had already been asked and answered in a way that you’re presuming it to be answered.  It is a way of skirting fundamental issues and avoiding having to prove a case.  In other words, it is willfully or accidentally disingenuous.

by

Neither jot nor tittle, but just a title

It is Friday.  Friday it is.  I do not, though, plan to eat any green eggs and ham, nor do I intend to train Jedi.  I merely like to fiddle around with words.  I have also even been known to write and speak about cellos and violins and violas and basses‒wording around with fiddles, that is.

Anyway, this should be the end of the work week for me, so don’t expect a blog post tomorrow.  I’m not saying that there definitely won’t be one; it’s an outcome with a low probability, but it’s not zero.  In principle, the probability of any physically possible event happening is never zero.  But the odds can be so vanishingly small as to be zero for all practical purposes.

For instance, it’s physically possible for the entire Earth (the Moon included) to quantum tunnel to the Andromeda Galaxy, but I wouldn’t hold your breath.  I suspect that the odds of it happening are so low that the time scale between now and the evaporation of the largest black holes due to Hawking radiation (roughly a googol* years) would not even begin to make it likely to happen, even if it weren’t for the fact that the Earth and the Moon will have been so dead and so disintegrated by then that even the memory of their memory’s memories would have been long since lost to any mind that might still exist at that time…probably.

So, you can treat that Earth-Moon Andromeda tunneling as “impossible” for all practical purposes, but in principle, it could happen…

…right…

…NOW!

Okay, well, as far as I can tell, it hasn’t happened.  The sky is too hazy for me to see if the stars have changed, but I don’t think they have.  It would be quite something to experience the local stars of a different galaxy, but of course, if we tunneled into Andromeda, we might be in a relative star desert, or we might be in a place with too many stars for our long-term safety.  Also, if our solar system’s net momentum persisted, we would be unlikely to arrive in any kind of stable orbit of the center of that galaxy.

And, of course, I did not say the sun would come with us‒that would make the whole thing even more vanishingly unlikely‒so we’d all freeze in fairly short order, apart from organisms that use geothermal sources as the base of their food chains and energy cycles.  Those might survive for eons.

Anyway, it’s vastly more likely that I’ll work and write a blog post tomorrow than that we will quantum tunnel to Andromeda**, but it is still a very small likelihood***.  It may be less than one percent, I don’t know.  But it’s quite unlikely.

So, though it might be worth a quick glance to check in come the morning, especially if you were going to do that sort of thing anyway, I would not go out of your way, and I certainly wouldn’t recommend holding your breath.  I don’t think even a sperm whale could hold its breath that long, and I think they have the longest breath-holding record of any mammal (if anyone knows otherwise, please let me know).

In other news‒not that I’ve really given you any news so far‒my keyboard arrived safe and sound (so to speak) yesterday afternoon, so hopefully this morning I’ll be able to finalize the chords to Native Alien.  Then, maybe this weekend, I’ll record a little guitar-chord and voice demo so I don’t lose track of the song.

Then, next week, I can start working on a song based on the trigger “humility”.  I still have no clear conscious notion of an idea for such a song, but I’m not worried about that.  I know I can produce something (not the Beatles song).

I have to keep reminding myself that I don’t need to produce anything great as far as lyrics go‒I think the lyrics I have for Native Alien, which I shared the other day, are okay but not terrific‒I just need to get some words down.  I can always edit and alter things as the process evolves, just as the first draft of a story (or to a lesser degree a blog post) is just the beginning.

I’m also continuing with the circuit course on Brilliant, and I’m alternating reading that book Vector and The Lord of the Rings (yet again) and my own book, The Chasm and the Collision (also yet again, though LotR still holds the 2nd place record for my number of reads, well ahead of CatC and only bested in number of readings by The Chronicles of Thomas Covenant the Unbeliever).

All these are things that I can do alone, of course.  If there’s something to do that would require someone else’s participation, well, I’m shit out of luck.

I think that’s a phrase that applies fairly well to me, come to think of it.  And the word “alone” might as well have my picture next to it in the dictionary.  Though that might be confusing, since I can think of other words that would merit my picture even more than “alone” would‒words that would do their part to explicate just why I am alone, no doubt.

Batman knows I don’t want to hang around with me.

Anyway, I hope you all have a nice weekend, and if anything truly improbable happens to you, I hope it’s a very good improbable thing.

*That’s 10 to the 100th power, or a 1 followed by 100 zeros, in case you’ve forgotten whence the software company cribbed their name.

**Quantum tunneling is not rare on small enough scales, though.  It happens countless times every second in the heart of the sun, for instance.  If it did not, there would not be enough heat and pressure to overcome the coulomb barrier to fusion, and the sun would be some very large equivalent of a brown dwarf…or maybe it would contract more and get hot enough for fusion to take place without tunneling, but then I think the sun would be hotter and brighter and more short-lived, and I think it’s unlikely that the Earth would have produced any life, let alone humans.

***Think about it:  if you took something with odds of ten to the minus 120‒that’s 119 zeroes between the decimal point and the first non-zero digit‒and then made it a billion times more likely than it is, you’d still have odds of 10 to the negative 111th power, or 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001.  This is a good reminder that relative risk (or probability) is not the same as absolute risk (or probability).

by

The pointless but occasionally enjoyable music of this sphere.

Well, it’s Tuesday now, as you will know if you’re reading this on the day of its release.  You might not be sure if you read it later.  As far as I know, it’s not possible for you to read this earlier than I write it, but if you have that capacity, presumably you don’t need me to tell you what day and time it is when I’m writing it.  Presumably, you have quite a handle on times that things happen if you have that kind of ability—though I suppose that if you travel through time a lot, you might eventually have a hard time keeping track of what the local labels are on dates and times.

Sorry, that’s a bit of frivolous nonsense, which I hope doesn’t offend any non-time-travelers out there.  I’m here again, writing a blog post on my way to work and wondering what the point is to anything.  Not that I honestly suspect that there is a point to anything, really.  As far as I can see, there is no point to anything, and there is also no point to everything.  Everything just happens, and there’s no more to any of it than that, as far as I can see, and as far as anyone knows.

There are people who will tell you otherwise.  Lots of people claim to have found or been taught the meaning of life or of existence and whatnot, but either they are trying to manipulate you and/or sell you something, or they are sincere but mistaken.  In any case, they are not correct.  They do not know the meaning of life.  If they were to know it (not merely believe it), it could be conveyed in a way that, presumably, would be convincing to pretty much any listener.  Certainly they should be able to muster arguments, and perhaps evidence, that would convince a highly intelligent but disinterested extraterrestrial.

Enough philosophy for now.

Looking back to yesterday, I mentioned my idea about setting myself a goal of writing a song a week or maybe every two weeks.  Well, I didn’t do any song writing yesterday, but I did go to the Shakespeare AZ quotes site and flip coins repeatedly to pick the topic of a first song, and what I got was:  Earth.

That’s a bit unusual as a song topic, but I guess it’s doable.  I wouldn’t want to try to do some “We are the world” kind of thing, because that’s not what I really think of when I think of the Earth.  I think of the planet, the physical things, including all the animals and plants and fungi and bacteria and archaea and all that, but also including the geology and the geography and the chemistry and physics and everything else.

Despite the saying, man is not the measure of all things.  Man is barely even the measure of man, so to speak.  Humans by and large are relatively impressive animals, but they tend to think far more highly of themselves than is merited, in almost every case.

There are probably exceptions, but none of them come immediately to mind.

So, I’ll come up first with some lyrics (AKA a poem) about the planet Earth, or at least taking off from there, so to speak.  I have to remind myself that it doesn’t have to be very long, indeed that it should not be very long—I tend to get carried away when writing things, as you probably know.

I also need to decide what structure the song should be, like verse-chorus-verse-chorus-bridge-verse-chorus or what have you.  Then, after that, I’ll think of an appropriate melody to go with the words.  It will probably all be quite mediocre, but the point of the exercise is not to worry about trying to be brilliant, but just to get something done.  We’ll see how that goes.

In other news—related, at least distantly—I just discovered that my former college roommate, who is also the best guitarist I’ve known, has begun producing and releasing more new music, on YouTube and on some other site.  His YouTube channel is bluetonegtr, which is a fun name because his name is Tony and of course, he plays guitar, and the blues is a big part of any really good guitarist’s repertoire (not mine).  I highly recommend checking his stuff out; he’s really good.  I’ll embed his latest song below, for your ease of access.

As for everything else, well—the world is still shit, though it certainly doesn’t have to be.  It just tends that way, or at least the human world does.  Maybe I could make that part of my song idea.  Or maybe I could deal with the fact that even life overall is pretty crappy, I don’t know.  I guess I’ll see.  Maybe I’ll just address the issue of absurd flat-Earth notions.  Maybe I could make it a comical song.

I don’t know.  This is all probably a stupid waste of time, anyway.  But time is a waste in any case, I guess, so I might as well use it stupidly.  Everyone else seems to do so.

I hope you at least enjoy at least part of your own wasted day today.

by

“There are times I almost think I am not sure of what I absolutely know…”

Since yesterday was Monday, the 30th of June, it’s almost inevitable that today would be Tuesday, the 1st of July.  And, in fact, that is the case, unless I am wildly mistaken.

If I were to be wildly mistaken about such a thing, it’s rather interesting to consider just how I could come to be so wildly mistaken about something so prosaic and so reliably consistent.  It is from such speculations that—sometimes—ideas for stories begin.

This is not one of those times, however.  I’m not thinking about any kind of story related to that notion at all, though at times I might consider it an interesting takeoff for some supernatural horror tale.  If any of you find yourselves inspired to write a story—of any kind—based on my opening “question”, you should feel free to write that story.  I, at least, will give you no trouble.

These sorts of thoughts also remind me of a post that Eliezer Yudkowsky wrote, and which also appeared as a section in his book Rationality: From AI to Zombies.  I won’t try to recapitulate his entire argument, since he does it quite well, but it was basically a response to someone who had said or written that, while they considered it reasonable to have an open mind, they couldn’t even imagine the sort of argument or situation that could convince them that 2 + 2 for instance was not 4 but was instead, say, 3.

Yudkowsky, however, said that it was quite straightforward what sort of evidence could make him believe that 2 + 2 = 3; it would be the same kind of evidence that had convinced him that 2 + 2 = 4.  In other words, if it began to be the case that, whenever he had two of a thing and added two more, and then he subsequently counted, and the total was always three, well, though he might be puzzled at first, after a while, assuming the change and all its consequences were consistent and consistent with all other forms of counting, he would eventually just internalize it.  He might wonder how he had been so obviously mistaken for so long with the whole “4” thing, but that would do it.

This argument makes sense, and it raises an important point related to what I said last week about dogmatic thinking.  One should always, at least in principle, be open to reexamining one’s conclusions, and even one’s convictions, if new evidence and/or reasoning comes to bear.

That doesn’t mean that all ideas are equally up for grabs.  As Jefferson pointed out about governments in the Declaration of Independence, things that are well established and which have endured successfully shouldn’t be cast aside for light or frivolous reasons.

So, for instance, if you’ve come to the moral conclusion that it’s not right to steal from other people, and you’re pretty comfortable with that conclusion, you don’t need to doubt yourself significantly anytime anyone tries to justify their own personal malfeasance.  Most such justifications will be little more than excuse making.  However, if one should  encounter a new argument or new data or what have you* that really seems to contradict your conclusion, it would be unreasonable not to examine one’s conclusions at least, and to try to do so rigorously and honestly.

There are certain purely logical conclusions that will be definitively true given the axioms of a particular system, such as “If A = B and B = C then A = C”, and these can be considered reasonably unassailable.  But it still wouldn’t be foolish to give ear if some reasonable and intelligent and appropriately skilled person says they think they have a disproof of even that.  They may be wrong, but as John Stuart Mill pointed out, listening to arguments against your beliefs is a good way to sharpen your own understanding of those beliefs.

For instance, how certain are you that the Earth is round, not flat?  How well do you know why the evidence is so conclusive?  Could you explain why even the ancient Greeks and their contemporaries all could already tell that the Earth was round?

How sure are you that your political “opponents” are incorrect in their ideas and ideals?  Have you considered their points of view in any form other than sound bites and tweets and memes shared on social media, usually by people with whom you already agree?  Can you consider your opponents’ points of view not merely with an eye to puncturing them, but with an eye to understanding them?

Even if there’s no real chance that you’ll agree with them, it’s fair to recognize that almost no one comes to their personal convictions for no reason whatsoever, or purely out of perversity or malice.  At the very least, compassion (which I also wrote a little bit about last week) should dictate at least trying to recognize and consider why other people think the way they do.

Sometimes, if for no other reasons, it is through understanding how someone comes to their personal beliefs that one can best see how to persuade them to change those beliefs (assuming you are not swayed by their point of view).

This is a high bar to set when it comes to public reasonableness, I know, but I think it’s worth seeking that level.  Why aim to be anything less than the best we can strive to be, as individuals and as societies?  We may never quite reach our ideals, but we may at least be able to approach them asymptotically.  It seems worth the effort.

But I could be wrong.

*I don’t have any idea what such an argument or such evidence would be, but that’s part of the point.  Presumably, if I were being intellectually honest, and someone raised such a new argument, I would recognize it for what it was.

by

Had we but time enough, and space…

It’s the beginning of a new week but the end of an old month:  Monday, June 30, 2025, AD (or CE, if you prefer).  After tonight at midnight, we will be in the second half of this year, for whatever that’s worth.

Of course, one can debate whether Monday is really the beginning of the week or just the beginning of the work week.  Many consider Sunday to be the start of the week, at least here in this region of the “West”.

But, of course, since mainstream Christianity sees Sunday as the sabbath day, a day which is supposed to commemorate the day on which God rested after creating the world, seeing Sunday as the beginning of the week doesn’t make a lot of sense.  In the “original” observance of the sabbath—the Jewish one—Shabbat falls on Saturday (beginning Friday at nightfall), which makes more sense.  Then, Sunday really is the beginning of the week.

Not that any of this actually signifies anything real.  The start of the week or the start of a month or the start of a year are all just as arbitrary as one’s choice of the location of the origin and the x and y axes in setting up a system of coordinates in Euclidean space (or a plane, in this case).  As long as one is consistent in applying them, any calculations involved will turn out the same.  It is, in a way, a kind of symmetry, which would—in physics, anyway, if one were applying Noether’s Theorem to such as absurd situation—imply a conservation law of some variety.

I suppose there is a sort of conservation of days and months, in that one cannot by adding or subtracting days or months on a calendar change the length of a year or of a lunar cycle.  Although, with a big enough rocket or explosion or whatever, one could noticeably alter those things—it would be catastrophic for creatures on Earth, but this is science we’re talking about here, and if life on Earth must suffer for the advancement of science, then so much the worse for life on Earth!

I was kidding with that last bit there.  I am currently alive and on Earth—though at times I rue both facts—so I don’t actually want to treat life on Earth frivolously for my own curiosity’s sake.  Also, and more importantly, the people who matter most to me live on Earth*.

Anyway, over time the orbit of the moon is going to lengthen, as the moon very slowly draws farther and farther away from the Earth (which it is doing).  The length of a day and of a year both also slowly and subtly change over time.  Those time scales are long, though, and probably the sun will go red giant before either rate has changed enough to cause significant trouble, barring some large-scale asteroid collision or something similar.

This does, however, raise a point about the relationship of symmetry and conservation laws, à la Emmy Noether’s theorem.

It is the symmetry of translation—moving something from one place to another doesn’t change the laws of physics—that implies conservation of momentum.  And it is the symmetry of rotation—it doesn’t matter in what direction you’re oriented, the laws of physics are the same—that implies conservation of angular momentum.  And it is the symmetry of time—the laws of physics don’t change from one moment to the next—that implies the conservation of energy.

But here’s the rub:  on the largest of scales, the universe is not time symmetric; the past is significantly different than the present (and the future).  And so, on long time scales, the conservation of energy does not apply.  This is not merely a case in which I’m playing word games, by the way.  In this instance, I am speaking the truth about the nature of energy at the level of the cosmos according physics as it is understood today.

It’s an interesting question whether our local asymmetry in time—i.e., that the direction toward the “Big Bang” looks quite different from the other direction in time—is really just a local phenomenon.  That may seem strange, but perhaps it will be useful to consider an analogy with the various dimensions of space.

In space, in general, there is no directionality to the three dimensions.  One can go up and down, back and forth, and from side to side with equal ease, at least in space in general.  However, if you live on the surface of the Earth**, there is a very real difference between “up-down” and the other two sets of directions.

This apparent directionality to space is caused, of course, by the gravitational effect of the mass of the Earth itself.  It is an entirely local directionality, caused by a local phenomenon.  And similarly, the seeming directionality of time may be merely because we are “near” (in time) to a local, powerfully influential phenomenon:  whatever caused the Big Bang and produced a region in time of extremely low entropy and significant expansion, whether it is cosmic inflation or something else.

It seems pretty clear that, as entropy increases “over time”, the difference between past and future will become less and less noticeable, until eventually, there will be effectively no directionality to time***.  And so, in the “heat death” of the universe, the conservation of energy would steadily apply more and more, even at cosmic scales.

Not that there would be anyone to notice.

Of course, one can ask if there exists more than one time dimension.  I have asked this before, myself, I think on my other blog, Iterations of Zero.  But now there are some serious physicists entertaining the notion.  This sort of thing always makes me feel at least a little bit clever:  when I thought of something before the mainstream physics articles were published (or at least before I encountered them).

Anyway, that’s enough of that for now, this morning.  I hope you all have as good a week as you can.  Well, you will inevitably have as good a week as you can, but I hope it will subjectively be good  for you, too.

*I am not one of those people.

**As I suspect most of you do, at least physically.

***Very much in the way that, as one gets farther and farther away from the surface of some strongly gravitating body, like a planet, the difference between up and down becomes less and less prominent and finally vanishes into undetectability.

by

Compassion is true justice, isn’t it?

It’s Friday, and I’m writing what should be my last blog post of the week, since I don’t think I’m going to work tomorrow—we’ve been having a good week, all things considered, though it doesn’t have a great deal of impact on me other than making it more likely for me to have Saturday off.

I guess I’m grateful for that.  After all, I really do seem to need frequent time to decompress by just lolling about and doing nothing.  Considering that, throughout my life, I’ve almost never given myself any time to rest beyond that which is absolutely necessary, I guess it’s not too surprising that I’ve worn myself out.

I feel a vague, general hostility this morning, bordering on unfocused hatred—not towards any specific or particular thing but toward everything in general.  It’s a bit of a shame.  It’s not really new for me, though.  I remember, well into my past, realizing that I didn’t like “people” overall, but that I had a hard time specifically hating people I knew, or at least the people I knew fairly well.

That’s a curious fact.  I could recognize that, at first glance, I found humans as a whole frustrating, often disgusting, frequently reprehensible, and in general just rather pathetic—but then, when I got to know someone, I usually found them at least tolerable, and usually in some ways likable.  It’s probably because, when you get to know a person, and you see the various aspects of their lives and their personalities, you realize that even their negative attributes are clearly not of their choosing, and you develop at least a sense of compassion for them, even if there is no actual affection.

I guess, in a way, it’s a realization that humans are not much more responsible for their character than, say, a dog is, though they delude themselves otherwise.  And although there are dogs that are unpleasant, with bad habits and so on, people mostly recognize that dogs are not the authors of their negative attributes (nor of their positive ones).

Humans in general have more agency than dogs, but not nearly as much as they think they have.  No one chooses their ancestry, of course, and so they do not choose their genes, nor the location and circumstances of their birth, nor the culture in which they live, nor the things they are taught—true and false and nonspecific.  It’s probably unnecessarily biasing to think of everyone as “victims”, since not all the things that happen to us (or within us) are negative.  But certainly, people are passengers in life rather than drivers.

Yes, even those who have great wealth and power are no more the authors of the world than are the most abjectly impoverished.  They are luckier, of course; it would be churlish and foolish to think otherwise.  But they are not really any more “in charge” than anyone else is.

They don’t like to admit it, but that’s probably because they are terrified of recognizing their own powerlessness, which is understandable.  But there is little to no doubt about the fact that they are just the same type of flotsam and jetsam as everyone else.  Even the vastly wealthy and successful (and reasonably smart) Steve Jobs fell victim not just to pancreatic cancer but to his own irrational biases in eschewing scientifically supported treatment for it.

This is not to imply that, had he been treated, he would definitely have survived.  Pancreatic cancer is no joke.  The pancreas has no tissue capsule around it, and it is not surrounded by firm structures that would lead to early pain and thus early diagnosis of the illness, so by the time most people know they have the disease, it is often very advanced and has spread quite far.

Jobs’s outcome might have been no better had he engaged the best, top-level, scientifically validated treatment available (which he certainly could have afforded).  His chances would just have been better.

Sooner or later he would have died anyway, just like everyone else.  Death is not optional, not even for the universe itself, as far as we can tell.  This is not to say that spacetime may not endure forever in some form or another—it quite possibly shall—but what we consider to be our universe, a place in which complexity and life itself can exist, even if only in a tiny, tiny, miniscule fraction of the cosmos, is inescapably working toward increasing entropy.  And while a Poincaré recurrence may also wait in the distant future (the mathematics suggests that it does), that’s not likely to be much consolation to anyone here and now.

No, in the scope of time even more so than in the expanse of space*, the place for any kind of life appears tiny indeed.  People say silly things like “our universe is fine-tuned for life”, but that’s absurd on its face.  Almost every location in the cosmos is incapable of supporting life as we know it, at least without significant modification**.

People are biased because they live in places where life is possible—but that’s tautological, when you think about it.  And even here, on the surface of the Earth, in a civilization that spontaneously self-assembled to house humans and their subordinate animals, most people could not survive without the technology and services provided by (and invented by) other humans.

So, perhaps compassion is the most reasonable attitude to have toward people, even when they are at their worst.  That doesn’t mean one shouldn’t try to stop people from doing bad things and hurting each other and themselves.  But thinking of them as evil is probably not merely counterproductive but actually unjust.  Evil is an adjective that can apply to deeds, but I think it’s never a very good description of individuals in real life.

That’s me being relatively positive and gentle, isn’t it?  I know, it’s disgusting.  I’ll try to avoid it in the future.  In the meantime, please try to have a good day and a good weekend, and repeat after that for as long as you can.

*If time and space are both infinite in extent, as they may be, it’s difficult to compare fractions of them to say which might, in some fashion, be a bigger proportion.  Is a googol (10100) a bigger percentage of infinity than 1 is?  Not mathematically.  Any finite number one can choose, no matter how large, is unreasonably close to zero when compared to infinity.  And that’s just the smallest version of infinity, ℵ0.  Don’t even try to start considering fractions of, say, the real numbers.  You can’t even begin to count them, because you cannot, even in principle, find a smallest one with which to begin, or the next one from any starting point.  There are an uncountably infinite number of real numbers between any two specific numbers you might pick, no matter how close together they are.

**I did a YouTube video related to this, that I titled There is NO life in the universe.  I don’t remember how good my points were, but if you’re interested, here it is.  Actually, even if you’re not interested, here it is.

by

Dogmas are a disease, a cancer of the mind. Avoid carcinogenic thinking if you can.

I’m going to try to keep this brief this morning, so even though I brought the mini laptop computer with me when I left work on Friday*, I am writing this on my smartphone.  It does make my thumbs sore, or at least it highlights their inherent soreness and stiffness, but that’s part of what makes me tend to write less.  Or at least, I write more slowly; it is not always easy to get me to write less.

I’m choosing this partly because I am just very tired.  On Friday nights and Saturday nights, I can take a couple of Benadryl and so on to help me sleep‒I know it’s not truly good sleep, but just being unconscious for more than an hour or two at a time is such a relief‒but on work nights that’s no good.  So, especially after the artificially extended sleep on the weekend, I tend to have a bad sleep on…well, on every other night, really, but Sunday is the first such night in the work week.

Another problem, and part of my reason for worse sleep, is that I am having a bit of a flare-up of my back/hip pain, and that makes nearly every effort feel that much harder, including simply trying to sleep‒although that’s a somewhat different type of effort than many others.

So, yeah, if there’s anything noticeably different in my writing style today than in my last handful of blog posts, it may be because of the fact that I’m writing on the smartphone.  It may also be something else entirely, of course, or even a combination of things (this seems most likely).  Just because one idea seems to provide a good explanation‒a good story, if you will‒doesn’t mean it’s right.

That’s a common trap into which I frequently see people fall, and it always annoys me (especially when I’m the person).  Some situation will happen, some occurrence will occur, and someone will propose‒perhaps just to themselves‒some reason, some explanation for the event(s), and it will seem at least somewhat plausible, and at least physically possible, and it doesn’t have any glaring logical inconsistencies.  And that’s where they stop.  In their heads, that will be what they think of as the actual explanation for whatever it is they’re explaining.

Unfortunately, this is actually‒at best‒a hypothesis.

Now, if people just recognized that fact and kept the notion in their heads as a hypothesis, then this would be no problem.  All knowledge about the world is, in principle, provisional**.  There’s nothing wrong with having a hypothesis that you recognize as such.  All good science proceeds from speculation (first triggered and then confirmed or denied by observation and testing).

If one has relatively non-crucial concepts to address, one need not even be particularly bothered about confirming or denying one’s little hypothesis.  One can simply have it, tacitly implied, sitting there in potentia in the process of one’s mind.  Then if, quite by chance, one should encounter data or concepts or arguments that bear on the likelihood of that hypothesis, one can‒sometimes quite unconsciously‒adjust one’s hypothesis, or one can discard or replace it or even find oneself more confident in it.

This is all well and good.  But all too often, humans take their first plausible seeming notion and decide that they must now have the answer.  And then, depending on their emotional connection to the idea, if they encounter disconfirming evidence or argument, they twist away from it, dismiss it, seek out only pseudo-confirming ideas and evidence or even (shudder) just the company of other people who share their epistemologically suspect ideas.

These are such things as conspiracy theories are made on, or even religions (literal or figurative ones, including cultish forms of economic theories and philosophical ideas).  And when one does not update one’s ideas, when one is not aligned with reality, sooner or later, one will collide with it.  When one collides with reality, it’s never reality that is damaged.

If it were only the person who persisted in self deception that got hurt in the crash, it would still be tragic but at least at least it would be tolerable.  But as with literal crashes, the innocent are all too often harmed and made to suffer as a consequence of someone else’s poor judgment.

This is part of why I despise all dogmatic thinking.  I even coined an expression in relation to it:  Spay and neuter your dogmas!

Do not let them propagate.  Dogmas are among the most perilous of meme-plexes because they are so stiff and brittle and they tend to have sharp edges.  But even when they don’t, there is still the problem of going against reality.  One can imagine the real nature of the world as a kind of tunnel or pipe or tube‒in places it is very wide and in places very narrow.  In some regions, a fair amount of variability in course is tolerable within it, but sooner or later, if one is not moving parallel to the course of reality, one will hit a wall.

How bad the collision will be can depend on many factors; one can have a mere scrape, or a glancing blow, or one can have a true “crash and burn” situation.

Those are generally worth avoiding.

Okay, that’s it for today.  I feel a bit grumpy and curmudgeonly right now, largely because of my pain and poor sleep, but sometimes it leads to decent writing.  Whether that’s been the case today, I’ll let you be the judge.  I am not impartial.

Have a good one.

*In case it wasn’t clear, I did not work on Saturday.

**Even the old cogito ergo sum.  And don’t get me started on cogitum ergot hatto.

by

The stochasticity of quantum interactions and the names of days of the week

It’s Wednesday today.  That’s a weird way to spell a day, and a weird way to spell a version of the name of the god Wotan or Odin, after whom the day is named (unless I am quite, quite mistaken).

Our days are peculiarly and seemingly haphazardly named here in the English-speaking West.  We’re not the only ones with inconsistent weekday names, but ours are certainly a strange hodgepodge.  Sunday and Monday are relatively straightforward:  they’re named for the sun and the moon.  Then, weirdly, we suddenly switch to Norse (!) mythology and name the next four days after four of the old Scandinavian deities.  Then, abruptly, we switch to a Roman god, Saturn, for Saturday.

This “names of the days of the week” thing was clearly not planned out.  It just sort of happened.  But that’s the way so many things occur in the real world—indeed, perhaps everything just sort of happens, and at multiple levels—not randomly but nevertheless stochastically and in a way that is functionally unpredictable, at least in its details.

The various quantum fields just sort of interact in ways that, at their lowest stable energy levels, give us quarks and gluons and electrons and photons and W and Z bosons and various neutrinos and a nonzero Higgs field that interacts with some (but not all) of the other fields.  The quarks and gluons just happen to form up stably into protons (and some neutrons, but neutrons are only stable within an atomic nucleus—they decay with a half-life of about ten minutes when existing freely).  And the protons happen to interact, via the electromagnetic field, with the electron field, and they stably pair up, and neutrons come into play “afterwards”, stabilizing larger atomic nuclei (though that’s not all they do).

Then, on large scales, the graviton field (if there indeed is such a thing, which is suspected but not certain) interacts with all the other fields, and where the density of stuff is slightly higher it pulls that stuff in towards itself, and where it is less, that rarefied stuff gets thinned out further as its components are pulled by neighboring stronger areas of gravity.

This process undergoes positive feedback—as stuff gets denser, its gravity gets more prominent, and that in turn tends to make the stuff get denser still.  And if there is any net angular momentum to larger collections of the stuff—and there almost always is some net angular momentum, since there’s only one way to have zero angular momentum, and there is a functionally limitless number of ways for it to be nonzero*—the stuff starts to rotate around a net common axis.

And then, of course, we get galaxies, and in those galaxies, we get stars, in which the interactions of the various quantum fields and gravity lead the protons and neutrons to get together into bigger clumps, some of which are quite stable (and the ones that aren’t stable simply don’t endure but transform into other states until they find ones that are stable).

Then stars run out of fuel, and the various field interactions and gravity produce various kinds of spectacular deaths, most of which involve scattering at least some heavier elements** out into the reaches of the galaxies.  Then we get next generations of stars, which (by the way) clump and develop angular momentum in a smaller but similar way to the galaxies.  And now, with heavier elements, we get planets, some of which are largely solid.

I think you know the broad strokes of the rest of the story.  If not, let me know.

Of course, this is a very general sketch of how stuff just came together to form the universe in which we exist, and there’s no indication that that is anything more than just small things—or esoteric things, really, such as quantum fields and their local perturbations—interacting with each other and making patterns on larger scales, much as water molecules can clump into fantastic patterns in the frost on windows or in snowflakes when they get cool enough.  Simple (well, relatively simple) rules at small scales can come together to produce surprising things at larger scales when they all interact at secondary, tertiary, quaternary and higher levels.

If you want to see how remarkable that tendency can be even in two dimensions, find a website that lets you play “John Conway’s Game of Life” and see how stable and active and interactive shapes can arise from even truly simple rules.

What was my point?  Sorry, I got distracted there for a minute.  Oh, right, I just meant to say that the things that happen and that all seem very real and important and even inevitable and fundamental are largely the products of stochastic processes interacting in ways that ultimately are far from being representable by any kind of linear equation.

It’s entirely possible and plausible that, if the rules of the quantum fields—or the specific types of quantum fields*** involved—were different, and thus interacted with each other differently, they might still accumulate into structures and functions on higher levels, and though they might produce a universe that would be all but incomprehensible to us, and in which we could not survive for an instant, they might nevertheless form structures and processes that could become what would have to be called “alive” and even “aware” and “intelligent”.

But in how many such universes would there be creatures that name the days of whatever passes for their weeks after various astronomical bodies (or whatever they have that is comparable) and random mythological figures from different places and times?

I leave it to the reader to speculate.

*There’s only so fast anything can be spinning, since no part of the spinning thing can exceed the speed of light.  Even black holes have a maximum angular velocity.  Nevertheless, both the angular velocity and the net axis of rotation can be more or less continuously variable.  If we can apply the real numbers—which ironically may not be possible in the real world—there is an uncountably infinite number of possible ways for angular momentum to be nonzero.  That makes zero really unlikely and unstable.

**Astronomers call any element but Hydrogen and Helium a “metal”, which is a very loose use of the term if you ask me.  I think many astronomers would agree, and sometimes I think I detect more than a tiny amount of embarrassment when they tell people that astronomical definition.

***Or the configurations of strings and branes if superstring/M theory turns out to be correct.

by

Monday morning, wearing down

Well, it’s Monday again.  Time keeps marching on without respite, as it is apparently wont to do, “progressing” in the direction of increasing entropy, whether time is a fundamental aspect of the universe or an emergent phenomenon.  In either case, there doesn’t seem to be any sort of time stream or time vortex like in Doctor Who, but rather a process that simply is a linear dimension with some “entanglement” (not to be confused with quantum entanglement) with the dimensions of space, such that motion and acceleration in space changes one’s “motion” in time, in an updated version of the Pythagorean Theorem.

For those of you who like to share the joke about “Yet another day when I didn’t use a2 + b2 = c2” you’re really depriving yourself of a deep understanding of something that turns up in and governs a ridiculous number of the things and processes in the physical reality in which you live.  Consciousness—despite clever but tortured sophistry (in my opinion) by some prominent philosophers of mind—in no way appears fundamental to the universe*.  On the other hand, the Pythagorean Theorem, which was neither invented nor discovered by Pythagoras, applies in all levels of dimensions, however many you might conjure, and with the modification to make it reflect velocities, it applies to spacetime as well.

There can be no readily conceivable brains** in two spatial dimensions, but Pythagoras nevertheless applies.  In one dimension, it doesn’t really apply, but in one dimension there are no triangles of any kind, so it doesn’t make much difference.  It’s difficult to imagine how consciousness could possibly occur in one dimension (notwithstanding the seemingly one-dimensional paucity of ideas held by so many people, especially in politics).

Anyway, enough of this nonsense.  Well, it’s not nonsense, but it is rather pointless meandering of random thoughts that interest no one but me, and will probably lose me readers.  Weirdly enough, people seem to come and read more often when I write about my depression and self-hatred and anxiety and ASD and how there’s absolutely nothing going on in my life that makes it worth living.

Well, rest assured, all those things are still present and active and driving me toward an early grave, which in some senses will be a release, or at least an escape of sorts.

I keep trying to think of things to engage myself and my interests, but so far to no avail.  I think about asking my boss to give me back my black Strat to play at the office, or I consider bringing in another guitar, or maybe even getting a portable keyboard or something, but when I think of any of them, I cannot even imagine doing anything but sort of staring at them as if I don’t even know what their purpose is.  I don’t play my guitars or my keyboard at the house, either.

It’s likewise with even fiction, other than silly Japanese light novels that take a day or so to read (not continuous time).  I think I like them mainly because of the social interactions of the characters, many of the main ones of whom are somewhat socially awkward.  It can feel, however briefly, that I have a social group of some sort, as I read the stories.  Of course, that means that once I’m done reading there is a comparative let down, which sometimes makes me feel worse than I did before.

I tried to read some of Feynman’s Lectures on Physics, but I lost interest almost immediately, though he was a brilliant and engaging teacher.  I also tried to read some of Anthony Padilla’s Fantastic Numbers and Where to Find Them, which is also very good and fun; if you’re interested in who he is, you can check out the YouTube channel Sixty Symbols, and sometimes Numberphile.  He shows up in both places fairly often.  But in any case, though I like his book (I’ve read it before) it has not been able to grip me.

I’ve also tried to start reading Stephen King’s novella The Life of Chuck, since it’s now a movie and is getting positive reviews.  At least Stephen King is almost always an engaging read.  But I’m not sure I’m getting into the story.  Quite a while ago, I started the first story in If It Bleeds, the collection in which the above novella appears, but I couldn’t get into it at all.  When I can’t even get into reading Stephen King***, things are looking bleak.

I did watch the rest of the latest series of Doctor Who, and it was pretty good, and quite surprising at the end, but Batman only knows when the next series is going to happen, and there will only be a handful of episodes if it keeps up as it has been.  That’s too little too late for me to use as motivation for continued existence.

I don’t know what to do.  I really don’t know.  I feel very lost and, more importantly, very much without any internal impetus.  I can’t even listen to songs I like, let alone try to sing along (or play) without feeling like I’m going to cry, though I don’t understand why.  I’m at the end of my rope (I have two, and both are tied into nooses, just for “fun”).

Anyway, that’s enough.  Sorry to bother you with my crap again, but in my mind, you asked for it by complaining about my tedious math and science stuff.  I hope you have a good day.  Unless you’re lucky (or I am) I’m sure to be back again tomorrow with another blog post.

*The only reason I can discern why some people think consciousness is fundamental to the universe is that consciousness is fundamental to human experience—indeed, one could say that it is human experience—and of course, such people seem tacitly or implicitly to think humans are the measure of all things simply because that is what they are.

**The degree of interconnectivity is just too low.  Connections between 2D neurons would be terribly limited, as would room for such things.  I suppose that, since we can always map anything three-dimensional onto some two-dimensional surface, à la Bekenstein-Hawking black hole entropy and the holographic principle, we could construct a sort of brain in 2D, but that’s a tortuous process, and seems quite unlikely.  Of course, 4D would give us even more available connectivity than 3D—also there are no knots or tangles in 4 spatial dimensions—but there are other issues with 4 (macroscopic) spatial dimensions that would seem to get in the way of life as we know it, such as the nature of gravity (and other forces) and the rate of such forces’ diminishment.  For instance, the force of gravity (and electromagnetism, etc.) in four dimensions would fall off at a rate proportional to r3 rather than r2, and there are apparently no stable orbits in such situations.

***What’s worse, I cannot even get into reading Tolkien.  I’ve tried.  When neither Stephen King nor Tolkien, nor even well-written science books, can engage me, something indeed has happened.