Ringing the changes

I find human behavior absolutely baffling a lot of the time.

I've spent a significant fraction of my life thinking, "Why did (s)he do/say that?"  One positive result of this is that it's turned me into a dedicated observer of the other members of my species.  Even so, I have to say that my efforts have, on the whole, been a failure.  After 64 years on this planet I'm no closer to figuring out why people act the way they do than I was on day one.

Mind you, I'm not saying all the behavior is bad.  It's just that a lot of it is weird.  Take, for example, the English practice of change ringing, one subset of a larger topic called campanology -- the study of bells.

[Image licensed under the Creative Commons Keichwa at German Wikipedia., Poppenreuth-glocke-1695, CC BY-SA 3.0]

"Ringing the changes" involves taking a sequence of tuned bells and using them to ring a series of patterned mathematical permutations.  So with six bells -- numbered from 1 (the highest-pitched) to 6 (the lowest) -- it might start with a straight cadence down the scale, 1-2-3-4-5-6.  But from there?

One possibility is called a "Plain Bob Minor" (being England, all of the patterns have extremely creative and quirky names), in which each bell takes a turn working its way down the sequence and then back up, and the rules are (1) no sequence can happen twice, and (2) each bell can only switch on each subsequent sequence by a single position.  Here's a part of the Plain Bob Minor pattern, following the positions of the #1 and #2 bells with blue and red lines, respectively:

As you can see, the pattern is mathematical; in fact, whole books have been written analyzing the math of change ringing.  And let me tell you, it's complex.

I first ran into change ringing in the wonderful mystery novel The Nine Tailors by the brilliant British author Dorothy Sayers.  The whole story revolves around it; even the chapters are named after change-ringing patterns, often involving clever puns (Sayers is at her sparkling, intellectual best in this book).  Despite being fairly good at math, how the patterns work (on the larger scale) escapes me; but -- amazingly -- practicing change-ringers have entire sequences memorized.

This is even more astonishing when you consider that a "Full Peal of Seven" -- seven tuned bells -- has 7! (seven factorial, or 5,040) different permutations, each of which has to be rung in its proper place. 

Ringing a Full Peal of Seven takes over three hours.

Here's a group of people doing a sequence called "Jump Changes," which requires twelve bells.  Fear not, this is only a small part of the sequence.  A Full Peal of Twelve would (literally) take years to ring.

What strikes me about change ringing is that although it's mathematically and historically interesting, it's not very interesting to listen to.  At least not for me.  Because a Full Peal goes through all possible permutations, it includes some that sound pretty random.  And long sequences just kind of go on and on.  And on.

In the case of Full Peals of Twelve, AND ON AND ON AND ON.

So it seems like kind of an odd hobby.  Don't get me wrong; I'm glad people are keeping it up.  For one thing, if you watched that video, you probably noticed that change ringing would be really good for building upper-body strength.  For another, it's a piece of English culture that goes back centuries, and it would be sad if it died out.  But more than that, I love that people are so devoted to something so purely weird.

I might not get why this pastime appeals to you, but more power to you if it does.  Hell, if I can spend my time making ceramic Doctor Who figurines, you can be deeply invested in memorizing mathematical patterns of bell ringing.

Maybe I don't understand all the strange side alleys of human behavior, but I definitely encourage them.  The world would be a far happier place if more people devoted their energy into odd and pointless, but entirely harmless, hobbies, rather than using it to figure out how to make groups of people they don't like as miserable as possible.

So hooray for weirdness.  Be proud of what you love, even if other people don't approve.  I was told over and over when I was a child, "No one wants to hear about that," whenever I talked about stuff I was interested in.  The experience left me with a lifelong reluctance to talk to people about what I love most.

And how sad is that?

So let your freak flag fly.  You collect bottle caps?  Cool!  You're a geocacher?  Awesome!  You carve little statues out of bars of soap?  Amazing!  We need more of that kind of thing, and less of... *gestures around vaguely at everything*

Time to ring the changes on your own individuality.  Proudly.

****************************************

This week in lunacy

On the whole, I'm an optimist.

It seems a happier way to be.  In general, I would rather expect people to behave well and occasionally be disappointed than to start from the assumption that everyone is an asshole and occasionally be pleasantly surprised.  I know a couple of people who are diehard pessimists, who believe that the worst of humanity is the rule and not the exception, and by and large they're chronically unhappy -- even when things turn out well.

On the other hand, the last few years have been a trial to my generally positive mindset.  I've been writing here at Skeptophilia for fifteen years, and the anti-science attitudes and loony counterfactual beliefs that impelled me to start this blog seem to be as common as ever.  Take, for example, the four stories I came across on Reddit, one after the other, while I was casting about for a topic for today's post.

First we have an article courtesy of the ever-entertaining Representative Marjorie Taylor Greene of Georgia, whose main function seems to be making sure that Lauren Boebert is never proclaimed the Stupidest Member of the United States Congress.  Greene just introduced a bill to make weather modification a felony, because -- and this is a direct quote -- "we need clean air, clean skies, clean rain water, clean ground water, and sun shine just like God created it!"

The irony here is that Greene has supported every one of Donald Trump's efforts to weaken environmental protection -- hobbling the Environmental Protection Agency and the Clean Water Act, crippling research into climate change, increasing the number of coal-fired power plants, clear-cutting forests on public land, and deregulating mining and oil production.  But sure, Marjorie, let's outlaw "weather modification," which she says was responsible for Hurricane Helene, the California wildfires, and most recently, the devastating flooding in central Texas.

Hell, if the evil liberal-controlled Deep State could modify the weather, they'd have dispatched EF-5 tornadoes to level Mar-a-Lago ages ago.  But I wouldn't expect logic like that to appeal to Greene, who responded to critics by using my least favorite phrase, "I've done my research," and based on that has come to the conclusion that people who say that hurricanes, wildfires, and floods are natural events are big fat liars.

Expect her "research" to that effect to appear in Nature any time now.

Then we had evangelical preacher Troy Brewer, who claimed that the Texas floods weren't weather modification, they were God sending a message to us.  It was significant, he said, that the flooding (well, some of the flooding) happened on July 4.  In a passage that I swear I'm not making up, Brewer said, "It was a divine signal...  Whenever this thing happened on July the 4th… this is not just about Texas.  This is a word for all the United States of America.  It's no coincidence that 1776 divided by two is 888, the numerical value of the name Jesus in Greek.  Did you know that there were 888 people rescued out of that creek?  888 is the number of Jesus...  And remember that the site of the flood, Kerrville, is the home to the 77-foot-high sculpture known as The Empty Cross."

It does strike me as odd that if this is God sending a message about how lawless and evil and wicked we all are, smiting the shit out of central Texas -- one of the most devoutly Christian places in America -- is kind of an odd move.  I mean, Kerrville isn't exactly Sodom and Gomorrah.  But "God drowned hundreds of good Christians to show you all how important it is to be a good Christian" isn't any crazier than a lot of what these people believe, so I guess it's not really all that surprising.

Next, there's Joe Rogan, who if this was a fair world would have zero credibility left, claiming that Lyme disease was a deliberately-leaked biological weapon from the secret labs on Plum Island.  It probably won't take you longer than a couple of nanoseconds to figure out where he got this amazing revelation from:

RFK Jr.

The only person out there with less scientific credibility than Joe Rogan.

"The ticks are an epidemic because of what happened at Plum Island and the other labs," RFK said in the January 2024 episode of the RFK Jr Podcast.  "We also know that they were experimenting with diseases of the kind, like Lyme disease, at that lab, and they were putting them in ticks and then infecting people."

Of course, this is the kind of thing that gives Joe Rogan multiple orgasms, so he was all in on the bioweapon claim. 

"Turns out there's a lot of real evidence that Lyme disease was weaponized," Rogan said.  "It came out of a lab called Plum Island, which was close to Lyme, Connecticut.  And RFK Jr. firmly believes that this was a weapons program...  What they were going to do is develop these fleas and ticks with a disease that spreads rapidly, wipes out the medical system of a community.  So, you could dump them from a plane, everybody gets infected, overwhelms their medical system, and then they're more vulnerable if you want to attack them...  Can you imagine if those cunts created a fucking disease and now everyone on the East Coast has it?  Because it's mostly out there."

The Rogan/RFK Jr. claim kind of falls prey to the fact that there's ample evidence that Lyme, caused by the bacterium Borrelia burgdorferi, has been around for a very long time.  To take just one example, Ötzi -- the "Ice Man," the five-thousand-year-old frozen human found in the Alps in Switzerland -- was found in 2012 to be Lyme-positive through DNA analysis of his tissues.

What, Joe -- did the evil Plum Island scientists use their time machines to go back and infect Ötzi in order to throw us all off their trail?  Or should we tune in next week to hear you come up with some even more insane explanation?

Finally, we have a loony claim surrounding a viral craze I hadn't even heard of.  To be fair, I'm not exactly the sort who immerses himself in pop culture, but this one is apparently huge and had escaped me entirely.  It's called a "Labubu doll," and is a "plush monster elf toy" created by Hong Kong designer Kaising Lung.  It got picked up by a couple of big names like Dua Lipa and Rihanna, and now everyone wants one.

Well, you can't have a popular toy out there without someone deciding that it's eeeeee-vil.  And especially... look at those teeth.  So now people on X and TikTok are warning that you should burn your Labubu doll because it's possessed by a demon called, I shit you not, Pazuzu.

Notwithstanding the fact that Labubu and Pazuzu sound like names that a rich old lady would give her poodles, people are taking this extremely seriously.  "I’m not superstitious, I’m a little stitious, but I’d never buy a Labubu," said one person on X.  "It comes from Pazuzu, which is a demon, and possessed the girl in The Exorcist."

So this individual is warning us not to buy a doll representing a fictional creature because it might be inhabited by a fictional demon who possessed a fictional girl in a fictional movie.

But do go on about how plausible all this is.

Then there's the person who commented, "Please before falling into the trap of Labubu or any trend nowadays, do your research.  THEY’RE MADE AFTER A DEMON DEITY (Pazuzu as they say)."

Yes, of course!  For fuck's sake!  Do your research!

Other people are blessing their Labubus or anointing them with holy water to "turn them into protector spirits." I guess this is better than burning them, at least from the standpoint of releasing toxins from burning plastic into the air, which would probably make Marjorie Taylor Greene think that the liberals were trying to modify the weather using smoldering demon flesh or something.

So.  Yeah.  Some days it's hard to remain optimistic.  Just yesterday, my wife and I were discussing how the average dog is a better person than the average person, and these stories haven't done anything to diminish that assessment.  So I think I'll spend the rest of the day socializing with my dogs.

I'll try being optimistic about humanity again tomorrow.  We'll see how long it lasts.

****************************************

Mental models and lying stones

Richard Feynman famously said, "The first principle is that you must not fool yourself -- and you are the easiest person to fool."

This insightful statement isn't meant to impugn anyone's honesty or intelligence, but to highlight that everyone -- and I'm sure Feynman was very much including himself in this assessment -- has biases that prevent them from seeing clearly.  We've already got a model, an internal framework by which we interpret what we experience, and that inevitably constrains our understanding.

As science historian James Burke points out, in his brilliant analysis of the scientific endeavor The Day the Universe Changed, it's a trap that's impossible to get out of.  You have to have some mental model for how you think the world works, or all the sensory input you receive would simply be chaos.  "Without a structure, a theory for what's there," Burke says, "you don't see anything."

And once you've settled on a model, it's nearly impossible to compromise with.  You're automatically going to take some things as givens and ignore others as irrelevant, dismiss some pieces of evidence out of hand and accept others without question.  We're always taking what we experience and comparing it to our own mental frameworks, deciding what is important and what isn't.  When my wife finished her most recent art piece -- a stunning image of a raven's face, set against a crimson background -- and I was on social media later that day and saw another piece of art someone had posted with a raven against red -- I shrugged and laughed and said, "Weird coincidence."

Quoth the Raven, pen/ink/watercolor by Carol Bloomgarden (2025) [Image used with permission]

But that's only because I had already decided that odd synchronicities don't mean anything.  If I had a mental model that considered such chance occurrences as spiritually significant omens, I would have interpreted that very, very differently.

Our mental frameworks are essential, but they can lead us astray as often as they land us on the right answer.  Consider, for example, the strange, sad case of Johann Beringer and the "lying stones."

Johann Bartholomeus Adam Beringer was a professor of medicine at the University of Würzburg in the early eighteenth century.  His training was in anatomy and physiology, but he had a deep interest in paleontology, and had a large collection of fossils he'd found during hikes in his native Germany.  He was also a devout Lutheran and a biblical literalist, so he interpreted all the fossil evidence as consistent with biblical events like the six-day creation, the Noachian flood, and so on.

Unfortunately, he also had a reputation for being arrogant, humorless, and difficult to get along with.  This made him several enemies, including two of his coworkers -- Ignace Roderique, a professor of geography and algebra, and Johann Georg von Eckhart, the university librarian.  So Roderique and von Eckhart hatched a plan to knock Beringer down a peg or two.

They found out where he was planning on doing his next fossil hunt, and planted some fake fossils along the way.

These "lying stones" are crudely carved from limestone.  On some of them, you can still see the chisel marks.

More outlandish still, Roderique and von Eckhart carved the word "God" in Hebrew on the backs of some of them.  Making it look like the artisan had signed His name, so to speak.

One colleague -- who was not in on the prank -- looked at the stones, and said to Beringer, "Um... are you sure?  Those look like chisel marks."  Beringer dismissed his objections, and in fact, turned them into evidence for his explanation.  Beringer wrote, "...the figures... are so exactly fitted to the dimensions of the stones, that one would swear that they are the work of a very meticulous sculptor...[and they] seem to bear unmistakable indications of the sculptor's knife."

They were so perfect, Beringer said, that they could only be the work of God.

So as astonishing as it may seem, Beringer fell for the ruse hook, line, and sinker.  Roderique and von Eckhart, buoyed up by their success, repeated their prank multiple times.  Finally Beringer had enough "fossils" that in 1726, he published a scholarly work called Lithographiae Wirceburgensis (The Writing-Stones of Würzburg).  But shortly after the book's publication -- it's unclear how -- Beringer realized he'd been taken for a ride.

He sued Roderique and von Eckhart for defamation -- and won.  Roderique and von Eckhart were both summarily fired, but it was too late; Beringer was a laughingstock in the scientific community.  He tried to recover all of the copies of his book and destroy them, but finally gave up.  His reputation was reduced to rubble, and he died twelve years later in total obscurity.

It's easy to laugh at Beringer's credulity, but the only reason you're laughing is because if you found such a "fossil," your mental model would immediately make you doubt its veracity.  In his framework -- which included a six-thousand-year-old Earth, a biblical flood, and a God who was perfectly capable of signing his own handiwork -- he didn't even stop to consider it.

The history of science is laden with missteps caused by biased mental models.  In 1790, a report of a fireball over France that strewed meteorites over a large region prompted a scientific paper -- that laughingly dismissed the claim as "impossible."  Pierre Bertholon, editor of the Journal des Sciences Utiles, wrote, "How sad, is it not, to see a whole municipality attempt to certify the truth of folk tales… the philosophical reader will draw his own conclusions regarding this document, which attests to an apparently false fact, a physically impossible phenomenon."  DNA was dismissed as the genetic code for decades, because of the argument that DNA's alphabet only contains four "letters," so the much richer twenty-letter alphabet of proteins (the amino acids) must be the language of the genes.  Even in the twentieth century, geologists didn't bother looking for evidence for continental drift until the 1950s, long after there'd been significant clues that the continents had, in fact, moved, largely because they couldn't imagine a mechanism that could be responsible.

Our mental models work on every level -- all the way down to telling us what questions are worth investigating.

So poor Johann Beringer.  Not to excuse him for being an arrogant prick, but he didn't deserve to be the target of a mean-spirited practical joke, nor does he deserve our derision now.  He was merely operating within his own framework of understanding, same as you and I do.

I wonder what we're missing, simply because we've decided it's irrelevant -- and what we've accepted as axiomatic, and therefore beyond questioning?

Maybe we're not so very far ahead of Beringer ourselves.

****************************************

Dream weavers

In Ursula LeGuin's amazing and disturbing novel The Lathe of Heaven, a very ordinary guy finds that he has a completely unordinary ability.

When he dreams, he wakes up and finds that whatever he dreamed has become reality.

George Orr, the protagonist, is terrified by this, as you might imagine.  It's not like he can control what he dreams; he isn't able to program himself to dream something pleasant in order to find he has it when he wakes.  No, it's more sinister than that.  Consider the bizarre, confusing, often frightening content of most of our dreams -- dreams that prompt you to say the next morning, "Where the hell did that come from?"

That is what makes up George's reality.

The worst part is that George is the only one who knows it's happening.  When his dream content alters reality, it alters everything -- including the memories -- of the people he knows.  When he wakes up and finds that the cityscape has changed and that some people he knew are gone, replaced with others he has never seen before, everyone else's memories changed as well.  George wakes to find he has a girlfriend, but she doesn't think it's sudden and weird; being George's girlfriend is what she remembers.

Only George sees that this is just the latest version of a constantly shifting reality.

So when he tries to explain to people what he can do, and (if possible) find a way to stop it, no one believes him.  No one... except a ruthless and ambitious psychiatrist who realizes that if he can figure out how to manipulate George's dreams, he can fashion a world to his own desires, using George as a tool to create the reality he wants.

LeGuin's terrifying vision of what happens when grasping amorality meets a naïve but useful skill is turning out not to be far from being realized.  George Orr's paranormal ability is the stuff of fiction, of course; but the capacity for influencing our dreams is not.

Nor, apparently, is the potential for using our dreams as a conduit for suggestions that might alter our behavior -- with or without our permission, possibly with or without our knowledge.

[Image licensed under the Creative Commons stephentrepreneur, Hurtle Square dreams, CC BY-SA 2.0]

I found out recently from a friend and loyal reader of Skeptophilia that there is a cohort of powerful corporations who have teamed up to see if there's a way to insert advertising content into our dreams.  Xbox, Coors, Microsoft, and Burger King, among others, have been experimenting on volunteers to see if they can introduce targeted advertising while we're asleep, and (especially) while we're at the neurologically hyperactive REM (rapid eye movement) stage of sleep, in order to induce people to alter their behavior -- i.e., purchase the product in question -- once they wake up.  They've had some success; a test by Coors found that sixty percent of the volunteers were susceptible to having these kinds of product-based suggestions influence their dream content.

Forty sleep and dream researchers are now pushing back, and have drafted a document calling for regulation of what the corporate researchers are calling "dream incubation."  "It is easy to envision a world in which smart speakers—forty million Americans currently have them in their bedrooms—become instruments of passive, unconscious overnight advertising, with or without our permission," the authors state.

My fear is that the profit motive will outweigh any reluctance people might have toward having their dreams infiltrated by corporate content.  If cellular service providers were willing to give users a discount on their monthly fees, provided they agreed to allow themselves to be exposed to ads during the nighttime hours, how many people would say, "Sure, okay, go for it"?  I know for myself, I'm often willing to tolerate ads on games and video streaming services rather than paying extra to go ad-free.  I'd like to think that I'm able to tune out the ads sufficiently that they're not influencing my behavior, but what would happen if I'm exposed to them for all eight to ten hours that I'm sleeping every night?

Not all scientists are concerned about the technique's efficacy, however.  "Of course you can play ads to someone as they are sleeping, but as far as having much effect, there is little evidence," said Deirdre Barrett, a dream researcher at Harvard University.  "Dream incubation doesn’t seem very cost effective compared with traditional advertising campaigns."

Even if it doesn't have the manipulative capability the corporations are hoping, the idea still scares the hell out of me.  When every moment of our days and nights become just another opportunity for monetization, where will it all stop?  "I am not overly concerned, just as I am not concerned that people can be hypnotized against their will," said University of Montreal dream researcher Tore Nielsen.  "If it does indeed happen and no regulatory actions are taken to prevent it, then I think we will be well on our way to a Big Brother state … [and] whether or not our dreams can be modified would likely be the least of our worries."

Which is it exactly.  As I've pointed out before, my main concern is about the increasing control corporate interests have over everything.  And here in the United States, the problem is that the people who could potentially pass legislation to limit what the corporations can get away with are being funded largely by corporate donors, so they're not anxious to put the brakes on and see that flow of cash dry up suddenly.  It's a catch-22 that would require the government to police its own behavior for no other reason than simple morality and ethics.

And you can guess how successful that is likely to be, especially considering the United States's current ethically-challenged administration.

I'm hoping that at least someone is listening, though. I tend to agree with Nielsen; I don't think our dream content will be as easily manipulable, or as behavior-altering, as the corporations hope.  But what I'm more worried about is that once we refuse to delineate a hard line around our personal lives, and say to them, "Here, and no further," we've opened ourselves up to there being no part of our personal space that isn't considered a target for monetization.

****************************************

Unto the breach

Today I dodged a battle on social media, and I honestly don't know if it makes me a coward or just someone who tries to be prudent about which battles are even winnable.

The person in question, an acquaintance I only know through a mutual friend but who connected to me a couple of years ago for reasons unknown, has thrown out some questionable stuff before, but nothing as bad as this. " There aren't many genders," she posted.  "There are TWO genders and many mental disorders."

After I stopped seeing red enough that I could tell what was on my computer screen, I pondered a variety of responses I could have made.  Among the top contenders:

• "Wow, that's some weapons-grade stupidity, right there."
• "Do you realize what a narrow-minded bigot this makes you sound like?"
• "Get off your fucking high horse and do some research."

Then I calmed down a little more, and considered other, marginally less obnoxious responses:

• "Maybe before you post stuff like this, you should talk to someone who is trans and get actual information on what it's like."
• "I believe the Bible you claim to be so fond of has a lot more to say about charity, kindness, and passing judgment than it does about the biology of gender.  You should reread those verses."
• "I hope like hell your grandchildren don't turn out to be LGBTQ.  For their sake, not for yours."

But finally I said nothing, and unfriended her.

I know it's the duty of every responsible person to confront racism, homophobia, bigotry, narrow-mindedness, and general idiocy.  Not doing so, leaving this kind of thing unchallenged, gives it tacit permission to continue.  I never would have let something like this go in my classroom; the few times I ever got really, truly angry at students during my 32 year career were over issues like this.

But lord have mercy, I am tired.  I'm tired of seeing this kind of bullshit trumpeted as if it was a proclamation of an eternal truth.  I'm tired of trying to convince the anti-vaxxers and climate change deniers, the nitwits who claim the 2020 election was stolen and that Trump is the Second Coming of Jesus, the people who believe that the January 6 insurrectionists were Antifa and liberals in disguise.

Plus, there's the question of what good it would have done if I had confronted her on her nasty, sneering post.  She barely knows me; I think we've maybe talked in person once.  Since then I've had zero interactions with her, online or anywhere else.  Why would she listen to me?  More likely she'd write me off as another godless liberal, getting all bent out of shape because she dropped a Truth Bomb on me.  What is the chance that anything I could have said, polite or rude, would have changed her attitude one iota?

[Image licensed under the Creative Commons Blaine A. White, The Argument 01, CC BY-SA 4.0]

Still, I can't help but feel that I took the coward's way out.  If I'm not going to challenge stupidity and bigotry, it kind of gives lie to the entire raison d'être of this blog I've written so diligently on for the last fifteen years.  Every time we let someone like her get away with something like this unchallenged, it does double damage -- it further convinces any LGBTQ people who read it that they don't have (or aren't deserving of) unequivocal support, and it gives any other bigots in the studio audience free license to perpetuate their own hateful views.

So I dodged my responsibility, and I'm still feeling a little sick about it.  I'm not going to go back and re-friend her just to have an opportunity to say, "Oh, and about that post...!", and I guess there's an outside (probably minuscule) chance that when she sees she's lost friends over it, she might reconsider.

But I still think I made the wrong decision.

Right now, I'm taking a deep breath and recommitting myself to fight like hell against this sort of thing.  I can't let bigotry slide, excuse it by saying "it's just their religion/politics/age," give it a pass because I'm afraid of what they might say in response or who else I might piss off.  Okay, I'm tired, but it's still a battle worth fighting -- and one that can be won, but only if we refuse to accept prejudice and hatred every damn time we see it.

Shakespeare put it far more eloquently, in Henry V:

Once more unto the breach, dear friends, once more;
Or close the wall up with our English dead.
In peace there's nothing so becomes a man
As modest stillness and humility:
But when the blast of war blows in our ears,
Then imitate the action of the tiger;
Stiffen the sinews, summon up the blood,
Disguise fair nature with hard-favour'd rage;
Then lend the eye a terrible aspect;
Let pry through the portage of the head
Like the brass cannon; let the brow o'erwhelm it
As fearfully as doth a galled rock
O'erhang and jutty his confounded base,
Swill'd with the wild and wasteful ocean.

****************************************

Tracking the hailstones

One of the most shocking results from mathematics -- or even scholarship as a whole -- is Kurt Gödel's Incompleteness Theorem.

Like (I suspect) many of us, I first ran into this startling idea in Douglas Hofstadter's wonderful book Gödel, Escher, Bach: An Eternal Golden Braid, which I read when I was an undergraduate at the University of Louisiana.  I've since reread the whole thing twice, but I'm afraid the parts about formal logic and Gödel's proof are still a real challenge to my understanding.  The gist of it is that Gödel responded to a call by German mathematician David Hilbert to come up with a finite, consistent set of axioms from which all other true statements in mathematics could be derived (and, significantly, which excluded all false or paradoxical ones).  Gödel picked up the gauntlet, but not in the way Hilbert expected (or wanted).

He showed that what Hilbert was asking for was fundamentally impossible.

Put succinctly, Gödel proved that if you come up with an axiomatic system that can generate all true statements of mathematics, it will also generate some untrue ones; if you come up with a system that generates only true statements, there will always be true statements that cannot be proven from within it.  In other words, if a mathematical system is complete, it's inconsistent; if it is consistent, it's incomplete.

The result is kind of staggering, and the more you think about it, the weirder it gets.  Math is supposed to be cut and dried, black-and-white, where things are either provable (and therefore true) or they're simply wrong.  What Gödel showed was that this is not the case -- and worse, there's no way to fix it.  If you simply take any true (but unprovable) mathematical statements you find, and add them to the system as axioms, the new expanded system still falls prey to Gödel's proof.

It's the ultimate catch-22.

The problem is, there's no way to tell the difference between a true-but-thus-far-unproven statement and a true-but-unprovable statement.  There have been a number of conjectures that have baffled mathematicians for ages, and finally been proven -- the four-color map theorem and Fermat's last theorem come to mind.  But one that has resisted all attempts at a proof is the strange Collatz conjecture, also known as the hailstone sequence, proposed in 1937 by the German mathematician Lothar Collatz.

What's wild about the Collatz conjecture is that it's simple enough a grade-school student could understand it.  It says: start with any natural number.  If it's even, divide it by two.  If it's odd, multiply it by three and then add one.  Repeat the process until you reach 1.  Here's how it would work, starting with 7:

7 - 22 - 11 - 34 - 17 - 52 - 26 - 13 - 40 - 20 - 10 - 5 - 16 - 8 - 4 - 2 - 1.

You can see why it's called a "hailstone sequence;" like hailstones, the numbers rise and fall, sometimes buffeted far upwards before finally "falling to Earth."  And what Collatz said was that, subject to this procedure, every natural number will finally fall to 1.

Simple enough, right?  Wrong.  The best minds in mathematics have been stumped as to how to prove it.  The brilliant Hungarian mathematician Paul Erdös said, "Mathematics may not be ready for such a problem."  American mathematician Jeffrey Lagarias was even bleaker, saying, "[The Collatz conjecture] is completely out of reach of present-day mathematics."

What's weirdest is that there does seem to be a pattern -- a relationship between the number you start with and the number of steps it takes to reach 1.  Here's what the graph looks like, if you plot the number of steps as a function of the number you start with, for every number from 1 to 9,999:

[Image is in the Public Domain]

It certainly doesn't appear to be random, but this doesn't get us any closer to proving that all numbers descend to 1 in a finite number of steps.

The reason all this comes up is a recent paper in The Journal of Supercomputing showing that every number between 1 and 2 to the 71st power obeys the Collatz conjecture.  That's a bit over twenty quintillion.  Of course, this still isn't proof; all it'd take is one single number in the octillions that either (1) keeps rising higher and higher forever, or (2) leads to an infinite loop, to disprove it.  So until a formal proof (or disproof) is found, all mathematicians can do is keep extending the list of numbers tested.

But is the Collatz conjecture one of Gödel's inevitable true-but-unprovable statements?  No way to know, even if it never does get proven.  That's the brilliance -- and the frustration -- of Gödel's proof.  Such statements are forever outside the axiomatic system, so there's no way to get at them.

So much for mathematics being firm ground.

Anyhow, that's our mind-blowing bit of news for this morning.  A simple conjecture that has baffled mathematicians for almost ninety years, and is no closer to being solved now than it was when it was first proposed.  It's indicative of how weird and non-intuitive mathematics can be.  As Douglas Hofstadter put it, "It turns out that an eerie type of chaos can lurk just behind a facade of order -- and yet, deep inside the chaos lurks an even eerier type of order."

****************************************

Linguistic Calvinball

I've written here before about the monumental difficulty of translating written text when you (1) don't know what the character-to-sound correspondence is (including whether the script is alphabetic, syllabic, or ideographic), (2) don't know what language the script represents, and (3) don't know whether it's read left-to-right, right-to-left, or alternating every other line (boustrophedonic script).  This was what Arthur Evans, Alice Kober, and Michael Ventris were up against with the Linear B script of Crete.  That they succeeded is a testimony not only to their skill as linguists and to their sheer dogged persistence, but to the fact that they had absolutely astonishing pattern-recognition ability.  Despite my MA in linguistics and decent background in a handful of languages, I can't imagine taking on such a task, much less succeeding at it.

The problem becomes even thornier when you consider that what appears to be a script might be asemic -- something that looks like a real written language but is actually meaningless.  (Just a couple of months ago, I wrote here about an asemic text called A Book From the Sky that the creator himself said was nonsense, but that hasn't stopped people from trying to translate it anyhow.)

Which brings us to the Rohonc Codex.

The first certain mention of the Rohonc Codex is in the nineteenth century, although a 1743 catalog of the Rohonc (now the city of Rechnitz, Austria) Library might refer to it -- it says, "Magyar imádságok, volumen I in 12" ("Hungarian prayers in one volume, size duodecimo"). 

As you'll see, that the text represents prayers, or is even in Hungarian, very much remains to be seen.  The size matches; duodecimo means "twelve sheets, approximately 127 millimeters by 187 millimeters in size," and given that some of the earliest guesses about the book's contents were that it was a prayerbook in archaic Hungarian, it's possible that the catalog entry refers to the Codex.  The paper it's printed on appears to be sixteenth-century Venetian in origin, but of course this doesn't mean that's when the book was written -- only that it's unlikely to be any older than that.

One page of the Rohonc Codex [Image is in the Public Domain]

The drawings are rather crude, and the lettering doesn't resemble any known script, although various linguists have compared it to Hungarian runes, Dacian, a dialect of early Romanian, and some variant of Hindi.  Others think it's simply a forgery -- asemic, in other words -- with a sizable number attributing it to the antiquarian Sámuel Nemes, who was known to have forged other documents.

There's no sure connection between Nemes and the Rohonc Codex, however.  He's not known ever to have handled the document, and certainly never mentioned it.  So this seems as tentative as all the other explanations.

Attempts to use the statistical distribution of clusters of symbols, invoking such patterns as Zipf's Law -- the tendency across languages for the word rank to be inversely proportional to word frequency -- have also failed.

Like with A Book From the Sky, this hasn't stopped hopeful scholars from claiming success.  Some of them have been eye-rollingly bad, like the solution proposed in 1996 by one Attila Nyíri of Hungary.  Nyíri combined some Sumerian symbols with chance resemblances to the Latin alphabet, and used such expedients as rearranging letters and letting the same symbol correspond to more than one sound, and still came up with gibberish like, Eljött az Istened. Száll az Úr.  Ó.  Vannak a szent angyalok.  Azok.  Ó.  ("Your God has come.  The Lord flies.  Oh.  There are the holy angels.  Them.  Oh."

I'm perhaps to be excused for being reminded of the Dick and Jane readers.  "Oh, Jane, see Spot.  See Spot run.  Oh, Spot, don't roll in that dead squirrel.  Oh."

Another attempt, this one only marginally more plausible, was made by Romanian linguist Viorica Enăchiuc, and hypothesized that the document (1) is read right-to-left and bottom-to-top, and (2) was written in a Dacian dialect of Latin.  This one came up with lines like Solrgco zicjra naprzi olto co sesvil cas  ("O Sun of the live let write what span the time"), which still isn't exactly what I'd call lucid writing.  

Then there's the Indian linguist Mahesh Kumar Singh, who said the Codex is written left-to-right and top-to-bottom in Hindi, using an obscure variant of the ancient Brahmi script.  Singh translated one passage as, He bhagwan log bahoot garib yahan bimar aur bhookhe hai / inko itni sakti aur himmat do taki ye apne karmo ko pura kar sake ("Oh, my God!  Here the people is very poor, ill and starving, therefore give them sufficient potency and power that they may satisfy their needs.")  His "translation," though, was immediately excoriated by other linguists, who said that he was playing fast-and-loose with the script interpretation, and had come up with symbol-to-sound correspondences that were convenient to how he wanted the translation to come out, not what was supported in other texts.

So the whole enterprise has turned into the linguistic version of Calvinball (from Bill Watterson's brilliant Calvin and Hobbes).  If you make up the rules as you go, and never play by the same rules twice, anything can happen.

The upshot of it all is that the Rohonc Codex is still undeciphered, if there's even anything there to decipher.  Like the more famous Voynich Manuscript, it retains its aura of attractive mystery, because most of us can't resist a puzzle, even if a lot of the best linguists think the script is nonsense.  Because how do you prove decisively that something isn't sensible language?

After all, there are still people who think that Donald Trump's speeches make sense, even when he says shit like, "I saw engines about three, four years ago.  These things were coming—cylinders, no wings, no nothing—and they’re coming down very slowly, landing on a raft in the middle of the ocean someplace, with a circle, boom!  Reminded me of the Biden circles that he used to have, right?  He’d have eight circles, and he couldn’t fill ’em up.  But then I heard he beat us with the popular vote.  He couldn’t fill up the eight circles.  I always loved those circles, they were so beautiful, so beautiful to look at."

So maybe "Oh.  There are the holy angels.  Them.  Oh," isn't so bad.

In any case, I'm sure there'll be further attempts to solve it.  Which falls into the "no harm if it amuses you" department.  And who knows?  Maybe there's a team made up of this century's Evans/Kober/Ventris triumvirate who will actually succeed.

All I know is that attempting it is way above my pay grade.

****************************************