Unwinding the spell

In C. S. Lewis's book Mere Christianity, he addresses the question of why there are unkind and unpleasant Christians (and, conversely, kind and pleasant atheists) by claiming that we should be making a comparison instead with how the people in question would have acted otherwise.  He uses the analogy of a toothpaste's advertising claim to give you healthy teeth:

Even then we must be careful to ask the right question.  If Christianity is true then it ought to follow that any Christian will be nicer than the same person would be if he were not a Christian…  Just in the same way, if the advertisements of Whitesmile’s Toothpaste are true it ought to follow that anyone who uses it will have better teeth than the same person would have if he did not use it.

But to point out that I, who use Whitesmile’s (and also have inherited bad teeth from both my parents), have not got as fine a set as some healthy young African boy who never used toothpaste at all, does not, by itself, prove that the advertisements are untrue.  Christian Miss Bates may have an unkinder tongue than unbelieving Dick Firkin.  That, by itself, does not tell us whether Christianity works.  The question is what Miss Bates’s tongue would be like if she were not a Christian and what Dick’s would be like if he became one.

The fact that we have no way of knowing what they would have been like had their beliefs been otherwise -- that C. S. Lewis himself wrote, "To know what would have happened?  No, no one is given that" -- is a snag here (and awfully convenient to his argument), but we'll leave that aside for the moment. 

Miss Bates and Dick, as a result of natural causes and early upbringing, have certain temperaments: Christianity professes to put both temperaments under new management if they will allow it to do so.  What you have a right to ask is whether that management, if allowed to take over, improves the concern.  Everyone knows that what is being managed in Dick Firkin’s case is much ‘nicer’ than what is being managed in Miss Bates’s...

We must, therefore, not be surprised if we find among the Christians some people who are still nasty. There is even, when you come to think it over, a reason why nasty people might be expected to turn to Christ in greater numbers than nice ones.  If you have sound nerves and intelligence and health and popularity and a good upbringing, you are likely to be quite satisfied with your character as it is.  ‘Why drag God into it?’ you may ask.  A certain level of good conduct comes fairly easily to you.  You are not one of those wretched creatures who are always being tripped up by sex, or dipsomania, or nervousness, or bad temper.  Everyone says you are a nice chap and (between ourselves) you agree with them.  You are quite likely to believe that all this niceness is your own doing: and you may easily not feel the need for any better kind of goodness.  Often people who have all these natural kinds of goodness cannot be brought to recognise their need for Christ at all until, one day, the natural goodness lets them down and their self-satisfaction is shattered.  In other words, it is hard for those who are ‘rich’ in this sense to enter the Kingdom.

It is very different for the nasty people – the little, low, timid, warped, thin-blooded, lonely people, or the passionate, sensual, unbalanced people.  If they make any attempt at goodness at all, they learn, in double quick time, that they need help.  It is Christ or nothing for them.  It is taking up the cross and following -- or else despair.  They are the lost sheep; He came specially to find them.  They are (in one very real and terrible sense) the ‘poor’: He blessed them.  They are the ‘awful set’ he goes about with-and of course the Pharisees say still, as they said from the first, ‘If there were anything in Christianity those people would not be Christians.’

Lewis's apologetics are, unfortunately, specious, and not only for the reason I noted.  His sharp writing style and folksy arguments are understandably appealing, but here -- like many places in Mere Christianity -- his logic doesn't hold up to close scrutiny.  In fact, in the case of "niceness," he's got it backwards.  There is abundant evidence that Christianity (or any other religion) doesn't take what you were born with and sanctify it, make it better than it would have been; instead, it amplifies your natural tendencies.  

So a person born with a kind, forgiving, loving, benevolent nature might well be impelled to do even better if (s)he espoused a religion that valued those things.  But a narrow-minded, spiteful, violent, arrogant person who joins a religion becomes a Tomás de Torquemada, a Cotton Mather, a Judge Jeffreys... or a Jim Bakker or John Hagee or Greg Locke or Rick Wiles.  Awful people who become devout rarely improve their behavior; all their conversion usually accomplishes is to give their hatefulness a nice added gloss of self-righteousness.

[Image licensed under the Creative Commons Aronsyne, C.S.-Lewis, CC BY-SA 4.0]

I got to thinking about Lewis's argument while I was reading an article yesterday in The Daily Beast entitled, "Why Jimmy Carter's Life Should Make the Christian Right Feel Ashamed," and my immediate reaction was to add, "... But It Won't."  As I'm sure all of you know by now, President Carter died a few days ago at the venerable age of 100, and there's been much attention given to his amazingly selfless work for charity, most notably Habitat for Humanity.  The difficulty for Christians, however, is the degree to which Carter's Christianity is being looked upon as an outlier.  In the last twenty years, Christianity has come to be associated with some of the most vile individuals I can think of, culminating in their wholehearted support of an amoral, viciously vengeful, narcissistic adjudicated rapist for president.

The article's author, Keli Goff, writes:

As a person of faith, I have been horrified to watch Christianity’s fall from grace in mainstream America today.  Having mentioned my church in passing to a group of peers, I was once recently met with surprise—surprise that I’m a practicing Christian because, I “seem like a nice person.”  I’m no biblical scholar, but I’m pretty sure that if people conflate your religion with being a terrible human being you’re probably doing it wrong.  Yet in recent years that has arguably become the face of mainstream Christianity, and any Christian who cares about the future of our faith should be deeply concerned.

But... other than a handful of exceptions, they're not.  The vast majority of them are completely unapologetic about their hatreds, whether it's toward minorities, immigrants, LGBTQ+ people, liberals, or just anyone who's not a straight white conservative American.  

Yesterday I drove past a house where there was a huge flag flying saying "God, Guns, and Trump."  How can this now be the rallying cry for people who claim to follow the same man who said "Turn the other cheek" and "Bring unto me the little children" and "Blessed are the meek, for they shall inherit the Earth"?

Or is that "Woke Jesus," and now we have to follow the new and improved gun-toting, anti-immigrant, Murika-loving, queer-bashing Jesus?

Given that this is the new public face of Christianity in the United States, it is perhaps unsurprising that churches are hemorrhaging members.  Goff quotes statistics that there has been a twelve-percent decline in self-identification as Christian just in the last decade; New York Times columnist Nicholas Kristof stated that "More people have left the church in the last 25 years than all the new people who became Christians from the First Great Awakening, Second Great Awakening and Billy Graham crusades combined."

I find this encouraging, but perhaps not for the reason you might be thinking.  It's certainly not because I'm a nonbeliever myself, and have some misguided desire for everyone to think like me.  I honestly have no issue with what answers people come up with for the Big Questions, about the meaning of life and their place in the universe and the existence of a deity.  We all have to figure those out (or not) as well as we can, and who am I to criticize how someone else squares that circle?  What I judge people on is not belief but behavior, and if the ugly, vitriolic diatribes of the likes of Kenneth Copeland are inducing people to say, "this is not for me," then... good.  That should be your reaction to ignorance, nastiness, and intolerance.

And if the leaders of the Christian churches who are seeing their congregations shrinking don't like this -- well, they'd best figure it out.

As I mentioned earlier, however, I'm not optimistic about their coming to the right conclusions.  Today's Christian leaders seem to excel at considering the question and then getting the wrong answer -- blaming it on secular education, the gays, the liberals, or even kicking it up a level and blaming Satan himself.  That the fault might lie in their own hateful, exclusive, judgmental attitudes doesn't seem to have crossed most of their minds.

C. S. Lewis at least recognized this much -- that if you're on the wrong road, you don't get to your destination safely by continuing to forge doggedly down the same path.  In The Great Divorce, he writes:

I do not think that all who choose wrong roads perish; but their rescue consists in being put back on the right road.  A sum can be put right: but only by going back til you find the error and working it afresh from that point, never by simply going on.  Evil can be undone, but it cannot 'develop' into good.  Time does not heal it.  The spell must be unwound, bit by bit, 'with backward mutters of dissevering power' -- or else not.

Which is exactly right.  The problem, though, is that first you have to realize you've done the sum wrong.  And in this case, I don't think that's happened yet.  There are too many other convenient targets to blame.  Even someone like the near-saintly Jimmy Carter holding up a mirror to what evangelical Christianity has become is unlikely to wake anyone up, especially now that the Christofascists are in the political ascendency here in the United States.

And as long as that's the case, they're almost certainly going to continue down this road, watching their flocks dwindling away to nothing, and acting entirely baffled about why their message has lost its appeal.

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The lure of nature

I didn't have an easy childhood.  There were a lot of reasons for this, some stemming from my own issues and some completely outside my control.  But one happy constant in my life, and the high point of every year, was that in the summer my dad and I always went on a three-week car trip to Arizona and New Mexico.

The reason for this was that my dad was an avid rockhound.  Not only did he simply like rocks, he was a talented lapidary -- he had the diamond-edged saws and grinding wheels and all the other equipment to turn agates and jaspers and turquoise into beautiful jewelry.  Our summer expeditions resulted in the car coming back weighing twice as much as it did going out, because the trunk was full of boxes of fist-sized chunks of brightly-colored rocks we'd found while hiking in the canyons.

I loved these trips.  My dad was an interesting guy but not very talkative -- a trait I definitely inherited myself -- so it left me lots of space to wander my own interior world while messing about outdoors.  I liked rocks as well (still do, in fact), but my favorite things about the desert were the blue skies and clear air, the stark, pristine beauty of the cliffs and mesas, the weird and wonderful cacti, and -- most of all -- the absolute silence.  Where I grew up, in southern Louisiana, was at the time a quiet, not-quite-suburban neighborhood not on the direct path to anywhere, but even so I was never far away from traffic noise.  In the canyons of southeastern Arizona, however, there was literally no sound but the sighing of the wind, and sometimes the far-off call of a hawk.  The rumble of a distant thunderstorm or the howling of a coyote at night sounded otherworldly.  It was a strange, beautiful, harsh, magical place, and I swore as a child one day I'd live in Arizona permanently.  It never happened, but over the years I've been back several times to visit some of my favorite childhood haunts, and the southwestern desert still has an attraction for me that borders on the spiritual.

[Image licensed under the Creative Commons BAlvarius, Cave Creek Canyon, CC BY-SA 3.0]

The reason this comes up is a study released a few weeks ago in the journal Ecopsychology by Joanna Bettmann (University of Utah) et al. that found that even a short exposure to nature generated symptom alleviation for adults with anxiety and/or depression -- and the longer and more consistent the exposure, the greater the benefit.  Add to this a study in The Journal of Environmental Education called, "How Combinations of Recreational Activities Predict Connection to Nature Among Youth," by Rachel Szczytko (Pisces Foundation), Kathryn Tate Stevenson and Markus Nils Peterson (North Carolina State University), and Howard Bondell (University of Melbourne).  The team of researchers looked into what activities were most likely to lead to kids feeling a lifelong connection to the outdoors, and they found that social activities -- family camping trips, Girl or Boy Scouts, programs like 4-H and Primitive Pursuits -- were good, but far better were activities outdoors that were solitary.  Give a kid time to explore outside on his/her own -- whether in the context of an activity like hunting or fishing, or just for the hell of it -- and (s)he's likely to form a permanent bond to nature.

"We saw that there were different combinations of specific activities that could build a strong connection to nature; but a key starting point was being outside, in a more solitary activity," said study co-author Kathryn Tate Stevenson, in a press release from North Carolina State University.  "Maybe we need more programming to allow children to be more contemplative in nature, or opportunities to establish a personal connection.  That could be silent sits, or it could be activities where children are looking or observing on their own.  It could mean sending kids to the outdoors to make observations on their own.  It doesn’t mean kids should be unsupervised, but adults could consider stepping back and letting kids explore on their own."

My dad certainly did that.  I got good instruction on safety -- always carry water and food, wear sturdy hiking boots, don't stint on the suntan lotion (a rule that had to be reinforced daily, given that as a kid I was kind of the half-naked savage type), stay on established trails, and so on.  I already had a healthy respect for wildlife, having grown up in a place that had water moccasins and copperheads galore, so I kept a good lookout for rattlesnakes and scorpions and the like.  As a result, I never got lost or injured, and spent many a happy hour exploring the desert, fostering a love for the outdoors that I still enjoy.

And we need more people growing up with a love of the natural world, given how much our current activities are imperiling it.  "There are all kinds of benefits from building connections to nature and spending time outside," Stevenson said.  "One of the benefits we’re highlighting is that children who have a strong connection to nature are more likely to want to take care of the environment in the future."

It certainly did that for me.  I never got to live in the desert, as I wanted as a child, but instead made my home in one of the most beautiful places on Earth -- the lake country of upstate New York, where I have 3.5 acres of woods and fields, a nice pond (suitable for skinnydipping), and if that's not enough, I'm five miles from a National Forest with miles of trails for running, hiking, and cross-country skiing.

Which is, to me, a recipe for bliss.

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Root and branch

Linguists estimate that there are a little over seven thousand languages spoken in the world, sorted into around four hundred language families (including linguistic isolates, languages or language clusters that appear to be related to no other known languages).

As a historical linguist, one of the most common questions I've been asked is if, ultimately, all of those languages trace back to a common origin.  Or, perhaps, did disparate groups develop spoken language independently, so there is no single "pre-Tower-of-Babel" language (if I can swipe a metaphor from the Bible)?  The honest answer is "we don't know."  Determining the relationships between languages -- their common ancestry, as it were -- is tricky business, and relies on more than chance similarity between a few words.  My own area of research was borrow words in Old English and Old Gaelic (mostly from Old Norse), a phenomenon that significantly complicates matters.  English has an unfortunate habit of appropriating words from other languages -- a selective list of English vocabulary could easily lead the incautious to the incorrect conclusion that it originated from Latin, for example.  (In the preceding sentence, the words unfortunate, habit, appropriating, language, selective, vocabulary, incautious, incorrect, conclusion, originated, and example all come directly from Latin.  As do preceding, sentence, and directly.  So none of those are original to English -- they were adopted by scholars and clerics between the thirteenth and sixteenth centuries C.E.)

As you might expect, the longer two languages have been separate, the further they diverge, not only because they borrow words from (different) neighboring languages but because of random changes in pronunciation and syntax.  There's a good analogy here to biological evolution; the process is much like the effect that mutations have in evolution.  Closely-related species have very similar DNA; extremely distantly-related ones, like humans and apple trees, have very few common genes, and it's taken a great deal of detailed analysis to show that all life forms do have a single common ancestor.

That feat has not yet been accomplished with language evolution.  Finnish and Swahili may have a common ancestor, but if so, they've been separate for so long that all traces of that relationship have been erased over time.

Even with groups of languages with a more recent common ancestor, it can remarkably difficult to piece together what their relationship is.  For Indo-European languages, surely the most studied group of languages in the world, we're still trying to figure out their family tree, and aligning it with what is known from history and archaeology.  This was the subject of a study out of the University of Copenhagen that was published last week, and looked at trying to reconcile the language groups in southern and western Europe with what we now know from genetic studies of ancient bones and teeth.

[Nota bene: the Germanic and Slavic peoples were not part of this study; the current model suggests that 

Germanic groups are allied to the neolithic northern Corded Ware and Funnelbeaker Cultures, which appear to have originated in the steppes of what are now western Russia and Ukraine; the Slavs came in much later, probably from the region between the Danube River and the Black Sea.]

The study found a genetic correlation between speakers of the Italo-Celtic language cluster (Italian, Spanish, French, Portuguese, Catalan, Occitan, and Romanian; Irish, Scottish Gaelic, Manx, Cornish, Breton, and Welsh) and one between speakers of the Greco-Armenian cluster (Greek, Cypriot, Albanian, and Armenian).  The southern branch of the Corded Ware culture seems to have undergone two influxes from the east -- one from the Bell Beaker Culture, starting in around 2800 B.C.E. (so called because of the characteristically bell-shaped ceramic drinking vessels found at their settlement sites), which ended up migrating all the way to the Iberian Peninsula, and the other from the Yamnaya, which came from the Pontic steppe but never got past what is now Switzerland and eastern Italy (most of them didn't even get that far).

It's tempting to overconclude from this; just like my earlier example of Latin borrow words in English, the genetic correlation between the Italo-Celtic and Greco-Armenian regions doesn't mean that the differences we see in those two branches of the Indo-European language family come from the Bell Beaker people and the Yamnaya, respectively.  The lack of early written records for most of these languages means that we don't have a good "fossil record" of how and when they evolved.

But the current study provides some tantalizing clues about how migration of speakers of (presumably) two different dialects of Proto-Indo-European may have influenced the evolution of the western and eastern branches of today's Indo-European languages.

So it's one step toward finding the common roots of (most) European languages.  Even if we may never settle the question of how they're related for certain, it's cool that they're using the techniques of modern genetics to find out about where our distant ancestors came from -- and what languages they may have spoken.

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Face forward

Life with prosopagnosia is peculiar sometimes.

Better known as "face blindness," it's a partial or complete inability to recognize people's faces.  I'm not sure where I fall on the spectrum -- I'm certainly nowhere as bad as neuroscientist and author Oliver Sacks, who didn't recognize his own face in the mirror.  Me, I'm hampered by it, but have learned to compensate by being very sensitive to people's voices and how they move.  (I've noticed that I'm often more certain who someone is if I see them walking away than I am if they're standing right in front of me.)

Still, it results in some odd situations sometimes.  I volunteer once a week as a book sorter at our local Friends of the Library book sale, and there's this one guy named Rich who is absolutely a fixture -- he always seems to be there.  I've seen him and spoken with him at least a hundred times.  Well, a couple of weeks ago, I was working, and there was this guy who was behind the counter, messing with stuff.  I was about to ask who he was and what he was doing, when he said something, and I realized it was Rich -- who had shaved off his facial hair.

Until he opened his mouth, I honestly had no idea I'd ever seen him in my life.

Then, a couple of nights ago, my wife and I were watching the Doctor Who Christmas episode "Joy to the World," and afterward got to see a thirty-second teaser trailer for season two, which is being released next spring.  Well, in season one, there was this mysterious recurring character named Mrs. Flood (played by British actress Anita Dobson) whose role we have yet to figure out, and who has the Who fandom in quite the tizzy.  And in the trailer, there's a quick clip of an old woman in formal attire watching a theater performance through opera glasses, and until another fan said, "What did you think about the appearance of Mrs. Flood in the trailer?" I had no clue -- not the least suspicion -- that it was her.

So it's kind of inconvenient, sometimes.  When people post still shots from movies or television shows on social media, I usually not only don't know who the actors are, I have no idea what film it's from (unless there's an obvious clue from the setting).  And as I've related before, there are times when even my voice-recognition strategy hasn't worked, and I've had entire conversations with people and then left still not knowing who it was I'd been talking to.

The reason the topic comes up (again) is some research out of Toyohashi University of Technology that was the subject of a paper in the Journal of Vision last week.  The researchers were trying to figure out if humans have a better innate ability to filter out extraneous visual distractions when it comes to facial recognition than they do for recognizing other objects.  Using a technique called "continuous flash suppression" (CFS), they presented volunteers with fast-moving high-contrast images in one eye, and a target image in the other, then using an fMRI measured how long it took the brain's visual recognition centers to "break through" the distraction and recognize the target image.

If the target image was a face -- or "face-like" -- that breakthrough happened much faster than it did with any other sort of image.  And, interestingly, the breakthrough time was significantly slowed for faces that were upside-down.

We're wired, apparently, to recognize right-side-up human faces faster than just about anything else.

"Our study shows that even vague, face-like images can trigger subconscious processing in the brain, demonstrating how deeply rooted facial recognition is in our visual system," said Makoto Michael Martinsen, who co-authored the study.  "This ability likely evolved to help us prioritize faces, which are critical for social interaction, even when visual information is scarce...  [However] we didn’t consider factors like emotion or attractiveness, which can affect facial perception...  Despite this, our study highlights the brain’s incredible ability to extract important information from minimal cues, especially when it comes to faces.  It emphasizes the importance of facial features in both conscious and subconscious perception and raises interesting questions about how this mechanism evolved."

Naturally, I found myself wondering how face-blind people like myself would do in this task.  After all, it's not that we can't tell something is a face; it's that the visual information in a face doesn't trigger the same instantaneous recall it does in other people.  When I do recognize someone visually, it's more that I remember a list of their features -- he's the guy with square plastic frame glasses and curly gray hair, she's the woman with a round face and dark brown eyes who favors brightly-colored jewelry.  This, of course, only takes me so far.  When someone changes their appearance -- like Rich shaving off his beard and mustache -- it confounds me completely.

So I'm curious whether I'd be like the rest of the test subjects and have faster recognition times for faces than for non-face objects, or if perhaps my peculiar wiring means my brain weights all visual stimuli equally.  I'd be happy to volunteer to go to Japan to participate, if anyone wants to find out the answer badly enough to spot me for a plane ticket.

No?  Oh, well, perhaps that'll be the next phase of Martinsen et al.'s research.  I'm willing to wait.

Until then -- if I know you, and happen to run into you in the local café, keep in mind I may have no idea who you are.  It helps if you start the conversation with, "I'm _____" -- I'm not embarrassed by my odd neurological condition, and it's better than spending the day wondering who the person was who came up and gave me a hug and asked about my wife and kids and dogs and whatnot.

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Taking flight

One of the many things I find fascinating about the evolutionary model is how different lineages can happen on the same "solution" to the problems of surviving and reproducing, leading to similarities cropping up that don't result from common ancestry.  This is a phenomenon called convergent evolution, and explains why the North American flying squirrel and Australian sugar glider look a lot alike, even though they are only distantly related.  (The flying squirrel is a rodent, and the sugar glider a marsupial more closely related to kangaroos.)

I put the word "solution" in quotes and use it with caution, because this makes it sound like evolution is forward-looking, which it is not.  As Richard Dawkins explains brilliantly in his book The Blind Watchmaker, to trigger evolution, all you have to have is an imperfect replicator (in this case, DNA) and a selecting agent.  To phrase it more like Darwin would have put it: variation coupled with differences in survival rate.

I recall how surprised I was to learn that the eye has actually evolved multiple times.  Starting with light-sensitive spots, such as you still find today in many microorganisms, variations on different lineages came up with a variety of different "solutions" -- the pinhole-camera eye of a chambered nautilus, the cup-shaped eye of a flatworm, the compound eye of a fly, and our own eye with a transparent lens like that of a refracting telescope.  All these adaptations work just fine for the animal that has them.  (Eye formation in a number of species is controlled by the paired-box 6 [PAX6] gene, without which eyes won't form at all.  It's such a critical gene that it is conserved across thousands of species -- in fact, your PAX6 gene and a mouse's are identical, base-pair-for-base-pair.)

The reason this subject comes up is because of some research published in the journal Current Biology that showed another trait -- flight -- not only evolved separately in groups like insects and birds, but even in the dinosaurian ancestors of today's birds, it evolved more than once.

A team led by paleontologist Rui Pei of the Chinese Academy of Sciences analyzed bone and feather structure of various dinosaur groups to see if they flew, glided, or were using their feathers for a different purpose (such as keeping warm).  To their surprise, it was found that multiple lineages were capable of flying, or nearly so.  The authors write:

We [used] an ancestral state reconstruction analysis calculating maximum and minimum estimates of two proxies of powered flight potential—wing loading and specific lift.  These results confirm powered flight potential in early birds but its rarity among the ancestors of the closest avialan relatives (select unenlagiine and microraptorine dromaeosaurids).  For the first time, we find a broad range of these ancestors neared the wing loading and specific lift thresholds indicative of powered flight potential.  This suggests there was greater experimentation with wing-assisted locomotion before theropod flight evolved than previously appreciated.  This study adds invaluable support for multiple origins of powered flight potential in theropods (≥3 times), which we now know was from ancestors already nearing associated thresholds, and provides a framework for its further study.

Here are their results, in graphical form:

As you can see, actual birds -- labeled "Later-diverging avialans" near the bottom of the tree -- were far from the only ones to have flight capability.  Rahonavis, Microraptor, and several of the anchiornithines were probably fliers, and only the last mentioned is on the same clade as today's birds.

Flying is pretty useful, so it's no wonder that when feathers evolved from scales -- probably, as I mentioned earlier, in the context of warmth and insulation -- it was only a small step remaining toward lengthening those feathers to the point that their owners could catch a breeze and glide.  After that, the same kind of refinement took over that happened with the eye, and eventually, you have true flight.

So that's yet another cool bit of research about prehistory.  Wouldn't you like to know what those prehistoric fliers looked like?  I'd love to see them.  From a distance, because a lot of them were predators.  For example, Microraptor is Greek for "tiny hunter," and were a little like miniature velociraptors with wings.

If you wanted an image to haunt your dreams.

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No guardrails

Ever since Donald Trump came on the political scene, bragging that he could shoot someone in full view on Fifth Avenue and not lose a single supporter, I and a lot of people on the leftish-side of things have wondered what it would take to get his followers to admit they'd been scammed by a career con-man who has zero moral code.

I think it was about a third of the way into the first Trump presidency that I realized he'd been, for once, telling the unvarnished truth.  I hear now and then of some Trump voter who publicly states that they've woken up and will never support him again, but I think they're very much the exception.  And I've long blamed it largely on the media; a study shortly after the election found that one of the strongest correlations to voting for Trump was lack of access to fact-based information.

So for a while, it was comforting to think that if only these people did have accurate information, they'd come to their senses.  But recently I've begun to think the situation is worse than that.

They know -- but they don't care.  There is no red line, no boundary he could cross that would make people say, "Okay, that's enough."

Since his re-election, Trump's behavior has become more and more unhinged, and instead of provoking a sense of "good lord, what have we done?", the reaction has been more, "Wheeeeee!"  In the last two weeks, the same man who said one of his top priorities was to get us out of military conflicts overseas has stated his intent to annex Greenland and Canada, invade Mexico, and retake the Panama Canal.  (And speaking of media complicity, CNN framed this story as "if he's serious, it'd be the biggest U.S. expansion since the Louisiana Purchase" rather than what any legitimate news source would say, which is, "fucking demented lunatic threatens our allies and risks international conflict with his unprovoked deranged saber-rattling.")

And the fact remains that he's still catastrophically ignorant.  He tweeted this image, apparently without having any idea that the Matterhorn isn't in Canada.

His supporters haven't batted an eyelash.  MAGA Republican Senator Marsha Blackburn said she was all in on taking back the Panama Canal, that "this is what Americans want to see."  Mini-Me, a.k.a. Eric Trump, thought it'd be a good idea to throw fuel on the fire, and posted this:

Next stop, the Sudetenland.

His supporters think Trump has some sophisticated plan here, but he's not playing three-dimensional chess.  He doesn't have the intelligence for tic-tac-toe, much less anything harder.  The Panama thing is most likely retribution, because businesses owned by Trump were recently shut down in the country after accusations of tax evasion and that they were being used as fronts for laundering drug money.  Strategy-wise, he's never progressed any further than "Thag hit me with rock, me hit Thag with rock."

It's why he's threatening to jail Liz Cheney, Anthony Fauci, Mark Milley, and Alexander Vindman.  They committed the cardinal sin of standing up to him, of calling him out on his lies, of demanding that he be held to the same standards of justice as anyone else in the country.  Anyone who dares to point out the Emperor Has No Clothes needs to be silenced by whatever means necessary.

But despite all this, his followers are still cheering -- and lambasting anyone who dares to contradict Dear Leader.

It's gotten so bad that even when one of Trump's favorites -- former Florida Representative Matt Gaetz, once nominee for Attorney General -- was credibly shown to have paid for sex, committed statutory rape, and gone on drug-fueled binges, the response by his supposed family-values followers was not to say, "this guy should be locked up," but to circle the wagons and claim Gaetz had been framed.

Lie after lie, grift after grift.  And yet -- somehow -- it's worked, and is still working.  He scams people in broad daylight, and his followers eagerly line up to be taken advantage of.  The evangelical Christians, who are somehow still behind him one hundred percent despite the fact that he embodies all Seven Deadly Sins in one individual, are just thrilled to pieces by the fact that he's hosting a pre-inauguration prayer service and allowing supporters to attend -- for $100,000 each.

"Pay-to-pray," it's being called.  

I may be off-base, here, being an atheist and all, but isn't this the sort of thing that caused Jesus himself to get violent?  Something about using a whip on money-lenders in the Temple, if I remember correctly.

I think the bottom line is that we on the other side of things have made the mistake of thinking this behavior is rational.  That somehow, if we argue, if we just present more information, use logic and facts, people will be convinced.  The truth is, what's happening here is fundamentally irrational; it's precisely the same appeal to emotion, anger, and nationalism that happened in Germany in the 1930s.  Just like Hitler did, Trump is taking the legitimate concerns of struggling citizens -- anger and anxiety over high cost of living, poor access and high cost of health care, lack of decent-paying jobs with benefits, concerns about crime rate -- and twisting the aim to focus on the wrong causes.  Trump's biggest allies are the super-wealthy corporate leaders, so at all costs we can't have them become the targets.  Instead, get the blame pinned on minorities, immigrants, liberal Democrats, non-Christians, LGBTQ+ people.  

It's why alleged CEO-killer Luigi Mangione has them so freaked out.  For a moment, it forced the attention back on corporate billionaires as a fundamental piece of what's wrong in the United States.

But don't expect the focus to stay there.  It's back to distract, distract, distract.  I don't think we're actually going to invade Greenland, Canada, Mexico, or Panama; Trump has the attention span of a toddler who just had eight Milky Way bars for lunch.  And in any case, actually accomplishing any of that was never the goal.  The real goal is to get Americans to stop thinking, and back to treating everything Trump says as the de facto gospel truth.

He knows that if in two years he hasn't followed through on a single one of his campaign promises, much less any of his idle threats, none of his followers will care -- or even remember.

There is no red line, no guardrails, no brakes, no point where the people who back him will say "enough."  Waiting for it to happen is a fool's errand.  We have to resist, we have to continue to fight, but the war won't be won through logical argument.

It's probably crossed your mind to wonder why, if I think the Trump voters are that unreachable through reasoning, I'm bothering to write this.  It's a valid question.  Besides just processing my own anger, for me it's also a way to connect with like-minded folks, to reassure them that there still are sane people in the world.  To quote British philosopher Edmund Burke, "When bad men combine, the good must associate; else they will fall, one by one, an unpitied sacrifice in a contemptible struggle."

Or as Benjamin Franklin put it, more succinctly and more pointedly: "We must all hang together, or we shall most assuredly all hang separately."

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Adventures in solid geometry

I've always been a bit in awe at people who are true math-adepts.

Now, I'm hardly a math-phobe myself; having majored in physics, I took a great many math courses as an undergraduate.  And up to a point, I was pretty good at it.  I loved calculus -- partly because my teacher, Dr. Harvey Pousson, was a true inspiration, making complex ideas clear and infusing everything he did with curiosity, energy, and an impish sense of humor.  Likewise, I thoroughly enjoyed my class in differential equations, a topic that is often a serious stumbling block for aspiring math students.  Again, this was largely because of the teacher, a five-foot-one, eccentric, hypercharged dynamo named Dr. LaSalle, who was affectionately nicknamed "the Roadrunner" because she was frequently seen zooming around the halls, dodging and weaving around slow-moving students as if she were late for boarding a plane.

I recall Dr. LaSalle finishing up some sort of abstruse proof on the board, then writing "q.e.d."  She turned around, and said in a declamatory voice, "Quod erat demonstrandum.  Which is Latin for 'ha, we sure showed you.'"  It was only much later that I found out her translation was actually pretty accurate.

But other than those bright spots, my math career pretty much was in its final tailspin.  At some point, I simply ran into an intellectual wall.  My sense is that it happened when I stopped being able to picture what I was studying.  Calculating areas and slopes and whatnot was fine; so were the classic differential equations problems involving things like ladders slipping down walls and water leaking out of tanks.  But when we got to fields and matrices and tensors, I was no longer able to visualize what I was trying to do, and it became frustrating to the extent that now -- forty-five years later -- I still have nightmares about being in a math class, taking an exam, and having no idea what I'm doing.

Even so, I have a fascination for math.  There is something grand and cosmic about it, and it underpins pretty much everything.  (As Galileo put it, "Mathematics is the language with which God wrote the universe.")  It's no wonder that Pythagoras thought there was something holy about numbers; there are strange and abstruse patterns and correspondences you start to uncover when you study math that seem very nearly mystical.

The topic comes up because of a paper in the journal Experimental Mathematics that solved a long-standing question about something that also came out of the ancient Greek fascination with numbers -- the five "Platonic solids", geometrical figures whose sides are composed of identical regular polygons and which all have identical vertices.  The five are the tetrahedron (four triangular faces), the cube (six square faces), the octahedron (eight triangular faces), the dodecahedron (twelve pentagonal faces), and the icosahedron (twenty triangular faces).  And that's it.  There aren't any other possibilities given those parameters.

[Image is in the Public Domain]

The research had to do with a question that I had never considered, and I bet you hadn't, either.  Suppose you were standing on one corner of one of these shapes, and you started walking.  Is there any straight path you could take that would return you to your starting point without passing through another corner?  (Nota bene: by "straight," of course we don't mean "linear;" your path is still constrained to the surface, just as if you were walking on a sphere.  A "straight path" in this context means that when you cross an edge, if you were to unfold the two faces -- the one you just left and the one you just entered -- to make a flat surface, your path would be linear.)

Well, apparently it was proven a while back that for four of the Platonic solids -- the tetrahedron, cube, octahedron, and icosahedron -- the answer is "no."  If you launched off on your travels with the rules outlined above, you would either cross another corner or you'd wander around forever without ever returning to your starting point.  Put a different way: to return to your starting point you'd have to cross at least one other corner.

The recent research looks at the odd one out, the dodecahedron.  In the paper "Platonic Solids and High Genus Covers of Lattice Surfaces," mathematicians Jayadev Athreya (of the University of Washington), David Aulicino (of Brooklyn College), and W. Patrick Hooper (of the City University of New York) showed the astonishing result that alone of the Platonic solids, the answer for the dodecahedron is yes -- and in fact, there are 31 different classes of pathways that return you to your starting point without crossing another corner.

The way they did this started out by imagining taking the dodecahedron and opening it up and flattening it out.  You then have a flat surface made of twelve different pentagons, connected along their edges in some way (how depends on exactly how you did the cutting and unfolding).  You start at the vertex of one of the pentagons, and strike off in a random direction.  When you reach the edge of the flattened shape, you glue a second, identical flattened dodecahedron to that edge so you can continue to walk. This new grid will always be a rotation of the original grid by some multiple of 36 degrees.  Reach another edge, repeat the process. Athreya et al. showed that after ten iterations, the next flattened dodecahedron you glue on will have rotated 360 degrees -- in other words, it will be oriented exactly the same way the first one was.

Okay, that's kind of when my brain pooped out.  From there, they took the ten linked, flattened dodecahedrons and folded that back up to make a shape that is like a polygonal donut with eighty-one holes.  And that surface is related mathematically to a well-studied figure called a double pentagon, which allowed the researchers to prove that not only was a straight line returning to your origin without crossing another corner possible, there were 31 ways to do it.

"This was one of the most fun projects I've worked on in my entire career," lead author Jayadev Athreya said, in an interview with Quora.  "It's important to keep playing with things."

But it's also pretty critical to have a brain powerful enough to conceptualize the problem, and I'm afraid I'm not even within hailing distance.  I'm impressed, intrigued, and also convinced that I'd never survive in such rarified air.

So on the whole, it's good that I ended my pursuit of mathematics when I did.  Biology was probably the better choice.  I think I'm more suited to pursuits like ear-tagging fruit bats than calculating straight paths on Platonic solids, but I'm glad there are people out there who are able to do that stuff, because it really is awfully cool.

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