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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Mad world

Given my dual fascination with history and botany, it's a bit surprising that yesterday I ran into a story I'd never heard before that involves both.  I wonder if you know about it?

It's the strange tale of "mad honey."

Turns out in eastern Turkey, near the Black Sea, there are two species of rhododendron -- Rhododendron ponticum and Rhododendron luteum -- that grow in such great profusion that they dominate the landscape.  When they flower, the effect is absolutely spectacular.

Rhododendron ponticum [Image is in the Public Domain]

But there's another species that appreciates the display, and that's bees.  Both species are pollinated by bees, which are lured in not only by the flowers' bright colors, but by the abundance of nectar.

So when these plants flower, the local honey comes almost exclusively from these two species.

The problem is, these plants don't only produce sugar, they produce organic compounds called grayanotoxins.  The grayanotoxins appear not to bother the bees at all -- it would be seriously counterproductive for the plants to poison their pollinators -- but humans who consume the honey made from the nectar of these species end up with serious problems, including hallucinations, dizziness, nausea, bradycardia, and vascular hypotension.  The symptoms are rarely fatal; you'd have to consume a lot of the stuff to die from it.  Most people with what is called "mad honey syndrome" recover in a day or two, although during that period they might well think they're not going to make it.

So, of course, humans being what they are, there are people who take it recreationally.  Me, if I want a mood-altering substance, I'll stick with a glass of red wine.

Where it gets interesting is that "mad honey" has intersected with history on more than one occasion.  The Greek historian Xenophon, in his chronicle Anabasis, recounts an interesting experience some of the troops had while traveling through eastern Anatolia on the way back to Greece from their time as mercenaries in Persia:

Now for the most part there was nothing here which they really found strange; but the swarms of bees in the neighborhood were numerous, and the soldiers who ate of the honey all went off their heads, and suffered from vomiting and diarrhea, and not one of them could stand up, but those who had eaten a little were like people exceedingly drunk, while those who had eaten a great deal seemed like crazy, or even, in some cases, dying men.  So they lay there in great numbers as though the army had suffered a defeat, and great despondency prevailed.  On the next day, however, no one had died, and at approximately the same hour as they had eaten the honey they began to come to their senses; and on the third or fourth day they got up, as if from a drugging.

A few centuries later, a similar incident happened, but deliberately, and with a much less happy ending.  The Greek historian Strabo writes in his book Geography of the unfortunate fate of some of Pompey the Great's soldiers during their campaign against King Mithridates VI of Pontus:

Now all these peoples who live in the mountains are utterly savage, but the Heptacometae are worse than the rest.  Some also live in trees or turrets; and it was on this account that the ancients called them Mosynoeci, the turrets being called mosyni.  They live on the flesh of wild animals and on nuts; and they also attack wayfarers, leaping down upon them from their scaffolds.  The Heptacometae cut down three maniples [around 1,500 soldiers] of Pompey's army when they were passing through the mountainous country; for they mixed bowls of the crazing honey which is yielded by the tree-twigs, and placed them in the roads, and then, when the soldiers drank the mixture and lost their senses, they attacked them and easily disposed of them.

Which raises the question of exactly how stupid these Roman soldiers were.  They were marching through a hostile region occupied by people who were known to be "utterly savage," and just happened upon bowls of honey left for them on the side of the road -- and instead of being suspicious, they were like, "Nom nom, looks good to me!"

My opinion is that the resulting massacre was just natural selection at work.

Anyhow, apparently "mad honey" is available for purchase if you go to Turkey, where it's (1) legal, but (2) strongly discouraged, because like many psychotropic substances, the difference between "whoa, far out" and "HOLY SHIT THE WORLD IS ENDING" is a very blurry line.  So even if there aren't savage bands of Heptacometae waiting for you to get high so they can stab you with sharpened sticks, you might find yourself regretting consuming it, like a middle-aged couple did in 2008 when they heard the stuff improved your sex life and instead of having a fun frolic ended up in the hospital because they thought they were having heart attacks.

So restraint is recommended.

Anyhow, that's our curious historical vignette of the day.  Greek military campaigns, beautiful flowers, and hallucinogenic honey.  And given what some plant toxins can do -- monkshood and manchineel come to mind -- this one is pretty mild.

But if I ever get to visit Turkey, I still think I'll still steer clear.

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Not easy being green

After recent posts dealing with politics, culture, the hazards of AI, and important scientific discoveries, I'm sure what you're all thinking is: yes, Gordon, but what about sightings of the mysterious Green Elf Chimp of Florida?

All I can say is that I'm sorry for the oversight, and will do my best to rectify the situation today.  I found out about the Green Elf Chimp from a loyal reader of Skeptophilia who was responding to my recent comment that the world has gotten so surreal lately that I'm beginning to wonder if the aliens who are running the simulation we're all trapped in have gotten bored and/or stoned, and now they're just fucking with us.  The reader sent me an email with a link and a message that said, "Yeah, there's no doubt about it.  The aliens are just throwing weird shit at us to see how long it takes us to stand up, flip the table, and say, 'That's it.  I'm done.'"

The link was to the website of one Karl Shuker, zoologist (of the crypto as well as the ordinary variety), who tells us about sightings of a strange cryptid near the town of New Port Richey, north of Tampa on Florida's west coast.  Here's one account:

"There's a terrible smell around here. Can't you smell it?" the girl complained...  As the others took deep breaths "an animal about the size of a large chimpanzee" sprang onto the hood of the car.

"Then we panicked!" the driver later told investigator Joan Whritenour.  "The thing looked like a big chimp, but it was glowing greenish in color, with glowing green eyes.  I started the motor and the thing jumped off and ran back into the woods. We tore like blazes back to the dance we were supposed to be attending."

A police officer from New Port Richey later visited the site and found a sticky green substance which remains unidentified.

One thing I've never understood is why cryptids and aliens and whatnot are so often described as having "glowing eyes."  And how many horror movies have you seen where evil creatures' eyes suddenly start emitting light, usually green or red?  Now, reflective eyes, sure; anyone who's ever caught a deer or raccoon in their car headlights at night knows that a lot of animals, especially nocturnal ones, have reflective eyes.  This is because of a structure called the tapetum lucidum, a reflective membrane behind the retina.  For diurnal animals (like ourselves), we're usually exposed to more light than we need; so if a lot of it passes right through the retina and gets passively absorbed by the tissue behind it, it's not really a problem.  But for nocturnal animals, they need every photon they can get.  That's why many of them have evolved a tapetum, which reflects the light back through the retina and gives the light receptors therein a second chance to catch it.

Glowing eyes, though?  What do they think, that there are little guys inside there with flashlights, shining them out through the pupils?

To Shuker's credit, he does point this out, although he still seems to give the whole incident a lot more credence than I would.

He also (rightly) wonders if it may have been an actual chimp, i.e., not a strange paranormal alien chimp or whatever.  But this doesn't explain why the chimp was green, which is definitely not a standard-issue color for chimps, and why the chimp itself was glowing.  He then speculated that perhaps the chimp was an escapee from a zoo that had gone for a swim in water containing bioluminescent algae, simultaneously explaining (1) green, (2) glowing, and (3) smelling bad.

Fig. 1: A non-green, non-glowing, non-elf chimp, for reference purposes. [Image licensed under the Creative Commons Chi King, Chimpanzee (13968481823), CC BY 2.0]

However, Shuker also goes on to suggest that the Green Elf Chimp might not itself be a separate species of cryptid, but a juvenile Florida Skunk Ape.  Which, I have to admit, had not occurred to me.  Maybe they fluoresce when they're juveniles and not when they're adults, which gives new meaning to the phrase "he has a youthful glow."

Of course, there's always the possibility that the whole account could be explained by the people reporting it having ingested a few controlled substances themselves.

Anyhow, that's the news from the world of cryptozoology.  As luck would have it, some dear friends of mine live in New Port Richey, so I'll definitely have them keep their eyes out.  They are also the keepers of varying numbers of absolutely enormous dogs (they have a soft spot for Great Danes and Mastiffs), who I'm sure would also notify the human inhabitants if a smelly green glowing chimp showed up in the back yard.

I'll keep you posted.

On the other hand, if this is all because of some stoned aliens twiddling the knobs on the simulation to try and see what they can get the humans to fall for -- enough, already.  I'm having sufficient difficulty accepting the fact that the same people who falsely claimed for eight years that an African immigrant was running the country now have zero problem with an actual African immigrant running the country, and a guy who admitted that a worm had eaten his brain was nominated to oversee the Department of Health and Human Services, and a guy so catastrophically dumb that he couldn't find the Bahamas on a map if there were arrows printed on it with the caption "HEY, STUPID, THE BAHAMAS ARE RIGHT HERE" was appointed Ambassador to the Bahamas.  We get it, aliens, you win.  Humans are idiots.

No Green Elf Chimps required.

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A lens on the past

We have an unfortunate tendency to idealize the past.

Well, unfortunate is probably the wrong word.  I don't guess it does any real harm, and in fiction it can be quite entertaining.  Unrealistic is probably a better choice.  Except for the (very) select privileged few, our ancestors' lives were -- to quote Thomas Hobbes -- "solitary, nasty, poor, brutish, and short."

This idealization creates a picture in our minds that is almost certainly false.  Consider, for example, Jean Auel's Clan of the Cave Bear series, which focuses on the meeting between some civilized, beautiful Cro-Magnon folks and some violent, nasty Neanderthals.  Reminiscent of Tolkien's Orcs and Elves, the Neanderthals all have names like Thok and Ugg and Glop, and the Cro-Magnons mellifluous names like Sondamar and Alidor.  (Before you start yelling at me, yes, I made those up because I don't own the book any more and I don't feel like looking it up.  But my point stands.)

But it's not just the prehistorics.  Contrast two different tales of medieval monastic life -- Ellis Peters's Brother Cadfael series and Umberto Eco's The Name of the Rose.  Don't get me wrong, I love Brother Cadfael; his logic, compassion, and love for botany are all endearing, and Peters was a great mystery writer.  But the reality of life in western Europe in the twelfth and thirteenth centuries was undoubtedly closer to Eco's harsh, unwashed, rough-shod reality, with its starving peasants and superstitions and religious fanaticism, than it was to Peters's genteel knights and tradesmen and monks.

Like I said, I don't really object to fictional portrayals, even with their inevitable inaccuracies.  I've written a few stories set in the past myself -- the English Midlands in the nineteenth century (Adam's Fall), pre-Civil-War Louisiana (The Communion of Shadows), eleventh century Iceland (Kári the Lucky), and Britain during the fourteenth century Black Death (We All Fall Down).  I hope I've skirted the line between realism and romanticism deftly enough to make it believable without being too dark and depressing.

But the fact remains that our ancestors didn't have it easy.  That we're here is a tribute to their tenacity, strength, and determination.  Whenever I consider archaeological finds, I'm always struck by how cushy a lot of us have it now, with our indoor plumbing and heat in the winter and electric appliances and modern medicine, all of which our forebears somehow survived -- at least for a while -- without.

The reason this comes up is a study out of the University of Oxford that was published last week in the journal Antiquity, describing a rather horrific archaeological discovery in Merrie Old England.  The remains of at least 37 people were found near Charterhouse Warren, Somerset, dating to the Early Bronze Age (preliminary dating puts them at around 2000 B.C.E.) that show signs not only of violent death -- but the bodies were butchered and eaten afterwards, and the remains thrown down a fifteen-meter-deep shaft.

"We actually find more evidence for injuries to skeletons dating to the Neolithic period in Britain than the Early Bronze Age, so Charterhouse Warren stands out as something very unusual," said Rick Schulting, who was the study's lead author.  "It paints a considerably darker picture of the period than many would have expected."

[Image credit: Schulting et al., Antiquity]

And it doesn't appear to be a case of desperation, where starving people resorted to cannibalism because they had no other options.  The same site yielded up plentiful cattle bones, so it's apparent the Bronze Age residents of Charterhouse Warren weren't hurting for chow.

Any explanation of this behavior is, of course, pure speculation, but one thought is that the victors ate their defeated enemies as a way either of dehumanizing them, or perhaps from some sort of belief that doing so would allow any courage or spirit the enemies had to pass into them.

"Charterhouse Warren is one of those rare archaeological sites that challenges the way we think about the past," Schulting said.  "It is a stark reminder that people in prehistory could match more recent atrocities and shines a light on a dark side of human behavior.  That it is unlikely to have been a one-off event makes it even more important that its story is told."

It certainly puts a clearer and harsher light on what life in the past was actually like.  "If people think of the past as something peaceful and idealized," said archaeologist Ludvig Papmehl-Dufay, of Kalmar University, who was not involved in the current study, "that needs to be revised."

In any case, it's probably for the best that we do see our history through softer lenses.  The rigors that 95% of humanity endured back then, that (fortunately) far fewer have to endure now, were seriously depressing stuff.  And I suppose it's encouraging, really; for all the horrific stories in the news, we have come a long way as a species.  Not that we don't still have a long way to go.  But when asked when I would choose to live if I had a time machine that could take me into the past, my answer is always "right here and right now."

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Eye of the storm

Ever heard of Wolf-Rayet stars?  They deserve more notice than they get, as one of the most violently energetic phenomena in the universe.  The fact that the name is not in common parlance -- when even the most scientifically-uninterested layperson has heard of supernovae and quasars and black holes -- is probably due to a combination of (1) their rarity, and (2) the fact that the ones that are visible to the naked eye are pretty unimpressive-looking at first glance.  Gamma Velorum and Theta Muscae, both of which are in the Southern Hemisphere and never visible where I live in upstate New York, are Wolf-Rayet stars that look completely ordinary until you check out their light spectra and find out that there's something really extraordinary going on.

The first thing that becomes apparent is that they are hot.  I mean, even by stellar standards.  Wolf-Rayet stars have a surface temperature between 30,000 K and an almost unimaginable 210,000 K.  (By comparison, the Sun's surface is about 5,700 K.)  These temperatures fuel an enormously strong stellar wind, which blows away almost all of the lightweight hydrogen in the outer layers, and also ionizes most of what is left -- predominantly oxygen, nitrogen, and carbon.  They're at the head of the list of potential gamma-ray bursters -- stars that undergo sudden collapse followed by a colossal explosion, resulting in a blast of gamma rays collimated into narrow beams along the star's rotational axis.  So having a Wolf-Rayet star's rotational axis pointed toward your planet would be like staring down the barrel of a loaded gun.

They're also beautiful.  At least from a distance.  The reason all this comes up is because of a paper in Monthly Notices of the Royal Astronomical Society about one that's been called "a stellar peacock" -- the star Apep, in the constellation Norma.  This Wolf-Rayet star has blown carbon-laden dust from its surface, which its high rotational speed swept into a pinwheel.

[Image licensed under the Creative Commons ESO/Callingham et al, The triple star system 2XMM J160050.7–514245 (Apep), CC BY 4.0]

The name Apep comes from Egyptian mythology -- Apep was the monstrous serpent who was the enemy of the god Ra.  Astronomer Joseph Callingham, one of the first to study Apep, thought the name was apt -- in his words it was "a star embattled within a dragon's coils."

All poetic license aside, the violent imagery is spot-on.  Wolf-Rayet stars eventually self-destruct, becoming black holes, but not until basically destroying anything unfortunate enough to be nearby.  So the bright spot at the center of Apep is the eye of a cosmic-scale storm.

The research I referenced, by a team led by University of Sydney student Yinuo Han, uses observational data from the Very Large Telescope in Chile to understand what is creating the spiral plumes.  The detail is phenomenal; in an interview with Science Daily, Han said, "The magnification required to produce the imagery was like seeing a chickpea on a table fifty kilometers away."

"[Wolf-Rayet stars] are ticking time bombs," said study co-author Peter Tuthill.  "As well as exhibiting all the usual extreme behavior of Wolf-Rayets, Apep's main star looks to be rapidly rotating.  This means it could have all the ingredients to detonate a long gamma-ray burst when it goes supernova."

It's hard to say anything about this group of stars without lapsing into superlatives.  "The speeds of the stellar winds produced are just mind-blowing," Han said.  "They are spinning off the stars at about twelve million kilometers an hour.  That's one percent the speed of light."

Fortunately for us, Apep is a safe 6,600 light years away, so it poses no danger to us.  If one was a lot nearer -- within 25 or so light years' distance -- it would be catastrophic.  The radiation bombardment could strip away the ozone layer, leaving the Earth's surface subject to massive irradiation.  There's decent evidence that some of the Earth's mass extinctions may have been caused by nearby supernovae (not necessarily Wolf-Rayets).  But to put your mind at ease, there aren't any supernovae candidates of any sort within what is rather terrifyingly called "the kill zone."

So that's a look at one of the most dangerous and beautiful phenomena in the universe.  I'm glad we're getting to see it, and find out a little bit about what makes it tick.

From a safe distance.

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