The halting problem

A couple of months ago, I wrote a post about the brilliant and tragic British mathematician, cryptographer, and computer scientist Alan Turing, in which I mentioned in passing the halting problem.  The idea of the halting problem is simple enough; it's the question of whether a computer program designed to determine the truth or falsity of a mathematical theorem will always be able to reach a definitive answer in a finite number of steps.  The answer, surprisingly, is a resounding no.  You can't guarantee that a truth-testing program will ever reach an answer, even about matters as seemingly cut-and-dried as math.  But it took someone of Turing's caliber to prove it -- in a paper mathematician Avi Wigderson called "easily the most influential math paper in history."

What's the most curious about this result is that you don't even need to understand fancy mathematics to find problems that have defied attempts at proof.  There are dozens of relatively simple conjectures for which the truth or falsity is not known, and what's more, Turing's result showed that for at least some of them, there may be no way to know.

One of these is the Collatz conjecture, named after German mathematician Lothar Collatz, who proposed it in 1937.  It's so simple to state that a bright sixth-grader could understand it.  It goes like this:

Start with any positive integer you want.  If it's even, divide it by two.  If it's odd, multiply it by three and add one.  Repeat.  Here's a Collatz sequence, starting with the number seven:

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

Collatz's conjecture is that if you do this for every positive integer, eventually you'll always reach one.

The problem is, the procedure involves a rule that reduces the number you've got (n/2) and one that grows it (3n + 1).  The sequence rises and falls in an apparently unpredictable way.  For some numbers, the sequence soars into the stratosphere; starting with n = 27, you end up at 9,232 before it finally hits a number that allows it to descend to one.  But the weirdness doesn't end there.  Mathematicians studying this maddening problem have made a graph of all the numbers between one and ten million (on the x axis) against the number of steps it takes to reach one (on the y axis), and the following bizarre pattern emerged:

[Image licensed under the Creative Commons Kunashmilovich, Collatz-10Million, CC BY-SA 4.0]

So it sure as hell looks like there's a pattern to it, that it isn't simply random.  But it hasn't gotten them any closer to figuring out if all numbers eventually descend to one -- or if, perhaps, there's some number out there that just keeps rising forever.  All the numbers tested eventually descend, but attempts to figure out if there are any exceptions have failed.

Despite the fact that in order to understand it, all you have to be able to do is add, multiply, and divide, American mathematician Jeffrey Lagarias lamented that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present-day mathematics."

Another theorem that has defied solution is the Goldbach conjecture, named after German mathematician Christian Goldbach, who proposed it to none other than mathematical great Leonhard Euler.  The Goldbach conjecture is even easier to state:

All positive integers greater than two can be expressed as the sum of two prime numbers.

It's easy enough to see that the first few work:

3 = 1 + 2
4 = 1 + 3
5 = 2 + 3
6 = 3 + 3 (or 1 + 5)
7 = 2 + 5
8 = 3 + 5

and so on.

But as with Collatz, showing that it works for the first few numbers doesn't prove that it works for every number, and despite nearly three centuries of efforts (Goldbach came up with it in 1742), no one's been able to prove or disprove it.  They've actually brute-force tested all numbers between 3 and 4,000,000,000,000,000,000 -- I'm not making that up -- and they've all worked.

But a general proof has eluded the best mathematical minds for close to three hundred years.

The bigger problem, of course, is that Turing's result shows that not only do we not know the answer to problems like these, there may be no way to know.  Somehow, this flies in the face of how we usually think about math, doesn't it?  The way most of us are taught to think about the subject, it seems like the ultimate realm in which there are always definitive answers.

But here, even two simple-to-state conjectures have proven impossible to solve.  At least so far.  We've seen hitherto intractable problems finally reach closure -- the four-color map theorem comes to mind -- so it may be that someone will eventually solve Collatz and Goldbach.

Or maybe -- as Turing suggested -- the search for a proof will never halt.

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Mystery relics

I was cleaning up my garage a while back, and I found this.

There are two holes on the squared-off lower edge, so it was evidently meant to be attached to something else by screws or bolts.  There was no context; it wasn't with anything else that might have given me a clue to what its purpose was.

It took way longer than it should have for me to figure out that it's a toe clip from a bicycle pedal.

This got me to thinking about how hard archaeologists have it.  They dig stuff up, often damaged or fragmentary, and have to figure out what it is, why it was created, what its uses may have been.  And if a relatively simple artifact from a device I use frequently left me scratching my head, how much harder is it when it's a creation of a long-dead culture about which we know very little?

I thought it might be entertaining to look at a few artifacts that have even the experts stumped -- where, like my pedal toe clip, we actually have the thing in hand and still can't figure out what it's used for.

1.  South Asian ringstones

In India and Pakistan, a number of beautifully-carved stone artifacts have been found.  They're circular, flat, with a hole in the center, and have fine decorative relief on one side and a polished surface on the other.

Indian ringstone, approximately 2,200 years old, in the New York Metropolitan Museum of Art [Image is in the Public Domain]

Over seventy ringstones have been found, but their purpose is entirely unknown.  They're too heavy to be jewelry.  It's possible they were some sort of object of veneration, but that's entirely speculation.  Another possibility is that they were used as a pattern mold for impressing another substance (perhaps clay or gold foil) to make jewelry or decorative objects, but there's no particularly good evidence for that, either; and if they're molds, why are they always circular, with a hole through the center?

2. The Disquis spheres

In the Disquis delta region of Costa Rica, there are over three hundred nearly perfect stone spheres, most of which are made of a hard rock called diorite.  They range from a few centimeters to over two meters in diameter; the largest weigh more than fifteen tons.

[Image licensed under the Creative Commons Axxis10, Parque de las Esferas de Costa Rica, CC BY-SA 3.0]

Whoever made them put an incredible amount of work into them.  Stone artifacts are hard to date accurately, but nearby archaeological sites are about a thousand years old, so it's presumed that whoever made them came from around that era.  What purpose did they serve?

No one knows.

3. Erdstalls

Sometimes an artifact being both widespread and relatively recent doesn't help much.  This is the situation with erdstalls -- low, narrow tunnels found throughout central Europe, and which are believed to date from the Middle Ages.  

An erdstall in Austria [Image licensed under the Creative Commons Pfeifferfranz, Erdstall Ratgöbluckn Perg Eingang, CC BY-SA 3.0 AT]

Some have theorized that they were hiding places or escape tunnels, but this doesn't seem very plausible.  Although they can be up to fifty meters in length, they average under a meter and a half tall and only sixty centimeters wide.  Any escape tunnel is good enough if you're desperate, I suppose, but it seems like if they were deliberately constructed for that purpose, the makers would have dug them to be a little more spacious.  They're mentioned a couple of times in medieval manuscripts, but their purpose is never specified -- so it's uncertain if even the people who wrote about them knew what they were used for.

4.  "Frying pans"

In graves from the Early Cycladic Period of ancient Greek history (ca. 3100-1000 B.C.E.), archaeologists have found over two hundred shallow ceramic bowls, decorated on the outside, with short handles.

[Image is in the Public Domain]

They were nicknamed "frying pans" because of the shape, although they show none of the wear you'd expect from a cooking implement (and are really too shallow to be useful for that anyhow).  Other than the general fallback of unspecified "ceremonial uses," one suggestion is that they might have been filled with a thin layer of water or oil and used as mirrors, although that seems to be a little awkward to be practical.  Others have suggested that they were used to evaporate sea water to produce salt -- but they've only been found in burial sites, and none of them have shown any traces of salt.

5. Perforated batons

These are carved pieces of deer antler, widely distributed across Europe, and dating from 12,000 to 23,000 years of age -- so whatever they were for, people made them for over ten thousand years.  

[Image licensed under the Creative Commons Johnbod, Perforated baton with low relief horse, CC BY-SA 3.0]

They're intricately carved, and all of them have a nearly perfect circular hole cut through the middle.  Despite one researcher's claim that the wear around the inside of the hole shows they were tools (possibly for fashioning or straightening arrows), there are lots of other explanations that have been suggested -- that they're cloak or scarf fasteners, calendars, jewelry, or phallic symbols (not seeing that last one, honestly).  A paper in the journal Archaeological and Anthropological Sciences in 2019 said, "Despite the large number of batons found (> 400), their use still remains enigmatic.  No fewer than forty functional hypotheses have been proposed, following debates that have persisted for over 150 years; the perforated baton has consequently become emblematic of our misunderstanding of some ancient objects’ functions."

Which seems a fitting place to end.  I wonder what future archaeologists will make of the stuff we leave behind -- which bits they'll figure out immediately, and which ones will baffle them?  And as far as the relics that today's archaeologists are frowning over, I've barely scratched the surface.  There are dozens of other kinds of artifacts that have even the experts saying "damned if we know."  Which is not a problem, honestly; being open about the perimeter of your own ignorance is absolutely essential in research of any kind.

But it does set up a lovely bunch of puzzles for us interested laypeople to think about, doesn't it?

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The beat goes on

I am blessed with a good innate sense of rhythm.

I've always felt rhythms in my body; I never had to struggle to keep the beat while playing music.  One of my band members nicknamed me "The Metronome," and quipped that if one of us missed a note, it might well be me -- but if someone screwed up the rhythm, it was definitely not me.

I've often wondered about the origin of this.  I've listened to music ever since I can remember, but I dropped out of band in sixth grade, was not allowed to take music lessons however much I begged my parents, and didn't participate in anything in the way of formal music training until I was in my mid-twenties.  The result is that I'm largely self-taught -- with all of the good and bad that kind of background brings.

I've always loved music with odd rhythms.  There's a reason two of my favorite classical composers are Igor Stravinsky and Dmitri Shostakovich.  Then, I discovered Balkan music when I was in my teens, and even before I knew cognitively what was going on, was magnetically attracted to the strange, asymmetrical beat patterns.

For example, what do you make of this tune?

If you know any Slavic languages, the name of it will give you a clue -- Dvajspetorka.  There are twenty-five beats (!) per measure; the name comes from the Macedonian word for "twenty-five" (dvaeset i pet).  But if you're wondering how the hell you count that, you'll no doubt be relieved to find that you don't count up to twenty-five and then start back at one.  Most of these Balkan tunes are dances (or derived from them), and they're all broken down into slow steps (that get a count of three beats) and fast steps (that get a count of two beats).  This one is slow-fast-fast, slow-fast-fast, fast-fast-slow-fast-fast.  When I've taught Balkan music workshops, I've found it helps to speak the rhythm, using the word "apple" for the fast, two-beat steps and "cinnamon" for the slow, three-beat ones.

So the rhythm of Dvajspetorka would be cinnamon-apple-apple, cinnamon-apple-apple, apple-apple-cinnamon-apple-apple.

Which, if you count it up, adds to an entire apple pie with twenty-five beats per measure.

What got me thinking about all of this is a couple of papers I ran into yesterday, one from PLOS-One Biology called, "The Nature and Perception of Fluctuations in Human Musical Rhythms," by Holger Henning et al., and the other from Psychonomic Bulletin and Review called, "Sensorimotor Synchronization: A Review of Recent Research" by Bruno Repp and Yi-Huang Su.  And what I learned from these is as fascinating as it is puzzling.  Among the takeaways:

• Humans tend not to like perfectly steady rhythms.  When musical recordings are made using a computer-synchronized beat, they're judged as "emotionless" and "devoid of depth."  So small, deliberate fluctuations in the tempo are part of what give music its poignancy.
• Throwing in random fluctuations doesn't work.  Test subjects caught on to that immediately, saying the alterations in tempo sounded like mistakes.  There's something about the fluid, organic sound of actual human musicians making minor shifts in rhythm that are what create emotional resonance in the listener.
• That said, really good musicians have extraordinarily accurate abilities to keep a steady beat when they want to.  Told to hold a rhythm as rock-solid as they can, professional percussionists deviated from the pulse of the music by an average of only a few milliseconds per beat.
• fMRI studies have shown that there is a specific part of the brain -- the basal ganglia-thalamo-cortical circuitry in the cerebellum -- that fires like crazy when people try to match a rhythm.  So the rhythmic ability in humans is hardwired.  In fact, research suggests that are are other animals that have this ability as well -- other primates, rats, and some birds all show various levels of rhythmic awareness.
• As far as why this apparently innate ability to keep a musical rhythm exists, evolutionary biologists admit that their current answer is "damned if we know."

It seems like an odd thing to evolve, doesn't it?  The obvious guess is that it might have something to do with communication, but there's no human language (or non-human animal communication we know of) that is sensitive to rhythm to an accuracy of a few milliseconds.  If I say "I'm leaving for work now" to my wife, and say it with various rhythms and speeds, the meaning doesn't change (although for certain speed and rhythm combinations, she might well give me a perplexed look).

So how such an incredibly precise ability evolved is still a considerable mystery.

Anyhow, that's our curious bit of science for the day.  How humans keep the beat.  And if you'd like to end with another challenge, what time signature do you think this is in?  Have fun!

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The Mad Gasser of Mattoon

One of the most difficult things about establishing what actually happened in an incident is that people are so damn suggestible.

It's nobody's fault, and psychologists understand the phenomenon pretty well, but it really complicates matters when you're trying to piece together what happened based on eyewitness testimony.  Once our brains have been contaminated by someone's suggestion of what they think happened, our memories simply aren't reliable any more.

Even a single word choice can make a difference.  Way back in 1989, researchers D. S. Lindsay and M. K. Johnson showed the same video of a car accident to a bunch of teenagers, and then afterward asked them to estimate how fast the vehicles were traveling at the time.  However, the researchers used different words to ask the question -- "How fast were they moving when they (bumped, contacted, collided, hit, crashed)?"  They found that the intensity/violence of the word choice strongly affected the volunteers' estimates of the speed -- they thought the cars were traveling far more slowly if the researchers used the word "bumped" as compared to using the word "crashed."

The video was the same each time; a single word choice by the researchers changed how the teenagers remembered it.

Suggestibility also comes into play when our emotions get involved, especially strong emotions like fear or anger.  This is thought to be the cause of mass hysteria (more formally known as mass psychogenic illness), when symptoms of an apparent illness spread through a population even though there's no known organic cause.  One person experiences symptoms -- whether from an actual physical illness or not -- and one by one, other people interpret their own conditions in that light.  Susceptible people then become frightened, and focus their attentions on every aberrant ache, pain, or twinge, which (of course) makes them more frightened.  The whole thing snowballs.  (This is likely the origin of the "witch fever" during the Salem Witch Trials -- combine mass hysteria with religious mania, and you've got a particularly deadly combination.)

This brings us to today's topic, which is the Mad Gasser of Mattoon.

On August 31, 1944, a man named Urban Raef, of Mattoon, Illinois, woke in the middle of the night because there was a strange, sweet odor in his house.  He felt nauseated and weak, and in fact threw up twice.  He woke his wife for help, but she found she was partially paralyzed and unable to get out of bed.  At some point the Raefs recovered sufficiently to open the windows, and made their way downstairs to the kitchen to see if there was a gas leak from the stove.  (Although gas leaks don't exactly smell "sweet.")  Everything seemed in order.

In the wee hours that same day, a neighbor living nearby experienced the same symptoms -- coughing, the presence of a cloyingly sweet odor "like cheap perfume," and temporary paralysis.

Within two days, four homes total had been affected, and that's when it hit the press.  A local paper blared the headline, "Anesthetic Prowler on the Loose!"  Between September 5 and September 13, twenty more incidents were reported to the police, including sisters Frances and Maxine Smith who claimed to have been attacked three separate times -- during one of which, they said they heard a "motorized buzzing sound" from the machinery being used to expel the gas.  Another individual found a white cloth on her front porch, sniffed it, and immediately became violently ill.

Only twice -- Fred Goble on September 6, and Bertha Burch on September 13 -- did victims report seeing anyone suspicious.  Neither one got a good look at the prowler's face, although Burch reported that she thought the person she'd seen was "a woman dressed as a man."

The police didn't have a lot to go on.  The symptoms reported by victims were similar to those you'd get from inhaling organic solvents like chloroform, carbon tetrachloride, or trichloroethylene, but analysis of the hard evidence (like the cloth) showed no traces of any toxic chemicals.  After the last report on the 13th, the attacks -- whatever they were -- stopped.  All of the victims made complete recoveries, and the "Mad Gasser of Mattoon" went down as yet another unexplained mystery in the annals of Fortean phenomena.

So, what actually happened here?

Hysteria needs a trigger; the experiences of the first three victims, the Raefs and the unnamed neighbor, were probably real enough, whatever their cause.  One person who has researched the incident extensively, Scott Maruna (in fact, he wrote a book about it called The Mad Gasser of Mattoon: Dispelling the Hysteria), believes that at least some of the attacks were perpetrated by a Mattoon resident named Farley Llewellyn, an alcoholic, chronically angry recluse who was known to dabble in chemistry, and in fact once blew a hole in one wall of his house in a laboratory explosion.

The problem is, no one has ever been able to prove Llewellyn was involved.  Every town has its oddballs, and (after all) being a peculiar, introverted science-nerd type is hardly a crime.

Fortunately for me.

Most of the people who've looked into the case believe that the majority of the reports were the result of mass hysteria induced by the rather terrifying headlines, possibly compounded by episodes of sleep paralysis.  (Which can be a pretty damn scary experience in and of itself, even without a crazy anesthetist running around.)

The bottom line, though, is that we'll probably never know for sure.  Once you've had an experience like that -- hooking into some powerful emotions -- it permanently alters what you remember.  At that point, trying to tease out what you actually did experience from what you feared and/or had heard about from other sources becomes next to impossible.  

And even in less alarming situations, our memories are remarkably plastic, and therefore unreliable.  It's always a good idea to keep this in mind -- just because something is in our heads doesn't mean it's true and accurate.

Or as Robert Fulghum put it, "Don't believe everything you think."

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The conservation conundrum

A major underpinning of our understanding of physics has to do with symmetry and conservation laws.

Both have to do with order, balance, and the concept that you can't get something for nothing.  A lot of the most basic research in theoretical physics is driven by the assumption that despite the seeming complexity and chaos in the universe, at its heart is a deep simplicity, harmony, and beauty. 

The mathematical expression of this concept reaches its pinnacle in the laws of conservation.

You undoubtedly ran into conservation laws in your high school science classes.  The law of the conservation of matter and energy (you can move matter and energy around and change its form, but the total amount stays the same).  Conservation of charge (the total charge present at the beginning of a reaction is equal to the total charge present at the end; this one is one of the fundamental rules governing chemistry).  Conservation of momentum, conservation of spin, conservation of parity.

All of these are fairly well understood, and physicists use them constantly to make predictions about how interactions in the real world will occur.  Add to them the mathematical models of quantum physics, and you have what might well be the single most precise system ever devised by human minds.  The predictions of this system match the actual experimental measurements to a staggering accuracy of ten decimal places.  (This is analogous to your taking a tape measure to figure out the length of a two-by-four, and your answer being correct to the nearest billionth of a meter.)

So far, so good.  But there's only one problem with this.

Symmetry and conservation laws provide no explanation of how there's something instead of nothing.

We know that photons (zero charge, zero mass) can produce pairs of particles -- one matter, one antimatter, which (by definition) have opposite charges.  These particles usually crash back together and mutually annihilate within a fraction of a second, resulting in a photon with the same energy as the original one had, as per the relevant conservation laws.  Immediately after the Big Bang, the universe (such as it was) was filled with extremely high energy photons, so this pair production was going at a furious rate, with such a roiling sea of particles flying about that some of them survived being annihilated.  This, it's thought, is the origin of the matter we see around us, the matter we and everything else are made of.

But what we know about symmetry and conservation suggests that there should have been exactly equal amounts of matter and antimatter created, so very quickly, there shouldn't have been anything left but photons.  Instead, we see an imbalance -- an asymmetry -- favoring matter.  Fortunately for us, of course.

So there was some matter left over after everything calmed down.  But why?

One possibility is that when we look out at the distant stars and galaxies, some of them are actually antimatter.  On the surface, it seems like there'd be no way to tell; except for the fact that every particle that makes it up would have the opposite properties (i.e. protons would have a negative charge, electrons a positive charge, and so on), antimatter would have identical properties to matter.  (In fact, experimentally-produced antihydrogen was shown in 2016 to have the same energy levels, and therefore exactly the same spectrum, as ordinary hydrogen.)  From a distance, therefore, it should look exactly like matter does.

So could there be antimatter planets, stars, and galaxies out there?  Maybe even with Evil Major Don West With A Beard?

The answer is almost certainly no.  The reason is that if there was a galaxy out there made of antimatter, then between it and the nearest ordinary matter galaxy, there'd be a boundary where the antimatter thrown off by the antimatter galaxy would be constantly running into the matter thrown off by the ordinary galaxy.  So we'd see a sheet dividing the two, radiating x-rays and gamma rays, where the matter and antimatter were colliding and mutually annihilating.  Nothing of the sort has ever been observed, so the conclusion is that what we see out in space, out to the farthest quasars, is all made of matter.

This, though, leaves us with the conundrum of how this happened.  What generated the asymmetry between matter and antimatter during the Big Bang?

One possibility, physicists thought, could be that the particles of matter themselves are asymmetrical.  If the shape or charge distribution of (say) an electron has a slight asymmetry, this would point to there being a hitherto-unknown asymmetry in the laws of physics that might favor matter over antimatter.  This conjecture is, in fact, why the topic comes up today; a paper last week in Science described an experiment at the University of Colorado - Boulder to measure an electron's dipole moment, the offset of charges within an electron.  Lots of molecules have a nonzero dipole moment; it's water's high dipole moment that results in water molecules having a positive end and a negative end, so they stick together like little magnets.  A lot of water's odd properties come from the fact that it's highly polar, including why it hurts like a sonofabitch when you do a belly flop off a diving board -- you're using your body to break simultaneously all of those linked molecules.

What the team did was to create a strong magnetic field around an extremely pure collection of hafnium fluoride molecules.  If electrons did have a nonzero dipole moment -- i.e., they were slightly egg-shaped -- the magnetic field would cause them to pivot so they were aligned with the field, and the resulting torque on the molecules would be measurable.

They found that to the limit of their considerable measuring ability, electrons are perfectly spherical and have an exactly zero dipole moment.

"I don’t think Guinness tracks this, but if they did, we’d have a new world record," said Tanya Roussy, who led the study.  "The new measurement is so precise that, if an electron were the size of Earth, any asymmetry in its shape would have to be on a scale smaller than an atom."

That's what I call accuracy.

On the other hand, it means we're back to the drawing board with respect to why there's something instead of nothing, which as a scientific question, is kind of a big deal.  At the moment, there don't seem to be any other particularly good candidates out there for an explanation, which is an uncomfortable position to be in.  Either there's something major we're missing in the laws of physics -- which, as I said, otherwise give stunningly accurate predictions of real-world experimental results -- or we're left with the even less satisfying answer of "it just happened that way."

But that's the wonderful thing about science, isn't it?  Scientists never write the last word on a subject and assume nothing will ever change thereafter.  There will always be new information, new perspectives, and new models, refining what we know and gradually aligning better and better with this weird, chaotic universe we live in.

So I'm not writing off the physicists yet.  They have a damn good track record of solving what appear to be intractable problems -- my guess is that sooner or later, they'll figure out the answer to this one.

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Do not cross

Back in 1859, renowned British naturalist Alfred Russell Wallace wrote a paper about a peculiar phenomenon, which has since been called Wallace's Line in his honor.  He had noted that west of a wavering line that runs basically from northeast to southwest across Indonesia, the flora and fauna is much more similar to what you find in India and tropical southeast Asia; east of that line, it resembles what you find in Australia and Papua-New Guinea.

Map from Wallace's original paper [Image is in the Public Domain]

The change is striking enough that it didn't take a naturalist of Wallace's caliber to notice it.  Italian explorer Antonia Pigafetta mentioned it in his journals way back in 1521, and various others considered it a curiosity worth noting.  None, though, did the thorough job of studying it that Wallace did, so naming it after him is justified.

However -- even Wallace had no idea why, or how, it had happened.

Ordinarily, faunal and floral assemblages change gradually, unless there's a major geographical barrier.  I saw an example of the latter first-hand when I was in Ecuador -- there's a completely different set of birds as you cross from the west slope to the east slope of the Andes Mountains.  (Some did make the leap, but by and large, you run into a whole different group of species from one side to the other.)

Here, though, there's no obvious barrier.  In fact, if you'll look closely at the map, you'll see that Wallace's Line goes right between the islands of Bali (on the west) and Lombok (on the east) -- a distance of only 35 kilometers, easily narrow enough for birds to cross, not to mention other species swimming or rafting their way from one island to the other.  Even so, the species on Bali are distinctly Asian, and the ones on Lombok distinctly Australian.

On one side, kangaroos and koalas, cockatoos and birds of paradise and cassowaries; on the other, bears and tigers, trogons and drongos and minivets and babblers.

How did this happen -- and more perplexingly, what's kept the line intact?

The explanation for the first part of this question had to wait until the discovery of plate tectonics in the 1950s.  The Australian region and Asia have very different species because they are on different tectonic plates that used to be a great deal farther away from each other; in fact, until 85 million years ago, Australia was connected to Antarctica (something we know not only from our understanding of plate movement, but because prior to that Australia and Antarctica have similar fossils, which began to diverge at that point as Australia moved north and Antarctica moved south).  Australia has been gradually approaching Asia ever since, with its unique assemblage of species riding in like some latter-day Noah's Ark.

What, though, is keeping them from mixing?  The reason the topic comes up today is because of a paper last week in Science that has proposed a neat explanation; the problem is the climate.

Researchers at ETH-Zürich led by evolutionary biologist Loïc Pellissier noted that there were exceptions to the boundary of Wallace's line, but the species that crossed it almost always went one way -- from the Asian region into the Australian region.  Some species of Australian snakes, for example, have their nearest relatives in Asia, as do the wonderful Australian flying foxes.  But there are virtually no examples of species that went the other way.

What was preventing organisms from island-hopping their way from Australia to Asia was Asia's much wetter climate -- if you go from west to east across Indonesia and into Australia, the average rainfall by and large goes steadily downward.  The contention is that it's easier for organisms from a rainy climate to adapt to gradually drying out than it is for extremely dry-adapted organisms to deal with the already high biodiversity (and thus much higher competition with species already well suited to the conditions) found in more rainy regions.

You have to wonder what will happen when Australia and Asia finally collide -- something that is, in a sense, already happening, but will result in a complete fusion of the two continents in two hundred million years or so.  This will result in a situation a little like the collision of India with Asia eighty million years ago, which raised the Himalaya Mountains.  (In fact, that collision is ongoing; as India pushes north, like a giant plow, the Himalayas are continuing to rise.  Which is why you find marine fossils at the top of Mount Everest -- the Himalayas aren't volcanic, they're marine and continental debris scooped together and piled up by the motion of India.)

The collision of Australia and Asia will, of course, eradicate Wallace's Line (although the mountain range it will create could still provide a barrier for species mixing, just as the Andes do in Ecuador and Peru).  Of course, two hundred million years is a very long time -- about three times as long as it's been since the extinction of the non-avian dinosaurs -- so who knows what species will have evolved in the interim?

Or if we'll have any distant descendants of our own around to see it?

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Flight into nowhere

Ever heard of Pan Am Flight 914?

The story goes that on July 2, 1955, Flight 914 -- a Boeing 727 -- took off on a routine run from New York to Miami, with 57 passengers on board.  Everything was going normally until the airplane got close to its destination.  As it was making its initial descent into Miami Airport, the aircraft suddenly disappeared from radar.

There was a massive search effort.  At the time of its disappearance, it was over the Atlantic Ocean -- actually near one corner of the infamous Bermuda Triangle -- so ships, planes, and helicopters were deployed to look for wreckage and (hopefully) survivors.

No trace of the airplane or the people on it were found.

But on March 9, 1985 -- a bit less than thirty years after it took off -- a Boeing 727, coming seemingly out of nowhere, landed in Caracas, Venezuela.  From its tail numbers, it was the missing plane.  Witnesses to its landing reported seeing astonished faces plastered to the windows, apparently aghast at where they were.  But before anyone could deplane, the pilot maneuvered the plane back onto the runway and took off.

This time, apparently for good.  No one has seen the plane, any of the crew, or the 57 passengers since.

[Image courtesy of photographer Peter Duijnmayer and the Creative Commons]

Flight 914 has become a popular staple of the "unsolved mysteries" crowd, and has featured in various books and television shows of the type you see on the This Hasn't Been About History For A Long Time Channel.  Explanations, if you can dignify them with that name, include time slips and/or portals, alien abduction, and the government secretly kidnapping the people on the flight and putting them into suspended animation for thirty years, for some unspecified but undoubtedly nefarious purpose.

There's just one problem with all of this.

None of it actually happened.

Pan Am Flight 914 is a hoax, but one that for some reason refuses to die.  You'll run into various iterations of the claim (the one I linked in the first line of this post is only one of hundreds of examples), all of which have the same basic story but differ in the details -- the number of passengers, the dates of departure and arrival, and so on.  (One site I saw claimed that the flight didn't land until 1992.)  But if you take all of those variations on the tale of the disappearing airplane, and track them backwards, you find out that the whole thing started with...

... The Weekly World News.

I should have known.  There's a rule of thumb analogous to "All roads lead to Rome," which is "All idiotic hoaxes lead to The Weekly World News."  For those of you Of A Certain Age, you will undoubtedly remember this tabloid as the one in the grocery store checkout line that had headlines like, "Cher Gives Birth To Bigfoot's Baby."  They also are the ones that created the recurring character of Bat Boy:

This spawned literally dozens of stories in The Weekly World News, my favorite of which was that a time traveler had come back from the future and told people that Bat Boy eventually becomes president.  The best part is that they call him "President Boy."

Me, I'm in favor.  Given some of the potential choices we've got in 2024, Bat Boy couldn't do much worse.

Bat Boy has also been the basis for countless pieces of fan fiction and a PS 5 game, was the inspiration for the monster in the truly terrifying X Files episode "Patience," and is the main character -- I shit you not -- in a Broadway musical.

But I digress.

The fact that Pan Am Flight 914 came from the same source as Bat Boy, the underwater crystal pyramids of Atlantis, and a coverup involving a mass burial of aliens in Uganda should immediately call the claim into question, but for some reason, it doesn't.  Woo-woo websites, books, and television shows still feature the flight as one of the best-documented examples of a mysterious disappearance, even though Pan Am itself has confirmed that Flight 914 never happened and the whole thing was made up.

Of course, that's what they would say.  *suspicious single eyebrow-raise*

What amazes me is that even though a minimal amount of snooping around online would be enough to convince you that the whole story is a fabrication, the websites claiming it's true far outnumber the ones debunking it.  Further illustrating the accuracy of the quote -- of uncertain origin, but often misattributed to Mark Twain -- that "a lie can go halfway around the world while the truth is still lacing up its boots."

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