Pieces of the puzzle

I'm curious about where the human drive to solve puzzles comes from.

It's a cool thing, don't get me wrong.  But you have to wonder why it's something so many of us share.  We are driven to know things, even things that don't seem to serve any particular purpose in our lives.   The process is what's compelling; many times, the answer itself is trivial, once you find it.  But still we're pushed onward by an almost physical craving to figure stuff out.

When I taught Critical Thinking, every few weeks I devoted a day to solving divergent thinking puzzles.  My rationale is that puzzle-solving is like mental calisthenics; if you want to grow your muscles, you exercise, and if you want to sharpen your intellect, you make it work.  I told the students at the outset that they were not graded and that I didn't care if they didn't get to all of them by the end of the period.  You'd think that this would be license for high school students to blow it off, to spend the period chatting, but I found that this activity was one of the ones for which I almost never had to work hard to keep them engaged, despite more than once hearing kids saying things like, "This is making my brain hurt."

Here's a sample -- one of the most elegant puzzles I've ever seen:

A census taker goes to a man's house, and asks for the ages of the man's three daughters. 

The man says, "The product of their ages is 36." 

The census taker says, "That's not enough information to figure it out." 

The man says, "Okay. The sum of their ages is equal to the house number across the street." 

The census taker looks out of the window at the house across the street, and says, "That's still not enough information to figure it out." 

The man says, "Okay. My oldest daughter has red hair." 

The census taker says thank you and writes down the ages of the three daughters. 

How old are they?

And yes, I just re-read this, and I didn't leave anything out.  It's solvable from what I've given you.  Give it a try!  (I'll post a solution in a few days.)

This drive to figure things out, even things with no immediate application, reaches its apogee in two fields that are near and dear to me: science and linguistics.  In science, it takes the form of pure research, which, as a scientist friend of mine put it, is "trying to make sense of one cubic centimeter of the universe."  To be sure, a lot of pure research results in applications afterwards, but that's not usually why scientists pursue such knowledge.  The thrill of pursuit, and the satisfaction of knowing, are motivations in and of themselves.

In linguistics, it has to do with deepening our understanding of how humans communicate, with figuring out the connections between different modes of communication, and with deciphering the languages of our ancestors.  It's this last one that spurred me to write this post; just yesterday, I finished re-reading the phenomenal book The Riddle of the Labyrinth by Margalit Fox, which is the story of how three people set out, one after the other, to crack the code of Linear B.

Linear B was a writing system used in Crete 4,500 years ago, and for which neither the sound values of the characters, nor the language they encoded, was known.  This is the most difficult possible problem for a linguist; in fact, most of the time, such scripts (of which there are a handful of other examples) remain closed doors permanently.  If you neither know what sounds the letters represent, nor what language was spoken by the people who wrote them, how could you ever decipher it?

One of the Linear B tablets found at Knossos by Arthur Evans [Image licensed under the Creative Commons vintagedept, Clay Tablet inscribed with Linear B script, CC BY 2.0]

I'd known about this amazing triumph of human perseverance and intelligence ever since I read John Chadwick's The Decipherment of Linear B when I was in college.  I was blown away by the difficulty of the task these people undertook, and their doggedness in pursuing the quest to its end.  Chadwick's book is fascinating, but Fox's is a triumph; and you're left with the dual sense of admiration at minds that could pierce such a puzzle, and wonderment at why they felt so driven.

Because once the Linear B scripts were decoded, the tablets and inscriptions turned out to be...

... inventories.  Lists of how many jugs of olive oil and bottles of wine they had, how many arrows and spears, how many horses and cattle and sheep.  No wisdom of the ancients; no gripping sagas of heroes doing heroic things; no new insights into history.

But none of that mattered.  Because of the form that the inscriptions took, Arthur Evans, Alice Kober, and Michael Ventris realized pretty quickly that this was the sort of thing that the Linear B tablets were about.  The scholars who deciphered this mysterious script weren't after a solution because they thought the inscriptions said something profound or worth knowing; they devoted their lives to the puzzle because it was one cubic centimeter of the universe that no one had yet made sense of.

That they succeeded is a testimony to this peculiar drive we have to understand the world around us, even when it seems to fall under the heading of "who cares?"   We need to know, we humans.  Wherever that urge comes from, it becomes an almost physical craving.  All three of the people whose work cracked the code were united by one trait; a desperate desire to figure things out.  Only one, in fact, had a particularly good formal background in linguistics.  The other two were an architect and a wealthy amateur historian and archaeologist.  Training wasn't the issue.  What allowed them to succeed was persistence, and methodical minds that refused to admit that a solution was out of reach.

The story is fascinating, and by turns tragic and inspirational, but by the time I was done reading it I was left with my original question; why are we driven to know stuff that seems to have no practical application whatsoever?  I completely understood how Evans, Kober, and Ventris felt, and in their place I no doubt would have felt the same way, but I'm still at a loss to explain why.  It's one of those mysterious filigrees of the human mind, which perhaps is selected for because curiosity and inquisitiveness have high survival value in the big picture, even if they sometimes push us to spend our lives bringing light to some little dark cul-de-sac of human knowledge that no one outside of the field cares, or will even hear, about.

But as the brilliant geneticist Barbara McClintock, about whom I wrote last week and whose decades-long persistence in solving the mystery of transposable elements ("jumping genes") eventually resulted in a Nobel Prize, put it: "It is a tremendous joy, the whole process of finding the answer.  Just pure joy."

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Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

A planetary Tilt-o-Whirl

A long-standing unsolved puzzle in physics is the three-body problem, which despite its name is not about a ménage-à-trois.  It has to do with calculating the trajectory of orbits of three objects around a common center of mass, and despite many years of study, the equations it generates seem to have no general solution.

There are specific solutions for objects of a particular mass starting out with a particular set of coordinates and velocities, and lots of them result in highly unstable orbits.  Take, for example, this one, which involves three objects of equal masses, starting out with zero velocity and sitting at the vertices of a scalene triangle:

[Animation licensed under the Creative Commons Dnttllthmmnm, Three-body Problem Animation with COM, CC BY-SA 4.0]

It's a problem that has application to our understanding of double and triple star systems, which seem to be quite common out there in the cosmos.  For people like me, who are fascinated with the possibility of extraterrestrial life, it's especially important -- because if the majority of planets in orbit around a double star (or worse, a triple star) follow unstable trajectories, that would represent a considerable impediment to the evolution of life.  Such planets would have wildly fluctuating climates, a possibility that resulted in a plot twist on the generally abysmal 1960s science fiction show Lost in Space, even though when it came up (1) the writers evidently didn't know the difference between a planet's rotation and its revolution, with the result that the blazing heat wave and freezing cold only lasted a few hours each, and (2) in subsequent episodes they conveniently forgot all about it, and it was never mentioned again.

Be that as it may, now that we have a vastly-improved ability to detect extrasolar planets and determine their orbits around their host star(s), it's given us more information about what kinds of trajectories these complex systems can take.  For example, consider the system GW Orionis, which was the subject of a paper last week in Science.

GW Orionis is a trio of young stars, two of which are quite close together, and the third further away.  The two closer ones are whirling around pretty quickly, and the third making long swoopy dives in toward (and then away from) the others.

Complicated enough, but add to that a set of proto-planetary rings.  Three of them, in fact.  And unlike our own rather sedate star system, where all the planets except for Pluto are orbiting within under seven degrees' tilt with respect to a flat plane -- even Pluto's orbit is only tilted by fifteen degrees -- this system is kind of all over the place.

Here's an artist's conception of what GW Orionis looks like, based on the measurements and observations we have:

[Image courtesy of L. Calçada/ESO, S. Kraus et al., University of Exeter]

Pretty cool-looking.  Given our lack of knowledge of (in this case) six-body problems -- the three stars and the three planetary rings -- no one knows for sure if this is going to be a long-lasting, stable system, or if it will eventually collapse or fly apart.  It seems likely that the system would be a planetary Tilt-o-Whirl, and any orbits formed would be as chaotic as the animation I included above, but honestly, that's just a guess.

However, it's entertaining to think of what life would be like on a planet with three suns in the sky.  One more even than Tatooine:

The more we scan the skies, the more awe-inspiring things we find.  I'm glad to live in a time when our ability to study the stars has improved to the point that we're able to consider not just systems like our own, but the vast array of possibilities that are out there.  One thing's for certain: if you are into astronomy, you'll never be bored.

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Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Sunspots and earthquakes

I'm going to start out with a quote from the brilliant Randall Munroe, whose comic strip xkcd is rightly beloved by science nerds and tech geeks the world over.  (Go into any college science building, and check out the professors' office doors.  You'll find as many xkcd comic strips as you did ones from The Far Side twenty years ago.)

The quote is:  "Correlation does not imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing, 'Look over there!'"

The reason this comes up is because of a recent paper in Nature Scientific Reports called, "On the Correlation Between Solar Activity and Large Earthquakes Worldwide."  The authors, Vito Marchitelli and Paolo Harabaglia (of the Università della Basilicata of Potenza, Italy), and Claudia Troise and Giuseppe De Natale (of the Istituto Nazionale di Geofisica e Vulcanologia of Naples) investigated a claim that was first made over a century and a half ago; that there is a connection between solar activity and earthquake frequency.

The first scientist who noticed this was the Swiss astronomer Rudolf Wolf, who also noted the 11.1 year cyclicity of sunspot frequency.  Sunspots are basically solar storms, regions where there is such a high concentration of magnetic flux lines that it inhibits convection and generates a region that is a little cooler and darker than the surrounding parts.  (A sunspot's darkness is relative; isolated from the rest of the bright disk of the Sun, a sunspot would have about the same luminosity as the full Moon, and would glow bright orange.)

Sunspots are also connected to some of the most violent activity our Sun engages in; solar flares, prominences, coronal loops, and coronal mass ejections.  Each of these is basically a different kind of enormous explosion on the Sun's surface, and results in a huge increase in the subatomic particle flux surging outward into the Solar System.  Our atmosphere protects us from some of that bombardment, but it's detectable on the Earth's surface not only with sensitive instruments but because it triggers the brilliant and gorgeous auroras near the poles.

It's not without its hazards, however.  Large events such as coronal mass ejections can damage or disable satellites, and because of the charged nature of the particles, can induce electrical activity in wires and potentially knock out the terrestrial electrical grid.

[Image is in the Public Domain courtesy of NASA]

But Marchitelli et al. found -- or, rather, confirmed Wolf's claim -- that there is a correlation between sunspot activity and earthquake frequency.  So how the hell could that work?

First, let's rule out that it's some kind of spurious correlation, such as the wonderful discovery by Tyler Vigen that per capita cheese consumption year-by-year correlates almost perfectly with the number of people who died from becoming tangled in their bedsheets.  Of course, you can correlate almost anything with anything else if you cherry-pick your data carefully enough; and there are statistical methods to catch out that sort of thing.  Here, an application of those statistical methods to the sunspot/earthquake correlation led to a vanishingly small -- less than 0.00001 -- chance that what they were looking at was not meaningful.

So what's going on here?  Turns out the likeliest explanation has to do with the induction of electrical activity I referenced earlier.  And this is where I had to stifle a chuckle.

If you read my piece "Vanished into the Wilderness" only a couple of days ago, you may remember that one of the goofy explanations proffered for unexplained disappearances of hikers is "the piezoelectric properties of granite."  Piezoelectricity is the property of certain substances to develop a charge if they're put under pressure; it's been thoroughly studied and in fact has a multitude of uses in technology, including push-start ignition on propane grills, the timekeeping device inside a quartz watch, and amplification pickups in electric guitars.

The key to how this could trigger earthquakes has to do with the fact that the piezoelectric effect works both ways; pressing on a piezoelectric substance induces a charge, and charging it induces a change in shape (altering the pressure).  So what Marchitelli et al. suspect is going on here is that the dramatic increase in charged particle flux striking the Earth during a peak time of sunspot activity is creating a piezoelectric change in the pressure of the rocks the particles are passing through -- generating a tension that makes it more likely for a stressed fault to rupture.

What's fun about all this is that not only do we have a correlation, but we have a possible mechanism explaining it.  That's often the problem; there might be odd correlations out there, but absent a plausible mechanism, chances are we're looking at something like Tyler Vigen's discovery that the number of letters in the winning word of the Scripps National Spelling Bee correlates with the number of people worldwide who are killed yearly by venomous spiders.  Here, we are looking at a meaningful correlation.

It also shows that we're being affected by forces of which the average person is entirely unaware.  Which is kind of cool but kind of scary.  It makes me wonder what other things are happening out there that are exerting influences on the world around us in strange and subtle ways.

For what it's worth, I still think that astrology, with all its alleged correspondences between the positions of the planets and stars and people's personalities and fates, is bunk.  And even if piezoelectricity might explain the connection between sunspots and earthquakes, I maintain that it doesn't have a damn thing to do with hikers disappearing.

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Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Dog songs

A couple of nights ago I woke up in the middle of the night (not an unusual occurrence for me) in time to hear our local pack of coyotes whooping it up.

I love coyotes.  Their wild screaming and yapping in the distance on an otherwise still night is an eerie, evocative, primal sound that reminds me that nature is out there, all around me, surrounding my comfortable and civilized life -- and it's far, far bigger than I am.

From another angle, my background in linguistics always makes me wonder what they're saying.  The formal definition of language is "arbitrary symbolic communication;" symbolic in the sense that the word stands as a symbol for the object, action, or concept, and arbitrary in that except for a few onomatopoeic words like "bang" and "splat," the connection between the word and what it symbolizes is more or less accidental and will vary from language to language.  (For example, étoile, stjerne, hoshi, and zvezda mean "star" in French, Norwegian, Japanese, and Russian, respectively, but the sounds of the words have nothing especially stellar about them.)

So by the definition, what the coyotes are doing probably isn't language.  It's communication, yes; it undoubtedly facilitates pack cohesion and performs functions like letting the others know if there's a danger or a potential prey nearby.  But any symbolism there (e.g. a high-pitched yelp means "I see a rabbit") is almost certainly extremely rudimentary and shallow at best.

I'm not running down the dogs, though.  Fortunately, neither of my dogs is an incessant barker, but we can tell the difference between the barks from our elderly hound, Lena, depending on whether she wants to be let inside, she sees a chipmunk, she saw my wife drive up, she's playing with our other dog, or she's standing on the end of the dock barking at the goldfish in the pond.  (Yes, she does that.  Nowhere above did I imply that she's smart.)

She's extremely happy, though.  Which is almost certainly better than being smart.

What brings this up is a fascinating study in Proceedings of the National Academy of Sciences last week showing that an elusive canine long thought to be extinct in the wild -- the New Guinea Singing Dog -- is still out there.

An audio recording of six Singing Dogs in chorus

The Singing Dog -- as you heard if you listened to the audio in the link -- has a mournful, but oddly musical, howl that isn't quite like a wolf's, and certainly nowhere near the wild cacophony of coyotes.  There are Singing Dogs in captivity in zoos, but the small gene pool has meant that they've begun to show signs of degradation from inbreeding, so the discovery that the elusive Highland Wild Dog of New Guinea is almost identical to the Singing Dog provides hope that the subspecies may be a good target for conservation.

Also, a study of the genome of the Singing Dog might give us some clues about where their fantastic repertoire of vocalizations comes from.  It's been known for some time that our own ability to speak is related in some way to the FOX-P2 gene, because mutations in it cause developmental dyspraxia.  But a great many mammals have a similar FOX-P2 gene to that of humans, and even birds do.  Further, mutations in birds' FOX-P2 gene causes problems in songs and calls, indicative that it has an important role in vocal communication throughout the animal world -- and is evolutionarily very old, given that the last common ancestor between birds and mammals was on the order of three hundred million years ago.

So the new discovery about the New Guinea Singing Dog is fascinating from a number of angles.  Not only do we have a chance to save a truly unique population, but the information we've gleaned might shed some light on how vocal communication evolved.

But now I need to go see what Lena's barking at.  Last time she made sounds like this, it turned out she was barking at a stick.  To be fair, it was a very threatening-looking stick.  Just protecting our home from danger, like a good dog should.

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Humans have always looked up to the skies.  Art from millennia ago record the positions of the stars and planets -- and one-off astronomical events like comets, eclipses, and supernovas.

And our livelihoods were once tied to those observations.  Calendars based on star positions gave the ancient Egyptians the knowledge of when to expect the Nile River to flood, allowing them to prepare to utilize every drop of that precious water in a climate where rain was rare indeed.  When to plant, when to harvest, when to start storing food -- all were directed from above.

As Carl Sagan so evocatively put it, "It is no wonder that our ancestors worshiped the stars.  For we are their children."

In her new book The Human Cosmos: Civilization and the Stars, scientist and author Jo Marchant looks at this connection through history, from the time of the Lascaux Cave Paintings to the building of Stonehenge to the medieval attempts to impose a "perfect" mathematics on the movement of heavenly objects to today's cutting edge astronomy and astrophysics.  In a journey through history and prehistory, she tells the very human story of our attempts to comprehend what is happening in the skies over our heads -- and how our mechanized lives today have disconnected us from this deep and fundamental understanding.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Vanished into the wilderness

As I've said many times before: I'm not saying that the paranormal is impossible.  I would really like it, however, if people would consider all of the natural possibilities before jumping straight to the supernatural ones.

This comes up because of a claim over at UFO Sightings Hotspot sent to me by a loyal reader of Skeptophilia, where much is being made about the alleged disappearance of people (hundreds of them, apparently) in parks around the world.  The article comes along with a 24-minute video, which is worth watching if you have the time and don't mind doing a few facepalms, but this passage from the post will give you the gist:

The mystery of hundreds of people vanishing in national parks and forests is possible linked to a strange and highly unusual predator that is living in the woods and forests all across the world and is able to overpower someone in an instant. 

People disappear in the Carpathian Mountains of Romania, Mount Kailash in Tibet, the Markawasi Stone Forest of Peru and in national parks and forests in U.S.A. 

While paranormal researcher Stephen Young described Markawasi as a dimensional portal and suggested the strange energy visitors have described feeling there is possibly caused by a confluence of ley lines or the piezoelectric properties of granite,  Glenn Canady from BeforeItsNews reported that David Paulidis, a former cop began investigating a story about the hundreds that vanished from National Parks and forests in U.S.A...  David began making his own list and discovered there were over 30 cluster sites where most of these vanishings were happening.  He noticed that the people that vanish often do so right under the noses of others in the area.  The missing also shed their clothes right away and they are folded neatly.  One of the Park Rangers said it was like you were standing straight up and you melted away, that’s what it looked like!

So that's the claim.  People are vanishing by the scores, and the only possible explanations are (1) a huge and vicious predator, with apparently worldwide distribution but completely unknown to science, (2) ley lines, (3) dimensional portals, or (4) the "piezoelectric properties of granite."

Let's consider for a moment a couple of other explanations, shall we?  Then I'd exhort you to weigh them along with the supernatural ones, and see what seems to you to be the most likely.

There are two things about hiking in the wilderness that people often fail to take into account.  My perspective from this comes from a long personal history of back-country hiking, starting when I was a kid and my dad and I used to go to the canyon country of Arizona every summer to hunt for rocks and fossils.  Later, after I moved to Washington state, I used to go out in summer for weeks at a time up into the Cascades and the Olympic Range, relishing the silence and the open space after spending the rest of the year in the bustle and noise of Seattle.

If you've never done this yourself, the first thing you need to realize is that the wilderness is freakin' huge.  And empty.  On my trips into the Cascades, there were times that I'd go a week without seeing a single person.  The place is a big expanse of mountains, glaciers, and trees; if I'd gotten lost and gone missing, perhaps been hurt, the chances are very much against my ever being found again.  I ran across a comment on a website about hiker disappearances that seems appropriate, here:

We were out rockhounding in the desert and followed some tank tracks.  Turns out they were WWII tank tracks, and in one gully we found a long dead US Army Jeep, upside down.  We were likely the first people to have seen it since 1940 or so.  We took the shovel.  That's how we know - it hadn't been stripped.  A Jeep - lost for 40 years.  So - yes, a body would be easy by comparison, especially since animals would eat most of it. 

Once you get off a trail, it's not hard to be on ground that hasn't been trod for decades.  And get lost.

Add to that the fact that there are countless false trails, some made by animals, some simply natural open spots, that could lead a hiker astray.  This is one reason why hiking manuals recommend always going camping with a friend (not that I listened, of course).  Having two people there doubles the chances that you'll both come back alive.

[Image licensed under the Creative Commons Miguel.v, Forest on Baxter Creek Trail in Great Smoky Mountains National Park, CC BY-SA 3.0]

And the "not that I listened" part highlights the second thing that a lot of people don't think about, and that's the penchant for people to do dumb stuff. Again, I have some personal experience in this regard.  Despite my "be careful if you're out in the wilderness" message, I was known to make seriously boneheaded choices back in my young-and-stupid days.  I recall being by myself up in the Cascades, and after a hot hike I decided to strip naked and jump into a little crystal-clear lake I'd come across, not noticing that the lake was fed by melting glacial ice until I was already mid-swan-dive.  I think on that day I may have set the world record for fewest milliseconds spent in the water.  I've also loved to climb since I was a kid, and have scaled many a cliff and rock face and tree -- all, of course, without any climbing equipment.  Any of those escapades could have resulted in my being seriously injured or killed.  That I wasn't is more a testimony to dumb luck than it is to skill.

Look at the moronic stuff people will do in front of witnesses, often while right next to gigantic "caution" signs.  A couple of summers ago, my wife and I went to Yellowstone National Park, and we saw many members of the species Homo idioticus doing things like walking right up to bison, elk, and bears, stepping off of boardwalks in order to get up close and personal with hot-enough-to-melt-your-skin-off hot springs, and climbing on crumbling rock formations.  At least here, if something bad happened, there were people around to help (not that in the case of the grizzlies or hot springs, there'd have been much we could do).  But out in the middle of nowhere?  You're on your own.  And I can use myself as a case-in-point that even in those much more precarious circumstances, people still do dumb stuff.

So you don't need to conjecture predators, ley lines, or anything else supernatural to account for disappearances.  The immensity of nature, coupled with natural human stupidity, is certainly sufficient.  Add to this our penchant for imagining stuff while alone or in unfamiliar surroundings, and you can explain the data, such as it is, without recourse to the paranormal.

And trust me.  Whatever the explanation, it has nothing to do with the "piezoelectric properties of granite."

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This week's Skeptophilia book recommendation of the week should be in everyone's personal library.  It's the parting gift we received from the brilliant astrophysicist Stephen Hawking, who died two years ago after beating the odds against ALS's death sentence for over fifty years.

In Brief Answers to the Big Questions, Hawking looks at our future -- our chances at stopping anthropogenic climate change, preventing nuclear war, curbing overpopulation -- as well as addressing a number of the "big questions" he references in the title.  Does God exist?  Should we colonize space?  What would happen if the aliens came here?  Is it a good idea to develop artificial intelligence?

And finally, what is humanity's chance of surviving?

In a fascinating, engaging, and ultimately optimistic book, Hawking gives us his answers to the questions that occupy the minds of every intelligent human.  Published posthumously -- Hawking died in March of 2018, and Brief Answers hit the bookshelves in October of that year -- it's a final missive from one of the finest brains our species ever produced.  Anyone with more than a passing interest in science or philosophy should put this book on the to-read list.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

A pandemic of isolation

When the pandemic started, and I first realized what the implications were, I thought the effect of it on me personally was going to be less than it has turned out to be.

I'm retired from my day job, and now am a full-time writer.  So even before the lockdown started, on a typical day I'd spend most of my time in my office.  (I was going to say "most of my time writing," but given how distractible I am, it'd be closer to the truth to say, "most of my time futzing around on social media and feeling guilty because I'm not writing."  The struggle is real.)  My social life consisted of gym nights with my pal Dave, weekly critique sessions with my writing partner Cly, and the occasional dinner out with my wife.

So I figured, "hey, I'm an introvert anyhow, this isn't going to change my day-to-day life much."

I was wrong.

The social isolation is really getting to me, and has been for some time.  Part of it, of course, is that now I can't socialize with people even if I want to.  I've tried to work in some socially-distanced visits; Dave and I do the occasional hike on a local trail, and I still meet with Cly on her front porch for our critiques, once every three weeks or so.  (What we'll do when the weather turns cold -- which in upstate New York could be by the end of September -- I have no idea.)

But it's been hard.  I miss people.  I miss being able to travel.  I was going to sign up for a three-week retreat in Thailand in January 2021 led by John Aigner, who led the transformative weekend retreat I attended last November (and about which I wrote here), but due to the piss-poor response our country's leaders had to the pandemic, there's now what amounts to a barrier around the United States preventing any of us from leaving and infecting the rest of the world.  (Donald Trump wanted a wall.  Well, he got one.)

I know in the grand scheme of things, this is all minor stuff.  First-world problems, you know?  And honestly, I'm fine with making these sacrifices to slow down the spread of this horrible disease.

But I'd be lying if I said it hasn't affected me.  And I'm not alone.  Research published this week in the Journal of the American Medical Association found that since the pandemic started, the rates of depression in the United States have tripled.  The increase, unsurprisingly, is higher amongst people with low income, who are not only facing the social isolation but fears of medical bills, loss of jobs, threats of eviction, what to do about their children who are now staying home from school when they can't afford daycare, and being in a situation where just to survive they have to expose themselves and their families to illness.  The effect, though, was there regardless of demographic.

[Image licensed under the Creative Commons Sander van der Wel from Netherlands, Depressed (4649749639), CC BY-SA 2.0]

We're social primates, and a strong social context is important even to us introverts.  A study published this week in Nature Neuroscience looked at the effects of early social isolation in mice, and found that being alone caused an inhibition in activity in the neurons that link the prefrontal cortex to the paraventricular thalamus -- known to be part of the reward circuitry active in adults.  While the research could lead to targeted medical treatments for psychiatric disorders impairing socialization, it immediately made me wonder whether this could be at the heart of the spike in depression we're currently seeing.

Because that's part of what I'm experiencing in my own behavior since the pandemic started -- less activity in areas where, prior to the lockdown, the primary reward was dependent on socializing.  Now that I'm not hitting the weights at the gym three times a week with Dave, I haven't been using my home weight bench nearly as much.  I don't have Cly expecting me to have a chapter to read every Tuesday night, so I've been writing way less.

It's been an interesting exercise in self-examination to find out that basically, I'm extrinsically motivated.  When I'm at home alone, and no one is expecting me to get my ass in gear and write something on my work-in-progress or get my gym gear together and head on down to lift for a couple of hours, it's way easier just to say "I'll do it later" and go back to the inevitable focus on the news and social media.  I do have some pastimes I've kept up with -- I'm an amateur potter (not all that good at it; in my hands it's more "playing in the mud for adults") -- and I still hit the wheel three or four times a week.  But it's kind of astonishing to me now that I have more free time, in that I'm no longer teaching eight hours a day, I actually spend less time engaged productively.  And I think a lot of that has to do with the aimlessness that comes from being adrift, on a typical day having no contact with anyone but my wife.

Zoom and Skype and social media only take you so far.

Put simply, I -- and lots of people like me -- are lonely.  It's a hard time for everyone, but I think we can't discount the emotional toll this is taking on ordinary, average people.  There are a lot of jokes going around about how once the pandemic is over, we'll all be celebrating with drunken orgies, but the truth is, I think it's going to take us a long time to recover our equilibrium.

Like I said earlier, I'm still completely willing to make these sacrifices for the common good, and I think the people who are flouting the rules and getting together in large groups anyhow (or people like Florida's governor Ron DeSantis who have steadfastly refused to mandate wearing masks) are simply assholes.  But the fact remains that a lot of us are struggling.  So check in on your friends and family, even the ones for whom it's easy to say, "Oh, well, (s)he's an introvert, I'm sure (s)he's fine."  We need to be kind to each other in these times, and to understand that the illness itself isn't the only concern.

And take care of yourself, okay?  We need all of you to stay happy and healthy and whole through this.

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This week's Skeptophilia book recommendation of the week should be in everyone's personal library.  It's the parting gift we received from the brilliant astrophysicist Stephen Hawking, who died two years ago after beating the odds against ALS's death sentence for over fifty years.

In Brief Answers to the Big Questions, Hawking looks at our future -- our chances at stopping anthropogenic climate change, preventing nuclear war, curbing overpopulation -- as well as addressing a number of the "big questions" he references in the title.  Does God exist?  Should we colonize space?  What would happen if the aliens came here?  Is it a good idea to develop artificial intelligence?

And finally, what is humanity's chance of surviving?

In a fascinating, engaging, and ultimately optimistic book, Hawking gives us his answers to the questions that occupy the minds of every intelligent human.  Published posthumously -- Hawking died in March of 2018, and Brief Answers hit the bookshelves in October of that year -- it's a final missive from one of the finest brains our species ever produced.  Anyone with more than a passing interest in science or philosophy should put this book on the to-read list.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

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 "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.

But 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 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 recent paper in 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 really glad there are people out there who are able to do that stuff, because it really is awfully cool.

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

This week's Skeptophilia book recommendation of the week should be in everyone's personal library.  It's the parting gift we received from the brilliant astrophysicist Stephen Hawking, who died two years ago after beating the odds against ALS's death sentence for over fifty years.

In Brief Answers to the Big Questions, Hawking looks at our future -- our chances at stopping anthropogenic climate change, preventing nuclear war, curbing overpopulation -- as well as addressing a number of the "big questions" he references in the title.  Does God exist?  Should we colonize space?  What would happen if the aliens came here?  Is it a good idea to develop artificial intelligence?

And finally, what is humanity's chance of surviving?

In a fascinating, engaging, and ultimately optimistic book, Hawking gives us his answers to the questions that occupy the minds of every intelligent human.  Published posthumously -- Hawking died in March of 2018, and Brief Answers hit the bookshelves in October of that year -- it's a final missive from one of the finest brains our species ever produced.  Anyone with more than a passing interest in science or philosophy should put this book on the to-read list.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]