Hardwired superstition

Despite my frequent railing against superstition and magical thinking, it's not that I don't see its attractions.  As a teenager and twenty-something I was fascinated with such things as Tarot cards (I actually own no fewer than seven decks, and I haven't been willing to part them with because of how beautiful the designs are), numerology, astrology, and a host of other kinds of woo.  That I eventually threw it all aside (well, figuratively, in the case of the Tarot cards) I attribute to my commitment to a rationalistic view of the world.  I decided in my mid-twenties that I had to establish some criterion for finding what I considered to be the truth, and that logic and evidence seemed a lot more solid than "I fervently wish this was so."

Since my conversion to skepticism, I've found myself looking at True Believers and wondering how they never made the same transition.  We apply the rules of the scientific method in scores of other ways -- "show me how you know this" isn't some kind of odd, esoteric rule only known to Ph.D. candidates (not that I've ever been one of those, but you get my drift).  So how can a person look at the extremely slim evidence for (say) astrology, and not say, "Okay, this makes no sense whatsoever?"

A study in the journal Applied Cognitive Psychology has given us at least a hint of why some people never leave behind their unsupported beliefs in the paranormal.  Its title -- which breaks the general rule that articles whose titles are questions always should be answered "No" -- is, "Does Poor Understanding of Physical World Predict Religious and Paranormal Beliefs?"  The researchers who conducted the study, Marjaana Lindeman and Annika M. Svedholm-Häkkinen of the Institute of Behavioral Studies at the University of Helsinki, looked at a group of 258 people and examined how real-world knowledge of science correlated with belief in the supernatural.  Perhaps unsurprisingly, the researchers found a series of strong correlations:

The results showed that supernatural beliefs correlated with all variables that were included, namely, with low systemizing, poor intuitive physics skills, poor mechanical ability, poor mental rotation, low school grades in mathematics and physics, poor common knowledge about physical and biological phenomena, intuitive and analytical thinking styles, and in particular, with assigning mentality to non-mental phenomena.  Regression analyses indicated that the strongest predictors of the beliefs were overall physical capability (a factor representing most physical skills, interests, and knowledge) and intuitive thinking style.

Note, of course, that correlation does not imply causation; it is by no means certain that the lack of scientific knowledge caused the belief in the supernatural.  In fact, if that were true, one of the other findings of the study would be less likely:

Nonscientific ways of thinking are resistant to formal instruction… which can affect individuals’ ability to act as informed citizens to make reasoned judgments in a world that is increasingly governed by technology and scientific knowledge.

If superstitious beliefs stemmed from something as simple as a lack of knowledge of the world around us, you'd think that you could eradicate magical thinking simply by enrolling people in a college-level physics course.  The fact that this isn't so makes me wonder if there is something else underlying a tendency toward belief in the supernatural -- perhaps something in the brain wiring -- that both makes a person likely to have less aptitude at science and technical subjects, and also results in a stronger likelihood of belief in the supernatural.  A previous study by Lindeman et al. suggests that this may be so:

We examined with functional magnetic resonance imaging the brain activity of 12 supernatural believers and 11 skeptics who first imagined themselves in critical life situations (e.g. problems in intimate relationships) and then watched emotionally charged pictures of lifeless objects and scenery (e.g. two red cherries bound together).  Supernatural believers reported seeing signs of how the situations were going to turn out in the pictures more often than skeptics did.  Viewing the pictures activated the same brain regions among all participants (e.g. the left inferior frontal gyrus, IFG).  However, the right IFG, previously associated with cognitive inhibition, was activated more strongly in skeptics than in supernatural believers, and its activation was negatively correlated to sign seeing in both participant groups.

So once again, we have some evidence that what we think and believe might not entirely be a choice -- it might be hardwired into our brains.  If so, despite my toying with paranormal woo as a young person, I might have been destined all along to become the hard-headed skeptic you all know and (I hope) love.

But I'm still not throwing away the Tarot cards.  They're kinda pretty, even if they're almost certainly useless for predicting the future.

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As someone who is both a scientist and a musician, I've been fascinated for many years with how our brains make sense of sounds.

Neuroscientist David Eagleman makes the point that our ears (and other sense organs) are like peripherals, with the brain as the central processing unit; all our brain has access to are the changes in voltage distribution in the neurons that plug into it, and those changes happen because of stimulating some sensory organ.  If that voltage change is blocked, or amplified, or goes to the wrong place, then that is what we experience.  In a very real way, your brain creates your world.

This week's Skeptophilia book-of-the-week looks specifically at how we generate a sonic landscape, from vibrations passing through the sound collecting devices in the ear that stimulate the hair cells in the cochlea, which then produce electrical impulses that are sent to the brain.  From that, we make sense of our acoustic world -- whether it's a symphony orchestra, a distant thunderstorm, a cat meowing, an explosion, or an airplane flying overhead.

In Of Sound Mind: How Our Brain Constructs a Meaningful Sonic World, neuroscientist Nina Kraus considers how this system works, how it produces the soundscape we live in... and what happens when it malfunctions.  This is a must-read for anyone who is a musician or who has a fascination with how our own bodies work -- or both.  Put it on your to-read list; you won't be disappointed.

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

Color my world

Our ability to perceive color is, when you think about it, a peculiar thing.

First, there's the rather hackneyed question of whether we all see color the same way (exclusive, of course, of people who are colorblind).  The way the question is usually phrased goes something like, "How could we tell if when you look at something red, what you see what I call green, but you still call it red because that's what you've learned?"  In other words, if I were to take a look through your eyes and brain, would the colors of objects be the same as what I see?

The answer is: we can't know for sure.  Thus far there's no way for one person to perceive the world through another person's sensory organs and brain.  But the great likelihood is that we all see colors pretty similarly.  All of our visual receptors are put together the same way, as are the visual cortices in our brains.  To assume that even with this structural and functional similarity, each person is still perceiving colors differently, runs counter to Ockham's Razor -- so without any evidence, it seems like a pretty untenable position.

More interesting is the comparison between how we see the world and how other animals do.  Once again, we run up against the issue that we can't see through another's eyes, but at least here we're on more solid ground because we can see that different animals have differently structured eyes.  Dogs, for example, have retinas with a much higher density of rods (the structures that operate in dim light, but only see in shades of gray) and a much lower density of cones (the structures that operate in bright light, and are able to differentiate by wavelength -- i.e., see colors).  Dogs aren't completely colorblind -- their two types of cones peak in sensitivity in the blue and yellow regions of the spectrum -- but they're relatively insensitive to colors outside that.  (This explains why my dog, Guinness, routinely loses his bright orange tennis ball in the bright green lawn -- to me, it stands out from fifty meters away, but he'll walk right past it without seeing it.) 

Then, there are bees and butterflies, which have eyes sensitive not only in the ordinary visible light spectrum but in the infrared and ultraviolet regions, respectively.  There are flowers that look white to our eyes, but to a butterfly they're covered with streaks and spots -- ultraviolet-reflecting markings that advertising nectar to those who can see it. 

A flower of the plant Potentilla reptans, photographed in ultraviolet light.  To the human eye, the flower looks solid yellow -- this is what it might look like to a butterfly.  [Image licensed under the Creative Commons Wiedehopf20, Flower in UV light Potentilla reptans, CC BY-SA 4.0]

But the winner of the wildly complex vision contest is the mantis shrimp, which has sixteen different color receptors (contrasted with our paltry three), rendering them sensitive to gradations of color we aren't, as well as detecting ultraviolet and infrared light, and discerning the polarization angle of polarized light.  How the world looks to them is a matter of conjecture -- but it certainly must be a far brighter and more varied place than what we see.

The reason all this colorful stuff comes up is because of a paper that appeared last week in Proceedings of the National Academy of Sciences, called "What We Talk About When We Talk About Colors," by Colin Twomey, Gareth Roberts, David Brainard, and Joshua Plotkin of the University of Pennsylvania.  The researchers looked at how words describing different colors vary from language to language.  "The color-word problem is a classical one," Plotkin said, in an interview with Science Daily.  "How do you map the infinitude of colors to a discrete number of words?"

And, more central to this research: does everyone do it the same way?  If you showed me a series of gradations from pure blue to pure green, at what point to I switch from saying "this is blue" to saying "this is green" -- or do I call the intermediate shades by a third, discrete name?

What the researchers found was that across 130 different languages, humans tend to group and name colors the same way.  Further, if you give people tiles with varying shades of red and asked them to pick out "the reddest red," the results show remarkable consistency.

Another interesting result of the research was that the sensitivity of our eyes to color variation isn't the same from color to color; we are much better at picking out subtle variations in red, orange, and yellow than we are at seeing differences in (for example) different shades of brown.  The researchers believe this is due to a difference in what they call communicative need; since reds, oranges, and yellows are the colors of ripe fruit, we've evolved eyes that are most sensitive to variations in those colors.  "Fruits are a way for a plant to spread its seeds, hitching a ride with the animals that eat them," Twomey said.  "Fruit-producing plants likely evolved to stand out to these animals.  The relationship with the colors of ripe fruit tells us that communicative needs are likely related to the colors that stand out to us the most...  No one really cares about brownish greens, and pastels aren't super well represented in communicative needs."

So it seems like the great likelihood is that we all see the world pretty much the same way.  Well, all humans, at least.  What the world looks like to a dog, with their better dim-light vision and better motion detection, but far poorer color discrimination, can only be guessed at; and what colors a mantis shrimp sees is beyond the ability of most of us to imagine.

Study lead author Colin Twomey wonders whether the same techniques could be used to study other facets of sensory perception.  "This is something that could be carried to other systems where there is a need to divide up some cognitive space," he said, "whether it's sound, weight, temperature, or something else."

One I wonder about is the sense of taste.  We know that taste differs a great deal between different individuals, not only because everyone likes (and dislikes) particular flavors, and those preferences differ greatly; but there are some people called "supertasters" who are sensitive to minor variations in flavor that the rest of us don't even notice.  (I am most definitely not a supertaster; the joke in my family is that I have two taste buds, "thumbs up" and "thumbs down.")  The daughter of a friend of mine, for example, has amazingly sensitive taste buds, to the point that she can discern whether the coffee was brewed with filtered water or ordinary tap water.

Me, as long as it's brewed with water and not turpentine, I'm fine with it.

But that's all potential future research.  For now, we have a better idea of how each of us colors our world.  And despite our individual differences, the answer appears to be that what you're seeing and what I'm seeing look very much alike.  

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As someone who is both a scientist and a musician, I've been fascinated for many years with how our brains make sense of sounds.

Neuroscientist David Eagleman makes the point that our ears (and other sense organs) are like peripherals, with the brain as the central processing unit; all our brain has access to are the changes in voltage distribution in the neurons that plug into it, and those changes happen because of stimulating some sensory organ.  If that voltage change is blocked, or amplified, or goes to the wrong place, then that is what we experience.  In a very real way, your brain creates your world.

This week's Skeptophilia book-of-the-week looks specifically at how we generate a sonic landscape, from vibrations passing through the sound collecting devices in the ear that stimulate the hair cells in the cochlea, which then produce electrical impulses that are sent to the brain.  From that, we make sense of our acoustic world -- whether it's a symphony orchestra, a distant thunderstorm, a cat meowing, an explosion, or an airplane flying overhead.

In Of Sound Mind: How Our Brain Constructs a Meaningful Sonic World, neuroscientist Nina Kraus considers how this system works, how it produces the soundscape we live in... and what happens when it malfunctions.  This is a must-read for anyone who is a musician or who has a fascination with how our own bodies work -- or both.  Put it on your to-read list; you won't be disappointed.

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

Judgment calls

I had two experiences in the last couple of weeks, one funny and one maddening, both of which at their heart boil down to the same thing.  I work as an aide for a developmentally disabled man, and mostly what he likes doing is going for long walks.  And both of these incidents happened in almost the same place -- a nearby park which is my friend's favorite spot to go on nice days.

The first I kind of saw coming.  We were heading around a bend in the path, and standing there was a guy holding pamphlets of some sort.  As soon as we got in range, he started telling us that he was there to spread Jesus's word, and could he give us some pamphlets to read.  I said, "No, thanks," but the guy wasn't gonna be brushed off that easily.

"We all need to hear the message of the Lord," he said.

I just kind of stared at him.

"It's how we know right from wrong."  He gave me a disapproving scowl.  "For example, St. Paul said that it is a disgrace for a man to have long hair."

I laughed, a little incredulously, and said, "Tell St. Paul he needs to mind his own damn business," and kept walking.

The second, though, just pissed me off.  There's a nice spot in the park down by a marina, where my friend likes to spend some time watching the boats.  He was standing near the water, and I sat on a bench close by.  I pulled out my phone to check my messages -- at the time, a dear friend of mine was in the hospital, and I wanted to see if there were any updates on her condition.

I was looking at my phone -- no texts or updates, unfortunately -- when a woman who was on the path nearby said, "Isn't it too beautiful a day to spend your time with your nose in your phone?"

I looked up at her, trying to figure out how to respond.  I certainly wasn't going to explain my actions to her; I didn't feel like I was obliged to justify myself to a prying stranger.  I finally shrugged and said, "Yeah," and slipped my phone back into my pocket.  Apparently gratified that she had awakened me to the beauty of nature, she went off with a smile.

In both cases, the issue is about judgment, isn't it?  Neither the fact that I have a ponytail nor my checking my text messages in the park is anyone's business but my own; I'm a bit baffled that anyone would even have an opinion on either of those things.  My mom used to say, "My rights end where your nose begins," and I think that's spot-on, but I'd extend it.

My right to pass judgment ends where your nose begins.

It's easy to judge someone harshly when you don't know the full story.  And you seldom ever do.  What does it cost you to start from the assumption that most people, most of the time, are working from good intentions?  I don't mean you should become gullible, or ignore or excuse truly obnoxious behavior; but why do so many people feel like it's required that they have an opinion about everything and everyone, whether or not it concerns them in the slightest -- the vast majority of them negative?

How about we all do our best to focus not on judging people, but on simply being kind?

The Doctor, as always, has things figured out.

You could argue that both the religious guy and the nature woman were themselves acting out of good intentions; the religious guy trying to save me from hell, the nature woman trying to clue me in to what she thought I was missing.  But the fundamental issue here is that neither of them had the least idea who I was, nor bothered to find out.  Without any knowledge of me or my situation, they both were convinced they knew what I needed to be doing better than I did.

The whole incident with the phone reminded me of this photograph that was making the rounds a couple of years ago, did you see it?

It was usually accompanied by a sneery message about teenagers and how they don't care about anything but social media and why would you even be in an art museum if all you want to do is stare at your phone.  Finally, someone who was there at the time tried to set the record straight; these young people were staring at their phones...

... because they were participating in an online self-guided tour about the lives and work of the artists in the museum.

But as far as I'm aware, that didn't cause any sheepish retractions, and I still sometimes see this photo making the rounds to highlight what slackers teenagers are and/or how technology will destroy us all.

Somehow, indignation seems to come far more easily to people than charity does.  

I'll end with another of my experiences -- this one when I was about six.  Something had happened at school -- I don't even recall what -- and I was bristling with annoyance toward some classmate of mine whom I perceived as having wronged me.  As I was walking home I passed the house of our wonderful friend Garnett, who was out working in her garden, and proceeded to her tell my tale of woe, assuming she'd commiserate with me a little.

What she said knocked me back, and I've never forgotten her gentle words to me that day.  "Gordon, I know you're mad at your friend, but whenever you're tempted to be angry, I want you to remember something," she said.  "Always be kinder than you think you need to be, because everyone you meet is fighting a terrible battle that you know nothing about."

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As someone who is both a scientist and a musician, I've been fascinated for many years with how our brains make sense of sounds.

Neuroscientist David Eagleman makes the point that our ears (and other sense organs) are like peripherals, with the brain as the central processing unit; all our brain has access to are the changes in voltage distribution in the neurons that plug into it, and those changes happen because of stimulating some sensory organ.  If that voltage change is blocked, or amplified, or goes to the wrong place, then that is what we experience.  In a very real way, your brain creates your world.

This week's Skeptophilia book-of-the-week looks specifically at how we generate a sonic landscape, from vibrations passing through the sound collecting devices in the ear that stimulate the hair cells in the cochlea, which then produce electrical impulses that are sent to the brain.  From that, we make sense of our acoustic world -- whether it's a symphony orchestra, a distant thunderstorm, a cat meowing, an explosion, or an airplane flying overhead.

In Of Sound Mind: How Our Brain Constructs a Meaningful Sonic World, neuroscientist Nina Kraus considers how this system works, how it produces the soundscape we live in... and what happens when it malfunctions.  This is a must-read for anyone who is a musician or who has a fascination with how our own bodies work -- or both.  Put it on your to-read list; you won't be disappointed.

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

Moving mountains

I live in a place that doesn't change very much, and I mean that not only in the human sense -- rural upstate New York is not exactly a center of urban development -- but even on the geological time scale.  The bedrock here is Devonian shale, slate, and limestone, on the order of three hundred million years old.  At the point this rock was forming, where I'm sitting right now would have been at the bottom of a shallow subtropical ocean.  Since then, things have dried out a tad, and it's no longer anywhere near subtropical.  There have been a few glaciers in the last few million years; the most recent one started to melt back about 75,000 years ago.  This left behind the Elmira Moraine, only thirty miles south of where I live -- a rubble pile that marks the southern edge of where the glacier pushed rocks and debris ahead of it like a plow.  (The gazillions of rocks of various descriptions that I curse every time I try to dig in my yard are gifts from that last glacier -- glacial erratics -- some of them carried hundreds of miles away from where they formed.)

Other than that, I live in a pretty calm part of the world.  It'd be easy to look around and think the world is static, that the way things are now is the way they'll always be.

Not so in some places.  There are areas of the world where people are well aware that the topography can change in an instant from earthquakes or volcanoes.  Unfortunately, geologically-active areas tend to be heavily populated -- the temblor-prone regions because the scenery is often beautiful (think coastal California) and the volcanic regions because the soil is so fertile (like the land near Naples, Italy, in the shadow of the infamous Mount Vesuvius).  But the fraction of the world's population that lives in an area where the land is changing shape quickly is honestly very small, so most of us figure the mountains and lakes and rivers and whatnot aren't going anywhere.

If you were under any illusions about the fact that the Earth is an active place, consider the paper that came out in Nature last week describing the largest underwater volcanic eruption ever recorded -- one that literally caused a mountain to appear where none had been five years earlier.  Check out the before-and-after photos of the ocean floor, from 2014 and 2019:

Even a non-geologist like myself hardly needs the giant red arrow to see the new mountain where there wasn't one before.

The volcano, fifty kilometers off the coast of the island of Mayotte in the Comoros Archipelago (which lie between the northern tip of Madagascar and the coast of northern Mozambique), is thought to be part of the extremely active East African Rift Zone, an incipient divergent fault system that will ultimately tear off the "Horn of Africa" and create a new microcontinent containing all of Somalia and pieces of Ethiopia, Kenya, and Tanzania.  The eruption seems to have begun in May of 2018, when an earthquake of magnitude 5.8 hit Mayotte.  A team of geologists from France was dispatched to see what was going on, and they installed a monitoring system in February of 2019.  They recorded more than 17,000 seismic events in the next three months, as the mountain grew.

A map showing the chronology of the eruption

Ultimately, the series of eruptions added five cubic kilometers of hardened magma to the seafloor -- a new undersea mountain.

"The volumes and flux of emitted lava during the Mayotte magmatic event are comparable to those observed during eruptions at Earth's largest hotspots," the researchers wrote.  "Future scenarios could include a new caldera collapse, submarine eruptions on the upper slope or onshore eruptions.  Large lava flows and cones on the upper slope and onshore Mayotte indicate that this has occurred in the past."

So if you have a beach home in Mayotte, you might want to consider moving.

All of which makes me once again thankful to live in a place as geologically quiet as we do.  The St. Lawrence Valley, about two hundred kilometers north of us, has earthquakes sometimes, and I recently found out that New York City has fault lines that could potentially generate earthquakes, and in fact have done (none, thus far, severe, at least not in recorded history).  

But here, all is tranquil.  Which is fine by me.  Given that an exciting day in upstate New York is when the farmer across the road bales his hay, I always hope for something unexpected, but if it comes to major earthquakes and volcanic eruptions, I'd just as soon not be anywhere near.

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Mathematics tends to sort people into two categories -- those who revel in it and those who detest it.  I lucked out in college to have a phenomenal calculus teacher who instilled in me a love for math that I still have today, and even though I'm far from an expert mathematician, I truly enjoy considering some of the abstruse corners of the theory of numbers.

One of the weirdest of all of the mathematical discoveries is Euler's Equation, which links five of the most important and well-known numbers -- π (the ratio between a circle's circumference and its diameter), e (the root of the natural logarithms), i (the square root of -1, and the foundation of the theory of imaginary and complex numbers), 1, and 0.  

They're related as follows:

Figuring this out took a genius like Leonhard Euler to figure out, and its implications are profound.  Nobel-Prize-winning physicist Richard Feynman called it "the most remarkable formula in mathematics;" nineteenth-century Harvard University professor of mathematics Benjamin Peirce said about Euler's Equation, "it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth."

Since Peirce's time mathematicians have gone a long way into probing the depths of this bizarre equation, and that voyage is the subject of David Stipp's wonderful book A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics.  It's fascinating reading for anyone who, like me, is intrigued by the odd properties of numbers, and Stipp has made the intricacies of Euler's Equation accessible to the layperson.  When I first learned about this strange relationship between five well-known numbers when I was in calculus class, my first reaction was, "How the hell can that be true?"  If you'd like the answer to that question -- and a lot of others along the way -- you'll love Stipp's book.

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

Poetry reading

A friend of mine and I were discussing poetry a few days ago, and the inevitable question came up: what is your favorite poem?  After our chat, I started thinking that this would be a good topic for Fiction Friday.

I'm not a poet myself, so I can't claim any particular expertise.  Poetry is a compact, crystallized way to tell a story or evoke an emotion, and I tend to be... a little long-winded.  Thus the fact that I'm a novelist.  I am always in awe of someone who can pull off a truly beautiful or evocative poem, because creating resonance in the reader in such a short form seems like such a challenge.  My own favorite poetry usually has some twist on the use of words, something that spins your brain around a little and makes you see the world in a different way.  That's why I've always loved e. e. cummings.  He has a way of turning simple language on its head to create uniquely surreal beauty.  Two of my favorites are the sweet, joyous "if everything happens that can't be done" and the short but chilling "me up at does."  Another contender is Elizabeth Bishop's beautiful "The Fish," and I would be remiss not to mention Stevie Smith's brilliant "Our Bog is Dood," which seems to make no sense at all until... suddenly... the message is crystal clear, and devastating.

But if I had to pick one only, it would be Walter de la Mare's "The Listeners," which (because it was written in 1912) I will reproduce here in full:

‘Is there anybody there?’ said the Traveller,
Knocking on the moonlit door;
And his horse in the silence champed the grasses
Of the forest’s ferny floor:
And a bird flew up out of the turret,
Above the Traveller’s head:
And he smote upon the door again a second time;
‘Is there anybody there?’ he said.
But no one descended to the Traveller;
No head from the leaf-fringed sill
Leaned over and looked into his grey eyes,
Where he stood perplexed and still.
But only a host of phantom listeners
That dwelt in the lone house then
Stood listening in the quiet of the moonlight
To that voice from the world of men:
Stood thronging the faint moonbeams on the dark stair,
That goes down to the empty hall,
Hearkening in an air stirred and shaken
By the lonely Traveller’s call.
And he felt in his heart their strangeness,
Their stillness answering his cry,
While his horse moved, cropping the dark turf,
’Neath the starred and leafy sky;
For he suddenly smote on the door, even
Louder, and lifted his head:—
‘Tell them I came, and no one answered,
That I kept my word,’ he said.
Never the least stir made the listeners,
Though every word he spake
Fell echoing through the shadowiness of the still house
From the one man left awake:
Ay, they heard his foot upon the stirrup,
And the sound of iron on stone,
And how the silence surged softly backward,
When the plunging hoofs were gone.

What I love about this poem is that it gives you a piece of a story, and leaves you to imagine what the rest might be.  What had the Traveller given his word to do, and to whom, and why?  Who are the listeners, and why didn't they answer?  The whole thing gives me chills every time I read it, because -- as Stephen King pointed out in his masterful analysis of horror fiction Danse Macabre, sometimes it's better for writers of horror to leave the door closed.  Left to their own, readers can conjure up some really scary explanations for what might be behind it.

[Image is in the Public Domain]

So that's my favorite poem, and I hope you'll take the time to check out the links I provided to some other wonderful ones.  Now, let's hear from you: what are some of your favorites?

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Mathematics tends to sort people into two categories -- those who revel in it and those who detest it.  I lucked out in college to have a phenomenal calculus teacher who instilled in me a love for math that I still have today, and even though I'm far from an expert mathematician, I truly enjoy considering some of the abstruse corners of the theory of numbers.

One of the weirdest of all of the mathematical discoveries is Euler's Equation, which links five of the most important and well-known numbers -- π (the ratio between a circle's circumference and its diameter), e (the root of the natural logarithms), i (the square root of -1, and the foundation of the theory of imaginary and complex numbers), 1, and 0.  

They're related as follows:

Figuring this out took a genius like Leonhard Euler to figure out, and its implications are profound.  Nobel-Prize-winning physicist Richard Feynman called it "the most remarkable formula in mathematics;" nineteenth-century Harvard University professor of mathematics Benjamin Peirce said about Euler's Equation, "it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth."

Since Peirce's time mathematicians have gone a long way into probing the depths of this bizarre equation, and that voyage is the subject of David Stipp's wonderful book A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics.  It's fascinating reading for anyone who, like me, is intrigued by the odd properties of numbers, and Stipp has made the intricacies of Euler's Equation accessible to the layperson.  When I first learned about this strange relationship between five well-known numbers when I was in calculus class, my first reaction was, "How the hell can that be true?"  If you'd like the answer to that question -- and a lot of others along the way -- you'll love Stipp's book.

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

I feel pretty

The drive to adorn our bodies is pretty close to universal.

Clothing, for example, serves the triple purpose of protecting our skin, keeping us warm, and making us look good.  Well, some of us.  I'll admit up front that I have a fashion sense that, if you were to rank it on a scale of one to ten, would have to be expressed in imaginary numbers.  But for a lot of people, clothing choice is a means of self-expression, a confident assertion that they care to look their best.  

Then there are tattoos, about which I've written here before because I'm a serious fan (if you want to see photos of my ink, take a look at the link).  Tattooing goes back a long way -- Ötzi the "Ice Man," a five-thousand-year-old body discovered preserved in glacial ice in the Alps, had no fewer than 61 tattoos.  No one knows what Ötzi's ink signifies; my guess is that just like today, the meanings of tattoos back then were probably specific to the culture, perhaps even to the individual.  

Then there's jewelry.  We know from archaeological research that jewelry fashioned from gems and precious metals also has a long history; a 24-karat gold pendant found in Bulgaria is thought to have been made in around 4,300 B.C.E., which means that our distant ancestors used metal casting for more than just weapon-making.  So between decorative clothing, tattoos, and jewelry, we've been spending inordinate amounts of time and effort (and pain, in the case of tattooing, piercing, and scarification) altering our appearances.  

Why?  No way to be sure, but my guess is that there are a variety of reasons.  Enhancing sexual attractiveness certainly played, and plays, a role.  Some adornments were clearly signs of rank, power, or social role.  Others were personal means of self-expression.  Evolutionists talk about "highly conserved features" -- adaptations that are between common and universal within a species or a clade -- and the usual explanation is that anything that is so persistent must be highly selected, and therefore important for survival and reproduction.  It's thin ice to throw learned behaviors in this same category, but I think the same argument at least has some applicability here; given that adornment is common to just about all human groups studied, the likelihood is that it serves a pretty important purpose.  What's undeniable is that we spend a lot of time and resources on it that could be used for more directly beneficial activities.

What's most interesting is that we're the only species we know of that does this.  There are a few weak instances of this sort of behavior -- for example, the bowerbirds of Australia and New Guinea, in which the males collect brightly-colored objects like flower petals, shells, and bits of glass or stone to create a little garden to attract mates.  But we seem to be the only animals that regularly adorn their own bodies.

How far back does this impulse go?  We got at least a tentative answer to this in a paper this week in Science Advances, which was about an archaeological discovery in Morocco of shell beads that were used for jewelry...

... 150,000 years ago.

"They were probably part of the way people expressed their identity with their clothing," said study co-author Steven Kuhn, of the University of Arizona.  "They’re the tip of the iceberg for that kind of human trait.  They show that it was present even hundreds of thousands of years ago, and that humans were interested in communicating to bigger groups of people than their immediate friends and family."

A sampling of the Stone Age shell beads found in Morocco

Like with Ötzi's tattoos, we don't know what exactly the beads were intending to communicate.  Consider how culture-dependent those sorts of signals are; imagine, for example, taking someone from three thousand years ago, and trying to explain what the subtle and often complex significance of appearances and behaviors that we here in the present understand immediately.  "You think about how society works – somebody’s tailgating you in traffic, honking their horn and flashing their lights, and you think, ‘What’s your problem?'" Kuhn said.  "But if you see they’re wearing a blue uniform and a peaked cap, you realize it’s a police officer pulling you over."

Unfortunately, there's probably no way to know whether the shell beads were used purely for personal adornment, or if they had another religious or cultural significance.  "It’s one thing to know that people were capable of making them," Kuhn said, "but then the question becomes, 'OK, what stimulated them to do it?'...  We don’t know what they meant, but they’re clearly symbolic objects that were deployed in a way that other people could see them."

So think about that next time you put on a necklace or bracelet or earrings.  You are participating in a tradition that goes back at least 150,000 years.  Maybe our jewelry-making ability has improved beyond shell beads with a hole drilled through, but the impulse remains the same -- whatever its origins.

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

Mathematics tends to sort people into two categories -- those who revel in it and those who detest it.  I lucked out in college to have a phenomenal calculus teacher who instilled in me a love for math that I still have today, and even though I'm far from an expert mathematician, I truly enjoy considering some of the abstruse corners of the theory of numbers.

One of the weirdest of all of the mathematical discoveries is Euler's Equation, which links five of the most important and well-known numbers -- π (the ratio between a circle's circumference and its diameter), e (the root of the natural logarithms), i (the square root of -1, and the foundation of the theory of imaginary and complex numbers), 1, and 0.  

They're related as follows:

Figuring this out took a genius like Leonhard Euler to figure out, and its implications are profound.  Nobel-Prize-winning physicist Richard Feynman called it "the most remarkable formula in mathematics;" nineteenth-century Harvard University professor of mathematics Benjamin Peirce said about Euler's Equation, "it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth."

Since Peirce's time mathematicians have gone a long way into probing the depths of this bizarre equation, and that voyage is the subject of David Stipp's wonderful book A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics.  It's fascinating reading for anyone who, like me, is intrigued by the odd properties of numbers, and Stipp has made the intricacies of Euler's Equation accessible to the layperson.  When I first learned about this strange relationship between five well-known numbers when I was in calculus class, my first reaction was, "How the hell can that be true?"  If you'd like the answer to that question -- and a lot of others along the way -- you'll love Stipp's book.

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

Illuminating Hessdalen

In his wonderful poem/performance piece Storm, Tim Minchin said: "Throughout history, every mystery ever solved has turned out to be 'not magic'."

As I've pointed out many times here before, it's not that I'm saying any of the thus-far-classified-as "out there beliefs" are impossible; it's that if they actually do exist, they should be accessible to scientific inquiry.  Auras, qi, chakras?  Demonstrate they're detectable by something other than a subjective viewer.  Hauntings?  Ditto.  Cryptids of various shapes and descriptions?  Give me something analyzable other than blurry photos and anecdotal eyewitness accounts.  Psychic abilities?  Show they work under controlled conditions.  

Interestingly, there was just an article in The Skeptic asserting that parapsychology has grown to the point that it deserves the title of science rather than pseudoscience.  I'm sure that the author, Chris French, professor of psychology at the University of London, will receive some blowback from this essay, as will The Skeptic in general for publishing it; but I agree with his central thesis, which is that parapsychological claims stand and fall on exactly the same basis as scientific claims do -- evidence.

And, as Minchin says, if a supernatural explanation turns out to be scientifically demonstrable, then it's no longer supernatural, is it?  It's just natural.  After that, it can be studied by the methods of science, just like every other feature of our weird, wonderful, amazingly complex universe.

What brings this up is a recent paper in Meteorology and Atmospheric Physics that considered the odd phenomenon of the "Hessdalen Lights" which occurs in a valley in central Norway, wherein people report seeing free-floating balls of light.  I'd written about the Hessdalen Lights (and various other accounts of lights in the sky) back in 2017, and described it as follows:

The Hessdalen Lights have been seen since the 1940s in the valley of Hessdalen in Norway.  They're stationary, bright white or yellow lights, floating above the ground, sometimes remaining visible for over an hour.  With such a cooperative phenomenon, you would think it would be easily explained; but despite the efforts of scientists, who have been studying the Hessdalen Lights for decades, there is yet to be a convincing explanation.  Hypotheses abound: that it is the combustion of dust from the valley floor; that it is a stable plasma, ionized by the decay of radon from minerals in the valley; or even that it is an electrical discharge from piezoelectric compression of quartz crystals in the underlying rock.  None of these is completely convincing, and the Hessdalen Lights remain one of the most puzzling natural phenomena I know of.

The lack of a convincing explanation opens the door to all sorts of wild speculation, and those abound -- ghosts, aliens, portals in time and space, you name it.  

Photograph of the Hessdalen Lights

As usual, my fallback position was, "I may not know what the scientific explanation is, but I'm certain that one exists."  Given how many times this phenomenon has been reported and photographed, it seemed pretty likely that it wasn't a hoax, or even misattributing it to something purely prosaic (like Neil deGrasse Tyson's story of a cop who was driving down a winding country road, chasing a "weird light in the sky" -- which turned out to be the planet Venus).  So accepting that the Hessdalen Lights actually occur as advertised, what the hell are they?

Much was my delight when I ran across the recent paper, by atmospheric chemist Gerson Paiva of Federal University Pernambuco (Brazil), which seems to have solved the mystery, using...

... wait for it...

... science.

Here's what Paiva writes:

Hessdalen lights are unusual, free-floating light balls presenting different shapes and light colors, observed in the Hessdalen valley in rural central Norway.  In this work, it is shown that these ghostly light balls are produced by an electrically active inversion layer above Hessdalen valley during geomagnetic storms.  Puzzling geometric shapes and energy content observed in the HL phenomenon may be explained through a little-known solution of Maxwell’s equations to electric (and magnetic) field lines: they can form loops in a finite space...  “Natural battery”, aerosols and global atmospheric electric circuits may play a crucial role for the electrification of the temperature inversion layers.

Now, I hasten to add that I don't know if Paiva's explanation is right.  But that's the other great thing about science; it's falsifiable.  When a researcher publishes something like this, it's immediately analyzed and taken to pieces by other experts in the field.  Unlike us fiction writers, who basically want everyone to read our writing and tell us how awesome it is, scientists are looking for rigorous criticism; they want their colleagues to try to tear it down, to see if their analysis is robust enough to withstand attempts to refute it.  So time will tell if Paiva has found the answer to this enduring mystery of atmospheric science.

But even if he hasn't, I'd bet cold hard cash that like Tim Minchin said, the answer will still turn out to be "not magic."

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

Mathematics tends to sort people into two categories -- those who revel in it and those who detest it.  I lucked out in college to have a phenomenal calculus teacher who instilled in me a love for math that I still have today, and even though I'm far from an expert mathematician, I truly enjoy considering some of the abstruse corners of the theory of numbers.

One of the weirdest of all of the mathematical discoveries is Euler's Equation, which links five of the most important and well-known numbers -- π (the ratio between a circle's circumference and its diameter), e (the root of the natural logarithms), i (the square root of -1, and the foundation of the theory of imaginary and complex numbers), 1, and 0.  

They're related as follows:

Figuring this out took a genius like Leonhard Euler to figure out, and its implications are profound.  Nobel-Prize-winning physicist Richard Feynman called it "the most remarkable formula in mathematics;" nineteenth-century Harvard University professor of mathematics Benjamin Peirce said about Euler's Equation, "it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth."

Since Peirce's time mathematicians have gone a long way into probing the depths of this bizarre equation, and that voyage is the subject of David Stipp's wonderful book A Most Elegant Equation: Euler's Formula and the Beauty of Mathematics.  It's fascinating reading for anyone who, like me, is intrigued by the odd properties of numbers, and Stipp has made the intricacies of Euler's Equation accessible to the layperson.  When I first learned about this strange relationship between five well-known numbers when I was in calculus class, my first reaction was, "How the hell can that be true?"  If you'd like the answer to that question -- and a lot of others along the way -- you'll love Stipp's book.

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