Halos and shadows

About two weeks ago, I wrote a piece here about a Scottish cryptid called the Am Fear Liath Mòr -- which roughly translates from Gaelic as "the big gray dude" -- a horrifying apparition that has been seen in the Cairngorms of northern Scotland.  It's described as a human figure, but huge and hulking, that appears in the distance, understandably creating "uneasy feelings" in the observer.

As I mentioned in my previous post, if I were to see such a thing, my "uneasy feelings" would include being so terrified I'd drop dead of a brain aneurysm.  Because I'm just that brave.

Well, thanks to a friend and long-time loyal reader of Skeptophilia, I've learned that this might be an unfortunate overreaction on my part.  The Am Fear Liath Mòr may have a completely rational, scientific explanation, and one that doesn't require belief in some enormous Sasquatch knock-off wandering around in the Highlands.  It seems like the Scottish Big Gray Dude might be an example of a phenomenon that occurs in foggy mountains called the "Brocken spectre."

The Brocken spectre (or "Brocken bow") is an optical effect that occurs when there are eye-level uniformly-dispersed water droplets of all about the same size -- as you find in a fog bank -- and you're backlit by sunlight.  This requires specific conditions, not only fog in front of you, but it being clear enough behind you that there's sufficient sunlight to cast a shadow.  The result is that your shadow, or more accurately the light rays that outline it, are refracted and reflected by the water droplets in the fog, creating a hugely magnified shadow surrounded by a halo of glare, sometimes with a rainbow sheen.

A Brocken spectre photographed near the Golden Gate Bridge, San Francisco, California [Image licensed under the Creative Commons Brocken Inaglory, Solar glory and Spectre of the Brocken from GGB on 07-05-2011, CC BY-SA 3.0]

The phenomenon gets its name from the Brocken, a peak in the Harz Mountains of Germany, where it has been observed for centuries, and was described in detail by scientist Johann Silberschlag in 1780.  The idea of the allegedly-supernatural Brocken spectre being nothing more than an optical illusion generated by a shadow and the refractive effects of water droplets is supported by the fact that it's always seen in the fog when the Sun is behind you, and it seems to shift size unpredictably -- unsurprising if you're moving (which I sure as hell would be if I saw one), and there's a breeze making the fog bank waver and shift.

So it turns out that the Big Gray Dude of Scotland may not be a cryptid at all, just a weird -- and fascinating -- localized weather phenomenon.  And it also accounts for other instances of eerie figures in the mist, such as the "Dark Watchers" of the Santa Lucia Mountains in California and the strange looming presence reported by British mountaineer Eric Shipton while climbing Mount Kenya.  It's also related to the optical phenomenon called heiligenschein ("holy light") which probably accounts for instances of people being seen surrounded by what appears to be a ghostly halo.  The somewhat anticlimactic explanation for this latter effect is that it's not Tongues of Fire or the Radiance of God descending upon you, it's light scattering and a thoroughly understood mechanism called retroreflection that happens regardless of the holiness level of the person involved.

In any case, one more win for the scientific approach, even if it kind of blows away the mystique of a giant scary shadow-man wandering about in the Scottish Highlands.  Skeptic though I am, I have to admit to being a little disappointed.  It seems like if there's anywhere that should actually be haunted, it's the Cairngorms.  But even so, it's somehow fitting that the thing that has been terrifying the superstitious for centuries turns out to be nothing more than...

... their own shadows.

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Last week's Skeptophilia book-of-the-week, Simon Singh's The Code Book, prompted a reader to respond, "Yes, but have you read his book on Fermat's Last Theorem?"

In this book, Singh turns his considerable writing skill toward the fascinating story of Pierre de Fermat, the seventeenth-century French mathematician who -- amongst many other contributions -- touched off over three hundred years of controversy by writing that there were no integer solutions for the equation  aⁿ + bⁿ = cⁿ for any integer value of n greater than 2, then adding, "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain," and proceeding to die before elaborating on what this "marvelous proof" might be.

The attempts to recreate Fermat's proof -- or at least find an equivalent one -- began with Fermat's contemporaries, Evariste de Gaulois, Marin Mersenne, Blaise Pascal, and John Wallis, and continued for the next three centuries to stump the greatest minds in mathematics.  It was finally proven that Fermat's conjecture was correct by Andrew Wiles in 1994.

Singh's book Fermat's Last Theorem: The Story of a Riddle that Confounded the World's Greatest Minds for 350 Years describes the hunt for a solution and the tapestry of personalities that took on the search -- ending with a tour-de-force paper by soft-spoken British mathematician Andrew Wiles.  It's a fascinating journey, as enjoyable for a curious layperson as it is for the mathematically inclined -- and in Singh's hands, makes for a story you will thoroughly enjoy.

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

Through the looking glass

Regular readers of Skeptophilia may remember that a couple of weeks ago, I attempted to write a post on the odd superstitions surrounding mirrors, but got sidetracked over and over.

In a curious almost-synchronicity, today I ran into an article about how artificial intelligence can learn how to detect mirror-reversed images, even when they don't have such obvious cues as text to go by.  So I figured I ought to give another shot at addressing the topic of mirrors, more seriously this time.

Mirror reversal is a peculiar phenomenon, and I recall when I was in introductory physics in college and we were studying the optics of mirrors and lenses, I spent an inordinate amount of time trying to figure out why a flat mirror reverses an image right-to-left but not top-to-bottom.

The answer, which many of you probably already know, is that mirrors don't reverse right-to-left, exactly; they reverse back-to-front.  This has the effect of a right/left reversal because it's like you're looking at the object from the other side (imagine the object in question was transparent, but you could still see its contours, and the reasoning becomes easier).

Look, I can prove it to you.  Stand in front of a mirror.  What it seems like is that there is another person who looks exactly like you standing behind a clear piece of glass, at the same distance from the glass as yourself and facing you.  Now, think about what it would be like if you were to join him/her -- go behind the mirror.  To get there, you would have to walk behind the glass and turn 180 degrees about the vertical axis to face you.  If you did that, your left hand would be opposite his/her right hand, and vice versa.  What actually happened is that your reflection didn't do a 180 degree turn.  It was reversed front to back with no rotation at all.  You're seeing yourself not so much reversed as turned inside-out.

Interestingly, there is a mirror that reverses objects top to bottom -- a concave mirror.  It also creates an image that appears to be in front of the mirror, not behind it, and in the right setup, the image seems to be floating in space (which is why the physicists call concave mirror images "real images," and ones that are behind the mirror -- as in flat and convex mirrors -- "virtual images").

[Image is in the Public Domain]

Whether concave mirrors reverse text is left as an exercise for the reader.

But what brought me to the subject of mirrors (again -- although my first attempt was pretty pathetic) is the paper "Visual Chirality," by Zhiqiu Lin, Jin Sun, Abe Davis, and Noah Snavely, of Cornell University, which was presented at the 2020 Conference on Computer Vision and Pattern Recognition.  What the researchers did was to use a trainable artificial intelligence program to analyze images, some of which were mirror-reversed and others which were not, to see if it was possible to determine reversal without using such giveaways as text, analog clocks, and so on.

And they got pretty good at it.  Some of the cues it picked up on were of the "oh, yeah, of course" type, such as looking at where the buttons were on a button-down shirt.  (Buttons tend to be on the right side -- although years ago women's shirts used to button from the other side, most shirts for either gender now usually have the buttons on the right.)  Wristwatches were also a giveaway, even when the faces weren't visible; most people wear them on the left wrist.  People carrying phones usually had them in their right hands, probably attributable to the fact that between seventy and eighty percent of us are right-handed.

But there were some curious ones.  Turns out the algorithm figured out that when people are in face-forward photographs but not looking directly at the camera, they usually gaze to the left.  Men with facial hair also were easy for the software to pick out when reversed -- the researchers suspect it has something to do with the way men trim their beards (perhaps also connected to using the right versus the left hand to do so), but what exactly the algorithm was picking up on, the researchers aren't certain.

"It’s a form of visual discovery," said study co-author Noah Snavely.  "If you can run machine learning at scale on millions and millions of images, maybe you can start to discover new facts about the world."

After training, the algorithm was getting the answer right eighty percent of the time even when all the obvious giveaways were removed -- not a bad score.  The study has applications in the analysis of images, and detection of when those images have been doctored or altered.

What it puts me in mind of is the facial asymmetry that most humans have, something well-known to portrait artists.  Take a sheet of paper, and stand in front of your bathroom mirror.  Relax your facial muscles -- try for a neutral expression -- and cover up first one, then the other, half of your face with the paper.  You'll be surprised at how different they look -- angle of the mouth, position of the eyebrows, and so on can vary greatly.  (There was an interesting study a while back that correlated facial symmetry with our perception of beauty -- and found that of the people tested, Denzel Washington had the most perfectly symmetrical face.  It may be that symmetry is an indication of freedom from some genetic flaws that influence skeletal development -- making symmetrical people good bets for producing healthy children -- but that, of course, is speculation.)

Anyhow, it's an interesting finding.  But I'm definitely going to pay more attention next time I trim my facial hair.

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This week's Skeptophilia book recommendation of the week is pure fun, and a great gift for any of your friends who are cryptid fanciers: Graham Roumieu's hilarious Me Write Book: It Bigfoot Memoir.

In this short but hysterically funny book, we find out from the Big Guy's own mouth how hard it is to have the reputation for being huge, hairy, and bad-smelling.  Okay, even he admits he doesn't smell great, but it's not his fault, as showers aren't common out in the wilderness.  And think about the effect this has on his self-image, not to mention his success rate of advertising in the "Personals" section of the newspaper.

So read this first-person account of the struggles of this hirsute Everyman, and maybe even next time you're out hiking, bring along a little something for our australopithecene distant cousin.

He's very fond of peach schnapps.

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