Glimpse of the dawn

A pair of words biologists (and interested laypeople) have to be careful with are primitive and advanced.

They're often used in place of the generally more appropriate simple and complex.  By that usage, an amoeba is primitive and an aardvark is advanced.  But where it gets confusing is that primitive and advanced are also sometimes used to mean "like something that evolved earlier" and "like something that evolved more recently," respectively -- so they use primitive to describe a stegosaurus and advanced to describe a spider monkey, when in fact both of those are about equally complex.  (It gets even murkier when you throw in questions of relative intelligence.)

It bears keeping in mind that while modern organisms vary greatly on the simple/complex spectrum, they all have lineages that have been around exactly the same amount of time -- 4.3 billion years, give or take a day or two.  All known lineages of terrestrial life converge on a single life form nicknamed LUCA -- the Last Universal Common Ancestor -- around four billion years ago.  To our eyes, LUCA probably wouldn't have looked like much.  It probably resembled species we now classify as bacteria.

But all life on Earth descends from it.  And as far as the primitive/advanced bit, the only difference is in that time, some of the lineages changed a great deal more than others did.

The reason this comes up is because of a link sent to me by a friend and frequent contributor of topics for Skeptophilia, about a species of fairly modern-looking jellyfish that was found in rock strata that are 505 million years old.

The species, named Burgessomedua phasmiformis, was a free-swimming, tentacle-laden predator with a bell on the order of twenty centimeters in diameter.  It, like many of the Cambrian explosion fauna, were found in the exceptionally well-preserved Burgess Shale Formation of the Canadian Rockies in British Columbia.

Artist's impression of live Burgessomedusa in the Cambrian seas [courtesy of artist Christian McCall]

Jellyfish and most of the other members of Phylum Cnidaria are generally scarce in the fossil record, because their bodies are primarily water.  If you've ever seen a dried-up jellyfish on the beach, you know what I'm talking about; there's barely anything left.  (Don't assume that this means they're harmless, though.  Even the dried tentacles of a Portuguese man-o'-war can pack a dangerous sting.)  But you can see how astonishing it is not only to have one create an impression in sedimentary rocks, but to have that impression last for 505 million years.

So the exceptional preservation of this extremely rare fossil animal is amazing enough.  But what I find even more mind-boggling when I think about the life back then is the bigger picture of what the Cambrian Period was like.  At that point, all life was in the water.  There was (more or less) the same amount of land as there is now, albeit configured completely differently -- but on that land was not a single living thing.  No plants, no fungi, no animals.  Nothing.  It was a vast expanse of empty rock, sand, and dust.

At this point, the first terrestrial plants wouldn't make their appearance for another fifty million years, and even then, they were highly water-dependent and very likely clustered along shorelines.  The first vascular plant -- one with the internal plumbing most plants have today -- that appears in the fossil record is Cooksonia, which appeared during the mid-Silurian Period (about 430 million years ago).  It was a strange, rather Dr. Seussian thing:

[Image licensed under the Creative Commons Smith609 Ground texture from Image:Mud closeup.jpg, Cooksonia pertoni, CC BY 3.0]

But when Burgessomedusa was swimming in the Cambrian oceans, all that lay millions of years in the future.  This glimpse of the dawn of time gives us a picture so alien to our current mental image of the Earth it's hard to believe it's the same planet.

What this tells paleontologists, though, is that even in the early Cambrian, there were relatively modern-looking jellyfish -- and that even though today's cnidarians are advanced in the sense of "length of their lineage on Earth," they haven't changed much at all during all those hundreds of millions of years.  The general reason for such stability is that the body plan works; there's little selective pressure to favor alterations in a system that does fine as is, however "primitive" it may look to us.

As a writer friend of mine posted yesterday:

The details might be off a little, but the gist is accurate enough.

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One language to rule them all

The aphorism "No matter what you know, there's always more to learn" is something you'd be likely to see on one of those cheesy "motivational posters" that cheery type-A personalities like to pin up on office walls, but there's a lot of truth to it.  I rather prefer the formulation credited to Socrates -- "The more I know, the more I realize how little I know."

I ran into a fun example of this principle a while back, when a member of the online linguistic geekery group Our Bastard Language posted an article from The Public Domain Review called "Trüth, Beaüty, and Volapük," about a constructed language (or "conlang," in the lingo of the field) called Volapük that I had never heard of before.

My M.A. is in linguistics, but my field of study was historical/reconstructive linguistics (my thesis was about the effects of the Viking invasions on Old English and Old Gaelic, and should have won some kind of award for research that has absolutely no practical application).  But even though conlangs aren't my specialty, I've always had a fascination from them, and in fact I created a conlang called Kalila as a part of my soon-to-be-released novel In the Midst of Lions.  There are a remarkable number out there, from the familiar (Esperanto, Klingon, Elvish) to the obscure but fascinating (such as John Quijada's Ithkuil, which attempts to express concepts in a combinatory way from the smallest possible number of root words).

A sample of Tolkein's lovely Elvish script [Image is in the Public Domain]

But despite my interest in conlangs, I had never run across Volapük, which is strange because next to Esperanto, it's apparently one of the most studied constructed languages ever created.  It was the invention of a German priest named Johann Schleyer, who not only wanted to create a regularized speech that came from familiar roots (to Europeans, anyhow) and was easy to learn, but was also "beautiful sounding."  Schleyer had an inordinate fondness for umlauts, which he added because he thought that "A language without umlauts sounds monotonous, harsh, and boring."

Which reminds me of the opening credits in Monty Python and the Search for the Holy Grail, especially the "A mööse once bit my sïster" part.  One of Schleyer's contemporaries couldn't resist poking some gøød-natured fün at him over his umlautophilia, and published the following limerick in the Milwaukee Sentinel:

A charming young student of Grük
Once tried to acquire Volapük
But it sounded so bad
That her friends called her mad,
And she quit it in less than a wük.

To my ears, it doesn't sound bad at all, and kind of has a Scandi-Slavic lilt to it. Here's a sample:

The author of the article in The Public Domain Review, Arika Okrent, attributes the relative failure of Volapük to its plethora of umlauts and the easier word roots of its competitor Esperanto, which currently has about two million fluent speakers (an estimated one thousand of whom learned it as their first language).  I'm a little doubtful about that; certainly umlautiness hasn't discouraged anyone from learning Finnish.  I think it's more that the idea of a universal language is one of those high-flown ideals that won't ever catch on because most people are going to be resistant to giving up their native tongue in favor of an invented system of speech, however easy it is to learn.  Language is such a deep part of culture that to jettison our own mode of communication runs counter to every social instinct we have.  (Note that one of the most common things conquerors do to conquered people is to outlaw the speaking of the native language -- it's a sure way to deal a death blow to the culture.)

Even so, I find the whole conlang thing fascinating, and was tickled to run across one I'd never heard of.  Back in my teaching days I every so often had students who participated in an independent study class I offered in introductory linguistics, and the final project was to invent the framework of a language -- a phonetic and phonemic structure, morphological scheme, and syntax, along with a lexicon of at least a hundred words.  They then translated a passage from English into their language.  (One of the best ones I've ever seen involved a charming translation of Eric Carle's The Very Hungry Caterpillar.)

The result of this project was twofold -- students found out how hard it is to create a realistic language, and they learned a tremendous amount about the structure of our own language.  And that's just from producing a rudimentary skeleton of a language.  For people like Schleyer, who created a rich and fully functional language, it was the result of many years of devotion, hard work, and love for language itself.

So it's kind of a shame that people didn't appreciate Volapük more.  Schleyer's dream of having a language that would bring the entire world together in a common mode of communication may be as far off as ever, but even so, it's a beautiful dream.  Even if it would mean making friends with the mäjestïc ümlaüt.

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Hero worship

I got into a curious exchange with someone on Twitter a couple of days ago about Richard Dawkins's recent statement that "biological sex is binary, and that's all there is to it," wherein he called the claims of trans people (and their requests to be referred to by the pronouns they identified with) "errant nonsense," and characterized the people who have criticized him and author J. K. Rowling (amongst others) for their anti-trans stances as "bullies."

The person I had the exchange with seemed to consider this a gotcha moment, and came at me with a gleeful "what do you think of your atheist idol now that he's broken ranks?"

I found this a puzzling question from a number of standpoints.  First, I've never idolized Dawkins.  I think he is an incredibly lucid writer on the subject of evolutionary biology, and his books The Blind Watchmaker, Climbing Mount Improbable, and The Ancestor's Tale remain three of the best layperson's explanations of the science and evidence behind evolution I've ever read.  But admiring his writing on one topic doesn't mean I think he's infallible.  In fact, I've always had the impression that Dawkins was a bit of a dick, and he certainly comes across as more than a little arrogant.  While I agree with him on the subject of evolution, it doesn't mean that he's someone I'd particularly want to have a beer with.

[Image is in the Public Domain]

When I responded to the question with something like this, the person on Twitter seemed a bit deflated, as if he'd expected me to alter my stance on LGBTQ+ issues and the biology of gender just because My Hero had made some sort of pronouncement from on high.

This struck me as a peculiar reaction.  Maybe this is how it works within the context of religion, where a leader (e.g. the Pope, the Imams, and so on) makes a statement and the expectation is that everyone will simply accept it without question.

But it's definitely not how things go in science.

In this case, it has nothing to do with Dawkins bucking the system against some kind of perceived party line.  In fact, I'll bring out one of his own quotes, which applies here: "If two people are arguing opposite viewpoints, it is not necessarily the case the the truth lies somewhere in the middle.  It is possible that one of them is simply wrong."  On the subject of sexuality being binary, Dawkins is simply wrong, something I explored in some detail in a post a couple of years ago.

But the point is, that doesn't detract from his excellent writing on evolution.  Being wrong about one thing, or even about a bunch of things, doesn't mean you're wrong on everything, nor invalidate other outstanding work you may have done.  (Although it can rightly tarnish your reputation as a decent human being.)  It's sad that Dawkins has gone off the rails on this topic, and a shame that his aforementioned arrogance is very likely to make him unwilling to see his own faulty assessment of the evidence and even less likely to admit it if he does.  And it's unfortunate that his air of authority is certainly going to carry some weight with people, especially those who want more ammunition for defending what they already believed about the supposed binary nature of gender.

The fact that this doesn't make me discount him completely is because I feel no need to engage in hero worship.

That extends to other areas as well.  I can appreciate the acting ability of Tom Cruise and Gwyneth Paltrow, and thoroughly enjoy watching (respectively) Minority Report and Sliding Doors, while at the same time acknowledging that in real life both of them appear to have a screw loose.  I can still be inspired by some of the stories of H. P. Lovecraft, while keeping in mind that he was a virulent racist (something that comes through loud and clear in the worst of his stories, but fortunately not all).

In fact, it's best if we look at all famous people through that lens.  The expectation that someone prominent or admired must be flawless -- and therefore, anyone criticizing him/her is de facto wrong -- is what leads to the behavior we're now seeing in Trump loyalists, who will defend him to the death regardless what charges are proven against him or how overwhelming the evidence is.

It is this sort of thinking that is characteristic of a cult.

In any case, I can say I'm disappointed in Dawkins, but it neither caused me to abandon his writing on evolutionary biology nor to revise my own thinking on LGBTQ+ issues because Dawkins Says So.  It's best to keep in mind that people are complex bundles of often contradictory traits, and there's no one person who is going to be in line with your understanding of the world all the time.  In the end, it's always best to form your beliefs based on where the actual evidence leads -- and above all, to think for yourself.

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False vacuum catastrophe

It's odd how enamored people are of things that could destroy the entire universe.

I mean, on one level I get it.  The sheer power of the natural world is pretty awe-inspiring, and as I've mentioned before, if I hadn't become a mild-mannered novelist, I definitely would have been a a tornado chaser.  That same love of extreme danger (especially when it's not you experiencing it) explains shows like The Deadliest Catch and the innumerable quasi-documentaries wherein divers swim around in chum-filled waters and still act surprised when they're attacked by sharks.

But on a larger scale, there's a real curiosity about things that could wipe out pretty much everything.  A while back, I wrote a piece about people sounding gleeful that we might be looking down the gun barrel of a gamma-ray burster (we're not), and over and over we've heard alarmists suggesting that CERN was going to create a black hole that would eat the Earth (it's not).  But that doesn't begin to exhaust the ways in which we all could die in horrible agony.

Which brings us to the concept of the false vacuum.

Sounds harmless enough, doesn't it?  Well, this is in the long tradition of physicists giving seriously weird things cutesy names, like "strange quarks" and "glueballs."

The idea of the false vacuum is that the universe is currently in a "metastable state."  What this means is that right now we're in a locally stable configuration, but if something destabilizes us a little bit, we might find ourselves suddenly plunging into a more stable state -- a "true vacuum."  The situation, then, would be similar to that of the little ball in the graph below:

As long as nothing disturbs the status quo, the ball is stable; but if something gives it a push up the hill in the middle, it'll crest the hill and find itself rushing downward into a more stable position -- the "true vacuum."

Why this concerns anyone but the physicists is that the result of our reconfiguring into a true vacuum would be that a bubble would form, rushing outward at the speed of light, and destroying everything in its path.

The Standard Model of Particle Physics suggests that from the mass of the Higgs boson and the top quark, an estimate could be made of just how likely this is.  Writer Robert Walker concludes, from the research of Joseph Lykken and others, that the answer is "not very:"

[I]f it could happen, then you’d expect it to have happened already in the first 1/10,000,000,000th of a second along with the other symmetry breaking when gravity split off from the other forces, when it was tremendously hot...

 
Since that hasn’t happened, the false vacuum has to be very stable, or else, probably as we find new physics we find out that it is not in a false vacuum state at all.

 
And yes, on the basis of the measured mass of the Higgs boson, the false vacuum has to be very stable.  Joseph Lykken says that an event that triggers a patch of true vacuum, if the theory is correct, happens on average once every ten thousand trillion, trillion, trillion, trillion, trillion, trillion, trillion, trillion years.

 
That means it is nothing to be worried about.

Walker, who is a mathematician, says that the likelihood of a true vacuum bubble occurring in any given century is less than the likelihood of purchasing tickets for twelve consecutive Euromillions lotteries, and winning the jackpot for all of them.

So "don't worry about it" seems to be an understatement.

However, that hasn't stopped the alarmists from freaking out about it, probably largely due to the fact that if it did happen, it would be pretty catastrophic.  Also, because a lot of them seem to feel that the physicists (for this, read "mad scientists") are actively trying to trigger the creation of a true vacuum, which would be an idiotic thing to do even if it were possible because they'd be the first ones to get vaporized, and wouldn't even have the pleasure of standing around rubbing their hands together and cackling maniacally for more than about a nanosecond.

But then there are the ones who think that it could happen accidentally (again, because of CERN, of course), and the physicists are simply being reckless, not suicidal.  I tend to agree with Walker, though.  I'm way more worried about the idiotic things humans are currently doing to the environment, and our determination to slaughter each other over things like who has the best Invisible Friend, than I am about triggering the Scary Bubble of Death.

Anyhow.  That's our Terrifying Thing That Can Kill you for today, along with some soothing words about why it's not very likely.  Now ya'll'll have to excuse me, because I'm gonna go have a pint of beer and watch Twister for the seventeenth time.

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Jersey devilry

Yesterday's post, about spurious claims of a curse (and associated terrible occurrences) in rural northwestern Connecticut, prompted an interesting comment from a reader.

I have a question, and please don't take this as criticism, because it's not meant that way.  Don't you think that the sheer number of claims of the paranormal counts for something?  I don't remember where I read this, but polls have found that wherever you go, the majority of people claim to have had at least one experience of the supernatural.  I'm not talking about Dudleytown in particular -- that may well be a hoax, as you explained -- but surely you can't attribute all of the claims of the paranormal to lies or hoaxes or people misinterpreting natural phenomena or whatever.  There has to be some wheat among the chaff, don't you think?

It's a good question, and I don't at all take it as criticism (after all, questioning is how we come to understanding).  She's certainly right about the commonness of the claims; a 2022 poll by YouGov found that over two-thirds of Americans claim to have had experiences of the supernatural.  But the fact is, no, I don't find this very convincing.  As we've seen all too often here at Skeptophilia, humans have an unfortunate tendency to make shit up and claim it's real.  Add that to our generally faulty sensory-perceptive apparatus and capacity for psychological priming (interpreting what we experience based upon what we expected to experience), and you have a combo that makes eyewitness accounts suspect right from the get-go.

As an example of this, let's take a look at one of the most famous examples of a supernatural entity -- the notorious Jersey Devil.

The Jersey Devil, or Leeds Devil, is a legend of the Pine Barrens region of southern New Jersey.  The area is atmospheric enough without the creature.  It's a thinly-occupied belt of poor, sandy soil running down the middle of the southern half of the state, home to a unique ecosystem dominated by pitch pine and other species that have evolved to thrive there.  Because the soil was lousy for farming, it never was heavily settled.  The few permanent residents somehow eked out a living for themselves, but other than that it was mainly a haunt of sketchy characters and criminals on the run from the law.  (As an interesting side note, one of these was my direct ancestor, Luke Rulong, who lived in the Pine Barrens in the late eighteenth century.  He was in and out of jail repeatedly for such crimes as poaching, mischief, and riot, and his only known child -- my ancestor, Aaron Rulong -- went all the way to Louisiana to get away from his father's bad reputation.)

In any case, the Jersey Devil is said to be a strange looking creature, a bit like a skinny kangaroo with wings.  Here's a drawing from the Philadelphia Bulletin in 1909:

[Image is in the Public Domain]

There have been hundreds (probably thousands) of alleged sightings of this thing, including by such luminaries as Commodore Stephen Decatur and Joseph Bonaparte, elder brother of Napoleon, who had emigrated to the United States and owned an estate near Bordentown.  There was a wave of sightings in 1909 (which is why the artist's impression of the Devil ended up in a Philadelphia newspaper that year).  However, the sightings have been steady throughout the twentieth century, probably bolstered by how many times the creature has appeared in fiction -- in fact, it was one of the first "monster of the week" episodes in The X Files.

Where we start running into trouble is that even the believers can't agree on the Jersey Devil's origins.  Here are three popular claims:

1. It is a spirit creature that has inhabited the area for millennia, and was known to the Native Lenape people as M'Sing.
2. It is the thirteenth child of one Jane (or Dorothy) Leeds and her husband Japhet, inhabitants of the Barrens.  Dorothy (or Jane) was understandably enough pissed off at the fact that twelve children weren't sufficient and cursed her child in utero.  "May you be the Devil!" she said, and sure enough, so it was.  It was born with wings and hooves and a horrible animal face, and shortly after birth flew up the chimney and out into the woods, where it lives lo unto this very day.
3.  Same as #2, except that the father of the child wasn't Japhet Leeds, but was Satan himself.

Japhet Leeds was apparently real enough, even if no one is quite sure what his wife's name was (in a lot of the versions of the legend, she's called "Mother Leeds" to obviate the need of figuring it out).  There's a place in Galloway Township, Atlantic County, New Jersey called Leeds Point, and a tradition that the Leeds family was in general up to no good -- although how much of that was due to their connection to the Jersey Devil legend is uncertain.  Certainly, they were a superstitious lot.  One of the Leedses, amusingly named Titan, was a writer of almanacs in the early eighteenth century, and included a lot of astrological mumbo-jumbo along with the usual folksy wisdom.  Apparently this attracted the attention of none other than Benjamin Franklin, who saw Titan Leeds's books as competition for his Poor Richard's Almanack.  So Franklin put an entry in his almanac saying that he'd used astrology to predict Leeds's death in 1733.  When Leeds published an objection, Franklin (who was not a man you wanted to engage in a battle of wits) responded how remarkable it was that he'd gotten a reply from a ghost.  He continued referring to Leeds as a disembodied spirit of the dead until the poor man finally became one in actuality in 1738.

In any case, a lot of the Jersey Devil legend probably stems from how generally accepted superstition was back then (and still is, to look at the polls).  But here's where we get to the other sticking point, and why the number of eyewitness accounts doesn't lead me toward belief -- but actually the opposite.

Of all the thousands of sightings of the Jersey Devil, there has never been one piece of hard evidence of its existence.  Not even a decent photograph (although these days, with digital image software and AI, photographs aren't really admissible as evidence anyhow).  Here we have something that has been seen countless times -- and has left behind not a single trace.

For me, if something has been seen on multiple occasions, a lack of hard evidence becomes a persuasive argument against its existence.  If you've got a single sighting of, I dunno, the Evil BunnyMan of Nebraska or something, and there's no evidence, that's one thing.  Maybe the one time he was seen, BunnyMan hippety-hopped in such a way as to not leave any footprints.

But thousands of accounts, and nothing?

That's mighty peculiar.

So in answer to my reader, no -- I don't find the number of sightings, by itself, convincing.  I'm going to require something other than an eyewitness account.  As always, though, I am open to having my mind changed.  But, as eminent astrophysicist Neil deGrasse Tyson put it, "As a scientist, I need more than 'you saw it.'"

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The demons of Dudleytown

There's a general rule that if you have to lie about the facts to support a claim, you might want to reconsider your stance.

That was my general response to a link sent to me by a loyal reader of Skeptophilia about the "Dudleytown Curse."  Dudleytown is an abandoned village in Litchfield County, Connecticut, which is a favorite of the "haunted places" crowd.  Here's the basic idea of the legend:

The area was first settled by people of European descent in the 1740s and 1750s, by Thomas Griffis and a cluster of either brothers or cousins (the records are uncertain on that count), Barzillai, Abiel, Martin, Obijah, and Gideon Dudley.  Presumably because of the strength-in-numbers principle, it was named Dudleytown even though Griffis had gotten there first.  Allegedly, the ancestor of the Dudleys was  disgraced English royal administrator Edmund Dudley, who had lost his head on Tower Hill in 1510, and the story goes that Edmund's kin had fled England because of some sort of curse the family was under.  (Which in itself is an odd claim.  The family certainly didn't suffer greatly from Edmund's disgrace; they remained wealthy and influential, and his grandson, Robert Dudley, First Earl of Leicester, was a great favorite of Queen Elizabeth I.)

Anyhow, the curse supposedly followed the Dudleys across the Atlantic, as curses are wont to do.  Abiel Dudley went mad and had to be confined to his home.  Gershon Hollister, who lived next door to Abiel in a home owned by William Tanner, was murdered.  Tanner himself also went insane, babbling about wild animals and demons attacking him.  After Abiel Dudley's death, his home belonged to Nathaniel Carter, who died along with his wife and three children when the settlement was attacked by Natives.  Heman Swift, a general in the American Revolution and a native of Dudleytown, lost his wife to a lightning strike and shortly afterward lost his mind as well.  The wife of Horace Greeley, unsuccessful candidate for president in 1872, was also a Dudleytown native -- when visiting her home town, she hanged herself for no apparent reason.

People started fleeing the area because of its bad reputation.  Soon there was hardly anyone left.  The place is so haunted even animals don't go there; visitors in the 1960s report not hearing so much as a single bird.  It is currently privately owned by a mysterious group called the Dark Entry Forest Association, and they're determined to stop anyone else from dying or going mad (or, if you'd like a more sinister version, to stop anyone from finding out what's really going on there).  They monitor the property and prosecute any trespassers to the fullest extent of the law.

The remnants of a railway station platform near Dudleytown

So, pretty creepy, right?

There's just one problem.

Almost none of the above is true.

So let's do this again, shall we?

There's no proof that the Connecticut Dudleys are descended from King Henry VIII's unfortunate counselor Edmund.  Abiel Dudley didn't go mad; he lived in relatively good health into his nineties.  Gershon Hollister wasn't murdered -- the records of the time show that he was participating in a barn raising and accidentally fell from the rafters, breaking his neck.  The Carter family massacre didn't happen in Dudleytown -- it happened along the Delaware River, and in fact all three of Nathaniel Carter's children survived (one became a State Supreme Court Justice).  Heman Swift did live in the nearby village of Cornwall, but didn't go mad and lived to be eighty-one.  Horace Greeley's wife, on the other hand, seems to have had nothing whatsoever to do with Dudleytown, and didn't commit suicide.  She died in New York City of lung disease.

Oh, and as far as the birds; the lack of birds in the 1960s had to do with the fact that all the farms in the area had been sprayed with DDT.  Northwestern Connecticut was hardly unusual in that regard (Cf. Rachel Carson's Silent Spring.)  And like many areas, now that DDT is no longer used, the wildlife has rebounded nicely, and the area around Dudleytown is as birdy as anywhere else in the Berkshires.

As far as why people left the area, it seems to have had more to do with the fact that the rocky soil was terrible for farming.  Records show that most of the people who left Dudleytown relocated to the Midwest, where there was lots of good farmland for sale.  The Dark Entry Forest Association is hardly mysterious -- it was founded in 1924 by a New York City physician, Walter Clarke, who had bought the property and hoped to reforest it (it had been largely clearcut in a forlorn hope of turning it into farms), and use it both for recreation and for logging.  For a while it was successful -- there were skiing and hiking trails, and organized canoeing and rafting trips on the nearby Housatonic River.

But then in the 1970s a couple named Ed and Lorraine Warren (the ones who did the famous investigation of the Amityville Horror) created a documentary supposedly chronicling all the supernatural terrors of the Dudleytown region, inventing out of whole cloth the various lies and half-truths I've mentioned above.  They said it was "demonically possessed" and "controlled by something terrifying."  It attracted huge amounts of attention from ghost hunters and tourists who wanted to see such an evil region...

... and the visitors proceeded to trash the place.

The residents of the nearby town of Cornwall finally got fed up, and petitioned the Dark Entry Forest Association to do something.  So they did; in 2011, they closed the property to visitors permanently.  These days, even if you ask permission to go, the answer will be no.

Harriet Clark, former president of the Cornwall Historical Society, wrote in her book The True Facts of Dudleytown, "Today’s owners and taxpayers of Dudleytown are professional people who live there for privacy and seclusion.  They do not welcome tourists or those seeking tales of chilling or wild experiences.  Please do not come.  There are no ghosts, no spirits and no curse."

Which, of course, dissuaded absolutely no one.  People are still trying to get in and still getting arrested and fined for trespassing.  And even if there's a persuasive argument that the demons of Dudleytown are entirely of human manufacture, the dismissive words of Clark and others are looked upon as more indication that there is something sinister there that they're trying to cover up.

You can't win with these people.

But to go back to my original point -- you'd think if there was anything to this kind of claim, they wouldn't find the need to make shit up in order to support it.  As always, I'm open to being convinced about claims of all sorts -- but don't expect me to accept what you're saying if the only thing going for it is a boatload of fabrications.

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The problem with Aristotle's wheel

There's an apparent mathematical paradox, of very long standing, that illustrates a fundamental problem with a lot of modern discourse.

It's called the Aristotle's wheel paradox, and it goes something like this.

Imagine you have a circular wheel, and attached firmly to it is a concentric smaller wheel.  You set the larger wheel on a flat surface, and allow it to roll one complete rotation without slipping.

The trouble comes in when you try to figure out how far each wheel has moved.  Let's call the radius of the outside wheel R.  So by the time it's turned once, it's traveled as far as its circumference, which we all know from high school geometry is a distance of 2πR.  So that should be the length of the horizontal blue dashed line in the above diagram.

But here's the snag; the same applies to the smaller wheel.  Let's say its (smaller) radius is r.  So by the same logic, after it's made one complete rotation, it's traveled a distance of 2πr, which is less than 2πR (because r < R).  That's the red dashed line in the diagram.

But... the two lines are obviously the same length!

While it's uncertain if Aristotle ever did puzzle over this seeming conundrum, it's definitely been known since antiquity.  The first written exposition of it was by Hero of Alexandria, who described it in his book Mechanics in the first century B.C.E.

The solution has to do with the fact that the way the question is posed is misleading.  Most people, reading the description of the paradox and (especially) looking at the diagram, would accept unquestioningly that this is a correct framing of the problem.  But in fact, by stating it that way I was engaging in deliberate sleight-of-hand -- giving you information that seems correct on first glance, but is disingenuous at best and an outright lie at worst.

[Nota bene: I'm not implying here that Aristotle and the other mathematicians who worked on it were lying; they seemed genuinely puzzled by it.  What I'm saying is that I was misleading you, because I know the answer and misdirected you anyhow, with complete malice aforethought.]

The truth is, the two circles haven't moved by the same amount, even if that's what the diagram plausibly leads you to believe.  In fact, the straight dashed lines in the diagram aren't the paths taken by a point on the circumference of either circle.  (Those lines' lengths are equal to the distance covered not by a point on the edge, but by the center of the wheel.)  If you trace the paths of actual points on the rims of the two wheels, here's what you get:

[Both this and the above diagram are licensed under the Creative Commons Merjet, AristotleWheel6, CC BY-SA 4.0]

Without even measuring it, you can see that a point on the outer wheel (the blue dashed curve) travels considerably farther than one on the inner wheel (the red dashed curve) -- and both, in fact, cover more distance than that traveled by the wheel's center (the green dashed line).

Just as you'd expect.

What strikes me about the Aristotle's wheel (non-)paradox is that this kind of thing underlies a great many of the problems with our current political situation.  How many of the hot-button topics in the news lately have come about because of a deliberate, disingenuous attempt to reframe the question in such a way that it ignores important facts or completely mischaracterizes the situation?  Examples include the Florida State Education Department's new standards for history requiring teachers to include information about how slaves benefitted from slavery, Richard Dawkins's statement to commentator Piers Morgan that biological sex is binary "and that's all there is to it," and Jason Aldean's defense of his controversial song and video "Try That in a Small Town," stating that "There is not a single lyric in the song that references race or points to it."

All three could be looked at with a shrug of the shoulders and a comment on the order of, "Okay, I guess that's true."  But in each case, that is to miss the deeper and far more critical truths those statements are deliberately overlooking.

This kind of thing is dangerous because it's so damned attractive.  We're taught to take things as given, especially when (1) they come from a trusted or respected source, and (2) they seem right.  This latter leads us onto the thin ice of confirmation bias, where we accept what someone says because it confirms what we already thought was true.  Here, though, the bias is more insidious, because the case is deliberately being presented to us so as to say nothing specifically false, and yet still to lead us to an erroneous conclusion.

So whenever you're reading the news, remember Aristotle's wheel -- and always keep in mind that what you're seeing may not be the whole story.  Like the two diagrams of the wheel's motion, sometimes all it takes is looking at things from another angle to realize you've been led down the garden path.

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