All set

How long is the coastline of Britain?

Answer: as long as you want it to be.

This is not some kind of abstruse joke, and if it sounds like it, blame the mathematicians.  This is what's known as the coastline paradox, which is not so much a paradox as it is the property of anything that is a fractal.  Fractals are patterns that never "smooth out" when you zoom in on them; no matter how small a piece you magnify, it still has the same amount of bends and turns as the larger bit did.

And coastlines are like that.  Consider measuring the coastline of Britain by placing dots on the coast one hundred kilometers apart -- in other words, using a straight ruler one hundred kilometers long.  If you do this, you find that the coastline is around 2,800 kilometers long.

[Image licensed under the Creative Commons Britain-fractal-coastline-100km , CC BY-SA 3.0]

But if your ruler is only fifty kilometers long, you get about 3,400 kilometers -- not an insignificant difference.

[Image licensed under the Creative Commons Britain-fractal-coastline-50km, CC BY-SA 3.0]

The smaller your ruler, the longer your measurement of the coastline.  At some point, you're measuring the twists and turns around every tiny irregularity along the coast, but do you even stop there?  Should you curve around every individual pebble and grain of sand?

At some point, the practical aspects get a little ridiculous.  The movement of the ocean makes the exact position of the coastline vague anyhow.  But with a true fractal, we get into one of the weirdest notions there is: infinity.  True fractals, such as the ones investigated by Benoit B. Mandelbrot, have an infinite length, because no matter how deeply you plunge into them, they have still finer structure.

Oh, by the way: do you know what the B. in "Benoit B. Mandelbrot" stands for?  It stands for "Benoit B. Mandelbrot."

Thanks, you're a great audience.  I'll be here all week.

The idea of infinity has been a thorn in the side of mathematicians for as long as anyone's considered the question, to the point that a lot of them threw their hands in the air and said, "the infinite is the realm of God," and left it at that.  Just trying to wrap your head around what it means is daunting:

Teacher: Is there a largest number?
Student: Yes. It's 10,732,210.
Teacher: What about 10, 732,211?
Student: Well, I was close.

It wasn't until German mathematician Georg Cantor took a crack at refining what infinity means -- and along the way, created set theory -- that we began to see how peculiar it really is.  (Despite Cantor's genius, and the careful way he went about his proofs, a lot of mathematicians of his time dismissed his work as ridiculous.  Leopold Kronecker called Cantor not only "a scientific charlatan" and a "renegade," but "a corrupter of youth"!)

Cantor started by defining what we mean by cardinality -- the number of members of a set.  This is easy enough to figure out when it's a finite set, but what about an infinite one?  Cantor said two sets have the same cardinality if you can find a way to put their members into a one-to-one correspondence in a well-ordered fashion without leaving any out, and that this works for infinite sets as well as finite ones.  For example, Cantor showed that the number of natural numbers and the number of even numbers is the same (even though it seems like there should be twice as many natural numbers!) because you can put them into a one-to-one correspondence:

1 <-> 2
2 <-> 4
3 <-> 6
4 <-> 8
etc.

Weird as it sounds, the number of fractions (rational numbers) has exactly the same cardinality as well -- there are the same number of possible fractions as there are natural numbers.  Cantor proved this as well, using an argument called Cantor's snake:

Because you can match each of them to the natural numbers, starting in the upper left and proceeding along the blue lines, and none will be left out along the way, the two sets have exactly the same cardinality.

It was when Cantor got to the real numbers that the problems started.  The real numbers are the set of all possible decimals (including ones like π and e that never repeat and never terminate).  Let's say you thought you had a list (infinitely long, of course) of all the possible decimals, and since you believe it's a complete list, you claimed that you could match it one-to-one with the natural numbers.  Here's the beginning of your list:

7.0000000000...
0.1010101010....
3.1415926535...
1.4142135623...
2.7182818284...

Cantor used what is called the "diagonal argument" to show that the list will always be missing members -- and therefore the set of real numbers is not countable.  His proof is clever and subtle.  Take the first digit of the first number in the list, and add one.  Do the same for the second digit of the second number, the third digit of the third number, and so on.  (The first five digits of the new number from the list above would be 8.2553...)  The number you've created can't be anywhere on the list, because it differs from every single number on the list by at least one digit.

So there are at least two kinds of infinity; countable infinities like the number of natural numbers and number of rational numbers, and uncountable infinities like the number of real numbers.  Cantor used the symbol aleph null -- ℵ₀ -- to represent a countable infinity, and the symbol c (for continuum) to represent an uncountable infinity.

Then there's the question of whether there are any types of infinity larger than ℵ₀ but smaller than c.  The claim that the answer is "no" is called the continuum hypothesis, and proving (or disproving) it is one of the biggest unsolved problems in mathematics.  In fact, it's thought by many to be an example of an unprovable but true statement, one of those hobgoblins predicted by Kurt Gödel's Incompleteness Theorem back in 1931, which rigorously showed that a consistent mathematical system could never be complete -- there will always be true mathematical statements that cannot be proven from within the system.

So that's probably enough mind-blowing mathematics for one day.  I find it all fascinating, even though I don't have anywhere near the IQ necessary to understand it at any depth.  My brain kind of crapped out somewhere around Calculus 3, thus dooming my prospects of a career as a physicist.  But it's fun to dabble my toes in it.

Preferably somewhere along the coastline of Cornwall.  However long it actually turns out to be.

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

The vanished legion

In the Doctor Who episode "The Eaters of Light," the Twelfth Doctor and his companions, Bill and Nardole, go back to second-century Scotland to settle a dispute they're having over what actually happened to the Roman Ninth Legion (the Legio IX Hispania), which was deployed in the British Isles during the first century but rather suddenly disappears from the records in around 120 C.E.

Being Doctor Who, of course there are aliens involved -- a mysterious and powerful creature that feeds off of light, and which the native Picts knew how to control, but the attacks by the Romans (specifically the Ninth Legion) disrupted their ability to manage the portal behind which it was trapped, and it was in danger of getting loose and wreaking havoc.  In the end, the Doctor convinces the Picts and the Romans to set aside their hostilities and work together to deal with the bigger danger, and the Pictish leader, along with some of her warriors, and the entire legion choose to sacrifice their lives to contain the creature behind the door (which lies amongst a very atmospheric ring of standing stones out on the windswept heather), thus saving the world and also explaining why the Ninth Legion suddenly vanished.

The disappearance of the Legio IX Hispania is one of the more curious historical mysteries.  An early hypothesis, promoted by German historian Christian Theodor Mommsen, was that the Ninth had been wiped out in a battle with the Picts in 108 C.E., but there are a couple of problems in this claim.  First, the Romans were meticulous record-keepers, and didn't shy away from writing down what happened even when they'd lost.  If an entire legion had been destroyed in battle, it's curious that no one ever mentioned it.  Second, there's some evidence that at least a few members of the Ninth survived -- there are inscriptions that may be from them in the ruins of the Roman base at Nijmegen (now in the Netherlands) dating from the 120s.  It's possible, of course, that the artifacts -- including a silver-and-bronze military medal with "LEG HISP IX" engraved on the back -- were brought there by someone else.  After all, inscriptions about the Ninth Legion showing up at a particular time and place doesn't mean the Ninth Legion was there at the time.

Despite this argument, some have suggested that there were members of the Ninth at Nijmegen -- perhaps only a handful of survivors of a rout in Scotland.  Other historians go even further, believing the entire legion survived and was merely redeployed elsewhere, ultimately meeting their end in the Bar Kokhba Revolt (132-135 C.E.) or even as late as Marcus Aurelius's war against the Parthians (161-166 C.E.).

But again, we run up against the fact that although there are records of both of those battles, the Ninth Legion is never mentioned.  If they fought -- and possibly were destroyed -- in either of those conflicts, why did no one ever say so?

Most historians still subscribe to the idea that the Ninth was wiped out in Scotland, despite it leaving considerable questions about how it happened and why no one documented it.  British archaeologist Miles Russell, in his book The Celtic Kings of Roman Britain, says, "by far the most plausible answer to the question 'what happened to the Ninth' is that they fought and died in Britain, disappearing in the late 110s or early 120s when the province was in disarray."

Of course, a historical mystery like this leaves fertile ground for fiction writers to invent their own solutions, and the episode of Doctor Who is far from the only fanciful solution that has been proposed.  A good many of them involve time slips and transportation to an alternate reality, but none is as out there as the fate proposed in a Doc Savage novel wherein the Ninth is transported through an interdimensional gateway and ultimately end up in the African Congo, where their descendants survive until the 1930s.

And people say the plots of Doctor Who are ridiculous.

In any case, from a factual perspective what we're left with is a great big question mark.  An entire legion of Roman soldiers suddenly stops showing up in the records, and no one is really sure why.  The frustrating thing is that given the unlikeliness of finding any documents from that time that we don't already know about, it's doubtful we'll ever know for certain -- a highly unsatisfactory answer to our natural human curiosity.

Me, I'm voting for the light-eating alien having something to do with it.

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

The drowned wall

Humans have been modifying their own environment for a very long time.

Our capacity for building stuff is pretty extraordinary.  Birds build nests, some mammals and reptiles burrow, spiders spin webs -- but compared to what we do, it's all pretty rudimentary stuff.  No other species on Earth looks around, takes materials from nature, and says, "Hey, if I cut this to pieces and move it around, I could do something new and useful with it" to the extent that we do.

I was thinking about all this when I read a paper this week about an archaeological discovery in the Baltic Sea off the coast of Germany.  As I discussed in more depth in a post a couple of days ago, ten thousand odd years ago the Earth (especially the Northern Hemisphere) was coming out of a catastrophic and sudden cooling episode called the Younger Dryas event, during which the sea levels were considerably lower (because so much seawater was locked up as polar and glacial ice).  In fact, much of what are now the Baltic and North Seas were dry(ish) land; you could walk from England to France across a broad, grassy valley that is now at the bottom of the English Channel.

The result is that a great many of the artifacts produced during that time are now underwater, and finding them can be a matter of luck.  That was certainly the case in this instance, where scientists demonstrating a multibeam sonar system for some students in a research vessel ten kilometers offshore in the Bay of Mecklenburg saw something extraordinary -- the remains of a 971-meter-long rock wall archaeologists say "may be the oldest known human-made megastructure in Europe."

Nicknamed the "Blinkerwall," it is made of rows of a total of fourteen hundred smaller stones connecting three hundred boulders that were pretty clearly too large to move.  What the wall's builders apparently did was built a barrier out of the smaller stones connecting the large ones into a zigzagged line.

Part of the Blinkerwall [Image credit: Philipp Hoy]

The purpose of the wall, of course, can only be guessed at, but the researchers suspect it was used for hunting.  "When you chase animals [such as reindeer], they follow these structures, they don’t attempt to jump over them," said Jacob Geersen, of the Leibniz Institute for Baltic Sea Research in Warnemünde, a German port town on the Baltic coast.  "The idea would be to create an artificial bottleneck with a second wall or with the lake shore."

Once the animals were funneled into the narrow strip of land between the two barriers, they would be more vulnerable to spear-wielding hunters lying in wait.

The next step in the research, Geersen said, is to send divers down to the base of the wall, now submerged under twenty-one meters of water, to try and bolster this explanation by finding spearheads or other hunting implements.

You have to wonder what else might be down there.  Our intrepid ancestors have been finding new ways to make stuff for tens of thousands of years.  Wherever that impulse came from, there's no denying that it's served us well.  It always makes me wonder what traces will be left of our culture in ten thousand, or a hundred thousand, or a million years -- and what deductions our descendants will make about our habits, practices, and lifestyles.

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

Music and the mind

In September, I started taking piano lessons.

I've played the piano off and on for years (more off than on, I'm afraid), but was entirely self-taught.  To say my formal music background is thin is an understatement; I had a lousy experience with elementary school band, said "to hell with it," and that was the end of my music education in public schools.  However, I was (and am) deeply in love with music, so I picked up the flute at age sixteen, and taught myself how to play it.  I took four years of lessons with a wonderful flutist and teacher named Margaret Vitus when I was in my twenties, but until last fall those accounted for the sum total of my instruction in music of any sort.

My experience as a student -- both with Margaret forty-odd years ago, and with J. P. (my piano teacher) now -- has been interesting from a number of standpoints.  In both cases I profited greatly by having someone tell me what bad habits are holding me back, and (more importantly) what I can do to remediate them.  But my spotty background has resulted in some unique challenges.  On the upside, I have an extraordinary ear and memory for melodies and rhythms, to the point that my wife calls it my "superpower."  I once heard a piece of Serbian music in a Balkan dance class when I was in my twenties, and heard it again thirty years later, and immediately knew it was the same tune even though I hadn't heard it or played it during that time.  

The downside, though, is that my lack of formal training means there are great gaping holes in my knowledge.  I'm currently working on a charming and whimsical piece by Claude Debussy, "Dr. Gradus ad Parnassum," which like much of Debussy's music twists around our sense of keys and harmonies. 

"How do you get to Carnegie Hall?  Every day, practice, practice, practice."

So J. P. -- for whom music is about as natural as breathing -- will look at some passage, and say something that sounds like, "Oh, that's a B-flat Minor Seven Demented chord."  Once I analyze what he told me using paper, pencil, and a slide rule, after three or four hours of study I can usually say, "Oh, okay, I guess I get it," but it definitely isn't anything close to intuitively obvious.  Like, ever.  So I'm still at the point of having to read each note slowly and painstakingly, and although I think the piece is lovely (well, when someone else plays it), I don't have any real comprehension of its structure.

If you're curious, here's how it's supposed to sound:

Fortunately, J. P. is an extraordinary teacher and gets my struggles, and is working to help me fill in the gaps in my knowledge.  It's slow going, but I guess that's no different from anyone learning a musical instrument.

The reason this comes up today is a study by a team from the University of L'Aquila and the University of Teramo that discovered an interesting correlation; people who have studied music seriously have better working memory -- the ability to retrieve and load information into their "attentional stream."  Stronger and faster working memory is positively associated with a greater capacity for divergent thinking, and thus the facilitation of creativity.

The authors write:

Musical practices have recently attracted the attention of research focusing on their creative properties and the creative potential of musicians.  Indeed, a typical cliché of musicians is that they are considered predominantly artistic individuals, meaning that they are creative and original.  Practicing music is certainly an intense and multisensory experience that requires the acquisition and maintenance of a range of cognitive and motor skills throughout a musician’s life.  Indeed, music practice increases a wide range of cognitive abilities, such as visuospatial reasoning, processing speed, and [working memory], from the early stages of life.  For this reason, musicians are considered an excellent human model for the study of behavioral, cognitive, and brain effects in the acquisition, practice, maintenance, and integration of sensory, cognitive, and motor skills...

[E]xperience in the music field enhances [divergent thinking] in terms of fluency, flexibility, and originality.  Strengthening the associative modes of processing, which facilitate the retrieval of information from long-term memory, and improving the working memory competences, which facilitate the online recombination of information, might explain the relationship between musical practice and [divergent thinking].

All of which bolsters something I've been saying for years; we need to be actively supporting art and music in schools.  Sadly, school boards much more often have the opposite mentality -- the esteemed "STEM" subjects (science, technology, engineering, and math) are emphasized and thus funded, and the arts (sometimes derisively called "extras") are on the chopping block when money gets tight.

Which, of course, is all the time.  But wouldn't it be nice if the educational powers-that-be actually read the research, and acknowledged that music and art are every bit as important as STEM?

In any case, it's good to know that my struggling to learn piano might provide some other benefits besides making Debussy turn over in his grave.  Hell, at age 63, I'm thrilled to have any boosts to my cognition I can get.  And even if I'll never be able to play "Dr. Gradus ad Parnassum" like Lang Lang does, maybe the skills I learn from my piano lessons will spill over into other creative realms.  

After all, as Maya Angelou said, "You can't use up creativity.  The more you use, the more you have."

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

Cutting off the circulation

Around 12,900 years ago, the world was warming up after the last major ice age.  Climatologists call it the "Late Glacial Interstadial," a natural warm-up due to the combined effects of the slow, gradual alterations in the Earth's orbit and precession cycle.  But then...

... something happened, and within only a few decades, the Northern Hemisphere -- especially what are now North America and western Europe -- were plunged back into the deep freeze.

The episode is called the "Younger Dryas" event, because the way scientists figured out it had happened was finding traces of pollen in ice cores from a plant, Dryas octopetala, which is only found in cold, dry, windswept habitats.  Areas that had been progressing toward boreal forest, or even temperate hardwood forest, suddenly reverted to tundra.

[Image licensed under the Creative Commons Steinsplitter, Weiße Silberwurz (Dryas octopetala) 2, CC BY-SA 3.0]

There are a number of curious features of the Younger Dryas event.  First, its speed -- climate shifts ordinarily take place on the scale of centuries or millennia, not decades.  Second, the fact that its effects were huge (the average temperature in Greenland dropped by something on the order of 7 C), but were limited in range; in fact, the Southern Hemisphere appears to have continued warming.  And third, after the initial plunge, the system righted itself over the next twelve hundred years -- by 11,700 years ago, the Northern Hemisphere was back on its warming track, and caught up with the rest of the world.

What could have caused such a strange, sudden, and catastrophic event is still a matter of some debate, but the leading candidate is that something halted the Atlantic Meridional Overturning Circulation, sometimes nicknamed "the Atlantic conveyor."  This is the massive ocean current of which the Gulf Stream is only a small part, and which is powered by warm water evaporating and cooling as it moves north, finally becoming cold and salty (and thus dense) enough to sink, somewhere south of Iceland.  This draws more warm water up from near the equator.  But as the Earth was warming during the Interstadial, the ice in the north was melting, eventually making the water in the North Atlantic too fresh to sink, and thus halting the entire circulation.  Some researchers think the process was sent into overdrive by the collapse of an ice dam holding back a massive freshwater lake called Lake Agassiz (encompassing what are now all five Great Lakes and the surrounding region), causing it to drain down the Saint Lawrence Seaway and into the North Atlantic, stopping the AMOC dead in its tracks.  (This point is still being debated.)

What's certain is that the AMOC stopped, suddenly, and took over a thousand years to get started again, plunging the Northern Hemisphere back into an ice age.

Why does this come up today?

Because a new study out of the University of Utrecht has found that our out-of-control fossil fuel use, and consequent boosting of the global temperature and melting of polar ice, is hurtling the AMOC toward the same situation it faced 12,900 years ago.  One of the consequences of anthropogenic global warming might be sending eastern Canada, the northeastern United States, and western Europe into the freezer.

One of the most alarming findings of the study is that climatologists have been systematically overestimating the stability of the AMOC.  It's an easy mistake to make; the current is absolutely enormous, amounting to a hundred million cubic meters of water per second, which is nearly a hundred times the combined flow of all the rivers in the world.  The idea of anything perturbing something that massive is a little hard to imagine.

But that's what happened during the Younger Dryas, and it happened fast.  The new study suggests that if the AMOC does collapse, within twenty years the temperature of Great Britain, Scandinavia, and the rest of northern Europe could see winter temperatures ten to thirty degrees Celsius colder than they are now, which would completely alter the ecosystems of the region (including agriculture).  It would also change precipitation patterns drastically, and in ways we are currently unable to predict.

If you're not already alarmed enough, here's how climatologist Stefan Rahmstorf put it, writing for the site RealClimate:

Given the impacts, the risk of an AMOC collapse is something to be avoided at all cost.  As I’ve said before: the issue is not whether we’re sure this is going to happen.  The issue is that we need to rule this out at 99.9 % probability.  Once we have a definite warning signal it will be too late to do anything about it, given the inertia in the system...  We will continue to ignore this risk at our peril.

The problem is that last bit -- we don't have a very good history of addressing problems ahead of time.  We're much more prone to waiting until things are really awful, at which point they're harder (if not impossible) to fix.  We've let the corporate interests and short-term expediency drive policy for too long; it's increasingly looking like we're close to hitting the now-or-never point.

We need to start electing candidates who take this whole thing seriously.  It is the most important issue of our time.  I try not to be a one-issue voter, but if someone's answer to "What do you intend to do to remediate climate change" is "Nothing" -- or, worse, "Climate change is't real" -- they've lost my vote.

And they should lose yours, too.  For the good of the planet.

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

The Nephilim visit Miami

If you needed further evidence that whoever is controlling the simulation we're all trapped in has gotten drunk and/or stoned, and now they're just fucking with us, today we have: giant shadow aliens visiting a mall in Miami.

The event in question took place over a month ago, so I have to apologize for being a half a measure behind the rest of the orchestra, here.  On the other hand, since then the story has taken on a life of its own, and has grown way beyond the original claim, which was bizarre enough.  Apparently on January 1, some rowdy teens started a large brawl at Bayside Marketplace, so the police were called in.  This isn't anything unusual for Miami, so you'd think it'd have passed for business as usual, but then someone -- no one seems quite sure who -- got on social media and claimed that the police weren't there to handle some teenage brawlers, but to deal with "eight to ten foot tall shadow aliens."

This would be eye-opening even by south Florida standards.  Oddly enough, despite the fact that everybody and his dog now has a phone capable of taking high-quality photographs, no one seems to have snapped a pic of these aliens.  So of course, very quickly people realized that it was just a stupid rumor, there were no aliens, and everyone calmed down and went home, chuckling about how silly they'd all been.

Ha-ha, just kidding!  Of course that's not what happened.  What happened is that the rumor exploded that the police had prevented people from photographing the aliens, even resorting to confiscating and/or destroying people's phones.  Or that the aliens were "interdimensional space beings" who could not be photographed.  Possibly both.  The Miami Police Department issued a statement that it had "just been an altercation between about fifty juveniles," adding, "There were no aliens, UFOs, or ETs.  No airports were closed, and there were no power outages," and followed it up with the facepalm emoji.

Which accomplished exactly nothing.  Because why would the police be denying it if it weren't true?

Inescapable logic, that.

After that, there were only two things left to figure out; why were the police suppressing information about the aliens?  And who exactly were these tall, shadowy beings that mysteriously could not be photographed? 

I think we can all agree that given the evidence, there's only one possible conclusion: we are seeing the return of the Nephilim, as hath been foretold in the Bible, and the police are under orders from the Illuminati to make sure that no one finds out.

You may think I'm making this up, but this claim went off on social media like some hundred-megaton stupidity bomb.  "Let's talk about these creatures that supposedly are UFOs," said one TikToker.  "If you're a Christian you should already know.  These UFOs are fallen angels.  Remember, the devil's main goal is to make sure you don't believe he is real, and that Jesus is also not real.  This is just a warning that time is running out, and you better get close to Jesus."  One guy calling himself "the Apostle Preston," who on the video appeared to be tuning into God via an earpiece, said, "I hear you, Lord.  Tell the people there will be sightings of giants.  Giants that have been in hiding.  There will be sightings of them.  He said, 'But tell my people also not to fear.  Because what's going to happen is that when these giants are sighted, there will be great fear among men, and many of you will forget who your God is.'  This is why you need to be in a place of preparation."  A TikToker called -- I swear I'm not making this up -- "endtimelady" did a long video about how the aliens in Miami are actually Nephilim but they're also demons, and they're going to come out and terrorize us.  Oh, and we should be careful to control our thoughts, because they're telepathic.  "This is going to get more and more common," she said.  "Because we're in the End Times."

I guess if your handle is "endtimelady" you gotta bring that up somehow.

My favorite, though, is the guy who kept saying, "Why is nobody talking about this?" when, in fact, every lunatic on social media seems to be doing nothing but talking about this.

It's been a month and a half since the incident took place, and it's showing no signs of slowing down.  You'd think that questions like, "Where have the giant aliens been hiding since January 1?" and "If the powers-that-be are so desperate to prevent anyone from finding out about this, how are there videos and posts by the tens of thousands all over the internet, and no one's doing anything about it?" would come to people's minds.  Not to mention, "Why am I paying any attention to the crazed ramblings of people who obviously have a pound and a half of Malt-O-Meal where the rest of us have a brain?"

But this is social media, where everything's made up, and logic and evidence don't matter.

Anyhow.  You might want to keep an eye out for giant shadowy aliens.  Seems like they'd be hard to miss, but you never know.  I'm going to place my three dogs on High Red Alert Mode, usually reserved for Extreme Danger Situations like the arrival of the UPS guy.  So we'll all be watching for new developments.  If "endtimelady" is right and these are the End Times, I'd actually be thrilled, because I live in rural upstate New York and it's kind of boring around here.  The arrival of the Scarlet Whore of Babylon and the Four Apocalyptic Horsepersons and the Beast With Seven Heads And Ten Crowns would be a welcome relief from the monotony.

On the other hand, if my initial take is correct and none of it is real and it is the result of superintelligent beings messing around with the computer simulation we're in, y'all just need to stop.  In the last few years the weirdness dial has already been turned up to eleven, and I think that's about all we can cope with, down here.  So y'all just sober up and simmer down, okay?

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

Thin places

My first trip overseas, back in 1995, was an ambitious one; I did a month-long solo hike across England, starting on the shore of the Irish Sea in Blackpool and ending on a hill overlooking the North Sea in Whitby.  I decided to have a theme for the trip -- a practice I have continued to this day -- and the theme I chose was monasteries.

A great many of the abbeys in England were destroyed during the "Dissolution of the Monasteries," when King Henry VIII decided the church was getting way too rich and powerful and decided to see what he could do to remedy that.  Between 1536 and 1541, over eight hundred monasteries, abbeys, and convents were closed and their property sold off, the abbots, priests, and nuns turned out or arrested outright, the majestic buildings left to sink slowly into ruin.

Along the path I took, which largely coincides with the North York Moors Trail, there were a number of these relics, and I made a point of seeing as many as I could.  They were impressive, beautiful, tragic places, monuments not only to spirituality but to greed (on both sides of the struggle).

Unsurprisingly, the spiritual side of it didn't have a great impact on me, except for my sympathy for the religious men and women who had dedicated themselves to the contemplative life and then had those lives turned upside down by the conflict.  But it all seemed relegated in the distant past, unable to touch my modern experience except as a historical footnote.

Until I got to Rievaulx Abbey, near the town of Helmsley.

My hike into Rievaulx was on a gorgeous day -- one of the few I had during a four-week period that was cold and rainy even by English standards.  That day the weather was mild and sunny, with only a few white clouds in an azure sky. I crested a low line of hills, and looked down into the little valley in which the ruins of the abbey sit, and was dumbstruck.

It was not solely because of the spot's beauty, although beautiful it certainly is.  The place gave me chills, as if I was looking at something that wasn't quite of this world -- a reaction I had never experienced before and haven't experienced since.

[Image licensed under the Creative Commons WyrdLight.com, RievaulxAbbey-wyrdlight-24588, CC BY-SA 3.0]

Now, twenty-five years ago, I was every bit as much of a skeptic as I am now, but I couldn't shake the feeling the entire time I wandered around the abbey grounds.  I dropped my pack and shucked my shoes by the side of a little tumbling river that runs through the valley, cooling my sore feet, and kept thinking about the men and women who had lived here -- and whose presence I could still, inexplicably, feel around me.

During my visit, I struck up a conversation with a friendly middle-aged couple, who ended up inviting me to have mid-afternoon tea with them.  I mentioned my odd sensations to them, and the woman immediately smiled.  "Oh, yes," she said.  "Lots of people feel that way about Rievaulx.  One gets the impression not that the place is sacred because it's the site of an abbey, but that the abbey was built there because the place was already sacred."

I have never been able to explain what I felt during that visit, other than my rational side's certainty that the beauty of the day and the history of the place simply got the better of me.  But I keep coming back to the fact that I never had those sensations in any of the other religious sites I saw on that trip -- which included gorgeous, history-laden places such as York Cathedral, Fountains Abbey, Kirkham Priory, and Grey Friars Tower.  There was something different about Rievaulx, but what that something is, I've never put my finger on.

The Scots call spots like Rievaulx "thin places."  We walk side-by-side with the spirit world, the legends go, separated by an invisible veil, but in some places the veil is thin and we get a glimpse, or sometimes just a feeling, that there's something more there than meets the eye.  Places like that aren't haunted in the conventional sense, but true believers will tell you that you can't go there and come away unscathed.

I won't say that my visit to Rievaulx convinced me of some kind of ineffable otherworld; after all here I am, over two decades later, still talking about rationalism and skepticism and for the most part casting a wry eye at claims of the paranormal.  But something happened to me in that little valley, whether I was picking up on a thin spot in the veil or it was simply the product of my senses acting on my often-overwrought imagination.

And while I don't agree with his basic assumptions, the whole experience makes the quote from the Romanian philosopher Mircea Eliade have a strange resonance for me: "Man becomes aware of the sacred because it manifests itself, shows itself, as something wholly different from the profane...  In each case we are confronted by the same mysterious act — the manifestation of something of a wholly different order, a reality that does not belong to our world, in objects that are an integral part of our natural profane world."

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