License to hate

By now, I'm sure all of you have heard about the 6-3 decision by the United States Supreme Court in favor of a Colorado web designer who felt like it was her right to refuse service to a gay couple on the basis of her "sincerely-held religious beliefs."

What you may not have heard is that upon looking into the details of the case, investigative reporters found that:

1. ... the man, named only as "Stewart" to protect his privacy, whom the plaintiff Lorie Smith said was one half of the gay couple who asked for her services, has never attempted to hire her, and in fact had never heard of her before the case became public;
2. ... he's a web designer himself, so in his own words, "It would make zero sense to hire a web designer when I can do that for myself;"
3. ... his gay fiancé, "Mike," doesn't exist;
4. ... and Stewart himself not only is not gay, he's been happily married to a woman for fifteen years.

So the upshot of it all is that Smith is so motivated by hatred of LGBTQ+ people that she invented an imaginary grievance, lied about it repeatedly through the various tiers of the court system, and eventually got license to deny service to a gay couple who doesn't, technically, exist.

The lawyers from the virulently anti-LGBTQ+ Alliance Defending Freedom, who defended Smith, don't seem at all upset by this.  After all, they got what they wanted; a court-sanctioned right to discriminate.  Kellie Fiedorek, who represented her, responded with a verbal shrug.

"No one should have to wait to be punished by the government to challenge an unjust law," Fiedorek said.

Apparently this allows you to invent a grievance, along with imaginary adversaries, and carry it to the highest levels of the judicial system.

And win.

Smith immediately took the mic on right-wing news to crow about this being a "victory for free speech and freedom of religion."  Because, of course, the explicit outcome was to allow her to get away with discriminating against a particular group she despises.  But what baffles me is how neither the six justices who sided with Smith, nor Fiedorek and the Alliance Defending Freedom, nor Smith herself, seem to realize how quickly this could be turned around.  What's to stop a queer-owned business from putting up a sign saying "No Straight People Allowed"?  Or an atheist-owned business refusing to serve Christians?  Or a liberal-owned business stating that no Republicans are allowed on the premises?

You have to wonder what the Religious Right will think if this decision starts being used against them.

Wasn't there already a battle over this sort of thing?  And didn't the bigots lose?  [Image of the February 1960 sit-in at Woolworth's, Durham, North Carolina is in the Public Domain]

Discrimination laws are there to prevent one individual's prejudice and hatred from impinging on the rights, security, safety, or life of someone based upon their demographics -- and especially, to protect members of oppressed or marginalized groups.  And before anyone comes at me about how oppressed and marginalized Christians are, allow me to point out that an overwhelming majority of Americans -- 63% -- self-identify as Christian.  In large swaths of the country, a non-Christian has a snowball's chance in hell of being elected to public office.  And in any case -- as I pointed out earlier -- Lorie Smith's grievance was completely spun from lies.  She created a bullseye herself, pasted it on her own forehead, and then claimed she'd been unfairly targeted.

And two-thirds of the Supreme Court agreed with her.

It's not just queer people who should be worried about this.  This ruling blows a gaping hole in prior protections from discrimination, not only on the basis of gender identity and sexual orientation, but race and religion.  "The worry is that this provides a green light to any business owner that they can refuse service to any person on the basis of their identity, whether they’re gay or lesbian, or Jewish or Black, or anything, because they have an objection to those sorts of people being in their business,” said Katherine Franke, a professor at Columbia Law School.  "There was nothing in the opinion that limits it to objections to same-sex marriage."

The only thing that keeps me from despairing completely about this situation is the sense that this is the last gasp of dying ideological bigotry.  Younger people are overwhelmingly in support of full rights for LGBTQ people, including the right to marry, and against the bogus outrage of people like Lorie Smith and the Alliance Defending Freedom.  So inevitably, as the younger generation becomes an increasingly large percentage of voters, it is devoutly to be hoped that the pendulum will swing the other way and sweep away the ugly vestiges of racism, sexism, and homophobia.

In the interim, of course, a lot of damage can be done.  Queer people and our allies need to stand up and speak.  Shout, even.  Friday's decision was a travesty of justice, driven by a warped definition of freedom of speech and freedom of religion, and flies in the face of every piece of civil rights legislation back into the 1960s.

But now's not the time to give up, as tempting as it is.

We can't let the hatred and bigotry of the Lorie Smiths of the world win.

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Planetary spin cycle

I try not to spend too much time focusing on completely loony ideas here at Skeptophilia.  Wackos are, after all, a dime a dozen, and grabbing the low-hanging fruit is kind of a cheap way to run a blog.  But sometimes I run into a claim that is so earnest, so serious, and at the same time so completely bizarre that it's kind of charming.

That was my reaction when a friend and loyal reader of Skeptophilia sent me a link to a site called Bibliotecapleyades.  I have to admit that I have no idea what that means.  I know that biblioteca means "library" in Spanish, and pleyades sounds a little like "Pleiades," the star cluster that is thought among some of the astro-woo-woos to be the home of the Nordic aliens, who are tall, blond, blue-eyed, muscular, and drop-dead sexy.

Sort of Liam Hemsworth from Outer Space, is how I think of them.

Whether that's the origin of the name or not, I have no idea.  The site doesn't mention aliens, but given the rest of the content, I wouldn't be surprised if it came up at some point.

Anyhow, this particular page on Bibliotecapleyades is called "Earth Changes: Future Map of the World," and goes into how "international known [sic] and respected futurist Gordon-Michael Scallion" has a vision of how the world is going to end up.  And I do mean "vision."  His ideas aren't based on science (big shocker, there) but on his "ongoing visions concerning the Earth" that he experiences "sometimes as many as ten or more in a day, lasting from a few seconds to minutes."  But instead of seeking professional help for this condition, he started writing it all down, and put them all together into a unified, consolidated picture of what we were in for.

You really should look at the website itself, preferably after consuming a double scotch.  It's just that good.  But in case you don't want to risk valuable brain cells going through it, I present below a few highlights of what's going to happen.  Forewarned is forearmed, you know.

1. First, we're going to have a pole shift.  Scallion seems unaware that the position of the magnetic pole and the position of the rotational axis of the Earth are related but aren't the same, so he gets a little confused talking about the precession of the Earth's rotational axis (which is real enough; the Earth wobbles like a top, meaning that Polaris won't be the North Star forever) as somehow triggering a shift in the magnetic pole.  You get the impression he thinks when the poles reverse, the Earth is kind of going to fall over or something.  But he soldiers on ahead, saying that the Earth is going to be like "a washing machine that is out of balance in the spin cycle," and this is going to fling the poles about like damp socks.  Havoc will ensue.
2. Africa is going to fall apart into three separate continents.  Some waterways will open up in a kind of a "Y" shape, inundating large parts of what is now dry land.  Madagascar is going to sink into the ocean.  Don't ask me why.  The Pyramids will also end up under water, but the flipside is that before then, "there will be great archaeological discoveries."
3. The news is more positive for Antarctica, which is going to "be reborn, and become fertile land again."  In addition, the relics of the lost civilization of "Lumania" will be found when the ice all melts, and "great cities and temples will be discovered."  I'm not sure how I feel about this.  In the historical document "At the Mountains of Madness" by H. P. Lovecraft, some explorers went into Antarctica, discovered big abandoned cities and temples, and almost all of them ended up getting eaten by Shoggoths.  So we might want to be a little cautious about investigating "Lumania."
4. The tectonic plate underneath Europe is going to "collapse."  This will cause Scandinavia and Great Britain to sort of slide off the edge into the Atlantic Ocean.
5. The Middle East will be engulfed in war.  For a change.  But this one will be a "holy war with purification of the land by fire and water," whatever that means.  I hope no one tells the End Times folks about this, because they already spend enough time yammering on about stuff like this, and I really don't want to add any more grist to their mill.
6. North America also looks like it's in for a rough time.  California will split up into 150 islands, and the "west coast will recede to Nebraska, Wyoming, and Colorado."  How that will work, given that Nebraska is east of Wyoming and Colorado, I have no idea.  The Appalachians will be a long skinny island.  At least here in upstate New York it looks like I'll have beachfront property.

He then ends with a disclaimer, a little like the "this preparation is not intended to treat or cure any medical condition" thing you see on bottles of homeopathic "remedies."  He says:

[N]o event or prediction is final.  Predictions are given as probabilities.  Even at this time, consciousness can alter an event, modify changes in a particular area or at the very least help us to prepare for what is to come...  One final note, the areas of change presented in the Future Map of The World should not be taken as absolute.  They may differ from a few miles to several hundred miles depending on many variables.  In the end, Mother Nature and our own collective consciousness will have the final say.

Be that as it may, he provides us with a map of the world showing all of the new land contours.  I'd post it here, but I don't know how Gordon-Michael Scallion feels about the copyright on images he's created, so you'll just have to go take a look for yourself if you want to figure out whether it's time to pack up and move.  Here's a map of what the world looks like now, so you'll have a basis for comparison.

[Image is in the Public Domain courtesy of NASA]

Anyhow, that's our excursion into the deep end of the pool for today.  Me, I'm not concerned.  He didn't provide a timeline for all of these catastrophes in any case, so right now I'm going to worry about more pressing issues, such as how the hell we here in the U.S. ended up with a a twice-impeached, twice-indicted near-illiterate wearing orange spray tan as a serious contender for re-election as president.  Frankly, compared to that, "Lumania" doesn't really bother me much.

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Ripples in the cosmic pond

Springboarding off yesterday's post, about a mysterious flare-up of Sagittarius A* (the supermassive black hole at the center of the Milky Way galaxy), today we have an even more momentous discovery -- a background thrum of gravitational waves from supermassive black holes in orbit around each other.

Gravitational waves are created when massive objects accelerate through space.  They're actually pulsed fluctuations in the fabric of space-time that propagate out from the source at the speed of light.  The idea has been around for a long time; English mathematician Oliver Heaviside proposed them all the way back in 1893.  Once Einstein wrote his paradigm-overturning paper on relativity in 1915, Heaviside's proposal gained a solid theoretical underpinning.

The problem was detecting them.  They're tiny, especially at large distances from the source; and the converse difficulty is that if you were close enough to the source that they were obvious, they'd be big enough to tear you to shreds.  So observing from a distance is the only real option.

[Image licensed under the Creative Commons ESO/L. Calçada/M. Kornmesser, Artist’s impression of merging neutron stars, CC BY 4.0]

The result is that it took a hundred years to get direct evidence of their existence.  In 2015 the LIGO (Laser Interferometer Gravitational Wave Observatory) successfully detected the gravitational waves from the merger of two black holes.  The whirling cyclone of energy as they spun around their center of mass, then finally coalesced, caused the space around the detector to oscillate enough to trigger a shift in the interference pattern between two lasers.  The physicists had finally seen the fabric of space shudder for a moment -- and in 2017, the accomplishment won the Nobel Prize for Rainer Weiss, Kip Thorne, and Barry Barish.

Now, though, a new study at the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has found a whole different kind.  Instead of the sudden, violent, there-and-gone-again waves seen by LIGO, NANOGrav has found a background "hum" in the universe -- the stirring of spacetime because of the orbiting of supermassive black holes around each other.

The accomplishment is made even more astonishing when you find out how long the wavelengths of these waves are.  Frequency is inversely proportional to wavelength, so the "nanohertz" part of the name of the observatory might have given you a clue.  The gravitational waves detected by NANOGrav have wavelengths measured in light years.  So how in the hell do you detect a wave in which -- even traveling at the speed of light -- the trough of the wave doesn't hit you until a year after the crest?

The way they did it is as clever as it is amazing.  Just as you can see a pattern of waves if you look across the surface of a pond, the propagation of these gravitational waves should create a ripple in space that affects the path of any light that travels through them.  The scientists at NANOGrav measured the timing of the light from pulsars -- the spinning remnants of collapsed massive stars, that because of their immense mass and breakneck rotational speed flash on and off with clocklike precision.  And sure enough, as the waves passed, the contraction and expansion of the fabric of space in between caused the pulsars to seem to speed up and slow down, by exactly the amount predicted by the theory.

"The Earth is just bumping around on this sea of gravitational waves," said astrophysicist Maura McLaughlin, of West Virginia University, who was on the team that discovered the phenomenon.

It's a little overwhelming to think about, isn't it?  Millions of light years away, two enormous black holes are orbiting around a common center of gravity, and the ripples that creates in the cosmic pond flow outward at the speed of light, eventually getting here and jostling us.  Makes me feel very, very small.

Which, honestly, is not a bad thing.  It's always good to remember we're (very) tiny entities in a (very) large universe.  Maybe it'll help us not to take our day-to-day worries quite so seriously.

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The glowing death spiral

One of the things that always blows my mind about astronomy is how good we've gotten at using indirect evidence to figure out what's going on up there.

In a way, of course, it's all indirect, at least in the sense that everything we're seeing is (1) wicked far away, and (2) in the past.  I remember how weirded out I was when I first ran into the latter concept, back when I was maybe twelve years old.  My first inkling of it happened when I was out on a walk with my dad, and down the street there was a guy using a sledgehammer to pound in a fence post.  The strange thing was, I saw the hammer's head strike the post, and then, a second or two later I heard the bang of the strike.  I asked my dad why that was.

"Well," he said, after a moment's thought, "the sound takes a moment to get to your ears.  It's why we always see the lightning before we hear the thunder.  And the farther away it is, the longer the delay.  So as we get closer to the guy, the delay should get smaller."

Which, of course, it did.

After I'd had a minute to process that, I said, "But light takes time to get to your eyes, too.  A very short amount of time, but still, some time.  So does that mean you're not seeing things as they are, but as they were in the past?"

My dad agreed that must be so.

Upon learning some more physics, I found out that the Sun is far enough away from the Earth that it takes a bit over eight minutes for light to travel the distance in between.  So if the Sun suddenly vanished -- an unlikely eventuality, fortunately -- we not only wouldn't know it for eight minutes, there is no possible way to know it.  Einstein showed that information can't travel any faster than the speed of light -- it really is the ultimate speed limit.

The nearest star, Proxima Centauri, is 4.25 light years, so we're seeing it as it was 4.25 years ago, and have no way of seeing what it looks like right now.  Given that it seems to be a fairly stable star, it probably looks much the same; but the fact remains that we can't know what its current appearance is.  The most distant objects we've seen through our most powerful telescopes are some of the quasars, at thirteen billion light years distant (and thus, what they looked like thirteen billion years ago).  So what those quasars look like right now -- where they are, if they even exist any more -- is impossible to know.  We're seeing them as they looked shortly after the universe began; what they are today is anyone's guess.

Impressively far away, but at least still in our own galaxy, is Sagittarius A*, the supermassive black hole at the center of the Milky Way.  It's 26,000 light years distant.  But despite how far away it is -- and the fact that massive dust clouds lie between it and us, obscuring what light it does emit -- we've been able to find out an astonishing amount about it.

Sagittarius A*, as imaged by NASA's Chandra X-Ray Observatory (Image is in the Public Domain]

This, in fact, is why the topic comes up today -- some research out of the Université de Strasbourg that found evidence of a sudden flare-up of Sagittarius A*, around two hundred years ago.  For such a behemoth, it's been relatively quiet since its discovery in 1990.  But astrophysicist Frédéric Marin has found a cosmic glow that resulted from a brief, powerful flare of x-rays, during which Sagittarius A* was radiating a million times brighter than it is now.

The x-rays caused the clouds of dust surrounding the black hole to fluoresce; from the distance of those clouds from the event horizon of the black hole, Marin and his team determined that they must have been hit by a strong blast of x-rays about two hundred years ago.  (Keep in mind that because of the time-lag effect I described earlier, these times are all as seen from Earth; the actual flare-up occurred 26,200 years ago, or thereabouts.)

What caused the burst isn't known, but is surmised to be the sudden swallowing by the black hole of a denser blob of cosmic dust and gas.  As material goes into a death spiral toward the event horizon of a black hole, it speeds up, and electrons are stripped from atoms, leaving a whirling funnel cloud of charged particles.  These particles radiate away some of that energy in the form of x-rays -- the "smoking gun" that allows us to see black holes, which otherwise would be entirely invisible.

If you get a little nervous about such astronomical violence, there's no cause for alarm; neither Sagittarius A* nor any of its radiation blasts pose any sort of danger to us.  We'd only be in trouble if we were a great deal closer to the galactic center.

So we can just sit back and appreciate the amazing capacity the astrophysicists have for sifting through data and painting us a picture of what the universe looks like.  In this case, the last blaze of glory for a dust cloud that got sucked into a supermassive black hole 26,000 light years away.

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Rodents of unusual size

My writer friend Vivienne Tuffnell, of the lovely blog Zen and the Art of Tightrope Walking, frequently amuses her friends with photos of the antics of her pet guinea pigs.  Her love for her little pals is undoubtedly what prompted her to post a somewhat more alarming photo a couple of days ago:

She captioned it, "Guinea pigs and guinea biggers?"

What's most amazing about this is that the smaller animal isn't even a guinea pig; it's a capybara, the largest living rodent species.  On this scale, your typical guinea pig would about fit in the space underneath the capybara's belly.

So, who's the big guy?

That's Josephoartigasia, a Pliocene (five million to one million years ago) animal from southeastern South America that is thought to be the largest rodent species ever.  From skulls found in Uruguay, a full-grown Josephoartigasia weighed something like five hundred kilograms -- heavier than an adult grizzly bear.

It's hard to talk about this thing without lapsing into superlatives.  The one that blew me away was a calculation of its bite force, putting it at an estimated 950 Newtons, which is right around what an adult jaguar can exert.  Because of this, its skull was heavily reinforced; the more powerful the muscle contraction, the stronger the bones have to be (given that bones provide anchorage and leverage for the pull of the muscles).

What it needed this kind of bite force for is a matter of conjecture.  It's possible it was just for gnawing things.  Like granite outcrops, or something.  On the other hand, South America during the Pliocene was replete with huge predators including Xenosmilus, a sabre-toothed cat, and phorusrhacids -- the aptly-named "terror birds" that looked like a cross between an ostrich and a velociraptor.  So it's possible its fearsome bite was defensive.

When food is abundant and there are lots of large carnivores around, there is a significant evolutionary pressure favoring large body size, and that seems to be what happened here.  Back then, South America's fauna resembled what now lives in southern Africa -- abundant wildlife and lots of very big animals.  Josephoartigasia would have shared the habitat with giant ground sloths, glyptodonts (think "an armadillo on steroids"), toxodonts (the Pliocene answer to hippos), and the giant peccary Platygonus. 

So it was a world of megafauna, and Josephoartigasia fit right in.

But we're used to thinking of large ungulates; even giant ground sloths are familiar to anyone who's seen a kid's book on prehistoric animals.

But rodents the size of an adult longhorn steer are a little hard to imagine.

So thanks to Vivienne, who has provided cool topics for Skeptophilia before and definitely didn't fail me this time.  Me, I'm just as glad Josephoartigasia is not around any more.  I have enough of a hard time keeping squirrels out of the birdfeeder.

Having a cow-sized squirrel that could eat the birdfeeder would be another thing entirely.

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Le comte éternel

When I was a kid, the high point of my year was the two-week trip my dad and I took every August to Arizona and New Mexico.  He was an avid rockhound and lapidary, so his goal was collecting agate and turquoise and jasper to bring home and make into jewelry.  Mine, on the other hand, was wandering in the beautiful, desolate hills that were so unlike the lush near-jungles of my native southern Louisiana.

Another thing I loved about that part of the country was the abundance of peculiar little curio shops.  Some were clearly tourist traps, but some were run by honest-to-goodness old-time eccentric southwesterners, and filled with weird and wonderful oddities.  One of these I recall well was in Alpine, Texas, and was mostly a used book store, but had all sorts of other stuff (including, to my dad's delight, rocks).

That's where I picked up a copy of Richard Cavendish's book The Black Arts, about the history of occultism.  At that age (I was about thirteen at the time) I was absolutely fascinated with this stuff.  And it was in The Black Arts that I first ran across the peculiar character known as the Comte de Saint-Germain.

Saint-Germain is one of a handful of people who are, supposedly, immortal.  Here's the passage about him from Cavendish's book:

One of of the most famous of all those who are supposed to have possessed the Elixir of Life is the Count of Saint-Germain.  "The Comte de Saint-Germain and Sir Francis Bacon," says Manly P. Hall, the leading light of the Philosophical Research Society of Los Angeles, "are the two greatest emissaries sent into the world by the Secret Brotherhood in the last thousand years."  The Secret Brotherhood is a group of Masters, whose headquarters are said to be in the Himalayas and who are attempting to guide mankind along higher paths.

Saint-Germain hobnobbed with the highest social circles in France, winning the favour of Madame de Pompadour in 1759 with his "water of rejuvenation."  Immensely erudite and enormously rich, he was a skillful violinist, painter, and chemist, had a photographic memory, and was said to speak eleven languages fluently, including Chinese, Arabic, and Sanskrit...  He was believed to be over two thousand years old...  He delighted in reminiscing about the great ones of the past with whom he had been on familiar terms, including the Queen of Sheba and Cleopatra.  He was a wedding guest at Cana when Christ turned the water into wine.  There is a pleasant story of him describing a dear friend of long ago, Richard the Lionheart, and turning to his manservant for confirmation.  "You forget, sir," the valet said solemnly.  "I have only been five hundred years in your service."

Saint-Germain attributed his astonishing longevity to his diet and his elixir...  He is supposed to have died in Germany in 1784, but occultists believe that he was probably given a mock burial... It is said that he was frequently seen alive in the next century and was known to Bulwer-Lytton.

It's a curious story, to say the least.  In Umberto Eco's brilliant novel Foucault's Pendulum, his character of Agliè coyly hints that he's the latest rebranding of the Comte de Saint-Germain -- but when the main character, Casaubon, tries to tell this to his psychologist, and that Agliè/Saint-Germain is at the center of a gigantic and murderous conspiracy, the doctor gives him a level look and says, "Monsieur, vous êtes fou."  ("Mister, you are crazy.")

Reading about this stuff can definitely leave you feeling that way, but there's no doubt Saint-Germain was a real guy.  He left behind a number of surviving musical compositions, and two extant written works are attributed to him.  He was employed on diplomatic missions by French King Louis XV.  Voltaire met him, and despite Voltaire's generally skeptical view of things, he apparently at least halfway believed the Comte's grandiose tales.  He called Saint-Germain "the Wonder-Man -- a man who does not die, and who knows everything."  Prince Charles of Hesse-Kassel called him "the greatest philosopher who ever lived."  

Giacomo Casanova, however, wasn't so impressed, although he had to admit to some grudging admiration for Saint-Germain's ability to lie so convincingly:

This extraordinary man, intended by nature to be the king of impostors and quacks, would say in an easy, assured manner that he was three hundred years old, that he knew the secret of the Universal Medicine, that he possessed a mastery over nature, that he could melt diamonds, professing himself capable of forming, out of ten or twelve small diamonds, one large one of the finest water without any loss of weight.  All this, he said, was a mere trifle to him.  Notwithstanding his boastings, his bare-faced lies, and his manifold eccentricities, I cannot say I thought him offensive.  In spite of my knowledge of what he was and in spite of my own feelings, I thought him an astonishing man as he was always astonishing me.

Throughout his life (assuming he did actually die!), Saint-Germain's ability to astonish kept him the darling of high society.  His portrait hangs in the Louvre:

[Image is in the Public Domain]

So who was he?

This is where it gets even more interesting, because no one knows for sure.  In fact, no one even knows his real name; he had a dozen or more by which he was regularly known.  He claimed to be the son of Francis II Rákóczi, Prince of Transylvania, but keep in mind that the guy also claimed to be thousands of years old, so that should be taken with a large handful of salt.  Rákóczi did have a son, named Leopold George -- but the records indicate Leopold died at age four.  The occultists, of course, have an answer for that (they seem to have an answer for everything, don't they?) -- they say that Rákóczi kept his son's survival a secret to protect him from the scheming Habsburgs, which accounts for Saint-Germain's education and wealth (and penchant for secrecy).  All through his life he wove a web of mystery around himself, and reveled in the cachet it gave him with the aristocracy.  

P. T. Barnum, though, in his 1886 book The Humbugs of the World, clearly wasn't having any of it:

The Marquis de Créquy declared that Saint-Germain was an Alsatian Jew, Simon Wolff by name, and was born at Strasbourg about the close of the 17th or the beginning of the 18th century; others insist that he was a Spanish Jesuit named Aymar; and others again intimate that his true title was the Marquis de Betmar, and that he was a native of Portugal.  The most plausible theory, however, makes him the natural son of an Italian princess and fixes his birth at San Germano, in Savoy, about the year 1710; his ostensible father being one Rotondo, a tax-collector of that district.

Barnum was an expert on fooling the gullible; there's the sense here that he wasn't fond of the competition.

Whoever Saint-Germain was, there's no doubt he was a fascinating character.  Predictably, I'm not buying that he was thousands of years old, nor that somehow, he's still alive.  And many of his claims are somewhere between "implausible" and "ludicrous."  But there's no doubt that he was an accomplished and skilled trickster, and relished the air of mystery his stories gave him.  It'd be nice to have some answers to the questions he surrounded himself with, but the truth is, he was too good at covering his tracks -- and like the more famous mystery of Jack the Ripper, we'll probably never know his identity for sure. 

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Advanced elegance

I think it's a natural human tendency to be awed by what we don't understand.

I know when I see some abstruse concept that is far beyond my grasp, I'm impressed not only by how complex the universe can be, but that there are people who can comprehend it.  I first ran into this in a big way when I was in college, and took a class called Classical Mechanics.  The topic was the mathematics of why and how objects move, how that motion affects other objects, and so on.

It was the first time in my life I had ever collided with something that regardless of my effort, I couldn't get.  The professor, Dr. Spross, was a very patient man, but his patience was up against a classical-mechanics-proof brain.  On the first exam, I scored a 19.

Percent.

And I'm convinced that he had dredged up the 19 points from somewhere so I wouldn't end up with a single-digit score.  I ended that class with a C-, which I think Dr. Spross gave me simply because he didn't want me back again the following semester, spending another four months ramming my poor physics-deficient head up against a metaphorical brick wall.

There's one memory that stands out from that experience, over forty years ago, besides the overwhelming frustration.  It was when Dr. Spross introduced the concept of the "Hamiltonian function," a mathematical framework for analyzing motion.  He seemed so excited about it.  It was, he said, an incredibly elegant way to consider velocity, acceleration, force, momentum, and so on.  So I thought, "Cool!  That sounds pretty interesting."

Following that cheerful thought was an hour and a half of thinking, "I have no fucking idea what any of this means."  It was completely opaque.  The worst part was that a number of my classmates were nodding their heads, writing stuff down, and seemed to get it with no problem.

So either I was the only complete dunderhead in the class, or they were just better at hiding their dismay than I was.

Anyhow, I think that was the moment I realized a career in research physics was not in the cards for me.

To this day, the "Hamiltonian function" remains something that in my mind symbolizes the Unknowable.  I have deep and abiding admiration for people for whom that concept makes sense (first and foremost, William Rowan Hamilton, who developed it).  And I'm sure it is elegant, just as Dr. Spross said.  But experiencing that elegance was (and probably still is) entirely beyond me.

It's this tendency to find what we can't understand awe-inspiring that has led to the idea of the God of the gaps -- in which gaps in our scientific knowledge are attributed to the incomprehensible hand of the divine.  Theologian Dietrich Bonhoeffer realized what the problem with this was, at least for people who are religious:

How wrong it is to use God as a stop-gap for the incompleteness of our knowledge.  If in fact the frontiers of knowledge are being pushed further and further back (and that is bound to be the case), then God is being pushed back with them, and is therefore continually in retreat.  We are to find God in what we know, not in what we don't know.

Anyhow, that was a long-winded preamble as an explanation of why all of this comes up in today's post.  I immediately thought of the awe-inspiring nature of what we don't understand when I read an article yesterday about two researchers at the University of Rochester, Tamar Friedmann and Carl Hagen, who found that a method for calculating the energy levels of a hydrogen atom generates the well-known number pi.

[Image is in the Public Domain]

It turns out to have something to do with a mathematical function called the Wallis product, which says that you can generate π/2 by a simple series of multiplications:

π/2 = (2/1) x (2/3) x (4/3) x (4/5) x (6/5) x (6/7) x (8/7) x (8/9)....

The pattern is that the numerators of the fractions are 2, 2, 4, 4, 6, 6, 8, 8... and the denominators 1, 3, 3, 5, 5, 7, 7, 9, 9...  And the cool thing is, the more terms you add, the closer you get to π/2.

Now, as for why this is so... well, I tried reading the explanation, and my eyes started spinning.  And I've taken lots of math courses, including calculus and differential equations, and like I said earlier, I majored in physics (as much of a mistake as that turned out to be).  But when I took a look at the paper about the energy levels of hydrogen and the Wallis product and gamma functions, I almost could hear Dr. Spross's voice, explaining it in a tone implying it would be immediately clear to a small child, or even an unusually intelligent dog.

And all of those feelings from Classical Mechanics came bubbling up to the surface.

So I'm left with being a little in awe about it all.  Somehow, even though I have no real understanding of why, the same number that I learned about in geometry class as the ratio between a circle's circumference and its diameter shows up in the energy levels of hydrogen atoms.  Predictably, I'm not inclined to attribute such correspondences to the hand of the divine, but they do seem to be (in Dr. Spross's words) "elegant."  And even if I never get much beyond that, I can still appreciate the minds of the people who can.

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