The fate of Flight 1282

In many people, there's a deep-seated need to find a reason for the bad things that happen in the world.

Well, of course, there always are reasons, but those are proximal causes; the car crashed into a telephone pole because the tires hit an icy spot on the road, Uncle Hubert died because his cancer recurred, the house caught fire because of an electrical short in the wiring.  But there's this strange desire to ascribe more to it than that, to find ultimate causes beyond the here's-why-it-happened proximal causes.

It's not limited to unfortunate events; that sort of thinking can extend to positive ones as well.  "It was meant to be" is a deeply seductive idea.  I remember running into it in the fantasy literature I grew up with, that certain outcomes were fated to be by some sort of overarching pattern to the universe.  Take this example from The Lord of the Rings:

"There was more than one power at work, Frodo," [Gandalf said.]  "The Ring was trying to get back to its Master.  It had slipped from Isildur's hand and betrayed him, then when a chance come it caught poor Déagol, and he was murdered; and after that Gollum, and it had devoured him.  It could make no further use of him: he was too small and mean, and as long as it stayed with him he would never leave his deep pool again.  So now, when its Master was awake once more and sending out his dark thought from Mirkwood, it abandoned Gollum.  Only to be picked up by the most unlikely person imaginable: Bilbo from the Shire! 

"Behind that there was something else at work, beyond any design of the Ring-maker.  I can put it no plainer than by saying that Bilbo was meant to find the Ring, and not by its maker.  In which case, you, Frodo, also were meant to have it.  And that is an encouraging thought."

I think I'm not alone in having read this passage and found it a comforting idea.  I ran into it again, even more explicitly, in the novel/fable for adults The Alchemist by Paulo Coelho, in which the main character is told repeatedly that if you are on the right path to accomplishing your life's goal, "the universe itself will conspire to make certain you succeed."

Wouldn't it be lovely if that were true?

Most people are profoundly uncomfortable with the idea that the universe might be simply a weird and chaotic place -- full of proximal causes, but damn few ultimate ones.  That it's a place where things sometimes work out even when you do everything wrong, and sometimes don't, even when you do everything right.

The reason the topic comes up is the much-publicized emergency landing made on January 5 by Alaska Airlines Flight 1282 from Portland, Oregon to Ontario, California, minutes after takeoff, when a chunk of the fuselage blew off.  Astonishingly -- some say miraculously -- there were no serious injuries.

Even weirder is that the two seats next to the place where the damage occurred, 26A and 26B, were empty at the time.

To say this is fortunate is a significant understatement.  Claims have surfaced since then that the two seats had been sold and the two passengers were delayed and missed the flight, but those claims have not been verified and it's possible the seats were simply empty.

Almost immediately, two explanations began to circulate, one benevolent and one of a darker hue.

The more positive one was that a divine power had intervened to save the two people who would have sat in those seats, as well as the rest of the people on the plane.  "God is great!" posted a devout Reddit user.  "How can anyone doubt His existence after something like this?"

Well, the sticking point is all the times circumstances conspire to produce a more gruesome outcome.  It's all very well to see God's hand in saving the two presumed passengers, and to utter platitudes like "God must have a plan for them!"  The problem starts when you apply it the other way.  In for a penny, in for a pound, you know?  If Great-Aunt Petunia falls down the stairs and breaks her neck, do you then say, "I guess God was done with her"?

Sometimes things end happily, but often they don't.  If you think there's a Grand Plan, you'd better be ready to explain both.  (Unless you fall back on "God works in mysterious ways," which is an unassailable position but explains exactly nothing.)

Also circulating, though, is a less pleasant option for the reason behind the aircraft accident, and that's the one taken by the conspiracy theorists.  I've already seen a variety of twists on this, but the most common is that Alaska Airlines was running a test of its emergency protocols and deliberately staged the rupture, but at least was kind enough to make sure the two seats next to the hole would be unoccupied at the time.  Besides being wildly unlikely -- airplanes are expensive, and there are lots of ways to test emergency protocols without blowing a hole in the side of one in midair -- there's the dubious logic of the airline company saving two people while simultaneously risking the lives of the other 177 people on board.

But as usual, the conspiracy theorists are convinced they've figured it out.  Better a horrifying reason, apparently, than no reason at all.

Whether you buy the first or second scenario, though, the urge to find an explanation for the happy outcome of the accident (beyond the proximal causes, such as the skill of the pilot and copilot in landing the damaged plane) is leading people onto some very thin philosophical ice.  I'm reminded of the brilliant and devastating novel The Bridge of San Luis Rey by Thornton Wilder, which I read when I was in eleventh grade.  I don't exaggerate when I say I never saw the world the same way afterward.  In the book, devout and innocent Brother Juniper, a monk in seventeenth-century Peru, is devastated when five members of the village where he lives were killed in the collapse of a bridge over a canyon.  Believing that God always has a reason for everything, for "the fall of every sparrow," he sets out to study the life histories of each of the victims, to see if he can determine why those five and no others were killed.

In the end, he reaches a deeply troubling conclusion; either the mind of God is so subtle that a human could never parse it, or else there was no reason.  Things simply happen because they happen; there are no patterns and no ultimate causes.  It's a heretical position, and at the end of the book Brother Juniper is burned at the stake by the Inquisition along with all of his writings.

So perhaps there is a reason that the two seats on Flight 1282 were unoccupied, beyond simple happenstance.  If so, it's beyond me to see what that might be, given how many times things go wrong and people do die.  Scary as it is, I think it's much more likely that the universe is simply a chaotic place where -- to quote the wonderful song "The Monkey's Paw" by Laurie Anderson -- "it's the roll of the dice, a shot in the dark, the big wheel, the big ride."

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Out of line

Every so often, I run into a claim that some archaeological site aligns with a particular astronomical object, and all too often, everyone decides that the alignment is why the site was built where and how it was.

Trying to parse the motives of long-dead people who left nothing in the way of written records is a dicey business.  In fact, sometimes it's hard enough even when you're talking about extant cultures.  This was brilliantly lampooned in Horace Miner's rightly famous 1956 article "Body Ritual Among the Nacirema," which appeared in American Anthropologist, and took a rigorous and scholarly look at the mysterious "shrines" we all have in our houses...

... better known as "bathrooms."  And, of course, reached the wrong conclusions about the purposes of nearly everything in them.

The problem arises because the human brain is a pattern-finding device, so it's often hard to resist our tendency to see a pattern when there is none there.  This is the origin of the phenomenon of ley lines -- which I wrote about twelve years ago, in one of my earliest Skeptophilia posts -- the claim that towns, cities, and religious sites are laid out along "lines of power" generated by some unknown forces in the Earth itself.  There are a couple of completely prosaic reasons this alignment happens:

1. Populated sites in areas with relatively flat topography are frequently connected by straight lines, because as Papa Euclid taught us, the shortest distance between two points is a straight line.
2. More interestingly -- and germane to the pattern-finding tendency referenced above -- if you aren't given any constraints about what particular places you're trying to connect, you can almost always find completely accidental correlations that look like deliberate alignment.

The latter is why the whole topic comes up, because of a fun site I stumbled on called Spurious Alignments: Bad Archaeoastronomy At Your Fingertips.  What this site does is allow you to overlay various astronomical benchmarks (e.g. sunrise on the Winter Solstice, the northernmost point on the horizon where Jupiter rises, and so on) on top of particular geographic locations -- and see what correlations you can find.

One of the best ones anyone's found so far is the airport in Palermo, Italy.  Here are a few of the relevant discoveries:

• Runway 07/25 tracks the relative motions of the Moon.
• Runway 02/20 aligns with the rise of the star Capella.
• Taxiways Bravo and Charlie align with the setting of the star Procyon.
• Taxiway Delta points directly toward the setting of the star Arcturus.

From this, we can clearly see that the Palermo Airport is a site built by ancient astronomers, and the whole complex is an observatory, or possibly the center of a sky-worshiping cult.

The difficulty, of course, is some sites were created because of astronomical alignments.  Many of our distant ancestors knew the motions of the skies better than your average person does today.  A good example, not really explainable any other way, is the famous Sun Dagger on Fajade Butte in New Mexico.  A spiral design carved into the side of a rock facing is across from a crack between two stones, and -- only on the Summer Solstice -- this crack allows light from the Sun at midday to form a "dagger" that perfectly bisects the spiral.

The Sun Dagger is pretty clearly a solstice marker, allowing people to keep track of the seasons in a climate that was hostile to say the least.

But as for most of the other "ancient astronomical observatory" claims -- well, maybe.  It's too easy to find spurious correlations and alignments, especially when there are no rules about what you're trying to get the site to align to.

Or, maybe, the people who built the Palermo Airport really were trying to tell us something.  You never know.

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The law of small numbers

A few days ago, I had a perfectly dreadful day.

The events varied from the truly tragic (receiving news that a former student had died) to the bad but mundane (losing a ghostwriting job I'd been asked to do because the person I was working for turned out to be a lunatic, and had decided I was part of a conspiracy against him -- the irony of which has not escaped me) to the "I'll-probably-laugh-about-this-later-but-right-now-I'm-not" (my dog, Guinness, recovering from his recent illness, and feeling chipper enough to swipe and destroy my wife's favorite hat) to the completely banal (my computer demanding an operating system update when I was in the middle of working, tying it up for two and a half hours).

All of this brought to mind the idea of streaks of bad (or good) luck -- something that you find people so completely convinced of that it's nearly impossible to get them to break their conviction that it sometimes happens.  We've all had days when everything seems to go wrong -- when we have what my dad used to call "the reverse Midas touch -- everything you touch turns to shit."  There are also, regrettably fewer, days when we seem to have inordinate good fortune.  My question of the day is: is there something to this?

Of course, regular readers of this blog are already anticipating that I'll answer "no."  There are actually three reasons to discount this phenomenon.  Two have already been the subjects of previous blog posts, so I'll only mention them in brief.

One is the fact that the human brain is wired to detect patterns.  We tend to take whatever we perceive and try to fit it into an understandable whole.  So when several things go wrong in a row -- even when, as with my experiences last week, they are entirely unrelated occurrences -- we try to make them into a pattern.

The second is confirmation bias -- the tendency of humans to use insignificant pieces of evidence to support what we already believe to be true, and to ignore much bigger pieces of evidence to the contrary.  I had four bad things, of varying degrees of unpleasantness, occur one day last week.  By mid-day I had already decided, "this is going to be a bad day."  So any further events -- the computer update, for example -- only reinforced my assessment that "this day is going to suck."  Good things -- like the fact that even though our dog is back to getting into trouble, he is recovering; like the the fact that we've been enjoying the International Ceramics Congress workshops this weekend; like the fact that lovely wife brought me a glass of red wine after dinner -- get submerged under the unshakable conviction that the day was a lost cause.

It's the third one I want to consider more carefully.

I call it the Law of Small Numbers.  Simply put: in any sufficiently small data sample, you will find anomalous, and completely meaningless, patterns.

To take a simple model: let's consider flipping a fair coin.  You would expect that if you flip said coin 1000 times, you will find somewhere near 500 heads and 500 tails. On the other hand, what if you look at any particular run of, say, six flips?

[Image licensed under the Creative Commons ICMA Photos, Coin Toss (3635981474), CC BY-SA 2.0]

In any six-flip run, the statisticians tell us, all possible combinations are equally likely; a pattern of HTTHTH has exactly the same likelihood of showing up as does HHHHHH -- namely, 1/64.  The problem is that the second looks like a pattern, and the first doesn't.  And so if the second sequence is the one that actually emerges, we become progressively more amazed as head after head turns up -- because somehow, it doesn't fit our concept of the way statistics should work.  In reality, if the second pattern amazes us, the first should as well -- when the fifth coin comes up tails, we should be shouting, "omigod, this is so weird" -- but of course, the human mind doesn't work that way, so it's only the second run that seems odd.

Another thing is that in the second case, the six-flip run of all heads, when it come to the seventh flip, what will it be?  It's hard for people to shake the conviction that after six heads, the seventh is bound to be tails, or at least that tails is more likely.  In fact, the seventh flip has exactly the same likelihood of turning up heads as all the others -- 1/2.

All of this brings up how surprisingly hard it is for statisticians to model true randomness.  If a sequence of numbers (for example) is actually random, all possible combinations of two numbers, three numbers, four numbers, and so on should be equally likely.  So, if you have a truly random list of (say) ten million one-digit numbers, there is a possibility that somewhere on that list there are ten zeroes in a row.  It would look like a meaningful pattern -- but it isn't.

This is part of what makes it hard to create truly randomized multiple-choice tests.  As a former science teacher, I frequently gave my classes multiple-choice quizzes, and I tried to make sure that the correct answers were placed fairly randomly.  But apparently, there's a tendency for test writers to stick the correct answer in the middle of the list -- thus the high school student's rule of thumb, which is, "if you don't know the answer, guess 'c'."

Randomness, it would seem, is harder to detect (and create) than most people think.  And given our tendency to see patterns where there are none, we should be hesitant to decide that the stars are against us on certain days.  In fact, we should expect days where there are strings of bad (or unusually good) occurrences.  It's bound to happen.  It's just that we notice it when several bad things happen on the same day, and don't tend to notice when they're spread out, because that, somehow, "seems more random" -- when, in reality, both distributions are random.

I keep telling myself that.  But it is hard to quell what my mind keeps responding -- "thank heaven it's a new week - it's bound to be better than last week was."

Well, maybe.  I do agree with another thing my dad used to tell me: "I'd rather be an optimist who is wrong than a pessimist who is right."  I'm just hoping that the statisticians don't show up and burst my bubble.

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It's astonishing to see what the universe looks like on scales different from those we're used to.  The images of galaxies and quasars and (more recently) black holes are nothing short of awe-inspiring.  However, the microscopic realm is equally breathtaking -- which you'll find out as soon as you open the new book Micro Life: Miracles of the Microscopic World.

Assembled by a team at DK Publishers and the Smithsonian Institution, Micro Life is a compendium of photographs and artwork depicting the world of the very small, from single-celled organisms to individual fungus spores to nerve cells to the facets of a butterfly's eye.  Leafing through it generates a sense of wonder at the complexity of the microscopic, and its incredible beauty.  If you are a biology enthusiast -- or are looking for a gift for a friend who is -- this lovely book is a sure-fire winner.  You'll never look the same way at dust, pollen, algae, and a myriad of other things from the natural world that you thought you knew.

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

The signature of the creator

The Star Trek: The Next Generation episode "The Chase" is justly revered by Trekkies, and also by people who simply like a good story.  The gist -- giving as little in the way of spoilers as I can manage, if you've not seen it -- is that there's a message implanted in our DNA and the DNA of alien species across the galaxy.  No one species has the entire thing, so to find out what it means requires getting tissue samples from all over the place, extracting the piece of the message, then somehow putting the entire thing together to decipher what it says.

A secret code dispersed through time and space, so to speak.

While the quasi-scientific explanation behind the whole thing was a little dubious for those of us who know something about genetics and evolution, it was a hell of a good idea for a story.  A mysterious, super-powerful someone left its thumbprint on life everywhere in the universe, and there the message has sat, waiting for us to become smart enough and technologically advanced enough to find it.

"The Chase" brings up a theological question I've debated before with religious-minded friends; how, starting from outside of the framework of belief, you could tell there was a God by what you see around you.  I often hear "natural beauty" and "love and selflessness" brought up, but (unfortunately) there seems to be enough ugliness, hatred, and selfishness to more than compensate for the good stuff.  Put simply, how would a universe with a divine presence look different from one without?  I've never been able to come up with a good answer to that.  To me, the God/no God versions of the universe look pretty much alike.

Which is a large part of why I'm an atheist.  I'm perfectly okay with revising that if evidence comes my way, but at the moment, I'm not seeing any particular cause for belief in any of the various deities humans have worshipped along the way.

What brings all this up is a paper released last week in arXiv called, "Searching for a Message in the Angular Power Spectrum of the Cosmic Microwave Background."  The CMB is a relatively uniformly-spread (or isotropic, as the scientists put it) radiation that is the remnant of the Big Bang.  In the 13.8-odd billion years since the universe started, the searing radiation of creation has become stretched along with the space that carries it until it has an average wavelength of two millimeters, putting it in the microwave region of the spectrum, and that radiation comes at us from everywhere in the sky.

What the author, Michael Hippke of the Sonnenberg Observatory in Germany, proposed was something that is reminiscent of the central idea of "The Chase."  If there was a creator -- be it a god, or a super-intelligent alien race, or whatever -- the obvious place to put a message is in the CMB.  The minor fluctuations ("anisotropies") in the CMB would be detectable by a technological society pretty much from any vantage point in the visible universe, and so hiding a pattern in the apparent chaos would be as much as having a signature from the creator.

So Hippke digitized the most detailed map we have of the CMB, and then estimated what part of the signal would have been lost or degraded in 13.8 billion years due to quantum noise and interference with the much closer and more powerful radiation sources in our own galaxy.  After some intense statistical analysis, Hippke determined that there should be at least a one-thousand-bit remnant of sense somewhere in there, so he set about to find it.

Nothing.

"I find no meaningful message in the actual bit-stream," Hippke wrote.  "We may conclude that there is no obvious message on the CMB sky.  Yet it remains unclear whether there is (was) a Creator, whether we live in a simulation, or whether the message is printed correctly in the previous section, but we fail to understand it."

Despite how I started this post, I have to admit to being a little disappointed.  It was a clever approach, and no one would be more excited than me if he'd actually found something.  I don't honestly like the idea that we live in a chaotic, meaningless universe -- or, more accurately (and optimistically) that the only meaning is the one we create within it.  But if there's one thing I've learned in my sixty years on Earth, it's that reality is under no particular obligation to order itself in such a way that it makes me comfortable.  

But still, if there had been a message there, how cool would that be?  Even if, as the Cardassian commander Gul Ocett said in "The Chase," "it might just be a recipe for biscuits."

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I've always had a fascination with how our brains work, part of which comes from the fact that we've only begun to understand it.  My dear friend and mentor, Dr. Rita Calvo, professor emeritus of human genetics at Cornell University, put it this way.  "If I were going into biology now, I'd study neuroscience.  We're at the point in neuroscience now that we were in genetics in 1900 -- we know it works, we can see some of how it works, but we know very little in detail and almost nothing about the underlying mechanisms involved.  The twentieth century was the century of the gene; the twenty-first will be the century of the brain."

We've made some progress in recent years toward comprehending the inner workings of the organ that allows us to comprehend anything at all.  And if, like me, you are captivated by the idea, you have to read this week's Skeptophilia book recommendation: neuroscientist Lisa Feldman Barrett's brilliant Seven and a Half Lessons About the Brain.

In laypersons' terms, Barrett explains what we currently know about how we think, feel, remember, learn, and experience the world.  It's a wonderful, surprising, and sometimes funny exploration of our own inner workings, and is sure to interest anyone who would like to know more about the mysterious, wonderful blob between our ears.

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

Funny you should say that...

Do coincidences mean anything?

This was the subject of a fantastic, and sadly little-known, movie -- I 'Heart' Huckabee's.  The main character (played by Jason Schwartzman) has the bizarre coincidence of seeing, in a big city, the same very tall African man several times in different places.  Freaked out by this, he hires two "existential detectives" (Lily Tomlin and Dustin Hoffman) to figure out if it really was a coincidence, or if it has some kind of significance beyond that.

In other words, if there is a coincidence, maybe even what seems to be a wildly improbable, weird, eye-opening one, does it have any meaning in the Cosmic Sense?  Or is it, to quote one of my favorite songs -- Laurie Anderson's "The Monkey's Paw" -- "a twist of fate, a shot in the dark, a roll of the die, the big wheel, the big ride?"

One of my students has been paying more attention to the little coincidences lately, and his claim is that they happen way more than is attributable to chance.  The whole thing came up yesterday because in my AP Biology class we were talking about the low caloric content of celery -- giving rise to the claim that you use more calories chewing celery than you get from eating it.  He then told me that only two periods earlier, the same topic came up in a different class... and then went on to tell me, excitedly, how "that sort of thing is always happening to me!"

Of course, if he thought that I was going to be willing to attribute coincidences to some sort of Larger Purpose At Work, perhaps due to the influence of a deity who liked celery, he was barking up the wrong tree.   My opinion is such things are simply the dart-thrower's bias -- we tend to notice the hits (in this case, the times when the same topic comes up twice) and ignore misses (all of the millions of things that don't get mentioned twice).  As a result, we tend to overestimate wildly how common such coincidences are.

[image courtesy of the Wikimedia Commons]

That's not to say that there aren't some peculiar ones.  I have had the experience myself of thinking about a song, turning on the radio, and the song is playing.  Take that minor mystery, and turn up the gain, and you get people whose dreams have come true, who have had premonitions of disaster and not taken the plane (or train or boat or whatever), and whose lives have been saved.  Is this true ESP, or the hand of god, or something more prosaic?

I'd opt for the latter, and I suspect that you knew I'd say that. In my opinion, for there really to be something "going on" here, there'd have to be some cause for it, some discernible mechanism at work.  I'm willing to entertain the idea -- momentarily, anyway -- that some supreme being who honestly cares about us might wish to intervene on our part, and save us from calamity via a vision, premonition, or dream.  But that opens up the troubling question about why said deity didn't bother to let the 235 other people who died in the plane crash know, so that they, too, could escape death.  That a deity exists who selectively warns some folks about impending doom while allowing others to perish is a pretty scary idea, and such a deity would have to be capricious to the point of evil.

How about the more benign explanation, that some of us are simply more "in touch" with the sixth sense than others, and therefore all those folks who died simply weren't wired to be aware of the coming catastrophe?  Again, there's that pesky lack of a mechanism.  Not one experiment designed to detect ESP of various sorts has succeeded, which is (to say the least) a bit troublesome to those who believe in such things.  Some of those true believers respond that lab conditions, run by skeptical scientists, are not conducive to the psychic energy field, and it's the lack of belief by the researchers that is interfering with the outcome.  I respond; that's mighty convenient.  Sounds like special pleading to me.

To quote Carl Sagan, from his masterful book The Demon-Haunted World (which should be required reading in every public school science program in America):

Seances occur only in darkened rooms, where the ghostly visitors can be seen dimly at best.  If we turn up the lights a little, so we have a chance to see what’s going on, the spirits vanish. They’re shy, we’re told, and some of us believe it.  In twentieth-century parapsychology laboratories, there is the ‘observer effect’: those described as gifted psychics find that their powers diminish markedly whenever sceptics arrive, and disappear altogether in the presence of a conjuror as skilled as James Randi.  What they need is darkness and gullibility.

So, we're left with the conclusion that coincidences happen just because -- they happen.  Given that we dream every night, and daydream every day, and listen to radios and read newspapers and such pretty much constantly, coincidences are bound to happen, just by the statistics of large numbers.  It doesn't make them feel any less weird when they do occur; but sooner or later, you're going to dream something, and a few days or weeks later, it will more or less "come true."  There are only so many things we dream about, and only so many kinds of things that happen in our lives, and given a large enough time axis, eventually those two will coincide.

I hope -- honestly, I do -- that I haven't just taken the magic out of your perception of the world's weirdness.  My own view is that I'd much rather know the truth than to believe a pretty falsehood.  And really, the idea of a god who selectively dabbles in the affairs of humans isn't even that pretty, when you think about it.  So if I've made the world seem a little more prosaic and dull, I sincerely apologize.  And if I get into my car in a half-hour or so, and turn on the radio, and hear Laurie Anderson's "The Monkey's Paw," it will serve me right.

Euler's identity, and seeing the divine in mathematics

Yesterday I ran into a "proof of the existence of god" I'd never seen before; the idea that there are mathematical patterns that suggest the hand of a deity.

One of the most popular patterns that religiously-inclined mathematicians point to is "Euler's identity:"

And on the surface of it, it does seem kind of odd.  "e" is the base of the natural logarithms; "i," the square root of -1, and thus the fundamental unit of imaginary numbers; pi, the ratio between the circumference of a circle and its diameter.  That they exist in this relationship is certainly non-intuitive, and the non-intuitive often makes us sit back, and go, "Wow."

Euler's identity isn't the only such set of patterns, though.  A gentleman named Vasilios Gardiakos goes through a good many mathematical gyrations to show that god wrote his signature in number patterns, including the presence of "Pythagorean triplets" in the decimal expansion of pi.  (A "Pythagorean triplet" is a set of three integers that solve the Pythagorean theorem, that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.  The most famous one is 3, 4, and 5.)

Gardiakos's messing about seems to me to stray a little too close to numerology for my comfort.  If you've already have decided that number patterns Mean Something, and you're willing to use any pattern you find, you're already off to a good start.  Add to that the fact that he was searching for patterns in decimal expansions that are infinite (pi, e, and √2), and it's a sure bet that given enough time, you'll come across whatever you need.

The use of the Euler identity, though, is a little harder to answer.  It certainly seems... well, perfect.  It relates five fundamental constants in mathematics -- e, pi, i, 1 and 0 -- in one simple, elegant equation.  And the mathematicians themselves have waxed rhapsodic over it.  Mathematician and writer Paul Nahin calls it "the gold standard for mathematical beauty."  Mathematician Keith Devlin of Stanford University states, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

Which is all well and good, but does it prove anything beyond a fascinating and complex mathematical relationship?  First of all, the fact that it's true might be non-intuitive, but it is hardly a coincidence.  For a lucid explanation of why Euler's identity works, you have to go no further than the Wikipedia page on the subject, which leads us step-by-step through a proof of how it was constructed.

And honestly, all of the theologizing over beautiful theorems in mathematics seems to me to turn on one rather awkward question; if you are claiming that Euler's identity, or any other mathematical pattern, proves the existence of god, you are implying that had god wanted, he could have made the math work differently.  God exists -- we get Euler's identity and various patterns of numbers in the decimal expansion of pi.  God doesn't exist -- we don't.

So then, can you conceive of a mathematical system in which Euler's identity is a false statement?  Because if not, then god (should he exist) was apparently constrained to creating a universe where Euler's identity was true, and the god/no god models end up looking exactly the same.

Kind of a poor proof, honestly.

What this sort of thing seems like, to me, is an extension of the Argument from Incredulity: "I don't really understand how this could be true, so it must be god."  Understanding Euler's identity does require that you know a good bit of mathematics; easier, maybe, just to marvel at its beauty, and attribute that beauty to a deity.

For me, I'd rather just try to understand the reality, which is marvelous enough as it is, and worth reveling in a little.  It might be time to break out Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid and K. C. Cole's The Universe and the Teacup again.

Digital fingerprints

I've always been fascinated with patterns.  Starting with a love for geometric patterns when I was a kid, I remember finding out about the Fibonacci sequence, and then its connection to the Golden Ratio, in 8th grade -- and feeling like I'd touched something magical, some fundamental superstructure of the universe.  Then I discovered tessellations, and thought that was the coolest thing I'd ever seen.  Then on to M. C. Escher, Penrose tiles, fractals, the Mandelbrot set...

 

 

We're all pattern-finders, really.  That's how the human brain works.  It's just that some of us are a little more obsessed than others.

 

Patterns exist all over nature, however chaotic it may appear, and those patterns apply to our behavior, as well.  We may think we're spontaneous and unpredictable, but our actions leave traces -- and those traces form patterns.  And if you analyze enough of the traces, you can make some pretty shrewd guesses about who left them.  This is the basis of a lot of forensic pathology work, and is the fundamental idea behind some fascinating new research out of Cambridge.  [Source]

 

Researchers at the Cambridge Psychometrics Centre developed software that can be used to analyze digital traces left by users -- in this case, Facebook "likes."  58,000 Facebook users agreed to be part of the study, and gave the study group demographic profiles as well as access to their Facebook accounts.  After that, the software went to town, coming up with correlations between a variety of demographics and which pages users had "liked."

 

And here's where even the researchers got a surprise.

 

Just from the Facebook "likes," the software achieved:

• 88% accuracy at determining gender
• 95% accuracy at telling African Americans from other ethnic groups
• 85% accuracy at telling Republicans from Democrats
• 82% accuracy at determining religious affiliation
• between 65% and 72% accuracy at determining relationship status
• between 65% and 72% accuracy at determining whether the user engaged in substance abuse
• 60% accuracy in determining if the user's parents were divorced
• "high" (but unstated, in the sources I read) accuracy at detecting such traits as extroversion, emotional stability, and openness
• a correlation between liking "Curly Fries" and high IQ (no, I didn't make that up)

Pretty stunning, eh?

 

The researchers made a point of checking to see if there were any "red flag" sorts of "likes;" but it turned out that in fact, there weren't, for the most part.  The software was quite good at determining sexual preference -- and yet, according to the study, less than 5% of homosexual users had "liked" such pages as "Gay Marriage."  (And, it's to be hoped, a good many progressive heterosexuals had "liked" that page as well.)  It was the aggregate of all of the person's "likes" that counted, not one or two specific ones.  It was the overall pattern that allowed the software to be so eerily accurate.

 

Of course, this opens up new avenues for data mining -- for good reasons and bad ones.  Expect targeted advertisement software to get a lot more sophisticated soon.  There could be more dire results, too.  "Similar predictions could be made from all manner of digital data, with this kind of secondary ‘inference’ made with remarkable accuracy -- statistically predicting sensitive information people might not want revealed," said Michal Kosinski, director of the study team.  "Given the variety of digital traces people leave behind, it’s becoming increasingly difficult for individuals to control...  I am a great fan and active user of new amazing technologies, including Facebook.  I appreciate automated book recommendations, or Facebook selecting the most relevant stories for my newsfeed.  However, I can imagine situations in which the same data and technology is used to predict political views or sexual orientation, posing threats to freedom or even life."

 

So, naturally, I had to go check out some of the things I'd "liked" on Facebook.  And no, unfortunately, "Curly Fries" wasn't one of them.  Here are a few of mine:

 

Music:

• Beck
• J. S. Bach
• Fun
• Angélique Kidjo
• Fiona Apple (okay, I have pretty eclectic musical tastes)

Books:

• Foucault's Pendulum
• Richard Dawkins
• Terry Pratchett
• Lord of the Rings
• Watership Down

Movies:

• The Usual Suspects
• Vanilla Sky
• The Matrix
• Ruthless People
• O Brother, Where Art Thou?
• I "Heart" Huckabee's
• Dogma
• Memento
• Scotland, PA

Television:

• The X Files
• Arrested Development
• Seinfeld
• Northern Exposure

Activities:

• Scuba Diving
• Wine Tasting
• Travel
• Writing
• Music Performance

Other:

• Kolibri Birdwatching Tours
• This American Life
• George Rodrigue (an artist I really like)
• Cthulhu
• The Tattoo Page
• Americans Against Protestors at Military Funerals

So, okay.  I'm not seeing a pattern here.  I guess that's not surprising, really.  This software is taking metrics on the entire sample, and coming up with a best guess -- however good the human brain is at ascertaining patterns, that kind of subtlety really requires a computer.  So other than a few obvious ones (anyone who makes a point of "liking" Richard Dawkins is pretty certain to be an atheist), it's no wonder that I don't see anything particularly pattern-like in my group of "likes."

 

Also, of course, the problem may just be that I don't "like" "Curly Fries."