Weird math

When I was in Calculus II, my professor, Dr. Harvey Pousson, blew all our minds.

You wouldn't think there'd be anything in a calculus class that would have that effect on a bunch of restless college sophomores at eight in the morning.  But this did, especially in the deft hands of Dr. Pousson, who remains amongst the top three best teachers I've ever had.  He explained this with his usual insight, skill, and subtle wit, watching us with an impish grin as he saw the implications sink in.

The problem had to do with volumes and surface areas.  Without getting too technical, Dr. Pousson asked us the following question.  If you take the graph of y = 1/x:

And rotate it around the y-axis (the vertical bold line), you get a pair of funnel-shapes.  Not too hard to visualize.  The question is: what are the volume and surface area of the funnels?

Well, calculating volumes and surface areas is pretty much the point of integral calculus, so it's not such a hard problem.  One issue, though, is that the tapered end of the funnel goes on forever; the red curves never strike either the x or y-axis (something mathematicians call "asymptotic").  But calc students never let a little thing like infinity stand in the way, and in any case, the formulas involved can handle that with no problem, so we started crunching through the math to find the answer.

And one by one, each of us stopped, frowning and staring at our papers, thinking, "Wait..."

Because the shapes end up having an infinite surface area (not so surprising given that the tapered end gets narrower and narrower, but goes on forever) -- but they have a finite volume.

I blurted out, "So you could fill it with paint but you couldn't paint its surface?"

Dr. Pousson grinned and said, "That's right."

We forthwith nicknamed the thing "Pousson's Paint Can."  I only found out much later that the bizarre paradox of this shape was noted hundreds of years ago, and it was christened "Gabriel's Horn" by seventeenth-century Italian physicist and mathematician Evangelista Torricelli, who figured it was a good shape for the horn blown by the Archangel Gabriel on Judgment Day.

There are a lot of math-phobes out there, which is a shame, because you find out some weird and wonderful stuff studying mathematics.  I largely blame the educational system for this -- I was lucky enough to have a string of fantastic, gifted elementary and middle school math teachers who encouraged us to play with numbers and figure out how it all worked, and I came out loving math and appreciating the cool and unexpected bits of the subject.  It's a pity, though, that a lot of people have the opposite experience.  Which, unfortunately, is what happened with me in my elementary and middle school social studies and English classes -- with predictable results.

So math has its cool bits, even if you weren't lucky enough to learn about 'em in school.  Here are some short versions of other odd mathematical twists that your math teachers may not have told you about.  Even you math-phobes -- try these on for size.


1.  Fractals

A fractal is a shape that is "self-similar;" if you take a small piece of it, and magnify it, it looks just like the original shape did.  One of the first fractals I ran into was the Koch Snowflake, invented by Swedish mathematician Helge von Koch, which came from playing around with triangles.  You take an equilateral triangle, divide each of its sides into three equal pieces, then take the middle one and convert it into a (smaller) equilateral triangle.  Repeat.  Here's a diagram with the first four levels:

And with Koch's Snowflake -- similar to Pousson's Paint Can, but for different reasons -- we end up with a shape that has an infinite perimeter but a finite area.

Fractals also result in some really unexpected patterns coming out of perfectly ordinary processes.  If you have eight minutes and want your mind completely blown, check out how what seems like a completely random dice-throwing protocol generates a bizarre fractal shape called the Sierpinski Triangle.  (And no, I don't know why this works, so don't ask.  Or, more accurately, ask an actual mathematician, who won't just give you what I would, which is a silly grin and a shrug of the shoulders.)

2.  The Four-Color-Map Theorem

In 1852, a man named Francis Guthrie was coloring in a map of the counties of England, and noticed that he could do the entire map, leaving no two adjacent counties the same color, using only four different colors.  Guthrie wondered if that was true of all maps.

Turns out it is -- something that wasn't proven for sure until 1976.

Oh, but if you're talking about a map printed onto a Möbius Strip, it takes six colors.  A map printed on a torus (donut) would take seven.

Once again, I don't have the first clue why.  Probably explaining how it took almost a hundred years to prove.  But it's still pretty freakin' cool.


3.  Brouwer's Fixed-Point Theorem

In the 1950s, Dutch mathematician Luitzen Brouwer came up with an idea that -- as bizarre as it is -- has been proven true.  Take two identical maps of Scotland.  Deform one any way you want to -- shrink it, expand it, rotate it, crumple it, whatever -- and then drop it on top of the other one.

Brouwer said that there will be one point on the deformed copy of the map that is exactly on top of the corresponding point on the other map.

It even works on three dimensions.  If I stir my cup of coffee, at any given time there will be at least one coffee molecule that is in exactly the same position it was in before I stirred the cup.

Speaking of which, all this is turning my brain to mush.  I think I need to get more coffee before I go on to...


4.  The types of infinity

You might think that infinite is infinite.  If something goes on forever, it just... does.

Turns out that's not true.  There are countable infinities, and uncountable infinities, and the latter is much bigger than the former.

Infinitely bigger, in fact.

Let's define "countable" first.  It's simple enough; if I can uniquely assign a natural number (1, 2, 3, 4...) to the members of a set, it's a countable set.  It may go on forever, but if I took long enough I could assign each member a unique number, and leave none out.

So, the set of natural numbers is itself a countable set.  Hopefully obviously.

So is the set of odd numbers.  But here's where the weirdness starts.  It turns out that the number of natural numbers is exactly the same as the number of odd numbers.  You may be thinking, "Wait... that can't be right, there has to be twice as many natural numbers as odd numbers!"  But no, because you can put them in a one-to-one correspondence and leave none out:

1-1
2-3
3-5
4-7
5-9
6-11
7-13
etc.

So there are exactly the same number in both sets.

Now, what about real numbers?  The real numbers are all the numbers on the number line -- i.e. all the natural numbers plus all of the possible decimals in between.  Are there the same number of real and natural numbers?

Nope.  Both are infinite, but they're different kinds of infinite.

Suppose you tried to come up with a countable list of real numbers between zero and one, the same as we came up with a countable list of odd numbers above.  (Let's not worry about the whole number line, even.  Just the ones between zero and one.)  As I mentioned above, if you can do a one-to-one correspondence between the natural numbers and the members of that list, without leaving any out, then you've got a countable infinity.  So here are a few members of that list:

0.1010101010101010...
0.3333333333333333...
0.1213141516171819...
0.9283743929178394...
0.1010010001000010...
0.13579111315171921...

And so forth.  You get the idea.

German mathematician Georg Cantor showed that no matter what you do, your list will always leave some out.  In what's called the diagonal proof, he said to take your list, and create a new number -- by adding one to the first digit of the first number, to the second digit of the second number, to the third digit of the third number, and so on.  So using the short list above, the first six decimal places will be:

0.242413...

This number can't be anywhere on the list.  Why?  Because its first digit is different from the first number on the list, the second digit is different from the second number on the list, the third digit is different from the third number of the list, and so forth.  And even if you just artificially add that new number to the end of the list, it doesn't help you, because you can just do the whole process again and generate a new number that isn't anywhere on the list.

So there are more numbers between zero and one on the number line than there are natural numbers.  Infinitely more.


5.  Russell's Paradox

I'm going to end with one I'm still trying to wrap my brain around.  This one is courtesy of British mathematician Bertrand Russell, and is called Russell's Paradox in his honor.

First, let's define two kind of sets:

• A set is normal if it doesn't contain itself. For example, the "set of all trees on Earth" is normal, because the set itself is not a tree, so it doesn't contain itself.
• A set is abnormal if it contains itself. The "set of everything that is not a tree" is abnormal, because the set itself is not a tree.

Russell came up with a simple idea: he looked at "the set of all possible normal sets."  Let's call that set R.  Now here's the question:

Is R normal or abnormal?

Thanks, I'll show myself out.

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In keeping with Monday's post, this week's Skeptophilia book recommendation is about one of the most enigmatic figures in mathematics; the Indian prodigy Srinivasa Ramanujan.  Ramanujan was remarkable not only for his adeptness in handling numbers, but for his insight; one of his most famous moments was the discovery of "taxicab numbers" (I'll leave you to read the book to find out why they're called that), which are numbers that are expressible as the sum of two cubes, two different ways.

For example, 1,729 is the sum of 1 cubed and 12 cubed; it's also the sum of 9 cubed and 10 cubed.

What's fascinating about Ramanujan is that when he discovered this, it just leapt out at him.  He looked at 1,729 and immediately recognized that it had this odd property.  When he shared it with a friend, he was kind of amazed that the friend didn't jump to the same realization.

"How did you know that?" the friend asked.

Ramanujan shrugged.  "It was obvious."

The Man Who Knew Infinity by Robert Kanigel is the story of Ramanujan, whose life ended from tuberculosis at the young age of 32.  It's a brilliant, intriguing, and deeply perplexing book, looking at the mind of a savant -- someone who is so much better than most of us at a particular subject that it's hard even to conceive.  But Kanigel doesn't just hold up Ramanujan as some kind of odd specimen; he looks at the human side of a man whose phenomenal abilities put him in a class by himself.

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

Truth, lies, and Facebook

There's been a whole lot of buzz lately on the subject of free speech and social media.

The maelstrom has centered around the controversial figure of Mark Zuckerberg, CEO of Facebook, whose rather lax policies about truth in political advertisements is said by many to have contributed to Donald Trump's nomination and eventual electoral win.  As we enter another presidential election season (lord help us all), the whole issue has come up again -- with Zuckerberg defending his position on allowing ads even if they contain factual inaccuracy.

I.e., "Fake News."  Oh, how I've come to loathe that phrase, which gets lobbed every time someone hears a piece of news unfavorable to their preferred politician.  Call it "Fake News," and you can forthwith stop thinking about it.

It's been a remarkably efficient strategy -- and is largely to blame for the current political mess we're in.

In any case, Zuckerberg isn't backing down.  He said:

While I certainly worry about the erosion of truth, I don’t think most people want to live in a world where you can only post things that tech companies judge to be 100% true...  We’re seeing people across the spectrum try to define more speech as dangerous because it may lead to political outcomes they see as unacceptable.  Some hold the view that since the stakes are now so high, they can no longer trust their fellow citizens with the power to communicate and decide what to believe for themselves.  I personally believe that this is more dangerous for democracy over the long term than almost any speech.

Which, to me, misses the point entirely.

Free speech covers opinions like, "I think Donald Trump has been a great president."  I have no right to censor that, whether or not I agree with it.  However, saying "Donald Trump eats live babies for breakfast" is not covered under free speech, because it's a false statement intended to discredit.

Which the law refers to as "libel."

[Image licensed under the Creative Commons Ibrahim.ID, Socialmedia-pm, CC BY-SA 4.0]

So allowing political ads is one thing.  You can craft a political ad that steers clear of libel even if it's highly critical of the candidate you're running against.   But when you post factual inaccuracies (better known as "lies") about someone, with the intent to cause harm to their reputation or electability, that's no longer a matter of free speech.

And as such, yes, Mark, you have an obligation to block such advertisements.

Elizabeth Warren responded to Zuckerberg's stance by putting together an ad claiming that Zuckerberg is a Trump supporter (which he claims is untrue).  But the salvo evidently didn't really strike the target.  Zuckerberg is still unapologetic for his position:

Do we ban ads about health care or immigration or women’s empowerment?  And if you’re not going to ban those, does it really make sense to give everyone a voice in the political debates except for the candidates themselves?  I believe when it’s not absolutely clear what to do, we should err on the side of greater expression.

Well, actually, you have banned ads about health care.  Earlier this year, Facebook (rightly) decided to block ads promoting the talking points of the anti-vaxxers.  Why?  Because what they were saying was false and harmful.  That's the acid test, you know?  (1) Is it false? and (2) is it harmful or damaging to the person or persons targeted?

If the answer to those two questions is "yes," then social media has an obligation to say no to the advertisement.

Hard to see how anything about "women's empowerment" would fall under those guidelines.

So what Zuckerberg is engaging in is a false equivalency -- and I believe he's perfectly well aware of it.  Those ads bring in millions of dollars of revenue, so he has a vested interest in turning a blind eye, regardless of the political or societal outcome.  As usual, it's all about the bottom line.

At present, I still have a Facebook.  For one thing, it's my primary way of keeping in touch with people who live far away and whom I rarely see.  For another, it's the main social media platform used by my publishing company, so I'd be cutting myself off from them pretty thoroughly if I deleted my profile.

So I'm sticking -- for the time being.  I'd love to see enough pressure put on Zuckerberg that he changes his stance, and at least pledges to stop advertisements that engage in spreading demonstrably false statements.  That's all we're asking, really -- not to take sides, but to stop all sides from lying for their own gain.

It's not a difficult concept.  And hard to see how you'd craft an argument that increasing the amount of truth in all kinds of media is a bad thing.

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This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

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

Saucy savagery

Kids these days, ya know what I mean?

Wiser heads than mine have commented on the laziness, disrespectfulness, and general dissipation of  youth.  Here's a sampler:

• Parents themselves were often the cause of many difficulties.  They frequently failed in their obvious duty to teach self-control and discipline to their own children.
• We defy anyone who goes about with his eyes open to deny that there is, as never before, an attitude on the part of young folk which is best described as grossly thoughtless, rude, and utterly selfish.
• The children now love luxury; they have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise.  Children are now tyrants, not the servants of their households.  They no longer rise when elders enter the room.  They contradict their parents, chatter before company, gobble up dainties at the table, cross their legs, and tyrannize their teachers.
• Never has youth been exposed to such dangers of both perversion and arrest as in our own land and day.  Increasing urban life with its temptations, prematurities, sedentary occupations, and passive stimuli just when an active life is most needed, early emancipation and a lessening sense for both duty and discipline, the haste to know and do all befitting man's estate before its time, the mad rush for sudden wealth and the reckless fashions set by its gilded youth--all these lack some of the regulatives they still have in older lands with more conservative conditions.
• Youth were never more saucy -- never more savagely saucy -- as now...  the ancient are scorned, the honourable are condemned, and the magistrate is not dreaded.
• Our sires' age was worse than our grandsires'.  We, their sons, are more worthless than they; so in our turn we shall give the world a progeny yet more corrupt.
• [Young people] are high-minded because they have not yet been humbled by life, nor have they experienced the force of circumstances…  They think they know everything, and are always quite sure about it.

Of course, I haven't told you where these quotes come from. In order:

• from an editorial in the Leeds Mercury, 1938
• from an editorial in the Hull Daily Mail, 1925
• Kenneth John Freeman, Cambridge University, 1907
• Granville Stanley Hall, The Psychology of Adolescence, 1904
• Thomas Barnes, The Wise Man's Forecast Against the Evil Time, 1624
• Horace, Odes, Book III, 20 B.C.E.
• Aristotle, 4th century B.C.E.

So yeah.  Adults saying "kids these days" has a long, inglorious history.  (Nota bene: the third quote, from Kenneth Freeman, has often been misattributed to Socrates, but it seems pretty unequivocal that Freeman was the originator.)

Jan Miense Molenaar, Children Making Music (ca. 1630) [Image is in the Public Domain]

I can say from my admitted sample-size-of-one that "kids these days" are pretty much the same as they were when I first started teaching 32 long years ago.  There are kind ones and bullies, intelligent and not-so-much, hard-working and not-so-much, readers and non-readers, honest and dishonest.  Yes, a lot of the context has changed; just the access to, and sophistication of, technology has solved a whole host of problems and created a whole host of other ones, but isn't that always the way?  In my far-off and misspent youth, adults railed against rock music and long hair in much the same way that they do today about cellphones and social media, and with about as much justification.  Yes, there are kids who misuse social media and have their noses in their SmartPhones 24/7, but the vast majority handle themselves around these devices just fine -- same as most of my generation didn't turn out to be drug-abusing, illiterate, disrespectful dropouts.

This comes up because of a study that was published in Science Advances this week, by John Protzko and Jonathan Schooler, called "Kids These Days: Why the Youth of Today Seem Lacking."  And its unfortunate conclusion -- unfortunate for us adults, that is -- is that the sense of today's young people being irresponsible, disrespectful, and lazy is mostly because we don't remember how irresponsible, disrespectful, and lazy we were when we were teenagers.  And before you say, "Wait a moment, I was a respectful and hard-working teenager" -- okay, maybe.  But so are many of today's teenagers.  If you want me to buy that we're in a downward spiral, you'll have to convince me that more teenagers back then were hard-working and responsible, and that I simply don't believe.

And neither do Protzko and Schooler.

So the whole thing hinges more on idealization of the past, and our own poor memories, than on anything real.  I also suspect that a good many of the older adults who roll their eyes about "kids these days" don't have any actual substantive contact with young people, and are getting their impressions of teenagers from the media -- which certainly doesn't have a vested interest in portraying anyone as ordinary, honest, and law-abiding.

Oh, and another thing.  What really gets my blood boiling is the adults who on the one hand snarl about how complacent and selfish young people are -- and then when young people rise up and try to change things, such as Greta Thunberg and the activists from Marjory Stoneman Douglas High School, they say, "Wait, not like that."  What, you only accept youth activism if it supports the status quo?

All well and good for kids to have opinions, until they start contradicting the opinions of adults, seems like.

Anyhow, I'm an optimist about today's youth.  I saw way too many positive things in my years as a high school teacher to feel like this is going to be the generation that trashes everything through irresponsibility and disrespect for tradition.  And if after reading this, you're still in any doubt about that, I want you to think back on your own teenage years, and ask yourself honestly if you were as squeaky-clean as you'd like people to believe.

Or were you -- like the youth in Aristotle's day -- guilty of thinking you knew everything, and being quite sure about it?

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This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

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

Universal languages

If we are ever lucky enough to contact intelligent extraterrestrial life, one of the difficulties will be communicating with them -- or even understanding what they say (whatever form that takes) as intelligent communication.

The problems with such contact, between not just different cultures but different species, were addressed in one of the most iconic episodes of Star Trek: The Next Generation -- "Darmok."  (If you don't believe me about its iconic status, go up to any fan of science fiction and say, "Darmok and Jalad at Tanagra."  I can nearly guarantee you that they will respond, "Shaka, when the walls fell."  Or possibly "Gilgamesh and Enkidu at Uruk."  And if they say the latter, they will follow it up by bursting into tears.  Amirite, Trek fans?)

The Tamarians, it turns out, always speak in myth-based metaphor; the classic phrase "Darmok and Jalad at Tanagra" is from a story of their culture and represents two people coming together to fight a common foe.  If you don't know the myths, though, the phrase makes no sense -- just as Deanna Troi points out, that if you know Shakespeare, "Juliet on the balcony" might represent doomed love, but if you don't know the play, it's completely without meaning.

Much as I love this episode -- and, like most TNG fans, ugly cry at the end of it -- as a linguist, it's always struck me as a little off.  It's hard to see how a race that speaks entirely in metaphor could become technological.  If to say, "Hand me the torque wrench" you had to come up with some kind of arcane analogy from a folk tale, fashioning anything more complicated than a slingshot would be pretty much out of the question.

A more realistic take on the alien communication thing (but in my opinion, not nearly as good a story) was the 2016 movie Arrival, in which the alien race "speaks" by drawing patterns in the air that are a little reminiscent of Circular Gallifreyan from Doctor Who.  A linguist (played by Amy Adams) is hired to decipher what they're trying to say, and head off a war -- the typical human assumption being, "If I don't know your motives, they must be bad."  The cool thing about this scenario is that the movie's creators came up with a mode of communication that's really alien, that shares essentially nothing with human speech (and damn little with human writing).

This comes up because of a paper by Christine Cuskley in Nature that looks at the human capacity for elucidating patterns, both from spoken or written language and from stimuli that aren't generally considered language at all (such as the tones of a slide whistle), when we have no referent at all for meaning.   Repeated experiments using a variety of different types of communication show that we're pretty good at abstracting and generalizing patterns from what we're given.  One example of the many given -- and you really should read the original paper, because it's freakin' cool -- is that in a test where people are given words for geometric shapes of different types, colors, and movements, within short order the test subjects figured out that if the word ended with the suffix -plo it designated a shape that was bouncing.

Cuskley writes:

A cornerstone of experimental studies in language evolution has been iterated artificial language learning: studies where participants learn of artificial ‘alien’ languages, and the product of their learning is then passed onto other participants successively.  Results over the last decade show that some defining features of human language can arise under these experimental conditions, which use iteration to simulate processes of cultural transmission...  These results have implications for how forms and modalities might constrain language systems, and demonstrate how the use of truly novel alien forms might be extended to address new questions in cultural and linguistic evolution.

All of which makes me hopeful that if we ever are confronted with something like the scenario in Arrival, we might actually have some hope of figuring out what the aliens are saying.  Can you imagine how exciting that would be?  Not just deciphering a non-human language -- something that gives linguistics geeks like me multiple orgasms -- but being able to find out what goes on in the brains (or whatever equivalent they have) of a species that shares no commonality with terrestrial biology at all?

Man, if we find it hard to conceive how people from other cultures on Earth think, this would stretch our capacity to the limit.  And it would knock us even further off our idea, which persists despite everything science has discovered, that humans are somehow special creations, and our thoughts, needs, desires, and hopes somehow lie at the very center of the universe.

Which is all to the good.  Our species could use a little more humility.  Maybe it'd allow us to take our place in the cosmos with a little more grace.

Who knows?  Maybe we'd even be able to say, "Picard and Dathon at El-Adrel."  And mean it.

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This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

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

Unreal estate

Following hard on the heels of yesterday's post about belief in the occult causing you to receive visits from the Shadow World, today we have: a real estate company who will provide a paranormal investigation of any home you're considering buying, to make sure that it doesn't come with spirits pre-installed, as it were.

Bungalo, a company with offices in Dallas, Atlanta, Charlotte, and Tampa, is offering a special during the spooky month of October, providing a "Paranormal Inspection Report" of properties for sale.  Their site says:

To perform the Paranormal Inspections on our homes, we brought in known experts in the paranormal sciences.  Utilizing their keen insight into the paranormal world and the latest realm-to-realm communication technology, these paranormal pros have examined our homes from top to bottom for anything out of the ordinary. 

The inspectors then disclose their findings to you, the home buyer, through an official Paranormal Inspection Report, which you can find on any listing’s document vault on our website.  If an inspector does encounter any unwanted paranormal activity in a home, the space in question will be properly cleansed for the buyer’s peace of mind.

One of their inspectors is paranormal researcher Becky Moyer, who wanders around with a device called a "Spirit Box" that detects the EMF fluctuations many believe are associated with the presence of supernatural entities.

[Image licensed under the Creative Commons LuckyLouie, Nightshot2, CC BY-SA 3.0]

So I looked into that a little, and man, there are a lot of models of "Spirit Box."  One of them, the "Ghost Meter EMF Sensor," is only $34.95 (plus shipping and handling), and I thought it might be instructive to take a look at some of the (804) ratings customers had given it.  Many of them were laudatory, claiming that the thing had found ghosts pretty much all over the place, but a few of them were less positive:

• I get no response with this even in circumstance where I know there should definitely be a reading of some type.
• Doesn't work.  A waste of money.  I should have got a different version of it, this thing beeps at unnecessary stuff, the fridge, the cereal, the car, the dog, the window.  This is such a gimmick.
• Goes off on most things like couch, plastic stuff, and clothes. I guess most things I own are haunted.
• Only beeps when close to rocks.  Otherwise it stays idle nonstop.  Won’t blink or beep.  Spent 2 hours in a cemetery without a single light blip until I got to the entrance where the rocks were.  As soon as I walk away from the rocks it stopped.

And then there's this one, that should win an award in the Run-On Sentence Competition 2019:

• Do not buy I want [sic] all around my house and there was only one place in my house I thought would [sic] haunted because every time I was there in my shower I felt like somebody was behind me so I go all around my house nothing beats [sic] go figure when I go into the bathroom it goes crazy I wanted to determine if something was making [sic] sure enough it was the vent making it go off when I turn them then [sic] off it wouldn't do it the second I turn them back on it went crazy so it detected a vent not a ghost

So I guess it's useful if you're not sure where your vents are.  Or, considering some of the other reviews, your couch, fridge, cereal, car, dog, window, rocks, or clothes.

In any case, it's to be expected anything you use will get mixed results, because if there was unequivocal evidence of ghostly presences, that would pretty much settle the debate over whether the paranormal world exists.  I actually have an EMF Ghost Detector app on my phone, and periodically I'll wander around my house to see what the Spiritual Plane is up to.  Not much, most days, although it does kind of go crazy when I get near my computer, which could either be because (1) it's a piece of electronic equipment and thus emits an EMF signal by default, or else (2) it's possessed.

The latter is as good an explanation for some of its behavior as any.

In any case, back to the real estate company's offer.  What I'm most curious about is the last bit, which is how you "cleanse" a place of paranormal entities.  I'm guessing bringing in a Catholic priest to do an exorcism is a bit extreme, so what are our other options?  Burning some incense?  That wouldn't work if it was, say, the spirit of a dead hippie.  Telling the spirit, politely but firmly, to get lost?  Can't imagine it'd be that easy.

But the agency's website didn't elaborate on that part, so I guess we'll just have to assume that they have their methods.

I kind of wish there'd been this option when I bought my house.  Our younger son said he always felt like there was "something there" when he was alone downstairs working in the workshop (which is where he spent a great many of his waking hours).  He said he didn't think it was hostile, but did catch movement out of the corner of his eye more than once when everyone, including the dogs, were upstairs.  And considering how weird this house is in other respects -- the previous owner was notorious for ill-conceived and (often) partly-completed home improvement ideas, what my dad called "Do It To Yourself Projects" -- it wouldn't surprise me if there were strange forces at work here.

But nothing was mentioned in the Disclosure Form, and in any case we've been here for seventeen years, so I guess we're stuck with it either way.

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

This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

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

Imagination into reality

Yesterday a friend and long-time loyal reader of Skeptophilia sent me a link to an article by the ever-entertaining Nick Redfern, well-known paranormal researcher and writer who has been featured a good many times on various television shows on the topic.  It's called "The Supernatural Hazards of Being a Writer," so naturally my interest perked up when I saw the headline.

Redfern's claim is that writing about paranormal stuff makes you more likely to experience it, and cites as examples stories about himself and his friends and colleagues who have had bizarre things happen after writing about the occult.  "When you immerse yourself in – and write about – the realms of the unknown," Redfern writes, "the 'things' that inhabit those same realms are quickly driven to intrude upon your personal space.  And, given the chance, they’ll manipulate you to mind-bending degrees."

So really, it's the New Age idea of the "Law of Attraction," wherein your positive or negative thoughts call such experiences into reality.  I shouldn't call it "New Age," though, because the Law of Attraction has been around for a very long time, especially in its negative connotations.  Worry and fear can conjure up such mental demons that it's very easy to slip into believing they're real, that your mind has given them form and substance.

And once you're there, the idea that you might have opened Pandora's Box is one more short step.  "I’m here to warn you," Redfern writes, "and to warn you to the absolute best of my ability – that opening doors of the occult variety is a relatively easy thing to achieve, whether deliberately, consciously, or even accidentally.  Closing the doors to the non-human things that so relish crossing the veil when called forth, however – or even as the mood takes them – is no easy task.  In fact, it’s nigh on impossible.  Unless, that is, you’re aware of certain procedures designed to forever banish their icy presence."

It's what H. P. Lovecraft wrote about so chillingly in The Case of Charles Dexter Ward -- "Do not call up that which you cannot put down."

So okay, pretty scary stuff.  The question, of course, is: is it true?

I'm pretty dubious, frankly.  Lovecraft himself is an interesting case-in-point; he wrote of some pretty terrifying supernatural entities, immersing himself in the evils of Yog-Sothoth and Cthulhu and Tsathoggua and the rest of the gang for his entire adult life, yet remained a staunch skeptic the whole time.  In fact, he once wrote to a fan who claimed to have had scary paranormal experiences while wandering in the ruins of the cursed town of Innsmouth, Massachusetts, "I rather hate to point this out, but Innsmouth doesn't exist.  I know this for certain, you see, because I made it up."

[Image licensed under the Creative Commons BenduKiwi, Cthulhu and R'lyeh, CC BY-SA 3.0]

On the other hand, it's been pointed out more than once that Lovecraft died at the young age of 46, something that causes much eyebrow-waggling amongst people who think he might have been taken out by the Deep Ones for giving away too many of their secrets.  (In fact, I riffed on that theme in my short story "She Sells Seashells," one of a handful of quasi-Lovecraftian things I've written.)

On yet another hand (I've got three hands), I wonder about my own case, given that I not only write paranormal fiction, I've been delving into paranormal claims in this blog for nine years now -- and a lot longer than that, if you count an ongoing fascination with the occult that runs back into my long-past teenage years.  And I have never -- not once -- had an experience of the paranormal.  Even considering my immersing myself in books and legends and spooky claims, and being (not to put too fine a point on it) a suggestible type who has way too vivid an imagination for his own good, my life has been remarkably specter-free.

So I think Redfern's claim really boils down to dart-thrower's bias.  I'd easily believe that since he and his friends live in the world of supernatural claims, they're more likely to notice any odd stuff that happens, and (once noticed) interpret it as a manifestation of the paranormal.  Whether any of those things are actually examples of what he calls "unrelenting supernatural attack," I doubt.

However, if I'm visited today by a creature from the Shadow World, I suppose it'll serve me right.  It's a good opportunity, because my wife is out of town, and I'm alone in the house with two dogs who are (frankly) completely useless as watchdogs.  One is laid back to the point that I sometimes check her pulse to make sure she's still alive, and the other (a pit bull mix who looks threatening) is such a big coward that he's been known to hide behind me when confronted by something scary, such as a chipmunk.  So I'll issue a challenge to any spirits or monsters or whatnot that read Skeptophilia (hey, it could happen) -- bring it on.  I'll be waiting.

As the old lady said in Monty Python and the Search for the Holy Grail, "Go ahead, do your worst."

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

This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

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

Windows of the soul

Yesterday I ran into a study in the journal Personality and Social Psychology Bulletin that strikes me as being substantially correct even though I have some misgivings about the general methodology.

The paper is called "Your Soul Spills Out: The Creative Act Feels Self-Disclosing," by Jack A. Goncalo and Joshua H. Katz, of the University of Illinois at Urbana-Champaign.  The researchers were looking into whether creative ideas would reveal the "true personality" (whatever that actually means), and if so, might clue in the listener/reader in ways that were never intended.

The study consisted of five separate experiments, with a total of over twelve hundred test subjects.  The first three experiments focused on whether a person asked to generate creative ideas (one of the ones used was "come up with five new scents for candles") felt afterward as if the researchers had a better lens into the person's core personality than they did before.  The fourth experiment looked at whether narrowing the range of choices (e.g., "name five new fruit scents for candles" rather than "name five new scents of any type for candles"), and the fifth asked the participants to rank their ideas on a scale of "creative" to "conventional," and looked at whether there was a correlation between that and the degree to which they felt they'd revealed themselves.

The authors write:

Breaking from the typical focus on the antecedents of creativity, we investigate the psychological and interpersonal consequences of being creative.  Across five experiments, we find that generating creative ideas is revealing of the self and thus prompts the perception of self-disclosure.  Individuals respond to the expectation to be creative with greater self-focus—adopting their own idiosyncratic perspective on the task and thinking about their own personal preferences and experiences in connection to the problem.  Because creative ideas derived from self-focused attention are uniquely personal, the act of sharing a creative idea is, in turn, perceived to be revealing of the self.  Finally, an interactive dyad study shows that sharing creative ideas makes partners more confident in the accuracy of judgments they made about each other’s personality.

On the one hand, this strikes me as kind of a "duh."  A person who comes up with candle scents like "vanilla chai" and "ocean breeze" is not the same type as someone who would come up with "dog farts" and "zombie breath."  Thinking outside the box (in this case way outside the box) does tell you something about a person's personality.

[Image licensed under the Creative Commons LaurMG, Glass creativity finalrevis, CC BY-SA 3.0]

However, there's the notoriously difficult factor of weighing how close a person's self-assessment is to reality.  We don't see ourselves very accurately, most of the time, which is why Robert Burns quipped, "O, would some power the giftie gi'e us. to see ourselves as others see us; it would from many a blunder free us, and foolish notion."

So a person saying she thinks her creative ideas revealed her soul, and those ideas actually telling us something about her we didn't already know, aren't the same thing at all.  Even when we're being creative, we show the parts of us we choose to, and suppress other parts that we'd rather people not see.

But.  I have more than once stated, "If you want to know me, read my fiction."  I've mentioned before how shy I am in person, which is why there are people I've known for years who don't really have much of a clue what I'm really like.  But a lot of my fiction embodies the things I think are deeply meaningful in life -- relationships, compassion, trust, loyalty, humor, perseverance, respect.  I think if you read a couple of my novels, you'll have a pretty good idea of who I am.

And I know you can sometimes reveal things you didn't intend to.  I related a few months ago how my writing partner, the inimitable Cly Boehs, was entirely unsurprised by my revelation that I was bisexual.  "Every novel you've written," she told me, "has at least one scene with a gorgeous shirtless guy."  And I still remember the student who read my novella House of Mirrors and came up to me with a grin after he'd finished it and said, "You know, you play the unemotional, plain-spoken, pragmatic science teacher at your day job, but deep down you are a complete romantic sap."

What could I do?  I laughed and said, "You figured me out."

So in some ways I agree with the results Goncalo and Katz found.  "The instruction to be creative is very common in organizations but it is not benign," Goncalo said, in an interview in PsyPost.  "In the process of being creative, you rely on your own idiosyncratic point of view and unique preferences, thus making the ideas you share revealing of your true self.  More importantly, other people listen to your ideas and make judgments about you.  We found that when people heard another individual’s creative ideas, they became more confident that their judgments about their personality were accurate.  People are not just judging your ideas, they are making personal judgments about you based on your ideas."

Creativity is a means for self-expression, and as such of course it reveals something about a person.  And also of course, people who see your creative ideas are going to judge them -- and you.  But I seriously doubt that an analysis of a person's creativity would tell you anything you couldn't have found out in other ways, and it's hard to see how it gives you a bead on the "true self" when there isn't even a good working definition of what that phrase means.

So (anecdotally) I'd say they're right, but I'm not really sure where it gets us.  Personality is complex, and our behaviors combine both conscious and unconscious efforts to show some features and hide others.  But we already kind of knew that.

Anyway, I'm off to work on my work-in-progress, which is a Lovecraftian sort of story about a guy trying to rescue his missing twin brother from a subterranean death-cult.  Make of it what you will.

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

This week's Skeptophilia book-of-the-week is from an author who has been a polarizing figure for quite some time; the British evolutionary biologist Richard Dawkins.  Dawkins has long been an unapologetic critic of religion, and in fact some years ago wrote a book called The God Delusion that caused thermonuclear-level rage amongst the Religious Right.

But the fact remains that he is a passionate, lucid, and articulate exponent of the theory of evolution, independent of any of his other views.  This week's book recommendation is his wonderful The Greatest Show on Earth, which lays out the evidence for biological evolution in a methodical fashion, in terminology accessible to a layperson, in such a way that I can't conceive how you'd argue against it.  Wherever you fall on the spectrum of attitudes toward evolution (and whatever else you might think of Dawkins), you should read this book.  It's brilliant -- and there's something eye-opening on every page.

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