What Would a Rational Gryffindor Read?

In the Harry Potter world, Ravenclaws are known for being the smart ones. That’s their thing. In fact, that was really all they were known for. In the books, each house could be boiled down to one or two words: Gryffindors are brave, Ravenclaws are smart, Slytherins are evil and/or racist, and Hufflepuffs are pathetic loyal. (Giving rise to this hilarious Second City mockery.)

But while reading Harry Potter and the Methods of Rationality, I realized that there’s actually quite a lot of potential for interesting reading in each house. Ravenclaws would be interested in philosophy of mind, cognitive science, and mathematics; Gryffindors in combat, ethics, and democracy; Slytherins in persuasion, rhetoric, and political machination; and Hufflepuffs in productivity, happiness, and the game theory of cooperation.

And so, after much thought, I found myself knee-deep in my books recreating what a rationalist from each house would have on his or her shelf. I tried to match the mood as well as the content. Here they are in the appropriate proportions for a Facebook cover image so that you can display your pride both in rationality and in your chosen house (click to see each image larger, with a book list on the left):

Rationality Ravenclaw Library

Rationality Gryffindor Library

Rationality Slytherin Library

Rationality Hufflepuff Library

What do you think? I’m always open to book recommendations and suggestions for good fits. Which bookshelf fits you best? What would you add?

Colbert Deconstructs Pop Music, Finds Mathematical Nerdiness Within

Stephen Colbert channeling Kurt Godel

And here I thought I didn’t like pop music. Turns out I just hadn’t found the songs that invoke questions about the foundations of logic and mathematics. Fortunately, Stephen Colbert brings our attention to the fascinating – and paradoxical! – pop song “That’s What Makes You Beautiful” by One Direction. Watch Stephen do his thing deconstructing the lyrics with glorious nerdy precision before we take it even further (the good part starts at 1:54 or so):

For those of you who can’t watch the video, here’s the nerdy part, hastily transcribed:

Their song “That’s What Makes You Beautiful” isn’t just catchy, it has a great message. “You don’t know you’re beautiful. That’s what makes you beautiful.”

First of all: great dating advice. Remember girls, low self esteem – very attractive to men. Guys always go for the low hanging fruit, easy pickings.

Second: the lyrics are incredibly complex! You see, the boys are singing “You don’t know you’re beautiful, that’s what makes you beautiful.” But they’ve just told the girl she’s beautiful. So since she now knows it, she’s no longer beautiful!

But – stick with me, stick with me, oh it goes deeper! – but she’s listening to the song, too. So she knows she’s not beautiful. Therefore, following the syllogism of the song, she’s instantly beautiful again!

It’s like an infinite fractal recursion, a flickering quantum state of both hot and not. I mean, this lyric as iterated algorithm could lead to a whole new musical genre. I call it Mobius pop, which would include One Direction and of course the rapper MC Escher.

They say the way to a man’s heart is through his stomach but honestly, talking about recursion, fractals, and flickering quantum states does far more to win my love.  We can find intellectual stimulation in anything!

And there’s more – we can go nerdier!

Stick With Me, Stick With Me, Oh It Goes Deeper

Let’s analyze the dilemma a bit further:

  1. She can’t KNOW she’s beautiful because, as Stephen points out, that leads to a logical contradiction – she would no longer be beautiful.
  2. She can’t KNOW that she isn’t beautiful, because that also leads to a logical contradiction – she would be beautiful again.
  3. It’s impossible for the girl to know that she is or isn’t beautiful, so she has to be uncertain – not knowing either way.
  4. This uncertainty satisfies the requirements: she doesn’t know that she’s beautiful, therefore, she’s definitely beautiful and can’t know it.

It turns out she’s not in a flickering state of hot and not, she’s perpetually hot – but she cannot possibly know it without logical contradiction! From an external perspective, we can recognize it as true. From within her own mind, she can’t – even following the same steps. How weird is that?

Then it hit me: the song lyrics are a great example of a Gödel sentence!

Gödel sentences, from Kurt Gödel’s famous Incompleteness Theorems, are the statements which are true but unprovable within the system.  Gödel demonstrated that every set of mathematical axioms complex enough to stand as a foundation for arithmetic will contain at least one of these statements: something that is obviously true from an outside perspective, but isn’t true by virtue of the axioms.  (He found a way to coherently encode “The axioms do not prove this sentence to be true.”)  This raises the question: what makes a mathematical statement true if not the fact that it can be derived from the axioms?

Gödel’s findings rocked the world of mathematics and have had implications on the philosophy of mind, raising questions like:

  • What does it mean to hold a belief as true?
  • What are our minds doing when we make the leap of insight (if insight it is) that identifies a Gödel sentences as true?
  • How does this set us apart from the algorithmic computers, which are plagued by their own version of Incompleteness, the Halting Problem?

I had no idea pop music was so intelligent!

Was the boy band comparing her, not to a summer’s day, but a turing-complete computer?  Were they glorifying their listeners by reminding us that, according to some interpretations of Incompleteness Theory, we’re more than algorithmic machines?  Were they making a profound statement about mind/matter dualism?

I don’t know, but apparently I should turn on the radio more often.

[For related reading, see various analyses of Mims’ “This is Why I’m Hot”]


As they say in the Sirius Cybernetics Corporation: Share and Enjoy!

Time Travel Art: Fantastic Video

It takes a lot for art to excite me.  But when I stumble upon a time-travel-themed YouTube video inspired by Dr. Who and Edward Gorey… I feel the urge to share it with everyone.  Yes, it’s every bit as cool as it sounds. The video is by ‘MaryDoodles’, who produces time-lapse videos of herself painting – but this time she found a way to work time-travel into the delivery as well as the content. You’ll just have to watch it:

I found myself hitting ‘replay’ over and over, figuring out how the hell she did it, spotting new things I’d missed (did you see all the things tying the scenes together?  How about the TARDIS?), and trying to piece the plot together. Alas, she’s not giving hints about the story she intended:

The discussions on Youtube are quite fun to watch as people try and piece together the order of events and what happened. I’ve decided to hold my tongue on this matter. There is an intentional order to the story but the fact that other people are seeing different orders of events, character relations and catalysts I figured I’d just leave my opinions out of it. It’s almost like a personality test when you hear someone’s take on the video. There are those that take the “glass is half empty” approach while others say the “glass is half full”. Happy ending? Tragic ending?”

I’m still making up my mind. Curiosity is a wonderful emotion, and I think the ambiguity is actually a positive factor.

Stereotypical koans take the ambiguity too far – “What is the sound of one hand clapping?” is just a broadside assault on semantics – but this is pleasantly confusing to me, like a puzzle.

My Little Pony: Reality is Magic!

(Cross-posted at 3 Quarks Daily)

You probably won’t be very surprised to hear that someone decided to reboot the classic 80’s My Little Pony cartoon based on a line of popular pony toys. After all, sequels and shout-outs to familiar brands have become the foundation of the entertainment industry. The new ‘n improved cartoon, called My Little Pony: Friendship is Magic, follows a nerdy intellectual pony named Twilight Sparkle, who learns about the magic of friendship through her adventures with the other ponies in Ponyville.

But you might be surprised to learn that My Little Pony: Friendship is Magic’s biggest accolades have come not from its target audience of little girls and their families, but from a fervent adult fanbase. I first heard of My Little Pony: Friendship is Magic from one of my favorite sources of intelligent pop culture criticism, The Onion’s AV Club, which gave the show an enthusiastic review last year. (I had my suspicions at first that the AV Club’s enthusiasm was meant to be ironic, but they insisted that the show wore down their defenses, and that it was “legitimately entertaining and lots of fun.” So either their appreciation of My Little Pony: Friendship is Magic is genuine, or irony has gotten way more poker-faced than I realized.)

And you might be even more taken aback to learn that many, if not most, of those adult My Little Pony: Friendship is Magic fans are men and that they’ve even coined a name for themselves: “Bronies.” At least, I was taken aback. In fact, my curiosity was sufficiently piqued that I contacted Purple Tinker, the person in charge of organizing the bronies’ seasonal convention in New York City. Purple Tinker was friendly and helpful, saying that he had read about my work in the skeptic/rationalist communities, and commended me as only a brony could: “Bravo – that’s very Twilight Sparkle of you!”

But when I finally sat down and watched the show, I realized that while Purple Tinker may be skeptic-friendly, the show he loves is not. The episode I watched, “Feeling Pinkie Keen,” centers on a pony named Pinkie Pie, who interprets the twitches in her tail and the itches on her flank as omens of some impending catastrophe, big or small. “Something’s going to fall!” Pinkie Pie shrieks, a few beats before Twilight Sparkle accidentally stumbles into a ditch. The other ponies accept her premonitions unquestioningly, but empirically-minded Twilight Sparkle is certain that Pinkie Pie’s successes are either a hoax or a coincidence. She’s detemined to get to the bottom of the matter, shadowing Pinkie Pie in secret to observe whether the premonitions disappear when there’s no appreciative audience around, and hooking Pinkie Pie up to what appears to be a makeshift MRI machine which Twilight Sparkle apparently has lying around her house, to see whether the premonitions are accompanied by any unusual brain activity.

Meanwhile, Twilight Sparkle is being more than a little snotty about how sure she is that she’s right, and how she just can’t wait to see the look on Pinkie Pie’s face when Pinkie Pie gets proven wrong. Which, of course, is intended to make it all the more enjoyable to the audience when — spoiler alert! — Twilight Sparkle’s investigations yield no answers, and Pinkie Pie’s premonitions just keep coming true. Finally, Twilight Sparkle admits defeat: “I’ve learned that there are some things you just can’t explain. But that doesn’t mean they’re not true. You just have to choose to believe.”

Nooo, Twilight Sparkle, no! You are a disgrace to empirical ponies everywhere. And I’m not saying that because Twilight Sparkle “gave in” and concluded that Pinkie Pie’s premonitions were real. After all, sometimes it is reasonable to conclude that an amazing new phenomenon is more likely to be real than a hoax, or a coincidence, or an exaggeration, etc. It depends on the strength of the evidence. Rather, I’m objecting to the fact that Twilight Sparkle seems to think that because she was unable to figure out how premonitions worked, that therefore science has failed.

Twilight Sparkle is an example of a Straw Vulcan, a character who supposedly represents the height of rationality and logic, but who ends up looking like a fool compared to other, less rational characters. That’s because the Straw Vulcan brand of rationality isn’t real rationality. It’s a gimpy caricature, crafted that way either because the writers want to make rationality look bad, or because they genuinely think that’s what rationality looks like. In a talk I gave at this year’s Skepticon IV conference, I described some characteristic traits of a Straw Vulcan, such as an inability to enjoy life or feel emotions, and an unwillingness to make any decisions without all the information. Now I can add another trait to my list, thanks to Twilight Sparkle: the attitude that if we can’t figure out the explanation, then there isn’t one.

Do you think it’s possible that anyone missed the anti-inquiry message?  Hard to imagine, given the fact that the skeptical pony seems mainly motivated by a desire to prove other people wrong and gloat in their faces, and given her newly-humbled admission that “sometimes you have to just choose to believe.” But just in case there was anyone in the audience who didn’t get it yet, the writers also included a scene in which Twilight Sparkle is only able to escape from a monster by jumping across a chasm – and she’s scared, but the other ponies urge her on by crying out, “Twilight Sparkle, take a leap of faith!”

And yes, of course, My Little Pony: Friendship is Magic is “just” a kids’ cartoon, and I can understand why people might be tempted to roll their eyes at me for taking its message seriously. I don’t know to what extent children internalize the messages of the movies, TV, books, and other media they consume. But I do know that there are plenty of messages that we, as a society, would rightfully object to if we found them in a kids’ cartoon – imagine if one of the ponies played dumb to win the favors of a boy-pony and then they both lived happily ever after. Or if an episode ended with Twilight Sparkle chirping, “I’ve learned you should always do whatever it takes to impress the cool ponies!” So why aren’t we just as intolerant of a show that tells kids: “You can either be an obnoxious skeptic, or you can stop asking questions and just have faith”?

Review: The Book of Mormon

(Re-posted with permission from my article in Issue 56 of The Philosopher’s Magazine)

Even if you’ve never watched a single episode of South Park, you’re probably aware that the show’s creators, Trey Parker and Matt Stone, love nothing more than a good bout of sacred cow tipping. Show me an ideology, political, religious or otherwise, and I’ll show you an episode of South Park that lampoons it with the show’s trademark blend of incisive satire and potty humour. So it was surprising that South Park’s terrible twosome wound up creating a smash- hit Broadway musical, which they have been describing, in interviews, as being pro-faith.

Well, the “smash-hit” part isn’t surprising. The Book of Mormon pulls off the impressive trick of winking at the clichés of musical theatre and embracing them at the same time. (After all, the clichés are clichés for a reason – they work.) The story follows two young Mormon men paired together for their mission to Uganda: Kevin, who’s used to being the golden boy and needs to learn that everything’s not always about him, and Arnold, a hapless schmuck who needs to learn some self-confidence. They’re an odd couple and, like all odd couples thrown together under unusual circumstances, they’re going to have to learn to get along. There’s also a sweet Ugandan ingénue, a villainous warlord threatening her village, and a whole lot of really catchy songs. It’s no wonder the musical garnered nine Tony awards this year, including Best Musical, and that it’s been selling out its shows since it opened in previews in February.

But to hear Parker and Stone refer to The Book of Mormon as “pro-faith” was surprising, especially given how often they poke fun at Mormonism. Mormon beliefs can seem so ridiculous to outsiders, in fact, that Parker and Stone wisely realise they don’t need to do much active mocking – instead, they simply step back and let the scripture speak for itself. “I believe,” one missionary warbles in a climactic number reaffirming his commitment to his faith, “that God lives on a planet called ‘Kolob’! And I believe that in 1978, God changed his mind about black people!” With raw material like this, parody is both unnecessary and impossible.

And it’s not just Mormonism that gets skewered. It’s also the self-images of all believers who like to see themselves, and their motivations, as more saintly than they really are. Against a back- drop of war, poverty and disease, one missionary wonders, “God, why do you let bad things happen?” and then adds what is, for many people, the true concern: “More to the point, why do you let bad things happen to me?” There’s only one thing Parker and Stone enjoy sinking their talons into more than absurdity, and that’s hypocrisy.

So in what sense is The Book of Mormon “pro- faith?” Well, it’s affectionate in its portrayal of Mormons as people, most of whom come off as well-meaning, if goofy and often naive. Parker and Stone have made no secret of the fact that they find Mormons just too gosh-darned nice to dislike. But what they’re mainly referring to when they call their musical “pro-faith” is the message it sends the audience home with: that religion can be a powerful and inspiring force for good, as long as you don’t interpret scripture too strictly.

By the end of The Book of Mormon, Africans and missionaries alike are united together in a big happy posse that preaches love, joy, hope and making the world a better place. Having learned by now that it’s more important to help people than to rigidly adhere to dogma, Kevin sings, “We are still Latter Day Saints, all of us. Even if we change some things, or we break the rules, or we have complete doubt that God exists. We can still all work together and make this our paradise planet.”

That’s an appealing sentiment, especially to the sort of theatregoer who prides himself on being progressive and tolerant. It means we can promote all the values we cherish – happiness, freedom, human rights and so on – without ever having to take an unpopular anti-religion stand. But is it plausible? How, exactly, can religion make the world a better place?

I don’t know and, apparently, neither does The Book of Mormon. The central confusion you’ll notice in the musical is that it keeps conflating two very different kinds of “faith”. One could be called “figurative faith”, the warm and fuzzy kind that emerges at the end of the show, which is explicitly about bettering the world but seems to be faith in name only, as it doesn’t involve any actual belief in anything. “What happens when we’re dead? Who cares! We shouldn’t think that far ahead. The only latter day that matters is tomorrow,” the villagers sing. Once you strip away God, and an afterlife, and the requirement of belief in particular dogma, it’s not clear that what’s left bears any resemblance to religion anymore. With its progressive values and its emphasis on the here-and-now rather than the hereafter, it’s basically just humanism.

The other kind of faith in The Book of Mormon is literal faith, but for the most part, it doesn’t actually help anyone. Ugandan sweet- heart Nabalungi believes in salvation in earnest – she’s under the impression that becoming Mormon means she’s going to be transported out of her miserable life to a paradise called “Salt Lake City”, which she imagines must have huts with gold-thatched roofs and “a Red Cross on every corner with all the flour you can eat!” she sings rapturously. But she ends up crushed when she eventually learns that, no, she doesn’t get to leave Uganda after all. (“Of course, Salt Lake City’s only a metaphor,” her fellow tribe members inform her, apparently in figurative faith mode at that point.)

To be fair, there is one example of the power of literal faith in The Book of Mormon. When a villager announces his plans to circumcise his own daughter, and another is about to rape an infant in an attempt to cure himself of AIDS, Arnold manages to stop them by inventing some new scripture for the occasion. “And the Lord said, ‘If you lay with an infant, you shall burn in the fiery pits of Mordor,’” he “reads” from the Bible. (Being a science fiction and fantasy nerd, and having slept through most of Sunday school, Arnold falls back on what he knows.) So I suppose that counts as a point in favour of faith’s power to help the world, albeit conditional on the bleak premise that the only way to get people to stop raping babies and mutilating women is to threaten them with Hell … or Mordor.

Of course, the fact that The Book of Mormon’s views on faith are less than fully coherent doesn’t detract much from the pleasures of its tart- tongued satire, story, and songs. There are just a handful of moments that might raise a philosopher’s eyebrow, such as when everyone sings, in the exuberant final number, “So if you’re sad, put your hands together and pray, that tomorrow’s gonna be a Latter Day. And then it probably will be a Latter Day!” It almost feels churlish to ask “Wait, how does that work?” when everyone onstage is having such a good time singing about joy and peace and brotherhood; nevertheless, one does wonder. Maybe that will be covered in the sequel.

Lies and Debunked Legends about the Golden Ratio

In my eyes, there’s a general pecking order for named mathematical constants. Pi is at the top, e gets a good amount of attention, and Tau, like a third-party candidate, sits by itself on the fringes while its supporters tell anyone who’ll listen that it’s a credible alternative to Pi. But somewhere in the middle is Phi, also known as the Golden Ratio. It’s no superstar, but it gets its fair share of credit in geometry and culture.

I was first introduced to Phi as a kid by watching the charming video Donald in Mathmagic Land. One of the things I remembered over the years is that the Greeks used the Golden Ratio in their paintings and architecture, particularly the Parthenon. Thanks to the power of the internet, I can share this piece of my childhood with you:

How brilliant and advanced of the Greeks, right? But there’s one problem…

It’s probably not true. My faith was first shaken reading Keith Devlin’s The Unfinished Game, where he entertained a quick digression:

Two other beliefs about this particular number [Phi] are often mentioned in magazines and books: that the ancient Greeks believed it was the proportion of the rectangle the eye finds most pleasing and that they accordingly incorporated the rectangle in many of their buildings, including the famous Parthenon. These two equally persistent beliefs are likewise assuredly false and, in any case, are completely without any evidence. For one thing, tests have shown that human beings who claim to have a preference at all vary in the rectangle they find most pleasing, both from person to person and often the same person in different circumstances. Also, since the golden ratio is actually not a ratio of two whole numbers, it is impossible to construct (by measurement) a rectangle having that proportion, even in theory.

What?! Donald, I trusted you! It was tempting to tell myself that the Greeks could have found ways to approximate the ratio, and that this is just one source, and I’ve heard it so many times it must be true, and la la la I don’t want Donald to have lied to me.

But I looked into it a bit more, checking out what Mario Livio had to say about it in his book The Golden Ratio. He acknowledges that it’s a very common belief, but ultimately backed Devlin up:

The appearance of the Golden Ratio in the Parthenon was seriously questioned by University of Maine mathematician George Markowsky in his 1992 College Mathematics Journal article “Misconceptions about the Golden Ratio.” Markowsky first points out that invariably, parts of the Parthenon (e.g. the edges of the pedestal [in a provided figure]) actually fall outside the sketched Golden Rectangle, a fact totally ignored by all the Golden Ratio enthusiasts. More important, the dimensions of the Parthenon vary from source to source, probably because different reference points are used in the measurements… I am not convinced that the Parthenon has anything to do with the Golden Ratio.

So, was the Golden Ratio used in the Parthenon’s design? It is difficult to say for sure… However, this is far less certain than many books would like us to believe and is not particularly well supported by the actual dimensions of the Parthenon. [emphasis mine]

Alas, claims about the Greeks using Phi in their architecture seem overrated. Some sites bring you celebrity gossip, we bring gossip about celebrated mathematical constants. Welcome to Measure of Doubt!

Watching the video again, I can’t tell exactly how they decided where to overlay the Golden Rectangles. How much of the pedestal do we include in the rectangle? How much of the pillar? Does the waist start here, or there? It seems a bit arbitrary, as though we’re experiencing pareidolia and seeing the Golden Rectangle in everything.

Talk about disillusionment.

RS#36: Why should we care about teaching the humanities?

Episode #36 of the Rationally Speaking podcast is out, and this one’s a lively debate between me and Massimo about the value of humanities departments in universities. While I don’t deny the huge amount of enjoyment we get from arts and literature, I express skepticism about many of the typical justifications for requiring humanities courses. Those justifications strike me as either (1) overly vague and subjective (“the humanities make you a complete person”) or (2) making contrived claims about the practical benefits of studying the arts (“the humanities build critical thinking skills”) to which I usually want to reply, “If that’s your goal, there are much more direct ways to pursue it than studying literature.”

Rationally Speaking #36: Why should we care about teaching the humanities?

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