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!

Basking in Reflected Glory: Football, Self Esteem, and Pronoun Choice

Sports fan? This might describe you. Not a sports fan? This will help you make fun of the sports fans! Everyone else who just doesn’t care either way, here’s a neat psychology study for you.

You’ve probably noticed that when a team wins, their fans are more likely to wear their jerseys around. Since the New York Giants beat the New England Patriots 21-17 in the Superbowl last night, I’ve seen a bunch of proud Giants fans gloating on Facebook. But it’s not just the bragging, it’s the way they brag.

It turns out that sports fans will actually change the words they use based on whether their favorite team won or lost. Once again, I turn to the impeccable Mitchell and Webb to illustrate the tendency:



I love that retort: “Remember when we were chasing the Nazis in Raiders of the Lost Ark?” Movies don’t inspire the same tribal attitudes that sports do, but Mitchell’s rant does highlight the absurdity of using the word “we” in this context.

It’s not just anecdotal. Mitchell and Webb are describing an actual social phenomenon: Even if they have nothing to do with the results, fans are more likely to use “we” pronouns when their favorite team is doing well.

Robert Cialdini called it Basking in Reflected Glory. In an attempt to gain social standing, we try to associate ourselves with success.

Basking in Reflected Glory

Conducting a creative study (pdf), Cialdini and his researchers called college students and asked them how their school’s team had done in a particular game. When describing victories, 32% of the students referred to the team as “we” – “We won,” “We beat them,” etc. In contrast, only 18% used the word “we” when talking about their school’s team losing.

Makes sense, right? People wanted to be seen as part of a winning group. But it gets better.

Cialdini added a twist to his study: before asking about the football game, he asked the students six quick, factual questions. Regardless of their answers, they were either told that they’d done well (gotten five correct) or poorly (gotten only one out of six correct). He hypothesized that the students who were told they’d failed would be more likely to grasp at straws to regain social status.

When the numbers were separated out, the tendency was clear: Almost all the increase in “we” pronouns was from the students who lost prestige by being told they’d failed.

Likelihood of using “we” pronoun(%)

“Succeeded” on Test “Failed” on Test Mean
Describing Win 24% (11/45) 40% (16/40) 32% (27/85)
Describing Loss 22% (9/41) 14% (6/42) 18% (15/83)

Students who were given a dose of self-esteem didn’t change their language based on whether their team won or lost.

But students who felt embarrassed? They were much more likely to latch onto a winning team and distance themselves from a losing team.

So you know all those Giants fans posting status updates on Facebook saying “We won!” or “We’re number one”? Ask them why their self-esteem is so low that they need to Bask in Reflected Glory.

That’ll show ‘em.

[Title changed after posting from "How Football Scores Actually Change The Way We Talk"]

Nerdy Romance Mistakes

As much as I hate the stereotype that nerds are hopeless at romance (and social life in general) today’s SMBC comic cracked me up:

At first it seemed like an example of the conjunction fallacy, in which people think the general conditions are less likely than a more specific example of the conditions.  (That’s mathematically impossible.)  But the comic isn’t about probability, it’s about utility.  And you know, it’s not just a GIVEN that owning the world has net positive utility!  It would be extraordinarily time-consuming to rule the world.

Yeah, I know, it’s a stretch.

And I’m forced to plead guilty to a similar situation.  A number of years back, a girl I was dating told me she worried sometimes that she liked me more than I liked her.  My unthinking response at the time was, “Well, it’s unlikely to be exactly equal.  Someone has to like the other more.”

I’ve gotten much better since then.

If only I’d heard of the Maxims of Conversation earlier:

Quantity:

  • Say no less than the conversation requires.
  • Say no more than the conversation requires.

Quality:

  • Don’t say what you believe to be false.
  • Don’t say things for which you lack evidence.

Manner:

  • Don’t be obscure.
  • Don’t be ambiguous.
  • Be brief.
  • Be orderly.

Relevance:

  • Be relevant.

We tend to assume that people are following these maxims in conversation.  While my reply is true in a strict sense, it implied a whole lot more.

Ah well, live and learn.

Self-Referential Haikus and Nerdy Math Shirts

I don’t always buy t-shirts. But when I do, I tend to make them really nerdy ones. ThinkGeek is a good source, but Snorg Tees might be my new favorite.

Self-reference, like this sentence, is hilarious.

But you can never have just one haiku. When they get out in public, they have a tendency to spawn as people are inspired to create their own. Here was my contribution to the arts:

Haiku are easy
but the ones I write devolve
into self-reference.

To which a friend responded,

Reference. Syllables?
If reference is two, I’m good.
Three? Then I am screwed.

If self-reference isn’t your cup of tea, SnorgTees also has a couple great math shirts:

That’s right: I keep it real. After I posted the picture to Facebook, a cousin commented:

It might be real…but it’s not natural.

and my dad chimed in with the brilliant:

Aren’t you the negative one.

I love my family and friends.

Video Short: Sentient Meat

One of my earlier posts quoted the Terry Bisson “Sentient Meat” short story – well, it turns out that there’s a film short based on the story!

Great exchange:

And the ones who have been aboard our vessels, the ones you have probed? You’re sure they won’t remember?

They’ll be considered crackpots if they do. We went into their heads and smoothed out their meat so that we’re just a dream to them.

A dream to meat! How strangely appropriate, that we should be meat’s dream.

I liked the feeling of surrealism surrounding something we take for granted every day: we are thinking, loving, dreaming meat.

And yes, that IS Ben Baily of Cash Cab.

When Literal Honesty Goes Awry

When is it NOT appropriate to bluntly speak the truth? We’ve all heard someone be insulting and resort to the defense of “Well, it’s true!” Even boring, inoffensive facts can become offensive if brought up inartfully. I think this is a perfect example, illustrated by the hilarious comedy team of David Mitchell and Robert Webb:

I mean, technically it’s true. The literal fact that “anyone we know is unlikely to be the most attractive person on earth” shouldn’t hurt feelings. Nobody should think that much of themselves!

…And yet, it’s rude to say. Why?

I think that’s because nobody took Robert’s original statement “this is the most beautiful woman in the world” at its face value. It violated the maxim of quality – the literal meaning was clearly false so people look for alternative interpretations (“She’s beautiful and I love her” or “She’s very attractive in a combination of ways”).

Since nobody took it seriously at face value, challenges to the claim are perceived as challenging the alternate interpretations rather than the literal meaning. The very decision to call attention to it makes a statement. Why would David be so motivated to discuss her beauty unless he strenuously disagreed with her beauty? So, in essence, he’s saying “No, she’s not very beautiful.”

Yes, David’s literal content is true: she’s not the most beautiful person in the world. But so much of our reaction to a statement is is really a reaction to its implied meaning, and it’s tough to get around that. Initial gut reactions can be powerful.

But it’s possible to do it right. I love having the opportunity to share the awesome and incredible Tim Minchin song If I Didn’t Have You:

Somehow, when Tim does it, the honest approach works better. People often claim that they DO have a soul mate, so it isn’t automatically interpreted as a figure of speech for something more casual.

But it’s particularly important the way he addresses the literal meanings. Compare “I don’t think you’re special. I mean, I think you’re special but not off the charts” with “I don’t think you’re special. I mean, I think you’re special but you fall within a bell-curve.” It’s a strange enough statement to make people think about it harder and realize he’s not being snide.

I found myself thinking of something Steven Pinker wrote in The Stuff of Thought:

The incongruity in a fresh literary metaphor is another ingredient that gives it its pungency. The listener resolves the incongruity soon enough by spotting the underlying similarity, but the initial double take and subsequent brainwork conveys something in addition. It implies that the similarity is not apparent in the humdrum course of everyday life, and that the author is presenting real news in forcing it upon the listener’s attention.

Pinker was writing about using new metaphors to emphasize non-literal meaning, but it works the other way as well. Fresh phrasings – in this case gloriously nerdy ones – make listeners pay more attention to parsing the intended meaning, metaphorical or literal.

If you’re worried about being misinterpreted, try a creative way of expressing the same thought. Protesting “But I was telling the truth!” won’t always be enough.

Oh Sidney, you wag

A linguistics professor lecturing at Oxford explained that although there are many languages in which a double negative implies a positive, there is no language in which a double positive implies a negative.

He was interrupted by legendary philosopher Sidney Morgenbesser, who piped up dismissively from the audience, “Yeah, yeah.”

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