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):

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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!

16 Responses to Colbert Deconstructs Pop Music, Finds Mathematical Nerdiness Within

  1. howard61 says:

    I think you would be doing yourself a very big favor if you totally banned the use of the word “deconstruct” from your vocabulary.

    Almost every time I see that word used, it seems to mean “analyze”. If you actually mean “analyze”, why not use that word?

    The word “deconstruct” actually has NO meaning, at least, no agreed-upon meaning. It was first used by the crackpot “philosopher” Jacques Derrida, who famously (? infamously?) refused to define it.


    • Jesse Galef says:

      Fair point – I haven’t thought about the word ‘deconstruct’ all that explicitly. I DO think that the connotations are better in this context than ‘analyze’ for exactly the reason you point out – Colbert is finding new meanings that the artists didn’t intend, using the literal words to launch in an entirely new direction.

      That seems – though I’m no expert on postmodernism – like what many postmodernists are doing when they “deconstruct” a work of art.

    • Havea Niceday says:

      Deconstructionism is a school of literary analysis. It says that two diametrically opposed statements both hold elements of truth, which in turn lead to a greater, more fundamental truth. Deconstruct means to take apart assumptions and analyze those specific assumptions rather than their result.

      Discussion of “agreed upon” meaning is very dangerous, because you haven’t stated who must agree. I agree with the author, does that make it agreed upon? If anyone disagrees, does that make it not disagreed upon?

      It’s generally wise to avoid using ad-hominem attacks such as “crackpot”. It’s safer to say “discredited by his/her peers” or “folk philosopher”.

      Have a nice day!

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  4. howard61 says:

    I enjoy reading the emails I get from MoD, and your web site, but I think you would be doing yourself a very big favor if you totally banned the use of the word “deconstruct” from your vocabulary.

    Almost every time I see that word used, it seems to mean “analyze”. If you actually mean “analyze”, why not use that word?

    The word “deconstruct” actually has NO meaning, at least, no agreed-upon meaning. It was first used by the crackpot “philosopher” Jacques Derrida, who famously (? infamously?) refused to define it.


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  6. Larry says:

    Derrida is considered a crackpot not least because he challenged cherished notions of truth.

    He thought that every text contains inconsistencies and self-contradictions, or what he called instability.

    He also thought that each and every reader is likely to take a different meaning from any given text due to his or her personal and intellectual history.

    The method he used to arrive at his conclusions is known as deconstruction, and has been criticized because many feel it ultimately leads to meaninglessness.

    Such ideas are most threatening to those to seek formulaic, systematic or algorithmic approaches to problems in living.

    Problems with such approaches are also made clear by the work of Hume, Ayers and Godel.

    Logic and mathematics are great, but they are the map of the terrain, not the terrain itself.

  7. Max says:

    I’m the most humble person in the world.

  8. Max says:

    Let us deconstruct the word “deconstruct”…

  9. Jeffrey says:

    I understand that I know nothing, therefore I know something.

    In the original context, I believe Plato was making a reasonable point, namely that acknowledging your ignorance of a particular topic is better than to be ignorant of your ignorance. But the same cannot necessarily be said for people who parrot their approximation of his idea.

  10. J. Goard says:

    There seems to be implicit here that the English construction [P is what makes Q] stands for the logical entailment P => Q. Really?

    “Vodka contains a high percentage of ethanol. That’s what makes it flammable.”

    “Grandma’s cookies have extra chocolate chips. That’s what makes them delicious.”

    Yet, if the vodka were in an oxygen-poor environment, it would still contain a high percentage of alcohol, but not be flammable. If grandma’s cookies continued to contain extra chocolate chips, but she also started adding garlic, they would no longer be delicious.

    Along the lines of Goodman’s analysis in “Fact, Fiction and Forecast”, we seem to need an understanding of causality that makes reference to relevantly similar possible worlds, rather than pure logical entailment.

  11. Jesse, You might “Satire and Dissent” by Amber Day. It’s about Stewart and Colbert among others.

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