Predicate Logic and Popular Culture (Part 92): Annie Get Your Gun

Let $W(x,y)$ measure how well $x$ can do $y$ . Translate the logical statement

$\forall y (W(\hbox{you},y) < W(\hbox{I},y))$ .

This needs no further introduction:

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 91): The Scarlet Pimpernel

Let $H(x,t)$ be the proposition “ $x$ happens at time $t$ ,” let $V(x)$ be the proposition “ $x$ is a valley,” let $M(x)$ be the proposition “ $x$ is a mountain,” let $S(x,y,t)$ be the proposition “ $y$ must scale $x$ at time $t$ ,” let $W(x)$ be the proposition “ $x$ are perilous waters,” and let $S(x,y,t)$ be the proposition “ $y$ must sail $x$ at time $t$ .” Translate the logical statement

$\forall t \exists x (V(x) \land H(x,t)) \land \forall t \exists x(M(x) \land H(x,t) \land \exists y S(x,y,t))$

$\land \forall t \exists x(W(x) \land H(x,t) \land \exists y S(x,y,t))$ .

This matches the second half of the opening verse of the showstopper “Into The Fire” from the musical The Scarlet Pimpernel.

I also recommend Steve Amerson’s rendition:

Predicate Logic and Popular Culture (Part 90): The Beatles

Let $N(x)$ be the proposition “You need $latex x.” Translate the logical statement

$N(\hbox{love}) \land \forall x (x \ne \hbox{love} \Rightarrow \lnot N(x))$ .

This matches the title of one of the Beatles’ greatest hits.

Predicate Logic and Popular Culture (Part 89): Into the Woods

Let $S(x)$ be the proposition “ $x$ is on your side” and let $A(x)$ be the proposition “ $x$ is alone.” Translate the logical statement

$(\exists x S(x)) \land (\forall x \lnot A(x))$ .

Of course, this matches the last two lines of “No One Is Alone,” which was released as a movie in 2014.

I’m personally partial to Steve Amerson’s rendition of this song:

Predicate Logic and Popular Culture (Part 88): Bob Dylan

Let $H(x)$ be the proposition “You have $x$ ,” let $L(x)$ be the proposition “You have $x$ to lose,” let $p$ be the proposition “You’re invisible now,” and let $S(x)$ be the proposition “ $x$ is a secret to conceal.” Translate the logical statement

$((\forall x \lnot H(x)) \Rightarrow (\forall x \lnot L(x))) \land p \land \forall x (S(x) \Rightarrow \lnot H(x))$ .

This matches the last two lines of the closing verse of this classic from Bob Dylan.

Predicate Logic and Popular Culture (Part 87): Bruce Springsteen

Let $R(x)$ be the proposition “ $x$ needs a place to rest,” let $H(x)$ be the proposition “ $x$ wants to have a home,” and let $A(x)$ be the proposition “ $x$ wants to be alone.” Translate the logical statement

$\forall x (R(x) \land H(x) \land \lnot A(x))$ .

This matches three of the lines in the closing verse of one Bruce Springsteen’s great hits from the 1980s.

Predicate Logic and Popular Culture (Part 86): My Fair Lady

Let $T(t)$ be the proposition “ $t$ is at night” and let $D(t)$ be the proposition “I could have danced at time $t$ .” Translate the logical statement

$\forall t (T(t) \Rightarrow D(t))$ .

This needs no further introduction:

I also really enjoyed this (she made the finals of Britain’s Got Talent in 2009):

Predicate Logic and Popular Culture (Part 85): Three Dog Night

Let $p$ be the proposition “Jeremiah was a bullfrog,” let $q$ be the proposition “Jeremiah was a good friend of mine,” let $W(x)$ be the proposition “ $x$ is a word,” let $S(x,t)$ be the proposition “Jeremiah said $x$ at time $t$ ,” let $U(x,t)$ be the proposition “I understood $x$ at time $t$ ,” let $r$ be the proposition “I helped Jeremiah drink his wine,” let $W(x)$ be the proposition “ $x$ is mighty fine wine,” and let $J(x,t)$ be the proposition “Jeremiah had $x$ at time $t$ .” Translate the logical statement

$p \land q \land \forall x \forall t<0(W(x) \land S(x,t) \Rightarrow \lnot U(x,t)) \land r \land \forall t<0 \exists x(W(x) \land J(x,t))$ ,

where time 0 is now.

Of course, this matches the opening verse of one of the classics of the 1970s.

Predicate Logic and Popular Culture (Part 84): OMD

Let $F(s,t)$ be the proposition “You said at time $s$ that we’d still be friends at time $t$ .” Translate the logical statement

$\forall s<0 \exists t>0 F(s,t)$ .

This matches the last line of the first chorus from “If You Leave.”

For what it’s worth, this was the opening song on the Pretty in Pink soundtrack, which remains for my money the best movie soundtrack ever made.

Predicate Logic and Popular Culture (Part 83): The Sound of Music

Let $C(x,y)$ be the proposition “ $x$ comes from $y$ ,” let $Y(t)$ be the proposition “ $t$ is in my youth or childhood,” let $D(x,t)$ be the proposition “I did $x$ at time $t$ ,” and let $G(x)$ be the proposition “ $x$ is good.” Translate the logical statement

$(\lnot \exists x \forall y \lnot C(x,y)) \Rightarrow \exists x \exists t(Y(t) \land G(x) \land D(x,t))$ .

The straightforward English translation is, “If it’s false that something can come from nothing, then there exists something good that I did in my youth or childhood.” More poetically, it’s the chorus of the great song that Captain Von Trapp and Maria sang before they got married in The Sound of Music.

See also the version with Carrie Underwood from the NBC live special: