Predicate Logic and Popular Culture (Part 72): AC/DC

Let $N(t)$ be the proposition “ $t$ is at night,” and let $S(t)$ be the proposition “You shook me at time $t$ .” Translate the logical statement

$\forall t (N(t) \Rightarrow S(t))$ .

The straightforward way of translating this into English is, “For all times at night, you shook me.” With a slight change in wording, it’s one of the great rock anthems of the 1980s.

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 71): Wilson Phillips

Let $T(x,t)$ be the proposition “ $x$ will make you want to turn around at time $t$ ,” and let $G(x,t)$ be the proposition “ $x$ will make you want to say goodbye at time $t$ .” Translate the logical statement

$\exists t \exists x (T(x,t) \land G(x,t))$ ,

where the domain for $x$ is all people and the domain for $t$ is all times.

The straightforward way of translating this into English is, “There exists a time and a person so that the person will make you want to turn around and say goodbye.” This matches the first line of the chorus of one of 1990’s biggest hits.

Predicate Logic and Popular Culture (Part 70): Spice Girls

Let $p$ be the proposition “You wanna be my lover,” and let $F(x)$ be the proposition “ $x$ is my friend,” and let $G(x)$ be the proposition “You have to get with $x$ .” Translate the logical statement

$p \Rightarrow \forall x (F(x) \Rightarrow G(x))$ ,

where the domain is all people.

The straightforward way of translating this into English is, “If you wanna be my lover, then you have to get with all of my friends.” This matches the first line of the chorus of one of the biggest hits of the 1990s.

Predicate Logic and Popular Culture (Part 69): Whitney Houston

Let $L(t)$ be the proposition “I will love you at time $t$ .” Translate the logical statement

$\forall t\ge 0 L(t)$ ,

where the domain is all times.

Of course, this is the iconic song by Whitney Houston.

Predicate Logic and Popular Culture (Part 68): Justin Bieber

Let $M(x)$ be the proposition “My momma likes $x$ .” Translate the logical statement

$\lnot M(\hbox{you}) \land \forall x M(x)$ ,

where the domain is all people.

The straightforward way of translating this into English is, “My momma does not like you, and my momma likes everyone.” (An amusing consequence of this syllogism is the conclusion “You are nobody.”) This almost precisely matches the memorable line of the chorus in Justin Bieber’s recent hit song.

Predicate Logic and Popular Culture (Part 67): Janet Jackson

Let $T(x,t)$ be the proposition “I think of $x$ at time $t$ ,” and let $M(x,t)$ be the proposition “ $x$ seems to matter at time $t$ .” Translate the logical statement

$\forall t (T(\hbox{you},t) \Rightarrow \forall x \ne \hbox{you}(\not M(x,t)))$ .

The straightforward way of translating this into English is, “If I think of you at a time, then everything else does not matter at that time.” More lyrically, it’s the first line of the chorus to Janet Jackson first #1 single, released in 1986.

Predicate Logic and Popular Culture (Part 66): West Side Story

Let $L(x,t)$ be the proposition “We find a new way of living at place $x$ and at time $t$ ,” and let $F(x,t)$ be the proposition “We find a way of forgiving at place $x$ and $t$ .” Translate the logical statement

$\exists x \exists t (L(x,t) \land F(x,t))$ .

This matches almost perfectly one of the lines from the classic song “Somewhere” from the musical West Side Story.

Predicate Logic and Popular Culture (Part 65): John Philip Sousa

Let $S(t)$ be the proposition “The Stars and Stripes wave at time $t$ .” Translate the logical statement

$\forall t (S(t))$ .

I tried to think of a fitting example for the Fourth of July, but the best that I could find was the closing line of the chorus of the Stars and Stripes Forever.

Which naturally leads me to this amazing version from the 1970s:

Predicate Logic and Popular Culture (Part 64): Abraham Lincoln

Let $F(x,t)$ be the proposition “You can fool $x$ at time $t$ .” Translate the logical statement

$\exists t_1 \forall x (F(x,t_1)) \land \exists x_1 \forall t(F(x_1,t)) \land \lnot(\forall x \forall t(F(x,t)))$ .

Of course, this is the famous quote commonly attributed to Abraham Lincoln: “You can fool all of the people some of the time, and some of the people all of the time, but you cannot fool all of the people all of the time.”

Predicate Logic and Popular Culture (Part 63): P. T. Barnum

Let $S(x) be the proposition "$ latex x$ is a sucker,” and let $B(x,t)$ be the proposition “ $x$ is born at time t.” Translate the logical statement

$\forall t \exists x (S(x) \land B(x,t))$ .

Naturally, this is the famous quote often attributed to P. T. Barnum: “There’s a sucker born every minute.”