Predicate Logic and Popular Culture (Part 204): Billy Joel

Let $T$ be the set of all times, and let $W(t)$ be the proposition “She is a woman to me at time $t$.” Translate the logical statement

$\forall t \in T( W(t))$.

This matches a line from “She’s Always a Woman” by Billy Joel.

Context: 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 203): Bill Withers

Let $P$ be the set of all people, let $T$ be the set of all times, let $P(x,t)$ be the proposition “$x$ has pain at time $t$,” and let $S(x,t)$ be the proposition “$x$ has sorrow at time $t$.” Translate the logical statement

$\forall x \in P( \exists t_1 \in T(P(x,t)) \land \exists t_2 \in T(S(x,t))$.

This matches a line from “Lean on Me.” Note: while I think the translation above matches the intent of the song, a case could be made that, literally rendered, the “there exists” symbols should come first — that there’s a single time that everyone has pain at that one time.

Context: 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.

In honor of her team winning the national championship on Saturday night, I’m reposting this video about Madeleine Gates, who is both a middle blocker for the Stanford women’s volleyball team and also a graduate student in statistics. There aren’t a whole lot of graduate students who play NCAA sports (which would necessarily mean finishing their undergraduate degrees in three years or less), let alone play at an exceptionally high level while also pursuing an advanced degree in a field as demanding as statistics. I really enjoyed watching this.

Here’s the video of championship point from Saturday night. Gates had the final swing.

Predicate Logic and Popular Culture (Part 202): The LEGO Movie

Let $T$ be the set of all things, let $p$ be the proposition “You’re part of a team,” let $A(x)$ be the proposition “$x$ is awesome,” and let $C(x)$ be the proposition “$x$ is cool.” Translate the logical statement

$p \Longrightarrow \forall x in T(A(x) \land C(x))$.

This matches the opening line of “Everything is Awesome!!!” from The LEGO Movie.

Context: 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 201): Hamilton

Let $T$ be the set of all times, let time 0 be now, and let $L(t)$ be the proposition “I like the quiet at time $t$.” Translate the logical statement

$\forall t \in T(t < 0 \longrightarrow \lnot L(t))$.

This matches a line from “It’s Quiet Uptown” from the hit musical Hamilton.

Context: 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 200): Spider-Man

Let $T$ be the set of all times, and let $R(t)$ be the proposition “I will rest at time $t$,” and let $M(t)$ be the proposition “You are unmasked and eliminated at time $t$.” Translate the logical statement

$\forall t \in T(\lnot M(t) \Longrightarrow \lnot R(t))$.

This matches a line by J. Jonas Jameson in the 1990s Spider-Man cartoons.

Context: 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 199): Justin Bieber

Let $T$ be the set of all times, let $K(t)$ be the proposition “You knock me down at time $t$,” and let $G(t)$ be the proposition “I am on the ground at time $t$.” Translate the logical statement

$\forall t \in T(K(t) \longrightarrow \lnot (\forall s \ge t (G(s))))$.

This matches part of the chorus of “Never Say Never” by Justin Bieber.

Context: 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 198): Smash Mouth

Let $P$ be the set of all people, let $T$ be the set of all times, and let $R(x,t)$ be the proposition “$x$ told me at time $t$ that the world is going to roll me. Translate the logical statement

$\exists x \in P \exists t \in T (R(x,t))$.

This matches the opening line of “All Star” by Smash Mouth.

Context: 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.

Slightly Incorrect Ugly Mathematical Christmas T-Shirts: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on slightly incorrect ugly mathematical Christmas T-shirts.

Part 1: Missing digits in the expansion of $\pi$.

Part 2: Incorrect computation of Pascal’s triangle.

Part 3: Incorrect name of Pascal’s triangle.