Predicate Logic and Popular Culture (Part 21): Whitney Houston

 

Let D(x,y,z) be the proposition “Said the x to the y, ‘Do you z what I z?'” Express the logical statement

D(\hbox{night wind}, \hbox{little lamb}, \hbox{see}) \land D(\hbox{little lamb}, \hbox{shepherd boy}, \hbox{hear}) \land D(\hbox{shepherd boy}, \hbox{mighty king}, \hbox{know})

in ordinary English.

Of course, this is the outline of the first three verses of the Bing Crosby classic… though I’m very partial to Whitney Houston’s rendition.

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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 20): Mariah Carey

 

Let W(x) be the proposition “I want x for Christmas.” Translate the logical statement

W(\hbox{you}) \land \forall x (x \ne \hbox{you} \Longrightarrow \lnot W(x)),

where the domain is all things.

The clunky way of translating this into English is,”I want you for Christmas, and if something isn’t you, then I don’t want that for Christmas.”

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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 19): Tennessee Christmas

Let S(x,t) denote the amount of snow at place x at time $t$. Express the logical expression

\forall t(S(\hbox{my roof}, t) < S(\hbox{Colorado}, 0))

in ordinary English.

In plain English, this would be “There will never be as much snow at my roof as there is in Colorado now.” More poetically, this is part of the first chorus of Amy Grant’s “Tennessee Christmas.”

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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 18): Sleigh Ride

 

Let H be the home of Farmer Gray, let B(x) be the proposition “x is a birthday party,” let P(x) be the proposition “x is the perfect ending of a perfect day,” let F(x) be the proposition “x is a fireplace,” let S(x) be the proposition “x sings that songs that x knows without a single stop,” and let W(x) be the proposition “x watches the chestnuts pop.” Translate the logical statement

\exists x \in H (B(x) \land P(x) \land \exists y \in H (F(y) \land \exists \epsilon > 0 \forall z \in x

(\parallel y - z \parallel < \epsilon \implies S(z) \land W(z) \, ) \, ),

where the domain for x and y are all places and the domain for z is all people.

I won’t spoil the fun of attempting a direct English translation, but this is one of the closing verses to “Sleigh Ride.”

And while I’m on the topic, I can’t resist also sharing The Three Tenors singing “Sleigh Ride” in perhaps the most delightful waste of immense talent in recorded human history… though the closing note is incredible.

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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 17): Richard Nixon

 

Let H(x,y) be the proposition “x hates y,” let W(x) be the proposition “x wins,” and let $D(x,y)$ be the proposition “x destroys y.” Translate the logical statement

\forall x (H(x,\hbox{you}) \Longrightarrow (H(\hbox{you},x) \Longleftrightarrow W(x) \land D(\hbox{you},\hbox{you}))),

where the domain is all people.

The clunky way of translating this into English is, “If anyone hates you, they win and you destroy yourself exactly when you hate them too.” When rewritten, this is one the remarkably poignant final remarks of Richard Nixon’s farewell address to the White House staff before resigning the presidency in 1974.

A technical note: this famous address of Nixon did not explicitly say “Others don’t win when you don’t hate them,” but this inverse implication was certainly implied.

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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 16): The Lord of the Rings

 

Let W(x) be the proposition “x is a wizard,” let L(x) be the proposition “x is late,” and let E(x) be the proposition “x is early.” Translate the logical statement

\forall x(W(x) \Longrightarrow \lnot(L(x) \lor E(x))),

where the domain is all people.

Naturally, this is one of the opening lines in Peter Jackson’s adaptation of J. R. R. Tolkien’s The Fellowship of the Ring.

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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 15): The Blues Brothers

 

Let H(t) be the proposition “It is hard to be a woman at time t.” Translate the logical statement

\exists t H(t),

where the domain is all times.

Compared to many other examples in this series, this is an exceedingly simple statement from predicate logic. But I couldn’t resist the reference to Bob’s Country Bunker and the Blues Brothers.

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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 14): Cyndi Lauper

 

Let W(x) be the proposition “Girls want x.” Translate the logical statement

W(\hbox{have fun}) \land \forall x(x \ne \hbox{have fun} \Longrightarrow \lnot W(x)),

where the domain is all things.

The clunky way of translating this into English is, “Girls want to have fun, and girls don’t want to have anything else except having fun. Of course, this is the chorus of Cyndi Lauper’s breakout hit of the 1980s.

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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 13): Safety Dance

 

Let F(x,y) be the proposition “x and y are friends,” and let D(x) be the proposition “x dances.” Translate the logical statement

\forall x (F(\hbox{you},x) \Longrightarrow \lnot D(x)) \land \forall x (\lnot D(x) \Longrightarrow \lnot F(\hbox{I},x)),

where the domain is all people.

The straightforward way of translating this into English is, “All of your friends do not dance, and anyone who doesn’t dance is not my friend.” But it’s much more catchy when sung with syntho-pop music to one of the great one-hit wonders of the 1980s.

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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 12): Frozen

 

Let H(x,t) be the proposition “x happens at time t.” Translate the logical statement

\exists t (H(\hbox{music},t) \land H(\hbox{light},t) \land H(\hbox{I dance through the night},t)) \land \forall s < t \lnot(H(\hbox{music},s) \lor H(\hbox{light},s) \lor H(\hbox{I dance through the night},s)))

where the domain is all times.

This very complex statement reads, “There is a time when there will be music, there will be light, and I will dance through the night, and at all previous times, there is no music, there is no light, and I will not dance through the night.” More briefly, there is a time that will be the first time for music, light, and dancing through the night.

Of course, this sounds a whole lot better when Princess Anna sings it.

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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.

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While I’m marginally on the topic, here’s the best parody of “For the First Time in Forever” that I’ve seen:

And here’s the best parody of a Frozen song that I’ve seen.