# World’s Largest Musical Instrument

Watch a musician play the world’s largest instrument, an organ built by a Pentagon mathematician in Luray Caverns, Virginia. (This was a favorite destination of mine when I was a boy.)

# Predicate Logic and Popular Culture: 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 using examples from popular culture to illustrate principles of predicate logic. My experiences teaching these ideas to my discrete mathematics students led to my recent publication (John Quintanilla, “Name That Tune: Teaching Predicate Logic with Popular Culture,” MAA Focus, Vol. 36, No. 4, pp. 27-28, August/September 2016).

Unlike other series that I’ve made, this series didn’t have a natural chronological order. So I’ll list these by concept illustrated from popular logic.

Logical and $\land$:

• Part 1: “You Belong To Me,” by Taylor Swift
• Part 21: “Do You Hear What I Hear,” covered by Whitney Houston
• Part 31: The Godfather (1972)
• Part 45: The Blues Brothers (1980)
• Part 53: “What Does The Fox Say,” by Ylvis
• Part 54: “Billie Jean,” by Michael Jackson
• Part 98: “Call Me Maybe,” by Carly Rae Jepsen.

Logical or $\lor$:

• Part 1: Shawshank Redemption (1994)

Logical negation $\lnot$:

• Part 1: Richard Nixon
• Part 32: “Satisfaction!”, by the Rolling Stones
• Part 39: “We Are Never Ever Getting Back Together,” by Taylor Swift

Logical implication $\Rightarrow$:

• Part 1: Field of Dreams (1989), and also “Roam,” by the B-52s
• Part 2: “Word Crimes,” by Weird Al Yankovic
• Part 7: “I’ll Be There For You,” by The Rembrandts (Theme Song from Friends)
• Part 43: “Kiss,” by Prince
• Part 50: “I’m Still A Guy,” by Brad Paisley
• Part 76: “You’re Never Fully Dressed Without A Smile,” from Annie.
• Part 109: “Dancing in the Dark,” by Bruce Springsteen.
• Part 122: “Keep Yourself Alive,” by Queen.

For all $\forall$:

• Part 3: Casablanca (1942)
• Part 4: A Streetcar Named Desire (1951)
• Part 34: “California Girls,” by The Beach Boys
• Part 37: Fellowship of the Ring, by J. R. R. Tolkien
• Part 49: “Buy Me A Boat,” by Chris Janson
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)
• Part 65: “Stars and Stripes Forever,” by John Philip Sousa.
• Part 68: “Love Yourself,” by Justin Bieber.
• Part 69: “I Will Always Love You,” by Dolly Parton (covered by Whitney Houston).
• Part 74: “Faithfully,” by Journey.
• Part 79: “We’re Not Gonna Take It Anymore,” by Twisted Sister.
• Part 87: “Hungry Heart,” by Bruce Springsteen.
• Part 99: “It’s the End of the World,” by R.E.M.
• Part 100: “Hold the Line,” by Toto.
• Part 101: “Break My Stride,” by Matthew Wilder.
• Part 102: “Try Everything,” by Shakira.
• Part 108: “BO\$\$,” by Fifth Harmony.
• Part 113: “Sweet Caroline,” by Neil Diamond.
• Part 114: “You Know Nothing, Jon Snow,” from Game of Thrones.
• Part 118: “The Lazy Song,” by Bruno Mars.
• Part 120: “Cold,” by Crossfade.
• Part 123: “Always on My Mind,” by Willie Nelson.

For all and implication:

• Part 8 and Part 9: “What Makes You Beautiful,” by One Direction
• Part 13: “Safety Dance,” by Men Without Hats
• Part 16: The Fellowship of the Ring, by J. R. R. Tolkien
• Part 24 : “The Chipmunk Song,” by The Chipmunks
• Part 55: The Quiet Man (1952)
• Part 62: “All My Exes Live In Texas,” by George Strait.
• Part 70: “Wannabe,” by the Spice Girls.
• Part 72: “You Shook Me All Night Long,” by AC/DC.
• Part 81: “Ascot Gavotte,” from My Fair Lady
• Part 82: “Sharp Dressed Man,” by ZZ Top.
• Part 86: “I Could Have Danced All Night,” from My Fair Lady.
• Part 95: “Every Breath You Take,” by The Police.
• Part 96: “Only the Lonely,” by Roy Orbison.
• Part 97: “I Still Haven’t Found What I’m Looking For,” by U2.
• Part 105: “Every Rose Has Its Thorn,” by Poison.
• Part 107: “Party in the U.S.A.,” by Miley Cyrus.
• Part 112: “Winners Aren’t Losers,” by Donald J. Trump and Jimmy Kimmel.
• Part 115: “Every Time We Touch,” by Cascada.
• Part 117: “Stronger,” by Kelly Clarkson.

There exists $\exists$:

• Part 10: “Unanswered Prayers,” by Garth Brooks
• Part 15: “Stand by Your Man,” by Tammy Wynette (also from The Blues Brothers)
• Part 36: Hamlet, by William Shakespeare
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)
• Part 94: “Not While I’m Around,” from Sweeney Todd (1979).
• Part 104: “Wild Blue Yonder” (US Air Force)
• Part 106: “No One,” by Alicia Keys.
• Part 116: “Ocean Front Property,” by George Strait.

Existence and uniqueness:

• Part 14: “Girls Just Want To Have Fun,” by Cyndi Lauper
• Part 20: “All I Want for Christmas Is You,” by Mariah Carey
• Part 23: “All I Want for Christmas Is My Two Front Teeth,” covered by The Chipmunks
• Part 29: “You’re The One That I Want,” from Grease
• Part 30: “Only You,” by The Platters
• Part 35: “Hound Dog,” by Elvis Presley
• Part 73: “Dust In The Wind,” by Kansas.
• Part 75: “Happy Together,” by The Turtles.
• Part 77: “All She Wants To Do Is Dance,” by Don Henley.
• Part 90: “All You Need Is Love,” by The Beatles.

DeMorgan’s Laws:

• Part 5: “Never Gonna Give You Up,” by Rick Astley
• Part 28: “We’re Breaking Free,” from High School Musical (2006)

Simple nested predicates:

• Part 6: “Everybody Loves Somebody Sometime,” by Dean Martin
• Part 25: “Every Valley Shall Be Exalted,” from Handel’s Messiah
• Part 33: “Heartache Tonight,” by The Eagles
• Part 38: “Everybody Needs Somebody To Love,” by Wilson Pickett and covered in The Blues Brothers (1980)
• Part 46: “Mean,” by Taylor Swift
• Part 56: “Turn! Turn! Turn!” by The Byrds
• Part 63: P. T. Barnum.
• Part 64: Abraham Lincoln.
• Part 66: “Somewhere,” from West Side Story.
• Part 71: “Hold On,” by Wilson Philips.
• Part 80: Liverpool FC.
• Part 84: “If You Leave,” by OMD.
• Part 103: “The Caisson Song” (US Army).
• Part 111: “Always Something There To Remind Me,” by Naked Eyes.
• Part 121: “All the Right Moves,” by OneRepublic.

Maximum or minimum of a function:

• Part 12: “For the First Time in Forever,” by Kristen Bell and Idina Menzel and from Frozen (2013)
• Part 19: “Tennessee Christmas,” by Amy Grant
• Part 22: “The Most Wonderful Time of the Year,” by Andy Williams
• Part 48: “I Got The Boy,” by Jana Kramer
• Part 60: “I Loved Her First,” by Heartland
• Part 92: “Anything You Can Do,” from Annie Get Your Gun.
• Part 119: “Uptown Girl,” by Billy Joel.

Somewhat complicated examples:

• Part 11 : “Friends in Low Places,” by Garth Brooks
• Part 27 : “There is a Castle on a Cloud,” from Les Miserables
• Part 41: Winston Churchill
• Part 44: Casablanca (1942)
• Part 51: “Everybody Wants to Rule the World,” by Tears For Fears
• Part 58: “Fifteen,” by Taylor Swift
• Part 59: “We Are Never Ever Getting Back Together,” by Taylor Swift
• Part 61: “Style,” by Taylor Swift
• Part 67: “When I Think Of You,” by Janet Jackson.
• Part 78: “Nothing’s Gonna Stop Us Now,” by Starship.
• Part 89: “No One Is Alone,” from Into The Woods.
• Part 110: “Everybody Loves My Baby,” by Louis Armstrong.

Fairly complicated examples:

• Part 17 : Richard Nixon
• Part 47: “Homegrown,” by Zac Brown Band
• Part 52: “If Ever You’re In My Arms Again,” by Peabo Bryson
• Part 83: “Something Good,” from The Sound of Music.
• Part 85: “Joy To The World,” by Three Dog Night.
• Part 88: “Like A Rolling Stone,” by Bob Dylan.
• Part 91: “Into the Fire,” from The Scarlet Pimpernel.

Really complicated examples:

• Part 18: “Sleigh Ride,” covered by Pentatonix
• Part 26: “All the Gold in California,” by the Gatlin Brothers
• Part 40: “One of These Things Is Not Like the Others,” from Sesame Street
• Part 42: “Take It Easy,” by The Eagles

# Random couscous snaps into beautiful patterns

I enjoyed watching this.

# Predicate Logic and Popular Culture: 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 using examples from popular culture to illustrate principles of predicate logic. My experiences teaching these ideas to my discrete mathematics students led to my recent publication (John Quintanilla, “Name That Tune: Teaching Predicate Logic with Popular Culture,” MAA Focus, Vol. 36, No. 4, pp. 27-28, August/September 2016).

Unlike other series that I’ve made, this series didn’t have a natural chronological order. So I’ll list these by concept illustrated from popular logic.

Logical and $\land$:

• Part 1: “You Belong To Me,” by Taylor Swift
• Part 21: “Do You Hear What I Hear,” covered by Whitney Houston
• Part 31: The Godfather (1972)
• Part 45: The Blues Brothers (1980)
• Part 53: “What Does The Fox Say,” by Ylvis
• Part 54: “Billie Jean,” by Michael Jackson

Logical or $\lor$:

• Part 1: Shawshank Redemption (1994)

Logical negation $\lnot$:

• Part 1: Richard Nixon
• Part 32: “Satisfaction!”, by the Rolling Stones
• Part 39: “We Are Never Ever Getting Back Together,” by Taylor Swift

Logical implication $\Rightarrow$:

• Part 1: Field of Dreams (1989), and also “Roam,” by the B-52s
• Part 2: “Word Crimes,” by Weird Al Yankovic
• Part 7: “I’ll Be There For You,” by The Rembrandts (Theme Song from Friends)
• Part 43: “Kiss,” by Prince
• Part 50: “I’m Still A Guy,” by Brad Paisley
• Part 76: “You’re Never Fully Dressed Without A Smile,” from Annie.

For all $\forall$:

• Part 3: Casablanca (1942)
• Part 4: A Streetcar Named Desire (1951)
• Part 34: “California Girls,” by The Beach Boys
• Part 37: Fellowship of the Ring, by J. R. R. Tolkien
• Part 49: “Buy Me A Boat,” by Chris Janson
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)
• Part 65: “Stars and Stripes Forever,” by John Philip Sousa.
• Part 68: “Love Yourself,” by Justin Bieber.
• Part 69: “I Will Always Love You,” by Whitney Houston.
• Part 74: “Faithfully,” by Journey.
• Part 79: “We’re Not Gonna Take It Anymore,” by Twisted Sister.
• Part 87: “Hungry Heart,” by Bruce Springsteen.

For all and implication:

• Part 8 and Part 9: “What Makes You Beautiful,” by One Direction
• Part 13: “Safety Dance,” by Men Without Hats
• Part 16: The Fellowship of the Ring, by J. R. R. Tolkien
• Part 24 : “The Chipmunk Song,” by The Chipmunks
• Part 55: The Quiet Man (1952)
• Part 62: “All My Exes Live In Texas,” by George Strait.
• Part 70: “Wannabe,” by the Spice Girls.
• Part 72: “You Shook Me All Night Long,” by AC/DC.
• Part 81: “Ascot Gavotte,” from My Fair Lady
• Part 82: “Sharp Dressed Man,” by ZZ Top.
• Part 86: “I Could Have Danced All Night,” from My Fair Lady.

There exists $\exists$:

• Part 10: “Unanswered Prayers,” by Garth Brooks
• Part 15: “Stand by Your Man,” by Tammy Wynette (also from The Blues Brothers)
• Part 36: Hamlet, by William Shakespeare
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)

Existence and uniqueness:

• Part 14: “Girls Just Want To Have Fun,” by Cyndi Lauper
• Part 20: “All I Want for Christmas Is You,” by Mariah Carey
• Part 23: “All I Want for Christmas Is My Two Front Teeth,” covered by The Chipmunks
• Part 29: “You’re The One That I Want,” from Grease
• Part 30: “Only You,” by The Platters
• Part 35: “Hound Dog,” by Elvis Presley
• Part 73: “Dust In The Wind,” by Kansas.
• Part 75: “Happy Together,” by The Turtles.
• Part 77: “All She Wants To Do Is Dance,” by Don Henley.
• Part 90: “All You Need Is Love,” by The Beatles.

DeMorgan’s Laws:

• Part 5: “Never Gonna Give You Up,” by Rick Astley
• Part 28: “We’re Breaking Free,” from High School Musical (2006)

Simple nested predicates:

• Part 6: “Everybody Loves Somebody Sometime,” by Dean Martin
• Part 25: “Every Valley Shall Be Exalted,” from Handel’s Messiah
• Part 33: “Heartache Tonight,” by The Eagles
• Part 38: “Everybody Needs Somebody To Love,” by Wilson Pickett and covered in The Blues Brothers (1980)
• Part 46: “Mean,” by Taylor Swift
• Part 56: “Turn! Turn! Turn!” by The Byrds
• Part 63: P. T. Barnum.
• Part 64: Abraham Lincoln.
• Part 66: “Somewhere,” from West Side Story.
• Part 71: “Hold On,” by Wilson Philips.
• Part 80: Liverpool FC.
• Part 84: “If You Leave,” by OMD.

Maximum or minimum of a function:

• Part 12: “For the First Time in Forever,” by Kristen Bell and Idina Menzel and from Frozen (2013)
• Part 19: “Tennessee Christmas,” by Amy Grant
• Part 22: “The Most Wonderful Time of the Year,” by Andy Williams
• Part 48: “I Got The Boy,” by Jana Kramer
• Part 60: “I Loved Her First,” by Heartland
• Part 92: “Anything You Can Do,” from Annie Get Your Gun.

Somewhat complicated examples:

• Part 11 : “Friends in Low Places,” by Garth Brooks
• Part 27 : “There is a Castle on a Cloud,” from Les Miserables
• Part 41: Winston Churchill
• Part 44: Casablanca (1942)
• Part 51: “Everybody Wants to Rule the World,” by Tears For Fears
• Part 58: “Fifteen,” by Taylor Swift
• Part 59: “We Are Never Ever Getting Back Together,” by Taylor Swift
• Part 61: “Style,” by Taylor Swift
• Part 67: “When I Think Of You,” by Janet Jackson.
• Part 78: “Nothing’s Gonna Stop Us Now,” by Starship.
• Part 89: “No One Is Alone,” from Into The Woods.

Fairly complicated examples:

• Part 17 : Richard Nixon
• Part 47: “Homegrown,” by Zac Brown Band
• Part 52: “If Ever You’re In My Arms Again,” by Peabo Bryson
• Part 83: “Something Good,” from The Sound of Music.
• Part 85: “Joy To The World,” by Three Dog Night.
• Part 88: “Like A Rolling Stone,” by Bob Dylan.
• Part 91: “Into the Fire,” from The Scarlet Pimpernel.

Really complicated examples:

• Part 18: “Sleigh Ride,” covered by Pentatonix
• Part 26: “All the Gold in California,” by the Gatlin Brothers
• Part 40: “One of These Things Is Not Like the Others,” from Sesame Street
• Part 42: “Take It Easy,” by The Eagles

# Predicate Logic and Popular Culture: 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 using examples from popular culture to illustrate principles of predicate logic.

Unlike other series that I’ve made, this series didn’t have a natural chronological order. So I’ll list these by concept illustrated from popular logic.

Logical and $\land$: Part 1

• Part 1: “You Belong To Me,” by Taylor Swift
• Part 21: “Do You Hear What I Hear,” covered by Whitney Houston
• Part 31: The Godfather (1972)
• Part 45: The Blues Brothers (1980)
• Part 53: “What Does The Fox Say,” by Ylvis
• Part 54: “Billie Jean,” by Michael Jackson

Logical or $\lor$:

• Part 1: Shawshank Redemption (1994)

Logical negation $\lnot$:

• Part 1: Richard Nixon
• Part 32: “Satisfaction!”, by the Rolling Stones
• Part 39: “We Are Never Ever Getting Back Together,” by Taylor Swift

Logical implication $\Rightarrow$:

• Part 1: Field of Dreams (1989), and also “Roam,” by the B-52s
• Part 2: “Word Crimes,” by Weird Al Yankovic
• Part 7: “I’ll Be There For You,” by The Rembrandts (Theme Song from Friends)
• Part 43: “Kiss,” by Prince
• Part 50: “I’m Still A Guy,” by Brad Paisley

For all $\forall$:

• Part 3: Casablanca (1942)
• Part 4: A Streetcar Named Desire (1951)
• Part 34: “California Girls,” by The Beach Boys
• Part 37: Fellowship of the Ring, by J. R. R. Tolkien
• Part 49: “Buy Me A Boat,” by Chris Janson
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)

For all and implication:

• Part 8 and Part 9: “What Makes You Beautiful,” by One Direction
• Part 13: “Safety Dance,” by Men Without Hats
• Part 16: The Fellowship of the Ring, by J. R. R. Tolkien
• Part 24 : “The Chipmunk Song,” by The Chipmunks
• Part 55: The Quiet Man (1952)

There exists $\exists$:

• Part 10: “Unanswered Prayers,” by Garth Brooks
• Part 15: “Stand by Your Man,” by Tammy Wynette (also from The Blues Brothers)
• Part 36: Hamlet, by William Shakespeare
• Part 57: “Let It Go,” by Idina Menzel and from Frozen (2013)

Existence and uniqueness:

• Part 14: “Girls Just Want To Have Fun,” by Cyndi Lauper
• Part 20: “All I Want for Christmas Is You,” by Mariah Carey
• Part 23: “All I Want for Christmas Is My Two Front Teeth,” covered by The Chipmunks
• Part 29: “You’re The One That I Want,” from Grease
• Part 30: “Only You,” by The Platters
• Part 35: “Hound Dog,” by Elvis Presley

DeMorgan’s Laws:

• Part 5: “Never Gonna Give You Up,” by Rick Astley
• Part 28: “We’re Breaking Free,” from High School Musical (2006)

Simple nested predicates:

• Part 6: “Everybody Loves Somebody Sometime,” by Dean Martin
• Part 25: “Every Valley Shall Be Exalted,” from Handel’s Messiah
• Part 33: “Heartache Tonight,” by The Eagles
• Part 38: “Everybody Needs Somebody To Love,” by Wilson Pickett and covered in The Blues Brothers (1980)
• Part 46: “Mean,” by Taylor Swift
• Part 56: “Turn! Turn! Turn!” by The Byrds

Maximum or minimum of a function:

• Part 12: “For the First Time in Forever,” by Kristen Bell and Idina Menzel and from Frozen (2013)
• Part 19: “Tennessee Christmas,” by Amy Grant
• Part 22: “The Most Wonderful Time of the Year,” by Andy Williams
• Part 48: “I Got The Boy,” by Jana Kramer
• Part 60: “I Loved Her First,” by Heartland

Somewhat complicated examples:

• Part 11 : “Friends in Low Places,” by Garth Brooks
• Part 27 : “There is a Castle on a Cloud,” from Les Miserables
• Part 41: Winston Churchill
• Part 44: Casablanca (1942)
• Part 51: “Everybody Wants to Rule the World,” by Tears For Fears
• Part 58: “Fifteen,” by Taylor Swift
• Part 59: “We Are Never Ever Getting Back Together,” by Taylor Swift
• Part 61: “Style,” by Taylor Swift

Fairly complicated examples:

• Part 17 : Richard Nixon
• Part 47: “Homegrown,” by Zac Brown Band
• Part 52: “If Ever You’re In My Arms Again,” by Peabo Bryson

Really complicated examples:

• Part 18: “Sleigh Ride,” covered by Pentatonix
• Part 26: “All the Gold in California,” by the Gatlin Brothers
• Part 40: “One of These Things Is Not Like the Others,” from Sesame Street
• Part 42: “Take It Easy,” by The Eagles

# A 100-Year old computer for computing Fourier transforms

Many famous machines have been built to do math — like Babbage’s Difference Engine for solving polynomials or Leibniz’s Stepped Reckoner for multiplying and dividing — yet none worked as well as Albert Michelson’s harmonic analyzer. This 19th century mechanical marvel does Fourier analysis: it can find the frequency components of a signal using only gears, springs and levers. We discovered this long-forgotten machine locked in a glass case at the University of Illinois. For your enjoyment, we brought it back to life in this book and in a companion video series — all written and created by Bill Hammack, Steve Kranz and Bruce Carpenter.

A free PDF of their book is available at the above link; the book is also available for purchase. Here are the companion videos for the book.

# MIT Scientists Figured Out How to Eavesdrop Using a Potato Chip Bag

From Gizmodo:

In a scenario straight out of “Enhance, enhance!,” MIT scientists have figured out that the tiny vibrations on ordinary objects like a potato chip bag or a glass of water or even a plant can be reconstructed into intelligible speech. All it takes is a camera and a snappy algorithm. Take a listen.

# Symphonic Equations: Waves and Tubes

This excellent and engaging video describes how sine and cosine functions can be applied to music.