Math fun with song lyrics

Song-writer Bill Calhoun is a faculty member in the Department of Mathematics, Computer Science and Statistics at Pennsylvania's Bloomsburg University (where I also hung out for many years). He belongs, along with colleagues Erik Wynters and Kevin Ferland, to a band called "The Derivatives."  And Bill has granted permission for me to include several of his math lyrics (parodies) here. (In this previous post, we consider the connection between song parodies and mathematical isomorphism.)  My first Calhoun selection deals with difficult mathematical questions concerning classification of infinite sets and decidability.  Following that, later lyrics consider proving theorems and finding derivatives.

Questions You Can’t Ever Decide*      by Bill Calhoun

(These lyrics match the tune of  "Lucy in the Sky with Diamonds" by Lennon and McCartney.)

Picture yourself in  a world filled with numbers,
But the numbers are really just words in disguise.
Gödel says “How can you prove you’re consistent,
If you can’t tell that this is a lie?”    

Cantor builds sets of uncountable size,
Towering over your head.
Cohen says “Guess where the real numbers lie.”
And it’s gone.

Questions you can’t Ever Decide.
Questions you can’t Ever Decide.
Questions you can’t Ever Decide.
Ah.

Follow them up to the top of a mountain,
With mountains ahead climbing up to the sky.
Tarski just smiles as you wonder aloud
“Can they grow so incredibly high?” 

Inaccessible cardinals: compact and strong,
Measurable, Woodin and huge.
Climb toward the top with your head in the clouds
And you’re gone.

Questions you can’t Ever Decide.
Questions you can’t Ever Decide.
Questions you can’t Ever Decide.
Ah.

Picture yourself in a world of computers,
Will they run on forever, will they ever die?
Suddenly Turing says “How can you tell,
If you can’t tell if this is a lie?”

Questions you can’t Ever Decide.
Questions you can’t Ever Decide.
Questions you can’t Ever Decide.
Ah.                                             

*QED (From the Latin, Quod Erat Demonstrandum -- an assertion used at the end 

of a mathematical proof, stating that it is now complete.)

Mathematicians named in the lyrics above include Kurt Godel, Georg Cantor, Paul Cohen, Alfred Tarski, and Alan Turing.

Provin' U.S.A.      by  Bill Calhoun 

(Calhoun's lyics parody "Surfin' U.S.A." -- with lyrics by Brian Wilson, tune by Chuck Berry.)

If everybody knew logic, across the USA,
Then everybody be provin' like the MAA.*
They’d be wearin' their khakis, and their shirts of blue. 
A bushy Einstein hairdo, provin' USA.

You’d catch 'em provin' their theorems about the real line,
Algebraic equations, tan, cos and sine.
They’d be hangin' at Starbucks, talkin' math all day.
Everybody’s gone provin', provin' USA. 

We’ll all be making conjectures we’re going to prove real soon.
We’d be reading math journals, we can’t wait for June.
We’re doing math all summer, on sabbatical to stay.
Tell the students we’re provin', provin' USA.

Math deduction, USA, Math induction, USA,
Math deduction, USA, Math induction USA,
Assume the negation, USA, get a contradiction,
Everybody’s gone provin', provin' USA.
Everybody’s gone provin', provin' USA.
Everybody’s gone provin', provin' USA.    *Mathematical Association of America


F Prime is the Steepness       by Bill Calhoun

(These lyrics match the tune of "The First Cut is the Deepest" by Cat Stevens).

You were given function f at the start       
And now you want to find a special part.     
You should be taking the derivative.
If you want to find the high or low 
Look where f prime goes to zero, cause

       Chorus:
          F prime is the steepness, you’ve gotta know.
          F prime is the steepness.
          And if you’re searching for the best or the worst,
          You ought to set f prime to zero first.

If you want to know where f’s going to rise,
It’s where f prime is on the positive side.
OK now go ahead and give it a try.
If you want to find the high or low,
Look where f prime goes to zero, cause

       Repeat Chorus.

If you want to know where f will decline
It’s where there’s a negative f prime.
OK now go ahead and give it a try.
If you want to find the high or low,
Look where f prime goes to zero.

       Repeat Chorus.

F prime is the steepness, you’ve gotta know
F prime is the steepness.
If you want to find the high or low,
Look where f prime goes to zero (or is undefined).