10.16.10

Friends, Romans, countrymen,

Quick update: yes, I am alive - school is going great; things are super busy, but quite enjoyable. It has been great to grow closer to my dear friends new and old.

Now, to business. As some of you may know, I am a classic movie fanatic. And as comedy goes, Danny Kaye is one of my all-time favorites - comic genius. Consequently, White Christmas was a childhood favorite of mine and continues to be, of movies, one of my most treasured.

In this vein, I was contemplating a couple weeks ago on one of the songs in the movie. As some of you may recall, the song goes like this:

"The best things happen while you're dancing

Things that you would not do at home come naturally on the floor

For dancing soon becomes romancing

When you hold a girl in your arms that you've never held before

Even guys with two left feet come out alright if the girl is sweet

If by chance their cheeks should meet while dancing

Proving that the best things happen while you dance"

Now, as I pondered over the song, my mind rested upon this last phrase: "Proving that the best things happen while you dance". And, as I was humming the tune to myself I realized: the authors of the song/ movie completely forgot to include their mathematical proof of the stated theorem! How ghastly! I mean, as much as I trust Danny Kaye, how can we be so sure without hard mathematical evidence? So I went to work and, as I'm sure you're all most pleased to hear, I have solved the proof. I present it here for your enjoyment and peace of mind:

Do the best things happen while you’re dancing?

Let the following function be given:

(Notes: all variables except Left foot_i and Left foot_j are significant at the 99% level. Home activities is measured on a per capita average for randomized districts. Foot and Cheek variables are binary and Girl sweetness is measured on a scale (0, 1). Best things is a compiled coefficient averaging surveyed perceptions of consumer happiness; scale is (0, 200). Dancing is a per capita hourly average.)

Also, let epsilon > 0 be given. We must show that: 

This, if proved, means substantively that as the effects of Girl sweetness and Cheek (signifying cheeks meeting in this case) approach the height of their interaction, the effects of left-footedness (measuring by the Left foot variables) are neutralized. Thus, the Best things are allowed to happen while dancing. I proceed by epsilon-delta proof. Therefore, we must find a delta such that if 0 < |x - 2| < delta, then |(8.3x + 18.5y) - 26.42| < epsilon. We proceed as follows (we hold y constant at its mean = 0.73):

Therefore, we choose delta such that:

  

Then,

 

Where (x - 1.556) < (x - 2), therefore,

And therefore,

Proving that the best things happen while you dance. QED.

Cheers.