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A SET-THEORETIC BALLET IN TWO ACTS—SELF-TAUGHT

I KNOW LITTLE about composing a ballet. On the other hand, I didn’t know much about magazine production when Larry Givens took me on as Associate Engineering Editor for SAE’s Automotive Engineering. In fact, back then I probably knew more about ballet than magazine production. 

Music has always been a love. And, though essentially devoid of rhythm despite having a grandfather who once played drums with the Dorsey Brothers, I am fascinated by dance, its subtle interweaving of music and motion. 

Venn I Dance For You. Here’s a set-theoretic ballet in two acts, enhanced by appropriate music. 

Act 1. Meet the Empty Set. Scenery: an empty stage, but for a backdrop displaying a giant ∅, the mathematical symbol  for the empty set, the unique set having no elements. 

This symbol was introduced in 1939 by the Bourbaki group, particularly André Weil. It was inspired by the letter Ø in the Danish and Swedish alphabets.

Music: Darius Milhaud’s La Création du Monde, written in 1923, uses jazzy tonality, rhythms, and instruments. It starts slowly, full of portent and befitting the empty set backdrop.

La Création du Monde, performed by the New World Jazz + New World Symphony, Michael Tilson Thomas conductor.

Choreography: Dancers enter, one by one, dressed like 1920s jazz musicians. They mill around, searching for a choreographic theme. Then ∅ enters from stage right. (This is considered the theatrically powerful entry, because people are conditioned from reading to look from left to right.) She’s attired in a black tutu. 

Black tutus are not entirely unknown in classic ballet. The Black Swan in Tchaikovsky’s Swan Lake is often wearing one. 

At first, the other dancers avoid ∅. Musicians, even ‘20s jazz musicians, have a sense of order and are uneasy about ∅’s emptiness.

Enter the mathematician. (Of course, there’d be one.) He explains that the empty set is logically a subset of any set. The backdrop changes from the giant ∅ to ∀ A: ∅ ⊆ A, which is mathematical shorthand for this fact. 

This inclusion elates ∅, now that she realizes that she’s not alone in her emptiness. Milhaud’s Création du Monde reaches its marvelous fugue (which begins at 3:31 in the video). 

Act I concludes in happy choreography of ∅, the ’20s’ jazz musicians, and the mathematician. 

Act II. The Barber of Cambridge. Act II opens with the backdrop suggesting a trendy hair salon near Cambridge University. Among its customers is Bertrand Russell, who posits his Paradox: Suppose the town’s barber is required to shave only those who do not shave themselves.

Then who shaves the barber? If he doesn’t shave himself, then he must shave himself. If he shaves himself, then he mustn’t.

Music.This intellectual quandary is enhanced by the 12-tone music of Alban Berg’s Lulu. Other people in the hair salon are perplexed by the Paradox, not to say by Berg’s controlled but discordant tonality. 

Here’s the palindromic interlude from Lulu, Act II, the score showing its mirrored midpoint.

The Paradox particularly affects ∅ and the mathematician, because Russell concocted it while researching the fundamentals of set theory in 1901. 

A trailer of Berg’s Lulu, as performed by the Metropolitan Opera in its 2015–2016 season. Image by Sara Krulwich/The New York Times, November 6, 2015.

Just when things get hectic, Berg’s music especially, ∅’s choreography brightens. She deftly resolves the Paradox by suggesting the barber be a woman. 

Everyone laughs at this hoary old math joke. The ballet concludes with a reprise of Milhaud’s fugue. Even the jazz musicians join in this final ensemble with ∅ and the mathematician. Curtain. ds

© Dennis Simanaitis, SimanaitisSays.com, 2021

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