The Mathematician’s Ballet

After having kept the book on a shelf for far too long, over the last several months I have been working my way through Apollo’s Angels: A History of Ballet by Jennifer Homans. This effort was probably motivated by the recent appearance of Homans’ second book, which is devoted entirely to George Balanchine. It would be fair to cite Balanchine as the  pioneering force in the development of American ballet, distinguishing it clearly from much of European ballet tradition. For the most part, Apollo’s Angels has made for a consistently enjoyable reading experience; but things became interesting for me when the timeline arrived at Balanchine’s achievements. Reading Homans evoked distant memories of the period when I took out my first subscription to New York City Ballet (NYCB) performances in Lincoln Center.

At that time I was an undergraduate at the Massachusetts Institute of Technology, majoring in mathematics and taking as many electives as I could manage in music courses. As I have previously observed on this site, my spare time (such as its was) was spent working at the campus radio station, devoting much of my time to programming twentieth-century music. As might be guessed, the mathematician in me was particularly drawn to techniques pursued by Arnold Schoenberg and Anton Webern that involved permutations of pitch classes, leading eventually to what became known as the twelve-tone technique.

In that context I became totally hooked on Igor Stravinsky’s “Agon,” which he composed for a Balanchine ballet with the same title. For the better part of his life, Stravinsky wanted nothing to do with Schoenberg. However, after Schoenberg’s death, Stravinsky took an interest in atonal technique, possibly as a result of the influences of Robert Craft.

“Agon” fascinated me for the ways in which atonality rubbed shoulders with tonal traditions, traditions that, in this case, reflected back to the seventeenth century of René Descartes, Étienne Pascal, and particularly Marin Mersenne, whose Harmonie universelle treatise was published in 1636. It was the bold rhetoric of “Agon” than convinced me that I had to see how Balanchine had created a ballet for it. So it was that I began following Balanchine’s choreography both at Lincoln Center and in works that were performed by the Boston Ballet.

Thus, after about 500 pages of reading, I found myself scribbling no end of marginal notes when Homans wrote about “Agon.” She cited the ballet as the third part of a “Greek trilogy” of Balanchine working with Stravinsky’s music. The first two ballets, “Apollo” and “Orpheus,” were grounded in familiar narratives. In sharp contrast, “Agon” was inspired by a seventeenth-century treatise on the dance. What was important, however, was that such dances were intended for “recreational activities” taking place in the setting of a royal court; they were not created to present narratives.

In that context “Agon” had less to do with ancient myths and drew, instead, upon Balanchine’s abstract approach to Paul Hindemith’s composition for piano and strings involving a theme with four variations, given the subtitle “The Four Temperaments.” Balanchine’s choreography realized each of the dispositions associated with those variations (melancholy, sanguine, phlegmatic, choleric). However, there was also an underlying “vocabulary” for the entire ballet; and all of the elements of that vocabulary were assembled into the choreographic interpretation of Hindemith’s coda. As a result, it was no surprise to me to observe that the choreography for “Agon” also wraps up with a coda that reflects on the opening measures of Stravinsky’s score.

All this should reflect back on the thoughts about “Agon” that I documented back in June of 2020 when, due to pandemic conditions, I had turned to YouTube when I was unable to attend “physical” performances. At that time I had discovered that John Clifford had uploaded digitizations of films of NYCB performances. The “Agon” film had no end of technical shortcomings; but I made it a point to cite “the rich interplay of abstraction and expressiveness.”

Because of the close partnership between Balanchine and Stravinsky, one could appreciate the many intricacies of abstraction based on how Balanchine chose to interpret Stravinsky’s music. At the same time there is an underlying foundation of expressiveness coming from all of the dancers, reflecting not so much on Stravinsky’s music as on a rich understanding of what it means to bring Balanchine’s choreography to life through the act of performance. From my own point of view, I feel that mathematics provided me with a platform on which I could grasp the elements of of abstraction; and those elements, in turn, provided a second platform from which I could view the “parallel” elements of expressiveness.

This may well be the only setting in which mathematics can serve as a prerequisite for appreciating a ballet!