Drametrics: what dramaturgs should learn from mathematicians
Magda Romanska · 2014
The relationship between math and music has long been known and analyzed. We know that a well-structured musical composition is like a well-structured mathematical formula. The mathematician and violinist James Stewart argues that mathematics, like music, is concerned with structure, “the way mathematical objects fit together and relate to each other.”1 The same can be said of art: from classical realist paintings and sculptures to the most abstract works of Picasso, Kandinsky, Malevich, Mondrian, and Pollock, each composition follows a carefully arranged structural order with colors, shapes, patterns, and empty space consciously complementing, supplementing, and juxtaposing one another. Like music and art, literature too has a long-standing relationship with mathematics. Drawing on the relationship between math, art, and music, in his 2012 New Yorker article Alexander Nazaryan attempts to trace implicit similarities between mathematicians and fiction writers. Like mathematicians, fiction writers create patterns that follow a well-defined structural order, from the meta levels (the sequence of chapters and paragraphs) to the sublevels of sentences, words, and syllables. Nazaryan quotes Ernest Hemingway, who is said to have written in 1945 to his colleague Maxwell Perkins: “The laws of prose writing are as immutable as those of flight, of mathematics, of physics.”2 From Hemingway to J. K. Rowling, fiction writers are known to draw elaborate diagrams for their novels, structuring the organization of their stories on the basis of mathematical formulas. The close affinity between math and poetry has also long been known to poets and literary theorists. As it is based on meter that defines the rhythmic structure of each verse, poetry is nothing more than the linguistic equivalent of a complicated mathematical pattern; it’s a highly intricate, word-based math game. Let’s take our basic iambic pentameter, one of the most often used meters in English poetry, a form favored by William Shakespeare, John Donne, and John Keats. Iambic pentameter has ten syllables per line that alternate unstressed and stressed beats. They are arranged in five pairs following a clear mathematical pattern: “1 2 1 2 3 4 3 4 5 6 5 6 7 7.” In Four Riddles, Lewis Carroll uses the iambic pentameter quadratic x2 + 7x + 53 = 11/3 in one of his riddles. Other poetic forms, the octave, for example, follow a different rhyming scheme that looks like “1 2 1 1 1 2 2 1.” In addition to the mathematical arrangement of their lines, the overall structures of poems follow mathematical formulas. A villanelle, for example, has six stanzas, with three lines in the first five stanzas and four in the last. Most recently, mathematicians, humanists, social and computer scientists have come together to devise algorithms that would explain such diverse phenomena as the progression of history and the development of language. Kevin Slavin, an MIT professor and a designer of large-scale, real-world games, argues in his popular TED Talk that algorithms guide our world.3 Likewise, the Harvard mathematician Jean-Baptiste Michel, for example, argues that there is a mathematical pattern to the evolution of the English language and that math can explain certain historical forces, including wars. Michel suggests that mathematics can be used to predict future events and perhaps even to prevent calamities. For Michel, the huge databases we’re currently amassing thanks to the digital revolution will allow us to process unimaginable amounts of data, which will reveal mathematical patterns in every sphere of life.4 This is where science and digital humanities are coming together. But what about drama and theatre? The idea that theatre is guided by the same rules of mathematics appears both absurd and absolutely logical. If all other art forms work according to the same rules, why shouldn’t theatre? Indeed, although the relationship between math and dramatic structure has never been explicitly explored, math has always been implicitly present in the development of Western drama and dramatic theory. In 1863, the German novelist and playwright Gustav Freytag published Die Technik des Dramas (Technique of the drama), in which he outlined a geometric pattern of dramatic structure in classic Greek tragedy. With (a) introduction, (b) rise, (c) climax, (d) return or fall, and (e) catastrophe, Freytag’s triangle outlines the basic flow of dramatic action: Although it doesn’t provide any actual numbers, Freytag’s triangle quite closely resembles the golden triangle, in which the ratio a:b is equivalent to the golden ratio Phi, φ = 1.61803398875.