In 2021 an unconventional pair of collaborators embarked on a bold experiment. For two years Steven Rayan, a mathematician and mathematical physicist, and Jeff Presslaff, a freelance composer, pianist and trombonist, prepared to answer one big question: Could they translate a mathematical physics research paper directly into music? Moreover, would their musical creation sound good?
In September Rayan and Presslaff released their brainchild, “Math + Jazz: Sounds from a Quantum Future.” Exactly two years to the date that Rayan, a researcher at the University of Saskatchewan, and Presslaff, who’s based in Winnipeg, Canada, first connected over e-mail, they gathered a 15-piece “hyperbolic band” of musicians to perform the five-section concert at the University of Saskatchewan. Each section corresponded to a portion of Rayan’s research article.
Part musical performance and part lecture, the concert was played to “a packed house,” Rayan says. The lecture portion dissected the paper’s scientific concepts and illustrated how those ideas were transmogrified into music. Some of the illustrations were literal: the slideshow featured hyperbolic art created by Elliot Kienzle.
Pulling off the concert was no easy feat. Because many of the musicians weren’t local, the band hadn’t rehearsed the music together in person until the night before the concert, Rayan notes.
The music was based on Rayan’s 2021 Science Advances article “Hyperbolic band theory,” which he wrote with Joseph Maciejko of the University of Alberta. Their objective was to explore whether band theory—which researchers use to consider the energy levels of materials and the atoms that they’re made of—could be reformulated to explain hyperbolic materials, which have irregular, warped arrangements.
In band theory a material’s energy levels are thought of as being contained in sheetlike bands hovering above the materials they belong to. These shadowy bands represent the material’s quantum properties, and interactions between these bands have consequences for the material’s behavior.
Rayan and Maciejko succeeded in discovering a band theory that works in the wonky world of hyperbolic geometry, a strange geometrical realm that breaks Euclid’s “parallel postulate.” Also called Euclid’s fifth postulate, this rule tells us the following: Suppose you’re given a line. For any point that isn’t on that line, there will be only one line that both goes through that point and is parallel to the original line. In hyperbolic land, a minimum of two lines will go through the point while also being parallel to the given line.