Jessica Shand’s journey to understanding the complexities of music and mathematics began when she discovered the fascinating field of topology. As a junior in college, Shand became captivated by the way shapes could deform and transform without losing their core properties. This concept resonated deeply with her passion for music, particularly experimental music. Shand’s love affair with music began at childhood ballet classes, where she fell in love with the flute parts in The Nutcracker. She eventually trained in classical flute, performed with youth orchestras, and even played at Carnegie Hall with the National Youth Orchestra. Shand’s fascination with music led her to explore new ways of making music. She worked with renowned flutists Claire Chase and Paula Robison, who were pushing the boundaries of classical music by experimenting with contemporary compositions. Shand also joined the Harvard College Opera, where she gained the opportunity to adapt centuries-old works by creating her own structures around them. This experience allowed her to see music in a new light, as she was building her own compositions and deciding how to approach them. At the same time, Shand was studying proof-based mathematics at Harvard, which introduced her to the abstract world of topology. She was captivated by the idea of focusing on the core properties of shapes, rather than their exact measurements. Shand realized that the simplicity of these concepts was at the heart of topology, and this resonated deeply with her own approach to music. She saw that music, like topology, was about transformation and continuity, rather than precise measurements. Shand’s interest in the intersection of music and mathematics led her to write a senior thesis on the subject. Her thesis explored the social and political contingencies of how math develops, and she used topology to challenge the idea of math as objective. Shand wrote five songs about topological graph theory, which delved into the “seven bridges problem” from the 1730s and explored the idea of how sounds can transform and change over time. One of the songs Shand wrote focused on the “seven bridges problem,” which was first solved by Leonhard Euler in 1736. The problem involved finding a path that crosses each of the seven bridges connecting two islands to the mainland without repeating any bridges. Shand’s song highlighted the significance of this problem in the history of mathematics, and how it had been used to illustrate the power of topology. Shand’s interest in sound and perception continued to grow as she delved deeper into the world of music and mathematics. She began to experiment with the idea of sound as a shape, and how it could be transformed and reshaped. Shand’s album, “Transmutations,” featured fragments of flute sound that were molded and reshaped using editing software. The album explored the question of how much sounds can change before they cross a threshold from one category to another. Shand’s research on sound and perception led her to conduct behavioral studies with humans and AI models. She found that humans were able to track the differences between sounds over time, while AI models had a hard time distinguishing between them until the very end. Shand’s findings highlighted the complex relationship between sound and perception, and how it can be used to create new and innovative music. Shand’s work continues to be shaped by her interests in music, mathematics, and technology. As a Ph.D. student in music and multimedia composition at Brown University, she is producing her own projects, including sound design for a short film. Shand’s research and creative work continue to explore the intersections of music, mathematics, and technology, and her findings are shedding new light on the complex relationship between sound and perception.
| Key Takeaways |
|---|
| Jessica Shand’s journey to understanding music and mathematics was sparked by her interest in topology. |
| Shand’s love for music led her to explore new ways of making music, including experimental and contemporary compositions. |
| Shand’s research on topology and sound perception led her to explore the intersection of music, mathematics, and technology. |
| Shand’s findings highlighted the complex relationship between sound and perception, and how it can be used to create new and innovative music. |
“The interaction between sound and a listener is magical,” says Jessica Shand. “It can open up so many different possibilities and associations, and that’s what I find really magical about music and mathematics.”
Definition:
Topology: a branch of mathematics that studies the properties of shapes that are preserved under continuous transformations, such as stretching and bending. Topology is concerned with the study of shapes and spaces that are transformed in a continuous manner, without tearing or gluing.
Example of Topology in Music
Jessica Shand’s music explores the idea of sound as a shape, and how it can be transformed and reshaped. Her album “Transmutations” features fragments of flute sound that are molded and reshaped using editing software. This approach to music highlights the power of topology in understanding the properties of sound.
Example of Topology in Real Life
The “seven bridges problem” is a classic example of topology in action. This problem has been used to illustrate the power of topology in solving complex problems.
Example of Topology in Technology
Jessica Shand’s research on sound and perception led her to explore the intersection of music, mathematics, and technology. Her findings highlighted the complex relationship between sound and perception, and how it can be used to create new and innovative music. This research has the potential to be applied in various fields, including music production, audio engineering, and computer science.
