Lila Snodgrass

Statement

My piece, Embodied Invariant, explores the mathematical field of topology through the lens of knot theory. Knots are three-dimensional forms that can be bent, stretched, and rearranged without self-intersection. These structures are studied using diagrams that preserve crossing information and are categorized using invariants. My collaborators and I developed a knot invariant called the danceability index, which determines how many dancers are required to physically realize a given knot diagram. Throughout the work, dancers traverse a knot made from LED lights, embodying the rules of the danceability index and revealing why this particular diagram requires three performers. While grounded in mathematical principles, the piece also explores themes of connection, dependency, and collective problem-solving.