The Banach-Tarski Paradox
for soloist on piano and percussion
The Banach-Tarski Paradox is a theorem in geometry that states that given a solid sphere in 3‑dimensional space, there exists a decomposition of the sphere into a finite number of parts, which can then be put back together in a different way to yield two identical copies of the original. The process involves using an infinite number of points on the sphere's surface to create the parts which are then only moved or rotated. For this piece, I drew comparisons between the theorem and musician Danny Holt, as from one person, two distinct performers emerge (pianist and percussionist), yet they are the same. The piece aims to represent the theorem aurally: a "paradoxical" feel is created within the music, with seemingly disjoint and dissonant rhythms and meters coming together to form one whole, moments when the piece seems to shift and phase between different time signatures, and pointillistic sections that represent the infinite number of points on a sphere's surface.
Recording by Danny Holt.