notes from the understory

Example 5.3 of my article Quantum metric Choquet simplices explains the geometric effect that an audio signal has on a C*-algebraic quantum metric space of observables of the circle. Here we illustrate this effect via a Python-fueled analysis of the track Burn Your Village To The Ground by The Halluci Nation (formerly A Tribe Called Red).

What is being shown is the boundary of the trace space of a C*-algebraic quantum metric Bauer simplex. At rest, this boundary is the unit circle embedded in the Euclidean plane, situated towards the centre of the vibrating membrane in the video. As the track plays, the waveform distorts the shape of the circle and correspondingly also the quantum metric structure. The position of the red band indicates the quantum Gromov-Hausdorff distance between the at-rest structure and the musically deformed one at any given time.