A Mathematician’s Take on Ethnomusicology Modeling of Protest Music Transmission and Cultural Memory using Stochastic Partial Differential Equations and Non-Linear Dynamics

Abstract

Protest music functions both as artistic expression and as a vehicle for collective identity and memory in social movements. Songs born out of resistance often spread across communities and generations, helping to sustain the movements’ ideals and preserving historical memory of struggles. Understanding how protest songs propagate through space and time, and how they evolve within cultural contexts, calls for a rigorous framework that can capture dynamical and stochastic aspects of this diffusion. In this paper, I develop a theoretical framework using Stochastic Partial Differential Equations (SPDEs) and dynamical systems theory to model the transmission and evolution of protest music. This approach treats the spread of songs akin to a propagating wave or diffusive process on a cultural landscape, subject to nonlinear feedbacks (from social reinforcement) and random perturbations (due to unpredictable social events). I leverage concepts such as attractors, Lyapunov stability, bifurcation theory, stochastic resonance, and symbolic dynamics to analyze the model’s behavior. My goal is to reveal structural insights into how protest music contributes to sociopolitical movements and cultural memory, providing quantitative measures for phenomena that ethnomusicologists have observed qualitatively – e.g. the way songs “have work to do” in coordinating and unifying communities and how they serve as repositories of cultural memory . I begin by formulating a general SPDE model for the spatiotemporal transmission of protest songs. I then introduce relevant dynamical-systems definitions (attractors, stability, etc.) and analytical tools to study this model. Existing results from the literature on cultural and linguistic diffusion are incorporated to ground my approach: for example, prior works have used PDEs to model information or language spread in social systems . I adapt such methods to the domain of music and resistance. Formal propositions are stated to characterize the stability of musical traditions and the conditions for their persistence or extinction. Next, I apply the framework to a detailed case study – the role of contemporary Tamil protest music in preserving the legacy of the Tamil Eelam struggle – demonstrating how the abstract model can illuminate real-world cultural dynamics. Finally, I discuss how this mathematical formalism can advance ethnomusicology by offering predictive insight into music as a dynamic carrier of resistance, identity, and memory.