When Time Is Language: Continuous Topic Differential Equations in Podcasts

This paper advances a theoretical framework for modelling podcast language as a continuous-time semantic process. Rather than treating episodes as independent and temporally discrete units, we conceptualise linguistic production as an ordered flow in which topics evolve smoothly with cumulative speech. Focusing on Italian podcasts addressing gender-based violence and empowerment, we formalise time as a continuous variable defined by cumulative word production. Topic proportions are interpreted as noisy observations of an underlying latent trajectory through Ordinary Differential Equations, allowing transitions among latent themes. The proposal shifts the perspective from descriptive temporal smoothing to dynamical modelling, enabling interpolation, structural interpretation of thematic change, and principled extrapolation of future semantic configurations within podcast discourse.