Mathematical Modelling of Cultural Continuity, Intergenerational Learning and Social Cohesion: A Socio-Mathematical Framework for the Agew Horse Festival
Keywords:
Mathematical modelling; socio-mathematical systems; cultural sustainability; Agew Horse Festival; social cohesion; intergenerational learning; cultural heritage; historical memory; fuzzy modelling; dynamical systems.Abstract
Cultural festivals constitute complex socio-cultural systems in which historical memory, cultural identity, intergenerational learning, symbolic representation, participation, and social cohesion interact dynamically. This paper develops a mathematical modelling framework for analysing the sustainability and evolution of the Agew Horse Festival in Injibara, Ethiopia. The model is motivated by the ethnographic evidence that the festival operates as a living cultural institution through which horsemanship, traditional practices, historical memory, symbolic values, and communal relationships are transmitted across generations. The original ethnographic investigation employed participant observation, 14 in-depth interviews, and two focus-group discussions involving youth and elders. A coupled system of nonlinear differential equations is proposed to represent five principal state variables: cultural knowledge, intergenerational transmission, social cohesion, historical memory, and cultural participation. A symbolic-value variable representing the cultural significance of the horse is incorporated into the system. External pressures such as modernization, globalization, commercialization, and weakening participation are represented as attenuation parameters. A composite Cultural Sustainability Index (CSI) is subsequently formulated to provide a measurable framework for evaluating the long-term resilience of the festival. Stability conditions, equilibrium behaviour, sensitivity analysis, scenario modelling, and numerical simulation strategies are proposed. The framework can subsequently be calibrated using longitudinal survey, participation, membership, youth-training, festival-attendance, and cultural-practice data. The model provides a bridge between qualitative anthropology and mathematical modelling and can potentially be adapted to other indigenous festivals and intangible cultural heritage systems.
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