Collective memories formation and evolution: A geometrical interpretation

To form a collective memory within a group, four conditions must be met: 1) memories must be transmitted through a communication network, 2) they must be shaped by interactions with others, 3) they must converge to a common form within the group, and 4) this representation must stabilize
over time, a process we call dynamic stability. While formalizing these conditions mathematically is crucial for defining the formation and evolution of collective memory—a task still to be fully explored—this paper presents a theoretical model to address it. We use concepts from geometry,
linear algebra, sociology, and psychology to define the formation, evolution, and dynamic stability of collective memories. Our approach incorporates both individual memories and group interactions, illustrating how collective memory can be modeled by means of an orthogonal matrix and a hypersphere in RD space, where D represents the number of questions in an evaluation questionnaire.