This research aims to model the behavior of complex social phenomena based on the principles of classical physics, analyzing the similarities between the flow of information in society and the physical interactions of particles within a system. Utilizing the metaphor of the “ink-water” system, the article examines how random particle interactions evolve into predictable macro-level behaviors and generalizes this mechanism to the phenomenon of rumor and information dissemination in human societies. The findings indicate that employing appropriate mathematical models enables the quantitative analysis of cultural shifts and the prediction of future trends in security and political domains. Ultimately, the paper provides numerous examples to underscore the necessity and significance of mathematical modeling across various disciplines, demonstrating how specific functions can identify and analyze the stability or transformation thresholds in collective behaviors.