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This lecture delves into network approaches to model the social dynamics of adoption, focusing on the exploration and contagion dynamics on complex networks. It explores the reinforced-random-walk model and interacting discovery processes to understand how social interactions contribute to the emergence of novelties. The discussion extends to complex contagion, where mechanisms of social reinforcement and peer pressure are examined. The lecture also covers the dynamics of correlated novelties, the adjacent possible concept, and the pace of discovery. It concludes with insights on the cognitive growth of modern science and the implications of higher-order interactions in social systems.