Modern advances in transportation and communication technology from airplanes to the internet alongside global expansions of media, migration, and trade have made the modern world more connected than ever before. But what does this bode for the convergence of global culture? Here we explore the relationship between centralization in social networks and contraction or collapse in the diversity of semantic expressions such as ideas, opinions, and tastes. We advance formal examination of this relationship by introducing new methods of manifold learning that allow us to map social networks and semantic combinations into comparable hyperbolic spaces. Hyperbolic representations natively represent both hierarchy and diversity within a system. We illustrate this method by examining the relationship between social centralization and semantic diversity within 21st Century physics, empirically demonstrating how dense, centralized collaboration is associated with a reduction in the space of ideas and how these patterns generalize to all modern scholarship and science. We discuss the complex of causes underlying this association, and theorize the dynamic interplay between structural centralization and semantic contraction, arguing that it introduces an essential tension between the supply and demand of difference.