Research has repeatedly demonstrated the influence of social connection and communication on convergence in cultural tastes, opinions and ideas. Here we review recent studies and consider the implications of social connection on cultural, epistemological and ideological contraction, then formalize these intuitions within the language of information theory. To systematically examine connectivity and cultural diversity, we introduce new methods of manifold learning to map both social networks and topic combinations into comparable, two-dimensional hyperbolic spaces or Poincar\'e disks, which represent both hierarchy and diversity within a system. On a Poincar\'e disk, radius from center traces the position of an actor in a social hierarchy or an idea in a cultural hierarchy. The angle of the disk required to inscribe connected actors or ideas captures their diversity. Using this method in the epistemic culture of 21st Century physics, we empirically demonstrate that denser university collaborations systematically contract the space of topics discussed and ideas investigated more than shared topics drive collaboration, despite the extreme commitments academic physicists make to research programs over the course of their careers. Dense connections unleash flows of communication that contract otherwise fragmented semantic spaces into convergent hubs or polarized clusters. We theorize the dynamic interplay between structural expansion and cultural contraction and explore how this introduces an essential tension between the enjoyment and protection of difference.