  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.
