  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.
