  An outstanding open problem is whether collective social phenomena occurring
over short timescales can systematically reduce cultural heterogeneity in the
long run, and whether offline and online human interactions contribute
differently to the process. Theoretical models suggest that short-term
collective behavior and long-term cultural diversity are mutually excluding,
since they require very different levels of social influence. The latter
jointly depends on two factors: the topology of the underlying social network
and the overlap between individuals in multidimensional cultural space.
However, while the empirical properties of social networks are well understood,
little is known about the large-scale organization of real societies in
cultural space, so that random input specifications are necessarily used in
models. Here we use a large dataset to perform a high-dimensional analysis of
the scientific beliefs of thousands of Europeans. We find that inter-opinion
correlations determine a nontrivial ultrametric hierarchy of individuals in
cultural space, a result unaccessible to one-dimensional analyses and in
striking contrast with random assumptions. When empirical data are used as
inputs in models, we find that ultrametricity has strong and counterintuitive
effects, especially in the extreme case of long-range online-like interactions
bypassing social ties. On short time-scales, it strongly facilitates a
symmetry-breaking phase transition triggering coordinated social behavior. On
long time-scales, it severely suppresses cultural convergence by restricting it
within disjoint groups. We therefore find that, remarkably, the empirical
distribution of individuals in cultural space appears to optimize the
coexistence of short-term collective behavior and long-term cultural diversity,
which can be realized simultaneously for the same moderate level of mutual
influence.
