  Function diversity, namely, the range of tasks individuals can perform, is
essential to productive organizations. This concept has been studied in
disparate discipline contexts, while general patterns and mechanisms remain
unclear. Here, we first analyze over five thousand observations of top-down
organizations -- US federal agencies, Norwegian companies, and US universities,
and find that the number of distinct functions scales with organizational size,
approximately as a power law with an exponent of 1/2. Further, we find common
patterns in the distribution of function abundance within organizations. This
universality suggests that human organizations, despite differences in their
purpose, structure, and culture, may share common mechanisms for creating
specializations. Additionally, we find that cities -- bottom-up organizations
-- differ from top-down organizations and exhibit logarithmic scaling. We
discuss potential avenues for modeling the mechanisms for these observations
using history-dependent random processes, and offer several criteria for model
selection.
