  The ``social brain hypothesis'' for the evolution of large brains in primates
has led to evidence for the coevolution of neocortical size and social group
sizes. Extrapolation of these findings to modern humans indicated that the
equivalent group size for our species should be approximately 150 (essentially
the number of people known personally as individuals). Here, we combine data on
human grouping in a comprehensive and systematic study. Using fractal analysis,
we identify with high statistical confidence a discrete hierarchy of group
sizes with a preferred scaling ratio close to 3: rather than a single or a
continuous spectrum of group sizes, humans spontaneously form groups of
preferred sizes organized in a geometrical series approximating 3, 9, 27,...
Such discrete scale invariance (DSI) could be related to that identified in
signatures of herding behavior in financial markets and might reflect a
hierarchical processing of social nearness by human brains.
