About human activity, long-term memory, and Gibrat's law

A central research question in the social sciences for several centuries has been whether any law like patterns in the unintended outcomes of human action exist. Here we investigate the existence of scaling laws in the human activity of communication, considering the number of messages sent by individuals as a growth process in time. We analyze millions of messages sent in two social online communities and uncover power-law relations between fluctuations in the growth rate and the activity of the members. We attribute this scaling law to a long-term persistence of human activity beyond daily or weekly cycles holding up to more than a year. Based on such an underlying long-term correlated dynamics, we elaborate a consistent framework for the empirical evidences, establishing a missing link between the scaling behavior in the growth and long-term persistence. Our results indicate that large fluctuations in communication activity can be expected as an unintended consequence of human interaction. This finding is of importance for both designing communication systems and for understanding the dynamics of social systems.