Collective Weibull behavior of social atoms: Application of the rank-ordering statistics to historical extreme events

¹ Department of Earth Science and Graduate Institute of Geophysics, National Central University Jhongli, Taiwan 320, R.O.C.
² Department of Oncology, University of Alberta, Cross Cancer Institute - Edmonton, AB T6G 1Z2, Canada
³ CNR, Institute of Methodologies for Environmental Analysis - C. da S. Loja, 85050 Tito (PZ), Italy, EU
⁴ Teaching Center of Natural Science, Minghsin University of Science and Technology - Xinfeng, Hsinchu, Taiwan 304, R.O.C.
⁵ Department of Electrical Engineering, Nan-Kai University of Technology - Caotun, Nantou, Taiwan 542, R.O.C.

^a luciano.telesca@imaa.cnr.it

Received: 14 November 2011
Accepted: 20 January 2012

Abstract

Analogous to crustal earthquakes in natural fault systems, we here consider the dynasty collapses as extreme events in human society. Duration data of ancient Chinese and Egyptian dynasties provides a good chance of exploring the collective behavior of the so-called social atoms. By means of the rank-ordering statistics, we demonstrate that the duration data of those ancient dynasties could be described with good accuracy by the Weibull distribution. It is thus amazing that the distribution of time to failure of human society, i.e. the disorder of a historical dynasty, follows the widely accepted Weibull process as natural material fails.