Unequal: A Matter of Scale

The transition of our mental models from a simple to a complex world view, entails the breakdown of Normalcy and the necessary adoption of Pareto’s inverse power-law distribution. The complexity measure in this new world view is the inverse power law index, whose magnitude determines whether or not variability of the underlying process can be described by a finite variance. It is often the case that in such phenomena the focus shifts away from continuous dynamics of mechanical systems, such as the trajectory of a person’s life, to the time intervals between discrete events, such as having a heart attack or receiving a message. This shifting is particularly evident in information-dominated systems, whose time series may not even possess an average time between events. The appropriate quantities to measure in such fractal dynamical systems are not easy to identify, in fact, what we choose to measure may well be determined by how we define information and how that information changes in time. How information flows in complex networks, or how information moves back and forth between two or more complex networks, is of fundamental importance in understanding how such networks or networks-of-networks operate. This information variability is determined by the inverse power-law distributions, which in turn are generated by a number of generic mechanisms that couple contributing scales together. We identify different mechanisms that produce empirically observed variability; each one prescribing how the scales in the underlying process are interrelated.

Keywords: Allometry, Contagion, Criticality, Decision making, Frequency, Inequality, Inverse power laws, Networks, Rank order, Scaling mechanisms, Space, Time, Universality.