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.
