The linear additive world view, in which uncertainty is described by Normal
statistics, is replaced by a nonlinear multiplicative world view in this chapter; the
simple yielding to the complex. One consequence of the complex world view is that
uncertainty is characterized by inverse power-law, rather than Normal, statistics. The
implications of this complex representation of the world are immediate and profound.
One inherent advantage is that the complex vantage point provides a single coherent
view of disruptive mechanisms in complex phenomena; mechanisms ranging in
physical science from earthquakes to floods; in social science from stock market
crashes to the failure of power grids; in medical science from heart attacks to flash
crashes in health care; and in biological science from the extinction of species to
allometry relations. Extrema are more frequent in the complex world than they are in
the simple world of Normalcy. The effects of extreme events are certainly unfair, and
fortunately they do not occur every day. But when disruptive events do occur they
introduce crossroads, and the selection of which road to take determines the subsequent
course of events in a person’s life. Consequently, understanding the source of extrema
enables an individual to take back control from the hands of fate.
Keywords: Bursting, Complexity, Crashes, Extrema, Fractals, Hospitals,
Intermittency, Nonlinear dynamics, Non-normal statistics, Power grids, Quakes,
Tipping point, Unfairness.
