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.