We begin by focusing on the ways we record the myriad of events that make up our lives, using simple models that are intended to capture the dominant features of those events and to provide coherent interlinking of events. If the world did not change in time, more and more detail could be added to these models, with each repetition of an event. Eventually we would have an accurate reconstruction of a successful economic relationship, of a nurturing family, or of a supportive organization. But things do change, even if our reactions to them do not. To understand these changes scientists have developed techniques that quantify and communicate objective models of these subjective events. Without presenting the technical details of how scientists construct such models, I use a combination of personal history and discussions of the science hidden by a variety of social problems, to lay the foundation for the understanding and resolution of these problems in subsequent chapters.

Everyone knows the future cannot be predicted and yet fortune cookies are invariably received with pleasant anticipation. In this chapter we review how science came to terms with uncertainty, through the invention of statistics and probability, but perhaps more importantly, how this world view was made compatible with the clockwork universe of Newton. If the changing events of one’s life are treated as being linear, then response is proportional to stimulus, with perhaps a little error. But the error in this view is subject to law, and is therefore controllable. The linear world view, with Normal statistics to explain uncertainty, is the model of reality adopted by most people, either implicitly or explicitly. It is this world view that promotes the idea that equality and fairness are not only what is true, but more importantly they are what ought to be true.

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.

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.

Science is about finding order in the panorama of the world and embracing a perspective that includes the falling of apples and the motion of planets; the behavior of the individual and the actions of groups, large and small; the information content of an encyclopedia and the Wikipedia; in short, science does not, and should not, have any boundaries with regard to content. The terrestrial and the cosmic are part of the give and take in science, with the goal of uncovering the principles and laws that determine how the universe functions, along with the individuals within it. For most people, science appears to be separate and apart from the world in which they live. The principles and laws of science do not seem to apply to the general interactions among people; due, in part, to the fact that principles have not been found for everyday decision making; laws have been notoriously absent from mundane thinking; rules have been sought in vain in the growth of society; and indeed canons go begging in the multiple complex phenomena within the human sciences, despite over two hundred years of effort to either invent or find them. In this chapter we examine the Principle of Complexity Management, whereby a system with greater information, but perhaps lesser energy, can dominate a system with lesser information, but greater energy. The principle is a recently proven generalization of an observation made by the mathematician Norbert Wiener, and may be one of these universal principles.

This chapter provides a summary of the material discussed; highlighting what is important and connecting those parts of the story that might have been obscured in presenting the details. This apology is my understanding of the formal justification for complexity in the real world. In turn, it is an examination of what complexity implies, about the difference between how we react to what we have, as opposed to reacting to what we want, but do not have. People always respond to events according to their mental maps of the world. Consequently, when they find the response to be inappropriate, the most reasonable thing to do is change the map. However, people are not always reasonable or logical.