Complex systems exist everywhere in nature and in the world created by human beings. A system is said to be "complex" if it is capable of generating unexpected results. "Emergence" is the name scientists have given to events that defy scientific laws based on order and stability. The most quoted example of "emergence" is the butterfly that flaps its wings in the Amazon and causes a hurricane in the Gulf of Mexico.
While traditional science has modeled systems as closed and in equilibrium, we are learning that reality is open and always ready to turn chaotic. A crowd turns into a mob. Smoothly flowing traffic suddenly increases and I-95 is blocked for hours. Human cells grow out of control and turn into cancerous tumors. A stable market suddenly shows signs of panic and crashes. A rock group comes from nowhere and sells 5 million CDs worldwide. Such things happen in airline traffic, and in the human body, in the financial and real estate markets, and in the global economy, in ecosystems and the Earth's climate.
Fifty years ago the science of complexity was in its infancy. The analysis of the behavior of systems started more or less in the 1940s. Until then, scientists worked in a linear world, and built ideal simplifications. Physics followed the straightforward rules of Newtonian mechanics. Neoclassical economics postulated that people always behaved in their rational self-interest, and markets moved toward quiet balance. These closed theories were powerful descriptors, and allowed the world to make great economic, scientific, and technological progress in less than two centuries. But we have reached the point in the evolution of scientific knowledge where straight-line, cause-and-effect explanations no longer account for a world where systems are open and interdependent, where events are sometimes self-generating — located, as scientists like to say, "on the edge of chaos."