Learn what the experts mean when they talk about “complex” systems. Discover why these networks of diverse, connected, and adaptive entities acting in interdependent ways are so powerful, and why understanding them is crucial to so many disciplines.

Using the concept of a mountainous landscape as both metaphor and mathematical object, you begin to grasp the ways in which concepts like “rugged” or “dancing” landscapes—where adaptation and learning are vital for survival—can be visualized even by nonmathematicians.

You develop your understanding of complexity’s key components of interdependence, connectedness, diversity, and adaptation/learning. And you learn—by figuratively dialing the strength of each of these components up or down—why the proper balance between them is essential if a system is to be complex.

Variance and diversity have very different meanings in the world of complexity theory. Grasping that difference puts you on the way to understanding how complex systems achieve diversity and why diversity enables them to be both innovative and robust, maintaining functionality even when the system is disturbed.

Actors in complex systems face a constant tradeoff. Do they exploit the knowledge already learned in past explorations to achieve a solution? Or do they continue to explore, seeking an even better solution? Learn the pros and cons of each, and how the best balance can be achieved.

One of the most fascinating ideas in complexity theory is that of emergence, the spontaneous creation of order and functionality from the bottom up, with no “central planner” putting them into place. You gain an appreciation of the two kinds of emergence and why each is a source of wonder.

Continuing the discussion of emergence, you see how emergence applies to networks and why network theory has become such an active discipline. And you understand how modern complexity theory adds to the study of networks the previously ignored element of space.

Agent-based modeling—in which computers model complex systems from interdependent agents—may be complexity theory’s most promising tool. Its full potential hasn’t yet been realized, but this lecture offers a taste of what it can already achieve in disciplines as disparate as fire prevention and disease transmission.

Drill even deeper into the implications of interdependent agents as you focus on the idea of feedbacks—both the positive ones, in which “more creates more,” and the negative ones, in which “more creates less.”

Complex systems often create large events. Using the example of how a single unscreened passenger in Atlanta delayed flights and passengers across the nation, you are introduced to one of the key concepts that explain how complex systems can be so powerful.

There is a vast difference between thinking of events as “random” and recognizing them as the output of a complex system. Explore three conventional explanations of randomness before turning to a fourth—the interdependent rules-based analysis offered by complexity theory.

Although complex systems can’t be controlled, we may well be able, with proper respect, to harness them. Learn why conventional decision theory doesn’t work in complex environments and what a proper use of complexity theory might promise us instead.