Contemporary physics has fundamentally challenged many of our intuitive conceptions. This is already the case for our conceptions of space and time with relativity, but this challenge goes even further with quantum mechanics. If we take its formalism literally, it is the very concept of reality that is challenged. The notion of a physical object with well-defined properties, existing independently of any observer, is incompatible with quantum theory. So what image of the world around us should we adopt?

It seems clear to everyone that a physical system subject to chance, or whose behavior is governed by extremely complicated rules, will not be predictable: knowing its future behavior will be impossible. On the other hand, it seems intuitive that a system governed by a small number of very simple and entirely deterministic rules (i.e. in which chance plays no part) will behave in a way that can be predicted fairly easily. Surprisingly, this is not the case! There are simple, fully deterministic systems for which, however, it is impossible to predict their behavior.

Complex systems” are omnipresent in the real world, from a computer network such as the Internet, to the brain, a traffic jam, a human population or a galaxy. Yet their general and systematic study, which attempts to identify their commonalities beyond their diversity, is relatively recent. Distinguishing between complicated and complex systems, identifying the type of “holistic” behavior that characterizes them, detecting and understanding the global emergent properties that result from the interactions between their constituents - all this is part of what we now call the sciences of complexity.