Abstract

Many examples exist of systems made of a large number of comparatively simple elementary constituents which exhibit interesting and surprising collective emergent behaviours. They are encountered in a variety of disciplines ranging from physics to biology and, of course, economics and social sciences. We all experience, for instance, the variety of complex behaviours emerging in social groups. In a similar sense, in biology, the whole spectrum of activities of higher organisms results from the interactions of their cells and, at a different scale, the behaviour of cells from the interactions of their genes and molecular components. Those, in turn, are formed, as all the incredible variety of natural systems, from the spontaneous assembling, in large numbers, of just a few kinds of elementary particles (e.g., protons, electrons).

To stress the contrast between the comparative simplicity of constituents and the complexity of their spontaneous collective behaviour, these systems are sometimes referred to as “complex systems”. They involve a number of interacting elements, often exposed to the effects of chance, so the hypothesis has emerged that their behaviour might be understood, and predicted, in a statistical sense. Such a perspective has been exploited in statistical physics, as much as the later idea of “universality”. That is the discovery that general mathematical laws might govern the collective behaviour of seemingly different systems, irrespective of the minute details of their components, as we look at them at different scales, like in Chinese boxes.