Stop some particle physicists in the street and they will soon be trying to persuade you that the world is altogether simple and symmetrical. But stop a biologist, an economist, or a social scientist and they will tell you quite the opposite: the world is a higgledy-piggledy collection of complexities that owes little to symmetry and displays precious little simplicity. So who is right : is the world really complicated or is it simple ? We shall look at the reasoning that leads to these different conclusions, show why we got different answers to our question, and look at some of the recent developments that have taken place in the study of systems from sand-piles to music on the border between order and chaos. We shall also look at some of ...