Human social systems are the most complex systems that we can conceive of, as interaction among their members is by messages which have to be interpreted before they can take any effect — and the interpretation of identical messages sent and received in identical situations can have divergent effects as human actors have long-term memories which makes the effects highly path-dependent. The emergent phenomena in human social systems are therefore even more difficult to understand than related phenomena in anthills or chemical systems. The paper introduces models of immergence and second-order emergence to explain the innovation of norms in human groups of moderate size — as opposed to the the emergent phenomena in human crowds which are quite similar to the phenomena that can be observed in physical and animal systems. Modelling the innovation of norms and norm systems makes it necessary that interactions between model agents can be manifold and path-dependent, i.e. that agents have a long memory and deliberation capabilities. This is shown with an example from modelling criminal or terrorist behaviour.