The point of "Complex Dynamic Systems" or "Chaos Theory" is that the more parts that are interacting, the more unpredictable the outcome will be. If they were ONLY the sum of their parts, the predictability would be easy.
Good point from Michael. An area that I am interested in is 'wickedness' / complexity in health promotion. The term wicked refers to the fact that they are devilishly complex systems - especially around policy. You can't gather all the policy together and then squeeze them into one overarching policy - so there is no single solution that can be the sum of all parts.
There are several examples we might use to explain how complex systems are not necessarily the sum of their components. A good example is biological complex systems such as the central nervous system, or the biological process in the liver, and the digestive system. Careful assessment of biological processes and outcomes of functions are far many. However, the complexity of the system at the molecular and cellular level and the integration across systems are behind such observation. Read for example the attached article