A Study of the Origin of Complexity in the Science of Complexity

The science of complexity has been one of the most concerned scientific fields. In the science of complexity, one of the most primary issues is about what is the origin of complexity. This paper aims to mathematically give its solutions in the context of general systems studies. It proves that for any complex system in nature and society, its complexity is caused and dominated by the relationship cycle over the so\|called fundamental level \$H\-d\$ of its hierarchy. On the other hand, it has obtained rich fruits in the study of physical, chemical, and biological systems, and has started on related questions in economics as development on the complex adaptive systems (CAS) to the effect that a new force suddenly came to the fore in Complexity Science in the 90s. However, the development of the CAS concept in the context of organizational and management research is still at its earliest stages. The advances in systems theory, mathematics and computer science on which the above progress rests should be useful also to management science. Research on the evolution or reengineering for business organization should focus ultimately on developing the adaptive enterprise models embodied in useful software packages. We present this paper in memory of Prof.Xu Guozhi and with the hope to carry forward his unfinished wishes.