Hierarchical Order I
The purpose of the hierarchical organization is to strengthen the response by means of two general implements: (i) specification of multi-level structure so that each level to respond to specific impacts; (ii) the levels cooperate one with another by means of inter-level feedbacks. The role of the inter-level feedbacks is to sustain the response of any given level bounded by means of keeping local amplifications, local damping, and other non-linear effects restrained. The general purpose of the inter-level feedbacks to sustain long-term stability suggests that they must obey boundedness. Further, the ubiquity of the universal properties of the complex systems promptly suggests that the inter-level feedbacks must appear as a bounded “environment” for every hierarchical level. The non-trivial application of the concept of boundedness to quantum phenomena is considered.