������������������������������������
intense internally — within the same box — than externally across boxes . Finally , Simon ( 1973 ) states his scientific preference for laws that describe relations across hierarchical levels , minimizing traditional approaches that simply describe the fundamental parts of the system .
Simon ( 1973 ) introduces the concept of nearly decomposability , according to which it is possible to distinguish the interactions of a system using the frequency of interaction among its components . If the interactions observed among the particles of a system occur less frequently than a given time T , then those interactions can be considered constant . Similarly if the interactions occur with a higher frequency than another given parameter τ , the interactions can be disregarded as nuisance .
Simon also contributes with the insight of loose coupling , according to which the independence among subsystems of a higher system implies functional effectiveness , in the sense that each subsystem is autonomous and self-organizes in the absence of other subsystems .
These interactions described by Simon — especially those involving citizens and the environment — often result in a ‘ common pool resources ’ problem . This kind of problems affect simultaneously a large number of involved parties that are all responsible , but not each one individually . These problems are not easy to solve , although a diversity of managerial solutions can be found ( Ostrom , 1990 ). Usually , large groups would find it especially hard to pursue common objectives ( Olson , 2007 [ 1965 ]).
Another concept that relates to the idea of boundaries , hierarchies , and interactions among parts , following Simon ’ s boxes is that of autopoiesis ( Maturana & Varela , 1980 ; Varela , Maturana , & Uribe , 1974 ). A system would exhibit autopoiesis when it is able to maintain its characteristics , functionality , and reproducibility , despite the external environment and its influences . In doing so , the system is autonomous . The most common example is a biological cell , although other systems such as animal colonies or even cities could also be considered as such .
When considering the dynamics of interactive systems , May ( 1976 ) points out that simple nonlinear models may behave in a number of dynamic ways , from stable points to apparently random fluctuations . He considers a model that shows how the magnitude of population in one generation correlates to the magnitude of that same population in the previous generation , and highlights that this logic of recurrence can be found in different fields of science . He uses the logistic equation to describe the intertemporal relation between population size in two periods . Depending on the value of the growth parameter , the system assumes different dynamic behaviors .
May demonstrates that a simple deterministic equation can lead to trajectories that are similar to a random noise . May states that the implications are disturbing . Firstly , apparently random fluctuations of a variable may , in fact , come from a rigidly deterministic structure . This would be ‘ deterministic chaos ’. Second , in a chaotic regime , very small variations in initial conditions may lead to highly diverging trajectories . Thus , even in a system in which parameters are strictly determined , long range predictions may be impossible . This is the classic concept of ‘ sensitivity to initial conditions ’, largely described within the theory of dynamic systems .
Turing ( 1950 ) hints at an early version of this ‘ butterfly effect ’:
The system of the ‘ universe as a whole ’ is such that quite small errors in the initial conditions can have an overwhelming effect at a later time . The
13