Broadly speaking, there is not a unique definition of what is local and global because a definition is related to the objective function of the problem for which we evaluate what is local and global. For instance, if the objective function is food safety, the matter of local vs global is related to see hoe the function food safety change with distance (or other criteria) used to define local vs global. Other criteria rather than distance may be related to the size of the produced coupled to the distance. Additionally, the definition of local vs. global is dependent on the resolution at which an observer look at the problem. Rochester, MN can be local for Minnesotans and for the US population, as well as India can be local for Asia but not for the World. What is the property for which we define local vs global? In all this apparent mess, rather than finding a definition for what is local and or global the solution is to look for scale-invariance of the objective function we want. Ideally the system should always be considered as a whole a multiscale analysis should be performed for any property we are interested.
There is no single natural scale at which biological and socio-technical phenomena should be studied; systems generally show characteristic variability on a range of spatial, temporal, and organizational scales. The observer imposes a perceptual bias, a filter through which the system is viewed. This has fundamental evolutionary significance, since every organism is an “observer” of the environment, and life history events alter the perceptual scales and the observed variability. Here variability is referred to the property or objective function defined to study. It likewise has fundamental significance for our own study of biological and socio-technical systems, since the patterns that are unique to any range of scales will have unique causes and biological consequences. The key to prediction and understanding lies in the elucidation of mechanisms underlying observed patterns of the stated objective function. Typically, these mechanisms operate at different scales than those on which the patterns are observed; in some cases, the patterns must be understood as emerging form the collective behaviors of large ensembles of smaller scale units. In other cases, the pattern is imposed by larger scale constraints. Typically it is a combination of both but the purpose of the study determines the complexity to consider. Examination of such phenomena requires the study of how pattern and variability change with the scale of description, and the development of laws for simplification, aggregation, and scaling. Model design aims to detect the right model complexity that is defined as the balance between accuracy, sensitivity, and relevance. This complexity can be found by the determination of scale invariant patterns which tell what is varying when scales are varied.
In conclusion, three bullet points as usual:
– the definition of local and global is DEPENDENT on the objective function that is investigated
– even for the same objective function local and global scales may be different; a scale-invariant analysis can reveal the invariance of the objective function over scales
– the definition of local and global may be much more complex considering not only geographical distance but also other actors that can characterize these words or ”distance” in a continuum