The purpose of this lecture is to provide an explanation of the process of complication, i.e. the deepening and evolution of complexity in evolving complex linear systems. The complication means the transfer from complex structure to much more complex structure in the evolution of complex systems. The main feature of the evolution of a complex system is the emergence of new properties which did not exist in previous trends and which add new information to the system. The growth of complexity means the appearance and increase of information and therefore the decrease of the (Shannon) entropy. Even the simplification of the system is the part of process of complication, since simplification is clearing the room for the further adoption of new information. This clearing presents the essential force acting against the modern information explosion and playing the important role in the process of self-organization. Spread of information within the complex system presents the essence of the process of complication. This spread shows itself through the partial adoption of new information and through the path dependent process of self-organization within socio-spatial complex system. In this study we will concentrate ourselves only on the forms of complication and self-organization in linear socio-economic systems, leaving behind the innovation diffusion and bifurcation analysis. The concept of complication is pointed out on the deficiency of purely economic considerations of socio-economic systems and stresses the necessity to widen the concept of "Homo Oeconomicus" to the concept of "Homo Socialis". Such a widening is radical in the study of complex socio-economic processes because of the important difference between the economic and socio-economic rationality: the traditional identification of economic rationality of "Homo Oeconomicus" as the optimization is complementary to socio-economic rationality of "Homo Socialis" as parsimony. In our lecture we will apply the paradigm of complexity and complication to several main branches spatially connected with the augmentation and development of flows, networks and superposition of their hierarchies in linear systems. We are using the concept of complication as the unifying frame for theories of linear spatial analysis of complex socio-economic systems: the Push-Pull theory of Migration Streams, the theory of Central Place hierarchies, the spatial production cycles and trade feedback loops, the Dynamic Input-Output Analysis and the theory of the Fields of Influence of changes in Input-Output systems, the classical Key Sector Analysis, the Structural Q-analysis and the Miyazawa model of income distribution within Input-Output systems and their "onion skins" extensions.
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