Journal on Policy & Complex Systems Volume 4, Number 1, Spring 2018 | Page 119

Journal on Policy and Complex Systems
interacting components , without central control , whose emergent ‘ global ’ behaviour — described in terms of dynamics , information processing , and / or adaptation — is more complex than can be explained or predicted from understanding the sum of the behavior of the individual components ” ( Santa Fe Institute , n . d .). Some of these properties , as lack of central authority , are self-explanatory , but others deserve to be briefly explained .
Nonlinearity in mathematics implies nonadditivity ( Boccara , 2004 , p . 56 ). A linear system is one that can be inferred “ by understanding its parts individually and then putting them together ,” but “ a nonlinear system is one in which the whole is different from the sum of the parts ” ( Mitchell , 2009 , pp . 22 – 23 ). Hence , nonlinear relationships between agents in a system imply “ that an independent variable does not have a constant effect on the dependent variable ” ( Richards , 2000a , pp . 1 – 2 ). Nonlinearity is also closely related to the concept of sensitive dependence on initial conditions and chaotic behavior .
The idea of sensitive dependence on initial conditions was first formalized by the mathematician Henri Poincaré at the end of the nineteenth century . Poincaré noticed that the initial configurations of a system play a determining role in setting the subsequent states of the system , and “ when the sensitivity is high , slight changes to starting conditions will lead to significantly different conditions in the future ” ( Santa Fe Institute , n . d .). Systems with sensitivity to initial conditions often manifest chaotic behavior , which is a specific dynamic where systems change following trajectories that appear to be random ( Mitchell , 2009 , p . 32 ). As it has been proved , even a simple and deterministic equation as the logistic map , which is used to describe population growth in the presence of overcrowding , can lead to chaotic behavior even if its parameters are determined exactly . As it can be inferred , sensitive dependence on initial conditions renders perfect prediction in modeling impossible in principle because variables cannot be measured “ to infinitely many decimal places ” ( Mitchell , 2009 , p . 33 ).
Emergent behavior is as well related to the principle of nonlinearity . Emergent properties can be defined as “ global-level attributes of a system that arise from the interactions of the components of the system , and that are not explainable by the behavior of individual components of the system or the sum of the components acting as individuals ” ( Santa Fe Institute , n . d .). It is important to underline that emergent properties at the systemic level are an outcome of the nonlinear interaction of agents , and not of the agent ’ s properties ( Boccara , 2004 , p . 97 ). Hence , knowing the rules to which agents obey is not enough to predict the behavior of the system . The system is computationally irreducible , and , for this reason , CASs has neither reductionist explanations nor yield to compact forms of representations ( Mitchell , 2015a ).
Self-organization , as defined by Melanie Mitchell ( 2015b ), is itself an emergent phenomenon , which can be described as the “ production of organized patterns , resulting from localized
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