Journal on Policy and Complex Systems
vapor to liquid to solid . In regional development , would the transition from agricultural to industrial to informational to networked stand the definition of phase change given here ? These are often referred to as phases of economic development , but in what sense would such developments be reversible ?
The Centrality of Phase Space
Understanding the dynamics of
phase in social systems is the sine qua non of our ability to develop and implement meaningful and effective policies in the realm of complex adaptive social systems . Researchers have , correctly in my opinion , focused on events involving “ spontaneous disassembly ,” like stampedes and riots ( Colander , et al ., 2004 ), because of the theoretical observation that a phase change involves a radical and spontaneous change in system structure .
It is important to remember , however , that change in system structure itself has an underlying cause : the crossing of a physical boundary , a phase line , in phase space . Phase lines appear where bifurcations occur . A bifurcation in the analysis of complexity is not the simple splitting of a whole into two parts , or the branching of a network . A bifurcation is the doubling of the number of values that a state variable can occupy . Bifurcations occur under the influence of a “ bifurcation parameter ,” the value of which is system-specific and reflective of the physicality of the system . A change in its value is usually associated with a change in the total energy available to the system . As the value of that parameter changes continuously , the system can at certain points undergo discontinuous changes , radically altering the behavioral properties of the system . The same system can go from simple and stable to complex and chaotic , depending upon the value of this driving parameter . As the value of this parameter changes , the system becomes unstable until it bifurcates and becomes once again stable and the process begins again . This process can produce an infinite series of bifurcations ; however , the range of the value of the bifurcation variable over which the system remains stable diminishes as the value of this parameter increases , so there is a limit to the number of times a bifurcation can occur that will result in stable states . This limit is a function of the physicality of the system , but systems where it goes beyond three are rare . Beyond that point , the system is chaotic ( May & Oster , 1976 ).
Identifying the bifurcation parameter would seem to be the prime objective of research in complex social systems . It would seem to me that enormous progress could be made on this question by a retrofit of existing data on social systems . Repositories are full of data on social systems . Much of it has been collected under the assumption that the relationships among the variables are time invariant and linear , which we now know is not true ; but so much is known about these systems already , that taking another look simply to determine the existence of bifurcations could be very productive . The modern frenzy over Big Data is also fortuitous . Care would have to be taken in mining
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