![]() This is the point of the series of differential equation models that Solé provides. But it also maintains that systems undergoing phase transitions can be studied using a mathematical framework that abstracts from the physical properties of those micro-components. This approach is consistent with the generativity view - the new property is generated by the interactions of the micro-components during an interval of change in critical variables. As a critical variable changes a qualitatively new macro-property "emerges" from the ensemble of micro-components from which it is composed. Fundamentally it demonstrates that the aggregation dynamics of complex systems are often non-linear and amenable to formal mathematical modeling. This work is interesting, but I am not sure that it sheds new light on the topic of emergence per se. ![]() It is distinct, because the approach leaves it entirely open that the system properties are generated by the dynamics of the components. This might be summarized with the slogan, "system properties do not require derivation from micro dynamics." Or in other words: systems have properties that don't depend upon the specifics of the individual components - a statement that is strongly parallel to but distinct from the definition of emergence mentioned above. ![]() It is enough to know that system S is formally similar to a two-dimensional array of magnetized atoms (the "Ising model") then we can infer that phase-transition behavior of the system will have specific mathematical properties. The point seems to be that for a certain class of systems, these systems have dynamic characteristics that are formal and abstract and do not require that we understand the micro mechanisms upon which they rest at all. What seems to be involved here is a conclusion that is a little bit different from standard ideas about emergent phenomena. ![]()
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