Whither nonlinear ?

I have been asked by the Editors to give some thoughts about the future of &complex systems approaches' and nonlinearist methodology in Economic Science. Since this will be an essay that will attempt to stimulate the readers into making up their own thoughts, projections, and guesstimates, this essay shall be written in &English'. This tack is taken here because the writing down of a particular model, especially in mathematics, tends to &freeze' the readers' thoughts onto that particular model. Before beginning, it is good to keep mental focus separated into two categories: (i) microphenomena and (ii) macrophenomena. The macro category is separated from the micro category by the degree of survival of the phenomena to aggregation. To put it another way, the phenomenon is classi"ed as &macro' if it survives a type of law of large numbers, i.e. there must be strong enough dependence across individual micro units in some kind of statistical sense so that the &averaging' e!ect of aggregation does not &wash out' the phenomenon of interest. In addition, in order to have macrodynamics, these limiting aggregates must have dynamical dependence. It is useful to have some precise goals of the research in mind. In the spirit of complexity theory which emphasizes robust explanations for &scaling laws' and &patterns' as well as conventional economics which emphasizes policy relevant prediction and prediction out of sample, we shall discipline our peering into the future by concentrating on innovations that have promise for doing a better job of matching (&explaining') observed patterns and scaling laws as well as prediction. This essay proceeds as follows. First, a rough attempt is made to illustrate what is meant by &complex systems' for the purpose of this essay. Second, although much complex systems based research is boundedly rational, a debate continues in economics on the costs and bene"ts of rational expectations modeling versus boundedly rational/evolutionary modeling (Kreps, 1997). The argument here will be to use computational advances and computer assisted methods to allow both approaches to compete in either a &nested' testing setting or, perhaps, in a &Bayesian'manner to give a decomposition of the variability and patterns seen in the data. Third, the &Resilience Network' view, which is a general &systems theoretic' framework is sketched. This view is rather like that of control systems engineering but with a temporal hierarchy of time scales and lots of &nonlinearity', &heterogeneity', and &adaptability', added.