Mathematical methods are only one moment in a layered process of theory generation in political economy, which starts from Schumpeterian vision, progresses to the identification of relevant abstractions, the development of mathematical and quantitative models, and the confrontation of theories with empirical data through statistical methods. But today the relevant abstract problems of political economy are modified to fit available mathematical tools. The role of empirical research in disciplining theoretical speculation, on which the scientific traditions integrity rests, was undermined by specific limitations of nascent econometric methods, and usurped by ex cathedra methodological fiats of theorists. These developmentssystematically favored certain ideological predispositions of economicsas a discipline. There is abundant room for New Thinking in political economy starting from the vision of the capitalist economy as a complex, adaptive system far from equilibrium, including the development of the theory of statistical fluctuations for economic interactions, redirection of macroeconomics and financial economics from path prediction toward an understanding of the qualitative properties of the system, introduction of constructive and computable methods into economic modeling, and the critical reconstruction of econometric statistical methods.
Qualitative properties for the 1 − D impulsive wave equation: controllability and observability
