ABSTRACT
This chapter first introduces the concept of the impredicative loop (Section 7.1) in general terms. Then, to make easier the life of readers not interested in hard theoretical discussions, additional theory has been omitted from the main text. Therefore, Section 7.2 provides examples of applications of impredicative loop analysis (ILA) to three metabolic systems: (1) preindustrial socioeconomic systems, (2) societies basing their metabolism on exosomatic energy and (3) terrestrial ecosystems. Section 7.3 illustrates key features and possible applications of ILA as a heuristic approach to be used to check and improve the quality of multi-scale integrated analyses. That is, this section shows that ILA can be used as a metamodel for the integrated analysis of metabolic systems organized in nested hierarchies. The examples introduced in this section will be integrated and illustrated in detail in Part 3, dealing with multi-scale integrated analysis of agroecosystems. The chapter ends with a two technical sections discussing theoretical aspects of ILA. The first of these two sections (Section 7.4) provides a critical appraisal of conventional energy analysis — an analytical tool often found in scientific analyses of sustainability of agroecosystems. Such a criticism is based on hierarchy theory. The second section (Section 7.5) deals with the perception and representation of autocatalytic loops of energy forms from a thermodynamic point of view (nonequilibrium thermodynamics). In particular, we propose an interpretation of ILA, based on the rationale of negative entropy, that was provided by Schroedinger and Prigogine in relation to the class of dissipative systems. Even though these last two sections do not require any mathematical skills to be followed, they do require some familiarity with basic concepts of energy analysis and nonequilibrium thermodynamics. In spite of this problem, in our view, these two sections are important since they provide a robust theoretical backup to the use of ILA as a meta-model for dealing with sustainability issues.
