171 7 Impredicative Loop Analysis: Dealing with the Representation of Chicken-Egg Processes* 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 meta-model 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. 7.1 Introducing the Concept of Impredicative Loop Impredicativity has to do with the familiar concept of the chicken-egg problem, or what Bertrand Russel called the vicious circle (quoted in Rosen, 2000, p. 90). According to Rosen (1991), impredicative loops are at the very root of the essence of life, since living systems are the final cause of themselves. Even the latest developments of theoretical physics—e.g., superstring theory—represent a move toward the very same concept. Introducing such a theory, Gell-Mann (1994) makes first reference to the bootstrap principle (based on the old saw about the man that could pull himself up by his own bootstraps) and then describes it as follows: “the particles, if assumed to exist, produce forces binding them to one another; the resulting bound states are the same particles, and they are the same as the ones carrying the forces. Such a particle system, if it exists, gives rise to itself ’ (Gell-Mann, 1994, p. 128). The passage basically means that you have to assume the existence of a chicken to get the egg that will generate the chicken, and vice versa. As soon as the various elements of the self-entailing process—defined in parallel on different levels—are at work, such a process is able to define (assign an identity) to itself. The representation of this process, however, requires considering processes and identities that can only be perceived and represented by adopting different space-time scales. * Kozo Mayumi is co-author of this chapter. © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems172 A more technical definition of impredicativity provided by Kleene and related more to the epistemological dimension is reported by Rosen (2000, p. 90): When a set M and a particular object m are so defined that on the one hand m is a member of M, and on the other hand the definition of m depends on M, we say that the procedure (or the definition of m, or the definition of M) is impredicative. Similarly when a property P is possessed by an object m whose definition depends on P (here M is the set of objects which possess the property P), an impredicative definition is circular, at least on its face, as what is defined participates in its own definition. (Kleene, 1952, p. 42) It should be noted that impredicative loops are also found in the definition of the identity of crucial concepts in many scientific disciplines. In biology, the example of the definition of the mechanism of natural selection is well known (the survival of the fittest, in which the “fittest” is then defined as “the surviving one”). The same mechanism is found in the basic definition of the first law of dynamics (F= m×a), in which the force is defined as what generates an acceleration over a mass, whereas an acceleration is described, using the same equation, as the result of an application of a force to a given mass. Finally, even in economics we can find the same apparently tautological mechanism in the wellknown equation P×Y=M×V (price level times real gross national product (GNP) equal to amount of money times velocity of money circulation), in which the terms define and are defined by each other. Impredicative loops can be explored by explicitly acknowledging the fact that they are in general occurring across processes operating (perceived and represented) in parallel over different hierarchical levels. That is, definitions based on impredicative loops refer to mechanisms of self-entailment operating across levels and that therefore require a set of representations of events referring to both parts and wholes in parallel over different scales. Exactly because of that, as it is discussed in the technical Section 7.4, they are out of the reach of reductionist analyses. That is, they are out of the reach of analytical tools developed within a paradigm that assumes that all the phenomena of the reality can be described within the same descriptive domain, just by using a set of reducible models referring to the same substantive definition of space and time. However, this does not imply that impredicative loops cannot be explored by adopting an integrated set of nonequivalent and nonreducible models. That is, by using a set of different models based on the adoption of nonequivalent descriptive domains (nonreducible definition of space and time in formal terms—as discussed by Rosen (1985) and in the technical section at the end of this chapter), it is possible to study the existence of an integrated set of constraints. These constraints are generated by the reciprocal effect of agency on different levels (across scales) and are referring to different relevant characteristics of the process (across disciplinary fields). The feasibility of an impredicative loop, with this approach, can be checked on different levels by using nonreducible models taking advantage of the existence of mosaic effects across levels (Giampietro and Mayumi, 2000a, 2000b; Giampietro et al., 2001). However, this approach requires giving up the idea of using a unique narrative and a unique formal system of inference to catch the complexity of reality and to simulate the effects of this multi-scale self- entailment process (Rosen, 2000). Giving up this reductionist myth does not leave us hopeless. In fact, the awareness of the existence of reciprocal constraints imposed on the set of multiple identities expressed by complex adaptive holarchies (the existence of different dimensions of viability, e.g., chemical constraints, biochemical constraints, biological constraints, economic constraints, sociocultural constraints) can be used to do better analyses. 7.2 Examples of Impredicative Loop Analysis of Self-Organizing Dissipative Systems 7.2.1 Introduction With the expression “impredicative loop analysis” we want to suggest that the concept of impredicative loop can be used as a heuristic tool to improve the quality of the scientific representation of complex © 2004 by CRC Press LLC Impredicative Loop Analysis: Dealing with the Representation of Chicken-Egg Processes 173 systems organized in nested hierarchies. The approach follows a rationale that represents a major bifurcation from the conventional reductionist approach. That is, the main idea is that first of all it is crucial to address the semantic aspect of the analysis. This implies accepting a few points that are consequences of what was presented in Part 1: 1. The definition of a complex dissipative system, within a given problem structuring, entails considering such a system to be a whole made of parts and operating in an associative context (which must be an admissible environment). In the step of representation this implies establishing a set of relations among a set of formal identities referring to at least five different hierarchical levels of analysis: (1) level n-2, subparts; (2) level n-1, parts; (3) level n, the whole black box; (4) level n+1, an admissible context; and (5) level n+2, processes in the environment that guarantee the future stability of favorable boundary conditions associated with the admissible context of the whole. An overview of such a hierarchical vision of an autocatalytic loop of energy forms is given in Figure 7.1. This representation can be directly related to the discussion in Chapter 6 about multi-scale mosaic effects for metabolic systems organized in nested hierarchies. 2. It is always possible to adopt multiple legitimate nonequivalent representations of a given system that are reflecting its ontological characteristics. Therefore, the choice of just one particular representation among the set of potential representations reflects not only characteristics of the observed system, but also characteristics of the observer (goals of the analysis, relevance of system’s qualities included in the semantic identity, credibility of assumptions about the models, congruence of nonequivalent perceptions of causal relations in different descriptive domains). 3. A given problem structuring (the system and what it does in its associative context) reflects an agreement about how to perceive and represent a complex adaptive holarchy in relation to the choices of (1) a set of semantic identities (what is relevant for the observer about the observed) and (2) an associated set of formal identities (what can be observed according to available detectors and measurement schemes), which will be reflected into the selection of variables used in the model. It is important to notice that such an agreement about what is the system and what the system is doing in its context is crucial to get into the following step of selection of formal identities (individuation of variables used as proxies for observable qualities). Prior to reaching such an agreement about how to structure in scientific terms the problem of how to represent the system of interest, experimental data do not count as relevant information. That is, before having a valid (and agreed-upon) problem structuring that will be used to FIGURE 7.1 Hierarchical levels that should be considered for studying autocatalytic loops of energy forms. © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems174 represent the complex system using different models referring to different scales and different descriptive domains, data per se do not exist. The possibility of using data requires a previous validated definition of (1) what should be considered relevant system qualities, (2) which observable system qualities should be used as proxies of these relevant qualities and (3) what is the set of measurement schemes that can be used to assign values to the variables, which then can be used in formal models to represent the system’s behavior. The information provided by data therefore always reflects the choices made when defining the set of formal identities adopted in the representation of the reality by the analyst. Sometimes scientists are aware of the implications of these preanalytical choices, and sometimes they are not. Actually, the most important reason for introducing complex systems thinking is increasing the transparency about hidden implications associated with the step of modeling. The approach of impredicative loop analysis is aimed at addressing this issue. The meat of ILA is about forcing a semantic validity check over the set of formal identities adopted in the phase of representation by those making models. To obtain this result, it is necessary to develop meta-models that are able to establish typologies of relations among parts and wholes, which can be relevant and useful when dealing with a class of situations. Useful meta-models can be applied, later on, to special (individual) situations belonging to a given typology. These meta-models, to be useful, have to be based on a standard characterization of the mechanism of self-entailment among identities of parts, whole and context, defined on different levels. Actually, this is exactly what is implied by the very concept of impredicative loop. Looking for meta-models, however, implies accepting the consequence that any impredicative loop does have multiple possible formalizations. That is, the same procedure for establishing relations among identities of parts and the whole within a given impredicative loop can be interpreted in different ways by different analysts, even when applied to the same system considered at the same point in space and time. Meta-models, by definition, generate families of models based on the adoption of different sets of congruent formalization of identities. Obviously, at the moment of selecting an experimental design (or a specific system of accounting), we will have to select just one particular model to be adopted (to gather experimental data) and stick with it. Experimental work is based on the selection of just one of the possible formalizations of the meta-model, applied at a specific point in space and time. This transparent arbitrariness of models that are built in this way should not be considered a weakness of this approach. On the contrary, in our view, this should be considered a major strength. In fact, after acknowledging from the beginning the existence of an open space of legitimate options, analysts coming from different disciplinary backgrounds, cultural contexts or value systems are forced to deal, first of all and mainly, with the preliminary discussion of semantic aspects associated with the selection of models. This certainly facilitates a discussion about the usefulness of models and enhances the awareness of crucial epistemological issues to be considered at the moment of selecting experimental designs. Below we provide three practical examples of dissipative systems: (1) a preindustrial society of 100 people on a desert island, (2) a comparison of the trajectory of development of two modern societies that base the metabolism of their economic process on exosomatic energy (Spain and Ecuador), and (3) the dynamic budget stabilizing the metabolism of terrestrial ecosystems. For the moment, we just describe how it is possible to establish a relation between characteristics of parts and the whole of these systems in relation to their associative contexts. Common features of the three analyses will be discussed in Section 7.3. More general theoretical aspects are discussed in Section 7.5. 7.2.2 Example 1: Endosomatic Societal Metabolism of an Isolated Society on a Remote Island 7.2.2.1 Goals of the Example—As noted earlier, the ability to keep a dynamic equilibrium between requirement and supply of energy carriers (e.g., how much food must be eaten vs. how much food can be produced in a preindustrial society) entails the existence of a biophysical constraint on the relative sizes and characteristics of various sectors making up such a society. The various activities linked to both production and consumption must be congruent in terms of an analysis based on a combined use © 2004 by CRC Press LLC Impredicative Loop Analysis: Dealing with the Representation of Chicken-Egg Processes 175 of intensive and extensive variables across levels (mosaic effects across levels—Chapter 6). That is, we can look at the reciprocal entailment among the definitions of size and characteristics of a metabolic system organized on nested hierarchical levels (parts and whole). Then we can relate it to the aggregate effect of this interaction on the environment. This is what we call an impredicative loop analysis. Coming to this first example, we want to make it immediately clear to the reader that the stability of any particular societal metabolism does not depend only on the ability of establishing a dynamic equilibrium between requirement and supply of food. The stability of a given human society can be checked in relation to a lot of other dimensions—i.e., alternative relevant attributes and criteria. For example, is there enough drinking water? Can the population reproduce in the long term according to an adequate number of adult males and females? Are the members of the society able to express coordinated behavior to defend themselves against external attacks? Indeed, using an analysis that focuses only on the dynamic equilibrium between requirement and supply of food is just one of the many possible ways for checking the feasibility of a given societal structure. However, given the general validity of the laws of thermodynamics, such a check cannot be ignored. As a matter of fact, the same approach (checking the ability of obtaining a dynamic equilibrium between requirement and supply) can be applied in parallel to different mechanisms of mapping that can establish forced relations among flows and sizes of compartments and wholes across levels, in relation to different flows (as already illustrated in Chapter 6), to obtain integrated analysis. The reader can recall here the example of the various medical tests to be used in parallel to check the health of a patient (Figure 6.3). In this first example of impredicative loop analysis we will look at the dynamic budget of food energy for a society. This is like if we were looking at the bones—using x-rays—of our patient. Other types of impredicative loop analysis (next two examples) could represent nonequivalent medical tests looking at different aspects of the patient (e.g., ultrasound scan and blood test). What is important is to have the possibility, later on, to have an overview of the various tests referring to nonequivalent and nonreducible dimensions of performance. This is done, for example, in Figure 7.6, which should be considered an analogous to Figure 6.3. 7.2.2.2 The Example—As soon as we undertake an analysis based on energy accounting, we have to recognize that the stabilization of societal metabolism requires the existence of an autocatalytic loop of useful energy (the output of useful energy is used to stabilize the input). In this example, we characterize the autocatalytic loop stabilizing societal metabolism in terms of reciprocal entailment of the two resources: human activity and food (Giampietro, 1997). The term autocatalytic loop indicates a positive feedback, a self- reinforcing chain of effects (the establishment of an egg-chicken pattern). Within a socioeconomic process we can define the autocatalytic loop as follows: (1) The resource human activity is needed to provide control over the various flows of useful energy (various economic activities in both producing and consuming), which guarantee the proper operation of the economic process (at the societal level). (2) The resource food is needed to provide favorable conditions for the process of reproduction of the resource human activity (i.e., to stabilize the metabolism of human societies when considering elements at the household level). (3) The two resources, therefore, enhance each other in a chicken-egg pattern. In this example we are studying the possibility of using the impredicative loop analysis related to the self-entailment of identities of parts and the whole, which are responsible for stabilizing the autocatalytic loop of two energy forms: chemical energy in the food and human activity expressed in terms of muscle and brain power. Within this framework our heuristic approach has the goal of establishing a relation between a particular set of parameters determining the characteristics of this autocatalytic loop as a whole (at level n) and a particular set of parameters that can be used to describe the characteristics of the various elements of the socioeconomic system at a lower level (level n-1). These characteristics can be used to establish a bridge with technological changes (observed on the interface of level n-1/level n-2) and to effect changes on environmental impact at the interface—level n/level n+1 (see Figure 7.1). In this simplified example, we deal with an endosomatic autocatalytic loop (only human labor and food) referring to a hypothetical society of 100 people on an isolated, remote island. The numbers given in this example per se are not the relevant part of the analysis. As noted earlier, no data set is relevant without a previous agreement of the users of the data set about the relevance of the problem © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems176 structuring (in relation to a specific analysis performed in a specific context). We are providing numbers— which are familiar for those dealing with this topic—just to help the reader to better grasp the mechanism of accounting. It is the forced relation among numbers (and the analysis of the mechanism generating this relation) that is the main issue here. Different analysts can decide to define the relations among the parts and the whole in different ways, and therefore this could lead to a different definition of the data set. However, when adopting this approach, they will be asked by other analysts about the reasons for their different choices. This then will require discussing the meaning of the analysis. The following example of ILA presenting a useful metaphor (meta-model) for studying societal metabolism has two major goals: 1. To illustrate an approach that makes it possible to establish a clear link between the characteristics of the societal metabolism as a whole (characteristics referring to the entire loop—level n) and a set of parameters controlling various steps of this loop (characteristics referring to lower- level elements and higher-level elements—defined at either level n-1 or level n+ 1). Moreover, it should be noted that the parameters considered in this analysis are those generally considered, by default, as relevant in the discussion about sustainability (e.g., population pressure, material standard of living, technology, environmental loading). This example clearly shows that these parameters are actually those crucial in determining the feasibility of the autocatalytic loop, when characterized in terms of impredicative loop analysis. 2. To illustrate the importance of closing the loop when describing societal metabolism in energy terms, instead of using linear representations of energy flows in the economic process (as done with input/output analyses). In fact, the conventional approach usually adopted in energy analysis, based on conventional wisdom, keeps its focus on the consideration of a unidirectional flow of energy from sources to sinks (the gospel says “while matter can be recycled over and over, energy can flow only once and in one direction”). As discussed in Section 7.4, a linear representation of energy flows in terms of input/output assessments cannot catch the reciprocal effect across levels and scales that the process of energy dissipation implies (Giampietro and Pimentel, 1991a; Giampietro et al., 1997). In fact, it is well known that in complex adaptive systems, the dissipation of useful energy must imply a feedback, which tends to enhance the adaptability of the system of control (Odum, 1971, 1983, 1996). Assessing the effect of such feedback, however, is not simple because this feedback can only be detected and represented on a descriptive domain that is different (larger space-time scale) from the one used to assess inputs, outputs and flows (as discussed at length in Sections 7.4 and 7.5). This is what GeorgescuRoegen (1971) describes as the impossibility to perform an analytical representation of an economic process when several distinct time differentials are required in the same analytical domain. Actually, he talks of the existence of incompatible definitions of duration for parallel input/output processes (the replacement of the term duration with the term time differentials is ours). Our ILA of the 100 people on the remote island provides practical examples of this fact. The representations given in Figure 6.6 of how endosomatic energy flows in a society is a classic example of the conventional linear view. Energy flows are described as unidirectional flows from left to right (from primary sources to end uses). However, it is easy to note that some of the end uses of energy (indicated on the right side) are necessary for obtaining the input of energy from primary energy sources (indicated on the left side) in the first place. That is, the stabilization of a given societal metabolism is linked to the ability to establish an egg-chicken pattern within flows of energy. In practical terms, when dealing with the endosomatic metabolism of a human society, a certain fraction of end uses (e.g., in Figure 6.6, the physical activity “work for food”) must be available and used to produce food. The expression autocatalytic loop actually indicates the obvious fact that some of the end uses must reenter into the system as input to sustain the overall metabolism. This is what implies the existence of internal constraints on possible structures of socioeconomic systems. In practical terms, when dealing with the endosomatic metabolism of a human society, a certain fraction of the end uses must be available and used to produce food before the input enters into the system (as indicated on the lower axis of Figure 7.2). © 2004 by CRC Press LLC Impredicative Loop Analysis: Dealing with the Representation of Chicken-Egg Processes 177 7.2.2.3 Assumptions and Numerical Data for This Example—We hypothesize that a society of 100 people uses only flows of endosomatic energy (food and human labor) for stabilizing its own metabolism. To further simplify the analysis, we imagine that the society is operating on a remote island (survivors of a plane crash). We further imagine that its population structure reflects the one typical of a developed country and that the islanders have adopted the same social rules regulating access to the workforce as those enforced in most developed countries (that is, persons under 16 and those over 65 are not supposed to work). This implies a dependency ratio of about 50%; that is, only 50 adults are involved in the production of goods and social services for the whole population. We finally add a few additional parameters needed to characterize societal metabolism. At this point the forced loop in the relation between these numerical values is described in Figure 7.2: • Basic requirement of food. Using standard characteristics of a population typical of developed countries, we obtain an average demand of 9 MJ/day/capita of food, which translates into 330,000 MJ/year of food for the entire population. • Indicator of material standard of living. We assume that the only “good” produced and consumed in this society (without market transactions) is food providing nutrients to the diet. In relation to this assumption we can then define two possible levels of material standard of living, related to two different qualities for the diet. The two possible diets are: (1) Diet A, which covers the total requirement of food energy (3300 MJ/year/capita) using only cereal (supply of only vegetal proteins). With a nutritional value of 14 MJ of energy/kg of cereal, this implies the need to produce 250 kg of cereal/year/capita. (2) Diet B, which covers 80% of the requirement of food energy with cereal (190 kg/year per capita (p.c.)) and 20% with beef (equivalent to 6.9 kg of meat/year p.c.). Due to the very high losses of conversion (to produce 1 kg of beef you have to feed the herd 12 kg of grain), this double conversion implies the additional production of 810 kg of cereal/year. That is, Diet B requires the primary production of 1000 kg of cereal/capita (rather than 250 kg/year of Diet A). Actually, the value of 1000 kg of cereal consumed per capita, in indirect form in the food system, is exactly the value found in the U.S. today (see the relative assessment in Figure 3.1). FIGURE 7.2 One hundred people on a remote island. © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems178 • Indicator of technology. This reflects technological coefficients, in this case, labor productivity and land productivity of cereal production. Without external inputs to boost the production, these are assumed to be 1000 kg of cereal/hectare and 1 kg of cereal/hour of labor. • Indicator of environmental loading. A very coarse indicator of environmental loading can be assessed by the fraction land in production/total land of the island, since the land used for producing cereal implies the destruction of natural habitat (replaced with the monoculture of cereal). In our example the indicator of environmental loading is heavily affected by the type of diet followed by the population (material standard of living) and the technology used. Assuming a total area for the island of 500 ha, we have an index of EL=0.05 for Diet A and EL=0.20 for Diet B (EL=hectares in production/total hectares available on the island). • Supply of the resource human activity. We imagine that the required amount of food energy for a year (330,000 MJ/year) is available for the 100 people for the first year (assume it was in the plane). With this assumption, and having the 100 people to start with, the conversion of this food into endosomatic energy implies (it is equivalent to) the availability of a total supply of human activity of 876,000 h/year (24 h/day×365×100 persons). • Profile of investment of human activity of a set of typologies of end uses of human activity (as in Figure 7.2). These are: 1. Maintenance and reproduction—It should be noted that in any human society the largest part of human activity is not related to the stabilization of the societal metabolism (e.g., in this case producing food), but rather to maintenance and reproduction of humans. This fixed overhead includes: a. Sleeping and personal care for everybody (in our example, a flat value of 10 h/day has been applied to all 100 people, leading to a consumption of 365,000 h/year of the total human activity available). b. Activity of nonworking population (the remaining 14 h/day of elderly and children, which are important for the future stability of the society, but which are not available—according to the social rule established before—for the production of food). This indicates the consumption of another 255,000 h/year (14×50×365) in nonproductive activities. 2. Available human activity for work—The difference between total supply of human activity (876,000 h) and the consumption related to the end use maintenance and reproduction (620,000 h) is the amount of available human activity for societal self-organization (in our example, 256,000 h/year). This is the budget of human activity available for stabilizing societal metabolism. However, this budget of human activity, expressed at the societal level, has to be divided between two tasks: a. Guaranteeing the production of the required food input (to avoid starvation)—work for food b. Guaranteeing the functioning of a good system of control able to provide adaptability in the future and a better quality of life to the people—social and leisure At this point, the circular structure of the flows in Figure 7.2 enters into play. The requirement of 330,000 MJ/year of endosomatic energy input (food at time t) entails the requirement of producing enough energy carriers (food at time t+1) in the following years. That is a biophysical constraint on the level of productivity of labor in the activity producing food. Therefore, this characteristic of the whole (the total demand of the society) translates into a nonnegotiable fraction of investment of available human activity in the end use work for food (depending on technology and availability of natural resources). This implies that the disposable fraction of available human activity, which can be allocated to the end use social and leisure, is not a number that can be decided only according to social or political will. The circular nature of the autocatalytic loop implies that numerical values associated with the characterization of various identities defining elements on different hierarchical levels (at the level of individual compartments; extensive—segments on the axis—and intensive variables; wideness of angles) can be changed, but only respecting the constraint of congruence among flows over the whole © 2004 by CRC Press LLC Impredicative Loop Analysis: Dealing with the Representation of Chicken-Egg Processes 179 loop. These constraints are imposed on each other by the characteristics and size—extensive (1 and 2) and intensive (3) variables—of the various compartments. 7.2.2.4 Changing the Value of Variables within Formal Identities within a Given Impredicative Loop —Imagine to change, for example, some of the values used to characterize this autocatalytic loop of energy forms. For example, let us change the parameter “material standard of living,” which in our simplified model is expressed by a formal definition of quality of the diet. The different mix of energy vectors in the two diets (vegetal vs. animal proteins) implies a quantitative difference in the biophysical cost of the diet expressed in terms of both a larger work requirement and a larger environmental loading (higher demand of land). The production of cereal for a population relying 100% on Diet A requires only 25,000 h of labor and the destruction of 25 ha of natural habitat (EL A =0.05), whereas the production of cereal for a population relying 100% on Diet B requires 100,000 h of labor and the destruction of 100 ha of natural habitat (EL B =0.20). However, to this work quantity required for producing the agricultural crop, we have to add a requirement of work for fixed chores. Fixed chores are preparation of meals, gathering of wood for cooking, getting water, and washing and maintenance of food system infrastructures in the primitive society. In this example we use the same flat value for the two diets—73,000 h/year (2 h/day/capita=2×365×100). This implies that if all the people of the island decide to follow Diet A, they will face a fixed requirement of “work for food” of 98,000 h/year. If they all decide to adopt Diet B, they will face a fixed requirement of “work for food” of 173,000 h/year. At this point, for the two options we can calculate the amount of disposable available human activity that can be allocated to social and leisure. It is evident that the amount of time that the people living in our island can dedicate to running social institutions and structures (schools, hospitals, courts of justice) and developing their individual potentialities in their leisure time in social interactions is not the result of their free choice. Rather, it is the result of a compromise between competing requirements of the resource “available human activity” in different parts of the economic process. That is, after assigning numerical values to social parameters such as population structure and a dependency ratio for our hypothetical population, we have a total demand of food energy (330,000 MJ/ year) and a fixed overhead on the total supply of human activity, which implies a flat consumption for maintenance and reproduction (620,000 h/year). Assigning numerical values to other parameters, such as material standard of living (Diet A or Diet B) and technical coefficients in production (e.g., labor, land and water requirements for generating the required mix of energy vectors), implies defining additional constraints on the feasibility of such a socioeconomic structure. These constraints take the form of (1) a fixed requirement of the resource “available human activity” that is absorbed by “work for food” (98,000 h for Diet A and 173,000 h for Diet B) and (2) a certain level of environmental loading (the requirement of land and water, as well as the possible generation of wastes linked to the production), which can be linked, using technical coefficients, to such a metabolism (in our simple example we adopted a very coarse formal definition of identity for environmental loading that translates into EL A = 0.05 and EL B =0.20). With the term internal biophysical constraints we want to indicate the obvious fact that the amount of human activity that can be invested into the end uses “maintenance and reproduction” and “social and leisure” depends only in part on the aspirations of the 100 people for a better quality of life in such a society. The survival of the whole system in the short term (the matching of the requirement of energy carriers’ input with an adequate supply of them) can imply forced choices (Figure 7.3). Depending on the characteristics of the autocatalytic loop, large investments of human activity in social and leisure can become a luxury. For example, if the entire society (with the set of characteristics specified above) wants to adopt Diet B, then for them it will not be possible to invest more than 83,000 h of human activity in the end use “social and leisure.” On the other hand, if they want, together with a good diet, also a level of services typical of developed countries (requiring around 160,000 h/year/100 people), they will have to “pay” for that. This could imply resorting to some politically important rules reflecting cultural identity and ethical believes (what is determining the fixed overhead for maintenance and reproduction). For example, to reach a new situation of congruence, they could decide to either introduce child labor or increase the workload for the economically active population (e.g., working 10 h a day for 6 days a week) (Figure 7.3). Alternatively, they can accept a certain degree of inequity in © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems180 the society (a small fraction of people in the ruling social class eating Diet B and a majority of the ruled eating Diet A). We can easily recognize that all these solutions are today operating in many developing countries and were adopted, in the past, all over our planet. 7.2.2.5 Lessons from This Simple Example—The simple assumptions used in this example for bringing into congruence the various assessments related to a dynamic budget of societal metabolism are of course not realistic (e.g., nobody can eat only cereal in one’s diet, and expected changes in the requirements of work are never linear). Moreover, by ignoring exosomatic energy, we do not take in account the effect of capital accumulation (e.g., potential use of animals, infrastructures, better technology and know-how affecting technical coefficients), which is relevant for reaching new feasible dynamic points of equilibrium of the endosomatic energy budget. That is, alternative points of equilibrium can be reached by, besides changing population structure and size, changing technology (and the quality of natural resources). Actually, it is easy to make models for preindustrial societies that are much more sophisticated than the one presented in Figure 7.2: models that take into account different landscape uses, detailed profiles of human time use, and reciprocal effects of changes on the various parameters, such as the size and age distribution of society (Giampietro et al., 1993). These models, after entering real data derived from specific case studies, can be used for simulations, exploring viability domains and the reciprocal constraining of the various parameters used to characterize the endosomatic autocatalytic loop of these societies. However, models dealing only with the biophysical representation of endosomatic metabolism and exosomatic conversions of energy are not able to address the economic dimension. Economic variables reflect the expression of human preferences within a given institutional setting (e.g., an operating market in a given context) and therefore are logically independent from assessment reflecting biophysical transformations. Even within this limitation, the example of the remote island clearly shows the possibility of linking the representation of the conditions determining the feasibility of the dynamic energy budget of societal metabolism to a set of key parameters used in the sustainability discussions. In particular, FIGURE 7.3 One hundred people on a remote island. © 2004 by CRC Press LLC [...]... the use of inputs for boosting the agricultural production, or a different mix of typologies of land uses It is important to build a network of analytical tools able to keep coherence in all these descriptions and to provide a multi- scale integrated analysis of changes, effects and trends © 2004 by CRC Press LLC 206 Multi- Scale Integrated Analysis of Agroecosystems FIGURE 7. 16 Application of ILA to... (Figure 7. 1) To explain the nature of the link bridging the representation given in Figure 7. 1 and the representation given in Figure 7. 7, it is necessary to address key features associated with the analysis of the dynamic © 2004 by CRC Press LLC 192 Multi- Scale Integrated Analysis of Agroecosystems FIGURE 7. 8 ILA: The rationale of the Meta Model energy budget of a dissipative system (Figure 7. 8a) This... mechanism of self-entailment of energy forms within ecological processes.The example presented below represents © 2004 by CRC Press LLC 188 Multi- Scale Integrated Analysis of Agroecosystems an attempt in this direction The ILA rationale is applied to the analysis of a self-entailment of energy forms stabilizing the identity of terrestrial ecosystems 7. 2.4.2 An ILA of the Autocatalytic Loop of Energy... size of the ecosystem (at level n) and the size of its relative components (at level n-1) in relation to the representation of events © 2004 by CRC Press LLC 190 Multi- Scale Integrated Analysis of Agroecosystems (intensive variables 3, associated with the identity of parts and lower-level elements) and the consumption and generation of energy carriers/chemical bonds (at level n-2) A detailed analysis of. .. reliability of predictions based on reductionist models 7. 3 Basic Concepts Related to Impredicative Loop Analysis and Applications 7. 3.1 Linking the Representation of the Identities of Parts to the Whole and Vice Versa The examples of four-angle figures presented in the previous section (e.g., Figure 7. 7) are representations of autocatalytic loops of energy forms obtained through an integrated use of a set of. .. terms of income, the account should be $25,000 when including also the © 2004 by CRC Press LLC 196 Multi- Scale Integrated Analysis of Agroecosystems FIGURE 7. 10 Examples of land use categories useful for characterizing a typology of farming system in highland Laos value of subsistence crops Changing hierarchical level would also imply a change in the mechanism of accounting For example, the assessment of. .. amount of food consumed to sustain 2 277 giga hours of human activity.As illustrated in Chapter 9, the same approach can be applied to an analysis of the reciprocal density of flows of added value The flow of added value associated with the production and consumption of goods and services in a year in the U.S.—related to total human activity, that is, 2 277 giga hours—has to be produced by 235 giga hours of. .. fraction of the available work Angle g—In this type of ILA the final supply of net disposable cash depends on (1) the identity of the option space (the set of possible work types considered, and their average return of labor—expressed in Yuan per hour) and (2) the profile of investment of available work over this set of possible works It should be noted that we found a profile of investments of hours of. .. described in Figure 7. 4 (What are the independent and dependent variables?), as well as all the other problems described in Chapter 3, can never be avoided, even when we explicitly introduce in our analysis multiple identities defined on multiple scales.What can be done when going for a multi- scale integrated analysis based on the parallel use of impredicative loop analysis is to take advantage of mosaic effects... required for the stability of an agroecosystem: © 2004 by CRC Press LLC 186 1 2 3 Multi- Scale Integrated Analysis of Agroecosystems Natural processes of energy conversions powered by the sun and totally out of human control These can include, for example, heat transfer due to direct radiation, evapotranspiration of water, generation of chemical bonds via photosynthesis and interactions of organisms belonging . different space-time scales. * Kozo Mayumi is co-author of this chapter. © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems1 72 A more technical definition of impredicativity. size of the ecosystem (at level n) and the size of its relative components (at level n-1) in relation to the representation of events © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems1 90 (intensive. assessment in Figure 3.1). FIGURE 7. 2 One hundred people on a remote island. © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems1 78 • Indicator of technology. This reflects technological