Part 2 Complex Systems Thinking: Daring to Violate Basic Taboos of Reductionism © 2004 by CRC Press LLC 129 6 Forget about the Occam Razor: Looking for Multi-Scale Mosaic Effects* This chapter first introduces the concept of mosaic effect (Section 6.1) in general terms. It then illustrates the special characteristics of holarchic systems with examples (Section 6.2). This class of systems can generate and preserve an integrated set of nonequivalent identities (defined in parallel on different levels and therefore scales) for their constituent holons. The expected relationship among the characteristics of this integrated set of identities makes it possible to obtain some free information when performing a multi-scale analysis. This is the basic rationale for the multi-scale mosaic effect. A multi-scale analysis requires establishing an integrated set of meaningful relationships between perceptions and representations of typologies (identities) defined on different hierarchical levels and space-time domains. This means that in holarchic systems we can look for useful mosaic effects when considering the relations between parts and the whole. Multi-scale multidimensional mosaic effects can be used to generate a robust multi-scale integrated analysis of these systems. This is discussed in detail in Section 6.3. In particular, examples are given of a multi-scale integrated analysis of the socioeconomic process. Finally, this chapter closes with a discussion of the evolutionary meaning of this special holarchic organization. Holarchic organization, in fact, provides a major advantage in preserving information and patterns of organization. This is done by establishing a resonating entailment across identities that are defining each other across scales. This concept is discussed—using a very familiar example, the calendar—in Section 6.5. The concept of holarchic complexity has been explored in the field of complex systems theory—under different names—in relation to the possible development of tools useful for the study of the sustainability of complex adaptive systems. An overview of these efforts is provided in Section 6.6. Different labels given to this basic concept are, for example, integrity, health, equipollence, double asymmetry, possible operationalizations of the concept of biodiversity. 6.1 Complexity and Mosaic Effects Before getting into a definition of this concept, it is useful to discuss two simple examples. 6.1.1 Example 1 Koestler (1968, Chapter 5, p. 85) suggests that the human mind can obtain compression when storing information by applying an abstractive memory (the selective removing of irrelevant details). In Chapter 2 we described this process as the systemic use of epistemic categories (the use of a type—dog—to deal with individual members of an equivalence class—all organisms belonging to the species Canis familiaris), based on a continuous switch between semantic identities (an open and expanding set of potentially useful shared perceptions) and formal identities (closed and finite sets of epistemic categories used to represent a member of an equivalence class associated with a type) assigned to a given essence. When dealing with the perception and representation of natural holarchies (such as biological systems of * Kozo Mayumi is co-author of this chapter. © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems130 socioeconomic systems), this compression is made easy by the natural organization of these systems in equivalence classes (e.g., the set of organisms of a given species are copies made from the same genetic information, as well as with human artifacts; the set of cars belonging to the same model are copies made from the same blueprint). Getting back to the ideas of Koestler, the compression obtained with language is not obtained by using a single abstractive hierarchy (in our terms, by using a single formal identity for characterizing a given semantic identity), but rather by relying on a “variety of interlocking hierarchies…with cross- references between different subjects” (Koestler, 1968, p. 87). This is a first way to look at mosaic effects: You can recognize a tune played on a violin although you have previously only heard it played on the piano; on the other hand, you can recognize the sound of a violin, although the last time a quite different tune was played on it. We must therefore assume that melody and timbre have been abstracted and stored independently by separate hierarchies within that same sense of modality, but with different criteria of relevance. One abstracts melody and filters out everything else as irrelevant, the other abstracts the timbre of the instrument and treats the melody as irrelevant. Thus not all the details discarded in the process of stripping the input are irretrievably lost, because details stripped off as irrelevant according to the criteria of one hierarchy may have been retained and stored by another hierarchy with different criteria of relevance. The recall of the experience would then be made possible by the co-operation of several interlocking hierarchies…. Each by itself would provide only one aspect only of the original experience— a drastic impoverishment. Thus you may remember the words only of the aria “Your Tiny Hand is Frozen,” but have lost the melody. Or you may remember the melody only, having forgotten the words. Finally you may recognize Caruso’s voice on a gramophone record, without remembering what you last heard him sing. (Koestler, 1968, p. 87) To relate this quote of Koestler to the epistemological discussions of Chapters 2 and 3, it is necessary to substitute the expression “abstracting hierarchies” with the expression “epistemic categories associated with a formal identity used to indicate a semantic identity” discussed there. Every time we associate the expected set of characteristics (a set of observable qualities) of members assumed to belong to an equivalence class with a label (a name), we are using types (an abstract set of qualities associated with those individuals assumed to belong to an equivalence class). As noted before, the relative compression in the information space obtained by using the characteristics of types (you say a dog and you include them all) to describe the characteristics of individual members perceived as belonging to the class has the unavoidable effect of inducing errors. Not all dogs are the same. It is not possible to cover the open universe of semantic identities (types of dogs) that can be associated with an essence (“dog-giness”) with a formal identity (a finite and closed set of relevant observable qualities—a formal definition of a dog). This is why humans are forced to use subcategories (e.g., a fox terrier), sub-subcategories (e.g., a brown fox terrier) and sub-sub-subcategories (e.g., a very young brown fox terrier) in an endless chain of possible categorizations. Adopting this solution, however, implies facing two setbacks: (1) In this way, we reexpand the information space required by individual observers to handle the representation (since more adjectives are required to individuate the new sub-subcategory) and (2) in this way, we lose generality and usefulness of the relative characterization. The class of “a very young brown fox terrier having had a stressful morning because of nasty diarrhea and therefore being now very hungry” is not very useful as an equivalence class. In fact, it is not easy to find a standard associative context that would make its use as a general type convenient. This is why we do not have a word (label) for this class. What gets us out of this impasse is the observation that within a given situation at a given point in space and time, within a specified context (e.g., children getting out of a given school at 13:30 on Thursday, March 23), a combination of a few adjectives (the tall girl with the red dress) can be enough to individuate a special individual in a crowd. The girl we want to indicate is the only one belonging simultaneously to the three categories: (1) girl (individual belonging to the human species, that is, woman and young at the same time), (2) tall (individual belonging to a percentile on the distribution of height of her age class above average) and (3) with the red dress (individual wearing a red dress). Obviously this mechanism of triangulation, based on the use of a few adjectives (the fewer the better), © 2004 by CRC Press LLC Forget about the Occam Razor: Looking for Multi-Scale Mosaic Effects 131 can be adopted only within the specificity of a given context (only if the triangulation is performed at a given point in space and time). The category “tall girl with the red dress” would represent a totally useless category if used in general to individuate someone within the U.S. The consequences of this example are very important. We can effectively describe a system using a limited set of categories (indicators) by triangulating them—relying on a mosaic effect—but only when we are sure that we are operating within a valid, finite and closed information space. When describing patterns in general, the type is described in general terms within its standard associative context, or a special system is individuated within a specific local setting (at a given point in space and time). When dealing with a specific description of events, the characteristic and constraints of the given context have to be reflected in the selection and definition of an appropriate descriptive domain. 6.1.2 Example 2 Bohm (1995, p. 187) provides an example of integrated mapping based on the mosaic effect: Let us begin with a rectangular tank full of water, with transparent walls. Suppose further that there are two television cameras, A and B, directed at what is going on in the water (e.g. fishes swimming around) as seen through the two walls at right angles to each other. Now let the corresponding television images be made visible on screens A and B in another room. This is a simple example in which we deal with two nonequivalent descriptions of the same natural system (the movements of the same set of fishes seen in parallel on two TV screens). The nonequivalence between the two descriptive domains is generated by the parallel mapping of events occurring in a tridimensional space into two two-dimensional projections (over the two screens A and B). Again, we have the effect of incommensurability already discussed regarding the Pythagorean theorem (Section 3.7)—in that case, a description in one dimension (a single number) was used to represent the relation of two two-dimensional objects (the ratio of two squares). As a consequence of this incommensurability, any attempt to reconstruct the tridimensional movement using just one of the two-dimensional representations could generate bifurcations. That is, two teams of scientists looking at the two parallel nonequivalent mappings of the same event, but looking at only one of the two-dimensional projections (either A or B), could be led to infer a different mechanism of causal relations between the two different perceived chains of events. In this case, the bifurcation is due to the fact that the step represent (what the scientists see over each of the two screens—A and B) is only a part of what is going on in reality in the tridimensional tank. The images moving on the two screens are two different narratives about the same reality. The problem of multiple narratives of the same reality becomes crucial, for example, in quantum physics, when the experimental design used to encode changes of a relevant system’s qualities in time can generate a fuzzy definition of simultaneity and temporal succession among the two representations (Bohm, 1987, 1995). It is important to recall here the generality of the lesson of complexity. The scientific predicament is related to the fact that scientists, no matter how hard they think, can only represent perceptions of the reality. As observed by Allen et al. (2001), “Narratives collapse a chronology so that only certain events are accounted significant. A full account is not only impossible, it is also not a narrative.” Put another way, a narrative is generated by a particular choice of representing the reality using a subset of possible perceptions of it. Any set of perceptions is embedded by a large sea of potential perceptions that could also be useful when different goals are considered. This implies that providing sound narratives has to do with the ability to share meaning about the usefulness of a set of choices made by the observer about how to represent events. That is, the very concept of narrative entails the handling of a certain dose of arbitrariness about how to represent reality—a degree of arbitrariness about which the scientist has to take responsibility (Allen et al., 2001). Getting back to our example of fish swimming in a tank in front of two perpendicular cameras, looking at the movements of these fish from camera A (on screen A) implies filtering out as irrelevant all the movements toward or away from that camera. A fish moving in a straight line toward camera A will be seen as moving on screen B but not moving on screen A. However, a sudden deflection from the original trajectory to a side of this fish will be © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems132 perceived as a dramatic local acceleration from camera A. This will generate a nonlinearity in the dynamic of the fish within the descriptive domain represented on screen A. This dynamic will be difficult to explain in physical terms (and to simulate by a dynamic model) by relaying only the information given by screen A. How did the fish manage to get this huge acceleration in the middle of the water without touching anything—moving suddenly away from total immobility? As soon as we check the information coming from screen B, we can easily explain this perceived nonlinearity. The nonlinear dynamic that is “impossible” to explain on the descriptive domain A is simply an artifact generated by the use of a bad descriptive domain (screen A). That is, the original speed of the fish (perceived when looking at screen B) was simply ignored in the descriptive domain A, since the movement was occurring on the direction considered irrelevant according to the selected set of relevant observable qualities associated with the experimental design. This is a very plain example of the types of problems related to the difficult interpretation of representation of changes when multiple dimensions have to be considered. In this very simple case, we are dealing only with a relevant observable quality: the position of a given object—a fish—that is moving in time. That is, no other relevant attributes but the vectors associated with speed and acceleration are considered when discussing trajectories. Imagine then, a case in which we were required to deal with a much more complex situation in human affairs that would require a much richer characterization (the simultaneous use of a larger set of relevant attributes), which in turn would require the simultaneous use of nonequivalent descriptive domains. In conclusion, when dealing with the sustainability of a socioeconomic system, we have to first decide what is relevant and irrelevant for explaining the past history of the system and guessing the future trajectory of development, but above all, we have to decide who (what) are the relevant observers who should be considered clients for the tailoring of the representation provided by the analysis. In fact, any formalization of the representation of complex systems behavior implies (1) a large dose of arbitrariness in deciding which are the nonequivalent descriptive domains to be considered to gather useful information (on different dimensions using different “cameras,” as in this example) and (2) the risk of making inferences using one of the possible models (based on what is perceived on just one of the possible screens). It is important not to miss crucial information detectable only when looking at different screens. 6.1.3 Mosaic Effect The two definitions of mosaic effect given below are taken from the field of analysis of language (Prueitt, 1998, Section 3 of the hypertext): Syntactic mosaic effect—Occurs when structural parts of a single image or text unit are separated into disjoint parts. Each part is judged not to have a certain piece of information but where the combination of two or more of these units is judged to reveal this information. Semantic mosaic effect—Occurs when structural parts of a single image or text unit are separated into perhaps overlapping parts. Each part is judged not to imply a certain concept but the combination of two or more of these units is judged to support the inference of this concept. Both definitions are clearly pointing to a process of emergence (a whole perceived as something different from the simple sum of the parts). The syntactic mosaic effect has more to do with pattern recognition (individuating a similarity within the reservoir of available useful patterns), whereas the semantic mosaic effect has more to do with the establishment of a meaningful contextual relation within the loop represent-transduce-apply. In both cases, as done often by famous fiction detectives, we can put together a certain number of clues, none of which can by itself identify the murderer we are looking for (they are not mapping 1:1 to the murderer) with a particular combination that provides enough evidence to clearly identify him or her. Another important aspect that can be associated with the concept of mosaic effect is that of redundancy in the information space, which can be used to increase its robustness. A good example of the “free ride” that can be obtained by an interlaced or interlocking of different systems of mapping generating © 2004 by CRC Press LLC Forget about the Occam Razor: Looking for Multi-Scale Mosaic Effects 133 internal redundancy (we are using here the expressions suggested by Koestler) is the process of solving crossword puzzles. Due to the given and expected organizational structure of the puzzle, you can guess a lot of missing information about individual words by taking advantage of the internal rules of coherence of the system (by the existing redundancy generated by the organization of the information space in crosswords). Examples of how to apply this principle to integrated analysis of sustainability are discussed in the rest of this chapter. Before concluding this introductory section, we can briefly recall the discussion (Chapter 2) of the innate redundancy of the information space used when describing dissipative adaptive holarchies. In this case, we are dealing with a Russian dolls’ structure (nested hierarchies) of equivalence classes generated by a replicated process of fabrication based on a common set of blueprints (e.g., biological systems made using common information stored in the DNA). This innate redundancy is the reason that we can rely so heavily on type-based descriptions related to expected identities. This means that it is easy to find labels about which the users of a given language can share their organized perceptions of types associated with the expected existence of the relative equivalence class. As discussed in Chapter 2, this mechanism used for organizing human perceptions is very deep. This means that, even when looking for the characterization (representation of a shared perception) of an individual human being, it is necessary to use typologies. For example, consider a famous human—let us say Michael Jordan. We can obtain a lot of free information about him from the knowledge related to equivalence classes to which this individual belongs, even without having a direct experience of interaction with him. For example, since we know that Jordan belongs to the human species, we can guess that he has two arms, two eyes, etc. Actually, we can convey a lot of information about him just by adding after his name the simple information “nothing is missing in the standard package of the higher category—human being—to which this individual belongs.” Within this basic typology of “human being” we can use a more specific subtype characterization linked to his identity as a male of a certain age (a smaller subcategory of human beings). This will provide us with another subset of expected standard characteristics (expected observable qualities) and behaviors (expected patterns) against which it will become easier (and cheaper in terms of information to be gathered and recorded) to track and represent the special characteristics of Mr. Jordan (e.g., he is much taller than the average male of his age; he has excellent physical fitness). It should be noted, however, that every time we get closer and closer to the definition of the special individual Michael Jordan in terms of characteristics of the organized structure generating signals, we remain trapped in the fuzziness of the definition of what should be considered as the relative type, against which to make the identification of the individual. In fact, even when we arrive to the clear characterization of an individual person, we are still dealing with a holon at the moment of representing him. This is due to the unavoidable existence of an infinite regression of potential simplifications linked to the very definition (representation of shared perception) of the same holon Michael Jordan. The universe of potential meaningful relations between perception and representation can be compressed in different ways to obtain a particular formal representation of Michael. This would remain true, even if we used firsthand experimental information about his anthropometric characteristics and behavioral patterns—e.g., by asking his family or by recording his daily life. Each characterization would still be based on various types related to Michael Jordan determining different sets of expected observable qualities and behaviors. That is, we will still end up using different types, such as sleeping Michael Jordan, full-strength Michael Jordan, angry Michael Jordan, affected-by-a-cold Michael Jordan, etc. Even at this point, we can still split these types into other types, all related to the special subset of qualities and behaviors that the individual Michael Jordan, when in full strength, could take. This splitting can be related to different positions in time during a year (spring vs. winter) or during a day (morning vs. night), or changes referring to a time scale of minutes (surprised vs. pleased), let alone the process of aging. As noted before, it is impossible to define in absolute terms a formal identity for holons (the right set of qualities and behaviors that can be associated in a substantive way with the given organized structure). Each individual holon will always escape a formal definition due to (1) the fuzzy relation between structure and function, which are depending on each other for their definition within a given identity; (2) the innate process of becoming that is affecting them and (3) the changing interest of the observer. The indeterminacy of such a process translates into an unavoidable openness of the information © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems134 space required to obtain useful perceptions and representations (holons do operate in complex time). Put another way, holons can only be described (losing part of their integrity or wholeness) in semantic terms using types, after freezing their complex identity using the triadic reading over an infinite cascade of categorizations and in relation to the characteristics of the observer. At this point, a formalization of the semantic description represents an additional simplification, which is unavoidable if one wants to use such an input for communicating and interacting with other observers/agents. The work of Rosen, Checkland and Allen discussed in Part 1 points to the fact that an observer or a given group of observers can never see the whole picture (the experience about reality is the result of various processes occurring at different scales and levels). At a given point in space and time, observers can see only a few special perspectives and parts of the whole. The metaphor of the group of blind people trying to characterize an elephant by feeling its different parts can be recalled here. Rather than denying this obvious fact, scientists should learn how to better deal with it. In fact, if it is true that holons are impossible to formalize—a con in epistemological terms—it is also true that they are able to establish reliable and useful identities (a valid relation between expected characteristics (types) and experienced characteristics of the members of the relative equivalence class (organized structures sharing the same template)), which is a major pro in epistemological terms. This implies that as soon as we are dealing with a known class of holarchic systems (as is always the case when dealing with biological and human systems), we should expect that across levels a few characteristics of the relative types can be predicted. Moreover, the characteristics of nested types are defining each other across levels. This means that, after having selected an opportune set of formal identities for looking at these systems, we can also expect to be able to guesstimate some hierarchical relations between parts and the whole. 6.2 Self-Entailments of Identities across Levels Associated with Holarchic Organization 6.2.1 Looking for Mosaic Effects across Identities of Holarchies First, we have to look for mechanisms of accounting (assigning a formal identity to the semantic identity of a dissipative system) that will make it possible to establish a link between assessments referring to lower-level components and assessments referring to the whole. The choice of a useful system of accounting is a topic that will be discussed in the next chapter about impredicative loop analysis. The following example has only the goal of illustrating the special characteristics of a nested holarchy. Imagine a holarchic system—e.g., the body of a human being—and imagine that we want to study its metabolism in parallel on two levels: (1) at the level of the whole body and (2) at the level of individual organs belonging to the body. To do that, we have to define a formal identity (a selection of variables) that can be used to characterize the metabolism over these two contiguous levels. That is, the selected formal identity will be used to characterize two sets of elements defined on different hierarchical levels: (1) the parts of the system (defined at level n-1) and (2) the whole body (defined at level n). This example has as its goal to show that the various identities associated with elements of metabolic systems organized in nested hierarchies entail a constraint of congruence on the relative values taken by intensive and extensive variables across levels. Let us start with two variables that can be used to describe the sizes of both the whole (level n) and parts (level n-1) in relation to their metabolic activities. The two variables adopted in this example to describe the size of a human body (seen as the black box) in relation to metabolic activity are: 1. Variable 1—kilograms of human mass (1 kg of body mass is defined at a certain moisture content). 2. Variable 2—watts of metabolic energy (1 W=1 J/sec of food metabolized). This assessment refers to energy dissipated for basal metabolism. These two variables are associated with the size of the dissipative system (whole body) and reflect two nonequivalent mechanisms of mapping. The selection of these two variables reflects the possibility of © 2004 by CRC Press LLC Forget about the Occam Razor: Looking for Multi-Scale Mosaic Effects 135 using two nonequivalent definitions of size. The first definition refers to the perception of the internal structure (body mass), and the second definition refers to the degree of interaction with the environment (flow of food consumed). That is, this second variable refers to the amount of environmental services associated with the definition of size given by variable 1. The same two variables can be used to characterize the system (human body) perceived and represented over two contiguous hierarchical levels: (1) size of the parts (at the level n-1) and (2) size of the whole (at the level n). In fact, after having chosen variables 1 and 2 to characterize the size of the metabolism of the human body across levels, we can measure both the size of the whole body (at the level n) and the size of the lower-level organs (at the level n-1) using kilograms of biomass or megajoules of food energy converted into heat. Again, assessment 1 (70 kg of body mass for the whole body) represents a mapping related to the black box in relation to its structural components, whereas assessment 2 (80 W of energy input required over a given time horizon—1 day—to retain the identity of the whole body) represents a mapping of the dependency of the identity of the system (black box) on benign environmental processes (stability of favorable boundary conditions). The fact that this second assessment is expressed in watts (joules per second) should not mislead the reader. Even if the unit of measurement is a ratio (an amount of energy per unit of time), it should not be considered an intensive variable when dealing with a metabolic system whose identity is associated by default with a flow of energy. In fact, according to the system of accounting adopted here, the size of these systems is associated with an amount of energy, required in a standard period of reference—either a day or a year, depending on the measurement scheme. That is, this is an assessment that is related to a given time window (required to obtain meaningful data) that is big enough to assume such an identity constant in relation to lower-level dynamics. The value is then expressed in joules per second, only because of a mathematical operation applied to the data. The value 80 W (for the whole body) has to be considered an extensive variable, since it maps onto an equivalent amount of environmental services (e.g., a given supply of food, amount of energy carriers and absorption of the relative amount of CO 2 and wastes), which must be associated with the metabolism of the system over a given time horizon. By combining these two extensive variables (1 and 2), we can obtain an average density of energy dissipation per kilograms of body mass, which is 1.2 W/kg. This should be considered, within this mechanism of accounting, an intensive variable (a variable 3 to be added to the set used to characterize metabolism within a formal identity of it). Variable 3 can be seen as a benchmark value (average value for the black box) that can be associated with the identity of the dissipative system considered as a whole at the level n. If we look inside the black box at individual components (at the level n-1), we find that the average (watts per kilogram, variable 3) assessed at the level n is the result of an aggregation of a profile of different values of energy dissipation per kilogram of lower-level elements (watts per kilogram, variable 3) assessed at the level n-1. For example, the brain, in spite of being only a small percentage of the body weight (around 2%), is responsible for about 20% of the resting metabolism (Durnin and Passmore, 1967). This means that the density of the metabolic energy flow dissipated in the brain per unit of mass (intensive variable 3) is around 12.0 W/kg. The average metabolic rate of the brain per unit of mass is therefore 10 times higher than the average of the rest of the body. If we write an equation of congruence across these two levels, we can establish a forced relation between the characteristics of the elements (whole and parts) across levels. Level n (the identity of the black box is known) Total body mass=70.0 kg Endosomatic energy=80.0 W EMRn=1.2 W/kg Level n-1 (the identity of the considered lower-level components is known) Brain=1.4 kg Endosomatic energy=16.2 W EMRn-1=11.6 W/kg Level n-1 (after looking for a closure we can define a weak identity for other components) Rest of the body=68.6 kg Endosomatic energy=63.8 W EMRn-1=0.9 W/kg © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems136 When we know the hierarchical structure of parts and the whole (how the whole body mass is distributed over the lower-level parts) and the identities of lower-level parts (the characteristic value of dissipation per unit of mass—intensive variable 3 (EMRn-1) i )—we can even express the characteristics of the whole as a combination of the characteristics of its parts: EMRn=Sx i (EMRn-1) i =1.2 W/kg=(0.02×11.6) brain +(0.98×0.9) rest of the body (6.1) That is, the hierarchical structure of the system and the previous knowledge of the expected identity of parts make it possible to obtain missing data when operating an appropriate system of accounting. Put another way, we can guess the EMR of the rest of the body (an element defined at the level n-1) by measuring the characteristics of the whole body (at the level n) and the characteristics of other elements at the level n-1 (brain). Alternatively, we can infer the characteristics of the whole body—at the level n—by our knowledge of the characteristics of the lower-level elements (level n-1), provided that the definition of identities (EMRj) on the level n-1 guarantees the closure over the total mass. This requires that the mapping of lower-level elements in kilograms has to satisfy the relation: Mass “whole body”=Mass “brain”+Mass “rest of the body” (6.2) This means that the selected system of accounting of the relevant system quality mass must be clearly defined (e.g., body mass has to be defined at a given content of water or on a dry basis) on both levels to obtain closure. In this example, only two compartments were selected (i=2), but depending on the availability of additional external sources of information (data or experimental settings available) we could have decided to assign more known identities to characterize what has been labeled here as the “rest of the body.” That is, we could have used additional identities for compartments at the level n-1 This approach makes it possible to bridge (by establishing congruence constraints) nonequivalent representations of a metabolic system across levels. However, this requires that the formal identities used to characterize lower-level elements have a set of attributes in common with the formal identity used to characterize the whole. That is, it is possible to adopt the same set of variables to characterize a relevant quality (e.g., size) of (1) the black box and (2) its lower-level components. In the example of a multi-scale analysis of the metabolism of the human body—an example is given in Figure 6.1—the two variables are (1) size in kilograms of mass (extensive variable 1) and (2) size in watts of metabolic energy (extensive variable 2). The combination of these two variables makes it possible to define a benchmark value—the metabolic rate of either the whole or an element expressed in watts per kilograms (intensive variable 3)—that can be used to relate the characteristics of the parts to those of the whole. Obviously, attributes that are useful to characterize crucial features of the whole body (emergent properties of the whole at level n), such as the ability to remain healthy, cannot be included in the definition of identity applied to individual organs (at level n-1). These characteristics are, in fact, emergent on level n and cannot be detected when using a descriptive domain relative to the parts. This is why variables that are useful for generating a multi-scale mosaic effect are not useful as multi-scale indicators. However, they are very useful to establish a bridge among analyses on different scales providing relevant indicators. An additional discussion of the possible use of equations of congruence (Equations 6.1 and 6.2) applied to a larger number of lower-level elements (level n-1) is given in the following section (also see Figure 6.1). Obviously, the more we manage to characterize the whole size of the black box (defined at the level n) using information gathered at the lower level (by using data referring to the identity of lower-level elements— parts—at level n-1), the more we will be able to generate a robust description of the system. In fact, in this way we can combine information (data) referring to external referents (measurement schemes measuring the metabolism of organs) operating at level n-1 with nonequivalent information (data) about the black box, which has been generated by a nonequivalent external referent (measurement scheme measuring the metabolism of the person) operating at level n. The parallel use of nonequivalent external referents, in fact, is what makes the information obtained through a cross-scale mosaic effect (avoid the tautology of reciprocal definitions in the egg-chicken process—as discussed in the next chapter) very robust. © 2004 by CRC Press LLC (e.g., brain, liver, heart, kidneys—see Figure 6.1). Forget about the Occam Razor: Looking for Multi-Scale Mosaic Effects 137 6.2.2 Bridging Nonequivalent Representations through Equations of Congruence across Levels In this section we discuss the mechanism through which it is possible to generate a mosaic effect based on the combined use of intensive and extensive variables describing parts and the whole of a dissipative holarchic system. This operation leads to a process of benchmarking based on the determination of a chain of values for intensive variables 3 across levels. With benchmarking we mean the characterization of the identity of a holon (level n) in relation to the average values referring to the identity of the larger holon representing its context (level n+1) and the lower-level elements that are its components (level n-1). Let us again use the multi-scale analysis given in Figure 6.1. The two nonequivalent mappings and their ratio (the intensive variable) are defined as follows: • Extensive 1—This is the size of the human body expressed in mass (a mapping linking black-box/lower-level components): 70 kg of body mass. • Extensive 2—This assessment of size measures the degree of dependency of the dissipative system on processes occurring outside the black box, that is, in the context. This can be translated into an number of carriers of endosomatic energy (e.g., kilograms of food) that is required to maintain a given identity (a mapping linking black box/context): 81 W of food energy. This is equivalent to 7MJ/day of food energy to cover resting metabolism. • Intensive 3—The ratio of these two variables is an intensive variable that can be used to characterize the metabolic process associated with the maintenance of the identity of the dissipative system. This ratio can been called the endosomatic metabolic rate of the human body (EMR HB ): 1.2 W/kg of food energy/kg of body mass. It is important to note that the values of EMR i can be directly associated with the identity of the element considered. That is, these are expected values as soon as we know that we are dealing with kilograms of mass of a given element (e.g., brain, liver or heart). As illustrated in the upper part of Figure 6.1, when considering the human body as the focal level of analysis (level n)—as the black box—we can use this set of three variables (Ext. 1, Ext. 2 and Int. 3) as FIGURE 6.1 Constraints on relative values taken by variables within hierarchically organized systems. © 2004 by CRC Press LLC [...]... throughput of a society (e.g., tons of oil © 2004 by CRC Press LLC 152 © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems FIGURE 6. 6 Endosomatic energy flow in human societies (Giampietro M and Mayumi K (2000a), Multiple -scale integrated assessment of societal metabolism: Introducing the approach Popul Environ 22(2): 109–153.) Forget about the Occam Razor: Looking for Multi- Scale. .. Exo/Endo ratio in Equation 6. 3 However, assessments of exosomatic energy can be handled in the same way as the assessment of © 2004 by CRC Press LLC 1 56 © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems FIGURE 6. 9 Population structure of societies at different levels of economic development (Giampietro M and Mayumi K (2000a), Multiple -scale integrated assessment of societal metabolism:... accounting of matter flows associated with crop production at the watershed level and over a time horizon of 50 years © 2004 by CRC Press LLC 142 Multi- Scale Integrated Analysis of Agroecosystems FIGURE 6. 2 Constraints on relative values taken by variables within hierarchically organized systems 6. 2.3 Extending the Multi- Scale Integrated Analysis to Land Use Patterns Linkages among characteristics of typologies... level (a-1) GNPi=HAi×ELPi=the added value productivity of the i-th sector—at the level (a-1) ELPi=GNPi/HAi=the economic labor productivity of the i-th sector—at the level (a-1) © 2004 by CRC Press LLC 162 Multi- Scale Integrated Analysis of Agroecosystems ETa=(ETi)a-1, e.g., TET=(ETPS+ETSG+ETHH) HAa=S(HAi)a-1, e.g., THA=(HAPS+HASG+HAHH) GNPa=S(GNPi)a-1, e.g., GNP=(GNPPS+GNPSG) In these examples, the values... terms (see Chapter 10) It is exactly the ability to handle the heterogeneity of information related to different scales and nonreducible criteria of performance that makes the approach of multi- scale integrated analysis of agroecosystems interesting Even in this very simple example we can appreciate that a multi- scale integrated analysis is able to handle the information related to indicators that are... selected set of six identities of lower-level elements, perceived and measured at the level n-1 The characterization of this seventh virtual lower-level element—the identity of “others” (about which we cannot provide any expected value a priori)—depends on (1) the values taken by the variables referring to the characteristics of the © 2004 by CRC Press LLC 140 Multi- Scale Integrated Analysis of Agroecosystems. .. the assessment of flows of energy: 1 Extensive variable 2 applies to the class of assessments defining aggregate amounts of either energy or added value per year of a particular element (the size of interaction with the context) © 2004 by CRC Press LLC 158 2 Multi- Scale Integrated Analysis of Agroecosystems Intensive variable 3 applies to the class of assessments referring to ratios of either energy... Mosaic Effects FIGURE 6. 7 Exosomatic energy flow in human societies (Giampietro M and Mayumi K (2000a), Multiple -scale integrated assessment of societal metabolism: Introducing the approach Popul Environ 22(2): 109–153.) 153 © 2004 by CRC Press LLC 154 Multi- Scale Integrated Analysis of Agroecosystems FIGURE 6. 8 Using redundancy to link nonequivalent assessments taking advantage of nonequivalent external... terms of © 2004 by CRC Press LLC 150 Multi- Scale Integrated Analysis of Agroecosystems space-time domain Also, in this case, this implies keeping a certain level of redundancy in the representation (e.g., in Figure 6. 5 the geographic border of Europe is the same in the two maps) This observation can appear absolutely trivial when dealing with the example of political and physical representations of geographic... export 6. 4 Applying the Metaphor of Redundant Maps to the Integrated Assessment of Human Systems The following two sections present an example of the application of this rationale to a multi- scale integrated analysis of societal metabolism A detailed presentation of the methodological approach and the database used for generating the material presented here are available in two special issues of Population . information when performing a multi- scale analysis. This is the basic rationale for the multi- scale mosaic effect. A multi- scale analysis requires establishing an integrated set of meaningful relationships. of the body =68 .6 kg Endosomatic energy =63 .8 W EMRn-1=0.9 W/kg © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems1 36 When we know the hierarchical structure of parts and. and representation of natural holarchies (such as biological systems of * Kozo Mayumi is co-author of this chapter. © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems1 30 socioeconomic