43 3 Complex Systems Thinking: New Concepts and Narratives This chapter provides practical examples that illustrate the relevance of the concepts introduced in Chapter 2 to the challenges faced by scientists working in the field of sustainable agriculture. In fact, it is important to have a feeling of practical implications of complexity, in terms of operation of scientific protocols of analysis, before getting into an analysis of the challenges faced by those willing to do things in a different way (Chapters 4 and 5), and before exploring innovative concepts that can be used to develop new analytical approaches (Part 2). 3.1 Nonequivalent Descriptive Domains and Nonreducible Models Are Entailed by the Unavoidable Existence of Multiple Identities 3.1.1 Defining a Descriptive Domain Using the rationale proposed by Kampis (1991, p. 70), we can define a particular representation of a system as “the domain of reality delimited by interactions of interest.” In this way, one can introduce the concept of descriptive domains in relation to the particular choices associated with a formal identity used to perceive and represent a system organized on nested hierarchical levels. A descriptive domain is the representation of a domain of reality that has been individuated on the basis of a preanalytical decision on how to describe the identity of the investigated system in relation to the goals of the analysis. Such a preliminary and arbitrary choice is needed to be able to detect patterns (when looking at the reality) and to model the behavior of interest (when representing it). To discuss the need of using in parallel nonequivalent descriptive domains, we can again use the four views given in Figure 1.2, this time applying to them the metaphor of sustainability. Imagine that the four nonequivalent descriptions presented in Figure 1.2 were referring to a country (e.g., the Netherlands) rather than a person. In this case, we can easily see how any analysis of its sustainability requires an integrated use of these different descriptive domains. For example, by looking at socioeconomic indicators of development (Figure 1.2b), we “see” this country as a beautiful woman (i.e., good levels of gross national product (GNP), good indicators of equity and social progress). These are good system qualities, required to keep low the stress on social processes. However, if we look at the same system (same boundary) using different encoding variables (e.g., a different formal identity based on a selection of biophysical variables)—Figure 1.2d in the metaphor—we can see the existence of a few problems not detected by the previous selection of variables (i.e., sinusitis and a few dental troubles). In the metaphor this picture can be interpreted, for the Netherlands, as an assessment of accumulation of excess nitrogen in the water table, growing pollution in the environment, excessive dependency on fossil energy and dependence on imported resources for the agricultural sector. Put another way, when considering the biophysical dimension of sustainability, we can “see” some bad system qualities that were ignored by the previous selection of economic encoding variables (a different definition of formal identity for perception and representation). Analyses based on the descriptive domain of Figure 1.2a are related to lower-level components of the system. In the Dutch metaphor, this could be an analysis of technical coefficients (e.g., input/output) of individual economic activities (e.g., the CO 2 emissions for producing electricity in a power plant). Clearly, the knowledge obtained when adopting this descriptive domain is crucial to determine the viability and sustainability of the whole system (the possibility of improving or adjusting the overall performance of the Dutch © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems44 economic process if and when changes are required). In the same way, an analysis of the relations of the system with its larger context can indicate the need to consider a descriptive domain based on pattern recognition referring to a larger space-time domain (Figure 1.2c). In the Dutch metaphor this could be an analysis of institutional settings, historical entailments or cultural constraints over possible evolutionary trajectories. 3.1.2 Nonequivalent Descriptive Domains Imply Nonreducible Assessments The following example refers to four legitimate nonreducible assessments and can again be related to the four views presented in Figure 1.2. This is to show how general and useful is the pattern of multiple identities across levels. The metaphor this time is applied to the process required to obtain a specific assessment, such as kilograms of cereal consumed per capita by U.S. citizen in 1997. The application of such a metaphor to the assessment of cereal consumption per capita is shown in Figure 3.1. Let us imagine that to get such a number a very expensive and sophisticated survey is performed at the household level. By recording events in this way, we can learn that, in 1997, each U.S. citizen consumed 116 kg of cereal/person/year. On the other hand, by looking at the Food and Agriculture Organization (FAO) Food Balance Sheet (FAO Agricultural Statistics), which provides for each FAO member country a picture of the flow of food consumed in the food system, we can derive other possible assessments for the kilograms of cereal consumed per capita by U.S. citizens in 1997. A list of nonequivalent assessments could include: 1. Cereal consumed as food, at the household level. This is the figure of 116 kg/year/capita for U.S. citizens in 1997, discussed above. This assessment can also be obtained by dividing the total amount of cereal directly consumed as food by the population of U.S. in that year. 2. Consumption of cereal per capita in 1997 as food, at the food system level. This value is obtained by dividing the total consumption of cereal in the U.S. food system by the size of the U.S. population. This assessment results in more than 1015 kg (116 kg directly consumed, 615 kg fed to animals, almost 100 kg of barley for making beer, plus other items related to industrial processing and postharvest losses). 3. Amount of cereal produced in U.S. per capita in 1997, at the national level, to obtain an economic viability of the agricultural sector. This amount is obtained by dividing the total internal production of cereal by population size. Such a calculation provides yet another assessment: 1330 kg/year/capita. This is the amount of cereal used per capita by the U.S. economy. 4. Total amount of cereal produced in the world per capita in 1997, applied to the humans living within the geographic border of the U.S. in that year. This amount is obtained by dividing the total internal consumption of cereal at the world level in 1997 (which was 2× 10 12 kg) by the world population size that year (5.8 billion). Clearly, such a calculation provides yet another assessment: 345 kg/year/capita (160 kg/year direct, 185 kg/year indirect). This is the amount of cereal used per capita by each human being in 1997 on this planet. Therefore, this would represent the share assigned to U.S. people when ignoring the heterogeneity of pattern of consumption among countries. The four views in Figure 1.2 can be used again, as done in Figure 3.1, to discuss the mechanism generating these numerical differences. In the first two cases, we are considering only the direct consumption of cereal as food. On a small scale (assessment 1 reflecting Figure 1.2a in the metaphor) and on a larger scale (assessment 2 referring to Figure 1.2b in the metaphor), the logic of these two mappings is the same. We are mapping flows of matter, with a clear identification in relation to their roles: food as a carrier of energy and nutrients, which is used to guarantee the physiological metabolism of U.S. citizens. This very definition of consumption of kilograms of cereal implies a clear definition of compatibility with the physiological processes of conversion of food into metabolic energy (both within fed animals and human bodies). This implies that, since the mechanism of mapping is the same © 2004 by CRC Press LLC Complex Systems Thinking: New Concepts and Narratives 45 (in the metaphor of Figure 1.2a and b, we are looking for pattern recognition using the same visible wavelength of the light), we can bridge the two assessments by an appropriate process of scaling (e.g., life cycle assessment). This will require, in any case, different sources of information related to processes occurring at different scales (e.g., household survey plus statistical data on consumption and technical coefficients in the food systems). When considering assessment 3, we are including kilograms of cereal that are not consumed either directly or indirectly by U.S. households in relation to their diet. The additional 315 kg of cereal produced by U.S. agriculture per U.S. citizen for export (assessment 3 minus assessment 2) is brought into existence only for economic reasons. But exactly because of that, they should be considered as “used” by the agricultural sector and the farmers of the U.S. to stabilize the country’s economic viability. The U.S. food system would not have worked the way it did in 1997 without the extra income provided to farmers by export. Put another way, U.S. households indirectly used this export (took advantage of the production of these kilograms of cereal) for getting the food supply they got, in the way they did. This could metaphorically be compared to the pattern presented in Figure 1.2d. We are looking at the same head (the U.S. food system in the analogy) but using a different mechanism of pattern recognition (x-rays rather than visible light). The difference in numerical value between assessments 1 and 2 is generated by a difference in the hierarchical level of analysis, whereas the difference between assessments 2 and 3 is generated by a bifurcation in the definition of indirect consumption of cereal per capita (a biophysical definition vs. an economic definition). Finally, Figure 1.2c would represent the numerical assessment obtained in assessment 4, when both the scale and the logic adopted for defining the system are different from the previous one (U.S. citizens as members of humankind). The fact that these differences are not reducible to each other does not imply that any of the assessments are useless. Also, in this case, depending on the goal of the analysis, each one of these numerical assessments can carry useful information. 3.2 The Unavoidable Insurgence of Errors in a Modeling Relation 3.2.1 Bifurcation in a Modeling Relation and Emergence To introduce this issue, consider one of the most successful stories of hard science in this century: the claimed full understanding achieved in molecular biology of the mechanism through which genetic information is FIGURE 3.1 Nonequivalent descriptive domains equals nonreducible models. © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems46 stored, replicated and used to guarantee a predictable behavior in living systems. This example is relevant not only for supporting the statement made in the title of this section, but also for pointing to the potential risks that a modeling success can induce on our ability to understand complex behaviors of real systems. To cut a long and successful story very short, we can say that, in terms of modeling, the major discoveries made in this field were (1) the identification of carriers of information as DNA bases organized into a double helix and (2) the individuation and understanding of the mechanisms of encoding based on the use of these DNA bases to (i) store and replicate information in the double helix, and (ii) transfer this information to the rest of the cell. This transfer of information is obtained through an encoding and decoding process that leads to the making of proteins. Due to the modulation of this making of proteins in time, the whole system is able to guide the cascade of biochemical reactions and physiological processes. In particular, four basic DNA bases were identified (their exotic names are not relevant here, so we will use only the first letter of their names: C, G, T and A), which were found to be the only components used to encode information within the DNA double helix. Two pairs of these bases map onto each other across helixes. That is, whenever there is a C on one of the two helices, there is a G on the other (and vice versa); the same occurs with A and T. This means that if we find a sequence CCAATGCG on one of the two helices of the DNA, we can expect to find the complementing sequence GGTTACGC on the other. This self-entailment (loop of resonating mappings in time) across linked sequences of bases is the mechanism that explains the preservation of a given identity of DNA in spite of the large number of replications and reading processes. By applying a system of syntactic rules to this mechanism of reciprocal mapping, it is also possible to explain, in general terms, the process of regulation of the biochemical behavior of cells (some parts of DNA strings made up of these four bases have regulative functions, whereas other parts codify the actual making of proteins). At this point this process of handling information from what is written in the DNA to what is done by the cells can be represented in a simplified form (modeled) by using types. That is, there is a closed set of types (triplets of bases) that are mapping onto a closed set of types (the amino acids used to make proteins). Obviously, there are a lot of additional specifications required, but details are not relevant here. What is relevant is the magnificent success of this modeling relation. The model was so good in explaining the behavior of interest that nowadays humans can not only manipulate genetic information within living systems to interfere with their original systems of storage of information and regulation, but also make machines that can generate sequences of DNA following an input given by the computer. The big success of this model is also reason for concern. In fact, according to this modeling relation, we are told at school—when learning about DNA behavior—that a mutation represents an error in the mechanism handling genetic information. The expression “error” refers to the fact that a given type on one side of the mapping (e.g., a given base A) is not generating the expected type on the other side of the mapping (e.g., the complementing base T). This can imply that a given triplet can be changed and therefore generate an incorrect insertion of an amino acid in the sequence making up a protein. According to Rosen (1977, p. 231) what the expression error means: is something like the following: DNA is capable of many interactions besides those involved in its coding functions. Some of these interactions can affect the coding functions. When such an interaction occurs, there will be a deviation between what our simple model tells us ought to be coded, and what actually is coded. This deviation we call a mutation, and we say that the DNA has behaved erroneously. Even with a cursory reflection we can immediately see that any system handling genetic information within a becoming system must have, to keep its ability to evolve, an open information space that has to be used to expand the set of possible behaviors in time (to be able to become something else). Such a system therefore must admit the possibility of inducing some changes in the closed set of syntactic entailments among types that represents its closed information space. The closed information space is represented by what has been expressed up to now by the class of individual organized structures that have been produced in the past history of the biological system with which the studied DNA is associated. To evolve, biological systems need mutations to expand this closed set; therefore, they must be able to have mutations. The existence and characteristics of this function (the ability to have mutations), © 2004 by CRC Press LLC Complex Systems Thinking: New Concepts and Narratives 47 however, can only be detected over a space-time window much larger than the one used to describe mechanical events in molecular biology. Being a crucial function, the activity of inducing changes on the DNA to expand the information space requires careful regulation. That is, the rate of mutations must not be too high (to avoid the collapse of the regulative mechanisms on the smaller space-time window of operations within cells). On the other hand, it has to be large enough to be useful on an evolutionary space-time window to generate new alternatives when the existing structures and functions become obsolete. The admissible range of this rate of mutation obviously depends on the type of biological system considered; for example, within biological systems high in the evolutionary rank, it is sexual reproduction of organisms that takes care of doing a substantial part of this job with fewer risks. In any case, the point relevant in this discussion is that mutations are not just errors, but rather the expression of a useful function needed by the system. The only problem is that such a function was not included in the original model used to represent the behavior of elements within a cell type, adopted by molecular biology in the 1960s and early 1970s. These models were based on a preliminary definition of a closed set of functions linked to the class of organized structures (DNA bases, triplets, amino acids) considered over a given descriptive domain. Within the descriptive domain of molecular biology (useful to describe the mechanics of the encoding of amino acids onto triplets in the DNA), the functions related to evolution or co-evolution of biological systems cannot be seen. This is what justifies the use of the term error within that term of reference. The existence of machines able to generate sequences of DNA is very useful, in this case, to focus on the crucial difference between biological systems and human artifacts (Rosen, 2000). When a machine making sequences of DNA bases includes in the sequence a base different from that written on the string used as input to the computer, then we can say that the machine is making an error. In fact, being a human artifact, the machine is not supposed to self-organize or become. A mechanical system is not supposed to expand its own information space. Machines have to behave according to the instructions written before they are made for (and used by) someone else. On the space-time scale of its life expectancy, the organized structure of a machine has no other role but that of fulfilling the set of functions assigned by the humans who made it. Living systems are different. Going back to the example of DNA, the more humans study the mechanism storing and processing genetic information, the more it becomes clear in both molecular and theoretical biology that the handling of information in DNA-based systems is much more complex than the simple cascade of a The lesson from this story is clear: whenever a model is very useful, those who use it tend to sooner or later confuse the type of success (the representation of a relevant mechanism made using types, that is, by adopting a set of formal identities) with the real natural system (whose potential semantic perceptions are associated with an open and expanding information space) that was replaced in the model by the types. Due to this unavoidable generation of errors, every time we make models of complex systems, Rosen (1985, chapter on theory of errors) suggests using the term bifurcations whenever we face the existence of two different representations of the same natural system that are logically independent of each other. The concept of bifurcation in a modeling relation entails the possibility of having two (or more) distinct formal systems of inference, which are used on the basis of different selections of encoding variables (selection of formal identities) or focal level of analysis (selection of scale) to establish different modeling relations for the same natural system. As noted earlier, bifurcations are therefore also entailed by the existence of different goals for the mapping (by the diverging interests of the observer), and not only by intrinsic characteristics of the observed system. The concept of bifurcation implies the possibility of a total loss of usefulness of a given mapping. For example, imagine that we have to select an encoding variable to compare the size of London with that of Reykjavik, Iceland. London would be larger than Reykjavik if the selected encoding for the quality size is the variable population. However, by changing the choice of encoding variable, London would be smaller than Reykjavik if the perception of its size is encoded as the number of letters making up the name (a new definition of the relevant quality to be considered when defining the sizes of London and Reykjavik). Such a choice of encoding could be performed by a company that makes road signs. In this trivial example we can use the definition of identity discussed in Chapter 2 to study the mechanism generating the bifurcation, in this case, two nonequivalent observers: (1) someone charac- © 2004 by CRC Press LLC couple of mappings: (C↔G, T↔A) and (closed set of triplets types→closed set of amino acid types). Multi-Scale Integrated Analysis of Agroecosystems48 terizing London as a proxy for a city will adopt a formal identity in which the label is an epistemic category associated with population size and (2) someone working in a company making road signs, perceiving this label as just a string of letters to be written on its product, will adopt a formal identity for the name in which the size is associated with the demand for space on a road sign. The proxy for the latter system quality will be the number of letters making up the name. Clearly, the existence of a different logic in selecting the category and proxy used to encode what is relevant in the quality size is related to a different meaning given to the perception of the label “London.” This is the mechanism generating the parallel use of two nonequivalent identities for the same label. Recall here the example of the multiple bifurcations about the meaning of the label “segment of coastal line” in Figure 2.1. This bifurcation in the meaning assigned to the label is then reflected in numerical assessments that are no longer necessarily supposed to be reducible into each other or directly comparable by the application of an algorithm. A bifurcation in the system of mapping can be seen as, as stated by Rosen (1985, p. 302), “the appearance of a logical independence between two descriptions.” As discussed in Chapter 2, such a bifurcation depends on the intrinsic initial ambiguity in the definition of a natural system by using symbols or codes: the meaning given to the label “London” (a name of a city made up of people or a six-letter word). As observed by Schumpeter (1954, p. 42), “Analytical work begins with material provided by our vision of things, and this vision is ideological almost by definition.” 3.3 The Necessary Semantic Check Always Required by Mathematics Obviously, bifurcations in systems of mappings (reflecting differences in logic) will entail bifurcations also in the use of mathematical systems of inference. For example, a statistical office of a city recording the effect of the marriage of two singles already living in that city and expecting a child would map the consequent changes implied by these events in different ways, according to the encoding used to assess changes in the quality population. of population is done using the variable number of households. Alternatively, it can be described as 1 city. In this simple example, it is the definition of the mechanism of encoding (implied by the choice of the identity of the system to be described, i.e., households vs. people) that entails different mathematical descriptions of the same phenomenon. The debate about the possibility of replacing external referents (semantic) with internal rules (syntax) is a very old one in mathematics. The Czech-born mathematician Kurt Gödel demonstrated that, in mathematics, it is impossible to define a complete set of propositions that can proven true or false on the basis of a preexisting internal set of rules and axioms. Depending on the meaning attributed to the statements about numbers within a given mathematical system, one has to go outside that system looking for external referents. This is the only way to individuate the appropriate set of rules and axioms. However, after such an enlargment of the system, we will face a new set of unprovable statements (that would require an other enlargement in terms of additional external referents). This is a process that leads to an infinite regress. Any formalization always requires a semantic check, even when dealing with familiar objects such as numbers: The formalist program was wrecked by the Gödel Incompleteness Theorem which showed that Number Theory is already nonformalizable in this sense. In fact, Gödel (1931) showed that any attempt to formalize Number Theory, to replace its semantic by syntax, must lose almost every truth of Number Theory. (Rosen, 2000, p. 267) 3.3.1 The True Age of Dinosaurs and the Weak Sustainability Indicator To elaborate on the need of a continuous semantic check when using mathematics, it can be useful to recall the joke proposed by Funtowicz and Ravetz (1990) exactly for this purpose. The subject of the © 2004 by CRC Press LLC The event can be described as 1+1→1 (both before and after the birth of the child) if the mapping +1→3 (after the birth of the child) if the mapping is done in terms of number of people living in the Complex Systems Thinking: New Concepts and Narratives 49 joke is illustrated in Figure 3.2. The skeleton of a dinosaur (an exemplar of Funtravesaurus) is in a museum with a sign saying “age 250,000,000 years” on the original label. However, the janitor of the museum corrected the age to reflect 250,000,008. When asked about the correction, he gave the following explanation: “When I got this job 8 years ago, the age of the dinosaur, written on the sign, was 250,000,000 years. I am just keeping it accurate.” The majority of the people listening to this story do interpret it as a joke. To explain the mechanism generating such a perception, we can use the same explanation about jokes discussed before about the leg named Joe. When dealing with the age of a dinosaur, nobody is used to associating such a concept with a numerical measure that includes individual years. However, as noted by Funtowicz and Ravetz (1990), commenting on this joke, when considering the formal arithmetic relation a+b=c, there are no written rules in mathematics that prevent the summing of a expressed in hundreds of millions to b expressed in units. Still, common sense (semantic check) tells us that such an unwritten rule should be applied. The explanation given by the janitor simply does not make sense to anybody familiar with measurements. In this case, it is the incompatibility in the two processes of measurement (that generating a and that generating b) that makes their summing impossible. A more detailed discussion of this point is provided at the end of this chapter (Section 3.7). What is bizarre, however, is that very few scientists operating in the field of ecological economics seem to object to a similar summation proposed by economists when dealing with the issue of sustainability. For example, the weak sustainability indicator proposed by Pearce and Atkinson (1993) is supposed to indicate whether an economy is sustainable. According to this formal representation of changes in an economy, weak sustainability implies that an economy saves more than the combined depreciation on human-made and natural capital. The formal representation of this rule is given in Equation 3.1: SуdHMC/dt+dNC/dt (3.1) where S is savings, HMC is human-made capital and NC is natural capital. There are very good reasons to criticize this indicator (for a nice overview of such a criticism, see Cabeza-Gutés (1996)), mainly related to the doubtful validity of the assumptions that it implies, that is, a full substitutability of the two different forms of capital mapped by the two terms on the right (e.g., technology cannot replace biodiversity). But this is not the argument relevant here. The epistemological FIGURE 3.2 The author’s drawing of the “true” age of the dinosaur. (From Funtowicz and Ravetz, 1990.) © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems50 capital sin of this equation is related to its attempt to collapse into a single encoding variable (a monetary variable) two nonequivalent assessments of changes referring to system qualities that can only be recognized using different scales, and therefore can only be defined using nonequivalent descriptive domains. An assessment referring to dNC/dt uses a formal identity expressing changes using 1996-U.S.$ as the relevant variable. Such an assessment can only be obtained by using a measurement scheme operating with a time differential of less than 1 year (assuming the validity of the ceteris paribus assumption for no more than 10 years). On the contrary, changes in natural capital refer to qualities of ecosystems or biogeochemical cycles that have a time differential of centuries. The semantic identity of natural capital implies qualities and epistemic categories that, no matter how creative the analyst is, cannot be expressed in 1996-U.S.$ (a measurement scheme operating on a dt of years). In the same way, changes measured in 1996-U.S.$ cannot be represented when using variables able to catch changes in qualities with a time differential of centuries. Each of the two terms dHMC/dt and dNC/ dt cannot be detected when using the descriptive domain useful to define the other. In conclusion, the sum indicated in relation 1, first, does not carry any metaphorical meaning since the two forms of capital are not substitutable and, second, in any case could not be used to generate a normative tool, since it would be impossible to put meaningful numbers into that equation. 3.4 Bifurcations and Emergence The concept of bifurcation also has a positive connotation. It indicates the possibility of increasing the repertoire of models and metaphors available to our knowledge. In fact, a direct link can be established between the concepts of bifurcation and emergence. Using again the wording of Koestler (1968) we have a discovery—Rosen (1985) suggests using for this concept the term emergence—when two previously unrelated frames of reference are linked together. Using the concept of equivalence classes for both organized structures and relational functions, we can say that emergence or discovery is obtained (1) when assigning a new class of relational functions (which indicates a better performance of the holon on the focal-higher level interface) to an old class of organized structures, or (2) when using a new class of organized structures (which indicates a better performance of the holon on the focal-lower level interface) to an existing class of relational functions. We can recall again the example of the joke, in which a new possibility of associating words is introduced, opening new horizons to the possibility of assigning meaning to a given situation. An emergence can be easily detected by the fact that it requires changing the identity of the state space used to describe the new holon. A simple and well-known example of emergence in dissipative systems is the formation of Bénard cells (a special pattern appearing in a heated fluid when switching from a linear molecular movement to a turbulent regime). For a detailed analysis of this phenomenon from this perspective, see Schneider and Kay (1994). The emergence (the formation of a vortex) requires the use in parallel of two nonequivalent descriptive domains to properly represent such a phenomenon. In fact, the process of self-organization of a vortex is generating in parallel both an individual organized structure and the establishment of a type. We can use models of fluid dynamics to study, simulate and even predict this transition. But no matter how sophisticated these models are, they can only guess the insurgence of a type (under which conditions you will get the vortex). From a description based on the molecular level, it is not possible to guess the direction of rotation that will be taken by a particular vortex (clockwise or counterclockwise). However, when observed at a larger scale, any particular Bénard cell, because of its personal history, will have a specific identity that will be kept as long as it remains alive (so to speak). This symmetry breaking associated with the special story of this individual vortex will require an additional source of information (external referent) to determine whether the vortex is rotating clockwise or counterclockwise. Thus, we have to adopt a new scale for perceiving and representing the operation of a vortex (above the molecular one) to detect the direction of rotation. This implies also the use of a new epistemological category (i.e., clockwise or counterclockwise) not originally included in the equations. To properly represent such a phenomenon, we have to use a descriptive domain that is not equivalent to that used to study lower-level mechanisms. Put another way, the information required to describe the transition on two levels (characterizing both © 2004 by CRC Press LLC Complex Systems Thinking: New Concepts and Narratives 51 the individual and the type) cannot all be retrieved by describing events at the lower level. More about this point is discussed in Section 3.7 on the root of incommensurability between squares and circles. Another simple example can be used to illustrate the potential pitfalls associated with the generation of policy indications based on extrapolation to a large scale of findings related to mechanisms investigated and validated at the local level. Imagine that an owner of a sex shop is looking for advice about how to expand business by opening a second shop. Obviously, when analyzing the problem at a local level (e.g., when operating in a given urban area), the opening of two similar shops close to each other has to be considered as bad policy. The two shops will compete for the same flow of potential customers, and therefore the simultaneous presence of two similar shops in the same street is expected to reduce the profit margin of each of the two shops. However, imagine now the existence of hundreds of sex shops in a given area. This implies the emergence of a new system property, which is generally called a red-light district. Such an emergent property expresses functions that can only be detected at a scale larger than the one used to study the identity of an individual sex shop. In fact, red-light districts can also attract potential buyers from outside the local urban area or from outside the city. In some cases, they can even draw customers from abroad. In technical jargon we can say that the domain of attraction for potential customers of a red-light district is much larger than the one typical of an individual sex shop. This can imply that—getting back to the advice required by the owner of an individual sex shop—there is a trade-off to be considered when deciding whether to open a new shop in a red-light district. The reduction of profit due to the intense competition has to be weighed against the increase of customer flow due to the larger basin of attraction. Such a trade-off analysis is totally different if the shop will be opened in a normal area of the city. In conclusion, whereas it is debatable whether the concept of emergence implies something special in ontological terms, it is clear that it implies something special in functional and epistemological terms. Every time we deal with something that is more than and different from the sum of its parts, we have to use in parallel nonequivalent descriptive domains to represent and model different relevant aspects of its behavior. The parts have to be studied in their role of parts, and the whole has to be studied in its role as a whole. Put another way, emergence implies for sure a change (a richer information space) in the observer-observed complex. The implications of this fact are huge. When dealing with the evolution of complex adaptive systems (real emergence), the information space that has to be used for describing how these systems change in time is not closed and knowable a priori. This implies that models, even if validated in previous occasions, will not necessarily be good in predicting future scenarios. This is especially true when dealing with human systems (adaptive reflexive systems). 3.5 The Crucial Difference between Risk, Uncertainty and Ignorance The distinction proposed below is based on the work of Knight (1964) and Rosen (1985). Knight (1964) distinguishes between cases in which it is possible to use previous experience (e.g., record of frequencies) to infer future events (e.g., guess probability distributions) and cases in which such an inference is not possible. Rosen (1985), in more general terms, alerts us to the need to always be aware of the clear distinction between a natural system, which is operating in the complex reality, and the representation of a natural system, which is scientist-made. Any scientific representation requires a previous mapping, within a structured information space, of some of the relevant qualities of the natural system with encoding variables (the adoption of a formal identity for the system in a given descriptive domain). Since scientists can handle only a finite information space, such a mapping results in the unavoidable missing of some of the other qualities of the natural system (those not included in the selected set of relevant qualities). Using these concepts, it is possible to make the following distinction between risk and uncertainty: Risk—Situation in which it is possible to assign a distribution of probabilities to a given set of possible outcomes (e.g., the risk of losing when playing roulette). The assessment of risk can come either from the knowledge of probability distribution over a known set of possible outcomes obtained using validated inferential systems or in terms of agreed-upon subjective probabilities. In any © 2004 by CRC Press LLC Multi-Scale Integrated Analysis of Agroecosystems52 case, risk implies an information space used to represent the behavior of the investigated system, which is (1) closed, (2) known and (3) useful. The formal identity adopted includes all the relevant qualities to be considered for a sound problem structuring. In this situation, there are cases in which we can even calculate with accuracy the probabilities of states included in the accessible state space (e.g., classic mechanics). That is, we can make reliable predictions of the movement in time of the system in a determined state space (Figure 3.3a). The concept of risk is useful when dealing with problems that are (1) easily classifiable (about which we have a valid and exhaustive set of epistemological categories for the problem structuring) and (2) easily measurable (the encoding variables used to describe the system are observable and measurable, adopting a measurement scheme compatible in terms of space-time domain with the dynamics simulated in the modeling relation). Under these assumptions, when we have available a set of valid models, we can forecast and usefully represent what will happen (at a particular point in space and time). When all these hypotheses are applicable, the expected errors in predicting the future outcomes are negligible. Alternatively, we can decide to predict outcomes by using probabilities derived from our previous knowledge of frequencies (Figure 3.3b). Uncertainty—Situation in which it is not possible to generate a reliable prediction of what will happen. That is, uncertainty implies that we are using to make our prediction an information space that is (1) closed, (2) finite and (3) partially useful, according to previous experience, but at the same time, there is awareness that this is just an assumption that can fail. Therefore, within the concept of uncertainty we can distinguish between: • Uncertainty due to indeterminacy—There is a reliable knowledge about possible outcomes and their relevance, but it is not possible to predict, with the required accuracy, the movement of the system in its accessible state space (e.g., the impossibility to predict the weather 60 days from now in London) (Figure 3.4a). Indeterminacy is also unavoidable when dealing with the reflexivity of humans. The simultaneous relevance of characteristics of elements operating on different scales (the need to consider more than one relevant dynamic in parallel on different space-time scales) and nonlinearity in the mechanisms of FIGURE 3.3 (a) Guessing Eclipse’s predictive power is very high. (b) Conventional risk assessment prediction using frequencies to estimate probabilities. © 2004 by CRC Press LLC [...]... side effects (e.g., generation of a lock-in of a larger -scale problem) Unfortunately, we can never know this type of information ahead of time © 2004 by CRC Press LLC 57 58 Multi- Scale Integrated Analysis of Agroecosystems • • • • Is our integrated assessment of changes reflecting existing multiple goals found in the system? Any integrated assessment of the performance of a system depends on: 1 Expectations... natural set of multiple identities integrated across scales found in biological and human systems (e.g., the different views of a person shown in Figure 1.2) In these systems, the stability of higher-level holons—individuals—is based on the validity of the identity of the class of realizations of lower-level holons—organs—(consistency of the characteristics of the members of equivalence classes of dissipative... consist of a set of integrated identities that are scaled, since FIGURE 3. 9 Different identities of the Mandelbrot set (Images from Julia and Mandelbrot Explorer by D.Joyce http://aleph0.clarku.edu/~djoyce/julia/explorer.html) © 2004 by CRC Press LLC 66 Multi- Scale Integrated Analysis of Agroecosystems they require an implicit step of realization to be preserved as types.This explains the existence of the... their efficiency and adaptability This can be obtained by a continuous change of structures to maintain existing functions and a continuous change of functions to maintain existing © 2004 by CRC Press LLC 60 Multi- Scale Integrated Analysis of Agroecosystems FIGURE 3. 7 Self-entailment of efficiency and adaptability across scales structures Put another way, neither a particular societal structure nor... solutions) carry the risk of curing symptoms rather than causes.That is, the adoption of a very small scale of analysis risks the locking-in of the system in the same dynamic that generated the problem in the first place, since this main dynamic, operating on a larger scale, has not been addressed in the location-specific analysis How should the trade-offs linked to the choice of one level rather than... this case, the death of a particular person © 2004 by CRC Press LLC 55 56 Multi- Scale Integrated Analysis of Agroecosystems solve the problem, but, to do that, we have to mediate between contrasting views found in the population of individuals to which we want to apply policies In this particular example, dealing with the trade-offs between individual freedom of smoking and the burden of health costs for... characteristics of the investigated system, but also on decisions made in the preanalytical steps of problem structuring.We can only deal with the scientific representation of a nested hierarchical system © 2004 by CRC Press LLC 68 Multi- Scale Integrated Analysis of Agroecosystems by using a strategy of stratification (by using a triadic reading based on the arbitrary selection of a focal space-time differential... in Chapter 1 The steps of this cycle (with an arbitrary choice of a starting step) are: 1 2 3 4 Accumulation of experience in the system leads to more efficiency (by amplification of the best-performing activities and elimination of the worst-performing ones) More efficiency makes available more surplus to fuel societal activities The consequent increase in the intensity and scale of interaction of. .. explanation on how to boost the supply of oxygen to the brain would be completely useless in a meeting discussing the opportunity of introducing a new tax on cigarettes 3. 6.2 The Impossible Trade-Off Analysis over Perceptions: Weighing Short-Term vs Long-Term Goals The example given in Figure 3. 6 addresses explicitly the importance of considering the hierarchical nature of the system under investigation... closure of the geometric object Put another way, the very identity of this complex object implies a self-entailment among the various identities of its component elements: (1) lower-level identities of segments (relative length) and (2) focal-level identity of the triangle (relative position of the sides within the whole).The existence of these constraints makes it possible to compress the requirement of . Press LLC Multi- Scale Integrated Analysis of Agroecosystems5 8 • Is our integrated assessment of changes reflecting existing multiple goals found in the system? Any integrated assessment of the performance. epistemological FIGURE 3. 2 The author’s drawing of the “true” age of the dinosaur. (From Funtowicz and Ravetz, 1990.) © 2004 by CRC Press LLC Multi- Scale Integrated Analysis of Agroecosystems5 0 capital sin of this. (1) someone charac- © 2004 by CRC Press LLC couple of mappings: (C↔G, T↔A) and (closed set of triplets types→closed set of amino acid types). Multi- Scale Integrated Analysis of Agroecosystems4 8 terizing