MULTI - SCALE INTEGRATED ANALYSIS OF AGROECOSYSTEMS - CHAPTER 6 ppt

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

Part 2

Complex Systems Thinking: Daring to Violate Basic Taboos

of Reductionism

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 thenillustrates the special characteristics of holarchic systems with examples (Section 6.2) This class ofsystems can generate and preserve an integrated set of nonequivalent identities (defined in parallel ondifferent levels and therefore scales) for their constituent holons The expected relationship among thecharacteristics of this integrated set of identities makes it possible to obtain some free informationwhen performing a multi-scale analysis This is the basic rationale for the multi-scale mosaic effect Amulti-scale analysis requires establishing an integrated set of meaningful relationships between perceptionsand representations of typologies (identities) defined on different hierarchical levels and space-timedomains This means that in holarchic systems we can look for useful mosaic effects when consideringthe relations between parts and the whole

Multi-scale multidimensional mosaic effects can be used to generate a robust multi-scale integratedanalysis 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 byestablishing a resonating entailment across identities that are defining each other across scales Thisconcept is discussed—using a very familiar example, the calendar—in Section 6.5 The concept ofholarchic complexity has been explored in the field of complex systems theory—under differentnames—in relation to the possible development of tools useful for the study of the sustainability ofcomplex adaptive systems An overview of these efforts is provided in Section 6.6 Different labelsgiven to this basic concept are, for example, integrity, health, equipollence, double asymmetry, possibleoperationalizations of the concept of biodiversity

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 storinginformation 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 potentiallyuseful shared perceptions) and formal identities (closed and finite sets of epistemic categories used torepresent a member of an equivalence class associated with a type) assigned to a given essence Whendealing with the perception and representation of natural holarchies (such as biological systems of

* Kozo Mayumi is co-author of this chapter.

socioeconomic systems), this compression is made easy by the natural organization of these systems inequivalence classes (e.g., the set of organisms of a given species are copies made from the same geneticinformation, as well as with human artifacts; the set of cars belonging to the same model are copiesmade from the same blueprint).

Getting back to the ideas of Koestler, the compression obtained with language is not obtained byusing a single abstractive hierarchy (in our terms, by using a single formal identity for characterizing agiven 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 havebeen abstracted and stored independently by separate hierarchies within that same sense ofmodality, but with different criteria of relevance One abstracts melody and filters out everythingelse as irrelevant, the other abstracts the timbre of the instrument and treats the melody asirrelevant Thus not all the details discarded in the process of stripping the input are irretrievablylost, because details stripped off as irrelevant according to the criteria of one hierarchy may havebeen retained and stored by another hierarchy with different criteria of relevance The recall ofthe experience would then be made possible by the co-operation of several interlockinghierarchies… 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 forgottenthe words Finally you may recognize Caruso’s voice on a gramophone record, withoutremembering 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 Everytime we associate the expected set of characteristics (a set of observable qualities) of members assumed tobelong to an equivalence class with a label (a name), we are using types (an abstract set of qualitiesassociated with those individuals assumed to belong to an equivalence class) As noted before, the relativecompression in the information space obtained by using the characteristics of types (you say a dog andyou include them all) to describe the characteristics of individual members perceived as belonging to theclass has the unavoidable effect of inducing errors Not all dogs are the same It is not possible to cover theopen 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 adog) This is why humans are forced to use subcategories (e.g., a fox terrier), sub-subcategories (e.g., abrown fox terrier) and sub-sub-subcategories (e.g., a very young brown fox terrier) in an endless chain ofpossible categorizations Adopting this solution, however, implies facing two setbacks: (1) In this way, wereexpand the information space required by individual observers to handle the representation (sincemore adjectives are required to individuate the new sub-subcategory) and (2) in this way, we lose generalityand usefulness of the relative characterization The class of “a very young brown fox terrier having had astressful morning because of nasty diarrhea and therefore being now very hungry” is not very useful as anequivalence class In fact, it is not easy to find a standard associative context that would make its use as ageneral 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 inspace and time, within a specified context (e.g., children getting out of a given school at 13:30 onThursday, 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 belongingsimultaneously 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),

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 totallyuseless 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 alimited set of categories (indicators) by triangulating them—relying on a mosaic effect—but onlywhen we are sure that we are operating within a valid, finite and closed information space Whendescribing patterns in general, the type is described in general terms within its standard associativecontext, or a special system is individuated within a specific local setting (at a given point in space andtime) When dealing with a specific description of events, the characteristic and constraints of the givencontext 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 thatthere are two television cameras, A and B, directed at what is going on in the water (e.g fishesswimming around) as seen through the two walls at right angles to each other Now let thecorresponding 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 naturalsystem (the movements of the same set of fishes seen in parallel on two TV screens) The nonequivalencebetween the two descriptive domains is generated by the parallel mapping of events occurring in atridimensional space into two two-dimensional projections (over the two screens A and B) Again, wehave the effect of incommensurability already discussed regarding the Pythagorean theorem (Section3.7)—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-dimensionalrepresentations could generate bifurcations That is, two teams of scientists looking at the two parallelnonequivalent 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 inreality in the tridimensional tank The images moving on the two screens are two different narrativesabout the same reality The problem of multiple narratives of the same reality becomes crucial, forexample, in quantum physics, when the experimental design used to encode changes of a relevantsystem’s qualities in time can generate a fuzzy definition of simultaneity and temporal successionamong 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 ofthe reality As observed by Allen et al (2001), “Narratives collapse a chronology so that only certainevents are accounted significant A full account is not only impossible, it is also not a narrative.” Putanother way, a narrative is generated by a particular choice of representing the reality using a subset ofpossible perceptions of it Any set of perceptions is embedded by a large sea of potential perceptionsthat could also be useful when different goals are considered This implies that providing sound narrativeshas to do with the ability to share meaning about the usefulness of a set of choices made by theobserver about how to represent events That is, the very concept of narrative entails the handling of acertain dose of arbitrariness about how to represent reality—a degree of arbitrariness about which thescientist 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 Afish moving in a straight line toward camera A will be seen as moving on screen B but not moving onscreen A However, a sudden deflection from the original trajectory to a side of this fish will be

perceived as a dramatic local acceleration from camera A This will generate a nonlinearity in thedynamic of the fish within the descriptive domain represented on screen A This dynamic will bedifficult to explain in physical terms (and to simulate by a dynamic model) by relaying only theinformation given by screen A How did the fish manage to get this huge acceleration in the middle ofthe water without touching anything—moving suddenly away from total immobility? As soon as wecheck the information coming from screen B, we can easily explain this perceived nonlinearity Thenonlinear dynamic that is “impossible” to explain on the descriptive domain A is simply an artifactgenerated 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 themovement was occurring on the direction considered irrelevant according to the selected set of relevantobservable qualities associated with the experimental design.

This is a very plain example of the types of problems related to the difficult interpretation ofrepresentation 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 ismoving in time That is, no other relevant attributes but the vectors associated with speed and accelerationare considered when discussing trajectories Imagine then, a case in which we were required to dealwith 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 simultaneoususe of nonequivalent descriptive domains

In conclusion, when dealing with the sustainability of a socioeconomic system, we have to first decidewhat is relevant and irrelevant for explaining the past history of the system and guessing the futuretrajectory of development, but above all, we have to decide who (what) are the relevant observers whoshould be considered clients for the tailoring of the representation provided by the analysis In fact, anyformalization 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 inferencesusing one of the possible models (based on what is perceived on just one of the possible screens) It isimportant 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 wherethe 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 thecombination 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 somethingdifferent from the simple sum of the parts) The syntactic mosaic effect has more to do with patternrecognition (individuating a similarity within the reservoir of available useful patterns), whereas thesemantic 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 arelooking for (they are not mapping 1:1 to the murderer) with a particular combination that providesenough 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 “freeride” that can be obtained by an interlaced or interlocking of different systems of mapping generating

internal redundancy (we are using here the expressions suggested by Koestler) is the process of solvingcrossword 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 incrosswords) 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 theinnate redundancy of the information space used when describing dissipative adaptive holarchies In thiscase, 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 madeusing common information stored in the DNA) This innate redundancy is the reason that we can rely soheavily on type-based descriptions related to expected identities This means that it is easy to find labelsabout which the users of a given language can share their organized perceptions of types associated withthe expected existence of the relative equivalence class As discussed in Chapter 2, this mechanism usedfor 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 Forexample, consider a famous human—let us say Michael Jordan We can obtain a lot of free informationabout him from the knowledge related to equivalence classes to which this individual belongs, evenwithout having a direct experience of interaction with him For example, since we know that Jordanbelongs to the human species, we can guess that he has two arms, two eyes, etc Actually, we can convey alot of information about him just by adding after his name the simple information “nothing is missing inthe 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 characterizationlinked to his identity as a male of a certain age (a smaller subcategory of human beings) This willprovide us with another subset of expected standard characteristics (expected observable qualities) andbehaviors (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 ismuch 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 MichaelJordan in terms of characteristics of the organized structure generating signals, we remain trapped inthe fuzziness of the definition of what should be considered as the relative type, against which to makethe identification of the individual In fact, even when we arrive to the clear characterization of anindividual person, we are still dealing with a holon at the moment of representing him This is due tothe 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 behavioralpatterns—e.g., by asking his family or by recording his daily life Each characterization would still bebased on various types related to Michael Jordan determining different sets of expected observablequalities 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 thispoint, we can still split these types into other types, all related to the special subset of qualities andbehaviors that the individual Michael Jordan, when in full strength, could take This splitting can berelated 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 rightset of qualities and behaviors that can be associated in a substantive way with the given organizedstructure) Each individual holon will always escape a formal definition due to (1) the fuzzy relationbetween structure and function, which are depending on each other for their definition within a givenidentity; (2) the innate process of becoming that is affecting them and (3) the changing interest of theobserver The indeterminacy of such a process translates into an unavoidable openness of the information

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 semanticterms using types, after freezing their complex identity using the triadic reading over an infinitecascade of categorizations and in relation to the characteristics of the observer At this point, aformalization 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, observerscan see only a few special perspectives and parts of the whole The metaphor of the group of blindpeople trying to characterize an elephant by feeling its different parts can be recalled here Rather thandenying 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 andhuman 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, afterhaving selected an opportune set of formal identities for looking at these systems, we can also expect to beable 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 semanticidentity of a dissipative system) that will make it possible to establish a link between assessmentsreferring to lower-level components and assessments referring to the whole The choice of a usefulsystem of accounting is a topic that will be discussed in the next chapter about impredicative loopanalysis The following example has only the goal of illustrating the special characteristics of a nestedholarchy Imagine a holarchic system—e.g., the body of a human being—and imagine that we want tostudy its metabolism in parallel on two levels: (1) at the level of the whole body and (2) at the level ofindividual organs belonging to the body To do that, we have to define a formal identity (a selection ofvariables) 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 therelative 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 assessmentrefers to energy dissipated for basal metabolism

These two variables are associated with the size of the dissipative system (whole body) and reflect twononequivalent mechanisms of mapping The selection of these two variables reflects the possibility of

using two nonequivalent definitions of size The first definition refers to the perception of the internalstructure (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 servicesassociated 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 mappingrelated to the black box in relation to its structural components, whereas assessment 2 (80 W of energyinput 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 environmentalprocesses (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 (anamount of energy per unit of time), it should not be considered an intensive variable when dealingwith 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 ofenergy, required in a standard period of reference—either a day or a year, depending on the measurementscheme That is, this is an assessment that is related to a given time window (required to obtain meaningfuldata) that is big enough to assume such an identity constant in relation to lower-level dynamics Thevalue is then expressed in joules per second, only because of a mathematical operation applied to thedata The value 80 W (for the whole body) has to be considered an extensive variable, since it mapsonto an equivalent amount of environmental services (e.g., a given supply of food, amount of energycarriers and absorption of the relative amount of CO2 and wastes), which must be associated with themetabolism of the system over a given time horizon

By combining these two extensive variables (1 and 2), we can obtain an average density of energydissipation per kilograms of body mass, which is 1.2 W/kg This should be considered, within thismechanism of accounting, an intensive variable (a variable 3 to be added to the set used to characterizemetabolism within a formal identity of it) Variable 3 can be seen as a benchmark value (average valuefor 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 istherefore 10 times higher than the average of the rest of the body If we write an equation of congruenceacross 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)

Level n-1 (the identity of the considered lower-level components is known)

Level n-1 (after looking for a closure we can define a weak identity for other

components)

When we know the hierarchical structure of parts and the whole (how the whole body mass isdistributed 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:

That is, the hierarchical structure of the system and the previous knowledge of the expected identity ofparts 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:

This means that the selected system of accounting of the relevant system quality mass must be clearlydefined (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 theavailability of additional external sources of information (data or experimental settings available) wecould 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) nonequivalentrepresentations of a metabolic system across levels However, this requires that the formal identitiesused to characterize lower-level elements have a set of attributes in common with the formal identityused 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—thetwo variables are (1) size in kilograms of mass (extensive variable 1) and (2) size in watts of metabolicenergy (extensive variable 2) The combination of these two variables makes it possible to define abenchmark 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 forgenerating 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 reciprocaldefinitions in the egg-chicken process—as discussed in the next chapter) very robust

(e.g., brain, liver, heart, kidneys—see Figure 6.1)

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 onthe combined use of intensive and extensive variables describing parts and the whole of a dissipative holarchicsystem This operation leads to a process of benchmarking based on the determination of a chain of valuesfor 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 andtheir ratio (the intensive variable) are defined as follows:

• Extensive 1—This is the size of the human body expressed in mass (a mapping linkingblack-box/lower-level components): 70 kg of body mass

• Extensive 2—This assessment of size measures the degree of dependency of the dissipativesystem on processes occurring outside the black box, that is, in the context This can betranslated into an number of carriers of endosomatic energy (e.g., kilograms of food) that isrequired to maintain a given identity (a mapping linking black box/context): 81 W of foodenergy 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 tocharacterize the metabolic process associated with the maintenance of the identity of thedissipative system This ratio can been called the endosomatic metabolic rate of the humanbody (EMRHB): 1.2 W/kg of food energy/kg of body mass It is important to note that thevalues of EMRi 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.

a formal identity to characterize its metabolism The same approach can be used to characterize the

identity and metabolism of lower-level elements of the body (level n-1) This implies assuming that it

is possible to perceive and represent both the black box and its components as metabolic elements onthe same descriptive domain (using a set of reducible variables, even if operating different measurementschemes) This means that the data obtained using nonequivalent measurement schemes can be reduced

to each other (e.g., the energy consumed by the brain in form of ATP can be expressed in energyequivalent consumed by the person in the form of kilograms of food) Both assessments refer to restingmetabolism Obviously, this requires having available in parallel two experimental settings—one used

to determine the data set for the black box (level n) and one used to determine the same data set but referring to lower-level components (level n-1) The experimental design used to measure the mass

and the energy requirement of the whole body, in fact, is different from that adopted to measure themass and the energy requirement of internal organs

Let us use this approach to characterize the metabolism of lower-level components of the humanbody Obviously, the mass of (extensive variable 1) and the amount of energy dissipated per unit oftime (extensive variable 2) in individual components must be smaller than the whole The same ruledoes not apply, however, to the value taken by intensive variable 3 describing the level of dissipationper unit of mass Actually, this is what makes it possible to establish a forced relation between the values

Brain: (1) size in mass=1.4 kg; (2) size in endosomatic energy=16.2 W; (3) EMRbr=11.6 W/kgLiver: (1) size in mass=1.8 kg; (2) size in endosomatic energy=17.4 W; (3) EMRlv=9.7 W/kg

In this example, both elements considered at the level n-1 have an endosomatic metabolic rate much

higher than the average found for the human body as a whole This means that in terms of requirement

of input per unit of biomass (e.g., the requirement of input flowing from the environment into the blackbox), 1 kg of brain is consuming (is equivalent to) almost 10 kg of average human body mass This ratioreflects the relative value of EMRi (11.6 W/kg for the brain vs 1.2 W/kg for the average body mass) Thisimplies the possibility of calculating different levels of embodied ecological activity for ecosystem elementsoperating at different hierarchical levels (Odum, 1983, 1996) This fact can also be used to calculatebiophysical limits of human exploitation of ecological systems (Giampietro and Pimentel, 1991) We canrecall here the joke about the national statistics on consumption of chicken per capita (p.c.) If there areparts of the body that consume much more than the average, other parts must consume much less Thisimplies that the value of the ratio between levels of consumption per unit of mass and the value of theratio between the sizes of the various parts must be regulated by equations of congruence

It is important to observe here the crucial role of the peculiar characteristics of nested metabolicelements They are made up of holons that do have a given identity (they are a realization of a givenessence, which implies the association between expected typologies and experienced characteristics inequivalence classes) The brain of a given human being has an expected level of metabolism per kilogram,

which we can guesstimate a priori from the existing knowledge of the relative type This level is different

from the expected level of metabolism of 1 kg of heart Both of them, however, can be predicted only to

a certain extent Individuals are just realizations of types (their assessments come with error bars).The situation would be completely different if we disaggregate the characteristics of the human

body—assessed at the level n—by utilizing a selection of mappings based on the adoption of identities

referring to much lower levels of organization For example, imagine using a set of identities referring

to the atomic level of organization—as done in the lower part of Figure 6.1, in the white box labeled

“chemical elements.” In this example, the whole body mass is characterized in terms of a profile offractions of oxygen, carbon, hydrogen, etc We can even obtain closure of the size of the whole body(assessed in kilograms) expressed as a combination of lower-level identities (assessed in kilograms).However, with this choice, the distance between the hierarchical levels at which we perceive and

represent the characteristics of the metabolism of the human body (at a level we call n) and those at which we can perceive and represent the identity of chemical elements (at a level we call w, with

taken by the size of the compartments and their levels of dissipation Looking at Figure 6.1,

w<<n) is so large that this nonequivalent set of identities—chemical elements—used to describe the

components of the human body cannot bring into our descriptive domain (on level n) any free

information In fact, atoms require a descriptive domain for their characterization that is not compatiblewith the perception and representation of the chemical processes associated with the metabolism offood and the maintenance of the organized structure of the organs through metabolism That is, withthis choice we are not able to reduce the formal definition of these two sets of identities to each other.From our knowledge of the typologies associated with oxygen, carbon and hydrogen (identity of

chemical components in relation to lower-level atomic components at the level w and level w-1), we

can just estimate the overall mass of the system—nothing about the rate of its metabolism

On the contrary, when we use a reliable set of identities for organs viewed as metabolic systems—at the

level n-1—for the representation of lower-level elements of the human body, we can use previous knowledge

about the given rate of energy dissipation associated with the functions expressed by the relative organizedstructure In fact, we expect that both components (organs and the whole) do have a metabolism, so thatthey can share the same formal identity, even if they require different measurement schemes This is where

we can get some free information from the knowledge of the relative types To take advantage of this freeride, however, we have to select two sets of identities (e.g., for the whole body and its organs) that can becharacterized using the same set of variables This implies a small distance between hierarchical levels Forexample, when using the disaggregating procedure shown in the white box labeled “organs of an adult man”(70 kg of body mass), we can infer, in principle, the dissipation rate of the whole body starting from ourknowledge of the dissipation rates of its parts and their relative sizes Basically, this is the rationale that will bepresented later on for generating mosaic effects in the representation of the stability of socioeconomicsystems (e.g., multiple-scale integrated analysis of societal metabolism (MSIASM))

This mechanism, however, requires introducing an additional concept that plays a crucial role in the

process: the concept of closure over the information space (Dyke, 1988) The bonus obtained when using

nonequivalent information derived from nonequivalent observations of a nested hierarchical system inparallel depends in fact on the degree of closure of the relative information space A mosaic effect isreached when we are able to aggregate the various assessments referring to the parts onto the total size ofthe whole in a consistent way In this case, the knowledge of the formal identity of the whole (at the level

n) and the knowledge of the formal identities of the various parts (at the level n-1) can be related to each

other to gain robustness This robustness is associated with the congruence of the values taken by the set

of different variables used to characterize the two sets of identities across levels (after characterizing theexisting relation of parts into the whole, in relation to the selection of formal identity)

To explain this concept, imagine that we want to guesstimate the overall metabolic rate of a human

body using only our knowledge of its parts (referring to the level n-1) To do that, we can use the data express the characteristics of the whole body (level n) as a combination of characteristics of seven typologies of lower-level components (level n-1) Of these, six types (liver, brain, heart, kidneys, muscle,

fat tissue) have a clear and known (expected) identity The seventh compartment, which is required forobtaining the closure, is not clearly defined in terms of an established correspondence between aninternal mapping (e.g., kilograms of mass) and an external mapping (e.g., energy required for itsmetabolism), associated with a previous knowledge of this type Actually, we are all familiar with thelabel given to this last compartment, which is often found at the bottom of this type of list—“others.”Obviously, this solution implies that the identity of the compartment labeled as “others” is not associated

with any previous knowledge of an established type at the level n-1 Therefore, the resulting numerical assessment is not obtained by a direct measurement (performed at the level n-1), an external referent,

of a sample of members of an equivalence class Put another way, “others” is not a known type with agiven and reliable identity Rather, the characteristics of this virtual compartment are inferred byconsidering the difference between (1) the information gathered about the characteristics of the whole

human body gathered at level n and (2) the information gathered about the 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

set included in the white box labeled “organs of an adult man” in Figure 6.1 In this case, we can

whole, (2) the selection of identities used to define the various compartments of the whole—the set oflower-level elements used in the disaggregated representation of the whole; and (3) the relative values

of the variables describing the selected set of identities of lower-level elements Getting back to theexample of the seven compartments in the white box, we could have used a different selection of sixtypes (e.g., by replacing the 1.8 kg of liver with 7.0 kg of skeleton), and this would have provided adifferent definition for the virtual identity of the seventh compartment “others.” In this case, “others”would have had a mass of 17.8 kg (rather than the 23.3 kg reported in the table) and a different EMR.This is an important aspect that can be associated with the next concept to be introduced in Chapter

7—impredicative loop analysis One of the standard goals of the triangulation of information whendealing with the reciprocal definition of identities across levels in a metabolic holarchy is that of reducingthe noise associated with unavoidable presence of informational leftovers as much as possible The amount

of information missed when adopting the category “others” as if it were a real typology can be important.Therefore, the analyst has to choose the most useful way to represent the system (disaggregate it intolower-level elements), trying to reduce as much as possible such a problem For example, getting back tothe example of the disaggregating choices made in the white box labeled “organs of an adult man” (sixtypes plus the seventh compartment labeled “others”), we have a relatively large size of the unaccountedpart of the whole in terms of mass (more than 33% of the total mass is included in “others”—that is, 23.2

kg out of 70 kg of the whole body) On the other hand, this mass might not be particularly relevant interms of metabolic activity, since the resulting level of EMR is quite low (0.6 W/kg) Therefore, bymaking such a choice, the analyst is ignoring the characteristics of the identity of a big part of the whole

in terms of mass However, if the analyst is concerned only with identifying those organs that are keepingthe metabolic rate high, this body part might not be particularly relevant in terms of energy dissipationper unit of mass (e.g., in terms of the qualities associated with extensive variable 2, that is, requirement ofservices—e.g., sustainable food—from the context) Obviously, any decision about what to include andwhat to leave out in the virtual category assigned to the “others” compartment will depend on the type

of problems faced and the type of questions we want to answer with the study

When facing a level of closure that is not satisficing for the goal of the analysis, the analyst can decide

to get into the remaining parts of the whole labeled as “others” and look for additional typologies(additional valid and useful natural identities) In this way, it becomes possible to reduce the amount oftotal mass of the whole, which remains unaccounted for in terms of a definition of identities at the lowerlevel An example of this additional investigation (which implies gathering more information—usingcompartment originally labeled as “others” in the white box (which is covering 23.2 kg of mass of thewhole) has been split into seven additional compartments, characterized using an additional six knowntypologies or identities of lower-level components (skeleton, bone marrow, blood, gastrointestinal tract,lungs, lymph tissue) Also in this new characterization of the black box in terms of an expanded set oflower-level compartments, we still face the presence of a residual compartment labeled “others.” However,after this additional injection of information about the identities of elements involved in the metabolism

of the human body of an adult man—at the level n-1—we are able to characterize the metabolism of the

whole using previous knowledge related to the characteristics of 12 known typologies or identities oflower-level elements This reduces the amount of residual unknown body mass not accounted for interms of expected characteristics of lower-level typologies to only 3.9 kg (over 70 kg) Depending on thequestions addressed by the study, the analyst can decide at this point whether this reduction is enough.Obviously, we cannot expect that it is always possible to keep splitting the residual required informationlabeled “others” into characteristics associated with known typologies (exploiting in this way preexistingknowledge of additional lower-level identities) The possibility of using this trick has limits

We can now leave the metaphor of the multi-scale analysis of the metabolism of the human body toget into a more general question What can be achieved by adopting this approach when studyingcomplex adaptive holarchic systems? What are the advantages of obtaining an adequate closure of theinformation space, based on a parallel characterization of the identities of metabolic systems organized

in holarchies on two contiguous levels (e.g., level n and level n-1)?

We believe that this approach can be used to achieve two important objectives:

additional external referents—at the level n-1) is given in the gray box in the lower part of Figure 6.1 The

1 It provides a general mechanism that can be used for benchmarking (contextualization of anelement in relation to the whole to which it belongs) Obviously, any benchmarking will alwaysreflect the previous selection of the formal identity (the set of significant variables) used to checkthe congruence among flows For example, a question like, “How well is a farmer doing whomakes $1000 per year?” can be answered only after comparing this value (an intensive variable ofadded value per unit of human time, which can be associated with the identity of a householdholon) with the average household income of a given year within a given society in which such

a farmer is operating (the identity of the larger holon within which the household holon isoperating) In the same way, a yield of 1000 kg of corn/ha can be a remarkable achievement for

a farmer operating in a desert area with poor soil when not using any fertilizers, whereas it would

be considered a totally unacceptable output if obtained in Iowa in the year 2000 By adopting amulti-scale integrated analysis of agroecosystems, it can be possible to build an integratedmechanism of mappings of flows that can be easily defined and tracked (e.g., flows of foodenergy, exosomatic energy, added value, water, nitrogen) in relation to (1) the characteristics ofthe system generating and consuming these flows and (2) the characteristics of the contextwithin which these flows are exchanged Since the very exchange of these flows is related to thedefinition and maintenance of an identity for the metabolic elements investigated (across variouslevels), such an analysis can carry useful free information when addressing the hierarchical structure

of the system and when linking identities and indicators referring to wholes and parts

As noted earlier, however, to do that we have to be able to express these flows against a matrix(e.g., against human activity or areas) in a way that makes it possible to obtain a closure of thenonequivalent representations of the various identities of compartments across levels After havingdone this, we can define whether the values taken by a set of variables used to characterize theperformance of a farmer (e.g., level of income, leisure time, life span) or the performance of aparticular farming activity (e.g., economic labor productivity, return on the investment, demand

of land, associated level of pollution per unit of land) are above or below averages characterizingthe equivalence class to which the farmer belongs, and how these values refer to the expectedvalues associated with larger-level holons determining the stability of the context

nonequivalent descriptive domains, and therefore to boost the coherence and reliability of

an integrated package of indicators The forced relation between parts and the whole (e.g.,using the relation between total EMR of the whole body and the various EMRj of its parts)can be applied to different typologies of flows in parallel (e.g., food produced and requiredper unit of land, exosomatic energy produced and consumed per unit of land, added valuegenerated and consumed per unit of land) and against different matrices (e.g., human activityand area) This makes it possible to also establish a mosaic effect among nonequivalentreadings (definition of different formal identities for the dissipative systems) in relation tothe feasibility of the various holons making up the investigated metabolic system Households,counties, states, macroeconomic reasons, in fact, all do produce and consume (and mustproduce and consume) flows of money, food, energy Whenever we map these flows acrosslevels against the same matrix (the same hierarchical frame of unit of lands, or the sameprofile of allocation of human time), we can establish links among analyses related to differentdisciplinary fields (e.g., producing the same flow of $10,000/year/ha either by agriculture

or by agro-tourism implies different requirements of labor, capital, water, and differentenvironmental impacts) The mosaic effect can also be used to fill knowledge gaps referring

to inaccessible information of residuals Put another way, important facts ignored or heavilyunderestimated by an economic accounting of farming (e.g., ecological services lost withsoil erosion) can be extremely clear when performing a parallel analysis based on a biophysicalaccounting (e.g., the huge material flow associated with soil erosion) The soil loss, negligible

in an economic accounting of profit and revenues per year at the farm level, can become animportant factor when adopting a biophysical accounting of matter flows associated withcrop production at the watershed level and over a time horizon of 50 years

6.2.3 Extending the Multi-Scale Integrated Analysis to Land Use Patterns

Linkages among characteristics of typologies belonging to different but contiguous hierarchical levels canalso be established by using a spatial matrix, which can provide closure across levels To explore thisoption, let us adopt the same approach used in Figure 6.1, but this time mapping densities of flowsassociated with typologies of land use An example of this analysis is given in the upper part of Figure 6.2.Imagine a county of a developed country inhabited by 100,000 people and total available land (TAL) of

1 million ha Assuming a consumption of exosomatic energy per capita (consumption of commercialenergy) of 200 GJ/year/person (EMRAS=2.3 MJ/h), we can calculate a total exosomatic throughput(TET) for that county of 20 PJ (petajoule) of exosomatic energy per year (PJ=1015 J) The possibility ofestablishing a relation between the values taken by these variables (the characterization of a social system

viewed at the focal level n) and the values of variables associated with the characteristics of lower-level elements defined at the level n-1 (societal compartments) is discussed in detail in Section 6.3.

In the example of Figure 6.2, the same rationale adopted in Figure 6.1 is applied The difference inthis case is that the common matrix across levels (extensive variable 1) consists of assessments of landarea In practical terms, we have to divide a given amount of TAL (the size of the whole system mapped

in terms of units of area), which is the equivalent of the total body mass indicated in Figure 6.1, into aset of typologies of land use (the lower-level compartments to which we assign the characteristics of atypology—the equivalent of organs) In the example of Figure 6.2, the selected set of five typologies is(1) natural land not managed by humans (NAL), (2) residential and infrastructures (R&I), (3) agriculturalland (AGL), (4) land used for economic activities belonging to the sector of manufacturing, energy andmining (MLPS) and (5) land used for economic activities belonging to the sector of services andgovernment (MLSG) As noted earlier, we have to obtain closure with this division That is, TAL (1million ha) has to be divided according to a given profile of investment of TAL over the five typologies

of land use, which provides an arrow of percentages that totals 100 In the example of Figure 6.2, such

a profile is (1) NAL, 50%; (2) AGL, 40%; (3) R&I, 6%; (4) MLPS, 2%; and (5) MLSG, 2%

The breaking down of the whole (TAL) into components, which is done in hectares (or other units

of area), provides an internal mapping of the size of the system (TAL defined at the level n), which is

also used for assessing the size of lower-level components (NAL+AGL+R&I+MLPS+MLSG) That is,

FIGURE 6.2 Constraints on relative values taken by variables within hierarchically organized systems.

the size of component is expressed as a part of the whole This would be the equivalent of the extensivevariable 1 discussed before for the metabolism of the human body.

We now need a nonequivalent assessment of the size of the whole system (the county) in terms of thedegree of interaction with the context We have to define a second extensive variable (variable 2), whichmakes it possible to adopt the same approach discussed above The choice adopted in the exampleprovided in the upper part of Figure 6.2 is to use an assessment of exosomatic energy consumption,which is required to guarantee the typical level of metabolism of the county This is the amount of fossilenergy that the county is getting from society in relation to its socioeconomic interaction As notedearlier, such a value is 20 PJ/year for the whole county This choice reflects an attempt to keep the analogywith the example provided in Figure 6.1—this is the equivalent of the extensive variable 2, and with thischoice, we also manage to respect the same selection of unit (energy over time) However, as will bediscussed later, this approach also works when selecting an economic variable—e.g., assessment of a flow

of added value or another biophysical variable, such as water—as extensive variable 2

Starting from the two values of extensive variables 1 and 2 used to characterize the metabolism ofthe whole county, we can calculate the intensive variable 3—the exosomatic metabolic density (averagefor the county), which is the amount of exosomatic energy consumed per unit of area, referring to thetotal area occupied by the county In this example, EMDAC is obtained by dividing TET (20 PJ) by TAL(1 million ha) The result is EMDAC 20 GJ/ha/year

At this point, we can apply the approach previously illustrated in the multi-scale analysis of the metabolism

of the human body The table in the upper part of Figure 6.2 can be used to get some free ride out of theredundancy existing within this organized information space Again, this redundancy is generated by ourprevious knowledge of identities of lower-level typologies, which can be found in our descriptive domainacross hierarchical levels For example, after having structured the information space in this way, we cantry to fill the values of the column of EMDi by using the column of assessments of the amounts of energyconsumed by the various sectors used to represent the economic structure of the county This economic

sector would be the equivalent of organs (elements defined at the level n-1) The values taken by extensive

variable 2, referring to the identities of the lower elements (reflecting the characteristics of the economicsector of the county), are given in the ETi column The values found in the EMDi column are referring

to the typologies of lower-level sectors That is, the EMD of residential and infrastructure can be calculated

by dividing the value of the relative ETR&I (6 PJ of exosomatic energy per year, which is spent in theresidential sector) by the area of 60,000 hectares, which is used by this compartment In this way, weobtain a value of EMDR&I, which is equal to 100 GJ/ha/year

On the other hand, we could have found the same value by using a different source of information—

a nonequivalent external referent for this assessment, which is related to a nonequivalent perception

and representation of events referring to the level n-2 In fact, we can use additional nonequivalent information to define the characteristics of household types at the level n-2 These characteristics will determine the characteristics of the household sector (HH) (at the level n-1) For example, we can start

with the average value of consumption per household in the county, related to a given typology ofhousing (e.g., by looking at the literature, we can find a value of 180 GJ/year/household for the typicalhouses found in that county) Knowing the average size of the households of that county—e.g., threepeople—we can estimate an average consumption of 60 GJ/year/person associated with direct energyconsumption in the household sector After using information on the housing typology (e.g., 300 m2 ofhouse per person and a ratio of 9/1 between the built area of houses and the additional land included

in the residential compound), we can assume—for the specific county characterized by such a residentialtypology—an amount of 3000 m2 of residential area per person To this area we have to add an additionalarea (e.g., 3000 m2 per person) for infrastructure (roads, parking lots, recreational areas, etc.) Putanother way, in this manner we can assess the total request of land per person for the residential orhousehold sector of that particular county

Using this information in our example of a hypothetical county of the U.S for which lower-levelhousehold typologies are known, we can characterize such a system as composed of 33,000 households(100,000 people divided by 3), generating an aggregate consumption in the residential sector of 6 PJ(180 GJ of exosomatic energy per household spent in the residential compartment), in relation to a

requirement of land of 18,000 m2 per household (that has to be included in the residential category).Using this set of data (different from what was used before), we can calculate a value of EMDR&I=100GJ/ha/year in a nonequivalent way.

In this example we have two nonequivalent ways for calculating EMDR&I:

1 Using information referring to the level n/(n-1) EMDR&I is the ratio between the total size

of the residential sector in terms of exosomatic energy consumption (6 PJ, e.g., as resultingfrom aggregate record of consumption of that sector in the county) and in terms of land(60,000 ha, e.g., as resulting from remote sensing analysis of land use in the county)

2 Using information referring to the level (n-1)/(n-2) EMDR&I is calculated from our previous

knowledge of the consumption level for a given typology of household, house spacerequirement per person, house size, ratio between the area of the house and the open spaceincluded in the housing compound, ratio between the area occupied by private housing andthe area required by common infrastructures

In a holarchic system made up of nested types, the characteristics of the types making up holons acrosslevels must be compatible with each other This redundancy is at the root of the existence of freeinformation when dealing with representation across levels of holarchic systems

This hierarchical structure is very robust; in fact, if more typologies of housing were known in that

area—at the level n-2—that is, for example, (1) individual family houses (180 GJ/year/household and

3000 m2/person of area of the residential compound) and (2) condominium apartments (100 GJ/year/household and 500 m2/person of area of the residential compound), the average value (variable 3) forEMDR&I at the level n-1 would have been different Still, such a characteristic value for the residential

sector (at the level n-1) can still be expressed in relation to the characteristics of the lower-level typologies (at the level n-2) This can be done by considering the profile of distribution of investments

of space and energy (using variable 1) within the household sector over the set of possible household

types characterized at the level n-2 (using information gathered at the level n-2) in terms of the

intensive variable 3 This mechanism is at the basis of impredicative loop analysis

Obviously, the example of a redundant definition of a given value is also valid for other typologies of

land use In the same way, starting from characteristics of typologies belonging to the level n-2 (e.g.,

typologies of industrial plants), it is possible to guesstimate the value of EMDMLSG and EMDMLPS,

characteristics referring to the level n-1 To calculate such a value, it is necessary to study the consumption

of different typologies of industrial building and other categories of land use associated with these typologies.The important aspect of this analysis is related to the ability to disaggregate the total area under thevarious land use categories, in a way that makes it possible to use equations of congruence later on.This is crucial for another reason Known typologies (a given typology of housing or a given typology

of power plants) make it possible not only to associate a defined density of flows (e.g., the amount ofadded value per hectare, the amount of food produced per hectare or the amount of exosomatic energyconsumed per hectare) per unit of land use in that category, but also to set up a package of differentindicators of performance That is, we can add to the possibility of performing a multi-scale analysis (bysimultaneously considering information gathered at different hierarchical levels) the possibility of performingmultidimensional analysis (by simultaneously considering the constraints affecting the flows of variables—food, exosomatic energy, added value—referring to different dimensions of sustainability) For example,

in the lower part of Figure 6.2 we have an example of a possible characterization of a farm in relation to

a given profile of four different typologies of land use: (1) natural area, (2) agriculture for subsistence, (3)agriculture for cash crops and (4) housing and infrastructures This would be the characterization of thewhole and the parts in relation to extensive variable 1

Imagine now that we are associating the relative mapping of relevant flows with each one of thesefour typologies defined, using the extensive variable land: (1) a flow of endosomatic energy—foodproduced by subsistence agriculture and (2) a flow of added value—associated with the production ofcash crops That is, we are using in parallel against the same definition of size (extensive variable 1) twoversions of extensive variable 2: an extensive 2 biophysical, which is referring to a biophysical mapping

of the interaction with the context in terms of exchange of flows (the flow of food produced, consumedand sold by the farm), and an extensive 2 economic, which is referring to an economic mapping of theinteraction with the context in terms of exchange of flows (the flow of added value produced, consumedand spent by the farm).

In this example, we already can extract a set of nonequivalent indicators of performance from thisvery simple database: (1) the amount of food available for self-consumption (a relevant indicator inthose areas in which the market is not reliable), (2) the amount of food supplied by the farm to the rest

of society (relevant for determining self-sufficency at the national level) and (3) the amount of addedvalue available to the farmers as net disposable cash (a relevant indicator to determine the potentiallevel of interaction of the household with the rest of society in terms of economic transactions).Because of the particular structure of this information space, we can establish a link between potentialchanges in the value taken by these indicators That is, relative constraints can be studied by usingbiophysical, agronomic, ecological and socioeconomic variables and models This example is important

to show how the same data set can be used to provide different results according to the adoption ofdifferent disciplinary perceptions and representations of changes

For example, talking of the amount of food available for self-consumption, we have a total of 90,000

kg of grain produced on this farm (50,000 kg of grain for subsistence and 40,000 kg of grain for cash);only 50,000 kg should be counted as an internal supply of food (as a relevant flow for food security forthe farmers) The reverse is true when we want to assess the amount of food supply that this farm isproviding for the socioeconomic system to which it belongs That is, the context of this farm isreceiving only 40,000 kg of grain of the investment of 100 ha of TAL Even more complicated is theaccounting of economic variables If we want to assess the income of the farm, we should add the value

of the self-consumed grain (the $25,000 indicated in bold) to the value of the net return of cash crop($15,000) On the other hand, if we want to assess the level of net disposable cash, we have to ignorethe $25,000 related to the value of the self-consumed crops And there still has to be an analysis aimed

at assessing the effect of the characteristics of this farming system on the gross national product (GNP)

of the country

The typology natural area (area not managed by humans) is completely irrelevant when dealingwith short-term perceptions and representations of economic performance and food security Thistypology of area is perceived as not producing anything useful (money or food) This is probably anexplanation for the fast disappearance of this typology of land use on this planet However, as soon as

we introduce a new set of relevant criteria and the consequent set of relevant indicators of performance(preservation of biodiversity, support for natural biogeochemical cycles, preservation of soil, quality ofthe water, etc.), it becomes immediately clear that those typologies of land use that are crucial fordetermining a high economic performance are at the same time the very same categories that can beassociated with the worse performance in ecological terms (see Chapter 10) It is exactly the ability tohandle the heterogeneity of information related to different scales and nonreducible criteria ofperformance 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 tohandle the information related to indicators that are in a way independent from each other, since theyare calculated using disciplinary representations of the reality, which are nonequivalent (e.g., the study

of the stability of the loop of food energy spent to generate the labor required for subsistence isindependent from the analysis of the economic loop associated with cost and return related to thecultivation of cash crops) However, within this integrated system of accounting across levels, these tworepresentations are indirectly connected In fact, autocatalytic loops of endosomatic energy (investment

of labor to feed the workers), added value (investment of money to pay back the investments), andexosomatic energy (investment of fossil energy to generate the useful energy required for the making

of exosomatic devices) all compete for the same budget of limiting resources: human activity and totalavailable land It is this parallel competition that determines a set of mutual constraint that each one ofthese autocatalytic loops implies on the others As noted earlier, the nature of this reciprocal constraintcan be explored by considering lower-level characteristics (e.g., technical coefficients) and higher-level characteristics (e.g., economic, social and ecological boundary conditions)

6.3 Using Mosaic Effects in the Integrated Analysis of Socioeconomic

Processes

6.3.1 Introduction: The Integrated Analysis of Socioeconomic Processes

In economic terms we can describe the socioeconomic process as one in which humans alter theenvironment in which they live with their activity (through labor, capital and technology) toincrease the efficacy of the process of production and consumption of goods and services In otherwords, they attempt to stabilize and improve the structures and functions of their society according

to a set of internally generated values and goals (what they perceive and how they representimprovements in the existing situation) In biophysical terms, the process of self-organization ofhuman society can be seen as the ability to stabilize a network of matter and energy flows (definedover a given space-time domain) representing what is produced and what is consumed in theeconomic process

To be sustainable, such a process has to be (1) compatible with the aspirations of the humansbelonging to the society, (2) compatible with the stability of both natural and human-managed ecosystems,(3) compatible with the stability of social and political institutions and processes, (4) technically feasibleand (5) economically viable The order of these five points does not reflect priorities or relativeimportance, since each one of these conditions is crucial

This is to say that when we perform a biophysical analysis of human societies (e.g., using variablessuch as kilograms of iron or joules of fossil energy), we can see only certain qualities of humansocieties (e.g., we cannot get any indication about the economic value of commodities), and therefore

we can check only a few of the five conditions listed above The same predicament applies toeconomic, engineering and political analyses To be able to see and describe a certain set of systemqualities considered relevant in certain disciplines, analysts will have to use a finite set of encodingvariables and descriptive domains (they have to assign to the system a formal identity that is usefulfor applying the relative disciplinary knowledge) However, this choice can imply losing track ofother system qualities considered relevant by other disciplines That is, not everything that iseconomically viable is, as a consequence, also ecologically compatible Not every solution thatoptimizes efficiency is, as consequence, also advisable for keeping social stress low or improvingadaptability, and so on

be used as a good metaphor on how to use scientific analyses in an integrated way when dealing withsustainability For the same concept, Neurath (1973) proposed the expression “orchestration of sciences.”Getting back to the example of Figure 6.3, which is limited only to the challenge of generating ameaningful representation of shared perception at a given point in space and time, if you want to seebroken bones you have to use x-rays, but you cannot see in this way soft tissue (for that you need anultrasound scan) In the same way, if you want to know whether a woman is in the first weeks ofpregnancy, you can use a chemical test based on her blood or urine Endoscopy can be the easiest way

in which to look at a local situation, whereas nuclear magnetic resonance (NMR) can also deal withthe big picture In these examples, x-rays, ultrasound scans, NMR, chemical tests and endoscopy arenonequivalent tools of investigation No matter how powerful or useful any one of them is, whendealing with the behavior of complex systems (i.e., health of humans), we cannot expect that one tool(based on the adoption of a formal identity in the representation of the investigated system) can do allthe relevant monitoring To be able to characterize several relevant nonequivalent aspects of patientbehavior, and also for economic criteria (to avoid shooting flies with machine guns), it is wise, depending

on the circumstances, to develop and use several nonequivalent analytical tools in different combinations.Sustainability analyses seem to be a classic case in which it is wise to be willing to work with anintegrated set of tools This is the only way to expand the ability of scientists as much as possible tocover the relevant perceptions about sustainability that should be considered, without putting all theireggs in the same basket

The integrated use of nonequivalent medical analyses to deal with human health (Figure 6.3) can

6.3.2 Redundancy to Bridge Nonequivalent Descriptive Domains: Multi-Scale

Integrated Analysis

Redundancy in scientific analysis is often seen as a villain The axiom used to justify the holy war ofscience against redundancy is the famous Occam’s razor principle: One should not increase, beyondwhat is necessary, the number of entities required to explain anything The principle is also called theprinciple of parsimony Such a principle requires that scientific analyses follow the goal of obtaining amaximum in the compression of the information space used in their models That is, sound sciencemust use as few variables and equations as possible It is worthwhile to observe here that one of themeasures of complexity for mathematical objects (computational complexity) is related exactly to theimpossibility of compressing the demand of information for their representation (Chaitin, 1987) That

is, if you are dealing with a complex object, you cannot expect to compress much in the step ofrepresentation (amplify your predictive power) just by developing more sophisticated inferential systems(more complicated models) Without getting into a sophisticated discussion related to this topic, wewant to again use a metaphor, that of geographic maps, to question the idea that redundancy should beeliminated as much as possible in scientific analyses

Using a metaphor based on geographic maps is appropriate since, after all, numerical values taken

by variables in an integrated analysis are generated by the application of a selected modeling relation tothe representation of a natural system (Rosen, 1985) These assessments are nothing but mappings ofselected qualities of the investigated natural system into a given mechanism of representation, whichreflects the characteristics of the selected model

The examples given in Figures 6.4 and 6.5 are related to the discussion in Chapter 3 on nonequivalentdescriptive domains The four different views provided in Figure 6.4 (Catalonia within Europe, a specificcounty in Catalonia, an area of a national park in the county, and roads within the natural park) reflect theexistence of different hierarchical levels at which a geographic mapping can be provided When thedifferences in scale are too large, it is almost impossible to relate the nonequivalent information presented

FIGURE 6.3 Nonequivalent complementing views used in medicine (Photos courtesy of E.B.T.Azzini.)

in distinct descriptive domains (e.g., in Figure 6.4 the upper and lower maps on the left) To linknonequivalent views across different scales, you need a certain level of redundancy among the maps.That is, to be able to appreciate the existing relation between two nonequivalent representations, youmust be able to recognize the element (pattern) described within one of the specific descriptivedomains in the next one For example, Catalonia within Europe—in the first map—becomes thewhole object within which Pallars Sobira’ County is located in the next map This happens, in Figure6.4, in all the couplets of maps linked by an arrow.

At this point, if we are able to establish a continuum between the various links across the nonequivalentmaps, then it is possible for us to structure the information provided by the set of maps (referring todifferent hierarchical levels) Distant maps are nonreducible to each other (upper and lower maps on theleft); contiguous maps can be bridged The bridging of nonequivalent information across different mapscan be easy, depending on the degree of overlapping of the information contained in them The higherthe level of overlapping, the lower the compression, but the easier it becomes to establish a relationbetween the information contained in the two maps On the other hand, very little degree of overlapping(e.g., the two maps on the higher level) implies a more difficult bridging of the meaning conveyed by themaps By establishing a continuous chain of bridges of meaning across maps, we can relate the informationabout the layout of the natural park (which is required by someone wanting to drive there) to theinformation about where such a park is located Depending on the characteristics of possible users, wehave to provide such information in relation to different definitions of such a context We can say that thepark is at the same time in Europe, in Spain, in Catalonia and in a given corner of Pallars Sobira’ County

It should be noted that, in this case, using some redundancy in this integrated system of representations(the partial overlapping of the information in contiguous maps) is the only way to handle such a task Ahuge map that would keep the same level of accuracy adopted for the representation of the area withinthe natural park, applied to the description of all of Europe, cannot be made or operated for theoreticaland practical issues (without a hierarchical structuring of the information space, it would not be possible

to handle the required amount of bits of information) A map as large as Europe in a scale of 1:1 wouldsimply result in excessive demand of computational capability in both the step of making the representative

FIGURE 6.4 Nonequivalent descriptive domains due to difference in scale of the map (Giampietro M and Mayumi K (2000a), Multiple-scale integrated assessment of societal metabolism: Introducing the approach—

Popul Environ 22(2): 109–153.)