A general theory of genericmodelling and paradigm shifts:

part 2 – cybernetic ordersMaurice Yolles

Business School, Liverpool John Moores University, Liverpool, UK, andGerhard Fink

IACCM, Vienna University of Economics and Business,Vienna, Austria

AbstractPurpose – Anticipating behaviour and responding to the needs of complexity and problematic issuesrequires modelling to facilitate analysis and diagnosis. Using arguments of anticipation as an imperativefor inquiry, the purpose of this paper is to introduce generic modelling for living systems theory,and assign the number of generic constructs to orders of simplex modelling. An nth simplex order rests inan nth order simplex cybernetic space. A general modelling theory of higher orders of simplexity is given,where each higher order responds to every generic construct involved, the properties of whichdetermining the rules of the complex system being that is represented. Higher orders of simplexity alsoexplain greater degrees of complexity relatively simply, and give rise to the development of newparadigms that are better able to explain perceived complex phenomena.Design/methodology/approach – This is part 2 of three linked papers. Using principles that arisefrom Schwarz’s living systems set within a framework provided by cultural agency theory, and witha rationale provided by Rosen’s and Dubois’ concepts of anticipation, the papers develop a generalmodelling theory of simplex orders. They show that with the development of new higher orders,paradigm shifts can occur that become responsible for new ways of seeing and resolving stubbornproblematic issues. Part 1 established the fundamentals for a theory of modelling associated withcybernetic orders. Using this, in this part 2 the authors establish the principles of cybernetic ordersusing simplex modelling. This will include a general theory of generic modelling. In part 3 the authorsshall extend this, developing a fourth-order simplex model, and exploring the potential for higherorders using recursive techniques through cultural agency theory.Findings – Cultural agency theory can be used to generate higher simplex through principles ofrecursion, and hence to create a potential for the generation of families of new paradigms. The ideaof conceptual emergence is also tied to the rise of new paradigms.Research limitations/implications – The use of higher order simplex models to represent complexsituations provides the ability to condense explanation concerning the development of particularsystem behaviours, and hence simplify the way in which the authors analyse, diagnose and anticipatebehaviour in complex situations. Illustration is also given showing how the theory can explain theemergence of new paradigms.Practical implications – Cultural agency can be used to structure problem issues that mayotherwise be problematic, within both a top-down and bottom up approach. It may also be used toassist in establishing behavioural anticipation given an appropriate modelling approach. It may also beused to improve and compress explanation of complex situations.Originality/value – A new theory of simplex orders arises from the new concept of generic modelling,illustrating cybernetic order. This permits the possibility of improved analysis and diagnosis ofproblematic situations belonging to complex situations through the use of higher order simplex models,and facilitates improvement in behavioural anticipation.Keywords Behaviour, Cybernetics, Adaptation, Emergence, Complexity, Systems theoryPaper type Research paper

KybernetesVol. 44 No. 2, 2015

pp. 299-310©Emerald Group Publishing Limited

0368-492XDOI 10.1108/K-12-2014-0302

The current issue and full text archive of this journal is available on Emerald Insight at:www.emeraldinsight.com/0368-492X.htm

The authors thank Tony Judge for his constructive comments on an early version of this paper.

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IntroductionIn part 1 of this paper we set up the fundamental principles and philosophy to enable us todevelop a general theory of cybernetic orders. This was based on simplex order modelling,each simplex order belonging to a cybernetic order space. This space has rules/propertiesthat the simplex model adopts. The simplex model was defined as a generic substructurethat arise from principles that are supported by various paradigms. The philosophicalposition of first-, second- and third-order cybernetic spaces was discussed.

In this part of the paper we shall present the first three orders of simplex models,and then develop a general theory of simplex orders. This general model will bediscussed in terms of both recursion and incursion, as indicated in part 1 of the paper.

First-order simplex modellingFirst-order cybernetic feedback is typically seen to be associated with Newtonianmechanical objectivity (Glanville, 2002). It is therefore positivist, centring on systemicobjects being observed by some external objective observer.

It rests on a relationship between a set of interactive systemic objects which may beidentified as operative systems populated by individuals who are principally responsiblefor the interactions that occur. These interactions are the result of actions (a set ofbehavioural or communications processes) and feedback, and they are not just random,but are assumed to have purpose, teleology, control and feedback. Feedback is related torecursive processes where the present state of a system is a function of its precedingstates so that the future is always a result of the past. This leads to a system outcome thathas an implied causality. Feedback implies that active feed-forward has occurred.

While a system can have internal pathologies, many of its problems can be expressedthrough generic pathologies. These can occur in a feedback system (shown symbolicallyin Figure 1) by the bars that cut across system interaction and feedback loops. Thesebars on the interactive loops indicate that the processes of interaction/feedback may notbe efficacious, or that the nature of the interactions may be inconsistent with interactiveor control needs (if there are any) of the systemic objects involved in the interaction.It may also indicate poor communications, or inappropriate/inadequate action in theinteractive processes.

While Rosen (1985) was interested in feedback in general terms (Louie, 2010),a concrete example of such a modelling approach is System Dynamics (Forrester, 1971)which is related to Checkland’s (1981) Rich Pictures, and explores the interconnected

Operativesystem 2

Operativesystem 1

Systemaction

Systemfeedback

Operativesystem 3

Systemaction

Systemfeedback

Figure 1.Illustration of firstsimplex ordermodel with invariantgeneric construct offeedback, showingaction and feedback(i.e. interaction)between threeviable operativesystems, withgeneric pathologies

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network of objects (indicated as human activity operative systems). They havefeedback and mutual influences offering vectored linkages with estimable intensities.Here then, in first-order simplex modelling, there is one invariant generic construct:feedback. This facilitates self-organisation in the operative system. All other aspects ofthe modelling process are a consequence of particular propositions in a positivist world.

Second-order simplex modellingSecond-order cybernetics embraces radical constructivism, allowing for instrumentallearning and agnosticism towards objective reality.

Relevant to simplex cybernetic orders, Beer (1959) adopted the term metasystemthat observes its operative systems and is “a controller of internal relations between thevariable subsystems and the relation of the whole environment” (cited in Espejo andSchwaninger, 1993, p. 44), and “as higher levels of management which define purposefor a system” (Flood and Jackson, 1991, p. 231). Overall, therefore, the metasystemfunctions to provide systemic self-regulation. Beer (1971) in his discussion of theconnection between the system and metasystem notes that society is a learningmachine, being controlled through adaptive processes. Feedback processes between thesystem and metasystem now have the capacity to amplify what is seen as sound, orcorrect misunderstandings and misfiring processes.

Here we shall formulate a second-order cybernetic generic model. It offers a principlethat relates to Argyris (1976, 1982) concerning instrumental (single-loop) learning. Thislimits personal complexity by restricting self-reference. Glanville’s adherence tosecond-order cybernetics as radical constructivism is quite consistent with a simplexorder modelling space that requires instrumental learning, where socially filteredself-created knowledge may occur informally.

A second-order simplex model substructure can be created in our second-ordercybernetic space as shown in Figure 2. It offers models of the simplest “living system”withinstrumental learning through Maturana and Varela’s (1979) autopoiesis. Autopoiesis isa network of processes through which strong anticipation is facilitated. It enables a systemto define its own boundaries relative to its environment, develop its own code of operations,implement its own programmes, reproduce its own elements in a closed circuit, liveaccording to its own dominant paradigms and have operations that cannot be controlledfrom outside its boundaries (Mingers, 1995). These attributes originate from instrumentaland cognitive learning. Instrumental learning, when it occurs without a cultural anchor, ismore susceptible to the instabilities of behavioural complexity. Cognitive learning providesa durable knowledge anchor able to underpin viability. However, in support of viabilityin a second cybernetics model, cognitive learning should at least be informally implied.

Metasystem

Executivesystems and

control

Operative system

Operationsmanagement and

processes

Autopoiesis

Autopoiesisfeedback

Figure 2.Symbolic illustration

of a second-ordersimplexity (viable

system) modelillustrating an

autopoietic couplingbetween a system

and metasystem, withgeneric (autopoietic)

pathologies

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This is explained by Schwarz (1994), since for him cognitive learning acts to facilitateautopoiesis which is essential to the viability of a system since it enables itto “digest” any unexpected fluctuation. The system does this through entropic drift toregenerate the system’s structure, and autopoiesis by (instrumentally) modifyingstructures and fluxes (form and behaviour), and by changing the causal networks thatderive from their paradigms and methods for achieving goals.

The two variant generic constructs are the operative system (populated by first cyberneticactive actors as shown in Figure 1), and a metasystem populated by observers of the systemwho are ultimately responsible for higher level control. It also has its invariant genericconstructs defined as autopoiesis and feedback. We shall refer to the system-metasystemassembly with its autopoietic connection as an autopoietic coupling, and associated with itare properties of viability (through adaptability and capacity for durability). The operativesystem may contain a plurality of systems in interaction representing a first-ordercybernetics situation. The metasystem contains observer schemas that might includestrategic formulations that develop through cognitive processes. The symbolic content(like knowledge or information) contained therein is manifested autopoietically to theoperative system, which is thereby guided subject to processes of misconception andinterference. Feedback provides imperatives for change or amplification for the observingmetasystem. The relationship between the operative system and its metasystem is suchthat cognitive and behavioural attributes are linked through a process of logical organising,and they are logically closed. This relationship facilitates (Beer, 1979, p. 260) or has apotential (Geyer and van der Zouwen, 1991, p. 5) for self-reference. This indicates theinformal influence of self-reference on second-order cybernetic models.

This may be set within the formal representations of Argyris (1976), where instrumental(single-loop) learning constitutes a means of operatively satisfying aims or goals throughaccepted routines. In contrast cognitive (double-loop) learning requires new routines to becreated that are based on adjusted conceptions of the universe. It is a recognition thatinstrumental learning relates to feed-forward/feedback action relationships which can bereinforced or corrected, and which do not require self-reference.

Recalling Beer’s (1959) proposition about recursion in autonomous systems, there isa consequence that the generic modelling process can be used recursively in theoperative system, applying it to each of its autonomous operative subsystems, withtheir implied local metasystem (Beer, 1979). This explains that the metasystem andoperative system constitute variant generic constructs that can change their naturesand meanings with every recursive application. All other aspects of the modellingprocess are particular superstructural formulations by a modeller that can provideepistemic systemic content.

Generic pathologies can occur in a second-order simplex model as shown by the barcutting the two invariant generic constructs of autopoiesis and feedback. In discussingautopoiesis, Beer (1979, pp. 408-412) suggests that pathologies might occur when themetasystem of the agency attempts to control, not just to satisfy agency purposes, butrather for the sake of control itself. Organisations having conditions like this are said byBeer to have pathological autopoiesis. This type of pathology may be reflected in Figure 2,the bar meaning that autopoiesis may not be efficacious through some network break orphysical/cognitive impairment, damaging the agency’s potential for viability and autonomy.

Third-order simplex modellingThird-order simplex cybernetic spaces should be seen to represent the observed andobserving systems together form another system, from which a new relativistic

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interactive worldview arises from self-observing viewers that have self-observedworldviews. In reference to Figure 2, the observing metasystem should therefore beformally influenced by developmental worldviews, allowing the notion, as per Argyris(1976), of double-loop learning to be applied to the generic model. We would argue thatgeneric double-loop learning is fundamentally constructivist.

There is another descriptor of third and potentially higher order cybernetics thatoriginates with Dubois which returns us to anticipation. Following Boxer and Cohen(2000), third-order cybernetics is characterised by the way it resolves undecidabilities,these being constituted in the logic of the present moment by the anticipations of thesystem. This calls on Dubois’s (1998) concepts (Boxer and Cohen say) of hyperincursion,where degrees of undecidability can be represented and resolved through higher ordersof anticipative cybernetic systems.

We shall propose a third-order simplex model which sits in a third-order (simplex)cybernetic space. Establishing a third-order simplex model narrows the need to explorethe interaction between model-based processes and the human activity systems theyrepresent. A generic explanation is that third-order simplexity involves collectivefeedback, autopoiesis and autogenesis as generic invariant constructs. It embraces anextension of Schwarz’s (2001) theory, taking autopoiesis as a first-level invariantgeneric construct, supported by a higher level network of processes called autogenesis.It is a network of processes throughwhich weak anticipation is facilitated as it influencesthe autopoietic coupling in the agency model shown in Figure 3 that links the figurativeand operative systems. It is responsible for manifesting identification information to thestrategic figurative system and to the operative system such that it can be understood.In addition elaborating information is manifested through autopoiesis to the operativesystem. The figurative and operative systems together form an autopoietic coupling thatgenerates feedback for the referent cognitive system. Feedback as a “collective” conceptconstitutes the third invariant generic construct.

The variant generic constructs have a capacity for context sensitivity that enablesthird-cybernetic models to be recursive under Beer’s (1959) proposition of viability. Therelationships between these generic constructs is that they provide for operative systemself-regulation, figurative system self-regulation and cognitive system self-reference thatanchors the living system through its identification information, however this arises.Beyond the generic constructs, all other modelling aspects are particular superstructuresthat necessarily occur within the generic substructure limiting arbitrariness. Figure 3 isan illustration of a third-cybernetic model, with two invariant generic constructs (autopoiesisand autogenesis) each with its indicative feedback.

Cognitivesystem

Self-referenceDefining/

identificationinformation

Operativesystem

Self-organisationOperative/execution

information

Autopoiesis

Autopoiesisfeedback

Figurativesystem

Self-regulationStrategic/

elaboratinginformation

Autogenesisfeedback

Autogenesis

Autopoieticcoupling

Figure 3.Third-order simplex

agency (viablesystem) model with

two invariant genericconstructs, and alsoillustrating generic

pathologies

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In Figure 3 there is an autopoietic coupling (connecting the figurative and operativesystems) and an autogenetic coupling (connecting the cognitive system and theautopoietic couple). The latter constitutes self-production of the rules of production forthe autopoietic couple through its connection to the cognitive system. Autogenesis isthus a second-order form of autopoiesis which defines the state of full autonomy for theautopoietic coupling, and like autopoiesis it is logically closed. Autogenesis worksthrough a channel operating as a network of second-order processes. This manifestsdefining information into the autopoietic coupling which sediments information thatfacilitates strategic structures like goals, ideologies and ethics in the figurative system.A well-known example of a non-generic metamodel that facilitates particular third (andas we shall see from part 2 of this paper, likely fourth) order cybernetic modelling isBeer’s (1979) VSM (Yolles and Fink, 2011).

Figure 3 shows the cognitive, figurative and operative systems: these are variantgeneric constructs, each with epistemic natures that can change with modellingcontext. The generic pathologies indicated by the autopoiesis/autogenesis bars refer toinefficacious, inadequate, inappropriate or damaged networks of first/second-orderprocesses that impact on the capacity of the agency to manifest cognitive informationstrategically or operatively.

A general theory of orders of simplex modellingUntil now there appear to be few who recognise the nature of third and higher ordercybernetics and their distinction from second-order cybernetics. Judge has proposeda challenge: to find relationships between different orders of cybernetics thus creating atheory of cybernetic order emergence. We propose such a relationship (Figure 4) thatrecursively generates higher orders of simplex model. Interest here lies in explaininghow simplex orders and their local structures can influences anticipatory behavioursin an action system. However, prior to doing this it will be of interest to explainwhy Figure 4 is a good model.

The recursive simplex generator is a good modelEarlier it was said that to better understand complex social situations a good model isrequired. This also applies to generic models. We would argue that Figure 4 is a goodgeneric model, and as such each individual order that it is able to generate will also bea good model since they all carry the same principles. Recall that a good model shouldbe satisfactory, and involve completeness, independence, minimalness and validity.In part 1 of this paper we discussed two forms of validity, pragmatic and technical, and

R(n+1) referentsystem

Embeddedrecursionsautopiesiscouplings

R(n–1), R(n–2),..

Autopoiesis (n)

Autopoiesis (n)feedback

R(n) referentsystem

Autopoiesis (n+1)feedback

Autopoiesis (n+1)(= Autogenesis (n))

Autopoieticcoupling A(n)

Figure 4.Recursive simplexgenerator for an nthorder simplexmodel through thegeneration of (n+1)higher order genericconstructs in animplied autopoietichierarchy

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both shall be referred to here. Figure 4 offers a satisfactory way of viewing a situationsince it adopts higher level concepts that constitute requisite variety in responding tothe variety that occurs in complex situations. Requisite variety is determined throughan appreciation of which simplex order should be adopted, which comes from a studiedreflection of the situation being examined. Higher order simplex modelling of lowerorder cybernetic problem situations does not provide satisfaction in the modellingprocess due to redundant modelling requirements. Complexity can be introduced intothe generic model by creating superstructural details in “particular” models in each ofthe connected systems, and by the use of recursive techniques that respond todetermined testable propositions. An illustration of this will be offered in due course.Figure 4 is complete since it is broad enough to encompass all possible modellingoption for higher cybernetic orders, and reduce surprises providing that higher orderconstructs can be envisaged. It is independent since it decomposes sets of inquiries intonon-interacting qualities (for analysis) thereby reducing metal effort. It is minimal inthat it is able to integrate, through compression, states of situations that are unnecessarilydiscriminated in order to make inquiry easier. Finally, it is pragmatically valid since thesimplex model is a generic substructure and its broad features are axiomatic. It istechnically valid since it adopts higher orders of metasystem that observe, control andcommunicate with lower orders, and lower level models can be viewed externally and asa whole using an alternate frame of reference. Only its superstructure requires specificpragmatic validation, and this is not a concern of this paper. Since it is a good model, weare encouraged to now consider its recursive nature.

RecursionIn Figure 4 the referent system R(n+1) is a generic variant construct of order n+1 thatbelongs to a cybernetic space Ȼ(n+1) of order n+1. TheR(n+1) for all n constitute systemswith embedded superstructure models that arise from its epistemic content sensitive tomodelling context. We note in passing that the special case of R(0) occurs in a pre-cybernetic space Ȼ(0), where n¼−1. However, since our interest here lies in cyberneticspaces, the case of n¼ 0 is more significant, where R(1) is an action referent system withcollective feedback, and a non-active (0) autogenetic invariant construct. It is indicative of afirst-order simplex interaction model that exists in the first-order cybernetic space Ȼ(1), andan example is Forrester (1971) System Dynamics. R(1) may be modelled using R(0)techniques, for instance to include direct decision-making management processes asrepresented, for instance, in “system 1” of Beer’s (1979) Viable System Model.

We note thatR(1) behaviours are explained by, and hence dependent on,R(i), i¼ 1, n+1,where higher orders for increasing n are inversely related to undecidability, since higherorderR provides more explanation for events inR(1). In the case of iWn+1, higher simplexorders create informal functional influences ultimately affecting R(1). These higher ordersare thus relevant to anticipation only as qualitative inference. In the case of Ȼ(2), thedistinction between formal and informal influences allows radical constructivism to implyknowledge self-creation. This occurs even if it be cannot explicitly modelled, thereby limitingrepresentative interactions. This is in extension to the idea that in radical constructivismemergent virtual knowledge occurs, perhaps supported with inferred social filtering.

We have said that R(n+1) is recursively dependent on {R(n+1), R(n), R(n−1), […]},and this includes its own influences on itself through feedback. Also, R(n+1) issummarily interactive with its antecedent autopoietic couplings A(n), this implying anautopoietic hierarchy. Such a hierarchy is a recursive structure composed of theautopoietic couplings A(i), where i¼ 0, 1, 2, […] n.

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The R(n+1) referent system may also be seen as an nth order metasystem for thenth order autopoietic coupling. It can be represented symbolically for some function Gas the recursive expression:

R nþ1ð Þ: ¼ G R nþ1ð Þ; R nð Þ; R n�1ð Þ; R n�2ð Þ; . . .½ � (1)

We adopt the identity :¼ to connect the two sides of Equation (1). This is becauseR(n+1)is not intended here as a solvable entity; the identity means “equal by definition”, thisreferring to the logical recursive dependency forR(n+1) represented in Figure 4. It would beof interest here to see how this equation can be shown in terms of ontological distinctions.

The ontology of referential systemsThere is an inherent hierarchic ontology for the referent systems shown in Figure 5suggested by Equation (1), but which only indicates the informal (or inferential)influence of higher orders of R on lower orders.

To explain this, we begin with the operative originR(0), which is some introspectiveisolated operative system, perhaps associated with an organisation, where socialinteractions may be inferred but not formally modelled, and change is often a result ofinfluences that are assumed to impact on the system from some inferred environment.Implied within it, however, are the higher orders {R(1), R(2) R(3) R(4) […]} that maymaintain an implicit, unexpressed and often unrecognised influence on R(0), thoughexplicit modelling representations may also develop. The primary order refers to a first-order cybernetic space Ȼ(1), where R(1) involves interactions between differentoperative systems. The dyad is the second-order cybernetic space Ȼ(2), where R(2)involves self-regulation. The triad is the third-order cybernetic space Ȼ(3), withR(3) maintaining self-referencing anchors, and so on to the (n+1)th cybernetic spaceȻ(n+1), and above. In this ontology, deeper orders represent a greater degree ofexplanatory power for R(0) and hence an increased bounding on undecidability.By undecidability, we refer to decision problem for which it is impossible toconstruct a single outcome to a complex issue that leads to a relevant definitive

The TriadOrder R (3)

The Primary Interaction: R (1)

The DyadOrder: R (2)

The TetradOrder R (3)

The Operative Origin: R (0)

The Hexad OrderR (6)

The SeptadOrder R (7)

The PentadOrder R (4)

Deeper levels ofcomplexity like theembedded Octad

cybernetic order andbeyond

Figure 5.The ontologicalhierarchy ofcybernetic orders

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answer. Bounding undecidability refers to the ability to improve the likelihood oflimiting the variety of possible outcomes relative to a problematic issue. Increasedbounding on undecidability is due to R(0) being dependent on higher cyberneticorders of R either formally or informally through inference.

That both formal and informal representations are possible in this structure thatindicate more than the recursive expressions shown in Equation (1). This draws us toseeking another expression that might more adequately represent Figure 5. To do thiswe need to extend our symbolic representation from recursion to incursion.

IncursionDubois (2003) is interested in formalising systems with anticipative capabilities, forwhich he introduces the idea of incursion. This is defined by him as an inclusive orimplicit recursion, while its dictionary definition is: the act of running or leaking into,or penetrating. Leydesdorff and Dubois (2004) explains that incursion can be useful foranticipation in decision making where it connects with potential future events that can becurrently anticipated. Recognising that anticipatory systems can be modelled, simulatedand controlled, Dubois (1998) defines an incursion for x with some function P as:

x tþ1ð Þ ¼ P . . .; x t�1ð Þ; x tð Þ; x tþ1ð Þ; . . .½ � (2)

where the quantitative value of a variable x(t+1) at time t+1 is a function of thisvariable at past, present and future times. Here, numerical estimates for x(t+1), forexample may be possible using appropriate techniques that seek stable outcomes.In the case that x has multiple solutions, Equation (2) is said to be hyperincursive.This constitutes “an anticipatory system [that] is a system containing a predictive modelof itself and/or of its environment, which allows it to change state at an instant inaccord with the model’s predictions pertaining to a latter instant” (Dubois, 2003, p. 2,citing Rosen, 1985). However, such models can be useful for the simulation of futurebehaviours given historical and current knowledge of events (e.g. Yolles, 1987).

Let us return to Equation (2) in order to connect x with R. If the variable x is takenas a matrix x¼ {xi}, then each vector xi ∈ R(i) (with i¼ 1, η for some η) hascomponents {xij}, where (for some i) j¼ 1, m for some m. In other words, the vector xiis a set of m variables that are elements of the epistemic models in R(i) that constituteits local i superstructure, and a consequence of its epistemic content. The whole set oflocal R structures for i¼ 1, 2, […] n, n+1, […] (to some undetermined limit) influencesthe referent action system R(1), resulting in implied anticipation.

Now, following Dubois, anticipation in simplex modelling can be improved byelaborating on the recursive Equation (1) to include incursion. This draws on thepotential for modelling higher order qualitative epistemic generic referent systems R(i)for iWn+1 indicating higher order constructs than we currently know about. Theincursive representation for R(n+1) for some function G’ now becomes:

R nþ1ð Þ: ¼ G ' . . .R n�1ð Þ; R nð Þ; R nþ1ð Þ; R nþ2ð Þ; R nþ3ð Þ. . .½ �: (3)

However, this model poses an issue. We can only generate epistemic content for therecursive referent generic constructs R(i), i¼ 1,n+1. This is because for iWn+1,superstructural epistemic content has not yet been formally created as part of themodelling process, not least because we may not know the nature of the genericinvariant construct that connects R(iWn+1) with the lower order R. Therefore, theincursive content cannot concretely contribute to either the modelling process or

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behavioural anticipation in R(1). The significance of this provides a rationale for us tomake a transformation of Equation (3). For some function Ĝ, the general referentsystem can now be incursively defined as:

R nþ1ð Þ :¼ G I . . .R nþ3ð Þ; R nþ2ð Þð Þ; F R nþ1ð Þ; R nð Þ; . . .ð Þ½ �: (4)

Here, R(n+1) has two types of influence. Formal influences occur through the functionF which concretely affects R(1) through the creation of epistemic content for each R(i),i¼ 1,n+1. It also has informal influences for iWn+1 through I for which there is noepistemic content and which virtually affects R(1).

So, the formal F component of Equation (4) constitutes recursive lower simplexorders. It has epistemic content through its particular modelling superstructure. Henceit has concrete influences on the anticipatory behavioural capacity in the referent actionsystem R(1) in its cybernetics space Ȼ(1).

In contrast, R membership of I has no identifiable epistemic content. Hence itpotentially creates a virtual impact by influencing the formulation of any contextualpropositions relating to R(n+1), these propositions bounding undecidability. Suchcontextual propositions may arise from insights associated with internal/externalsystem environment(s) that are not formally expressed within the modelling process.Sometimes such conditions are invalid, and this may detract from of anticipation,decrease the bounding of undecidability and impoverish viability. Where they arevalid, these three attributes can be improved.

Thus for instance the involvement of I can enhance the setting of estimable controlparameters within any analytic and diagnostic process. In some cases I might arisethrough intuition. In others it may derive from an independent external modellingprocess that has been coupled inferentially to R(1) at some level of incursion, andperhaps expressed as logical extrapolation.

ConclusionThis paper began by discussing social complexity and the need to model it simply,using Schwarz’s living systems theory. Orders of cybernetics provides a propositionalenvironment for the creation of anticipatory models – that is, models of a systemthe structures of which broadly determine their patterns of behaviour. Until now thediscussion of cybernetic orders in the literature has been an arbitrary process. This paperhas led towards the development of a general theory for cybernetic orders of modelling. Todo this in part 1 it explored the needs of anticipation, and the idea of generic structuringdeveloped. This was linked with Cohen and Stewart’s concept of simplexity that throughemergence enables complexity to be reduced. As a result, orders of simplex modelling wereintroduced. A simplex structure is the generic substructure of a system model, housed ina given cybernetic space. Orders of simplex model come about through the conceptualemergence of invariant generic constructs. The idea of conceptual emergence is also tied tothe rise of paradigms. This enables us to formulate a general theory of generic modelling,set within the framework of orders of simplex modelling, which has its seat in the work ofDubois (1998) on hypericursive anticipatory systems.

In this part 2 of the paper we have developed simplex models for first, second andthird orders of cybernetic space. These models represent substructures that canfacilitate in inclusion of detailed superstructural modelling that generates epistemiccontent for the simplex structure. In principle, however, the structural nature ofsimplex model dictates how anticipation occurs, while the epistemic content determinesthe possible natures of the behaviour that is possible.

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In conclusion, this paper developed a general theory of simplex ordering. Discussionoccurred about the distinction between recursive and incursive modelling, andthe related distinction between formal and informal influences of higher ordersof metasystem.

This work will be extended in part 3 of the paper, and develop a fourth-order simplexmodel set in a fourth-order cybernetic space. It will also discuss how this relates tocultural agency theory.

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Further readingAshby, W.R. (1968), “Principles of self organising systems”, in Buckley, W. (Ed.),Modern Systems

Approach for the Behavioural Scientist, Adline Pub. Co., Chicago, IL, pp. 108-118.Beer, S. (1980), “Autopoiesis: the organization of the living”, in Maturana, H. and Varela, F.J. (Eds),

Autopoiesis and Cognition, Boston Philosophy of Science Series, Vol. 40, Boston, pp. 63-72,available at: www.cogsci.ed.ac.uk/,jwjhix/Beer.html

Beer, S. (1984), “The viable system model: its provenance, development, methodology andpathology”, Journal of the Operational Research Society, pp. 7-25.

Beer, S. (1994), Decision and Control: The Meaning of Operational Research and ManagementCybernetics, John Wiley & Sons Ltd, Chichester.

Boot, R. and Hodgson, V. (1987), “Open learning: meaning and experience”, in Hodgson, V., Mann, S.and Snell, R. (Eds), Beyond Distance Teaching – Towards Open Learning, Open UniversityPress, Milton Keynes, pp. 5-15.

Boxer, P. and Kenny, V. (1990), “The economy of discourses: a third order cybernetics?”, HumanSystems Management, Vol. 9 No. 4, pp. 205-224.

Cohen, J. and Stewart, I. (1995), The Collapse of Chaos, Penguin Books, Viking, London.

Dubois, D. (2000), “Review of incursive hyperincursive and anticipatory systems – foundation ofanticipation in electromagnetism”, in Dubois, D.M. (Ed.), AIP Conference Proceedings,CASYS’99 – Third International Conference, Vol. 517, The American Institute of Physics,New York, pp. 3-30.

Dubois, D.M. (1995), General Methods for Modelling And Control, 14th International Congress onCybernetics, Namur.

Jackson, M.C. (1992), Systems Methodologies for the Management Sciences, Plenum, New York, NY.Piaget, J. (1950), The Psychology of Intelligence, Harcourt and Brace, New York, NY, Republished

in 1972 by Totowa, Littlefield Adams, NJ.Piaget, J. and Inhelder, B. (1973), Memory and Intelligence, Routledge and Kegan Paul, London.Schwaninger, M. (2006), “System dynamics and the evolution of the systems movement”, Systems

Research and Behavioral Science, Vol. 23 No. 5, pp. 583-594.Schwaninger, M. and Pérez Ríos, J. (2008), “System dynamics and cybernetics: a synergetic pair”,

System Dynamics Review, Vol. 24 No. 2, pp. 145-174.

Corresponding authorDr Maurice Yolles can be contacted at: prof.m.yolles@gmail.com

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