Social systems theory and, more particularly, concepts like self-organization, self-referentiality, autopoiesis, and reflexivity, have been the subject of intensive philosophical discussions. However, less attention has been paid to the fruitfulness of using these concepts as heuristics in sociological research. As Giddens (1984, at p. xxxvii), for example, noted:

Sociology, in Giddens' opinion, should retain a firm focus on observable action and empirical explanation. In structuration theory, structure is implicated recursively in the reproduction of social systems. The assumption of a duality of structure provides a methodology for relating institutional analysis and the analysis of strategic conduct: the one narrative can be used as a context for informing the other (Giddens 1976). The two narratives, however, remain juxtaposed by "bracketing" the one perspective when focusing on the other (Giddens 1984). This model was intended to offer a specific solution to the gap between action theory and institutional analysis in American sociology (Giddens 1981, at p. 167).

Although differently inspired, Luhmann's (1984) sociology can with hindsight be considered as another attempt to bridge the gap between action theory and social systems theory. During the 1960s and 1970s, leading scholars among symbolic interactionists and Parsonian systems theoreticians had recognized the "incommensurability" of their respective perspectives (Grathoff 1978). Luhmann suggested resolving this debate by considering the core concept of symbolic interactionism, that is, the interactive construction of social meaning, as the unit of operation of social systems. Whereas Parsons (1937) had considered action as the unit of the system's operation, Luhmann's social systems theory thus provides a mirror-image of Parsons's so-called "structural functionalism." The analysis of social structure should not be based on (the aggregate of) action, but on the interactions between actions.

Interaction constitutes a system of reference for the observable events different from action or its aggregates. While both Parsons and Giddens (but also Habermas (1981) and Münch (1982/1988)) had attributed actions to actors and/or aggregates of actors performing via institutions, Luhmann's theory sided with symbolic interactionism by defining human action in terms of its interactive meaning at the network level (Blumer 1969). Note that the interaction term is by definition the remaining uncertainty at the network level after accounting for the "within-group" variation in the aggregate.

When action is attributed to communication at the network level, this system of reference is expected to have its own dynamics. The dynamics of the interactions are assumed to "self"-organize the roles that are attributed to the actors. The actors carry the network at the nodes while the links of the network span an architecture which develops additional complexity in terms of its recursive interactions. The architecture of relations can be considered as a structure containing the expected information of the network's further development (Leydesdorff 1993).

The network structure is latent for the actors involved, but it can be hypothesized by an observer (Lazarsfeld and Henry 1968). The reflexive observers, however, are also able to act as participants. As noted, Giddens (1976, at p. 162) introduced in this context the idea of a "double hermeneutics." The roles of observers and participants can be combined and/or distinguished; all combinations are possible. For example, actors may have similar positions in a network while not maintaining active relations. The positional and the relational analysis (Burt 1982) are expected to lead to different narratives, analogously to Giddens' distinction between institutional and action-oriented descriptions as noted above.

If one extends the latency of structure at each moment in time using a dynamic perspective, the recursive operation of structure over time remains virtual from the perspectives of the actors involved. The actors observe change in the "instantiations" only as a consequence of the interactions assuming the otherwise unobservable operation of what Giddens has indicated with the term "duality of structure." The specification of this virtual operation as both recursive and interactive will bring us into the algorithmic domain of non-linear dynamics. The instantiations can then be considered as spatial, that is, geometrical representations of a complex dynamics. Self-organization is one among the possible operations of the network system (Maturana 1978).
 

Self-organization

A self-organizing network propels its own operation recursively, that is, by restructuring its organizational basis in the present on the basis of its interactions. The observable network, that is, the architecture at each moment in time, contains an expectation of its future operation. This uncertainty is contained in the distribution of nodes and links over the network.

The expected information content of a subsequent message reporting change in the network system is equal to the sum-total or aggregate of all the mutual informations of the network with communicating agencies. The remaining uncertainty, that is, the structure of the interactions, recurs on the previous state of the network since it was not affected by the interactions with actors. This uncertainty, however, cannot be fully perceived by any of the participating actors. They are embedded and therefore the network structure remains (at least partially) latent for them and the operation of the network consequently remains virtual. Structure at the network level is communicated with actors through their respective windows of mutual information (Leydesdorff 1995a).

Being only partially informed the actors run their own programs on the basis of their perceptions. The distribution over the network is expected to be disturbed by local actions, and particularly by aggregates of action. The expected information content of the network is thus changed, and this is again available for local, that is, partial observation. The systems of communication and action propel each other in a "structural coupling."

Social network systems are multi-layered: the events provide Shannon-type information, that is, uncertainty which can be used for the update. Thus, the information is provided with meaning. At each moment, there is both a network of events and a network of perceptions of these events. These two layers are expected to interact over time. This model is so dynamic and interactive that the emerging system is no longer expected to stabilize completely: it is transient and thus it "self-organizes" its next stage, while leaving traces of its operation behind. The system can therefore not be defined in terms of observables, but only in terms of operations.

In other words, at each next stage an evolving network has two incoming arrows: one from its previous state and one from the various interactions. Hence, there is always an interactive term and a recursive term. Analogously, actors interact and build on their previous state while self-organizing their own evolution. For analytical reasons, actors and structure determine each other insofar as they interact ("structural coupling"). In the remaining variation, the systems only condition each other.[1] An interaction is mutually informative: the interactive event can be attributed as action to the actor or as communication to the network system. The systems update one another through their mutual information.

The interaction between recursive systems implies a reflection: the update in the present assesses the complexity by reorganizing it into a system. The constitution of meaning is a consequence of this operation. "Meaning" as a unit of operation, however, adds a reflexive layer to the basic exchange relations. While engaged in their interactions, reflexive actors may have reasons to select actively given their individual self-organization in relation to options provided by their environments and/or to options perceived by them. The expected information content of the social network is processed in this distributed mode, that is, as uncertainty. If the reflected (that is, internally meaningful) information can again be communicated, the network is provided with an additional layer, allowing for a similar process of constituting a distributed "meaning," but as a consequence. This sub-symbolic (since distributed) meaning can be compared to situational meaning as previously defined from the perspective of symbolic interactionism. Since it remains uncertain, it can be identified only by taking a perspective.

All interaction is already reflexive in itself with reference to a previous communication. Therefore, let us introduce the concept of "hyper-reflexivity" for the reflection implied in the active communication of meaning. Additionally, the attribution of what is information and what meaning remains uncertain at each receiving end. While a biological signal (for example, a spike at a neuron) can have a function in addition to containing information, one is additionally able to distinguish in human communication between the function and the meaning of a message. Human communication takes place at two levels, at the same time: a message is expected to have a meaning and the message is expected to contain information.

In human interaction systems the coupling between these two layers of the network is not given, but it is (re-)constructed and it remains uncertain. In other words, human interaction is reflexive and hyper-reflexive. The information can be bounced back and forth, like between mirrors. But in contrast to communication, for example, among ants, the interactive result can be used as input for a layer of communications that one is able to use for enriching the first-order communication reflexively. These two layers can be distinguished by an observer, while as participant one is able to interact. Let me follow Latour (1988) by calling the interactive operation of the observer/participant "infrareflexive," and, among others, Woolgar (1988) by calling the self-referential processing of meaning "hyperreflexive" (cf. Ashmore 1989). The hyperreflexive observer has a degree of freedom which allows him, for example, to abstain from participation.

The two layers of communication select upon each other and the various loops are expected to disturb each other. The results of an interaction about an event can be considered as another event about which one can communicate meaningfully. The social system is non-computable in principle: as opposed to formal languages, informal communication allows for intersections of the loops. Events in the "life-world" (Habermas 1981) and their reflections in social communication interact in a number of ways. Among other things, the definition of a "life-world" can be changed reflexively.

The different communications may use different time horizons so that a "double hermeneutics" is continuously generated and reproduced (Giddens 1984). The relations between the layers are a priori asymmetrical and asynchronous: for example, the situational meaning of an interaction may change without regard to the intentions of the participants. The emerging context may then happen to the actors involved as an (unintended) event. The distinction to be drawn between an event and its interpretation can also be debated.
 

Luhmann's restriction

Luhmann defined communication explicitly as the unity of information, message, and understanding. By taking the communication of an information and its reception as a single—albeit complex—unity,[2] the concept of "meaning" could be made constitutive of his idea of a social system.

Understanding is necessarily reflexive. The social system as defined by Luhmann exists exclusively at this reflexive level, that is, in terms of expectations. Consequently, the operation of interactive meaning ("Sinn") is claimed by Luhmann as the proper domain of sociological analysis. His social systems theory is a special theory focusing exclusively on human interactions as events. The human being itself is defined outside this domain of sociology as another system of reference; Luhmann attributes this subject to psychology. Psychology shares with sociology a focus on "meaning" as the unit of operation (e.g., Luhmann 1986).

The focus of Luhmann's sociology is on reflexive selections, that is, on the operation of providing meaning, while the original variation from which one selects, is black boxed as an "external referent." Luhmann (1990a), for example, declares the substance as "a reality that remains unknown." Uncertainty is considered relevant insofar as it is provided with meaning and more particularly communicated. Luhmann (1984, at p. 103), consequently, defined information as "meaningful information," that is, "a difference that makes a difference" (cf. Bateson 1972, at p. 489).

The reflexive layer, however, focuses on the representation of the reflected substance, while the not yet reflected difference or the remaining uncertainty is declared as noise. This noise is to be filtered away by the reflexive operation which provides us with "meaningful information." As Luhmann (1984/1995, at p. 67) emphasized: "By information we mean an event that selects system states." Using this definition of information, the uncertainty can no longer be informative to sociology. The meaningful information is not specified as an operation on the Shannon-type information or uncertainty (Leydesdorff 1996).

In other words, options provided by the network or events not perceived by human carriers ("observers") cannot be provided with social meaning under these definitions. These events remain operationally external to the social system. Thus, this theory focuses on the reflexive top layer of the complex network of human consciousness and interhuman interactions. Indeed, Luhmann shared with Parsons an interest in cybernetics and control. Self-organization theory can be considered as a theory about the limits of control given the wealth of possible combinations at the reflexive level.
 

The self-organization of the social system and biological autopoiesis

The metaphor of "self-organization" enabled Luhmann to relate his theory to the new biological theorizing about autopoiesis (Maturana 1978 and 1988; Maturana and Varela 1984). This theory has its basis in neuro-physiology: the operation of the brain cannot be understood by using input/output models. The neural network processes input as the disturbance that allows it to distinguish between signal and noise by differentiating itself. Whenever a disturbance of this otherwise "plastic" medium is recursive, a structure emerges. As Maturana (1978, at p. 49) formulated:

Maturana (1978) explicitly distinguished this embedded observer from a super-observer. The latter, like a biologist, observes the system (as a structure) from the outside using human language to formulate hypotheses concerning biological phenomena. Note that the operation of generating a participant/observer is in itself recursive, but it cannot generate a super-observer with a meta-biological status. Each next-order participant/observer participates infra-reflexively in the operation. As Maturana and Varela (1980, at p. 121) formulated:

Using simulation models, it can be shown that a self-generated "lock in" of the variation into a pattern at the network level can be expected when the variation is not completely random, but, for example, conditioned by previous events (Arthur 1988 and 1989). When the pattern matters for the reproduction, this pattern has to be recognized in one way or another (Leydesdorff & Van den Besselaar 1998). The recognition assumes an observer, but this observer/participant —or network effect— is not able by itself to communicate with other observers reflexively as among human beings. The recognition is not translated into a cognition and then symbolically communicated; it remains subsymbolic. The observation does not have an active (e.g., psychological) meaning for the observer as long as the observer is not defined other than as a network effect.

In other words, when a contingency or a context is involved, the variation is conditioned and then also partly determined by previous variation. The non-random pattern of a network distribution implies a condition, since randomness can be defined as the unconditional generation of noise. The covariation between the network and its generators at each moment in time is expected to develop into a coevolution over time at the interface because of the recursivity of the selective condition.[3] In other words, evolutionary systems follow and produce their histories in terms of coevolutionary trajectories.

Coevolving systems shape each other mutually along these trajectories by selecting upon each other in terms of signals and noise. A reflexive system is embedded in the systems of reference for the reflection, as in such a coevolution. The reflexive system is expected to provide feedback on the reflected system to a different extent, depending on the organization of the reflected and reflexing networks involved. With increasing reflexivity the nature of the feedback is expected to change. For example, when the reflections by local observers can be communicated reflexively, this reflexive communication can be reflected sociologically. Different mechanisms can be distinguished within the coevolutions when the reflexive operation itself is differentiated, that is, when both meaning and information can be transmitted.
 

Habermas' objections

In a thorough reflection on Luhmann's sociological systems theory, Habermas (1987, at p. 385) acknowledged that Luhmann's theoretical focus on meaning "yields novel, not merely objectivating but objectivistic descriptions of subtle phenomena of the lifeworld." Despite this appreciation, "objectivistic" in this context means that Luhmann is behaving as a super-observer who claims to be able to detach himself (like a biologist) from the meaning provided by the participants in the systems that he observes. In this sense, Luhmann's sociological systems theory is characterized by Habermas as a "metabiology."

Habermas noted that the metabiological perspective solves the reflexivity issue which had hitherto remained a stumbling block for metaphysical approaches. While physics asks for causes and origins, evolutionary theorizing assumes that the same effects can be caused by different underlying arrangements. Additionally, similar disturbances may have other effects in different systems and/or at different moments in time. Thus, there is no longer a need for the specification of an unambiguous origin. The metaphysical quest for last causes and foundational origins is replaced with a (potentially empirical) focus on emerging order.

In Darwin's evolution theory, selection was identified with the assumption of natural selection. In a metabiology, however, the selection mechanism itself can be made the subject of theorizing. What is selecting and how, remains a hypothesis. In sociology, for example, different selection mechanisms (e.g., the market or a tradition) can be assumed. The various selectors may compete and thus a variety of phenotypes can be generated.

As reflexivity can increasingly be understood as the selection of a discourse, the metabiological approach of sociology gains priority over metaphysics and philosophy. The sociologist no longer needs a transcendental or universal basis for human understanding, given the proliferation of discourses as empirical domains, for example, within the sciences (Whitley 1984). In the metabiological model, the cause/effect scheme of independent and dependent variables is replaced with a model of fluxes in different contexts. When action balances reaction (in interaction) next-order stabilizations (and even meta-stabilizations or globalizations) can be generated. The distributed systems in flux are expected to exhibit both stability and change while performing a "life-cycle" in a variety of contexts.

Geometrical metaphors provide us with representations of these complex dynamics. For example, as a result of structural analysis one is able to exhibit mappings of the complexity at each moment in time, while historical analysis usually pictures a trajectory over time. In general, discursive theories provide a selective window on the complexity. In evolutionary terms, they remain "genotypical" reductions of the "phenotypical" complexity (Langton 1989). Even evolutionary theorizing cannot escape from this reflexivity implied in the scientific discourse: while both Luhmann and Habermas have always maintained that the sociological understanding of communication is metabiological, these authors have drawn completely different inferences from this assumption because of their different perspectives.

Society, in Luhmann's opinion, should not be considered as a living system: it is the network of interactions between the carriers who perform their respective life-cycles while they are alive (e.g., Luhmann 1986). Luhmann has emphatically and repeatedly argued that society does not perform an evolutionary "life"-cycle, since this system is not expected to be alive.[4] When a carrying system dies, its social role can be reattributed at the level of the social system, that is, on the basis of social interactions. The social system operates in terms of meaning and not in terms of (biological) life. Although the social system is disturbed by events at the biological level, it is not steered by them nor causally dependent on them. The biosphere provides only a context for the social system. Self-organizing systems use contexts as potential resources.

According to Luhmann's theory, the observable events have to be provided with meaning—that is, understood by a psychological system—before they can be made relevant at the level of the social system. In this sense, the social system is "operationally closed." Thus, Habermas is correct that the "life world" events are defined as external to the domain of social systems theory. From Luhmann's perspective, one is able to communicate about "real life" in a sociological discourse, and people are also able to "make music together" (Schutz 1951), feel each other's pain or celebrate vital events using other media of communication among human beings. All these phenomena can be made the subject of special sociologies. However, only the inter-human interactions can be provided with meaning. Meaning is generated as a consequence of communication because of the recursivity of the selection. The individual and his/her life are left outside the social system and thus made the subject of psychology, just as the human body can be made the subject of biology.[5]

This isolation of the individual identity has been central to Habermas' philosophical critique. For example, Habermas (1987, at p. 378) formulated:

Luhmann defined language as a medium of communication, and he distinguished media theory from systems theory (e.g., Luhmann 1975a). Habermas objects to this major decision in the construction of the theory and points to its implied assumption about language:

Language

Whereas Habermas has clearly formulated a problem in Luhmann's sociology, he has also tended to construct a metaphysical divide between those who believe in "linguistically generated intersubjectivity" and the adherents of "self-referentially closed systems." Metabiological theorizing, however, has taught us that perspectives may offer different windows on rather similar subject matter. Can this fundamental divide perhaps be formulated as a metatheoretical puzzle? How does language as an evolutionary achievement enable us to act both as Maturana's participant/observers and as Luhmann's super-observers?

Habermas (1987) proceeded, indeed, from a philosophical critique to sociological theorizing, but he was not able to provide a clear answer to the problem he had raised. He argued that, on the one hand, "suprasubjective linguistic structures would entwine society and individual too tightly with one another." On the other hand, the assumption of "intersubjectivity" would be too simplistic: how is this intersubjectivity mediated? Language is assumed to have a complex inner structure that allows us to communicate and to regulate our communications internally both at the level of the social system and as individuals.

Given these insufficiently solved problems, Habermas assumed that "common" language is a "given." "Natural" languages provide the mediation between nature and culture, while cultural communication is rooted in community life. Common language is then considered as the integrating operator of the social system. As Habermas keeps emphasizing, this integration is counterfactual to the differentiation that is observed. It is an idealization that cannot and should not be denied. One may wish to compare this assumption with Giddens' virtual structure which is assumed to operate "outside time and space". In both cases, a meta-integration is assumed, but the operation is not specified.[6]

As noted, Luhmann considers language as a medium of communication. Media are distinguished from systems, and at some places Luhmann (e.g., 1997a) argues emphatically that language—not being a social system—cannot be self-organizing. Following Parsons, Luhmann furthermore focuses on the differentiation of society in relation to symbolic media: each subsystem generates a specific code that allows it to speed up the communication by reducing complexity selectively. For example, the science system communicates according to Luhmann insofar as its communications are assessed in terms of their truth-value, while in political communications power provides another medium of communication. Thus, similar communications can be attributed various meanings by using other symbolic media of communication. The symbolic media provide codes to the differentiation of the communication.

Luhmann insisted that the functional codes of communication are binary. A scientific communication, for example, is considered to be either true or false (since tertium non datur). In my opinion, true/false options can, like other codes, be considered as qualities that span dimensions as additional degrees of freedom. These additional dimensions enable us to differentiate in terms of the meaning of a communication. For example, the truth of a statement is analytically different from its value on the market or its rhetorical function. The analytical distinction between different dimensions, however, does not imply that the variables are necessarily dichotomous: some statements may be more true than others. Luhmann did not distinguish sufficiently between the epistemological analysis of the categories and the methodological model.

In methodological terms, one can think of codes as degrees of freedom in differentiated communications. The codes enable us to focus on specific selections. From an evolutionary perspective, selections can be codified if they are functional for the reproduction of the larger system. Since the social system exists only as a network of distributed expectations, the functions remain uncertain and are likely to disturb one another. Various function systems resonate in all inter-human communication, but some communications are more specifically selected at some places and not at others. Some selections can be provisionally stabilized by further selection. For example, theoretical and methodological reflections on scientific communications can begin to coevolve by selecting on each other as constraining and enabling conditions, potentially and temporarily closing the specificity of this communication as in the case of the development of a paradigm (Luhmann 1990b; cf. Leydesdorff 1995b).

This reformulation of Luhmann's theory in terms of uncertainties operating in relation to each other enables me to formalize the model and then to discuss the issues of integration and differentiation of codes of communication in relation to language in more detail. Let us define the undifferentiated communication (i) as a primitive language. Differentiation attaches a suffix (j, k or l, etc.) to the communication providing each communication with a specific meaning. Translation remains possible because of the common dimension i between differently coded communications (e.g., ij and ik). A translation provides a specific communication (ij) with another meaning (ik). The translation assumes a (provisional) stability of the translated information (i) in the message when the latter's a priori form (j) is transformed into an a posteriori one (k).

Following Luhmann, a human carrier is assumed to perform this reflexive operation (in i, j, and k). The reflexive actor, however, has to be able to understand all three dimensions of the translation (the substance, the prior, and the posterior meaning) in terms of a single operation. The unity of the act of translation (ijk) cannot be based on the underlying information (i) only. One has to operate by invoking additionally one's own autopoiesis for translating ij into ik, since neither the input-value nor the output-value can be identified with the meaning for the reflexive translator. Providing meaning to the action in three dimensions (ijk) requires an internal—that is, fourth—degree of freedom. This degree of freedom enables us to relate the input with the output reflexively and without becoming confused. Let's call this dimension h. In Luhmann's semantics, the internal reflection corresponds to the psychological meaning for the individual carrier of the communication.

Note that each additional dimension can also be considered as an uncertainty. Using h for the projection, translations can be improved, but they can also be disturbed; for example, when the translation is biased because of the idiosyncracies of the translator. One is able to reflect on one's (and each other's) reflections using an internal degree of freedom. Above, I proposed to use the concept "hyper-reflexivity" for this internal operation, in contrast with "infra-reflexivity" as a network function. I shall now relate these concepts to analytically distinguishable operations of the communication systems. However, let me first point to the unobservability of a four-dimensional system.

A virtual dimension can be hypothesized analytically, but only three-dimensional (that is, geometrical) representations of a four-dymensional dynamic can be observed. The fourth dimension allows us to bring together what has been remote, that is, by providing it with a new meaning in terms of a translation of one geometrical representation into another. The representations can be conceptualized as either instantiations or trajectories using geometrical metaphors. In the case of an instantiation one explains the complexity in the aggregate at a certain moment and in the case of describing a trajectory the time axis is used for structuring the narrative. As Giddens (1984) argued, one of the dimensions is bracketed in either case. Luhmann (1984) used the metaphor of a blind spot implied in a theoretical appreciation, more generally. One needs to select one background or another to stabilize a perspective.

Specification of the relation between the various perspectives presumes a reflexive theory of observation. If there is no one-to-one correspondence, how and in how many ways can the perspectives of an observer/participant and of a super-observer be related? As noted, a proposal for a theory of observation was precisely the theme of Maturana's (1978) contribution. As a biologist, however, Maturana was able to separate the two domains. Habermas (1987) objected to Luhmann's unreflected importation of this separation into sociology, although he admitted that the focus on the reflexive domain had been highly fortunate. The construction of a theory of objectified meaning tends to alienate us from the meaning that is reconstructed, and thereby sociology might lose its practical value.
 

Infrareflexivity

Napoleon's diplomat Talleyrand (1754-1838) is supposed to have said that "God has given us language for hiding our thoughts."[7] Human language allows us to relate the roles of participant/observer and super-observer in a way which cannot be specified from a biological perspective. While muscles are expected to operate when the innervating nerves fire, we are able to interpret the message and this provides us with options for the selection. We may wish to distinguish between the function and the meaning of a communication, and sometimes our reflections and interactions change these dimensions of the communication with hindsight.

As argued above, the crucial difference from Maturana's biological model is the double structure of the linguistic communication itself. Whereas neurons fire signals that can be selected by structural nodes ("observers"), human language is an evolutionary achievement that enables us to communicate in two dimensions at the same time, notably, in terms of both information and meaning. A message can be understood in terms of its information content and in terms of its meaning in the same act. Above I have expressed this as (i and j) or (i and k). The four-dimensional receiving system can change the interpretation with hindsight (translate between ij and ik), and recursively it is able to revise the translation with reference to its internal axis h, that is, by learning.

When translating the information content (i) of a message (j) from one context to another (k), the actor has to invoke an internal axis (h) for discarding the noise. The translation has to be provided with a meaning, that is, a value has to be selected on the internal degree of freedom. Since this is a dynamic operation, one is able to improve on one's translative capability and thus to strengthen one's communicative competence. Note that the explanation of communicative competences has been one of Habermas' central objectives.

In a biological system the hypothesized fourth degree of freedom is fixed at each moment since otherwise the system might fail to operate. The biological system can be identified with the supersystem and the translations can be considered as subdynamics. The fixation can then only degenerate by wear and tear, thus feeding back on the life-cycle of the (super-)system. At a meta-biological level, however, the dynamics remain uncertain, and human communication is accordingly failure-prone. (Habermas' assumption of a common language is counter-factual, indeed.) The private worlds of the actors are not expected to correspond with a common language operating in the social system as another system of reference. On the contrary, the communication theoretical framework suggests that the translation of messages between different contexts, that is, a differentiated social system with symbolic media of communication, induces reflexivity about the contingencies of communication at the level of the individual.

The pervasiveness of reflexivity at the level of the social system enables us to control for understanding, and then to change and improve the aperture of the reflection. An affirmation, for example, stabilizes the meaning of the communication being affirmed. Two dually layered signals (ij and ik) can contain, in principle, sufficient redundancy to provide for an unambiguous meaning by using a fourth dimension (h) for the projection. The projection is needed for discarding the uncertainty as noise. However, one has to learn to do this; the operation is not naturally given. Languages operate discursively and recursively; linguistic utterances tend to generate uncertainty if they are not understood. Embeddedness in reflexive language induces higher-order reflexivity because the meaning of the utterances may change.

The super-observer can be reintegrated into the linguistic domain only if the medium allows for reflexive communication. While a biological function has to be reproduced (following the pattern given in the life-cycle), it remains dependent upon the reception among the participant/observers whether and how a social function is shaped. In a high-culture, roles were pre-ordained and function tended to be equated with meaning while this social system was stratified. In this configuration, the super-system is still identifiable (Figure 1). When the cosmological order is broken, roles may be reflexively acknowledged or not and the meaning of a communication can increasingly be distinguished from its function. Let me paraphrase the quote from Maturana above: "When this takes place, even to the slightest extent, an observer and a super-observer are generated within the same, yet differentiated medium." Since all dimensions can be appreciated as degrees of freedom, the participant/observer can then be both infrareflexive and hyperreflexive.
 

Figure 1 Three functionally differentiated subsystems with a communality	Figure 2 Three differentiated subsystems with a differentiated communication

The hyperreflexive communication can be distinguished from the infrareflexive one from the perspective of a super-observer to whom "language was given for hiding one's thoughts." In the case of infrareflexivity, however, one processes the reflexive communication along what we have called above the output axis k, that is, the observable output of the system. The communicative competence can then be defined in terms of whether one is able to express meaningfully what one has learned in the hyperreflexive mode. Similarly, providing meaning to a signal along the input axis is necessary for the understanding, whereas the internal reflection on the complex operation enables us to improve our capacity for translating.
 

Figure 3 Emerging integration at the hypercyclic level (h)

The operation in four dimensions at the level of the social system is formally analogous. However, the substance is expected to be different: whatever the information i, it is packaged when it is a message in the network (ij). By using a local translator, this message can be changed in meaning (ik) (see Figure 2). The distribution of (potentially interactive) translators provides a degree of freedom that constitutes the internal dynamics of a social network (Figure 3). This distribution, however, can no longer be fixed as in the case of a stable identity; it operates as a meta-stable regime in four dimensions (Leydesdorff 1997a). Note that no communication is expected that is only substance i; all information is packaged in messages for transmission at the network level. Thus, the substance tends to be uncertain at the network level. This uncertainty can be formalized using the mathematical theory of communication.
 

Communication of "information" in messages

The network is expected to process messages regardless of their contents. The perspective of the communication network therefore is different from that of the communicators. Only by operating at a next, that is, receiving interface, can the substance of the message be reconstructed and further processed. This next interface may be a (human) receiver or another differentiation of the network. As the differentiation changes, the message is expected to have another situational meaning (Granovetter 1985).[8]

The substance of communication can only be reconstructed if the communication systems are sufficiently complex for packaging the original signal. The original substance of the message, however, remains an assumption at the receiving end and decoding is based on theoretical assumptions. Although this may in practice be taken for granted, all sense of an original communality is recognizable as based on a specific coding, for example, in terms of basic affections. At the level of the social system, the communication of information not only transmits, but also translates and potentially transforms the expected information content.

The full formalization of the substance of communication in terms of messages expected to contain information was accomplished by Shannon's (1948) mathematical theory of communication. From this perspective, information is content-free and equated with uncertainty; it is formalized in terms of binary digits or bits. When the uncertainty is complete, the system is assumed to be "dead" in a formal sense. A system can only process information, that is, communicate, as long as the expected information is not complete but contained within a communication.

A communication system communicates with other communication systems. The latter provide contexts insofar as they communicate, that is, insofar as these systems are neither completely certain ("fixed") nor completely uncertain ("dead"). Thus, a model of co-variation and remaining variation in otherwise orthogonal dimensions can be formalized (Leydesdorff 1994). By differentiating the systems suppress the co-variation and tend to become nearly decomposable (Simon 1973). Whereas the covariation between two systems (A and B) is mutually determined, the remaining variation provides a structure over time in the one system (A) that is a latent condition for the coevolving system (B). From the perspective of the latter system (B), the structure (in A) can also be considered as redundancy or failing information.[9] Therefore, structure is latent from this perspective.

The covariations provide windows at which the systems share information mutually. The remaining variations are based on the recursive code of the communication over time and remain internal to each of the co-evolving systems. In the case of a dually layered communication medium like human language (see above), the same communication can be nearly decomposable in one dimension while firmly related in another. For example, we may agree despite a deep misunderstanding in terms of the information exchange, while one is also able to disagree about a given meaning when one fully agrees about the underlying exchange. Thus, a two-dimensional communication medium allows for differentiation and integration at the same time. The operation has become complex in itself.

With increasing differentiation the system has to improve on its internal operation of integration because of the risk of otherwise falling apart from an excess of differentiation. Keeping this balance under the pressure of increasing uncertainty can be considered as the driving force for developing communicative competences in a communication system.

The communicative competences are expected to be differentiated in the case of inter-human communication. Whereas the substance of social communication (i) is packaged, the communicative competencies tend also to become formalized. The social network system, however, remains structurally coupled to human agency in the substantive dimension. As long as one maintains Luhmann's assumption that human agency has to be the substantive carrier of the reflexive translation at the node, the social system cannot be completely virtual. One has to abandon the complete idealization in the historical case since observable reproduction has to be realized as one of the subdynamics of otherwise virtual networks. In this respect, sociology is different from the study of artificial systems.

The historical instantiations contain the fingerprints of the social system's reproduction. Institutional dynamics exhibit codifications of communication that have been useful hitherto to the extent that they have been institutionalized. These "real life" phenomena are part of the social system as are we ourselves, that is, as subdynamics which can be invoked. In other words: human agency is structurally coupled to the social system, but only along one of the two dimensions of inter-human communication at each time. The other dimension is the way our communication is processed as a message. Along this dimension, the expectation is that we are only operationally coupled, since operational coupling allows for differentiation.

The social system operates in terms of expectations (that is, uncertainties) and expectations concerning expectations (that is, meaningful selections). This differentiation in the communication provides parallel channels in the medium that the network system has available for propelling the communication. Language supports this dual-layeredness in the communication by providing a means of codification of the relation between the message and the information. The interactions among the two layers provide the system with variation that can recursively be selected as meaningful.

For example, one is able to play with the meanings and the functions of communications. Furthermoe, one is sometimes able to control some of the selections by improving one's own communicative competences. Although each of us is able to select individually by providing meaning to some information and not to other, the reflections are socially distributed and hence they contain also an update value for the network behind the backs of the participants involved. In each communication, one degree of freedom may be hidden hyperreflexively or it can be made available to the communication, that is, infrareflexively.

When the socially distributed reflections can be communicated, they are provided with situational meaning. The latter interaction is expected to interact with the not-yet communicated layer of reflections, and by generating this new variation the system propels itself. On the side of the human agency involved, this configuration provides us with opportunities for building niches within the system or, in Habermas' terminology, with options for improving the quality of life, for example, by fine-tuning communicative competencies to the exigencies of the communicated culture.
 

Conclusion

Luhmann recognized the need to incorporate the theory of communication into his evolutionary theory of social systems as early as 1975 (1975b, at p. 196), using the following formulation:

In later work, Luhmann (e.g., 1984, 1990b, and 1997b) defined communication as the evolutionary operator of the social system. However, this operation was then no longer theoretically reflected in terms of available theories of communication. Instead of a failure-prone operation, communication was declared as a unity with an unambiguously defined structure. Although Luhmann (1984) acknowledged the possibility of misunderstanding, his theory has not left sufficient room for the grey shades of mixtures of misunderstandings and understandings that generate uncertainties and, in my opinion, propel the communication process. In other words, the noise generated by the propulsion of a communication through a medium is not systematically analyzed.[11]

The hypothesis concerning the evolving unit is crucial to evolution theory at the metabiological level (Andersen 1994). Since the evolving unit is no longer given, but constructed, one has to ask "what" precisely is evolving? The theory of communication now enables us to understand that in the case of the social system, the complexity of the communication itself is evolving. The uncertainty is continuously reorganized by being communicated. By implication the communicative competences of human carriers of the communication become crucial for their survival. The communication is expected to change both substantively and in terms of its structure.

How can communication itself evolve in terms of its complexity? Since the communication network is not a living system, reproduction is not guaranteed. The communication system has continuously to be kept "alive:" these dynamics, however, are endogenous to the system, since otherwise the system cannot adapt to its surrounding complexities. The different dimensions of the communication select upon each other, thereby producing new recombinations that may be innovative. New recombinations can be codified in principle. If codification succeeds, a new pathway for propelling the communication is generated and the communication system is enriched. The layers of selectivity that operate upon each other can be considered as codifications of the medium.

The observable variation is observable only because other possible variations have already been deselected: the co-variation between randomness and historicity evolves in a coevolutionary process. On top of the coevolutionary trajectories a next-order system can become recursive as the new recombinations are repeated and then further codified. Because the medium of language itself is double-layered, the coevolution of culture as an emerging phenomenon in the social system can be contained within it and its recursive ramifications. The code of the emerging regime feeds back on the constituting interactions in the trajectories as another selector driving the underlying systems into a next-order cultural fit.

On the one hand, the social system should not be reified as something additional to language (and its further codifications), while the latter is sufficiently complex for the function of an operating system of social communications. Linguistic utterances are meaningful, since the messages are expected to contain information. Thus, the information is always coded. On the other hand, the observable use of language should be considered as only an instantiation of social structure, while from a dynamic perspective the operator is contained in the intentionality of the usage of language. The communication transcends the contingencies that it reshapes, but the dual-layeredness of the network causes the transcendency to be contingent at a next moment.

When the code itself is so flexible and subject to redefinition as in language, then the selector is already socially constructed. In other words: people tend to disagree, but they are able to understand each other (provisionally) using language and higher-order codifications. A non-linear dynamics among possible reflections is expected in which nearly-decomposable perspectives can sometimes be stabilized (Leydesdorff 1997b).

The hypothesis of self-organization in social networks is one among the possible expectations, since the development of this network is complex. The hyperreflexive perspective of a super-observer's discourse, however, remains in this configuration more fragile than the infrareflexive arguments because the former has to be selected from the latter communications. Habermas' crucial assumption about a communality remaining latent in linguistic communication tends to become counter-factual when the counter-factuality of this assumption is not sufficiently understood. The complex communication culture can be maintained only when it is reflexively celebrated.

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