autopoietic systems - Constructivist Foundations

Theory of Autopoiesis

Biological–epistemological Concepts in the Theory of Autopoiesis

Autopoietic Systems: A Generalized Explanatory Approach – Part 2

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Hugo Urrestarazu • Independent Researcher • hugo.urrestarazu/at/wanadoo.fr > Context • In this paper I expand aspects of the generalized bottom-up explanatory approach devised in Part I to ex-

pound the natural emergence of composite self-organized dynamic systems endowed with self-produced embodied boundaries and with observed degrees of autonomous behavior. In Part I, the focus was on the rules defined by Varela, Maturana & Uribe (VM&U rules), viewed as a validation test to assess if an observed system is autopoietic. This was accomplished by referring to Maturana’s ontological-epistemological frame and by defining distinctions, concepts, and abstractions necessary to describe dynamic systems in any observational domain. This approach concentrates on pure causation flow rather than on domain-specific interaction mechanisms. > Problem • It is essential to analyze the requirements imposed by the VM&U rules on the “intra-boundaries” phenomenology for compliance with the selfproduction capabilities expected from an autopoietic system. Beyond what is merely implied by the compact wording of the VM&U rules, a key point needs to be addressed explicitly: how to describe some “peculiar” capabilities that the components should be endowed with to participate in new component production (as macro-molecules do in the biological domain) so that system’s self-production can be assessed. > Method • Using this approach, I first describe the process of constituting self-organized dynamic structures provided with embodied boundaries. Then I explain how a capability of self-organization emerges and how this results in ephemeral configurations that may evolve into self-regulated long-lasting dynamic system stability within a continuous causation flow inside the boundaries, up to the emergence of some “specialized” subsets of components. This explication allows us to distinguish the medium, the boundaries, and the core of a self-organized dynamic system and to focus attention on the “intra-boundaries” phenomenology that should be at the heart of self-production capabilities, as prescribed by the 5th and 6th VM&U rules. > Results • I propose an abstract, domain-free description of the “peculiar” composition and decomposition transformation capabilities that components should possess while subject to state transitions triggered within the “intraboundaries” causation flow. This is combined with a discussion concerning the “intra-boundaries” causation structure’s possible topological layouts that could be compliant with the 6th rule. > Implications • The above-mentioned results allow us to improve our analytic criteria when observing dynamic systems existing in non-biological domains in order to assess their autopoietic nature. They also reveal that the task of consistently identifying possible non-biological autopoietic systems is harder than merely identifying self-organized dynamic systems provided with boundaries and some observable autonomous behavioral capabilities in a given observational domain. More implications will be discussed further in Part III. > Key words • Autopoiesis, dynamic system, self-organization, self-production, boundary, autonomy, operational closure, causation, structure determined, meta-molecular, embodiment, interaction network, organizational invariance.

Introduction to Part II Due to space limitations, this paper has been organized into three parts that are not completely independent but are published separately. Part I was published earlier (Urrestarazu 2011); the developments of this part and Part III (to be published subsequently) refer to terminology, concepts, and developments presented in the previous parts. Above all, Part I is essential to understanding the terminology used in this and following parts and sections.

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Humberto Maturana, the original author of the concept of autopoiesis, and Francisco Varela addressed the biological domain exclusively, and described the concept using rigorous distinctions, definitions, and epistemological considerations. However, there is an ongoing debate about the possibility of identifying autopoietic systems in non-biological domains, such as social systems, economical organizations, or software and/or hardware entities (artificial life artifacts). The question is whether autopoiesis can be conceived as a domain-free rather

than domain-specific concept – regardless of Maturana’s and Varela’s opinions. In Part I, I defined some concepts that refer to a generalized notion of a realm in which autopoietic systems could be observed and identified as such, which I called the “observational domain.”1 I also proposed 1 | The meaning ascribed in this paper to the term “observational,” as derived from terms such as “observing” and “observer,” is meant to correspond to the notions explained by Maturana (1988). The term “observational domain” refers


Autopoietic Systems: A Generalized Explanatory Approach – Part 2 Hugo Urrestarazu

a general description of dynamic systems composed of dynamic entities (or objects) capable of performing state transitions and related to each other by observable causeeffect interactions, a view that allowed us to describe those systems as networks of causation flow and represent them with welldefined abstractions. These abstractions are useful to describe in a very general way the evolution of dynamic systems and to propose non-ambiguous distinctions for bringing forth generalized composite dynamic entities that behave as totalities existing in any observational domain. My aim is to go beyond the original purpose of explaining autopoiesis for biological systems by broaching a generalization of the concept in order to make explanations applicable to different kinds of observational domains. The concept of autopoiesis, as defined by the rules in Varela, Maturana & Uribe (1974, hereafter the VM&U rules), lends itself to an explicit generalization, provided that the focus is on the most common aspect of all possible types of dynamic interactions between system components, namely on their causation structure, regardless of any explicit description of particular physical interaction mechanisms responsible for the dynamic links established between system components. to any domain of perceived phenomena in which we, as human observers, can perform sensorial and operational experiences through interactions with the observable entities under consideration. It is assumed that any observational domain is a physical domain and that ordinary physical laws are applicable in it. These interactions should occur as phenomena pertaining to our own biological domain (i.e., phenomena of our own direct sensorimotor perception capabilities) or as indirect biological effects resulting from the use of suitable transducers (measurement apparatus). Hence, the attention is focused on the occurrence of humanly observable and describable events occurring in what appears to us as the ordinary physical space. This definition can be extended to software entities evolving in a virtual space since all simulated virtual “objects,” “events,” “causation flows,” etc., correspond to strictly isomorphic and traceable physical events occurring in a material substrate (hardware) that – by virtue of being humanly designed – is entirely accessible to human observation.

In Part I, I discussed the applicability of the VM&U rules to generalized meta-molecular domains, presented the basic definitions and conceptual tools used in a bottom-up explanatory approach for understanding dynamic systems, and presented an overview of the six VM&U rules (viewed as a validation test to qualify a system as autopoietic), explained and interpreted from within this explanatory approach. The present paper is an expansion of the above-mentioned explanatory approach applied to the explication of the natural emergence of composite self-organized dynamic systems endowed with self-produced embodied boundaries. The aim is to discuss the “intra-boundaries” phenomenology that should be observable with regard to the selfproduction of components and the topology of the components’ interaction structure, as required by the VM&U rules. Part III (to be published separately) will address several issues: the “scale of description problem” posed when trying to identify a possible autopoietic system; the relation between the “intra-boundaries” phenomenology and the fundamental notion of operational closure; and a discussion about the possibility of establishing a strict equivalence between the generalized notion of autopoietic system and the notion of living being. These developments are followed by the section, “Self critique,” where I discuss the validity of my bottom-up explanatory approach, and the section, “New reflection perspectives,” with a discussion concerning the potential use of the proposed methodology to analyze existing complex systems, to design and build artificial self-organized and autonomous systems, and to attempt to overcome the debate about the purported existence of non-biological autopoietic systems.

Self-organization and the embodied boundary In this section, I describe the time evolution of composite dynamic structures through stabilization, self-organization, and the emergence of a boundary. The terminology used here has been defined and explained in Part I of this work and it should be considered in both papers within a continuum of meaning.

For a better understanding of this bottom-up explanatory approach, I beg the reader to imagine the process of constitution of very general dynamic structures from multiple dynamic components that “become connected” to each other (for the observer) through interactive cause-effect coupling (Urrestarazu 2011: 314). This process is not what we usually encounter in practice: normally, we either observe dynamic systems as unities that are already constituted as a whole or we observe separate dynamic objects that we suspect or know to be part of a suspected larger unity. The very process of constitution is seldom observed as such, so this explanatory path should be considered only as a sort of “thought experiment” in which we, as observers, focus attention successively on different aspects of the dynamics of an already constituted system and sequentially produce descriptions of phenomena that in fact occur simultaneously. The autopoietic nature of an observed system needs to be assessed step by step, but the phenomenon of autopoiesis does not manifest itself either incrementally or progressively: in an autopoietic unity, all the conditions considered in the VM&U rules are achieved at once. The notion of a “dynamic system” used along this explanatory path does not refer to an autopoietic unity from the start but to a yet-unqualified general system put under observation and scrutiny. Using a bottomup approach, the focus is first on components and their mutual interaction relations in order to bring forth the composite unity in language and proceed to determine the kind of system that it could be. Prior to addressing the analysis of the requirements imposed upon the “intraboundaries” phenomenology for compliance with the self-production capabilities that autopoietic systems should show, according to Varela, Maturana & Uribe (1974), we need to understand how dynamic structures may self-organize themselves, produce an embodied boundary, and thereby be considered by observers as emerged entities. What follows is a step-by-step explanation process aimed at clarifying what I understand as the “intra-boundary” phenomenology. Only then will I be able to pay special attention to what happens “inside” the limits imposed by the emerged boundaries and give focus to the consequences derived from

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Biological–epistemological Concepts in the Theory of Autopoiesis 50

the application of the 5th and 6th component “production rules.” My aim is to depict the processes by which a general dynamic system may be described as following a path of structural changes and at the same time manifesting conservative properties. To bring forth what is subject to changes and what might be conserved (in space and time) within an entity composed of intrinsically dynamic and mutually interacting components is not a trivial exercise. In order to accomplish this bottom-up explanatory approach, I propose that the reader focuses on some considerations that will provide us with the basis for understanding the general abstract notion of organizational invariance, which is at the heart of the theory of autopoiesis. In the next sections I will discuss the natural but ephemeral “stabilization” of general dynamic structures, and the possible manifestation of long-lasting “stability” and of selforganization.

Natural “stabilization” of dynamic structures A dynamic structure being observed as an emerging entity within an environment of interacting dynamic objects may evolve naturally over time.2 This evolution is perceived as changes affecting the topological shape of its network of cause-effect relations (represented by a graph made of changing nodes and time dependent oriented relations, Urrestarazu 2011: 315). These network changes can be ascribed to state transitions occurring to its nodes as the outcome of the propagation of causation events. According to this view, the causation flow, resulting from the causal laws attached to underlying interaction mechanisms, produces self-sustained sequences of triggered state transitions in its connected components. 2 | I neglect here the case of dynamic systems that may become “static,” with no evolution in time (i.e., when all components reach states in which neither further causal interactions nor state transitions actually occur, but when they are still potentially sensitive (poised) to state transitions in other objects). Obviously, as long as it lasts, this situation might be also qualified as “organizational invariance.”


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One possible outcome would be the disintegration of the emerged structure by its splitting into several separated sub-structures (sub-graphs can be considered as separate if their respective nodes are not connected by any relational arrow) or even into isolated former components. The opposite effect would be also possible – i.e., an apparent integration or new coupling of “prior” environmental objects into larger composite structures (I will discuss this case in the section, “Component membership flow“). According to the specific characteristics of the interaction mechanisms at work, the observer may identify a tendency of dynamic components to remain coupled together. This tendency may persist and the resulting structure may become “stabilized.” I mean by this that the network of relations would not disintegrate or split “naturally” into several separate pieces while undergoing sequences of internal state transitions. It would grow or extend as a result of the state transitions and still be “stabilized” in the sense that the network connectivity would not break down. If this was observed, we could talk about “natural stabilization” in order to emphasize that there would be no point in searching for a “specially driven goal” or “trend” that would makes the system reach such a state. For an observer, it would be just a particular outcome of interactive structure determined phenomena that we may consider as one possible causal result among others. When we observe that a dynamic structure evolves into a “stabilized” configuration of relations it does not mean that all its components are definitively attached to it (we saw that components can enter and leave a dynamic structure, Urrestarazu 2011: 317). In such a situation, both external and internal interactions may change the structure of the dynamic system, but without provoking its disintegration, so that it continues to be observed as an identifiable subset of dynamic objects interacting together. In this sense, a “stabilized” dynamic structure is observable if the observer can represent the result of the propagation of triggered state transitions by means of a changing but distinct network of oriented relations – even if the resulting set of nodes and graph topology differs with respect to the original configuration observed prior to the beginning of the triggered state transitions’ sequences. Because of this com-

ponent membership flow, the graph topology can change (i.e., the relative connections between nodes can be rearranged), but it may do so in such a way that an identifiable subset of dynamic objects interacting together continues to be observable after the occurrence of a causation flow. Note that we do not need to qualify the resulting structure as something “similar” to the original structure, but just be able to identify it as a topologically connected structure of nodes (a single graph). In other words, in spite of the evolving membership of its components and of the changing interaction connectivity between components, the “stabilized” dynamic structure may continue to exist as a unity for the observer. In this case we can say that after the triggered state transitions’ sequences occur there is still an observable causation network showing a “dynamic steady state” configuration. This configuration is reached once the causation propagation flow has taken place and all possible “cascading” effects of the initial triggering transitions have settled in the whole network. The global state reached is dynamic because it is open to new causation propagation, but it is steady because, in the absence of externally triggered (or non-interactive, spontaneously provoked) transitions, a dynamic causation network continues to be observable, even if the resulting topology may differ from the original one. Further down, when addressing the explanation of organizational invariance, I will use this proposed distinction of a steady state configuration, which corresponds to a transient global state3 that the observer can ascribe to the system.

Ephemeral nature of dynamic steady states Whether a dynamic structure that has reached a steady state configuration can last indefinitely through time is another subject of discussion. For now, I will settle on the idea that it lasts sufficiently to be observable 3 | A global state is a particular instantaneous configuration of the states of all the components of a system at a given time; see Table 1 in Urrestarazu (2011: 318).



for a life span longer than the time necessary for the propagation of all the triggered transitions’ sequences within the network to occur. This consideration is necessary in order to distinguish between systems where a single wave of effect propagation continues endlessly in an apparent chaotic manner and those where a tendency to “stabilize” into identifiable configurations of relations is observable. It should be noted that it is the causation relationship that allows us to make the distinctions necessary to explain the emergence of a configuration of relations that have reached a dynamic steady state configuration. As phenomena occurring in the observational domain, causal effects occur in time (moment after moment). Hence, causation flow occurs in time, so that observers can make distinctions that are separable from one observation time to another. The identification of a causation flow allows observers to trace the interaction propagation path backwards and explain how a dynamic steady state is reached and how the configuration of relations is a result of a chain of successive interactions occurring in time. In other words, the self-organizing4 property of the system is explained by a history of a flow of deterministic state transitions affecting its components in which no instantaneous holistic “magic” is involved. Causal traceability is the only notion needed that is involved in this explanatory path, regardless of the nature of the underlying interaction mechanism responsible for the interaction flow. Such observed stabilized configurations of relations can be ascribed to organized sets of dynamic objects. What do we mean by that? Basically, that the corresponding composite unities may be described as possessing an emergent capability produced by the particular topology of their networks of oriented relations. This capability is explained as the outcome of the particular flow of interactions occurring within the dynamic 4 | Up to here, the words “organized,” “selforganized,” and “organization” are invoked in a broad colloquial sense, and are not yet related explicitly to the notion of “organization” as proposed by Varela, Maturana & Uribe (1974: 187–188) and by Maturana (1978: 33). I will address this concept in the section, “The search for an invariant.”

structure that allows the composite unity to be observable as an identifiable subset of dynamic objects among all the dynamic objects that interact together in a given observational domain through time. We call this property self-organization, where this term connotes the observation of an interaction process that leads to a steady state configuration as defined above. In the most general case, this achieved configuration is open to further externally triggered causation flows that may disrupt the unity thus emerged, so that any steady state configuration would most probably be a short-lived global state of the emerged structure. The particular way in which self-organization manifests itself is structure determined. By this, we mean that the self-organization process of a dynamically stabilized structure can be described by the observer as a consequence of the action of underlying interaction mechanisms responsible for all the cause-effect coupling interactions occurring within the composite unity and only within the composite unity. It is not causally dependent on any other triggering event occurring elsewhere in the observational domain where the stabilized configuration of relations emerges for an observer. One may argue that this account neglects the dissipative flux necessary to maintain the steady state against entropic disintegration and that the discussion has been oversimplified by neglecting the necessary energy flows coming from the external environment that keep the causal self-organization process going. However, these thermodynamic considerations are not addressed in this explanatory approach, which is focused on causation flow in a very general manner and assumes that all the physical conditions necessary for the occurrence of transitions in components are fulfilled (availability of energy reservoirs, energy flows, dissipation, local entropy reduction, etc., cf. Urrestarazu 2011: 320). Any observable phenomenon can occur only if all necessary physical conditions are present, but these are not the causes of specific structure determined phenomena such as self-organization. Up to here, my explanation of the emergence of a dynamic structure organized as a stabilized configuration of relations does not lead to a clear idea about the “frontier” or boundary between the unity and its environment.

In the most general case, any component of the system could interact with dynamic objects existing in the environment, provided that they reach states compatible with the occurrence of such interactions (which depend on the nature of the underlying interaction mechanisms). These interactions may either lead the composite unity to disintegrate or to evolve into new steady state configurations. The notion of an “identifiable subset of dynamic objects interacting together” implies that within an observed time interval no system component is affected by interactions with other environmental dynamic objects. If a dynamic steady state is reached at a given moment, it means that the dynamic structure has reached a state in which it changes only through interactions between its components, be it locally (the causation flow is limited to a few connected nodes) or globally (the causation flow propagates to the whole graph). An emerged dynamic steady state corresponds, in this sense, to a transient phase (a time limited global state) of an evolving dynamic structure during which only internal components’ interactions are observed to occur. If no steady state configuration is reached (i.e., the internal causation flow continues to produce endless self-sustained stochastic structure changes), it means that the observer would be unable to distinguish an identifiable subset of dynamic objects interacting together and the initial system would thus become non-circumscribable. The result of an internal causation flow may be a new relational configuration in which the new graph topology can either lead to a new dynamic steady state or not. Let us suppose that the overall causation flow results in a new steady state. If this condition repeats itself after each causation flow, these successive steady state configurations may be observed as a lasting dynamic structure existing/changing during a certain period and be considered thus as being in a single continuous steady state with an intrinsic self-sustained life span. In the most general case, the “frontier” between the unity and its environment could include the whole set of components belonging to the structure during the dynamic steady state period in which no other external interactions with the environment


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are observed to occur. In other situations, external interactions could affect only a subset of components. In an extreme case, only one component could be interacting with the environment. In all cases, the most probable situation is that the interaction structure is continuously open to interactions with the environment. Externally triggered state transitions impinging on the mutually interacting objects may disrupt the steady state condition of the emerged structure, either by reacting to transitions occurred in environmental objects or by being affected by globally acting5 causation mechanisms. In the absence of external interactions, the life span of a configuration of relations showing a dynamic steady state is completely structure determined. Nevertheless, it may also be affected by interactions with environmental dynamic objects that could provoke transitions unpredictably (i.e., transitions that are not determined by the interactions occurring within the system) in one or more components of the dynamic structure.6 In other words, the structure determined property of self-organization of an evolving dynamic structure can be ephemeral in the face of external interactions.7

Emergence of long-lasting self-organized dynamic systems Given the ephemeral nature of a dynamic steady state, it is necessary to highlight the fact that long-lasting self-organized dynamic structures are observed to emerge in some observational domains. Observation of a long-lasting self-organized system 5 | Globally acting causation mechanisms are environmental events that produce synchronous or asynchronous effects on all the components of a dynamic system, regardless of the topological configuration of its internal interaction network (i.e., changes in temperature, pressure, intensity of a force field, etc.) 6 | Maturana (1988: 15) calls this the “instantaneous domain of the possible perturbations of the composite unity.” 7 | “[I]nstantaneous domain of the possible destructive interactions of the composite unity” (Maturana 1988: 15).


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means observation of a non-interrupted succession of dynamic steady state configurations in the continuous causation flow between the system and the environment. What threatens the persistence of a stabilized configuration of relations and may reduce its life span? On the one hand, we need to consider the internal structure determined evolution phases of the interaction network itself, because some or all connected dynamical objects may naturally reach states in which they no longer participate in a previously emerged structure (i.e., the topology of the graph changes in a way in which multiple nodes become isolated and/or the graph breaks down into several separated pieces). On the other hand, the observed stabilized structure is subject to unpredictable disrupting effects produced by environmental encounters. However, in spite of these unpredictable events, we observe the emergence of long-lasting selforganized dynamics systems. How can this be accomplished? The first approach is to think about homeostatic dynamic structures in which some self-sustained structure determined mechanisms are always available to compensate for disruptive external interactions.8 Which is the homeostatic variable that is controlled by such mechanisms? This is a tricky question because we are dealing with a swarm of continuously evolving dynamic objects performing endless state transitions and in this endless causation flow apparently nothing remains constant through time. We need to search for a describable feature of the dynamic system that remains invariant throughout all the history of state transitions affecting its components (I will show further down that this feature corresponds to the system’s organization: see the section, “The search for an invariant”). We can imagine some possible ways by which a system may achieve long-lasting stability. One way could be, for example, to limit the impact of external interactions by reducing somehow the scope of the propa8 | Neither the nature, nor the origin, nor the way of action of these compensation mechanisms can be properly discussed in this domain-free explanatory approach because they would be specific to the interaction mechanisms available in a given observational domain.

gation of triggered transitions within the interaction network so that their causal effects produce only minor perturbations to the dynamic structure. A minor perturbation is an interaction that modifies the topology of the network of relations only locally,9 leaving the rest of the structure unchanged. This consideration has led many authors to focus on the role that a protecting “boundary” could play in limiting the effects of external potentially disruptive interactions with the environment. I will analyze this approach in the next section.

Emergence of structure determined boundaries A dynamic system can achieve a global state in which some of the components reach states in which they do not interact with environmental dynamic objects and some of the components reach states in which they interact with environmental dynamic objects only through “local” neighborhood causation. This means that we can distinguish a subset of components that is “specialized” in performing all possible interactions of the whole structure with environmental dynamic objects situated in the causal neighborhood of the components of this subset. If this distinction is based on observed interaction phenomena (i.e., the system under scrutiny complies with the 4th VM&U rule10) the subset corresponds to a 9 | I remind the reader to keep in mind that the term “local” does not refer necessarily to “spatial vicinity” but to direct cause-effect coupling between dynamic objects. Spatial vicinity is a particular case in which one of the state variables involved in causal interactions corresponds to the position of objects in space (mutual distance dependency). In general, the notion of “locality” refers to the existence of a direct oriented relation linking a node to its “causal neighbors” in the multi-dimensional relational space. 10 | “[T]he components that constitute the boundaries of the unity constitute these boundaries through preferential neighborhood relations and interactions between themselves […] If this is not the case, […the observer is] determining its boundaries, not the unity itself.” (Varela, Maturana & Uribe 1974: 193). See also the section, “Selfreferential” in Urrestarazu (2011: 322).



self-generated substructure of the system at a given moment of its dynamic evolution. Thus, we can say that this “specialized” substructure constitutes an instantaneous “frontier” between the system and the environment. Furthermore, if these “local frontier” interactions do not induce disruptive causation propagation within the whole dynamic structure, we can say that the “frontier” components act as a shield for the whole causation network with respect to cause-effect couplings originated by triggering transitions undergone by “external” dynamic objects.

The role of the identification of a boundary The distinction of an emerged boundary is just a step in the generative process of identifying a dynamic system as an autopoietic unity. Pertinent hypothetical distinctions made by an observer should coincide with the observation of components linked to the system in such a way that they can be described as nodes of the corresponding graph (network of oriented relations) representing boundary components (as I will discuss below). Only then can the observer claim that a described boundary is structurally determined by the system itself and not by the observer’s distinctions. This distinction-observation-description-explanation process is just a step because it still does not guarantee that the entity distinguished in this way is definitely autopoietic. From the proposed definition of a boundary that I propose in the next paragraphs, it will become evident that nonautopoietic dynamic structures may be endowed with boundaries as well and the identification of such a “specialized” subset of components in a composite unity does not guarantee the existence of a compensating mechanism responsible for the conservation of its organization through time. Moreover, an accreting self-organized system can have no “boundary” at all (as defined above). I mean by this that all of its components may interact with the medium (in which case we could say that the whole system is a boundary without an “inner core”) provided that the compensating mechanisms at work are able to maintain homeostatically a sustained

Medium objects in the observationaldomain Boundary components of an emerged system Core components of an emerged system Oriented relation (cause–effect interaction) Figure 1: Example of graph showing the “connectivity” between medium, boundary, and core related dynamic objects at a given time.

(non-interrupted) succession of dynamic steady states within the system through time (in the sense defined above). Intuitively, the notion of a boundary is also invoked as a “mediating structure” for the interactions of the system with its environment. I will address this notion in the next paragraphs.

Definition of a boundary

In order to better understand how these considerations are related to the notion of boundary, I propose to use the following distinctions in the languaging domain11 (they are illustrated graphically in Figure 1). 11 | I recall that the term “languaging domain” refers to the domain of human conversations in which language, conceived as a consensual coordination of consensual coordinations of behavior between humans, is the fundamental interaction used by scientific observers to express their descriptions of their experiences performed in the observational domain under consideration, to explain their operations of distinction, and

1 | The “medium”12 of a dynamic system is the set of all dynamic objects existing in the observational domain that do not belong to its structure (i.e., that cannot be represented as connected nodes of the equivalent graph, but can be described by means of the same set of state variables). The medium is a part of the environment, namely the collection of those dynamic objects that are potentially capable of becoming components of the dynamic system. 2 | An object pertaining to the medium may interact with objects pertaining to an emerged dynamic structure, but the oriented relations representing to formulate their claims about phenomena observed within these domains. 12 | This definition of “medium” is not isomorphic with Maturana’s wider notion used in the case of molecular systems, where he distinguishes a “molecular medium” and a “non-living medium,” for example (Maturana 2002: 7–8 and Maturana 2002: 17).


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such interactions should go only from the medium component to the system components. In other words, a medium object may trigger transitions on system components but not inversely (otherwise the medium object would be a node “connected” to the graph representing the system and, thus, would be a system component). 3 | A system component interacts with the medium if it interacts directly with at least one dynamic object of the medium (i.e., it is “sensitive” to a state transition occurring in the latter). An interaction of a system component with a medium object is called an external interaction. All other interactions affecting a dynamic system component are called internal interactions.13 4 | The “boundary” of a dynamic system is a subset of components having reached states in which they are subject to external interactions. Boundary components may interact or not with other boundary components. 5 | The “core” of a dynamic system is a subset of components that have reached states in which they are not subject to external interactions. Core components may interact or not with boundary components.

Boundary features

1 | A boundary component, as a member of the interaction network, interacts with at least one core component, either directly or indirectly via another boundary component. 2 | We can say that a boundary component absorbs an external interaction if, after the occurrence of the interaction, it reaches a state in which it interacts only locally with neighbor core components (i.e., it does not provoke the propagation of chained interactions14 to the core of 13 | It is to be noted that there are also other external causes that may trigger state transitions in the components of a system that are not due to interactions, either with medium dynamic objects or with other components: these may be globally acting causation mechanisms affecting all components. 14 | The term “chained interactions” refers to the successive state transitions affecting groups of topologically connected nodes as a consequence


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the dynamic structure). Nevertheless, it may induce the propagation of chained interactions in the boundary, provided that the propagation does not reach core components. 3 | We can also say that a boundary component transmits an external interaction if, after the occurrence of the interaction, it reaches a state in which it provokes the propagation of internal chained interactions to the core of the dynamic structure. 4 | Concerning the transmission of external interactions, we could also qualify the properties of the whole boundary set with adjectives such as: a | opaque,15 if all boundary components absorb all external interactions; b | or translucent, if some boundary components transmit external interactions to the core and are opaque elsewhere; c | or transparent, if all boundary components transmit external interactions to the core. One may argue that I might be defining the notion of “boundary” with exclusive regard to an “outside-in” perspective by describing it in terms of the “peripheral extent” of the medium’s effects on the given composite unity. In contrast, in their literature, Maturana and Varela address the “boundary” issue in a manner that may be called “inside out.” The latter relates to the consideration that in autopoietic systems, the boundary may be discerned as the peripheral extent of the self-producing processes intrinsic to these systems (the boundary is where the constitutive processes/structure of the unity “end”). The definition proposed here admits that both dynamic objects pertaining to the of an initial state transition triggered in one of these nodes. 15 | I use here the adjectives “opaque,” “translucent,” and “transparent” where other similar related words could be used (“tight,” “porous,” and “loose,” for example). To avoid confusion I deliberately neglected the use of “permeable,” “semi-permeable,” and “impermeable” since in biological terminology they are used to connote the movement of components across a boundary (membrane), not the transmission of causal effects.

medium and components pertaining to the core may become boundary components at any time. The only imposed conditions are that they should be connected to the interaction network and be found in states in which they may be affected by external interactions with the medium. The interactive events that contribute to the “self-emergence” of the boundary are neither “outward” nor “inward” directed; they are just the outcome of the cause-effect mutual relationships established between generically described dynamic objects pertaining to either the medium or the core that may integrate the boundary according to the states in which they might be found at a given moment. In fact, this definition applies to a wider spectrum of dynamic systems and the “boundary” is not seen as an exclusive and defining characteristic of an autopoietic unity per se, which means that it cannot be used as a the sole discriminator in attributing “autopoiesis” to an observed composite dynamic system.

Boundary cases

By definition, the presence of an opaque boundary would prevent the disruption of the configuration of relations within a dynamic composite unity provoked by external interactions and a long-lasting stability could be achieved in this way. If a composite unity is “encapsulated” by an opaque boundary, the graph topology corresponding to the connected core components cannot be changed by interactions with the medium, as all external interactions are absorbed by the boundary, propagating interactions only within the boundary. So, if the boundary does not disintegrate, the only way by which the core could disintegrate is by its own internal dynamic evolution (remember that disintegration can always happen if this evolution leads to graph topologies where the causation flow does not lead to stabilized steady states). For the moment, I will concentrate on composite unities that do not disintegrate spontaneously (i.e., where their self-organization mechanism is such that all possible instantaneous global states reached through the internal causation flow correspond to steady states with an unlimited life span). As an example, think about an isolated vegetable seed in the biological domain.



Under certain circumstances (humidity, temperature, presence/absence of light), the nutrient or toxic macromolecules existing in the medium cannot interact with macromolecules existing inside the husk of the seed. The husk acts as an opaque boundary shell that absorbs all external interactions of the seed with the medium. Nevertheless, the internal network of relations of the macromolecules within the seed might still evolve dynamically according to its specific self-organization mechanisms as it is still subject to the ability of the encapsulated components to continue operating without external interactions. Now, let us examine the case of a composite unity with a translucent boundary, that is to say, a self-organized system in which some external interactions can be transmitted to the core. A chained sequence of internal structure determined interactions can occur and lead to a new configuration of relations between the components of the composite unity. Two situations are possible: a | a new stable global state is reached through rearrangement of the graph topology; b | no stable global state is reached and the interaction propagates indefinitely, leading to a breakdown in the graph topology (i.e., the system’s self-organizing mechanisms are no longer capable of preserving the existence of the system as a single recognizable composite unity). In the first case, we can say that the system “compensates” for the external interaction, and in the second case that the system “yields” to the external interaction. It is the nature of the interaction mechanism that will determine if the self-organized composite unity compensates for external interactions and continues to exist, or if, by yielding to them, it disintegrates.16 16 | I mean “disintegrates” when the observed system “ceases to operate as a single composite unity.” Another possible outcome would be that the system became “something else,” in which case I would prefer to use the verb “to yield.” It is to be noted that Maturana extends the notion of “disintegration” to the case of a “mutation” of the system into “something else,” which could well be a “different” composite unity in its own right: “The structure of a system can undergo changes

Following the logic of the previous example, think about the same seed placed in a humid environment. The presence of water would make the husk porous, as diluted macromolecules could cross the shell and reach the core of the seed. Biochemical reactions between internal seed macromolecules and incoming macromolecules may occur. If these are nutrient macromolecules, the chained sequence of interactions may lead to seed growth (non-disruptive rearrangement of the graph topology). If they are toxic macromolecules, the chained sequence of interactions may lead to the seed’s death. We can say that for a specific type of interaction, the ability of an observed composite unity to compensate for external interactions is wholly structure determined: at the time when an external triggering event occurs, the manifestation of a compensating mechanism depends only on the configuration of the interaction network (i.e., on the instantaneous topological shape of the corresponding graph and the instantaneous states of its nodes). But, it is to be noticed that these considerations are also applicable to the extreme case of a composite unity with a transparent boundary. In this case, external interactions are not absorbed by boundary components: the boundary is not a “protective” shield for the system. The ability of the composite unity to compensate for interactions with the medium could depend exclusively on adequate dynamic rearrangements of the graph topology by following a path of successive stable global states in which this ability was preserved through time. The distinction of a boundary is useful only to bring forth the composite unity and separate it from its environment (for an observer), but the presence of a boundary cannot be invoked as a necessary condition when explaining the ability of the composite unity to compensate for external interactions. Only in some particular cases of dynamic systems existing in particular observational domains could the presence of a boundary be invoked as a suffithrough which the organization of the changing system (its class identity) is lost, is not conserved. I shall call these changes disintegrative changes […in which] the original system disappears and something else arises in its place” (Maturana (2002: 16).

cient condition to explain the system’s ability to compensate for external perturbations. An example of dynamic system possessing a transparent boundary is the immune system, which constitutes a distributed dynamic network composed of cells populating the whole organism as a medium (Varela et al. 1988). The ability of this system to produce compensating reactions against perturbations produced by external agents, and to continue to exist as a network, does not depend on the presence of an “absorbing” boundary. The network produces a delocalized17 self-identifying mechanism involving the participation of uncountable “non-contiguous” components that results in perturbation compensation. In fact, an opaque boundary merely avoids disruptive external interactions by “encapsulating” the system and a translucent boundary only “filters” some external interactions out. The overall ability to compensate for external interactions is a conservative capability of the whole dynamic system expressed through structure determined rearrangements of its network of relations (graph topology evolution). These rearrangements are induced by the chained sequence of interactions triggered in its boundary and in its core alike. Through these examples we may be led to the conclusion that the boundary could be considered as a mediator structure that “protects” the system from external disruptive perturbations. This is true only with respect to components’ interactions with medium dynamic objects. However, we must keep in mind that the medium is only part of the environment. Apart from interactions with dynamic objects, there could exist external events triggering state transitions in core components without affecting boundary components and there could be observable state transitions occurring (synchronously or not) in all components due to globally acting causation mechanisms observable in the domain being considered. These are influences capable of inducing effects in core components without any mediation or “relaying” by the boundary components. For example, we may consider 17 | The identity of the immune system “provides a surface for interaction, but it’s not evident if you try to locate it. It’s completely delocalized […]” (Varela 1995: 211).


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the effects of targeted radiation therapy on internal cells of the body. Such effects are physically realized in the inner cells, but they are in no way mediated by the boundary components (which are essentially “bypassed” by the effective confluence of electromagnetic beams).

The search for an invariant Any rearrangement induced on the graph topology is an outcome of the causation flow among dynamic objects (the nodes of the graph). Structural changes occur through such rearrangements (changing node connectivity). The causation flow may result in the loss of some nodes (some components leave the system, becoming medium dynamic objects) and the acquisition of new nodes (medium dynamic objects become system components). Also, some connections between nodes may disappear and others may be established. This is the picture that we can gather if we consider only cause-effect coupling interactions between already existing nodes that are subject only to changes of state. We will discuss later the case in which nodes might be also subject to “productive/destructive transformations.” The capability of a system to compensate for disruptions provoked by successive external interactions by maintaining an interrupted succession of steady states is a conservative property of the system. This does not mean the conservation of the members of the set of components nor of the number of components of the composite unity. Neither does it mean that the system reaches a global state identical to the global state in which it was before any external interaction occurred. It only means that the flow of interactions continuously produces new topological arrangements of the network of relations in such a way that all global states reached are steady states, whatever the configuration of relations may be at a given time. When a composite unity shows this kind of behavior and is also capable of producing a structure determined compensating mechanism that is repeatedly available after each graph rearrangement then we can say that the composite unity conserves a particular kind of configuration of relations, namely its


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organization (for a specific type of interaction with the medium). Maturana’s notion of “organization”

“

refers to the relations between components that define and specify a system as a composite unity of a particular class, and determine its properties as such a unity. Hence, the organization of a composite unity specifies the class of entities to which it belongs. It follows that the concept or generic name that we use to refer to a class of entities points to the organization of the composite unities that are members of the class. (Maturana 1978: 32, my emphasis)18

”

The maintenance of the configuration of relations that define the system as pertaining to a specific class of systems means conservation of its organization. Here, the class of system being considered is composed of all those systems that, due to their internal dynamics, evolve, moment by moment, by reaching successive global steady states, and are provided with compensating mechanisms repeatedly available after each graph rearrangement provoked by external perturbations. This is the invariant feature that we were searching for. The system behaves as an autonomous homeostatic “device,” where the “self-controlled” variable is its own organization. Everything can change: structure, component membership, medium objects; but the organization is preserved as long as a compensating mechanism is available after each encounter with the medium. Up to here, we have said nothing concerning the way of action of those compensating mechanisms so that, in principle, and depending on distinctions related to their nature, it would be possible to distinguish distinct classes of systems endowed with organizational invariance. Autopoietic systems pertain to one of these classes. 18 | Varela, Maturana & Uribe (1974: 188) provide a similar definition: “[…] It is these relations which define a complex system as a unity and constitute its organization. Accordingly, the same organization may be realized in different systems with different kinds of components as long as these components have the properties which realize the required relations. It is obvious that with respect to their organization such systems are members of the same class, even though with respect to the nature of their components they may be distinct.”

Component membership flow Among other outcomes, a compensating mechanism can result in a systematic acquisition and/or loss of nodes in an equivalent graph. In the case of node acquisition, medium objects acquire the status of components, and in the case of node loss, components become medium objects. We saw (Urrestarazu 2011: 317) that medium objects may become components of a given dynamic structure if they share at least one state variable with system components and reach states in which they interact with at least one component.19 Let us look more closely at this point: according to my previous definitions, an object belonging to the medium interacts with system components only in one way: at a specified time it triggers state transitions on them, but – by definition – it is not affected by state transitions occurring in component objects within the system’s internal interaction network. By undergoing a state transition or as a consequence of transitions occurring in system components, at another later time it may become “sensitive” to further transitions occurring in at least one system component. If this happens, the object belonging to the medium becomes a component of the system, as its equivalent multi-dimensional representation becomes a node of the graph representing the system (a new oriented relation appears, starting from a previously existing graph node that “points” to the former medium object). This is the mechanism of accretion involved in component production by “cooptation” of medium objects. Accretion is an almost inevitable result. When a composite unity systematically acquires new dynamic objects as components without disintegrating, I propose to say that the composite unity is an accreting self-organized system. Conversely, components may lose their status if, after participating in network rearrangements, they reach states in which 19 | Again, I only consider here the causeeffect coupling interactions between already existing dynamic objects that are subject only to changes of state. We will discuss later the case in which nodes might be also subject to “productive/ destructive transformations.”



they are no longer “sensitive” to other components triggering transitions and thus become medium objects. The loss of components is also an almost inevitable result. Through this continuous component membership flow, the overall component balance may be negative or positive and be subject to self-regulation through the action of emerged structure determined mechanisms. This self-regulation may imply a control over both the loss and the acquisition of components that would maintain the system within certain limits of upper and lower size. When a composite unity self-regulates its component membership flow, I propose to say that the composite unity is a stabilized self-organized system. I think that the distinctions proposed so far allow for a partial generative explanation of the processes responsible for some of the basic properties involved in the emergence of an autopoietic composite unity as deduced from the VM&U rules. Beyond its self-organization capability, an accreting or stabilized self-organized system provided with compensating mechanisms for all types of interactions involved in the constitution of its network of relations is what can be inferred from the VM&U rules as a necessary (although not sufficient) condition to determine if a composite unity is an autopoietic system or not. In this sense, we may conclude that an autopoietic system – beyond plain organizational invariance – is also capable of “coopting” medium objects as some of its own components by accretion in the realization of the conservation of its organization. Strictly speaking, this is not an internal component “production” mechanism, as I will discuss later in the section, “Self-production “inside the boundary”” but just an aspect of the mechanisms involved in self-organization and in the realization of the organizational invariance of the system. These are not the only observational criteria considered in the VM&U validation test (see Urrestarazu 2011: 320). I will explain the additional requirements below, but up to here we can say that accreting and stabilized self-organized systems are just particular cases of long-lasting self-organized systems.

Intra-boundary requirements The main purpose of this work is to emphasize the particular role played by the notion of component self-production, as stated in the VM&U rules, considered as a central criterion for identifying autopoietic unities. This notion is more restrictive with respect to self-production capabilities than most considerations usually discussed when trying to apply the definition of autopoietic entities to systems existing in non-molecular observational domains. The distinctions and generative explanations proposed so far in order to observe and distinguish structure determined boundaries, self-organization, organizational invariance, and “trans-boundary” component flow are related to the first four rules. The last two rules reviewed in Part I (Urrestarazu 2011: 322–323) are related to the component self-production requirements that are to be expected from autopoietic systems with respect to transformation capabilities of components and to the topology of the interaction structures resulting from the components’ coupling activity. In the following sections I will refer to some key considerations addressed by Maturana in his following statement: [W]hile answering questions about whether “ there were other autopoietic systems in other domains, and whether they were living systems or not, I thought that it was perhaps possible that autopoietic systems could exist in domains different from the molecular one. However, as I have become more aware of the uniqueness of the molecular domain, I have realized that it is only in the molecular domain that systems like living systems can exist because it is only in this domain where autopoiesis can take place […] The molecular space is peculiar in that: (a) It is constituted by dynamic composite entities (the molecules) that as a result of their interactions produce through composition and decomposition elements of the same kind (namely new molecules). (b) The composition and decomposition of the elements of this space (the molecules) occurs while these elements exist as composite entities under thermal agitation that operationally constitutes the energy for their composition and decomposition. (c) The course of the compositions and decomposition to which the elements of this space give rise in their

interactions is determined at every instant by the dynamic architecture (the structure) of the interacting elements (the molecules). (Maturana 2002: 14)

”

My aim is to express these considerations in terms of the generalized abstract notions proposed in this explanatory approach in order to render them applicable to the analysis of dynamic systems observed in observational domains other than the biological-molecular realm.

Component properties

It is important to notice that the 3rd VM&U rule is essential to emphasize that the observer’s focus should be centered on the organizational aspects of the composite unity under observation. By stating that the properties of an autopoietic system should be explained as the “outcome of the relations between components and not as the expression of properties of the component themselves” (Urrestarazu 2011: 313), this rule points to the kind of distinctions that observers should consider as pertinent to explain the possible emergence of autopoietic behavior and, thus, let this feature become eminent and recognizable. This requires some detailed considerations. One may possibly argue that “properties, as the outcome of the relations between components,” emerge from the properties of the components themselves. In fact, the higher level features or properties of a composite system may be operationally contingent upon lower properties of the components. Another way to put it is that whatever happens and is observed at a macroscopic level cannot be dissociated in fine from the deterministic outcomes of underlying microscopic phenomena. Because components can be described by means of a set of state variables whose values change in a specific manner according to the cause-effect couplings with other components, questions such as “why, when, and how” these values are subject to transitions, or “what” do these variables represent in terms of observable phenomena occurring within single components, cannot be answered without a lower level explanatory approach. Of course, this is a scientifically legitimate stand, though inappropriate for our explanatory purposes.


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In this proposed explanatory approach, this is a matter of focus: components are described as totalities provided with some dynamic properties and our analysis is deliberately limited to the description of the outcomes of their mutual interactions. We will later see in the section, “Consequences of the ‘production rules’” that the components of autopoietic systems should be endowed with some specific properties, for example, concerning their ability to participate in the production and destruction of other components. However, I avoid a reductionist attitude and do not enter into a description of the “intra-component” phenomena that would explain these properties. The reductionist attitude,20 by demanding systematically the lowest level explanatory path (at the atomic scale, for example), forestalls the possibility of making the systemic organization noticeable. When dealing with a higher level phenomenon such as autopoiesis, it is natural to consider that the scale of description of the causation network is at least necessary in any explanatory approach.21 However, when dealing with an observed system in a specified observational domain it might not be sufficient to generate explanations concerning systemic self-organization and self-production without referring to some specific components’ properties that explain the manifestation of specific interaction mechanisms at work. But this contingency does not impose a lower level scale of description applicable to the whole system. In this approach, I aim to deal with nonspecified observational domains and therefore I will describe components’ properties only with respect to the necessary relational outcomes of their manifestation. This criterion will be applied to the description of the component production properties presented below in the section, “A generalized description of component production mechanisms.” 20 | I will discuss the reductionist attitude further in Part III. 21 | “In a mechanistic explanation the relations between components are necessary […],” and “[…] the observer explicitly or implicitly accepts that the properties of the system to be explained are generated by relations of the components of the system and are not to be found among the properties of those components.” (Maturana 1978: 30)


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Self-production “inside the boundary” I was able to show that a mechanism of component acquisition by accretion can be explained simply as a result of the history of the system’s flow of causation while encountering objects in the medium. Indeed, we saw that to explain acquisition of non-components there is no need to refer to any special property of the components themselves, provided that all objects are of the “same kind.” In this explanatory path, two dynamic objects are considered to be of the same kind if their dynamic states at a given time can be described by the observed variable values of a unique set of variables common to all objects, i.e. – they share the same multi-dimensional relational space. That is to say, the evolution in time of each object can be described as state transitions seen as changes occurring in the values of any variable belonging to this unique and common set of variables.22 But accretion is a general mechanism that is not specific to autopoiesis and is a phenomenon related directly to the activity at the boundaries, where components are “in contact” with the environment. The two last VM&U rules (cf. Varela, Maturana & Uribe 1974: 193) refer to a different component production capability occurring inside the boundaries. This capability is specific to autopoietic systems and does not necessarily involve the system’s boundaries. The 5th VM&U rule reinforces a simple accretion capability by stating that component production should also be observable as the outcome of transformations undergone by existing components. This requirement implicitly demands some additional distinctions concerning the ability of components to undergo transformations resulting in component production. Varela, Maturana & Uribe (1974) did not specify, either explicitly or in general, which particular components’ 22 | This definition is intended only as a way of abstracting the observable features of dynamic objects that are pertinent to describing their observed mutual cause-effect relationships. A chosen set of variables is not meant to represent all the distinguishing features that could be ascribable to dynamic objects in a given observational domain, but only those features that play a role in the type of interactions under scrutiny.

capabilities would be necessary to meet this particular requirement. In this work, I intend to be more specific on this issue. Moreover, the 6th rule reinforces the component production requirements even further by stating that: a | all system components should be produced as a result of interactions occurring between system components; b | all system components should participate, through interaction with other components, in the production of system components (however, this rule accepts the case of components not produced by interactions between other components provided that they do participate as permanent constitutive components in the production of other components). It is my opinion that these requirements are more fundamental for identifying an autopoietic system than the mere distinction of emerged boundaries. In fact, they are more specific to the kind of phenomena that characterizes living beings than the sole boundary identification criteria that are also applicable to a more general and wider range of dynamic systems. The VM&U rules requirements for component production refer clearly to phenomena occurring inside the boundary of the observed dynamic system. Component production is not only an outcome of the encounters of the system with its environment, but it is primarily the result of the autonomous dynamic activity of the system itself and it involves both – the boundary and the core of the system alike. Component production can take place in the absence of external interactions triggered by medium dynamic objects: it is also an activity sustained internally by the system’s components interaction dynamics. Thus, the distinctions necessary to observe and discriminate an autopoietic system existing in a given observational domain must go beyond the distinction of boundaries. These distinctions concern the network transformations that may occur as an outcome of external interactions and internally sustained interactions. Nevertheless, when for a given system we fail to demonstrate that phenomena occurring in the core are compliant with the MV&U production rules, it does not mean that the said system is deprived of a certain level of autonomous dynamic activity. The



highest levels of “autonomous behavior”23 are attained by autopoietic systems precisely because their whole component build-up process may be accomplished by means that are completely (or to a large extent) independent from environmental encounters.

a. Externally triggered network transformat

At a first glance (see the example graphs in Box 1), the evolution of a network of oriented relations in time, from one successive steady state to another, is characterized by three basic types of transformations occurring in the network topology: a | accretion and/or loss of nodes through the boundary; b | production of new oriented relations and/or destruction of existing oriented relations; c | inducement of state changes in all causally connected nodes affected by a succession of interactions. Yet, in autopoietic systems, a fourth kind of transformation occurs: node transformations giving rise to new internally produced nodes or to the destruction of existing nodes. We will see below that these node transformations are mainly triggered internally and obey phenomena occurring almost24 entirely within the system (in its core and its boundary alike). The three kinds of transformations described above are structure dependent, as they are the outcome of individual state transitions occurring in causally connected nodes subject to triggered transition sequences following the propagation paths allowed by the initial graph topology. However, they occur as a consequence of interactions between boundary components and objects belonging to the medium and in this sense they may occur unpredictably (in relation to internal interactions within the system), depending

23 | In Part III of this work, I will develop further the notion of “autonomy” and its closely related notion of “operational closure,” as discussed by Varela (1980). 24 | Some phenomena occurring in the environment may also influence the self-production of components within the system, such as globally acting causation mechanisms such as the ambient temperature in the case of molecular systems.

on the history of cause-effect encounters of the system with its environment. These transformations are not independent of each other because they are the outcome of the specific underlying interaction mechanisms responsible for cause-effect coupling between components, which are in turn determined by the specific properties of the components under scrutiny in a given observational domain. We have to keep in mind that, in terms of events occurring in the observational domain where components exist, it is the nature of these causation mechanisms that determines the state in which every component will be found after achievement of all the interactions occurring within a time limited causation flow. Also, the creation or destruction of an oriented relation linking two nodes depends on the particular end-states reached by each of them after the respective transitions have occurred to both nodes. The existence of an oriented relation between two nodes means that the component represented by one node is “sensitive” to a change of state occurring in the component represented by the other node or, in other terms, that a dynamic change of state occurring in the latter “affects” the first one because they are causally connected via the underlying interaction mechanism. The role of this mechanism is determinant for the specific network configuration attained after all the above-mentioned transformations occur. The end-state of a particular component also depends on the timely order in which several successive interactions affect it during the cascading flow of interactions, that is to say, it depends on interaction propagation speed, on the number of intermediate steps, and on the cause-effect delays occurring in those intermediate steps. This dependency on interaction propagation speed is an essential feature of observational domains because it affects the order in which transitional events occur in an interaction propagation flow: in fact, the order in which cascading transitions occur affects all the deterministic outcomes of the propagating interactions. The notion of a “succession of dynamic steady states” (see above, section, “Emergence of longlasting self-organized dynamic systems”) implies that there is a timeframe bound to be considered for the propagation of causation flow until the whole network settles

into steady states after being perturbed by external interactions: a sort of network characteristic “relaxation time.”25 This “relaxation time” would depend on the network’s characteristic interaction propagation speed and on the structure determined “extent” of the propagation within the network. If external perturbations occur within time intervals shorter than this “relaxation time,” the network would be submitted to excessively frequent perturbations and this could hinder the achievement of successive steady states. From these considerations, we conclude that interaction propagation speed and intrinsic components’ state transition delays should be taken explicitly into account in any attempt to formalize the dynamic system (i.e., by means of a suitable mathematical model) as an abstract entity evolving in the associated multi-dimensional relational space.

b. Internally sustained network transformations

Focus is given here to transformations occurring mainly in the core of the system and due to internal interactions between components. In autopoietic systems, a specific kind of transformation occurs that affects not only the topology of the equivalent graph but also the nodes themselves. I will refer here to node transformations that give rise to new internally produced nodes or to the destruction of existing nodes. Moreover, as a consequence of these node production and destruction transformations, new oriented relations are created and existing relations are destroyed as well (I describe these transformations below). This activity entails permanent structural changes in the system’s interaction network, even when external interactions are not actually involved in component acquisition via accretion. These internally sustained network transformations also depend on the nature of the underlying interaction mechanisms. However, as far as autopoietic systems are concerned, they strongly depend on the nature of the dynamic objects themselves. We 25 | Usually, the notion of “relaxation” is employed in physical sciences to connote the return of a perturbed system to equilibrium and this relaxation process can be characterized by a relaxation time. Dynamic systems are far from equilibrium, so the use of this term is not strictly appropriate.


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BOX 1: Example of network transformations R(A , B)


A[1]

60

A[2]

B[1]

B[2]

R(A , C)

R(A , D) R(D , C)

C[1]

D[1]

R(D , E)

R(E , C)

time

E[1] R(F , D)

E[2] R(E , F)

R(E , F)

R(F , G)

R(C , G)

R(G , E)

R(G , E) F[1]

C[2]=C[1]

D[2]

G[1]

F[2]

R(F , G)

Medium objects in the observationaldomain

Core components of an emerged system

Boundary components of an emerged system

Oriented relation (cause–effect interaction)

G[2]

The left figure represents the graph of a relational network before a state transition occurs in external object A, which belongs to the medium and is in state [1], (denoted by A[1]). The right figure represents the graph of the resulting relational network after the occurrence of triggered transition sequences propagation induced by the state transition in object A from state [1] to state [2]. The objects causally connected by an oriented relation R {X, Y} to the triggering transition in A perform state transitions from states A[1] to states A[2]. Let us suppose for the sake of the example that the nature of the underlying interaction mechanism is such that the resulting relational network is represented by the graph in the right figure. By comparing both graphs we see that: 1. External object C became a boundary component of the system, although it did not perform a state transition (it was not causally connected to object A) although it remained in the same state – its new state C[2] is identical to its previous state C[1], as shown in the graph– so that it is now “sensitive” to the new state transitions occurring in core component E, which changed to state E[2] (a new relation, R {E, C} appeared). 2. Boundary component D became an object belonging to the medium because in its new state D[2], it is no longer “sensitive” to a state transition occurring in a system component (relations R {A, D} and R {F, D} disappeared). 3. The relations connecting core components E, F and G remain unchanged, although E is no longer “sensitive” to state transitions in D (relation R {D, E} disappeared) and G became “sensitive” to state transitions in C (a new relation, R {C, G} appeared). This hypothetical example shows how components may enter or leave the system and how the graph topology of the relational network configuration can change after the occurrence of triggered transition sequences propagation within the system. The global state reached is a steady state if the externally triggered transitions’ sequence (cascade of interactions) propagation ceases and the stabilized resulting network of relations no longer changes when objects belonging to the medium do not trigger state transitions. saw that the components of autopoietic systems, in order to comply with VM&U rules 5 and 6, must show peculiar component “production” capabilities. I intend to show that the distinctions necessary to describe component production from existing components in general abstract terms (i.e., node production in the


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equivalent graph) do not need to refer to a specific mechanism responsible for internal node production. The only assumption to be made is that the production of new nodes from existing nodes depends on the states reached by the participating nodes at a given time and on the local configuration of oriented relations linking them at that moment.

Nevertheless, as the underlying interaction mechanism responsible for cause-effect coupling is specific to a particular observational domain, any particular network configuration resulting from these kinds of transformations is specific to the observational domain in which the corresponding observed dynamic system exists.



c. The component production “diktat”

In a few words, the 5th and 6th “component production rules” are the strongest requirements of the whole set of rules of the VM&U validation test. In order to consider the system as an autopoietic machine, they introduce a sort of “diktat” to all system components: a | they must all be of the same kind; and b | all must participate in the production of other components. The first requirement is not stated explicitly in these VM&U rules (Varela, Maturana & Uribe 1974: 193), but has been argued for by Maturana (2002; see quote in the section, “Intra-boundary requirements”) as an essential feature of the component production process in molecular autopoietic systems. It is my opinion that the “same kind” requirement is implicit in the combination of both the 5th and 6th rules. This is so because, even for a non-specified observational domain, these rules impose a double constraint on all components. Namely they should: a | be produced by other components or be acquired as full-fledged components from the medium; and b | be producers of other components or, for those acquired from the medium, participate as necessary permanent constitutive components in the production of other components. This could not be accomplished if the said components did not share at least some common properties related to component production. Put in other words, components should be somehow of the “same kind” with respect to these transformation/ production capabilities. If it was not the case, there would be a diversity of previously existing or newly produced components in which not all components would share these capabilities. The problem left is how to describe in a general (abstract) way these shared properties of components with regard to their transformation/production capabilities. In my interpretation, components of the “same kind” are not necessarily identical as they are not assumed to perform the same state transition sequences and do not need to enter into the same states as other components when subject to the same trigger-

ing interactions. Within this explanatory approach, components are considered to be of the same kind if their behavior can be described with the same set of state variables. Even so, some specific components’ properties need to be distinguished and I will address this subject below in the section, “A generalized description of component production mechanisms.” These requirements in the MV&U rules are an obvious consequence of observed phenomena occurring in the kind of observational domain for which the concept of autopoiesis was invented in the first place: the biological macromolecular domain. In my opinion, this is also the main obstacle raised in front of observers trying to identify autopoietic systems in other observational domains. One may argue that both last rules seem to overstate the requirements needed to rigorously define the basic properties of autonomous component self-production machineries, but we will later see that their strength corresponds precisely to the kind of “specification” needed to propose a generative mechanism able to explain the processes of self-production as an internal structure determined phenomenon. This is essential in the case of living beings because it corresponds to what is observed in the macromolecular domain, so that the “diktat” corresponds to an observed fact. My aim then is to show that this “diktat” imposes relevant constraints to: a | the kind of dynamic objects that can be considered as components of an autopoietic system; and b | the topology of the interaction network in which they participate as producers of components of the same kind.

Consequences of the “production rules” The component “production rules” are the two last rules considered in the VM&U validation test. They introduce strong requirements concerning the transformation capabilities of components and of their mutual causation connectivity. They are essential to ensure the continuous self-maintenance of the unity’s physical structure and organization through the non-interrupted

compensation of component loss (either by de-coupling from the system to the medium, or by disaggregation) and topological disruptions of the components interaction network. These features are at the core of the notion of autopoiesis.

a. Consequences on component capabilities

The 5th rule supposes that all components are “building blocks” of the composite unity and that these building blocks are available as such in the medium. That is to say, objects belonging to the medium and all components belonging to the system should be describable by an observer with the same elementary distinctions. If this were not the case, simple accretion of objects in the medium could not be considered a component acquisition mechanism for the system. This is so because the accretion mechanism must be only of a relational nature: the acquired object represented as an acquired node must become the endpoint of at least one oriented relation starting in a network node. The system “does nothing” on the acquired object, but both enter into a coordinated mutual relationship in which one or more system (boundary) components may trigger a state transition in the acquired object via a cause-effect coupling. In this explanatory approach, component production does not mean component build-up from “lower level” constitutive parts acquired by accretion. It is irrelevant to consider components as composite unities themselves: all objects (components included) are considered as dynamic totalities capable of state transitions. Nothing else is said about their internal workings to explain how they perform such state transitions. Even the underlying interaction mechanism responsible for cause-effect coupling is not explained or described, it is simply assumed to exist. All identifiable substructures26 within the dynamic system structure should be composed of objects described as totalities of the same kind as those described for the 26 | The word “substructure” connotes here a partial set of interacting components within the whole composite unity (it may be represented by a partial graph of connected nodes).


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cause–effect interaction

62

t0

time

A'[S{v1, v2, …, vn}]t1 t1

A[S{v1, v2, …, vn}]t0

A"[S{v1, v2, …, vn}]t1 Figure 2: Example of node production from a splitting node: At time t0 a “similarly separable” node, A, is in a state [S], defined by the values of a set of n variable variables {v1, v2, …, vn}. A causeeffect coupling triggers a splitting process of node A into two nodes of the same kind, A' and A". This means that at time t1 the observer can describe them as two distinct nodes in their respective states defined by the same observable set of variables {v1, v2, …, vn}, with resulting values determined by the nature of the specific production mechanism (splitting) at work in the observational domain. At time t1 the resulting oriented relations linking nodes A’ and A” to the relational network representing the system structure depend on the nature of the underlying interaction mechanism at work (they are not represented on the figure).

whole system. If a system acquires a whole structure by establishment of a cause-effect coupling with an object linked to other objects belonging to the medium, this acquisition should be describable as a “merging interaction” of the system with a set of objects of the same kind (as described totalities) as those that constitute the system. A whole structure acquired from the medium should be considered as a new substructure of the system, not as a component. Even if the acquired substructure happens to belong to the class of autopoietic systems, its description should still remain at the same scale of description level as that of the objects (seen as totalities of the same kind as system components) that compose the substructure. This is the reason why multi-cellular organisms cannot be considered as single autopoietic systems when the chosen scale of description level is bottom-limited to cells, seen as system components. To illustrate this, consider the fact that an organism does not accrete whole cells as a mechanism of cell production: it accretes molecules or sets of mutually interacting molecules. So the basic components of the organism are not cells but molecules. Cells (which are composed of molecules) do indeed build other cells from


vol. 7, N°1

molecules existing in the molecular domain constituted by the whole organism, but this is not a component production mechanism: it is an internal subsystem building process. Thus, cells are to be considered as particular subsystems27 within the global “multi-cellular organism” system. In order to make this point more explicit, I refer the reader to a pertinent statement of Maturana’s: […] as I claim that living systems are molecular “ autopoietic systems I do not make a claim about some particular molecular structure in them, but I make a claim about the kind of molecular network that constitutes them, and the domain in which they exist. In these circumstances, the claim that living systems exist as singular autonomous molecular autopoietic unities through interactions in a medium with which they are in a continuous molecular interchange, is a claim about how they exist in their internal composition as well as about how they exist as totalities. (Maturana 2002: 13)

”

27 | The word “subsystem” connotes here an embedded substructure that can be considered as a unity in its own right because the observer is able to distinguish it as such and the rest of the composite system as its environment.

A generalized description of component production mechanisms Maturana’s description of the peculiar “molecule production” properties of molecules can be phrased in general abstract terms within the context of this explanatory path so that they could possibly be applied to other domains in which those generalized component properties would be observable. I consider that we can summarize the peculiarity concerning molecular production (observed as the result of molecule transformation processes) in the three following basic mechanisms: a | a molecule can split and result in two or more molecules that can be still described as totalities of the same kind;28 b | two or more molecules can merge into one molecule that can still be described as a totality of the same kind; c | two or more interacting molecules can participate in the buildup process of new molecules that can be described as totalities of the same kind as well. If we transpose these descriptions into the abstract language proposed in this explanatory approach, in the corresponding network of oriented relations (the equivalent graph), these transformations correspond to the creation of new nodes and/or destruction of existing nodes. Thus, if we want to apply VM&U’s 5th rule, the “component production” rule, to a generalized observational domain, we need to state the rule in terms of general dynamic objects and cause-effect coupling interactions (or in a formally equivalent manner). Let me propose some new distinctions related to component composition and decomposition properties but stated in terms of the multidimensional relational space explanatory domain. 28 | Some molecular decompositions can directly/intermediately produce individual atoms that do not constitute “molecules.” However, in this case, these atomic fragments would no longer be molecular components and could be considered as byproducts leaving the system and integrating into the environment. In fact, biological systems exist in an all pervading “soup” of atoms, ions and other biologically inert molecules diluted in water. These basic elements are usually considered as being part of the physical “substrate” in which “active” biochemical macro-molecules interact with each other.



I propose the following definitions: 1 | A node within a network of oriented relations is similarly separable if, after a network transformation, it can be described as a set of n nodes (where n > 1) representing objects of the same kind as the object represented by the original node (see the graphic description in Figure 2). 2 | n causally connected nodes (where n > 1) representing objects of the same kind within a network of oriented relations are similarly compoundable if, after a network transformation, they can be described as a single node representing an object of the same kind as the objects represented by the original n nodes (see graphic description in Figure 3). 3 | n causally connected nodes (where n > 1) representing objects of the same kind within a network of oriented relations are similar node co-producers if, after a network transformation, they can be described as m nodes (where m > n) representing objects of the same kind as the objects represented by the original n nodes (see graphic description in Figure 4). Generalized self-producing dynamic systems By applying the above-defined component composition and decomposition properties to the generalized description of a dynamic system proposed in this work, we can state that to observe compliance with VM&U’s 5th rule, each component of an autopoietic unity should be describable as a node of the same kind fulfilling the following conditions: a | it is either a similarly separable, a similarly compoundable, or a similar node co-producer node, or any combination of these; and b | it pertains to a same graph representing the dynamic unity under investigation. When, as an outcome of the underlying interaction mechanism, these properties are observable in system components, the observer can say that the dynamic system produces its own components by transformation of previously existing components as a result of their mutual cause-effect couplings. These processes should correspond to an observable intra-boundary phenomenology that

cause–effect interaction A[S{v1, v2, …, vn}]t0

t0

AB[S{v1, v2, …, vn}]t1

time

t1

B[S{v1, v2, …, vn}]t0 Figure 3: Example of node destruction by two merging nodes: At time t0 two “similarly compoundable” nodes, A and B, are in their respective states [S], defined by the values of a set of n variables {v1, v2, …, vn}. A cause-effect coupling triggers a merging process of nodes A and B into one node of the same kind, AB. This means that at time t1 the observer can describe it as a single node in a state defined by the same observable set of variables {v1, v2, …, vn} with resulting values determined by the nature of the specific destruction mechanism (merging) at work in the observational domain. At time t1 the resulting oriented relations linking node AB to the relational network representing the system structure depend on the nature of the underlying interaction mechanism at work (they are not represented on the figure).

A[S{v1, v2, …, vn}]t0

A[S{v1, v2, …, vn}]t1

B[S{v1, v2, …, vn}]t0

C[S{v1, v2, …, vn}]t0

B[S{v1, v2, …, vn}]t1

C[S{v1, v2, …, vn}]t1 t0

time

t1 D[S{v1, v2, …, vn}]t1

Figure 4: Example of node production by co-producing nodes: At time t0 three “similar node co-producer” nodes, A, B, and C, are in their respective states [S], defined by the values of a set of n variables {v1, v2, …, vn}. A cause-effect coupling triggers a co-producing process involving nodes A, B and C resulting in the creation of a new node, D, of the same kind. This means that at time t1 the observer can describe a new node D in a state defined by the same observable set of variables {v1, v2, …, vn} with resulting values determined by the nature of the specific co-production mechanism at work in the observational domain. At time t1 the resulting oriented relations linking nodes A, B, C and D to the relational network representing the system structure depend on the nature of the underlying interaction mechanism at work (they are not represented on the figure).


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may also concern those external dynamic objects within the medium that the system may acquire by simple accretion (see the section, “Component membership flow”). The question of whether known observational domains other than the molecular domain comply with this requirement is completely open and Maturana (2002, see quote in the section, “Intra-boundary requirements”) is convinced that the molecular domain is the only known observational domain where the 5th production rule is verified. He argues that the component transformation processes involved in this “peculiar” component production mechanism observed in the molecular domain are not observed in sub-molecular or supramolecular domains. Why are the component self-production properties described above so peculiar? When confronted with this question four decades ago, I realized that my first spontaneous approach was to think about “production” in terms of a fashioning and assembling process in which lower order entities were manipulated as building bricks by a sort of molecular machinery with inputs (bricks) and outputs (full-fledged components). I asked Maturana where this machinery was situated in living beings and he replied more or less with the following idea: what you call “machinery” is situated everywhere in the body, not only in specialized processing “machines” assembling lower order bricks,29 but in all molecules participating in the production of other molecules by themselves. All intervening agents may be seen as totalities (the molecules), that is to say, dynamic objects of the same kind interacting together, nothing else. At that time, this was for me the very striking consideration that led me to understand in a flash the whole concept of autopoiesis. An autopoietic system builds itself up from the “inside” and “everywhere,” in the relational locality of every single component, in a totally spontaneous, distributed and structure dependent manner. Maturana and Varela admitted earlier (Maturana & Varela 1973) the existence of 29 | Cell organelles such as ribosomes or mitochondria can be described as circumscribable embedded dynamic systems on their own and be considered as macro-molecule “building” machines.


vol. 7, N°1

second order autopoietic systems in which components are autopoietic entities playing an allopoietic role, as subordinate composite structures, in the establishment of relations with composite structures of the same kind in the internal dynamics of the second order unity.30 In my opinion, this stand is not compatible with the 5th component production rule as stated in the early 1970s unless the autopoietic unities, described as components, show the above-mentioned component composition/decomposition capabilities as totalities. It is here where we encounter the “scale of description” problem mentioned earlier in this work. I will develop this subject further in Part III.

b. Consequences on network topology

The reinforced “component production” requirement stated by the 6th rule needs to be thoroughly analyzed because it entails restrictions on the kind of network topology that should be observable in a dynamic system in order for it to be compatible with the definition of autopoietic systems as proposed in Varela, Maturana & Uribe (1974). The question is whether: a | all system components are produced as a result of interactions between components; b | all system components participate in component production; or not. If these conditions are to be verified positively, we need to clarify what it means “to participate in component production.” We are dealing with similar node composition, decomposition, and co-production processes triggered by interactions, that is to say, by relational network transformations involving cause-effect coupling flow affecting its components through time. Components become involved in component production if they are “in the path” of causation flows within the system and/or if they undergo 30 | “If the autopoiesis of the component unities of a composite autopoietic system conforms to allopoietic roles that through the production of relations of constitution, specification, and order define an autopoietic space, the new system becomes in its own right an autopoietic unity of second order.” (Maturana & Varela 1980: 110)

special transitions resulting in these similarity production transformations. In the corresponding relational space, a node is directly involved in node production if it undergoes such a transformation itself. But a component may also be indirectly involved in component production if it is found in the path of a causation flow resulting in composition/decomposition transformations of other components that could not have taken place if the component had not causally contributed to the propagation flow. In the corresponding relational space, a node is indirectly involved in node production if it is found in a chain of oriented relations and nodes in which the last oriented relation of the chain points to a node directly involved in node production. Let me be more explicit by introducing some new distinctions: 1 | A linear path of oriented relations within a network of oriented relations is a subset of nodes connected by successive onward-oriented relations at a specified time. It represents a subset of system components linked by cause-effect coupling interactions that constitutes a path for one-way interaction propagation. This definition does not prevent the existence of backward-oriented relations linking some or all of the nodes or other nodes in different paths; it simply states that the set of onward-oriented relations linking all the involved nodes should exist at a specified time. 2 | A linear path of oriented relations has a starting node, zero or more intermediate nodes, and a final node.31 The final node is considered to be the node that is actually involved in a similar node composition, decomposition or co-production process.

31 | This would mean that a linear path should be comprised of no fewer than two nodes. An interesting situation arises if we accept that a starting node could be also a final node (i.e., a linear path comprised of only one node). This would mean including the case in which a component undergoing a triggered transition interacts with itself (triggers a new transition on itself within a non-null time interval). This situation is irrelevant to the desired usefulness of the notion of linear path being defined.



3 | A starting node within a linear path of oriented relations represents a component capable of triggering a succession of interactions in the linear path, that is to say, of inducing successive state transitions in all the components found in the linear path. 4 | An intermediate node within a linear path of oriented relations represents a component subject to a state transition triggered by a backward-connected component and capable of triggering a state transition in a forward-connected component. Intermediate nodes may be absent in a linear path, in which case the linear path reduces to a single onward-oriented relation (all belowmentioned distinctions are not affected by this situation). 5 | A final node within a linear path of oriented relations represents a component subject to a state transition triggered by a state transition in the component represented by the last intermediate node (or by the starting node if there are no intermediate nodes). 6 | The combined set of nodes and of onward-oriented relations connecting them in a linear path represents a succession of causally connected events occurring in the subset of components represented by the nodes of the linear path of oriented relations. 7 | A node of a network of oriented relations is said to be deterministically involved in an observed network transformation if it is found in at least one linear path of oriented relations in which the final node reaches a state in which it actually performs that same observed network transformation. 8 | A node is said to participate in the production of new nodes if it is deterministically involved in a network transformation that results in the acquisition or the internal production of new nodes, either by accretion or by transformation of existing nodes (see example in Figure 5). In other words, the “participating” node should be found in the propagation path of the interaction flow and take part in the deterministic succession of causally connected events responsible for the production of a new node. Conversely, if a node happens

A

B C

D E

Figure 5: Example of a linear path of oriented relations: The subset of nodes {A, B, C, D, E} is a structure of nodes linked by a linear path, i.e., the subset of oriented relations {R {A, B}, R {B, C}, R {C, D}, R {D, E}} (represented by the bold arrows). A is the starting node, B, C, and D are intermediate nodes, and E is the final node of the linear path under consideration. This nodes subset together with the relations subset represent a succession of causally connected events. Intermediate nodes B, C, and D are deterministically involved in the transition undergone by final node E due to a state transition in the starting node A.

to be of no concern in a particular succession of causally connected events (within the whole interaction flow) leading to the production of a new node, it does not “participate” in the production of that particular new node. Now, strictly speaking, the requirement that all nodes should participate in the production of new nodes means that in the history of transformations undergone by the system through time, every node should be involved at least once in the causal chain of events leading to the production of a node.32 If it happens that one single node of the net32 | This requirement seems to contradict biological common sense. Most living organisms and cells contain structural (i.e., skeletal) components that, once formed, are inert (i.e., not participating in the formation of new nodes) but are nonetheless essential to the continued survival of the living entity. As I explain two paragraphs below, these inert “components” are in fact not part of an autopoietic system: they are part of a wider

work never participates in the production of new nodes because it is never found in the path of a node-producing deterministic succession of causally connected events, then – according to VM&U rules – we cannot consider the system as autopoietic. I think that at this point the “all nodes are node producers” requirement is unnecessarily strong. Without loss of generality, we can soften this requirement by saying that for any node there is a non-null probability to be found in a node-producing deterministic succession of causally connected events. A bottom line argument would be that the network topology should by no means prevent any single node from participating in node production, even if this participation actually never occurs. The requirement can then be worded as: “all nodes are potential node producers.” An alternative to this stand system in which an autopoietic system is embedded as a substructure.


65


{

66

would be to consider that the network of connected components needs to be re-circumscribed because it could happen that non-participating nodes represent dynamic objects mistakenly attributed by the observer to the candidate system rather than to the medium. But in that case we would be dismissing the relational criterion proposed in this explanatory approach for considering a dynamic object as being a component of the network: namely, that it suffices that it undergoes any kind of state transition triggered by state transitions occurring in other components of the network. This could actually be the case even if the considered dynamic object does not participate in component production processes despite its capability to do so at any moment. In the molecular domain, this would be the case of biomolecules such as non-replicating DNA, which do not replicate unless subject to the addition of other specific DNA sequences. One may argue that this requirement is still too strong. Biological organisms “contain” biochemically inert molecules and even internal inert structures that do not participate in component production, such as skeletal organs. These elements (dynamic objects) or structures may trigger transitions in the system’s components without being affected by them. By “contain” and “internal” I mean that these elements or structures are located inside the outer spatial topological surface of the boundary structure that delimits the organism and separates the medium from the core. But we discussed before that the spatial boundary is not to be confused with the relational boundary. In this sense, an “inert” skeleton


vol. 7, N°1

Hugo Urrestarazu

was a teacher-researcher in nuclear and solid state physics at the Universidad de Chile and conducted postgraduate Ph.D. research on semiconductors at Imperial College in England. He possesses 13 years of industrial experience in design and development of embedded real time operating systems and object oriented design and programming at Alcatel in France. He also worked as a consulting engineer in Central America and as a linguistic consultant in France. Back in 1972 he attended Humberto Maturana’s Biology of Cognition lectures and was Francisco Varela’s friend and colleague at the Facultad de Ciencias in Chile. Since 1990, he has been involved in independent interdisciplinary scientific extension activities concerning the theory of autopoietic systems.

structure can be considered as part of the environment, even if it is spatially embedded in the system’s embodied structure. In terms of the topology of a network of oriented relations, such elements or structures can be considered as not being connected to “active” network nodes. These “inert” elements or structures can participate as a substrate for the maintenance of self-organization, even if they do not participate directly in self-production. In the same manner, “external” elements or structures (with respect to a spatial boundary) can be essential for the survival of an organism (the material substrate in which the organism exists as an ordinary material entity, for example). The same argument is applicable to artificial organs implanted in an organism by the way of surgery or the administration of disposable non-degradable drug molecules, for example.33 This strong requirement demands, in fact, a special kind of network topology in which all nodes should be found in a possible path of node-producing successions 33 | Here we are in the face of the observer’s freedom of choice concerning the applied description level for identifying a composite system. If attention is focused on the identification of an autopoietic system, the spatially embedded “inert” structures are to be considered as part of the environment of the autopoietic system. If attention is focused on the identification of a wider autonomous system (although not autopoietic as a whole), a spatially embedded autopoietic system, composed of productively “active” components, is to be considered as a substructure of the autonomous whole.

of events. As far as node production is concerned, this special kind of network topology should never produce “isolated” nodes with respect to node production transformation processes. In other words, the set of all possible node-producing paths should involve all existing and produced nodes in the history of transformations undergone by the system through time. We can imagine a number of possible ways by which a network of oriented relations can produce this result. One extreme case of topological layout that we can think of is one in which every node is causally connected to all other nodes by two-way oriented relations: this configuration ensures that every node will be found in the path of any possible interaction flow. But this is an extreme situation. More realistic topological layouts, made of tree-like structures with bifurcating and circular propagation paths involving the participation of all nodes, may also ensure this requirement is met. In any case, we are led to imagine graph topologies that are densely populated by oriented relations ensuring that in the corresponding dynamic system every component can be “visited” by a component producing causation flow in the history of changes undergone by the system through time. This kind of topology leads inevitably to the build-up of closed causation network flows and to configurations in which the history of the state changes of each component is determined by causation flows generated almost entirely within this closed network. I will address these issues in Part III.



Acknowledgements I owe to the loving encouragement of my late dear wife Anne-Marie Lopez del Rio the necessary force and determination to work on and publish this work in spite of all our shared distress endured before she sadly passed away in May 2011. I especially thank William P. Hall for his valuable comments and suggestions expressed over several years of fruitful discussions. I also thank Alexander Riegler for publishing this, as well as the anonymous Constructivist Foundations peer reviewers, who helped me to improve the presentation of my views. Finally, I warmheartedly thank my former professor Humberto Maturana, who, 40 years ago, managed to enthuse my mind with a lifelong and meaningful reflection process that has been going on ever since.

References Maturana H. R. & Varela F. J. (1973) De máquinas y seres vivos: Una teoría sobre la organización biológica. Editorial Universitaria, Santiago. Maturana H. R. (1978) Biology of language: The epistemology of reality. In: Miller G. & Lenneberg E. (eds.) Psychology and biology of language and thought: Essays in honor of Eric Lenneberg. Academic Press, New York: 27–63. Available at http://www.enolagaia. com/M78BoL.html Maturana H. R. (1988) Ontology of observing: The biological foundations of selfconsciousness and the physical domain of existence. In: Donaldson R. E. (ed.) Texts in cybernetic theory: An in-depth exploration of the thought of Humberto Maturana, William T. Powers, and Ernst von Glasersfeld. American Society for Cybernetics (ASC) conference workbook. Available at http:// www.inteco.cl/biology/ontology/index.htm Maturana H. R. (2002) Autopoiesis, structural coupling and cognition: A history of these and other notions in the biology of cognition. Cybernetics & Human Knowing 9(3–4): 5–34.

Maturana H. R. & Varela F. J. (1980) Autopoiesis and cognition: The realization of the living. Reidel, Boston. Urrestarazu H. (2011) Autopoietic systems: A generalized explanatory approach. Part I. Constructivist Foundations 6(3): 307–324. Available at http://www.univie.ac.at/constructivism/journal/6/3/307.urrestarazu Varela F. J. (1980) Principles of biological autonomy. Elsevier North Holland, New York. Varela F. J. (1995) The emergent self. In: Brockman J. (ed.) The third culture: Beyond the scientific revolution. Simon & Schuster, New York: 209–222. Available at http:// www.edge.org/documents/ThirdCulture/tCh.12.html Varela F. J., Coutinho A., Dupire B. & Vaz N. (1988) Cognitive networks: Immune, neural, and otherwise. In: Perelson A. (ed.) Theoretical immunology Part II. AddisonWesley, Reading MA: 359–375. Varela F. J., Maturana H. R. & Uribe R. (1974) Autopoiesis: The organization of living systems, its characterization and a model. BioSystems 5(4): 187–196. Received: 21 September 2011 Accepted: 5 November 2011

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