Autopoiesis

Humberto R. Maturana, Francisco J. Varela . The Realization of the Living (Originally: De maquinas y seres vivos 1972) . ISBN 90-277-1015-5 . 1980 . D. Reidel Publishing Company . Dordrecht: Holland / Boston: USA / London: England

Foreword

A theoretical biology which is topological where the topology is self-referential from the point-of-view of the system itself and has no outside, ‘.. Leibnizian for our day’ (p v). Cognition is defined as a biological phenomenon and as the very nature of biological systems. Hence: ‘Living systems are cognitive systems, and living as a process is a process of cognition’ (p vi).

Essay 1: Biology of Cognition

1) What is the organization of the living? AND 2) What takes place In the phenomenon of perception? Ad 1) No valid definition is available that accounts for all systems: we can recognize them when we encounter them but we cannot say what they are. What is the invariant feature around which selection operates? NB that this is similar to my question concerning the invariant in business change! Look at systems not as open systems, exchanging energy and information with their environment, but closed. In addition a language is needed to describe autonomy as a feature of the system specified by the description. As a consequence notions of purpose, intent, use and function must be rejected. The definition of these systems as unities through their self-reference is their autonomy. Living systems are defined as unities through the circularity of the production of their components. Ad 2) With this theory the activity of the nervous system can be treated as the activity of the system itself and not of its environment. The external world only has a triggering role in the release of the internally determined activity. Moreover the working of the nervous system can only be understood by closing it off: perception is not the grasping of but the specification of an external reality. This can be connected with the Wagensberg model, but some modifcations are required to clean it from thermodynamical arguments. The question changes from: ‘How does the organism obtain information about its environment’ to ‘How does it happen that the organism has the structure that permits it to operate adequately in the medium in which it exists?’ (p xvi).

It was in these circumstances that one day, while talking to a friend (José Bulnes) about an essay of this on Don Quixote de la Mancha, in which he analyzed Don Quixote’s dilemma of whether to follow the path of arms (praxis, action) or the path of letters (poiesis, creation, production), and his eventual choice of the path of praxis deferring any attempts at poiesis, I understood for the first time the power of the word ‘poiesis’ and invented the word that we needed: autopoiesis. This was a word without a history, a word that could directly mean what takes place in the dynamics of the autonomy proper to living systems’ (p xvii)

In a sense it has been my way to a transcendental experience: to the discovery that matter, metaphorically speaking, is the creation of the spirit (the mode of existence of the observer in a domain of discourse) and that the spirit is the creation of the matter that it creates’(p xviii). I would refer to this as the meeting of content and process: beliefs lead to decisions which in turn lead to behavior which lead to a new context which, given beliefs, lead to new action and perhaps to a change of the belief also.

Unity, Organization and Structure

Unity. An observer performs the cognitive operation of distinguishing an entity from its background. They are distinguished for the separability of the respective properties endowed them through this cognitive operation. If this operation is performed recursively by the observer then the components of the entity can be distinguished and the entity is defined by the properties of its components. The observer can also observe the entity as a single unity and distinguish it in the domain of its properties as a unity and not in the domain of the properties of its components. If an autopoietic system is treated as a composite unity, it exists in the space defined by its components, but if it is treated as a simple unity then it is defined in the domain of the distinctive properties of the unity.

Organization and Structure. The relations between the components of a composite unity that define it as a particular kind of a unity constitute its organization. Only those properties are considered and only to the extent that they participate in the constitution of the unity they integrate. The actual components and their actual relations, concretely realizing a system as a member of a class of systems in which it categorizes because of its organization, constitutes its structure. Any given organization may be realized by many different structures and different subsets of components and their relations in a given structure may be abstracted by an observer as organizations defining different classes of composite unities. The organization specifies the class identity of a system and must remain invariant for the class identity to remain invariant; if its organization changes then its identity changes and the unity becomes a unity of a different kind. Conversely because an organization can be realized in systems with different structures, the identity of a system can stay invariant while its structure changes within limits determined by its organization.

Structural coupling. Unity and medium as independent systems operate in each interaction by triggering in each other a structural change, and select in each other a structural change. If the organization in a composite system remains invariant while it undergoes structural changes induced by its medium, then its adaptation is conserved. The structural change in the unity follows the structural change in the medium through a process of structured coupling. Else the outcome of the unity is disintegration. If the unity is structurally plastic, then its conservation of adaptation results in a history of structural couplings to the medium that selects its path of structural change. The configuration of constitutive relations that remain invariant in the adapted composite unity determines the possible perturbations that the unity can admit; it is a reference for the selection of the path of structural changes that take place in it in its history of interactions.

Epistemology. If a composite unity is specified as a simple system then the phenomenological domain is specified by the properties of the simple unity. Because that differs from the domain of the properties of the components phenomenal reduction is not possible. The relations between the components of a composite system interact through a system of contiguity. Necessarily relations such as control and regulation are not of contiguity, but referential relations specified by the observer using their meta-domain by using their view of the whole. The observer creates a meta-domain of descriptions that allows them to speak as if a unity existed as a separate entity that they can characterize by specifying the operations that must be performed to distinguish it. Having characterized it as a distinguishable entity, in that meta-domain can he only cognize the entity in terms of that meta-domain.

Society and Ethics

(1) ‘It is apparent that natural social systems as systems constituted by living systems require these for their actual realization. What is not apparent, however, is the extent to which the coupling of living systems in the integration of a social system entails the realization of their autopoiesis’ (p xxiv). Why is the use of the term ‘autopoiesis’ in the sentence above with regards to the organization of the social system avoided? ‘If, however, the autopoiesis of the components of a natural social system were not involved in its constitution because the relations that define a system as social do not entail them, then the autopoiesis of the components (and hence their autonomy and individuality) would be intrinsically dispensable’ (p xxiv). This means that if autopoiesis of the components of a social system is not involved in the constitution of a social system, then the autopoiesis of the components is not required. Hence the autonomy and individuality of the components would be ‘intrinsically dispensable’. This seems to be a hint at the status of people making up a social group. It does not take into account the existence of memes as components of a memeplex that forms the social fabric of a group.

(2) ‘Accordingly, I propose that a collection of autopoietic systems that, through the realization of their autopoiesis, interact with each other constituting and integrating a system that operates as the (or as a) medium in which they realize their autopoiesis, is indistinguishable from a natural social system. Or, in other words, I propose that the relations stated above characterize the organization of a social system as a system, and that all the phenomena proper to social systems arise from this organization’(p xxv) This must serve as the connection of the autopoiesis theory with the theory of memetics. The autopoietic systems are the belief systems of the components of the social system, namely individual people. Their autopoiesis is realized through the existence of the autopoiesis of the autopoietic social system. The component autopoietic systems and the social autopoietic systems both are realized through the other’s autopoiesis. Implications of this proposition are: (i) ‘The realization of the of the autopoiesis of the components of a social system is constitutive to the realization of the social system itself’ (p xxv) (ii) ‘A collection of living systems integrating a composite unity through relations that do not involve their autopoiesis is not a social system, and the phenomena proper to its operation as such a composite unity are not social phenomena’ (p xxv). (iii) ‘Therefore, the domain of social phenomena, defined as the domain of the interactions and the relations that an observer sees taking place between the compnents of a society, results from the autopoietic operation of the components of the components of the society while they realize it in the interplay of their properties’ (p xxv) (iv) ‘In a society, at any instance of observation, the structures of the components determine the properties of the components, the properties of the components realize the structure of the society, and the structure of the society operates as a selector of the structure of its components by being a medium in which they realize their ontogeny’ (p xxv) NB: this is the notion of the connection between process and content in a social system (v) ‘An autopoietic system participates in the constitution of a social system only to the extent that it participates in it, that is, only as it realizes the relations proper to a component of the social system’(p xxv)

(3) ‘A society defines the domain in which it is realized as a unity’(p xxv) Such a domain constitutes at least an operationally independent medium that operates as: a) a selector of the path of structural change that the society follows in its individual history, and b) ‘if stable, a historical stabilizer of the structures that realize the selected invariant relations that define the society as a particular social system’ (p xxvi).

(4) ‘To the extent that human being are autopoietic systems, all their activities as social organisms must satisfy their autopoiesis’ (p xxvii) ‘In man as a social being, therefore, all actions, however individual as expressions of preferences or rejections, constitutively affect the lives of other human beings and, hence, have ethical significance’ (p xxvi)

(5) ‘What determines the constitution of a social system are the recurrent interactions of the same autopoietic systems. In other words, any biological stabilization of the structures of the interacting organisms that results in the recurrence of their interactions, may generate a social system’ (p xxvi). Gene >> Meme. Also Kevin and Gavin.

(6) ‘A social system is essentially a conservative system. This is so because it is generated through the interactions of structure-determined autopoietic systems and operates as a medium that selects the path of ontogenic structural change of its components, which, thus, become structurally coupled to it. In our case, we as social beings generate, through our structure-determined properties, our societies as the cultural media that select our individual paths of ontogenic change in a manner that leads each one of us to the structure that makes us generate the particular societies to which we belong. A society, therefore, operates as a homeostatic system that stabilizes the relations that define it as a social system of a particular kind’ (p xxvi- xxvii).

(7) The domain of states of a system as a composite unity is determined by the properties that realize its organization. It follows that a social change in a human society can only take place if the individual properties and hence conduct of its members change.

(8) ‘All that matters for the realization of a society is that the component autopoietic systems should satisfy certain relations regardless of the actual structures (internal processes) through which they realize them’ (p xxvii) Hypocrisy.

(9) ‘Interactions within a society are necessarily confirmatory of the relations that define it as a particular social system; if not, the organisms that interact do not interact as components of the society which they otherwise integrate. It is only through interactions operationally not defined within the society that a component organism can undergo interactions that lead to the selection, in its ontogeny, of a path of structural change not confirmatory of the society that it integrates. ..social creativity, as the generation of novel social relations, always entails interactions operationally outside the society.. Social creativity is necessarily anti-social in the social domain in which it takes place’ (p xxvii-xxviii)

(10) ‘In general any organism, and in particular any human being, can be simultaneously a member of many social systems, such as family, a club, an army, a political party, a religion or a nation, and can operate in one or another without necessarily being in internal contradiction. .. An observer always is potentially antisocial’ (p xxviii)

(11) ‘To grow as a member of society consists in becoming structurally coupled to it; to be structurally coupled to a society consists in having the structures that lead to the behavioral confirmation of the society’ (p xxviii)

(12) ‘We as human beings exist in a network of social systems and move from to another in ou daily activities. Yet, not all human beings caught in the mesh of relations generated in this network of social systems participate in it as social beings’ (p xxviii-xxix). This means that if the interaction of someone in this social system does not involve their autopoiesis, is being used by the system but not a member or it is social abuse.

(13) (14) (15)

Biology of Cognition

1. Introduction

Man knows and his capacity to know depends on his biological integrity; furthermore he knows that he knows’ (p 5). This statement also explains the requirement of the existence of human beings as biological organisms for the existence of memes. ‘As a psychological, and hence biological function cognition guides people’s handling of the universe and knowledge gives certainty to their acts; objective knowledge seems possible and through objective knowledge the universe appears systematic and predictable. Yet knowledge as an experience is something personal and private that cannot be transferred, and that which one believes to be transferable, objective knowledge, must always be created by the listener: the listener understands and objective knowledge appears to be transferred, only if he is prepared to understand’ (p 5) Thus cognition is a biological function; it is known through knowledge.

(a) If an organism is a unity, in what sense are its component properties its parts? Has some property arisen from the properties of its organization or from its mode of life?

(b) ‘Organisms are adapted to their environments, and it has appeared adequate to say of them that their organization represents the ‘environment’ in which they live, and that through evolution they have accumulated information about it, coded in their nervous system. Similarly it has been said that the sense organs gather information about the ‘environment’, and through learning this information is coded in the nervous system [Cf. Young, 1967]. Yet this general view begs the questions, ‘What does it mean to ‘gather information?’ and ‘What is coded in the genetic and nervous system?’ (p 6)

III Cognitive Function in General

The Observer

(1) ‘Anything said is said by an observer’ (p 8)

(2) The observer can observe an object and its environment simultaneously. This allows them to interact with both independently and have interactions that are outside of the domain of the observed entity.

(3) An attribute of the observer is that they can interact both with the observed entity and with its relations. Both are units of interaction (entities)

(4) To the observer an entity is an entity if they can describe it. They can describe it if at least one other entity exists so as to distinguish the observed entity from in its description; the ultimate reference is the observer themselves.

(5) The set of all interactions of an entity is its domain of interactions and the set of all possible interactions with the observer (relations) is its domain of relations; the latter lies within the cognitive domain of the observer. ‘An entity is an entity if it has a domain of interactions, and if this domain includes interactions with the observer who can specify for it a domain of relations’ (p 8)

(6) The observer can define himself as an entity by specifying his own domain of interactions.

(7) ‘The observer is a living system and an understanding of cognition as a biological phenomenon must account for (the existence of DPB) the observer and his role in it (the phenomenon DPB)’ (p 9)

The Living System

(1) ‘Living systems are units of interactions; they exist in an ambience. From a purely biological point of view they cannot be understood independently of that part of the ambience with which they interact: the niche; nor can the niche be defined independently of the living system that specifies it’ (p 9)

(2) ‘Living systems as they exist on earth today are characterized by .. a closed circular process that allows for evolutionary change in the way the circuitry is maintained, but not for the loss of the circuitry itself. .. This circular organization constitutes a homeostatic system whose function is t produce and maintain this very same circular organization by determining that the components that specify it be those whose synthesis or maintenance it secures’ (p 9)

(3) ‘It is the circularity of its organization that makes a living system a unit of interactions, and it is this circularity that it must maintain in order to remain a living system and to retain its identity through different interactions’ (p 9)

(4) ‘Due to the circular nature of its organization a living system has a self-referring domain of interactions (it is a self-referring system), and its condition of being a unit of interactions is maintained because its organization has functional significance only in relation to the maintenance of its circularity and defines its domain of interactions accordingly’ (p 10)

(5) ‘Living systems as units of interactions specified by their condition of being living systems cannot enter into interactions that are not specified by their organization. The circularity of their organization continuously brings them back to the same internal state (same with respect to the cyclic process). Each internal state requires that certain conditions (interactions with the environment) be satisfied in order to proceed to the next state’ (p 10). The circular organization implies the prediction that an interaction will take place again. If it does not then the system will disintegrate, if it does it will maintain its integrity (identity vis a vis the observer) and move on to the next prediction. In a continuously changing environment the system can only remain intact if the environment does not change in that which is predicted. The predictions implied in the organizations are not predictions of particular events but of classes of interactions; interactions the features of which allow the organization of the system and hence its identity to remain intact. This makes living system inferential systems and their domain of interactions a cognitive domain.

(6) A niche is defined by the classes of interactions into which a system can enter. The environment is defined as the classes of interactions into which an observer can enter; they treat it as a reference for their interactions with the system. The observer considers the niche of a system the set of interactions that they observe to lie in its part of the domain of interactions of the environment. For the observer a niche is a part of the environment, for the system it is the entire set of possible interactions. As such a niche cannot be ‘part’ of the environment which lies exclusively in the cognitive domain of the observer. ‘Niche and environment, then, intersect only to the extent that the observer (including instruments) and the system have comparable organizations, but even then there are always parts of the environment that lie beyond any possibility of the intersections with the domain of interactions of the organism, and there are parts of the domain of the niche that lie beyond any possibility of intersection with the domain of interactions of the observer. Thus for every living system its organization implies a prediction of a niche, and the niche thus predicted as a domain of classes of interactions constitutes its entire cognitive reality’ (pp. 10-11) This is relevant for the observation of the firms by people as observers and vice versa.

(7) ‘Every unit of interactions can participate in interactions relevant to other, more encompassing units of interactions. If in doing this a living system does not lose its identity, its niche may evolve to be contained by the larger unit of interactions and thus be subservient to it. If this larger unit of interactions is (or becomes) in turn also a self-referring system in which its components (themselves self-referring systems) are subservient to its maintenance as a unit of interactions, then it must itself be (or become) subservient to the maintenance of the circular organization of its components’ (p 11). This is possibly relevant concerning acquisition of firms by other firms (DPB): cells >> bees >> beehive; cells >> people >> firms >> larger firms &c.

Evolution

(1) Evolutionary change is an aspect of the circular organization that preserves the system’s basic circularity. ‘Reproduction and evolution are not essential for the living organization, but they have been essential for the historical transformation of the cognitive domains of the living systems on earth’ (p 11)

(2) For a change in a unity without losing its identity with respect ot the observer, it must suffer an internal change. If an internal change occurs without the identity of the unity changing then the domain of interactions must change.

(3) After reproduction the new unity has the same domain of interactions as the parent if it has the same organization.

(4) Predictions about the niche are inferences about classes of interactions. Particular interactions may be of the same class and not distinguishable for the system but they may be to the observer.

(5) Aspects of the organization that are subservient to the maintenance of the basic circularity but do not determine it change from generation to generation. The system maintains its organization and its identity through interactions. The basic circularity remains unchanged, the way it is maintained changes. ‘The evolution of the living systems is the evolution of the niches of the units of interactions defined by their self-referring circular organization, hence, the evolution of the cognitive domains’ (p 12)

The Cognitive Process

(1) ‘A cognitive system is a system whose organization defines a domain of interactions in which it can act with relevance to the maintenance of itself, and the process of cognition is the actual (inductive) acting of behaving in this domain. Living systems are cognitive systems, and living as a process is a process of cognition’ (p13)

(2) ‘If a living system enters into a cognitive interaction, its internal state is changed in a manner relevant to its maintenance, and it enters into a new interaction without loss of its identity’ (p 13)

(3) The function of the nervous system is subservient to the necessary circularity of the living organization.

(4) The nervous system has expanded the domain of interactions and hence has transformed the unit of interactions and had subjected interacting to the process of evolution.

(5) This expansion of the cognitive domain (into the domain of ‘pure relations’) allows for non-physical interactions between systems such that the systems orient each other towards interactions within their respective domains. ‘Herein lies the basis for communication: the orienting behavior becomes a representation of the interactions toward which it orients, and a unit of interaction in its own terms. .. there are organisms that generate representations of their own interactions by specifying entities with which they interact as if these belonged to an independent domain, while as representations they only map their own interactions. .. a) We become observers through recursively generating representations of our interactions, and by interacting with several representations simultaneously we generate relations with the representations of which we can then interact.. b) We become self-conscious through self-observation; by making descriptions of ourselves (representations), and by interacting with our descriptions we can describe ourselves describing ourselves, in an endless recursive process’ (p 14)

Description

(1) A living system is an inductive system: what happened once will occur again. Its organization is conservative and repeats only that which works. The present state is always specified by the previous state that restricts the field of possible modulations by independent concomitances.

(2) For the observer any one of the system’s behaviors appears as an actualization of the niche, that is, as a first order description of the environment (denoted as Description); this is a description in terms of the behavior (interactions) of the observed system, not representations of environmental states. The relation between behavior and niches exists in the cognitive domain of the observer only.

(3) A living system can modify the behavior of another system by: a) interacting with it in a way that directs both toward each other such that the following behavior of the one depends strictly on the previous behavior of the other. In this case the two systems can be said to interact. b) By orienting the behavior of the other system to some part of its domain of interactions different from the present interaction but comparable to the orientation of the orienting system. This takes place if the domains of interactions of both systems are coincident; no interlocking chain of behavior takes place because the systems’ behavior is based on parallel but independent behavior. In this case the systems can be said to communicate; this is the basis for linguistic behavior. The first generates a Description of its niche that orients the second within its cognitive domain to an interaction, which ensues a conduct parallel but unrelated to the first. The orienting behavior to the observer is a second order behavior, denoted in italics as description (linguistic utterance DPB), that denotes whatever denotation they assign to it: ‘.. that which an orienting behavior connotes is a function of the cognitive domain of the orientee, not the orienter’ (p 28).

(4) In an orienting interaction the orienter’s behavior as a description generates activity in the orientee, which then, in turn makes a Description of its niche connoted by the orienting behavior of the first.

(5) ‘If an organism can generate a communicative description and then interact with its own state of activity that represents this description, generating another such description that orients towards this representation…, the process can in principle be carried on in a potentially infinite recursive manner, and the organism becomes an observer: it generates discourse as a domain of interactions with representations of communicative descriptions (orienting behaviors). Furthermore, if such an observer through orienting behavior can orient himself towards himself, and then generate communicative descriptions that orient him towards his description of his self-orientation, he can, by doing so recursively, describe himself describing himself .. endlessly. This discourse through communicative description originates the apparent paradox of self-description: self-consciousness, a new domain of interactions’ (p 28-9).

Thinking

(1) Thinking is the neuro-physiological process of interacting with some of its own internal states as if these were independent entities. From thinking behavior emerges in a deterministic manner. The difference with a reflex action is that the concerning the latter a signal can be traced back to the sensory system. In thinking the signal begins with a distinguishable state of activity of the nervous system itself (2) This process above is independent from language.

Natural Language

(1) ‘Linguistic behavior is orienting behavior; it orients the orientee within his cognitive domain to interactions that are independent of the nature of the orienting interactions themselves. .. Only if the domains of interactions of the two organisms are to some extent comparable, are such consensual orienting interactions possible and are the two organisms able to develop some conventional, but specific, system of communicative descriptions to orient each other to cooperative classes of interactions that are relevant for both’ (p 30). These are the interactions as per Knorr-Cetina.

(2) –

(3) ‘Behavior (function) depends on the anatomical organization (structure) of the living system, hence anatomy and conduct cannot legitimately be separated and the evolution of behavior is the evolution of anatomy and vice versa; anatomy provides the basis for behavior and hence for its variability; behavior provides the ground for the action of natural selection and hence for the historical anatomical transformations of the organism’ (p 31).

(4) ‘However, when it is recognized that language is connotative and not denotative, and that its function is to orient the orientee within his cognitive domain, without regard for the cognitive domain of the orienter, it becomes apparent that there is no transmission of information through language. It behooves the orientee, as a result of an independent internal operation upon his own state, to choose where to orient his cognitive domain; the choice is caused by the ‘message’, but the orientation thus produced is independent of what the ‘message’ represents for the orienter. In a strict sense then, there is no transfer of information from the speaker to his interlocutor; the listener creates information by reducing his uncertainty through his interactions in his cognitive domain. Consensus arises only through cooperative interactions in which the resulting behavior of each organism becomes subservient to the maintenance of both. .. The cooperative conduct that may develop between the interacting organisms from these communicative interactions is a secondary process independent of their operative effectiveness. If it appears to be acceptable to talk about transmission of information in ordinary parlance, this is so because the speaker tacitly assumes the listener to be identical with him and hence as having the same cognitive domain which he has (which never is the case), marveling when a ‘misunderstanding’ arises’ (p 32-3).

(5) –

(6) ‘If one considers linguistic interactions as orienting interactions it is apparent that it is not possible to separate, functionally, semantics and syntax, however separable they may seem in their description by the observer. This is true for two reasons: a) A sequence of communicative desriptions (words in our case) must be expected to cause in the orientee a sequence of successive orientations in his cognitive domain, each arising from the state left by the previous one… b) An entire series of communicative descriptions can itself be a communicative description; the whole sequence once completed may orient the listener from the perspective of the state to which the sequence itself has led him’ (p 33)

(7) ‘Linguistic behavior is an historical process of continuous orientation’ (p 34)

(8) –

(9) ‘Orienting behavior in an organism with a nervous system capable of interacting recursively with its own states expands its cognitive domain by enabling it to interact recursively with descriptions of its interactions. As a result: a) Natural language has emerged as a new domain of interactions in which the organism is modified by its descriptions of its interactions.. b) Natural language is necessarily generative because it results from the recursive application of the same operation (as a neurophysiological process) on the results of this application c) New sequences of orienting interactions (new sentences) within the consensual domain are necessarily understandable by the interlocutor (orient him), because each one of their components has definite orienting functions as a member of the consensual domain that it contributes to define’ (pp. 34- 5)

Memory and Learning

(1) ‘Learning as a process consist in the transformation through experience of the behavior of an organism in a manner that is directly or indirectly subservient to the maintenance of its basic circularity’ (p 35)

(2) ‘Learning occurs in such a manner that, for the observer, the learned behavior of the organism appears justified from the past, through the incorporation of a representation of the environment that acts, modifying its present behavior by recall; notwithstanding this, the system itself functions in the present, and for it learning occurs as an atemporal process of transformation. An organism cannot determine in advance when to change and when not to change during its flow of experience, nor can it determine in advance which is the optimal functional state that it must each; both the advantage of any particular behavior and the mode of behavior itself can only be determined a posteriori, as a result of the actual behaving of the organism subservient to the maintenance of its basic circularity’ (pp. 35-6)

(3 tm 7) –

(8) ‘Past, present and future and time in general belong to the cognitive domain of the observer’ (p 38)

The Observer

(1) The cognitive domain is the entire domain of interactions of the organism. It can be enlarged if new modes of interactions are generated or instruments are applied.

(2) –

(3) The observer generates a spoken description of his cognitive domain (which includes his interactions with and through instruments).

(4) ‘The observer can describe a system that gives rise to a system that can describe, hence, to an oberver. A spoken explanation is a paraphrase, a description of the synthesis of that which is to be explained; the observer explains the observer. A spoken explanation, however, lies in the domain of discourse. Only a full reproduction is a full explanation’ (p 39)

(5) ‘The domain of the discourse is a closed domain, and it is not possible to step outside of it through discourse. Because the domain of discourse is a closed domain it is possible to make the following ontological statement: the logic of the description is the logic of the describing (living) system (and his cognitive domain)’ (p 39) This bears a relation with the Wolfram statement that natural processes are the same as the processes that produced the human powers of perception and analysis.

(6) ‘This logic demands a substratum for the occurrence of the discourse. We cannot talk about this substratum in absolute terms, however, because we would have to describe it, and a description is a set of interactions into which the describer and the listener can enter, and their discourse about these interactions will be another set of descriptive interactions that will remain in the same domain. Thus, although this substratum is required for epistemological reasons, nothing can be said about it other than what is meant in the ontological statement above’(p 39)

(7) ‘We as observers live in a domain of discourse interacting with descriptions of our descriptions in a recursive manner, and thus continuously generate new elements of interaction. As living systems, however, we are closed systems modulated by interactions through which we define independent entities whose only reality lies in the interactions that specify them (their Description)’ (p 40)

(8) ‘For epistemological reasons we can say: there are properties which are manifold and remain constant through interactions. The invariance of properties through interactions provides a functional origin to entities or units of interactions; since entities are generated through the interactions that define them (properties), entities with different classes of properties generate independent domains of interactions: no reductionism is possible’ (p 40)

Post Scriptum

(i) ‘.. That is, man changes and lives in a changing frame of reference in a world continuously created and transformed by him. Successful interactions directly and indirectly subservient to the maintenance of his living organization constitute his only final source of reference for valid behavior within the domain of descriptions, and, hence, for truth; but, since living systems are self-referential systems, any final frame of reference is, necessarily, relative. Accordingly, no absolute system of values is possible and all truth and falsehood in the cultural domain are necessarily relative’ (p 57)

(ii) ‘Language does not transmit information and its functional role is the creation of a cooperative domain of interactions between speakers through the development of a common frame of reference, although each speaker acts exclusively within his cognitive domain where all ultimate truth is contingent to personal experience. Since a frame of reference is defined by the classes of choices which it specifies, linguistic behavior cannot be but rational, that is, determined by relations of necessity within the frame of reference within which it develops. Consequently, no one can ever be rationally convinced of a truth which he did not have already implicitly in his ultimate body of beliefs’ (p 57)

(iii) ‘Man is a rational animal that constructs his rational systems as all rational systems are constructed, that is, based on arbitrarily accepted truths (premises); being himself a relativistic self-referring deterministic system this cannot be otherwise. But if only a relative, arbitrarily chosen system of reference is possible, the unavoidable task of man as a self-conscious animal that can be an observer of its own cognitive processes is to explicitly choose a frame of reference for his system of values. .. ‘ (p 58)

Essay 2:

Autopoiesis – The Organization of the Living

Preface (Stafford Beer)

General: knowledge is categorized and so is our world view. Not wholes seen through different filters but parts derived through analysis and categorized.

The stuff of systems is relations between components. Relation is the essence of synthesis. During categorization the relations between the components are not included. Relations are discarded and alienated and distantiated from. ‘It is an Iron Maiden in whose secure embrace scholarship is trapped‘ (p64).

The world develops exponentially because it is a complex system. Knowledge is developed at a categorically at a linear pace and so in effect the understanding of the world is receding. This book is important in a general sense in that its meaning in a meta-systemic level and not at a interdisciplinary level. And so what appears is not classifiable under the old categories.

Particular: autopoietic systems are homeostats: the variable that keeps a critical system stable is the system’s own organization. Anything can change about the system but as such it survives.

Beer states that human societies are biological systems: ‘..any cohesive social institution is an autopoietic system – because it survives, because its method of survival answers the autopoietic criteria, and because it may well change its entire appearance and its apparent purpose in the process. As examples I list: firms and industries, schools and universities, clinics and hospitals, professional bodies, departments of state, and whole countries’ (p70).

If this view is valid, it has extremely important consequences. In the first place it means that every social institution (in several of which any one individual is embedded at the intersect) is embedded in a larger social institution, and so on recursively – and that all of them are autopoietic. This immediately explains why the process of change at any level of recursion (from the individual to the state) is not only difficult to accomplish but actually impossible – in the full sense of the intention: ‘I am going completely to change myself’. The reason is that the ‘I’, that self-contained autopoietic ‘it’, is a component of another autopoietic system’. These last statements also bear a relation to the experience with change management. It is related to the idea of a funnel resulting from the Western belief in the idea of progress (aka capitalism, aka free-market mechanism).

BELANGRIJK regarding social systems: the authors claim: ‘Our purpose is to understand the organization of living systems in relation to their unitary character’. This formulation of the problem begs the question as to what is allowed to be a called a living system, as theey themselves admit. ‘Unless one knows which is the living organization, one cannot know which organization is living’. They quickly reach the concusion however (Subsection (b) of Section 2 of Chapter 1) that ‘autopiesis is necessary and sufficient to characterize the organization of living systems’. THEN they display some unease, quoting the popular belief: ‘… and no synthetic system is accepted as living.’(p71). This is an important connection with memetics: now it is possible to claim that social systems (that is to say the memetic systems that bring them about) are natural systems and so they are not synthetic by design. I have argued that because it evolves it must be alive so as to be able to define the subject of evolution via the concept of living systems.

AUTOPOIESIS – The Organization of the Living

Systeem causaliteit

Introduction

Common experience is that living systems are autonomous and they can reproduce. Conversely if something shows signs of autonomy then it is naively often deemed to be alive. Autonomy is exhibited by living systems through their self-asserting capacity to maintain their identity through the active compensation of deformations. The endeavor of the authors is to disclose the nature of the living organization. Their purpose is to understand the organization of living systems in relation to their unitary character. Their approach is mechanistic: no forces or principles will be adduced which are not found in the physical universe. Their interest is in processes and relations between processes realized through components, not in the properties of components (p75). It is assumed that an organization exists that is common to all living systems, regardless the nature of their components (p76). It is assumed that living systems are machines: a non-animistic view, relations are the pivot, not the components, dynamism is a feature of many machines also. The research question is: ‘What is the organization of living systems,, what kind of machines are they, and how is their phenomenology, including reproduction and evolution, determined by their unitary organization?’ (p76).

Chapter I – On Machines, Living and Otherwise

1. Machines

The properties of the components are irrelevant apart from those that participate in the interactions and transformations that constitute the system. The relevant properties determine those relations that determine the working of the machine which they integrate and constitute as a unity.

The organization of the machine is constituted by the relations that define it as a unity and determine the dynamics of the interactions and the transformations it may undergo as such a unity. The structure of the machine is constituted by the actual relations holding between the components integrating the machine in a given space. In this way a given machine can be realized by many different structures (p77).

‘Purpose’ is a means to explain more efficiently the workings of a machine: by using this concept, the imagination of the listener is invoked to reduce the task of explaining of the organization of a particular machine. It is not one of the constitutive properties of such a machine.

2. Living machines

a) Autopoietic machines

Machines can maintain some of their variables constant or within a limited range. This is expressed in the organization of the machine such that the process occurs within the boundaries of the machine which the very organization specifies. These machines are homeostatic and all feedback is internal to them. If there is a machine M with a feedback loop external to it such that a change in the output changes the input, then a M’ exists that includes the feedback loop in the organization that defines it. This is how autopoiesis is defined by the authors: ‘An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in the space in which they (the components) exist by specifying the topological domain of its realization as such a network’ (p79). In this way the autopoietic machine generates and specifies its own organization through its operation as a system of production of its own components in their endless turnover under conditions of perturbations and compensation thereof.

The relations of production of components are given as processes; if these processes stop then the production stops. In an autopoietic system these relations must be regenerated by the components which they produce such that the system remain autopoietic.

Autopoietic organization means that processes interlace a network of processes of production of components which constitute the network as a unity as they realize it. Every time this organization is realized as a concrete system in a given space, the domain of deformations, which this system can withstand without loss of identity as it maintains its organization constant, is the domain of changes in which it exists as a unity (p80). Autopoietic machine:

(i) are autonomous because they subordinate all change to the maintenance of their own organization

(ii) have an individuality because they keep their organization as an invariant through its continuous production. This represents their identity which is independent of their interactions with an observer

(iii) are unities because of their autopoietic organizations and their operations specify their own boundaries in the processes of self-production

(iv) have no inputs or outputs because even though they can be perturbed by independent events and they can repeatedly undergo structural changes to compensate these. These changes are always subordinated to the maintenance of the autopoietic organization of the machine

The actual implementation of the organization in physical space depends on the properties of the physical materials that embody it. A machine will disintegrate if it is perturbed such that the organization would have to compensate outside of its domain of compensations. The actual way a machine is realized determines the particular perturbations it can suffer without disintegrating.

b. Living systems

In other words we claim that the notion of autopoiesis is necessary and sufficient to characterize the organization of living systems’ (p82).

Chapter II – Dispensability of Teleonomy

Teleology means to describe things by their apparent goal or purpose. Teleonomy means the quality of apparent purposefulness or goal-directedness in living organisms. Both are unnecessary for the understanding of the living organization.

1. Purposelessness

Ontogeny is generally considered as an integrated process toward an adult state following some internal project or program. At different stages certain structures are attained that allow it to perform certain functions. Phylogeny is viewed as the history of adaptive transformations via reproductive processes aimed at satisfying the project of the species with complete subordination of the individual to this end. Purpose or aim and function are not functions of any machine (allo or auto) but they belong to the domain of our actions, namely the domain of descriptions. When applied to some system independent from us, they reflect our considering the machine or system in some encompassing context. Define a set of circumstances that lead the machine to change following a certan path of variations in its output. The connection between these outputs and the corresponding inputs in the selected context is called the aim or purpose of the machine. This aim is necessarily in the domain of the observer. Function can be treated in the same way. Neither aim nor function of the machine constitute its organization and so they are not part of its operation. ‘Living systems, as physical autopoietic machines, are purposeless systems’ (p86).

2. Individuality

In fact, a living system is specified as an individual, as a unitary element of interactions, by its autopoietic organization which determines that any change in it should take place subordinated to its maintenance, and thus sets the boundary conditions that specify what pertains to it and what does not pertain to it in the concreteness of the realization’(p87). In its history as an autopoietic organization, change in a living system can only take place so the extent that it does not interfere with the system’s functioning as a unity; the autopoietic organization remains invariant. Ontogeny in this sense is an expression of the individuality of living systems and the way it is realized; it is a process of the becoming of a system that is fully autopoietic, at every point, the unity in its fullness and not a transit from an incomplete to a complete system. The notion of development (or even progress) is relevant from the perspective of the observer and belongs to their domain.

Chapter III – Embodiments of autopoiesis

The assertion that physical autopoietic systems are living systems requires the proof that all the phenomenology of a living system can be either reduced or subordinated to its autopoiesis .. This proof must consist in showing that autopoiesis constitutes or is necessary and sufficient for the occurrence of all biological phenomena..’(p88).

1. Descriptive and causal notions

The existence of an autopoietic system requires the existence of components with properties that determine their relations such that these realize its organization as a unity. The components are defined by their role in this organization; the domain of the relations of an autopoietic organization is closed. And in this way the autopoietic organization defines a ‘space’ in which it can be realized as a concrete system; the dimensions of this space are the relations of production of the components that realize it, namely Relations of:

(i) Constitution, that determine that the components produced constitute the topology in which the autopoiesis is realized

(ii) Specificity, that determine that the components produced be the specific ones defined by their participation in the autopoiesis

(iii) Order, that determine that the concatenation of the components in the relations of specification, constitution and order be the ones specified by the autopoiesis.

Notions that apply to all autopoietic systems are:

(i) energetic and thermodynamic considerations are not part of the design of autopoietic systems. They are however in vigor implicitly: if the components and their properties, including the relational ones, can be realized then the autopoietic system can be realized.

(ii) Specificity and Order are referential notions in the sense that they carry meaning only in the context of their part in the autopoietic organization of the system under review.

(iii) An autopoietic organization acquires topological unity via its embodiment in a concrete autopoietic system. ‘Furthermore, the space defined by an autopoietic system is self-contained and cannot be described by using dimensions that define another space. When we refer to our interactions with a concrete autopoietic system, however, we project this system upon the space of our manipulations and make a description of this projection… Our description, however, follows the ensuing change of the projection of the autopoietic system in the space of our description, not in the autopoietic space’ (p90)

(iv) Concepts such as coding and transmission of information do not refer to actual processes in an autopoietic system. They do not enter in the realization of the autopoietic system. And so the notion of specificity as described above does not imply coding, information or instructions, but it describes relations between components determined by and produced by the autopoietic organization. The notions of coding and regulation are cognitive and they represent interactions of the observer, not phenomena in the observed domain.

2. Molecular embodiments

(i) Production of constitutive relations; these relations determine the topology of the autopoietic organization including its physical boundaries: ‘There is no specification in the cell of what it is not’(p91)

(ii) Production of relations of specification; these relations determine the identity (properties) of the components of the autopoietic organization and as a consequence its physical factibility. There is no production in the autopoietic system (such as a cell) of relations of specification that do not pertain to it.

(iii) Production of relations of order

These relations determine the dynamics of the autopoietic organization by deteminning the concatenation of the production of relations of constitution, specification and order, and hence its actual realization. This occurs via the production of components that realize the production of relations the production of relations of constitution, specification and order.’There is no ordering through the autopoietic organization of the cell of processes that do not belong to it.’ (p92)

Compensation of deformation keeps the autopoietic system in the autopoietic space.’(p93)

3. Origin

The geometric properties of molecules determine their relations of constitution, namely the topology. Their chemical properties determine their possible interactions hence their relations of specificity. Taken together they determine the sequence and concatenation of the molecular interactions, namely their relations of order. An autopoietic system can exist if its relations of order, is produced and remains constant, concatenate the relations of constitution and specificity in such a way that the system remains autopoietic. Asa consequence, the question about the origin of an autopoietic system is the question about the conditions that must be satisfied for the establishment of an autopoietic space: ‘This problem (of origin DPB), then, is.. a general one of what relations .. any constitutive units should satisfy.’(p93). This leads to the following considerations:

(i) ‘An autopoietic system is defined as a unity by and through its autopoietic organization.’ (p93) ‘Without unity in some space an autopoietic system is not different from the background in which it is supposed to lie, and, hence, can only be a system in the space of our description where its unity is conceptually stipulated’ (p94)

(ii) ‘The establishment of an autopoietic system cannot be a gradual process; either a system is an autopoietic system or it is not’ (p94). ‘Accordingly there are not and there cannot be intermediate systems.’ (p94)

(iii) ‘Auto-catalytic processes do not constitute autopoietic systems because among other things, they do not determine their topology.’ (p94) A unity is defined by operations of distinction as provided by the autopoietic system; .. its origin is co-circumstantial with the establishment of this operation’(p94)

(iv) Two aspects concerning the origin of autopoietic systems: a) factibility and b) the possibility of their spontaneous occurrence. a) the establishment of a system depends on the availability of the components that constitute it and the proper concatenation of their interactions. If these occur then the system is realized. b) given factibility and given the existence of factual autopoietic system, natural conditions exist for the occurrence of autopoietic systems.

Chapter IV – Diversity of Autopoiesis

Reproduction requires the existence of a unity to be reproduced. This is necessarily secondary to the establishment of such a unity. Evolution requires reproduction and the possibility of change and it is necessarily secondary to the establishment of reproduction.

1. Subordination to the condition of unity

Unity is the distinguishability of a unity from a background, hence from other unities. It is the sole necessary condition for existence in a given domain. Its nature and the domain in which it exists are specified by the process of its distinction and determination. ‘Unity distinction is .. an operative notion referring to the process through which a unity becomes asserted or defined: the conditions which specify a unity determine its phenomenology. In living systems, these conditions are determined by their autopoietic organization. In fact, autopoiesis implies the subordination of all change in the autopoietic system to the maintenance of its autopoietic organization, and since this organization defines it as a unity, it implies total subordination of the phenomenology of the system to the maintenance of its unity’ (p97). Consequences of this subordination are:

(i) the establishment of a unity defines the domain of its phenomenology, but the structure of the unity determines the realization of the phenomenology in that domain.

(ii) if the new unity is autopoietic then its phenomenology depends on maintenance of the autopoiesis, which in turn may or may not depend on the autopoiesis of its components

(iii) The identity of an autopoietic unity is maintained while it is autopoietic: as long as it is a unity in physical space and it is a unity in autopoietic space, regardless of the extent to which it is otherwise transformed.

(iv) Only after the autopoietic unity as such is established can it reproduce as a biological phenomenon.

2. Plasticity of ontogeny

The ontogeny means the history of the structural transformation of a unity; in the case of an autopoietic system, it means the history of the maintenance of its identity through continuous autopoiesis in physical space. Comments:

(i) Different classes of autopoietic systems have different classes of ontogenies

(ii) Given that it does not have inputs or outputs, the organization of an autopoietic system determines which changes the system may undergo without loss of identity

(iii) The way the autopoiesis is realized during ontogeny may change, but it should take place without loss of identity meaning uninterrupted autopoiesis

(iv) The changes that an autopoietic system may undergo without a loss of identity are a consequence of deformations; the sequence of the compensating of the deformations is determined by the sequence of the deformations. Nota bene: ‘Although in an autopoietic system all changes are internally determined, for an observer its ontogeny reflects its history of interactions with an independent ambience.’(pp. 98-9)

(v) An observer may distinguish internally and externally generated perturbations even though these are intrinsically indistinguisshable to the autopoietic system itself.

(vi) Changes that an autopoietic system can undergo while maintaining identity can be: a) conservative change in which only the relations between the components change and b) innovative changes, in which the components themselves change. In the first case the system remains positioned on the same point in the autopoietic space, because its components are invariant. In the second case, the interaction leads to a change in the way the autopoiesis is realized and to a change in the position in the autopoietic space, because its components have changed.

3. Reproduction, a complication of the unity

Reproduction is operationally secondary to the establishment of the unity: it cannot be a defining feature of the organization of a unity such as a living system. Living systems are characterized by their autopoietic organization and as a consequence reproduction must be a complication of the autopoietic organization during autopoiesis. ‘.. and its origin must be viewed and understood as secondary to, and independent from the origin of the living organization… in order to understand reproduction and its consequences in autopoietic systems we must analyze the operational nature of this process in relation to autopoiesis’(p100)

(i) Replication – a system generates unities different from itself but in principle identical to each other. Copy – an object or phenomenon is mapped upon a different system so that an isomorphic object or phenomenon is realized in it. Self-reproduction – a system produces another system with a similar organization through a process that is coupled to the process of its own production. ‘It is apparent that only autopoietic systems can self-reproduce because they are realized through a process of self-production (autopoiesis)’ (p101).

(ii) Only in self-replication is the mechanism of reproduction internal (in principle identical) to the pattern reproduced.

(iii) In terrestrial living systems currently known autopoiesis and reproduction are directly coupled. In them reproduction is a moment in autopoiesis and the same mechanism that constitutes the one also constitutes the other, and consequentially: a) self-reproduction must take place during autopoiesis, b) the individuals produced are self-contained and no external self-reproduction is a form of autopoiesis; variation and constancy in each reproductive step are part of the reproductive mechanism but an expression of autopoiesis c) variation of the way autopoiesis is realized can only arise as a modification from a pre-existing autopoietic structure. As a consequence, to maintain autopoiesis constant, variation can only arise from perturbations that require further homeostatic complications d) Replication takes place independently from autopoiesis, copy takes place in heteropoiesis, self-reproduction is exclusive for autopoiesis and its origin is bound to it as a historically secondary phenomenon e) coding, message or information are not applicable to the phenomenon self-reproduction: ‘Thus, in self-reproduction there is no transmission of information between independent entities; the reproducing and the reproduced unities are topologically independent entities produced through a single process of autopoiesis in which all components have a constitutive participation’ (p102).

4. Evolution, a historical network

A state in a sequence of states arises as a modification of a previous state and not as an independent state. The notion of history may refer to the antecedents of a given phenomenon as a succession of events leading up to it or it may be used to characterize the phenomenon as a process.

(i) Evolution is the history of change in the realization of an invariant organization embodied in independent unities sequentially realized through reproductive steps while the structural realization of the unity at each step arises as a modification of the previous one which constitutes its sequential and historical antecedent.

(ii) Reproduction by replication or by copy of an unchanging model implies an uncoupling of the organization of the unities produced and their producing mechanism.

(iii) Ontogeny and evolution are completely different phenomena: in ontogeny the identity is never interrupted, while in evolution a succession of identities is generated through sequential reproduction. Only unities have ontogenies.

(iv) ‘Selection, as a process in a population of unities, is a process of differential realization in a context that specifies the unitary structures that can be realized’ (p105). This is illustrated by the genotypical space and phenotypical space, the first via variation ‘offering’ possibilities to the second as an experiment to select the ones for survival in that specific context a/p quote above.

(v) Evolution takes place as a history of change in the realization of an invariant organization embodied in the realization of successively generated unities. Reproduction must allow for change in the structure of the sequentially reproduced unities.

(vi) ‘Of the two possible mechanisms that can give rise to sequential reproduction, the only one which is accessible to autopoietic systems in the absence of an independent copying mechanism, is self-reproduction, because of the coincidence between the reproducing mechanisms and the reproducing unity. Sequential reproduction through copy takes place a present only in relation to the operation of living systems in their domain of interactions, particularly in cultural learning; cultural evolution takes place through sequential copy of a changing model in the process of social indoctrination, generation after generation’ (p106)

(vii) ‘A species is a population or a collection of populations of reproductively connected individuals which are thus the nodes in a historical network’(p106)

Strictly, a historical network is defined by each and every one of the individuals which constitute its nodes, but it is at any moment represented historically by the species as the collection of all the simultaneously existing nodes of the network; in fact, then, a species does not evolve because as a unity in the historical domain it only has a history of change. What evolves is a pattern of autopoietic realization embodied in many particular variations in a collection of transitory individuals that together define a reproductive historical network. Thus, the individuals, though transitory, are essential, not dispensable, because they constitute a necessary condition for the existence of the historical network which they define. The species is only an abstract entiry in the present, and although it represents a histoorical phenomenon it does not constitute a generative factor in the phenomenology of evolution, it is its result’(p107)

5. Second and third order autopoietic systems

If the conduct of two or more unities is such that is a domain where the conduct of one or more of them is a function of the conduct of the others then the unities are said to be coupled. Coupling arises as a result of mutual modifications undergone by the unities in the course of their ongoing interactions while their identities remain intact. If the identity of a unity is lost then a new unity may be generated as a result of it, but no coupling takes place.’.. coupling leads also to the generation of a new unity that may exist in a different domain from the domain in which the component-coupled unities retain their identity’ (p107)

The nature of the coupling is determined by their autopoietic organization:

(i) Autopoietic systems can interact without loss of identity as long as reciprocally inflicted perturbations lead to compensable disturbances in their structures. They can couple and constitute a new unity while their individual paths of autopoiesis become sources of the specification of each other’s ambience. To persist as a unity the disturbances must remain in the domain permitted by their organizations. As a result the coupling can become invariant while the coupled systems undergo structural changes as a consequence of it. In this way a composite system can develop in which the autopoiesis of the individual systems is subordinate to the ambience defined by the autopoiesis of all the other autopoietic components of the composite unity. Such a system will be defined as a unity by the coupling relations of its component autopoietic systems. A system whose autopoiesis entails the autopoiesis of the coupled unities which realize it, is an autopoietic system of a higher order.

(ii) ‘An autopoietic system can become a component of another system if some aspects of its path of autopoietic change can participate in the realization of this other system’ (p110)

(iii) ‘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 the second order’ (p110) An example on earth is the multicellular pattern of organization.

Chapter 5 – Presence of Autopoiesis

1. Biological Implications

.., hence in a living system, loss of autopoiesis is disintegration as a unity and loss of identity, that is, death’ (p112).

(i) ‘The phenomenology of living systems, then, is the mechanical phenomenology of physical autopoietic machines’(p113)

(ii) ‘A biological explanation must be a reformulation of in terms of processes subordinated to autopoiesis, that is, a reformulation in the biological phenomenological domain’ (p114)

(iii)

(iv) ‘.. the biological phenomenological is not less and not more than the phenomenology of autopoietic systems in the physical space’ (p114)

2. Epistemological implications

(i) ‘As a result, the biological domain is fully defined and self-contained, no additional notions are necessary, and any adequate biological explanation has the same epistemological validity that any mechanistic explanation of any mechanistic phenomenon in the physical space has’(p116)

(ii) ‘.. an autopoietic system .. must be explained through autopoietic mechanical relations in the mechanical domain, the phenomena generated through interactions of the autopoietic unities must be explained in the domain of interactions of the autopoietic unities through the relations that define that domain’ (p117)

(iii) ‘The organization of the individual is autopoietic and upon this fact rests all its significance: it becomes defined through its existing, and its existing is autopoietic. Thus biology cannot be used anymore to justify the dispensability of the individuals for the benefit of the species, society or mankind under the pretense that its role is to perpetuate them. Biologically the individuals are not dispensable’ (p 118)

3. Cognitive Implications

The domain of all the interactions into which an autopoietic system can enter without loss of identity is its cognitive domain; this is the domain of all the descriptions it can possibly make. The particular mode of autopoiesis determines its cognitive domain hence the diversity of its behavior.

(i) knowledge (its conduct repertoire) is relative to the cognitive domain of the knower. If the way in which the autopoiesis is realized changes then the knowledge of the unity changes. In that sense knowledge is a reflection of the ontogeny of an organism, because it is a process of continual structural change without loss of autopoiesis and a continual specification of the behavioral capacity hence of its actual domain of interactions.

(ii) Autopoietic systems may interact with each other under conditions that result in behavioral coupling. Autopoietic conduct of A is the source of a deformation in B. The compensatory behavior in B is the source of a deformation in A, whose compensatory behavior for B is the source ..&c. These interactions occur in a chain while A and B interact independently based on their internal structure. Their behavior however is a source of compensable deformations to the other which can be described as meaningful in the context of the interactions in light of the coupled behavior. These are communicative interactions. This consensual domain of communicative interactions where behaviorally coupled organisms orient each other with modes of behavior based on their internal structure is the linguistic domain. Communicative and linguistic interactions are non-informative; organism A does not determine the conduct of organism B; that is determined by their proper organizations.

(iii) ‘An autopoietic system capable of interacting with its own states, and capable of developing with others a linguistic consensual domain, can treat its own linguistic states as a source of deformations and thus interact linguistically in a closed linguistic domain’ (p121). Properties of such systems are: a) An autopoietic system can treat some recursively generated states as objects of further interactions. This can give rise to a meta-domain of consensual distinctions appearing to the observer as a domain of interactions with representations of interactions. The system now operates as an observer. This can occur at any time and so the domain of these recursive interactions with its own states is in principle infinite, unless autopoiesis is lost b) A living system capable of being an observer can interact with descriptive states of itself in the sense of interactions with its own self-linguistic states. It is now an observer of itself as an observer, which can be repeated in an endless manner. The domain is called self-observation and consider self-conscious behavior is self-observing behavior, namely in the domain of self-observation. The observer as an observer remains in a descriptive domain as no description of absolute reality is possible. Some such description would require an interaction with the absolute by the autopoietic organization of the observer, not by an agent of it.

Living systems are an existential proof; they exist only to the extent that they can exist. The fantasy of our imagination cannot deny this. Living systems are concatenations of processes in a mechanistic domain; fantasies are concatenations of descriptions in a linguistic domain. In the first case, the concatenated unities are processes; in the second case, they are modes of linguistic behavior’ (p122)

A New Kind of Science

Wolfram concludes that ‘the phenomenon of complexity is quite universal – and quite independent of the details of particular systems’. This complex behaviour does not depend on system features such as the way cellulare automata are typically arranged in a rigid array or that they are processed in parallel. Very simple rules of cellular automata generally lead to repetitive behaviour, slightly more complex rules may lead to nested behaviour and even more complex rules may lead to complex behaviour of the system. Complexity with regards to the underlying rules means how they can be intricate or their assembly or make-up is complicated. Complexity with regards to the behaviour of the overall system means that little or no regularity is observed.

The surprise is that the threshold for the level of complexity of the underlying rules to generate overall system complexity is relatively low. Conversely, above the threshold, there is no requirement for the rules to become more complex for the overall behaviour of the system to become more complex.

And vice versa: even the most complex of rules are capable of producing simple behaviour. Moreover: the kinds of behaviour at a system level are similar for various kinds of underlying rules. They can be categorized as repetitive, nested, random and ‘including localized structures’. This implies that general principles exist that produce the behaviour of a wide range of systems, regardless of the details of the underlying rules. And so, without knowing every detail of the observed system, we can make fundamental statements about its overall behaviour. Another consequence is that in order to study complex behaviour, there is no need to design vastly complicated computer programs in order to generate interesting behaviour: the simple programs will do [Wolfram, 2002, pp. 105 – 113].

Numbers
Systems used in textbooks for complete analysis may have a limited capacity to generate complex behaviour because they, given the difficulties to make a complete analysis, are specifically chosen for their amenability to complete analysis, hence of a simple kind. If we ignore the need for analysis and look only at results of computer experiments, even simple ‘number programs’ can lead to complex results.

One difference is that in traditional mathematics, numbers are usually seen as elementary objects, the most important attribute of which is their size. Not so for computers: numbers must be represented explicity (in their entirety) for any computer to be able to work with it. This means that a computer uses numbers as we do: by reading them or writing them down fully as a sequence of digits. Whereas we humans do this on base 10 (0 to 9), computers typically use base 2 (0 to 1). Operations on these sequences have the effect that the sequences of digits are updated and change shape. In tradional mathematics, this effect is disregarded: the effect of an operation on a sequence as a consequence of an operation is considered trivial. Yet this effect amongst others is by itself capable of introducing complexity. However, even when the size only is represented as a base 2 digit sequence when executing a simple operator such as multiplication with fractions or even whole numbers, complex behaviour is possible.

Indeed, in the end, despite some confusing suggestions from traditional mathematics, we will discover that the general behavior of systems based on numbers is very similar to the general behavior of simple programs that we have already discussed‘ [Wolfram, 2002, p 117].

The underlying rules for systems like cellular automata are usually different from those for systems based on numbers. The main reason forr that is that rules for cellular automata are always local: the new color of any particular cell depends only on the previous colour of that cell and its immediate neighbours. But in systems based on numbers there is usually no such locality. But despite the absence of locality in the underlying rules of systes based on numbers it is possible to find localized structures also seen in cellular automata.

When using recursive functions of a form such as f(n) = f(n – f(n- 1) then only subtraction and addition are sufficient for the development of small programs based on numbers that generate behaviour of great complexity.

And almost by definition, numbers that can be obtained by simple mathematical operations will correspond to simple such (symbolic DPB) expressions. But the problem is that there is no telling how difficult it may be to compute the actual value of a number from the symbolic expression that is used to represent it‘ [Wolfram, 2002, p143].

Adding more dimensions to a cellular automaton or a turing machine does not necessarily mean that the complexity increases.

But the crucial point that I will discuss more in Chapter 7 is that the presence of sensitive dependence on initial conditions in systems like (a) and (b) in no way implies that it is what is responsible for the randomness and complexity we see in these systems. And indeed, what looking at the shift map in terms of digit sequences shows us is that this phenomenon on its own can make no contribution at all to what we can reasonably consider the ultimate production of randomness‘ [Wolfram, 2002, p. 155].

Multiway Systems
The design of this class of systems is so that the systems can have multiple states at any one step. The states at some time generate states at the nex step according to the underlying rules. All states thus generated remain in place after they have been generated. Most Multiway systems grow very fast or not at all and slow growth is as rare as is randomness. The usual behaviour is that repetition occurs, even if it is after a large number of seemingly random states. The threshold seems to be in the rate of growth: if the system is allowed to grow faster then the chances that it will show complex behaviour increases. In the process, however, it generates so many states that it becomes difficult to handle [Wolfram 2002, pp. 204 – 209].

Chapter 6: Starting from Randomness
If systems are started with random initial conditions (up to this point they started with very simple initial conditions such as one black or one white cell), they manage to exhibit repetitive, nested as well as complex behaviour. They are capable of generating a pattern that is partially random and partially locally structured. The point is that the intial conditions may be in part but not alone responsible for the existence of complex behaviour of the system [Wolfram 2002, pp. 223 – 230].

Class 1 – the behaviour is very simple and almost all initial conditions lead to exactly the same uniform final state

Class 2 – there are many different possible final states, but all of them consist just of a certain set of simple structures that either remain the same forever or repeat every few steps

Class 3 – the behaviour is more complicated, and seems in many respects random, although triangles and other small-scale structures are essentially always on some level seen

Class 4 – this class of systems involves a mixture of order and randomness: localized structures are produced which on their own are fairly simple, but these structures move around and interact with each other in very complicated ways.

‘There is no way of telling into which class a cellular automaton falls by studying its rules. What is needed is to run them and visually ascertain which class it belongs to’ [Wolfram 2002, Chapter 6, pp.235].

One-dimensional cellular automata of Class 4 are often on the boundary between Class 2 and Class 3, but settling in neither one of them. There seems to be some kind of transition. They do have characteristics of their own, notably localized structures, that do neither belong to Class 2 or Class 3 behaviour. This behaviour including localized structures can occur in ordinary discrete cellular automata as well as in continuous cellular automata as well as in two-dimensional cellular automata.

Sensitivity to Initial Conditions and Handling of Information
Class 1 – changes always die out. Information about a change is always quickly forgotten

Class 2 – changes may persist, but they remain localized, contained in a part of the system. Some information about the change is retained in the final configuration, but remains local and therefore not communicated thoughout the system

Class 3 – changes spread at a uniform rate thoughout the entire system. Change is communicated long-range given that local structures travelling around the system are affected by the change

Class 4 – changes spread sporadically, affecting other cells locally. These systems are capable of communicating long-range, but this happens only when localized structures are affected [Wolfram 2002, p. 252].

In Class 2 systems, the logical connection between their eventually repetitive behaviour and the fact that no long-range communication takes place is that the absence of long-range communication forces the system to behave as if its size were limited. This behaviour follows a general result that any system of limited size, discrete steps and definite rules will repeat itself eventually.

In Class 3 systems the possible sources of randomness are the randomness present in initial conditions (in the case of a cellular automaton the initial cells are chosen at random versus one single black or white cell for simple initial conditions) and the sensitive dependence on initial conditions of the process. Random behaviour in a Class 3 system can occur if there is no randomness in its initial conditions. There is not an a priori difference in the behaviour of most systems generated on the basis of random initial conditions and one based on simple intial conditions1. The dependence on the initial conditions of the patterns arising in the pattern in the overall behaviour of the system is limited in the sense that although the produced randomness is evident in many cases, the exact shape can differ from the initial conditions. This is a form of stability, for, whatever the initial conditions the system has to deal with, it always produces similar recognizable random behaviour as a result.

In Class 4 there must be some structures that can persist forever. If a system is capable of showing a sufficiently complicated structure then eventually at some initial condition, a moving structure is found also. Moving structures are inevitable in Class 4 systems. It is a general feature of Class 4 cellular automata that with appropriate initial conditions they can mimick the behaviour of all sorts of other systems. The behaviour of Class 4 cellular automata can be diverse and complex even though their underlying rules are very simple (compared to other cellular automata). The way that diffferent structures existing in Class 4 systems interact is difficult to predict. The behaviour resulting from the interaction is vastly more complex than the behaviour of the individual structures and the effects of the interactions may take a long time (many steps) after the collision to become clear.

It is common to be able to design special initial conditions so that some cellular automaton behaves like another. The trick is that the special initial conditions must then be designed so that the behaviour of the cellular automaton emulated is contained within the overall behaviour of the other cellular automaton.

Attractors
The behaviour of a cellular automaton depends on the specified initial conditions. The behaviour of the system, the sequences shown, gets progressively more restricted as the system develops. The resulting end-state or final configuration can be thought of as an attractor for that cellular automaton. Usually many different but related initial conditionss lead to the same end-state: the basin of attraction leads it to an attractor, visible to the observer as the final configuration of the system.

Chapter 7 Mechanisms in Programs and Nature
Processes happening in nature are complicated. Simple programs are capable of producing this complicated behaviour. To what extent is the behaviour of the simple programs of for instance cellular automata relevant to phenomena observed in nature? ‘It (the visual similarity of the behaviour of cellular automata and natural processes being, DPB) is not, I believe, any kind of coincidence, or trick of perception. And instead what I suspect is that it reflects a deep correspondence between simple programs and systems in nature‘ [Wolfram 2002, p 298].

Striking similarities exist between the behaviours of many different processes in nature. This suggests a kind of universality in the types of behaviour of these processes, regardless the underlying rules. Wolfram suggests that this universality of behaviour encompasses both natural systems’ behaviour and that of cellular automata. If that is the case, studying the behaviour of cellular automata can give insight into the behaviour of processes occurring in nature. ‘For it (the observed similarity in systems behaviour, DPB) suggests that the basic mechanisms responsible for phenomena that we see in nature are somehow the same as those responsible for phenomena that we see in simple programs‘ [Wolfram 2002, p 298].

A feature of the behaviour of many processes in nature is randomness. Three sources of randomness in simple programs such as cellular automata exist:
the environment – randomness is injected into the system from outside from the interactions of the system with the environment.
initial conditions – the initial conditions are a source of randomness from outside. The randomness in the system’s behaviour is a transcription of the randomness in the initial conditions. Once the system evolves, no new randomness is introduced from interactions with the environment. The system’s behaviour can be no more random than the randomness of the initial conditions. In practical terms many times isolating a system from any outside interaction is not realistic and so the importance of this category is often limited.
intrinsic generation – simple programs often show random behaviour even though no randomness is injected from interactions with outside entities. Assuming that systems in nature behave like the simple programs, it is reasonable to assume that the intrinsic generating of randomness occurs in nature also. How random is this internally generated randomness really? Based on tests using existing measures for randomness they are at least as random as any process seen in nature. It is not random by a much used definition classifying behaviour as random if it can never be generated by a simple procedure such as the simple programs at hand, but this is a conceptual and not a practical definition. A limit to the randomness of numbers generated with a simple program, is that it is bound to repeat itself if it exists in a limited space. Another limit is the set of initial conditions: because it is deteministic, running a rule twice on the same initial conditions will generate the same sequence and the same random number as a consequence. Lastly truncating the generated number will limit its randomness. The clearest sign of intrinsic randomness is its repeatability: in the generated graphs areas will evolve with similar patterns. This is not possible starting from different initial conditions or with external randomness injected while interacting. The existence of intrinsic randomness allows a discrete system to behave in seemingly continuous ways, because the randomness at a local level averages out the differences in behaviour of individual simple programs or system elements. Continuous systems are capable of showing discrete behaviour and vice versa.

Constraints
But despite this (capability of constraints to force complex behaviour DPB) my strong suspicion is that of all of the examples we see in nature almost none can in the end best be explained in terms of constraints‘ [Wolfram 2002, p 342]. Constraints are a way of making a system behave as the observer wants it to behave. To find out which constraints are required to deliver the desired behaviour of a system in nature is in practical terms far too difficult. The reason for that difficulty is that the number of configurations in any space soon becomes very large and it seems impossible for systems in nature to work out which constraint is required to satisfy the constraints at hand, especially if this procedure needs to be performed routinely. Even if possible the procedure to find the rule that actually satisfies the constraint is so cumbersome and computationally intensive, that it seems unlikely that nature uses it to evolve its processes. As a consequence nature seems to not work with constraints but with explicit rules to evolve its processes.

Implications for everyday systems
Intuitively from the perspective of traditional science the more complex is the system, the more complex is its behaviour. It has turned out that this is not the case: simple programs are much capable of generating compicated behaviour. In general the explicit (mechanistic) models show behaviour that confirms the behaviour of the corresponding systems in nature, but often diverges in the details.
The traditional way to use a model to make predictions about the behaviour of an observed system is to input a few numbers from the observed system in your model and then to try and predict the system’s behaviour from the outputs of your model. When the observed behaviour is complex (for example if it exhibits random behaviour) this approach is not feasible.
If the model is represented by a number of abstract equations, then it is unlikely (nor was it intended) that the equations describe the mechanics of the system, but only to describe its behaviour in whatever way works to make a prediction about its future behaviour. This usually implies disregarding all the details and only taking into account only the important factors driving the behaviour of the system.
Using simple programs, there is also no direct relation between the behaviour of the elements of the studied system and the mechanics of the program. ‘.. all any model is supposed to do – whether it is a cellular automaton, a differential equation or anything else – is to provide an abstract representation of effects that are important in detemining the behaviour of a system. And below the level of these effects there is no reason that the model should actually operate like the system itself‘ [Wolfram 2002, p 366].
The approach in the case of the cellular automata is to then visually compare (compare the pictures of) the outcomes of the model with the behaviour of the system and try and draw conclusions about similarities in the behaviour of the observed system and the created system.

Biological Systems
Genetic material can be seen as the programming of a life form. Its lines contain rules that determine the morphology of a creature via the process of morphogenesis. Traditional darwinism suggests that the morphology of a creature determines its fitness. Its fitness in turn detemines its chances of survival and thus the survival of its genes: the more individuals of the species survive, the bigger its representation in the genepool. In this evolutionary process, the occurrence of mutations will add some randommness, so that the species continuously searches the genetic space of solutions for the combination of genes with the highest fitness.
The problem of maximizing fitness is essentially the same as the problem of satisfying constraints..‘ [Wolfram 2002, p386]. Sufficiently simple constraints can be satisfied by iterative random searches and converge to some solution, but if the constraints are complicated then this is no longer the case.
Biological systems have some tricks to speed up this process, like sexual reproduction to mix up the genetic offspring large scale and genetic differentiation to allow for localized updating of genetic information for separate organs.
Wolfram however consides it ‘implausible that the trillions or so of generations of organisms since the beginning of life on earth would be sufficient to allow optimal solutions to be found to constraints of any significant complexity‘ [Wolfram 2002 p 386]. To add insult to injury, the design of many existing organisms is far from optimal and is better described as a make-do, easy and cheap solution that will hopefully not immediately be fatal to its inhabitant.
In that sense not every feature of every creature points at some advantage towards the fitness of the creature: many features are hold-overs from elements evolved at some earlier stage. Many features are so because they are fairly straightforward to make based on simple programs and then they are just good enough for the species to survive, not more and not less. Not the details filled in afterwards, but the relatively coarse features support the survival of the species.
In a short program there is little room for frills: almost any mutation in the program will tend to have an immediate effect on at least some details of the phenotype. If, as a mental exercise, biological evolution is modeled as a sequence of cellular automata, using each others output sequentially as input, then it is easy to see that the final behaviour of the morphogenesis is quite complex.
It is, however, not required that the program be very long or complicated to generate complexity. A short program with some essential mutations suffices. The reason that there isn’t vastly more complexity in biological systems while it is so easy to come by and while the forms and patterns usually seen in biological systems are fairly simple is that: ‘My guess is that in essence it (the propensity to exhibit mainly simple patterns DPB) reflects limitations associated with the process of natural selection .. I suspect that in the end natural selection can only operate in a meaningful way on systems or parts of systems whose behaviour is in some sense quite simple‘ [Wolfram 2002, pp. 391 – 92]. The reasons are:
when behaviour is complex, the number of actual configurations quickly becomes too large to explore when the layout of different individuals in a species becomes very differnent then the details may have a different weight in their survival skills. If the variety of detail becomes large then acting consitently and definitively becomes increasingly difficult when the overall behaviour of a system is more complex then any of its subsystems, then any change will entail a large number of changes to all the subsystems, each with a different effect on the behaviour of the individual systems and natural selection has no way to pick the relevant changes
if chances occur in many directions, it becomes very difficult for changes to cancel out or find one direction and thus for natural selection to understand what to act on iterative random searches tend to be slow and make very little progress towards a global optimum.

If a feature is to be succesfully optimized for different environments then it must be simple. While it has been claimed that natural selection increases complexity of organisms, Wolfram suggests that it reduces complexity: ..’it tends to make biological systems avoid complexity, and be more like systems in engineering‘ [Wolfram 2002, p 393]. The difference is that in engineering systems are designed and developed in a goal oriented way, whereas in evolution it is done by an iterative random search process.

There is evidence from the fossil record that evolution brings smooth change and relative simplicity of features in biological systems. If all this evoltionary process points at simple features and smooth changes, then where comes the diversity from? It turns out that a change in the rate of growth changes the shape of the organism dramatically as well as its mechanical operation.

Fundamental Physics
My approach in investigating issues like the Second Law is in effect to use simple programs as metaphors for physical systems. But can such programs in fact be more than that? And for example is it conceivable that at some level physical systems actually operate directly according to the rules of a simple program? ‘ [Wolfram 2002, p. 434].

Out of 256 rules for cellular automata based on two colours and nearest neighbour interaction, only six exhibit reversible behaviour. This means that overall behaviour can be reversed if the rules of each automaton are played backwards. Their behaviour, however, is not very interesting. Out of 7,500 billion rules based on three colours and next-neighbour interaction, around 1,800 exhibit reversible behaviour of which a handful shows interesting behaviour.

The rules can be designed to show reversible behaviour if their pictured behaviour can be mirrored vertically (the graphs generated are usually from top to bottom, DPB): the future then looks the same as the past. It turns out that the pivotal design feature of reversible rules is that existing rules can be adapted to add dependence on the states of neighbouring cells two steps back. Note that this reversibily of rules can also be constructed by using the preceding step only, if, instead of two states, four are allowed. The overall behaviour showed by these rules is reversible, whether the intial conditons be random or simple. It is shown that a small fraction of the reversible rules exhibit complex behaviour for initial conditions that are simple or random alike.

Whether this reversibility actually happens in real life depends on the theoretical definition of the initial conditions and in our ability to set them up so as to exhibit the reversible overall behaviour. If the initial conditons are exactly right then increasingly complex behaviour towards the future can become simpler when reversed. In practical terms this hardly ever happens, because we tend to design and implement the intial conditions so that they are easy to describe and construct to the experimenter. It seems reasonable that in any meaningful experiment, the activities to set up the experiment should be simpler than the process that the experiment is intended to observe. If we consider these processes as computations, then the computations required to set up the experiment should be simpler than the computations involved in the evolution of the system under review. So starting with simple initial conditions and trace back to the more complex ones, then, starting the evolution of the system there anew, we will surely find that the system shows increasingly simple behaviour. Finding these complicated seemingly random initial conditions in any other way than tracing a reversible process to and fro the simple initial conditions seems impossible. This is also the basic argument for the existence of the Second Law of Thermodynamics.

Entropy is defined as the amount of information about a system that is still unknown after measurements on the system. The Second Law means that if more measurements are performed over time then the entropy will tend to decrease. In other words: should the observer be able to know with absolute certainty properties such as the positions and velocities of each particle in the system, then the entropy would be zero. According to the definition entropy is the information with which it would be possible to pick out the configuration the system is actually in from every possible configuration of the distribution of particles in the system satisfying the outcomes of the measurements on the system. To increase the number and quality of the measurements involved amounts to the same computational effort as is required for the actual evolution of the system. Once randomness is produced, the actual behaviour of the system becomes independent of the details of the initial conditions of the system. In a reversible system different initial conditions must lead to a diffent evolution of the system, for else there would be no way of reversing the system behaviour in a unique way. But even though the outcomes from different initial conditions can be much different, the overall patterns produced by the system can still look much the same. But to identify the initial conditions from the state of a system at any time implies a computational effort that is far beyond the effort for a practical and meaningful measurement procedure. If a system generates sufficient randomness, then it evolves towards a unique equilibrium whose properties are for practical reasons independent of its initial conditions. In this why it is possible to identify many systems based on a few typical parameters.

‘With cellular automata it is possible, using reversible rules and starting from a random set of initial conditions, to generate behaviour that increases order instead of tending towards more random behaviour, e.g. rule 37R [Wolfram 2002, pp. 452 – 57]. Its behaviour neither completely settles down to order nor does it generate randomness only. Although it is reversible, it does not obey the Second Law. To be able to reverse this process, however, the experimenter would have to set up initial conditions exactly so as to be able to reach the ‘earlier’ stages, else the information generated by the system is lost. But how can there be enough information to reconstruct the past? All the intermediate local structures that passed on the way to the ‘turning point’ would have to be absorbed by the system on its way back to in the end to reach its original state. No local structure emitted on the way to the turning point can escape.

The evolution in systems is therefore intrinsically? not reversible. All forms of self organisation in cellular automata without reversible rules can potentially occur?

For these reasons it is possible to parts of the universe get more organised than other parts, even with all laws of nature being reversible. What the cellular automata such as 37R show is that this is even possible for closed systems to not follow the Second Law. If the systems gets partitioned then within the partitions order might evolve while simultaneously elsewhere in the system randomness is generated. Any closed system will repeat itself at some point in time. Until then it must visit every possible configuration. Most of these will be or seem to be random. Rule 37R does not produce this ergodicity: it visits only a small fraction of all possible states before repeating.

Conserved Quantities and Continuum Phenomena
Examples are quantities of energy and electric charge. Can the amount of information in exchanged messages be a proxy for a quantity to be conserved?

With nearest neighbour rules, cellular automata do exhibit this principle (shown as the number of cells of equal colour conserved in each step), but without showing sufficient complex behaviour. Using next-neighbour rules, they are capable of showing conservation while exhibiting interesting behaviour also. Even more interesting and random behaviour occurs when block cells are used, especially using three colours instead of two. In this setup the total number of black cells must remain equal for the entire system. On a local level, however, the number of black cells does not necessarily remain the same.

Multiway systems
In a multiway system all possible replacements are always executed at every step, thereby generating many new strings (i.e. combinations of added up replacements) at each step. ‘In this way they allow for multiple histories for a system. At every step multiple replacements are possible and so, tracing back the different paths from string to string, different histories of the system are possible. This may appear strange, for our understanding of the universe is that it has only one history, not many. But if the state of the universe is a single string in the multiway system, then we are part of that string and we cannot look into it from the outside. Being on the inside of the string it is our perception that we follow just one unique history and not many. Had we been able to look at it from without, then the path that the system followed would seem arbitrary‘ [Wolfram 2002, p 505]. If the universe is indeed a multiway system then another source of randomness is the actual path that its evolution has followed. This randomness component is similar to the outside randomness discussed earlier, but different in the sense that in would occur even if this universe would be perfectly isolated from the rest of the universe.

There are sufficient other sources of randomness to explain interesting behaviour in the universe and that by itself is no sufficient reason to assume the multiway system as a basis for the evolution of the universe. What other reasons can there be to underpin the assumption that the underlying mechanism of the uiverse is a multiway system? For one, multiway systems are much capable of generating a vast many different possible strings and therefore many possible connections between them, meaning different histories.

However, looking at the sequences of those strings it becomes obvious that these can not be arbitrary. Each path is defined by a sequence of ways in which replacements by multiway systems’ rules are applied. And each such path in turn defines a causal network. Certain underlying rules have the property that the form of this causal network ends up being the same regardless of the order in which the replacements are applied. And thus regardless of the path that is followed in the multiway system. If the multiway system ends up with the same causal network, then it must be possible to apply a replacement to a string already generated, to end up at the same final state. Whenever paths always eventually converge then there will be similarities on a sufficiently large scale in the obtained causal networks. And so the structure of the causal networks may vary a lot at the level of individual events. But at a sufficiently large level, the individual details will be washed out and the structure of the causal network will be essentially the same: on a sufficiently high level the universe will appear to have a unique history, while the histories on local levels are different.

Processes of perception and analysis
The processes that lead to some forms of behaviour in systems are comparable to some processes that are involved in their perception and analysis. Perception relates to the immediate reception of data via sensory input, analysis involves conscious and computational effort. Perception and analysis are an effort to reduce events in our everyday lives to manageable proportions so that we can use them. Reduction of data happens by ignoring whatever is not necessary for our everyday survival and by finding patterns in the remaining data so that individual elements in the data do not need to be specified. If the data contains regularities then there is some redundance in the data. The reduction is important for reasons of storage and communication.
This process of perception and analysis is the inverse of the evolving of systems behaviour from simple programs: to identify whatever it is that produces some kind of behaviour. For observed complex behaviour this is not an easy task, for the complex behaviour generated bears no obvious relation to the simple programs or rules that generate them. An important difference is that there are many more ways to generate complex behaviour than there are to recognize the origins of this kind of behaviour. The task of finding the origins of this behaviour is similar to solving problems satisfying a set of constraints.
Randomness is roughly defined as the apparent inability to find a regularity in what we perceive. Absence of randomness implies that redundancies are present in what we see, hence a shorter description can be given of what we see that allows us to reproduce it. In the case of randomness, we would have no choice but to repeat the entire picture, pixel by pixel, to reproduce it. The fact that our usual perceptional abilities do not allow such description doesn’t mean that no such description exists. It is very much possible that randomness is generated by the repetition of a simple rule a few times over. Does it, then, imply that the picture is not random? From a perceptory point of view it is, because we are incapable to find the corresponding rule, from a conceptual point of view this definition is not satisfactory. In the latter case the definition would be that randomness exists if no such rule exists and not only if we cannot immediately discern it. However, finding the short description, i.e. the short program that generates this random behaviour is not possible in a computationally finite way. Resticting the computational effort to find out whether something is random seems unsatisfactory, because it is arbitrary, it still requires a vast amount of computational work and many systems will not be labelled as random for the wrong reasons. So in the definition of randomness some reference needs to be made to how the short descriptions are to be found. ‘..something could be considered to be random whenever there is essentially no simple program that can succeed in detecting regularities in it‘ [Wolfram 2002, p 556]. In practical terms this means that after comparing the behaviour of a few simple programs with the behaviour of the observed would-be random generator and if no regularities are found in it, then the behaviour of the observed system is random.

Complexity
If we say that something is complex, we say that we have failed to find a simple description for it hence that our powers of perception and analysis have failed on it. How the behaviour is described depends on what purpose the description serves, or how we perceive the observed behaviour. The assessment of the involved complexity may differ depending on the purpose of the observation. Given this purpose, then the shorter the description the less complex the behaviour. The remaining question is whether it is possible to define complexity independent of the details of the methods of perception and analysis. The common opinion traditionally was that any complex behaviour stems from a complex system, but this is no longer the case. It takes a simple program to develop a picture for which our perception can find no simple overall description.
So what this means is that, just like every other method of analysis that we have considered, we have little choice but to conclude that traditional mathematics and mathematical formulas cannot in the end realistically be expected to tell us very much about patterns generated by systems like rule 30‘ [Wolfram 2002, p 620].

Human Thinking
Human thinking stands out from other methods of perception in its extensive use of memory, the usage of the huge amount of data that we have encountered and interacted with previously. The way human memory does this is by retrieval based on general notions of similarity rather than exact specifications of whatever memory item is that we are looking for. Hashing could not work, because similar experiences summarized by different words might end up being stored in completely different locations and the relevant piece of information might not be retrieved on the occasion that the key search word involved hits a different hash code. What is needed is information that really sets one piece of information apart from other pieces, to store that and to discard all others. The effect is that the retrieved information is similar enough to have the same representation and thus to be retrieved of some remotely or seemingly remote association occurs with some situation at hand.
This can be achieved with a number of templates that the information is compared with. Only if the remaining signal per layer of nerve cells generates a certain hash code then the information is deemed relevant and retrieved. It is very rare that a variation in the input results in a variation in the output; in other words: quick retrieval (based on the hash code) of similar (not necessarily exactly the same) information is possible. The stored information is pattern based only and not stored as meaningful or a priori relevant information.

But it is my strong suspicion that in fact logic is very far from fundamental, particularly in human thinking‘ [Wolfram 2002, 627]. We retrieve connections from memory without too much effort, but perform logical reasoning cumbersomely, going one step after the next, and it possible that we are in that process mainly using elements of logic that we have learned from previous experience only.

Chapter 11 The Notion of Computation
All sorts of behaviour can be produced by simple rules such as cellular automata. There is a need for a framework for thinking about this behaviour. Traditional science provides this framework only if the observed behaviour is fairly simple. What can we do if the observed behaviour is more complex? The key-idea is the notion of computation. If the various kinds of behaviour are generated by simple rules, or simple programs then the way to think about them is in terms of the computations they can perform: the input is provided by the initial conditions and the output by the state of the system after a number of steps. What happens in between is the computation, in abstract terms and regardless the details of how it actually works. Abstraction is useful when discussing systems’ behaviour in a unified way, regardless the different kinds of underlying rules. For even though the internal workings of systems may be different, the computations they perform may be similar. At this pivot it may become possible to formulate principles applying to a variety of different systems and independent of the detailed structures of their rules.

At some level, any cellular automaton – or for that matter, any system whatsoever – can be viewed as performing a computation that determines what its future behaviour will be‘ [Wolfram, 2002, p 641]. And for some of the cellular automata described it so happens that the computations they perform can be described to a limited extent in traditional mathematical notions. Answers to the question of the framework come from practical computing.

The Phenomenon of Universality
Based on our experience with mechanical and other devices it can be assumed that we need different underlying constructions for different kinds of tasks. The existence of computers has shown that different underlying constructions make universal systems that can be made to execute different tasks by being programmed in different ways. The hardware is the same, different software may be used, programming the computer for different tasks.
This idea of universality is also the basis for programming languages, where instructions from a fixed set are strung together in different ways to create programs for different tasks. Conversely any computer programmed with a program designed in any language can perform the same set of tasks: any computer system or language can be set up to emulate one another. An analog is human language: virtually any topic can be discussed in any language and given two languages, it is largely possible to always translate between them.
Are natural systems universal as well? ‘The basic point is that if a system is universal, then it must effectively be capable of emulating any other system, and as a result it must be able to produce behavior that is as complex as the behavior of any other system. So knowing that a particular system is universal thus immediately implies that the system can produce behavior that is in a sense arbitrarily complex‘ [Wolfram 2002, p 643].

So as the intuition that complex behaviour must be generated by complex rules is wrong, so the idea that simple rules cannot be universal is wrong. It is often assumed that universality is a unique and special quality but now it becomes clear that it is widespread and occurs in a wide range of systems including the systems we see in nature.

It is possible to construct a universal cellular automaton and to input initial conditions so that it emulates any other cellular automata and thus to produce any behaviour that the other cellular automaton can produce. The conclusion is (again) that nothing new is gained by using rules that are more complex than the rules of the universal cellular automaton, because given it, more complicated rules can always be emulated by the simple rules of the universal cellular automaton and by setting up appropriate initial conditions. Universality can occur in simple cellular automata with two colours and next-neighbour rules, but their operation is more difficult to follow than cellular automata with a more complex set-up.

Emulating other Systems with Cellular Automata
Mobile cellular automata, cellular automata that emulate Turing machines, substitution systems2, sequential substitution systems, tag systems, register machine, number systems and simple operators. A cellular automaton can emulate a practical computer as it can emulate registers, numbers, logic expressions and data retrieval. Cellular automata can perform the computations that a practical computer can perform.
And so a universal cellular automaton is universal beyond being capable of emulating all other cellular automata: it is capable of emulating a vast array of other systems, including practical computers. Reciprocally all other automata can be made to emulate cellular automata, including a universal cellular automaton, and they must therefore itself be universal, because a universal cellular automaton can emulate a wide array of systems including all possible mobile automata and symbolic systems. ‘By emulating a universal cellular automaton with a Turing machine, it is possible to construct a universal Turing machine‘ [Wolfram 2002, p 665].

And indeed the fact that it is possible to set up a univeral system using essentially just the operations of ordinary arthmetic is closely related to the proof af Godel’s Theorem‘ [Wolfram 2002, p 673].

Implications of Universality
All of the discussed systems can be made to emulate each other. All of them have certain features in common. And now, thinking in terms of computation, we can begin to see why this might be the case. They have common features just because they can be made to emulate each other. The most important consequence is that from a computational perspective a very wide array of systems with very different underlying structures are at some level fundamentally equivalent. Although the initial thought might have been that the different kinds of systems would have been suitable for different kinds of computations, this is in fact not the case. They are capable of performing exactly the same kinds of computations.
Computation therefore can be discussed in abstract terms, independent of the kind of system that performs the computation: it does not matter what kind of system we use, any kind of system can be programmed to perform any kind of computation. The results of the study of computation at an abstract level are applicable to a wide variety of actual systems.
To be fair: not all cellular automata are capable of all kinds of computations, but some have large computational capabilties: once past a certain threshold, the set of possible computations will be always the same. Beyond that threshold of universality, no additional complexity of the underlying rules might increase the computational capabilties of the system. Once the threshold is passed, it does not matter what kind of system it is that we are observing.

The rule 110 Cellular Automaton
The threshold for the complexity of the underlying rules required to produce complex behaviour is remarkably low.

Class 4 Behaviour and Universality
Rule 110 with random initial conditions exhibits many localized structures that move around and interact with each other. This is not unique to that rule, this kind of behaviour is produced by all cellular automata of Class 4. The suspicion is that any Class 4 system will turn out to have universal computational capabilities. For the 256 nearest-neighbour rules and two colours, only four more or less comply (rule 124, 137 and 193, all require some trivial amendments). But for rules involving more colours, more dimensions and / or next-neigbour rules, Class 4 localized structures often emerge. The crux for the existence of class 4 behaviour is the control of the transmission of information through the system.

Universality in Turing Machines and other Systems
The simplest Universal Turing Machine currently known has two states and five possible colours. It might not be the simplest Universal Turing Machine in existence and so the simplest lies between this and two states and two colours, none of which are Universal Turing Machines; there is some evidence that a Turing Machine with two states and three colours is universal, but no proof exists as yet. There is a close connection between the appearance of complexity and universality.

Combinators can emulate rule 110 and are known to be universal from the 1930s. Other symbolic sytems show complex behaviour and may turn out to be universal too.

Chapter 12 The Principle of Computational Equivalence
The Principle of Computational Equivalence applies to any process of any kind, natural or artificial: ‘all processes, whether they are produced by human effort or occur spontaneously in nature, can be viewed as computations‘ [Wolfram 2002, p 715]. This means that any process that follows definite rules can be thought of as a computation. For example the process of evolution of a system like a cellular automaton can be viewed as a computation, even though all it does is generate the behaviour of the system. Processes in nature can be thought of as computations, although the rules they follow are defined by the basic laws of nature and all they do is generate their own behaviour.

Outline of the principle
The principle asserts that there is a fundamental equivalence between many kinds of processes in computational terms.

Computation is defined as that which a universal system as meant here can do. It is possible to imagine another system capable of computations beyond universal cellular automata or other such systems but they can never be constructed in our universe.

Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication. In other words: there is just one level of computational sophistication and it is achieved by almost all processes that do not seem obviously simple. Universality allows the construction of universal systems that can perform any computation and thus they must be capable of exhibiting the highest level of computational sophistication. From a computational view this means that systems with quite different underlying structures will show equivalence in that rules can be found for them that achieve universality and that can thus exhibit the same level of computational sophistication.
The rules need not be more complicated themselves to achieve universality hence a higher level of computational sophistication. On the contrary: many simple though not overly simple rules are capable of achieving universality hence computational sophistication. This property should furthermore be very common and occur in a wide variety of systems, both abstract and natural. ‘And what this suggests is that a fundamental unity exists across a vast range of processes in nature and elsewhere: despite all their detailed differences every process can be viewed as corresponding to a computation that is ultimately equivalent in its sophistication‘ [Wolfram 2002, p 719].

We could identify all of the existing processes, engineered or natural, and observe their behaviour. It will surely become clear that in many instances it will be simple repetitive or nested behaviour. Whenever a system shows vastly more complex behaviour, the Principle of Computational Equivalence then asserts that the rules underlying it are universal. Conversely: given some rule it is usually very complicated to find out if it is universal or not.

If a system is universal then it is possible, by choosing the appropriate initial conditions, to perform computations of any sophistication. No guarantee exists, however, that some large portion of all initial conditions result in behaviour of the system that is more interesting and not merely obviously simple. But even rules that are by themselves not complicated, given simple initial conditions, may produce complex behaviour and may well produce processes of computational sophistication.

Introduction of a new law to the effect that no system can carry out explicit computations that are more sopisticated than that can be carried out by systems such as cellular automata or Turing Machines. Almost all processes except those that are obviously simple achieve the limit of Computational Equivalence implying that almost all possible systems with behaviour that is not obviously simple an overwhelming fraction are universal. Every process in this way can be thought of as a ‘lump of computation’.

The Validity of the Principle
The principle is counter-intuitive from the perspective of traditional science and there is no proof for it. Cellular automata are fundamentally discrete. It appears that systems in nature are more sophisticated than these computer systems because they should from a traditional perspective be continuous. But the presumed continuousness of these systems itself is an idealization required by traditional methods. As an example: fluids are traditionally described by continuous models. However, they consist of discrete particles and their computational behaviour must be of a system of discrete particles.
It is my strong suspicion that at a fundamental level absolutely every aspect of our universe will in the end turn out to be discrete. And if this is so, then it immediately implies that there cannot ever ultimately be any form of continuity in our universe that violates the Principle of Computational Equivalence’ [Wolfram 2002, p 730]. In a continuous system, the computation is not local and every digit has in principle infinite length. And in the same vein: ‘.. it is my strong belief that the basic mechanisms of human thinking will in the end turn out to correspond to rather simple computational processes’ [Wolfram 2002, p 733].

Once a system reaches a relatively low threshold of complexity then any real system must exhibit the same level of computational sophistication. This means that observers will tend to be computationally equivalent to the observed systems. As a consequence they will consider the behaviour of such systems complex.

Computational Irreducibility
Scientific triumphs have in common that almost all of them are based on finding ways to reduce the amount of computational work in order to predict how it will behave. Most of the time, the idea is to derive a mathematical formula that allows to detemine what the outcome of the evolution of the system will without having to trace its every step explicitly. There is great shortage of formulas describing all sorts of known and common systems’ behaviour.
Traditional science takes as a starting point that much of the evolutionary steps perfomed by a system are an unnecessarily large effort. It is attempted to shortcut this process and find an outcome with less effort. However, describing the behaviour of systems exhibiting complex behaviour is a difficult task. In general not only the rules for the system are required to do that, but its initial conditions as well. The difficulty is that, knowing the rules and the initial condtions, it might still take an irreducible amount if time to predict its behaviour. When computational irreducibility exists there is no other way to find out how it will behave but to go though its every evolutionary step up to the required state. The predicting system can only outrun the actual system of which we are trying to predict its future with less effort if its computations are more sophisticated. This idea violates the Principle of Computational Equivalence: every system that shows no obviously simple behaviour is computationally exactly equivalent. So predicting models cannot be more sophisticated than the systems they intend to describe. And so for many systems no systematic predictions can be done, their process of evolution cannot be shortcut and they are computationally irreducible. If the behaviour of a system is simple, for example repetitive or nested, then the system is computationally reducible. This reduces the potential of traditional science to advance in studying systems of which the behaviour is not quite simple.

To make use of mathematical formulas for instance only makes sense if the computation is reducible hence the system’s behaviour is relatively simple. Science must constrain itself to the study of relatively easy systems because only these are computationally reducible. This is not the case for the new kind of science, because it uses limited formulas but pictures of the evolution of systems instead. The observed systems may very well be computationally irreducible. They are not a preamble to the actual ‘real’ predictions based on formulas, but they are the real thing themselves. A universal system can emulate any other system, including the predictive model. Using shortcuts means trying to outrun the observed system with another that takes less effort. Because the latter can be emulated by the former (as it is universal), this means that the predictive model must be able to outrun itself. This is relevant because universality is abound in systems.

As a consequence of computational irreducibility there can be no easy theory for everything, there will be no formula that predicts any and every observable process or behaviour that seems complex to us. To deduce the consequences of these simple rules that generate complex behaviour will require irreducible amounts of computational effort. Any system can be observed but there can not be a guarantee that a model of that system exists that accurately describes or predicts how the observed system will behave.

The Phenomenon of Free Will
Though a system may be governed by definite underlying laws, its behaviour may not be describable by reasonable laws. This involves computational irreducibility, because the only way to find out how the system will behave is to actually evolve the system. There is no other way to work out this behaviour more directly.
Analog to this is the human brain: although definite laws underpin its workings, because of irreducible computation no way exists to derive an outcome via reasonable laws. It then seems that, knowing that definite rules underpin it, the system seems to behave in some way that it does not seem to follow any reasonable law at all doing this or that. And yet the underpinning rules are definite without any freedom yet allowing the system’s behaviour some form of apparent freedom. ‘For if a system is computationally irreducible this means that there is in effect a tangible separation between the underlying rules for the system and its overall behaviour associated with the irreducible amount of computational work needed to go from one to the other. And it is this separation, I believe, that the basic origin of the apparent freedom we see in all sorts of systems lies – whether those systems are abstract cellular automata or actual living brains‘ [Wolfram 2002, p 751].
The main issue is that it is not possible to make predictions about the behaviour of a system, for if we could then the behaviour would be determined in a definite way and cannot be free. But now we know that definite simple rules can lead to unpredictability: the ensuing behaviour is so complex that it seems free of obvious rules. This occurs as a result of the evolution of the system itself and no external input is required to derive that behaviour.
‘But this is not to say that everything that goes on in our brains has an intrinsic origin. Indeed, as a practical matter what usually seems to happen is that we receive external input that leads to some train of thought which continues for a while, but then dies out until we get more input. And often this the actual form of this train of thought is influenced by the memory we have developed from inputs in the past – making it not necessarily repeatable evn with exactly the same input‘ [Wolfram 2002, p752 – 53].

Undecidability and Untractability
Undecidability as per Godels Entscheidungsproblem is not a rare case, it can be achieved with very simple rules and it is very common. For every system that seems to exhibit complex behaviour, its evolution is likely to be undecidable. Finite questions about a system can ultimately answered by finite computation, but the computations may have an amount of difficulty that makes intractable. To assess the difficulty of a computation, one assesses the amount of time it takes, how big the program is that runs it and how much memory it takes. However, it is often not knowable if the progam that is used for the computation is the most efficient for the job. Working with very small programs it becomes possible to assess their efficiency.

Implications for Mathematics and its Foundations
Applications in mathematics. In nature and in mathematics simple laws govern complex behaviour. Mathematics has distantiated itself increasingly from correspondence with nature. Universality in an axiom system means that any question about the behaviour of any other universal system can be encoded as a statement in the axiom system and that if the answer can be established in the other system then it can also be given by giving a proof in the axiom system. Every axiom system currently in use in mathematics is universal: it can in a sense emulate every other system.

Intelligence in the Universe
Human beings have no specific or particular position in nature: their computational skills do not vary vastly from the skills of other natural processes.

But the question then remains why when human intelligence is involved it tends to create artifacts that look much simpler than objects that just appear in nature. And I believe the basic answer to this has to do with the fact that when we as humans set up artifacts we usually need to be able to foresee what they will do – for otherwise we have no way to tell whether they will achieve the purposes we want. Yet nature presumably operates under no such constraint. And is fact I have argued that among systems that appear in nature a great many exhibit computational irreducibility – so that in a sense it becomes irreducibly difficult to foresee what they will do‘ [Wolfram 2002, p 828].

A firm as such is not a complicated thing: it takes one question to know what it is (answer: a firm) and another to find out what it does (answer: ‘we manufacture coffee cups’). More complicated is the answer to the question: ‘how do you make coffeecups’, for this requires some considerable explanation. And yet more complicated is the answer to: ‘what makes your firm stand out from other coffeecup manufacturing firms?’. The answer to that will have to involve statements about ‘how we do things around here’, the intricate details of which might have taken you years to learn and practice and now to explain.

A system might be suspected to be built for a purpose if it is the minimal configuration for that purpose.

It would be most satisfying if science were to prove that we as humans are in some fundamental way special, and above everything else in the universe. But if one looks at the history of science many of its greatest advances have come precisely from identifying ways in which we are not special – for this is what allows science to make ever more general statements about the universe and the things in it‘ [Wolfram 2002, p 844].

‘So this means that there is in the end no difference between the level of computational sophistication that is achieved by humans and by all sorts of other systems in nature and elsewhere’ [Wolfram 2002, p 844].

The Meme Machine

The Meme Machine – Susan Blackmore

 

My introduction

To cut a long story short – don’t worry I will summarize in some detail the train of thought hereafter anyway, because I am not going to get away with it just like that and you will miss nothing – Blackmore suggests to annihilate Dawkins’ hope for the human condition and Dennetts expectations (however small) about it: we cannot rebel against the tyranny of the selfish replicators (the gene), because there is no one to rebel. And it is exactly this realisation, according to Blackmore, that allows us to live a truly free life. Wow.

We humans in her view are susceptible to the thought that we are capable of thinking, hoping and expecting, but in fact she suggests we are ‘meme machines’. These thoughts above are memes themselves. Humans are biological computing machines, fit to run any utterable program. The programs fight or negotiate between themselves, in our heads, for attention. They may or may not be favourable to us humans, their hosts, where they live.

It is them, the memes, that live in our minds. And it is them that make us think we think, memorize, expect, and hope. We believe we do these things. But we don’t, not really. In other words: humans are susceptible to invasions of ideas and concepts that shape their thought and, henceforth, their actions. These memes have their own intention to survive. Like all natural processes they are ‘stupid’ processes, they don’t have a ‘will’, they just survive.

Let’s call large complexes of integrated and complex sets of memes, their subsets and their interrelations memeplexes. Then culture is an ‘ensemble’ of memeplexes, say related to work ethics, cooking habits, dinner etiquette, religions and their interrelations, economic behaviour, traffic regulations and customs and so on and so forth. In this world, humans are the computing machine that culture runs on. Cultural elements called memes are struggling to survive on a human substrate.

And conversely: if a human being actively enters any such cultural environment, by upbringing, by local or social circumstances, or for personal reasons or a profession, the memes in vigor in that environment at that time will have an influence on the thoughts of that individual. And consequently on his or her actions and behaviour, and lastly, on her or his own utterances, thus propagating the culture in his environment.

The linking pin between this train of thought and my research subject is that people, when dealing with a company or in fact any organisation, willingly give up some of their autonomy to have their behaviour increasingly steered by the culture in vigor in this (new) environment: by the ruling memes. In many cases company culture shows some traits resembling religious belief and in some cases to work at a company requires a faith bordering the religious. When defining company behaviour, I suggest that the leading principle be therefore not defined by the specific details of the people and processes it encompasses, but by the ‘ensemble’ of cultural elements that shapes it and defines its corporal behaviour. That is: behaviour that is autonomous and in a sense independent of the behaviour of the constituent human beings that are merely the computer that the company runs on.

The central thesis of my research project is this: companies are behavioural patterns in space and time steered by memes, through which material, people and information flow. Lees verder The Meme Machine

Gedachtengang Samengevat

Turing machines zijn universele computers: ze kunnen alle goedbeschreven algoritmes in een gekozen domein uitrekenen.

Van systemen van elementaire (1-dimensionele) cellulaire automaten van (gedrags-) klasse IV is bewezen dat ze turing machines zijn.

Het is aannemelijk en logisch dat ook andere systemen die bestaan uit onderling en met andere systemen in hun omgeving interacterende deelsystemen (agent-based netwerk systemen) turing machines kunnen zijn. Dit is op dit moment niet bewijsbaar.

Het gedrag van systemen die turing machines zijn bevindt zich in een fase-overgang tussen ordelijk en chaotisch gedrag, zogenaamd complex gedrag.

Voor NK Boolean agent-based netwerksystemen is bewezen dat een selectieproces het gedrag van die systemen in het complexe gebied brengt en houdt. Daar is de totale fitness van het systeem het hoogst. Dit is op dit moment niet bewijsbaar voor alle dergelijke systemen.

Turing machines kunnen iedere fysieke vorm aannemen, zolang het fysieke voorkomen van de turing machine open is voor uitwisseling van informatie en materie met de omgeving en ver uit evenwicht is. Het gedrag van het systeem kan de kortste beschrijving zijn van het systeem zelf.

Het is logisch en aannemelijk maar niet bewijsbaar dat een bedrijf als entiteit een levend organisme is.

De evolutie van bedrijven is een integraal onderdeel van evolutionaire ontwikkeling en is een extensie van biologische evolutie die door het bestaan van mensen mogelijk is. Dit is niet bewijsbaar.

Technologische ontwikkeling is leidend voor de ontwikkeling van het economisch voortbrengingsproces en dus voor de evolutie van bedrijven. De relatieve fitness van een bedrijf op de langere termijn wordt bepaald door de mate waarin het in staat is om zich te onderscheiden van andere bedrijven.

Een agent leeft in samenhang met zijn omgeving. De omgeving bestaat uit een netwerk van andere agents waarmee hij interacteert en vaste aanwezige middelen. In het geval van een bedrijf zijn die agents andere bedrijven, de middelen zijn bijvoorbeeld grondstoffen en informatie. De interactie bestaan uit de transmissie van informatie en materie. De eenheid van culturele transmissie, concepten, zijn memes.

Een bedrijf co-evolueert als gevolg van die interacties met de andere entiteiten in dat netwerk in een proces van mutatie, en selectie op grond van hun fitness. De aard van het evolutieproces van bedrijven is, anders dan in het geval van biologische evolutie, cultureel en dus niet generatiegebonden en selectie is niet-natuurlijk.

Het gedrag van een complex systeem zoals een bedrijf wordt bepaald door de positie van het systeem in zijn parameterruimte. Het kan worden gestuurd door aanpassingen aan de parameters van het systeem.