Chemical Organization Theory as a Modeling Tool

Heylighen, F., Beigi, S. and Veloz, T. . Chemical Organization Theory as a modeling framework for self-organization, autopoiesis and resilience . Paper to be submitted based on working paper 2015-01.

Introduction

Complex systems consist of many interacting elements that self-organize: coherent patterns of organization or form emerge from their interactions. There is a need of theoretical understanding of self-organization and adaptation: our mathematical and conceptual tools are limited for the description of emergence and interaction. The reductionist approach analyzes a system into its constituent static parts and their variable properties; the state of the system is determined by the values of these variable properties and processes are transitions between states; the different possible states determine an a priori predefined state-space; only after introducing all these static elements and setting up a set of conditions for the state-space can we study the evolution of the system in that state-space. This approach makes it difficult to understand a system property such as emergent behavior. Process metaphysics and action ontology assume that reality is not constituted from things but from processes or actions; the difficulty is to represent these processes in a precise, simple, and concrete way. This paper aims to formalize these processes as reaction networks of chemical organization theory; here the reactions are the fundamental elements, the processes are primary; states take the second place as the changing of the ingredients as the processes go on; the molecules are not static objects but raw materials that are produced and consumed by the reactions. COT is a process ontology; it can describe processes in any sphere and hence in scientific discipline; ‘.. method to define and construct organizations, i.e. self-sustaining networks of interactions within a larger network of potential interactions. .. suited to describe self-organization, autopoiesis, individuation, sustainability, resilience, and the emergence of complex, adaptive systems out of simpler components’ [p 2]. DPB: this reminds me of the landscape of Jobs; all the relevant aspects are there. It is hoped that this approach helps to answer the question: How does a system self-organize; how are complex wholes constructed out of simpler elements?

Reaction Networks

A reaction network consists of resources and reactions. The resources are distinguishable phenomena in some shared space, a reaction vessel, called the medium. The reactions are elementary processes that create or destroy resources. RN = <R,M>, where RM is a reaction network, R is a reaction, M is a resource: M = {a,b,c,…} and R is a subset of P(M) x P(M), where P is the power set (set of all subsets) of M and each reaction transforms a subset Input of M into a subset Output of M; the resources in I are the reactants and the resources in O are the products; I and O are multisets meaning that resources can occur more than once. R:x1+x2+x3+..→y1+y2+… The + in the left term means a conjunction of necessary resources x: if all are simultaneously present in I(r) then the reaction takes place and produces the products y.

Reaction Networks vs. Traditional Networks

The system <M,R> forms a network because the resources in M are linked by the reactions in R transforming one resource into another. What is specific for COT is that a reaction represents the transform from a multiplicity of resources into another multiplicity of them: a set I transforms to a set O. DPB: this reminds me of category theory. My principal question at this point is whether the problem of where organization is produced is not relocated: first the question was how to tweak static object into self-organization, now it is which molecules in which quantities and combination to conjuncture to get them to produce other resources and showing patterns at it. In RN theory the transform of resources can occur through a disjunction or a conjunction: the disjunction is represented by the juxtaposed reaction formulae, the conjunction by the + within a reaction formula.

Reaction Networks and Propositional Logic

Conjunction: AND: &; Disjunction: OR: new reaction line; Implication: FOLLOWS: →; Negation: NOT: -. For instance: a&b&c&..x. But the resources at the I side are not destroyed by the process then formally a&b&..→a&b&x&… Logic is static because no propositions are destroyed: new implications can be found, but nothing new is created. Negation can be thought of as the production of the absence of a resource: a+bc+ d = ac+ d – b. I and O can be empty and a resource can be created from nothing (affirmation, a) or a resource can create nothing (elimination, aor →-a). Another example is aa and hence a+(-a) = a-aand a-a: the idea is that a particle and its anti-particle annihilate one another, but they can be created together from nothing.

Competition and cooperation

The concept of negative resources allow the expression of conflict, contradiction or inhibition: a→-b what is the same as a+b0 (empty set): the more of a produced, the less of b is present: the causal relation is negative. The relation “a inhibits b” holds if: : a is required to consume but not produce b. The opposite “a promotes b” means that a is required to produce but not to consume b. When the inhibiting and promoting relations are symmetrical, a and b inhibit (a and b competitors) or promote (a and b cooperators) each other, but they do not need to be. Inhibition is a negative causality and promotion is a positive influence. If only positive influences or an even number of negative influences are included in a cycle then negative feedback occurs. When the number of negative influences is uneven then a positive feedback occurs. Negative feedback leads to stabilization or oscillation, positive feedback leads to exponential growth. In a social network a particular message can be promoted, suppressed or inhibited by another. Interaction sin the network occur through their shared resources.

Organizations

In COT and organization is defined as a self-sustaining reaction system: produced and consumed resources are the same: ‘This means that although the system is intrinsically dynamic or process-based, constantly creating or destroying its own components, the complete set of its components (resources) remains invariant, because what disappears in one reaction is recreated by another on, while no qualitatively new components are added’ [p 8]. DPB: I find this an appealing idea. But I find it also hard to think of the basic components that would make up a particular memeplex, even using the connotations. What in other words would the resources have to be and what the reactions to construct a memeplex from them? If the resource is an idea then one idea leads to another, which matches my theory. But this method would have to cater for reinforcement: and the idea itself does not much change, it does get reinforced as it is repeated. And in addition how would the connotation be attached to them: or must it be seen as an ‘envelope’ that contains the address &c, and that ‘arms’ the connoted idea (meme) to react (compare) with others such that the ranking order in the mind of the person is established? And such that stable network of memes is established such that they form a memeplex. The property of organization above, is central to the theory of autopoiesis, but, as stated in the text, without the boundary of a living system. But I don’t agree with this: the RC church has a very strong boundary that separates it from everything that is not the RC church. And so the RN model should cater for more complexity than only the forming of molecules (‘prior to the first cell’). The organization of a subRN <M’,R> of a larger RN <M,R> is defined by these characteristics: 1. closure: when I(r) is a part of M’ then O(r) is a part of M’ for all resources 2. semi-self-maintenance: no existing resource is removed, each resource consumed by some reaction is produced again by some other reaction working on the same starting set and 3. self-maintenance: each consumed resource x element of M’ is produced by some reaction in <M’,R> in at least the same amount as the amount consumed (this is a difficult one, because a ledger is required over the existence of the system to account for the quantities of each resource). ‘We are now able to define the crucial concept of organization: a subset of resources and reactions <M’,R> is an organization when it is closed and self-maintaining. This basically means that while the reactions in R are processing the resources in set M’, they leave the set M’ invariant: no resources are added (closure) and no resources are removed (Self-maintenance)’( emphasis of the author) [p 9]. The difference with other models is that the basic assumption is that everything changes, but this concept of organization means that stability can arise while everything changes continually, in fact this is the definition of autopoiesis.

Some examples

If a resource appears in both the I and the O then it is a catalyst.

Extending the model

A quantitative shortcoming, a possible extension, is the absence of relative proportions and of the relative speeds of the reactions. To extend quantitatively the model can be detailed to encompass all the processes that make up some particular ecology of reactions.

Self-organization

If we apply the rules for closure and maintenance we can know how organization emerges. If a reaction is added, a source for some resource is added which interrupts closure, or a sink is added which interrupts the self-maintenance. In general a starting set of resources will not be closed; their reactions will lead to new resources and so on; but the production of new ones will stop if no new resources are possible given the resources in the system; at that point closure is reached: ‘Thus, closure can be seen as an attractor of the dynamics defined by resource addition: it is the end point of the evolution, where further evolution stops’ [p 12]. In regards to self-maintenance, starting at the closed set, some of the resources will be consumed but not produced in sufficient amounts to replace the used amounts; these will disappear from the set; this does not affect closure because loss of resources cannot add new resources; resources now start to disappear one by one from the set; this process stops when the remaining resources only depend on the remaining ones (and not the disappeared ones): ‘Thus, self-maintenance too can be seen as an attractor of the dynamics defined by resource removal. The combination of resource addition ending in closure followed by resource removal ending in self-maintenance produces an invariant set of resources and reactions. This unchanging reaction network is by definition an organization’ [p 12]. Every dynamic system will end up in a attractor, namely a stationary regime that the system cannot leave: ‘In the attractor regime the different components of the system have mutually adapted, in the sense that the one no longer threatens to extinguish the other they have co-evolved to a “symbiotic”state, where they either peacefully live next to each other, or actively help one another to be produced, thus sustaining their overall interaction’ [p 12]. DPB: from the push and pull of these different attractors emerges (or is selected) an attractor that manages the behavior of the system.

Sustainability and resilience

An organization in the above sense is by definition self-maintaining and therefore sustainable. Many organizations grow because they produce more resources than they consume (e.g. positive feedback of resources: overproduced). Sustainability means the ability of an organization to grow without outside interference. Resilience means the ability to maintain the essential organization in the face of outside disturbances; a disturbance can be represented by the injection or the removal of a resource that reacts with others in the system. Processes of control are: buffering, negative feedback, feedforward (neutralizing the disturbance before it has taken effect). The larger the variety of controls the systems sports, the more disturbances it can handle, an implementation of Asby’s law of requisite variety. Arbitrary networks of reactions will self-organize to produce sustainable organizations, because an organization is an attractor of their dynamics. DPB: this attractor issue and bearing in mind the difficulties with change management, this reminds me of the text about the limited room an attracted system takes up in state-space (containment) explains why a system once it is ‘attracted’ it will not change to another state without an effort of galactic proportions. ‘However, evolutionary reasoning shows that resilient outcomes are more likely in the long run than fragile ones. First, any evolutionary process starts from some arbitrary point in the state space of the system, while eventually reaching some attractor region within that space. Attractors are surrounded by basins, from which all states lead into the attractor (Heylighen, 2001). The larger the basin of an attractor, the larger the probability that the starting point is in that basin. Therefore, the system is more likely to end up in an attractor with a large basin than in one with a small basin. The larger the basin, the smaller the probability that a disturbance pushing the system out of its attractor would also push it out of the basin, and therefore the more resilient the organization corresponding to the attractor. Large basins normally represent stable systems characterized by negative feedback, since the deviation from the attractor is automatically counteracted by the descent back into the attractor. .. However, these unstable attractors will normally not survive long, as nearly any perturbation will push the system out of that attractor’s basin into the basin of a different attractor. . This very general, abstract reasoning makes it plausible that systems that are regularly perturbed will eventually settle down in a stable, resilient organization’ [p 15].

Metasystem transitions and topological structures

A metasystem transition = a major evolutionary transition = the emergence of a higher order organization from lower order organizations. COT can be understood in this way if an organization S (itself a system of elements, albeit organized) behaves like a resource of the catalyst type: invariant under reactions but it has an input of resources it consumes I(S) and an output of resources it produces O(S), resulting in this higher order reaction: I(S) + S S + O(S), assume that I(S) = {a,b} and O(S) = {c,d,e}, then this can be rewritten as a+b+S S+c+d+e. S itself constitutes of organized elements and it behaves like a black box processing some input to an output. If S is resilient it can even respond to changes in its input with a changed output. Now the design space of meta-systems can be widened to include catalyst resources of the type S, organizations that are self-maintaining and closed.

Concrete applications

It is possible to mix different kinds of resources; this enables the modeling of complex environments; this is likely to make the ensuing systems’ organizations more stable. ‘Like all living systems, the goal or intention of an organizatrion is to maintain and grow. To achieve this, it needs to produce the right actions for the right conditions (e.g. produce the right resource to neutralize a particular disturbance). This means that it implicitly contains a series of “condition-action rules” that play the role of the organization’s “knowledge”on how to act in its environment. The capability of selecting the right (sequence of) action(s) to solve a given problem constitutes the organization’s “intelligence”. To do this, it needs to perceive what is going on in its environment, i.e. to sense particular conditions (the presence or absence of certain resources) that are relevant to its goals. Thus, an organization can be seen as a rudimentary “intelligence” or “mind”’ [p 20]. DPB: I find this interesting because of the explanation of how such a model would work: the resources are the rules that the organization needs to sort out and to put in place at the right occasion.

Gepubliceerd door

dpbruin

PhD Candidate The Firm as an Emergent Phenomenon