Thoughts on trivial vs non-trivial closure
Semi-random thoughts following Tom’s post.
1. I cannot recall where I’ve read it in the primary literature, but I’m almost certain that Varela has written somewhere that what at some point he referred to as operational closure he was now calling organizational closure (or vice versa). The point is that I have never actually distinguished the two phrases. But of course, formulating a refined distinction could be useful. But I didn’t quite understand the distinction that Tom is proposing (what would be an example that is one and not the other?).
2. Operational closure (because I’m working from memory I’ll use only this term) comes in trivial and non-trivial varieties. But this is never said explicitly anywhere as far as I know.
3. The trivial variety only requires that a network of “processes” be such that its operation results in the continuation of the processes that compose this network. This is another way of saying that the processes, whatever they are, form a closed system in the mathematical or group theory sense. For instance, the set of even numbers is closed under multiplication, the symmetries of a sphere are closed under all solid rotations, a glider is closed under the rules of the game of life. Notice that in all cases there is a distinction between operator and operant. Trivial closure is when this distinction remains unbroken. It may admit of very simple examples, e.g., the continuous self-identity of a static entity.
4. Some cases of trivial closure, however, are strong enough to support non-representationalist alternatives to cognitive explanation. Consider Bittorio, the CA wrapped around itself interacting with a sea of random binary numbers (Varela et al 1991) or a simple fully connected CTRNN showing some endogenous activity (e.g., an unstable centre-crossing network). Do all cases of trivial closure afford this? No. I propose that the key factor is when trivial closure involves dynamical processes (i.e., process of explicit transformation where states differ over time). Why do they support non-representationalism (support here used in the sense of allowing such interpretations, not demanding them)? Because, as long as we’re describing the system’s operation, we need not involve any relational element describing the system’s interactions. Or rather, such elements will appear in our descriptions as perturbations to its operation, as contextual changes to the system’s structure and hence to its particular form of realizing its closure. Therefore, a relational concept such as a representation (doubly relating itself to a content or referent and a consumer; R represents O to S) cannot be part of the operation of an operationally closed system. If it were, we would have a system that is not closed, or we would have to open up the system so that an extended enough new system becomes closed.
5. Life and other forms of biological autonomy go beyond trivial closure. How they do so is now a matter of intense debate and investigation. I can mention two ways, which I still don’t know exactly how related they are (one implies the other, at least, and this may be reciprocal too): i) contextual precariousness leading to a self-defined unity; ii) breaking of distinction between operator and components operated upon.
6. Precariousness. If and when an operationally closed system is established out of processes that not only sustain themselves as a network, but additionally, would not be able to sustain themselves unless they were organized as such a network, we are in the presence of a precarious operationally closed system. Fundamentally, component processes would not normally be present or durable enough, unless the conditions that are sustained by the rest of the network were in place. The operationally closed system not only maintains itself; it enables itself. It produces its own preconditions (cf. Zizek’s comments on autopoiesis in The Parallax View who focuses this crucial point). An isolated component process, under the same physical conditions — but in the absence of the network’s organization — would not be sustainable. There are two consequences of this. The operationally closed system (in general a system of relations distinguished by the observer) implies in addition a self-distinction; i.e., it produces itself as a unity, rather than sustaining itself as a set of invariant relations. An environment is thereby co-defined. In addition, a precarious closed system must engage in interactions to sustain itself. It must actively keep the natural tendencies of isolated component processes to disintegrate at bay. Hence a non-trivially closed system is by necessity interactionally open. This, and not internal operations, is the locus of mind.
7. Tail-biting. I think that a consequence of a precarious system with a self-generated identity (as described in 6) is that the processes that compose it must blur the distinction between operator and that which is operated upon. This is hard to deal with with linear causality, but trivially true in natural, self-organized systems (proteins are products of genetic regulation and regulators themselves, language can be used to talk about language, etc.). This is what makes autopoiesis difficult to capture in a model. A simulation model, for instance, must keep at some level a strict separation between operations of transformation and those elements that are transformed. There is a way around this, which is to model the system at an underlying level (e.g., chemical interactions on a spatial grid) and observe tail-biting effects on the properties that are distinguished at a higher level (the classic example in biological modelling in the 90s was spiral-wave patterns in Pauline Hogeweg’s work on autocatalysis, but there are many others). I think eventually, a limitation is found in such models that maybe it’s not present in real living processes and this is what Robert Rosen’s book Life Itself attempts to demonstrate, the non-computability of life. This issue is badly in need of clearer formalization.
8. A note on material non-trivial closure (autopoiesis). Physical self-construction implies both of the above conditions (precariousness and tail-biting). Does it imply others? I copy a footnote from my Autopoiesis, Adaptivity, etc. paper on this point. Talking about the requirement of materiality in defining autopoiesis: “The demand for physicality seems at first ad hoc and arbitrary in a definition that is proposed as strictly formal and systemic. This is an unresolved issue at the core of continuing debates about the possibility of computational, or other non-physical kinds of autopoietic processes (Boden, 1999; McMullin, 2004; Moreno & Ruiz-Mirazo, 1999). The existence of computer realizations of algorithmic processes showing sometimes surprisingly lifelike properties such as growth, membrane construction, and self-repair (e.g., Ono & Ikegami, 2000) belies the fact that removing physicality from autopoiesis elevates trivial examples such as attractor states in cellular automata to the category of the living. Varela (1979) attempts to resolve the issue by defining autonomy or generalized operational closure as the class of self-producing processes occurring in arbitrary domains. Autopoiesis is the restriction of this class to the physical, molecular domain. But this merely defers the problem which is now that of trivial cases of autonomy. It is very likely that physicality brings more to the interpretation of autopoiesis than initially anticipated and that these elements also need to be spelled out for an improved definition of life. This worry had led some researchers like Alvaro Moreno and colleagues to explore the implications of thermodynamic constraints on autopoiesis, (see Ruiz-Mirazo & Moreno, 2004). The important result that this line of research is achieving is precisely determining what it is about physical constraints that make real life non-trivial. Interestingly, anyone who believes that life is a formal, substrate-independent, property, as opposed to formal and material, should follow these developments closely because any chance of substantiating their beliefs lies in being able to formalize the restrictions brought by physical constraints that make life a non-trivial affair.” In view of things said in 7, I’m inclined to say that the formalist view is flawed. Life is both form and matter. Or rather, it trascends that distinction. Hence, computational models of life can never be instantiations of life.