More thoughts on closure
These are the references that I know of which seem to make a distinction between operational and organizational closure:
Thompson (2005): “An autonomous system can also be defined as a system that has organizational and operational closure: the result of any process within the system is another process within the system (Varela 1979, p. 55-60; Varela and Bourgine 1991)”.
And in a footnote to this sentence he refers to Varela’s Closure Thesis which states that “every autonomous system is organizationally closed (Varela 1979, p. 58)”, and goes on to say that “‘organizational closure’ is a technical notion used to define the imprecise notion of autonomy.” Unfortunately, he does not contrast this with a definition of operational closure. Perhaps it would be a good idea to get in touch with him and ask his opinion on this matter?
Another reference I found was Rudrauf et al. (2003), who claim that “moreover, there are two aspects of closure: organizational, which defines the possible interactions in a “static” circular ramework, and operational, i.e. the recurrent dynamics that closure elicits.”
And in a footnote to this sentence they write:
“The system’s stability is dynamic. It centers on a huge internal movement, a perpetual flow. Therefore, autonomy is the result of the set of possible internal transformations or endomorphisms [Sn => Sn] defined by the system closure into its domain or state space. The indefinite recursion of component interactions, sustained through systemic re-entries, has the central role in the flux of constitution of the system. (Francisco referred to Wiener who introduced the fundamental revolutionary concept of feedback).
As we are considering real physical processes, the scientific paradigm for such a concept, beyond a general theory of systems, would be biophysics. The whole dynamical process that organisational closure defines can thus be represented, in a very general way, by a system of non-linear differential equations:
dX = S(x, p, t)
including the set x of co-dependent variables, the set of interaction laws S, and a space of internal and external parameters p (we have drawn the generic properties of such a system in Figure 1). If in such a formalism the closure remains implicit, “the stability of a dynamical system can be considered as the representation of the operational closure of an autonomous system” (Varela, 1979).”
As I understand it they use the notion of organizational closure to refer to the organization of a particular system, and use operational closure to talk about the concrete dynamics which this organization brings forth in the domain in which it is distinguished.