The Life & Mind Seminar Network

More thoughts on closure

Posted in General by Tom Froese on March 1, 2007

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.



5 Responses

Subscribe to comments with RSS.

  1. tomfroese said, on March 8, 2007 at 2:07 pm

    I got in touch with Evan Thompson in order to find out what his position was with regard to the notions of organizational and operational closure. I’m sure he does not mind me sharing his response with you, so here it is:

    Hi Tom,

    Maturana and Varela never systematically distinguished between these terms. Yet one can distinguish some differences based on how they used them. Organizational closure is static or synchronic, whereas operational closure is dynamic and diachronic.

    Both were originally formulated in the context of molecular autopoiesis, which thus serves as a paradigm, but were then generalized as a way of specifying what makes a system autonomous (and this sort of system is precisely the sort not best understood in terms of input/output functions).

    I do have some discussion of this in Chapter 3 of my book, which should be available in a couple of weeks. You can see the website for it at:

    Best regards,

  2. tomfroese said, on March 9, 2007 at 2:43 pm

    I also found the following footnote in Fleischaker’s (1988) paper called “Autopoiesis: the status of its system logic”:

    Varela now prefers “operational closure” to “organizational closure”, a term he used prior to September 1982 in stating his Closure Thesis (Varela,
    1977; Varela, 1979).

  3. tomfroese said, on May 30, 2007 at 8:27 am

    Here’s another attempt at separating out the different connotations of the notion of operational or organizational closure. Let’s compare two recent definitions:

    1) This is a definition of ‘operational closure’ from Varela (1997): “operational closure (Varela, 1979), that is, a circular reflexive interlinking process, whose primary effect is its own production.”

    2) Thompson (2007, p.448n4) defines it as follows: ” ‘Closure’ is used here in its algebraic sense: an operation K exhibits closure in a domain D if every result of its operation yields results within D. Thus the operation of a system has operational closure if the results of its activity remain within the system itself.”

    It seems that the first definition is much more restrictive than the second, since it requires self-production rather than mere conservation of domain. Thus Ezequiel’s example, that “a set of even numbers remains closed under multiplication” as a case of trivial closure, satisfies the second but not the first definition. Otherwise the multiplication would somehow have to be produced by the set of even numbers.

    Even though the notion of operational closure has recently been the more popular one, I suggest that it would be best to use it only in the second sense, namely in reference to a particular kind of mathematical operation, which conserves its domain, and where the distinction between operator and operant remains unbroken (Ezequiel’s notion of ‘trivial’ closure). On the other hand, organizational closure was explicitly defined in Varela (1979) as kind of self-production reminiscent of autopoiesis but not tied to the molecular domain. This interpretation would entail that all organizationally closed systems are also operationally closed but not vice versa.

    Of course, this is just my proposal for conceptual clarification since, as Thompson (2007, p. 448n4) points out, “Varela in his writings does not distinguish between organizational and operational closure; he uses the two terms more or less interchangeably.”

    Nevertheless, I believe it is better to use organizational closure to refer to self-producing dynamic systems for several reasons: 1) the term operational closure has often been used loosely in cases of trivial closure, 2) the term operational closure easily evokes a misunderstanding with interactional closure (which is, of course, non-sense), and 3) even when the term operational closure has also been used to characterize non-trivial closure in previous literature, these statements will not be false (though the emphasis has changed).

  4. xabier said, on May 30, 2007 at 4:03 pm

    I like the distinction Tom. It is useful as demarcating trivial from non-trivial closure (as suggested by Ezequiel), in addition organization (as I understand it) implies both structural and functional/operational notions and thus it makes sense to speak in terms of organizational closure a that of a system where its operations construct or maintain its structure. The term operation on the other hand does not imply that of structure (you can use a structure to perform different operations) and thus it is closer to the trivial sense of closure.


  5. […] “closure” Varela doesn’t mean “cut off” or “independent”—autonomous systems […]

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: