by Philip Boxer Bsc MBA PhD
Open systems and their 1st-order behavioral closures
Individuals identified with an enterprise, the formal behavioral model of which is thought to be deterministic, believe that the enterprise can dictate responses to all events, which are believed to be completely enclosed within its boundary. This formal behavioral model is denoted by the transitions between its sets of input and output symbols and is referred to as a first-order system. Such a system-of-interest is said to be over-determined if its structure over-determines its behavior in the sense of rendering it deterministic. Such a system-of-interest is a closed first-order system with a first-order structure.
Conversely, a non-deterministic formal model of behavior signifies an under-determined system-of-interest, the behavior of which is uncertain because there is more than one outcome possible from any given set of input conditions. A first-order system that cannot be assumed to have all its inputs within its boundary is an open first-order system because we cannot know that its first-order behavioral closure is deterministic. An open system is therefore one for which the first-order closure of its behavioral model is non-deterministic.
Sentient organisation and 2nd order behavioral closure
Consider now the elements of a system-of-interest with a first-order behavioral closure whose degree of non-determinism may be modified by an alteration to its behavior through choices exercised over the transitions available at each of its states, exercised through control of the behavior of its elements. Any agency that so modifies the system-of-interest’s behavior must be outside the system-of-interest, and may be said to be controlling it. If the behavioral model of this controlling behavior is itself deterministic, then such behavior may be treated as further elements of an expanded system-of-interest through processes of mechanization. If the model of controlling behavior is not deterministic, however, then this agency may usefully be referred to the way the enterprise is organised, defining the forms of novel emergence that are possible with respect to the components of the system-of-interest with its first-order behavioral closure. The relation of 2nd order organisation to 1st order structure is a stratified relation.
The characteristic of such 2nd order organisation is that it is sentient. However, we may redefine the system-of-interest so as to include the elements (aka people!) of its sentient organisation that are the sources of controlling behaviors, defining a second-order system-of-interest referred to as a socio-technical system. The boundary of a second-order system-of-interest whose behavioral closure can be made deterministic is its perimeter.
Each deterministic second-order closure that may be constructed by the exercise of sentient organisation may be considered to be a point in a model space, just as each state of a first-order system is a point in its state space. Each possible modification by its sentient organisation of the structure of the first-order system-of-interest that changes the nature of the second-order deterministic closure is a transition in that model space. The behavior of the enterprise may therefore follow a set of possible trajectories through model space which together comprise its repertoire of possible deterministic second-order behavioral closures. While some changes to sentient organisation may reduce the variety of these possible trajectories of the enterprise through model space, this is unlikely to be the case given that the elements of a sentient organisation are people, the controlling behaviors of whom are not going to be (‘reliably’) deterministic.
Sovereignty and 3rd order behavioral closure
To remove this non-determinism in the second-order behavioral closures, a further form of agency, a governance process, will be needed to restrict the set of trajectories through model space. The power to impose such a third-order closure through a governance process is the power of sovereignty over the 1st order structure and 2nd order sentient organisation of an enterprise. We may again re-define the system-of-interest to include the elements of the governance process (again, people), referring to it as a third-order system. If this governance process is able to make the 2nd order behavioral closure deterministic, then it defines the perimeter of the enterprise. This allows the enterprise to be defined as a system-of-interest in which its governance processes have the power to impose third-order behavioral closure, i.e. single trajectories through model space. We may say that the enterprise can be identified with a 2nd order system-of-interest, but its behaviors are realized through the way sovereignty is exercised over that 2nd order system.
What is frequently referred to as an ‘open system’ therefore, when used to refer to the way an enterprise is organised, is a third-order system, the behavioral closure imposed by which is deterministic. Continuing with the example of Bob Martin, used in distinguishing emergence from hierarchy, clearly there was a need for 2nd order organisation to manage the 1st order systems of production. But the maintenance of 3rd order sovereignty over all this is apparent in its continuing status as a family firm:
In 1938 Bob Martin’s opened a showpiece factory in Southport – it was to play an important role in providing vital medical supplies for British soldiers [during the Second World War] as well as in maintaining the growth of the company. Robert Martin continued to run the company after 1948 and maintained an active involvement up until his death in 1979. His son, now Sir Bruce Martin QC, took up the reins of the business in his turn and Bob Martin has remained a privately owned, family firm to this day.
Distinguishing edge from perimeter
If the enterprise must organise its behaviors differently as a function of different kinds of client-customer relationship, then its governance processes must surrender sovereignty to the particular relationship to some extent. The relation across its perimeter will therefore be different for each different kind of client-customer relationship, becoming an edge. An enterprise may thus have many edges to the extent that there need to be many such ways in which it must surrender sovereignty in its interactions with its client-customers, the most interesting of which involves network formation within a larger ecosystem – interesting because sustaining such surrendering of sovereignty demands asymmetric leadership.
The person and the enterprise
A difference between the person and the enterprise, therefore, is
- the relationship of a person’s identification to their singular embodiment as a person, whereas with an enterprise, its 1st, 2nd and 3rd order systems provide multiple forms of support for identification by persons.
- a person takes up a role in the life of an enterprise, whereas with an enterprise, it takes up a role in the lives of its client-customers.
 This posting is based on a joint paper with Bernie Cohen on “Modeling and the Modeler”, July 2007.
 Novel because if the relation is one of weak emergence, then by increasing the resolution of the state space, then the behavioral model of the 2nd order system may be rendered deterministic. This is what is done to the business models of enterprises through the effects of digitalisation with its attendant de-layering of sentient organisation.
 Miller, E. J. and A. K. Rice (1967). Systems of Organization: The Control of Task and Sentient Boundaries. London, Tavistock.
 The biological systems from Maturana derived his distinction between structure- function-organisation are 2nd order systems with deterministic 2nd order closures of their behavior. See Lacan and Maturana: Constructivist origins for a 30 Cybernetics in Communication and Cognition (1992) Vol 25. Number 1 pp73-100. For some of the issues facing ‘open systems’ thinking, see Leading organisations without boundaries: ‘quantum’ organisation and the work of making meaning.
 The formation of such networks around their social objects involves new forms of stratification aka novel forms of emergence demanding new governance processes that are incommensurable with the sovereignty of the existing enterprise as a whole. This gives rise to the challenges requiring a double alignment of ‘know-how’.
 Note that the implications of the word ‘role’ here are different, in the former use referring to an individual, in the latter a whole system-of-interest. In dilemmas as drivers of change I argue that this latter perspective requires a systemic view of the enterprise.