PAN Projective Analysis Tools

What is the challenge that PAN technology is
designed to tackle?

Many current software engineering problems, arising from the need for agility and security in the interoperability of systems-of-systems, seem to defy analysis by classical systems engineering techniques. Classic techniques, which have served science and engineering well for many years, treat systems as objective entities that can be described and implemented with respect to a generic requirement without reference to the needs of any particular user or context. This presumption of universal applicability limits the analytical power of classical systems engineering techniques when applied to any enterprise that seeks to take power-to-the-edge [Alberts & Hayes].

An enterprise takes power-to-the-edge when it is prepared to respond to situations in ways that address need in a particular context-of-use. The effect of this is to make demand asymmetric, i.e. to take a form that is particular to the context-of-use.  Power-at-the-edge contrasts with holding power centrally, where it is assumed that demand takes a form that is common across all the demand situations that the enterprise is prepared to satisfy, i.e. demand is assumed to be symmetric. The gap between any particular asymmetric demand and the demand that can be satisfied by a supplier’s symmetric assumptions is defined as a value deficit.  Taking power-to-the-edge is necessary to address this value deficit, but presents the infrastructures of an enterprise with a particular challenge: are they agile enough to satisfy the variety of forms of demand encountered at their edges? [Boxer & Veryard]

What is the purpose of PAN technology?

Projective Analysis (PAN) is a set of analytical approaches to help in evaluating the risks encountered in taking power-to-the-edge. PAN is based on the assumption that the model implicit in the way an enterprise is organised is based on three distinct ‘logics’ that it has to hold in a particular relation to each other (triply articulated): a model of how things ought to be, a model of what it is possible to do, and a model of what customers want [Boxer & Cohen 04].   The third of these does not need to be elaborated under assumptions of symmetric demand, so that in meeting the challenge of asymmetric demand, the enterprise faces a double challenge:  to consider top-down what are the risks attendant upon, and governance consequences of, addressing asymmetric forms of demand; and to consider bottom-up how to enable its infrastructures to mitigate those risks.

The approach PAN takes to addressing the interoperation of enterprises and systems is to examine the way their triply articulated top-down and bottom-up models compose with each other.  It is a technology that may be used to address the problems of interoperability in relation to a number of challenging problems:

§         Improving the understanding, control and predictability of the impact of modifications in systems-of-systems

§         Developing improved methods to enable coordinated evolution and interoperability of systems-of-systems.

§         Introducing new ways of managing the procurement of capabilities within systems-of-systems environments.

In a wider context, it appears that PAN is the type of technology necessary to the analysis of the asymmetries between demand and supply that are inherent in the concepts in power-to-the-edge.

What forms of analysis are supported by PAN technology?

The PAN technology is comprised of a number of tools:

  • Visual representation for the modeling of enterprises and the organisation of the particular forms of demand that they face in support of top-down process.

§         ‘Reading’ the triple articulation of observers’ models and composing the triply articulated models of multiple observers in the bottom-up analysis of systems-of-systems.

§         Projecting stratified matrices from composite triple articulations and performing landscape analysis on the topology of those matrices in order to identify risks.

What is the history of PAN?

PAN has been developed and used by Boxer Research Ltd over some 15 years, undertaking projects 2001-2003 under the European EUREKA programme jointly funded with the Department of Trade and Industry (DTI) in the UK, with City University as a subcontractor. The project developed parts of the PAN technology further in the form of a Composition Agent, under the E!2187 AgentWorks project.. Enterprises in which it has been applied include manufacturing, healthcare, defence, telecoms and charities [Boxer & Eigen]. PAN builds on, and considerably extends, concepts from philosophy [Lane & Maxfield], cybernetics [Maturana & Varela] and biology [Rosen] and technologies used in psychology [Kelly] and sociology [Atkin].

The theoretical foundations of triple articulation have been a-temporal [Boxer & Cohen 00], and represent the graphs of the triple articulation by the C*-algebra associated with its graphs. A C*-algebra can be associated to a directed graph in such a way that the structure of the graph is reflected in the structure of the algebra [BRA72], [LAZ80], [RHO2001]. This representation has the potential to provide a powerful analytical basis for composition since the C*-algebra of a Cartesian product of graphs is a tensor product of the individual graph C*-algebras.  BRL has continued to work on these foundations in order to bring two kinds of time into the theory by moving from a two-dimensional structure (complex field) to a four-dimensional one (quaternions), as outlined in a current paper [Boxer, Cohen & de Freitas].


[Alberts & Hayes] David S. Alberts and Richard E. Hayes Power to the Edge, CCRP 2003

[Atkin] R. H. Atkin, Q-analysis: a hard language for the soft sciences. Futures December 1978: pp.492-499.

[Boxer & Cohen 00] Philip Boxer and Bernie Cohen, ‘Doing Time: The Emergence of Irreversibility’, Annals of the New York Academy of Sciences 901:13-25, 2000.

[Boxer & Cohen 04] Philip Boxer and Bernie Cohen, ‘Triply Articulated Modelling of the Anticipatory Enterprise’, Proceedings of the International Conference on Complex Systems, Boston 2004.

[Boxer, Cohen & de Freitas] Philip Boxer, Bernie Cohen and Antonio de Freitas, ‘The structure of Triple Articulation’, Boletín de la Asociación Matemática Venezolana, Volumen 13, number 1, 2006 (july 2006).

[Boxer & Eigen] P. Boxer and C. Eigen, ‘Taking power to the edge of the organisation: role as praxis’, The International Society for the Psychoanalytic Study of Organizations (ISPSO) Symposium, Baltimore, MD, 2005

[Boxer & Veryard] Philip Boxer and Richard Veryard ‘Metropolis and SOA Governance Part 1: Towards the Agile Metropolis’, Microsoft Architecture Journal Vol 5, 2005.

[BRA72] Bratteli, O., (1972), ‘Inductive Limits of Finite Dimensional C*-Algebras’ in Transactions of the American Mathematical Society, Vol. 171, 195-234.

[Kelly] George Kelly, The psychology of personal constructs, 2 vols., New York: Norton, 1955.

[Lane & Maxfield] D. A. Lane and R. Maxfield, ‘Ontological Uncertainty and Innovation’, Santa Fe Institute working paper.

[LAZ80] Lazar, A. J.  and Taylor, D. C., (1980), ‘Approximately Finite Dimensional C*-Algebras and Bratteli Diagrams’, in Transactions of the American Mathematical Society, Vol. 259, No. 2, 599-619.

[Maturana & Varela] Humberto R. Maturana and Francisco J. Varela, The Tree of Knowledge. Boston and London: New Science Library, Shambala Publications, Inc, 1988.

[RHO2001] Rho, Seung-Jai, (2001), Properties of graphs and their C*-Algebras, MSc Dissertation, University of  Newcastle.

[Rosen] Robert Rosen, Life Itself, Columbia University Press, 1991.