## 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 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 ## 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 ( 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][4]. PAN builds on, and considerably extends, concepts from philosophy [Lane & Maxfield][5], 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][6], 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][7]. ## References[Alberts & Hayes] David S. Alberts and Richard E. Hayes [Atkin] R. H. Atkin, [Boxer & Cohen 00] Philip Boxer and Bernie Cohen, ‘Doing Time: The Emergence of Irreversibility’, [Boxer & Cohen 04] Philip Boxer and Bernie Cohen, ‘Triply Articulated Modelling of the Anticipatory Enterprise’, [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’, [Boxer & Veryard] Philip Boxer and Richard Veryard ‘Metropolis and SOA Governance Part 1: Towards the Agile Metropolis’, [BRA72] Bratteli, O., (1972), ‘Inductive Limits of Finite Dimensional C*-Algebras’ in [Kelly] George Kelly, [Lane & Maxfield] D. A. Lane and R. Maxfield, ‘Ontological Uncertainty and Innovation’, [LAZ80] Lazar, A. J. and Taylor, D. C., (1980), ‘Approximately Finite Dimensional C*-Algebras and Bratteli Diagrams’, in [Maturana & Varela] Humberto R. Maturana and Francisco J. Varela, [RHO2001] Rho, Seung-Jai, (2001), [Rosen] Robert Rosen, |