Strategy is Mathematics and Meditation: CAS thinking about organizations Robin Matthews Kingston University Business School Academy of National Economy Moscow Summary The fundamental concept of the paper is the organization matrix; a multi layered matrix of interconnected activities. The organization matrix is a complex adaptive system, in which evolution takes the form of forming and reforming coalitions between activities; a co-operative or coalitional game. Activities are defined at many levels of organization. They form a hierarchy stretching from the macro level, the organization or the set of organizations in an industry or sector, through to constituent businesses, projects, teams, and fundamental activities and processes at the micro level. Activities include production and consumption: activities at one level are consumed as inputs at another level. Coalitions are embedded in the matrix. Evolution occurs through shifting coalitions of activities creating new firms industries, and products. The organization matrix is a multi dimensional entity that can be viewed in a number of ways; as an interconnected set of potential activities, payoffs or information. Payoffs represent the energy of the system. They can be distributed in many different ways to stakeholders, the decision- making agents at the various tiers of organization. Decisions are represented by binary strings (0’s and 1’s), indicating participation and co-operation within coalitions. Payoffs are merely potential until they are activated by decisions. Strategy takes the form of ceaseless evolutionary search by agents for coalition structures that offer higher payoffs. Shifting coalition structures are triggered by technological change and competition. The organization matrix can be transformed into a co-operative game by breaking down payoffs into constituent benefits and costs. Another way of viewing the organization matrix is as an information network. In fact, information is the elementary system that underlies the two other forms. In successive tiers of the matrix, information becomes locked into processes and products. We can view the organization matrix (a) as a structure in time, or (b) as a timeless infinite structure, containing all potential and possibilities, there to be discovered. As a set of realised coalitions of activities or payoffs, it is subject entropy and the arrow of time. As pure potential it has a timeless aspect, and accessible only to the imagination. Another way of putting this is to say that the organization matrix exists not only at many activity (or information and payoff) levels, but also at different levels of being. New activities emerge as discoveries. New (or remembered) understanding and ideas become candidates for realisation and transformation into technologies, processes, products and markets and new coalition structures emerge. In terms of realised payoffs for example the organization matrix exists at the material level: corresponding more or less to Heidegger’s Dasein, Being in the world. As potential the organization matrix exists in the world of the imagination, the imaginal world. In brief, the organization matrix is a complex adaptive system, a many body system or surface and evolution is takes place as potential is discovered and realised through an unending procession of coalitional games. Strategy is evolutionary search: a trajectory

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that is subject to a grammar, a morphology of formal and informal rules, regulations, norms, values and habits. Grammar confines the set of all potential to a subset that may be realised by agent decisions. The grammar and the matrix are inter-acting adaptive systems. The issue arises as to the extent to which strategy is conscious search or not. Undeniably it is an NP hard problem, subject (a) to the impossibility theorem that no single search algorithm can possible outperform all others in all respects and (b) to the existence of many local solutions that can be carried out (at least in principle) by strong AI; John Searle’s unconscious zombie. To this extent strategy and much of management is merely a combinatorial problem of sifting through alternative coalition structures. The conscious aspects of strategy selected for discussion are temporal consciousness, empathetic consciousness and imagination. The argument is that the conscious aspects are at a fairly primitive state of evolution as compared to the explosion in combinatorial capabilities. However languages and methodologies exist in mystical traditions, Zen and Sufism; the latter being the methodology discussed in the paper. Hence the title of the paper. Further remarks The background notes to the workshop are provocative and I make a few remarks in (rather haphazard order) about them. 1. The organization matrix discussed briefly above is a CAS. Non linearity follows from the interdependence of the activities and payoffs; in evolutionary terms, activities constitute the genotypes and payoffs the phenotypes. At the level of realised payoffs the matrix is subject to entropy and the arrow of time: mutations multiply errors. Evolutionary processes work through the interaction of the many levels of the matrix, which may hold the system far from equilibrium. 2. We must remember that in capitalism survival of the individual organization is irrelevant: what matters is the evolution of the system as a whole. So the system itself may be self-adaptive, and so may be parts of the system, and so they are for some of the time, whilst many organizations are not. 3. Further we need to clarify what we mean by evolution, at least in terms of tiers of the matrix. Clearly the organization matrix has a fractal dimension: at a point in time a dimension of 3+: (it is fruitless at this stage to try to gauge the Hausdorff-Besicovitch dimension). However the fractal nature expressed as self-similarity in the archetypal structure of the organization matrix: interdependence and independence. 4. Kauffman’s restrictions on the extent of interdependence (3 ≥ K) makes no sense for organizations. Clearly they have much higher levels of interdependence and he makes no allowance for what I have called grammar. Statistical mechanics including the spin glass offers a solution in terms of ergodic search combined with rules (Maxwell Boltzman conditions) or annealing. Again this approach casts aside the question of grammar and the issues raised by Georgescu- Roegen about ergodicity. 5. Remembering its fractal dimensionality, it is possible to envisage the organization matrix as enclosed in a chaotic attractor, poised in a critical state with high frequencies of low level avalanches or evolutions, which go unnoticed. We notice only major transformations, which are much less frequent. I think, the notion of self ordered criticality, as a statistical regularity (an inverse relation between the size of

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avalanches, or scope of the shift in coalition) is a reasonable interpretation and one that fits with observation. 6. Rather than unambiguous universal self-organization, we have coexistence of emergence, entropy (the arrow of time), periodicity (cyclical time) on the matrix, and within coalitions (remember they are multi layered). 7. When researchers seek institutionalization of self-organization, they are searching the wrong scale and the wrong periodicity; missing the frequency of small-scale adaptations. 8. Spatial organization, coalitions in physical space, is the result of path dependence and competitive processes. What we call hypercompetition, in fact is the impact of competition at deeper and deeper levels of the organization matrix. Two major response mechanisms to compatition are (a) to extend the number and geographical scope of activities (especially at the product level) and (b) to narrow the scope of activities at one level, focussing instead on lower level coalitions (around capabilities). 9. The image of industries emerging and maturing and declining through coalition behaviour is quite consistent with spatial concentration. 10. The problem of the spatial location of coalitions is critical. We can envisage a situation in which the Russian economy becomes strongly orientated spatially on natural resource industries, and therefore subject to the variability and cyclicality of such industries. 11. Global superadditivity may be consistent with a kind of geographical specialisation that leaves nation states vulnerable. This is especially so since information flows are much faster, freer and responsive to variations in demand than human resource flows. Concentration of ownership and power at the nodes aggravates the problem. The situation with the Middle East oil producers illustrates the issue. 12. The intentionality of strategy is wrongly taken for granted. Organizations and individuals are often so bounded by grammar that they are no more conscious of the majority of decisions (including major ones) than one is of the process of opening a door to enter a room (turning the handle pushing the door and so on). They notice when something goes wrong (the door sticks) but pretty soon other aspects of the grammar kick in and the pre-programming continues. 13. The idea of coalition structures is preferred to clusters. Coalitions embedded in the organization matrix capture the many body aspects of externalities. 14. Apart from its existence as an archetypal structure of interdependence and independence, the organization matrix exists in a realised sense (R), an imaginal sense (P), and a yet to be imagined sense (Π). 15. A group of researchers are working on applications in the UK and Russia. Applications of the model includes; cross border alliances in education, oil pipelines and information sharing; emergence of the Natural Gas Vehicle Industry; new product development; self organizing maps and the risk of bank failure in Russia. References Will be supplied on request

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