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Adaptivity is a property that arises naturally in the growth of complex systems, and leads to such desirable features as resilience to shocks and damage, the ability to discover and exploit advantages and resources in the environment, to recognise and avoid dangers, and to produce innovative and effective behaviours in the face of unpredictable challenges. Not surprisingly, as the world becomes more complex and unpredictable, there is a growing requirement for adaptivity in our own systems and processes, and interest in how to design for it, or rather, foster its emergence. The feasibility of engendering more adaptivity in our systems and processes rests on advances in detailed understanding of how adaptivity works in the natural world, and how that might be extended, and on what is being made possible by the continuing explosion in information and information technology. We recognise the potential for multiple nested levels of adaptivity, from adaptive action-in-the-world, to applying double-loop learning to the adaptive action capability elements themselves, through applying the power of adaptivity to the difficult problem of articulating sufficiently precise measures of success suitable to drive the adaptive action and the double-loop learning levels, and ultimately at the level we might call co-adaptation. The term co-adaptation acknowledges that in practice we are never looking at an isolated system adapting to a relatively static environment, but rather at a number of systems interacting with each other, and thereby creating a constantly changing context for each other to adapt to. This invites a higher level view and further options for targetted interventions in aspects of the roles, boundaries and relationships of the interacting systems (or that subset of them over which we may have some influence) in order to more effectively shape the outcomes.