Towards an Integration Science

In this paper, we describe the influence of Richard Bellman’s work on our research. The influence is primarily felt in the attitude we take towards the research, which is that whenever the right mathematical tool for a problem that we are considering is not available, then some mathematical invention is required. We describe our research studies in software and system engineering for what we have called Constructed Complex Systems Žwe call them that to distinguish them from the mathematically more popular use of the term to refer to studies of fractals, chaos, and other behaviors in dynamical systems., which are large systems mediated or managed by computing systems, and the Integration Science that we believe is necessary for adequately designing, building, and analyzing such systems. The two technical topic areas we describe are Wrappings, which is our knowledge-based integration infrastructure for Constructed Complex Systems, and Virtual Worlds, which provide a very interesting testbed for integrating a wide range of processes, from human activities to formal systems. In both cases, we describe some of the mathematical implications and requirements of our approach