Collaborative Problem-Solving for the ‘Polycrisis’

The paper focuses on the “Polycrisis,” which is first defined and then positioned as the context for a subsequent discussion about both the formal and social conditions for effective collaborative problem-solving. It then highlights the potential for diagrammatic reasoning to contribute to solving what some commentators choose to call ‘wicked-problems’ including those associated natural, economic, and social forms of fragility. This discussion is informed by pertinent advances in applied category theory, which has a wide range of application-domains including cyber-physical systems, scientific systems, dynamical systems, software engineering, and machine learning. The formal constructs and techniques to be surveyed include optics and parametric lenses, as well as David Spivak’s organisational categories. Optics and lenses have not only been applied to software engineering but also to the modelling of dynamical systems and machine learning. They possess a diagrammatic representation (as string diagrams), which serves as an aid in their deployment (e.g. AlgebraicJulia, Symbolica AI, Haskell applications). The paper argues that these developments should assist users in their collaborative modelling of the Polycrisis by: (i) integrating machine learning, differential programming, and calibration and simulation of dynamical systems; (ii) accounting for subsystem interactions within a larger system that features different stock-flow rates; (iii) accommodating non-linear mappings and weight-sharing; (iv) formally supporting a variety of stochastic influences over the systems that are being modelled; and, (iv) imposing on the whole, the internal logic associated with a topos.