Sanjay Jain (Department of Physics and Astrophysics, University of Delhi; Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore; and SFI External Professor)
Abstract: "Innovations" are central to the evolution of life and the evolution of societies, but we do not have an analytical framework for describing them. Which events or sets of events in an evolving complex system deserve to be called "innovation?" After the event, when its impact or consequences are known we can often agree that something was an innovation (e.g., the appearance of photosynthesis, eye, wheel, computer), and even on whether it was a "big" innovation or a "small" one. But can we recognize an innovation as it appears, "on the fly?" Successful entrepreneurs sometimes can. Can we formalize that intuition? Do innovations have a special ‘structural’ character with respect to the existing context?
In this talk I would like to describe a mathematical example of an evolving complex system that exhibits events that seem to qualify as (very rudimentary) innovations. In this stochastic model an evolving network of interacting molecules and their populations shows repeated rounds of random evolution followed by self-organization and growth of structure, stasis, collapse, recovery, re-collapse, etc. An innovation is an event that forges new relationships between existing structures, relationships that can be recognized as special and that produce a new structure with a potential to transform the subsequent evolution. There turn out to be a set of exhaustive and mutually exclusive classes of new relationships that arise in the model; these can be mathematically characterized in structural terms as a hierarchy, and they correspond to different kinds of innovation, big and small. The simple model draws particular attention to certain local events that introduce new feedbacks that can affect the system dynamics globally, which may help in thinking about innovation in real evolving systems.