Artificial life with autonomously emerging boundaries

The boundary conditions of biological systems are not controllable, due to the perpetual disequilibration of force. This means that the possibilities for the future are open (i.e. one-to-many mapping). However, the future is uniquely determined a posteriori. We argue that such an idea is a basic concept for biological and evolutionary systems and implies unprogrammable systems. But it cannot be described only in a forward-time description. We propose a model in which the uncontrollable boundaries can be described in introducing a backward-time dynamics (a posteriori description). With respect to the extent of the controllability of boundary conditions, systems are classified into constant, microscopic, macroscopic, and disequilibrium systems. In the last, the local transition rule is perpetually transformed as time progresses, due to the uncontrollable microscopic boundary conditions. Our paradigm deviates from the Newtonian paradigm (i.e. the paradigm of prediction), and its purpose is not to describe the physics of being but to describe that of becoming (evolution).