Toward a generalized theory comprising digital, neuromorphic, and unconventional computing

The accelerating race of digital computing technologies seems to be steering towards impasses—technological, economical and environmental—a condition that has spurred research efforts in alternative, 'neuromorphic' (brain-like) computing technologies. Furthermore, for decades, the idea of exploiting nonlinear physical phenomena 'directly' for non-digital computing has been explored under names like 'unconventional computing', 'natural computing', 'physical computing', or 'in-materio computing'. In this article I investigate coordinates and conditions for a generalized concept of 'computing' which comprises digital, neuromorphic, unconventional and possible future 'computing' paradigms. The main contribution of this paper is an in-depth inspection of existing formal conceptualizations of 'computing' in discrete-symbolic, probabilistic and dynamical-systems oriented views. It turns out that different choices of background mathematics lead to decisively different understandings of what 'computing' is. However, across this diversity a unifying coordinate system for theorizing about 'computing' can be distilled.