Exploring the landscapes of "computing": digital, neuromorphic, unconventional -- and beyond

TL;DR

This paper provides a comprehensive survey of various formal conceptualizations of computing, including digital, neuromorphic, and unconventional paradigms, proposing a unifying framework to guide future foundational theories.

Contribution

It offers a wide-scope survey of formal models of computing from different mathematical backgrounds and proposes a unifying coordinate system for future theoretical development.

Findings

Different mathematical approaches lead to distinct understandings of computing.

A unifying coordinate system can integrate diverse computing paradigms.

Foundations for a future computing discipline are identified.

Abstract

The acceleration race of digital computing technologies seems to be steering toward impasses -- technological, economical and environmental -- a condition that has spurred research efforts in alternative, "neuromorphic" (brain-like) computing technologies. Furthermore, since 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". This has been taking place in niches which are small compared to other sectors of computer science. In this paper I stake out the grounds of how a general concept of "computing" can be developed which comprises digital, neuromorphic, unconventional and possible future "computing" paradigms. The main contribution of this paper is a wide-scope survey of existing formal conceptualizations of "computing". The survey inspects approaches rooted in three different kinds of background mathematics: discrete-symbolic formalisms, probabilistic modeling, and dynamical-systems oriented views. It turns out that different choices of background mathematics lead to decisively different understandings of what "computing" is. Across all of this diversity, a unifying coordinate system for theorizing about "computing" can be distilled. Within these coordinates I locate anchor points for a foundational formal theory of a future computing-engineering discipline that includes, but will reach beyond, digital and neuromorphic computing.