A note on discreteness and virtuality in analog computing

Abstract

The need for physically motivated discreteness and finiteness conditions emerges in models of both analog and digital computing that are genuinely concerned with physically realizable computational processes. This is brought out by a critical examination of notional analog superTuring devices which involve physically untenable idealizations about the perfect functioning of analog apparatuses and infinite precision of physical measurements. The capability for virtual behaviour, that is, the capability of interpreting, storing, transforming, creating the code, and thereby mimicking the behaviour of (Turing) machines, is used here to introduce a new dimension in the discussion of the analog–digital watershed. In the light of recent results on the analog simulation of digital computing, we examine the role of virtuality as a discriminating factor between these two species of computing, and immerse this problem in the context of natural computing. Is virtuality instantiated in parts of the natural world other than computer technology? This broad issue is examined in connection with the computational modelling of brain and mental information processing.