Theoretical Computer Science 371 (2007) 106–114
www.elsevier.com/locate/tcs
A note on discreteness and virtuality in analog computing
Giuseppe Trautteur, Guglielmo Tamburrini
Dipartimento di Scienze Fisiche, Universit`a di Napoli Federico II, Compl. Universitario Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
Abstract
The need for physicallymotivated 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.

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