Analog and digital, continuous and discrete

Abstract

Representation is central to contemporary theorizing about the mind/brain. But the nature of representation-both in the mind/brain and more generally-is a source of ongoing controversy. One way of categorizing representational types is to distinguish between the analog and the digital: the received view is that analog representations vary smoothly, while digital representations vary in a step-wise manner. I argue that this characterization is inadequate to account for the ways in which representation is used in cognitive science; in its place, I suggest an alternative taxonomy. I will defend and extend David Lewis's account of analog and digital representation, distinguishing analog from continuous representation, as well as digital from discrete representation. I will argue that the distinctions available in this fourfold account accord with representational features of theoretical interest in cognitive science more usefully than the received analog/digital dichotomy.

Discrete and Continuous: A Fundamental Dichotomy in Mathematics

“…But it is in one sense "analog", as in analogous, because it represents time by a quantity (angle) that varies linearly with time. It, so to speak, pictures time directly [1,22,24]. How finely it does so is irrelevant to the mode in which it represents, and is quite different from the way a digital display does so.…”

Computational Dynamics of Natural Information Morphology, Discretely Continuous

“…On a quantum-mechanical level, the universe performs computation [17] on characteristically dual wave-particle objects, i.e., it performs both continuous and discrete computing. Even though they are often used interchangeably, Maley [25] argues that it is necessary to distinguish between analog and continuous, and between digital and discrete representations. Although typical examples of analog representations use continuous media, this is not what makes them analog.…”

Dynamics of Information as Natural Computation

“…Of course if the computing system is continuous then computation should be continuous at least on some level of abstraction. The continuous/discrete and analog/digital are interesting questions with deep consequences and there has been no consensus on this topic in the scientific community to date [7]. Some would claim that space-time can be discretized without loss of explanatory power, while the others argue that discretization necessarily breaks symmetry in such a fundamental way that Lorentz invariance is lost.…”

“…Now it should be emphasized that "computational" is not identical with "digital", and Maley [7] demonstrates that it is necessary to distinguish between analog and continuous, and between digital and discrete representations. Even though typical examples of analog representations use continuous media/formats, this is not what makes them analog; rather, it is the relationship that they maintain with what they represent.…”