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2.4 Irrelevances to the debate

2.4.2 Analogue vs. digital

There is a basic difference between what can be theoretically modelled using analogue and formalisms
*1. Sometimes this is on the grounds of the importance of noise (for this see Section 2.4.4 below).

There is an essential difference between analogue and digital in the abstract. You can not encode all analogue values as digital, only some of them. This can be proved with a classical diagonal argument. This means that literally we can not talk about most analogue values, except as a collective abstraction ("let x be a real number..."), as there are no finite descriptions of them.

The digital and analogue can arbitrarily approximate each other, thus the colour of a pixel on a VDU is composed of different wavelengths (analogue), which is encoded by the computer as a binary number (digital), which is encoded as voltages in circuits (analogue), which correspond to energy levels (digital).

The natural world may, at root, be analogue or digital, we do not know*2. Even with matter and energy one could argue that the quanta are a result of observing a continuous wave function. Thus arguments which rely on a fundamental difference between the analogue nature of reality and the digital nature of formalisms and the modern computer, must be somewhat arbitrary.

This is not to say that either simulating the analogue by the digital (or visca versa) does not present considerable practical difficulties.

Pragmatic Holism - Bruce Edmonds - 22 FEB 96
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