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From: harnad@mind.UUCP (Stevan Harnad)
Newsgroups: net.ai,sci.electronics
Subject: Re: Defining the Analog/Digital Distinction
Message-ID: <13@mind.UUCP>
Date: Mon, 27-Oct-86 01:08:33 EST
Article-I.D.: mind.13
Posted: Mon Oct 27 01:08:33 1986
Date-Received: Mon, 27-Oct-86 05:43:28 EST
References: <7@mind.UUCP> <45900003@orstcs.UUCP>
Organization: Cognitive Science, Princeton University
Lines: 52
Xref: watmath net.ai:3824 sci.electronics:8
Summary: Continuity, exploiting the physical medium, and information preservation under transformations


Tom Dietterich (orstcs!tgd) responds as follows to my challenge to
define the A/D distinction:

>	In any representation, certain properties of the representational
>	medium are exploited to carry information. Digital representations
>	tend to exploit fewer properties of the medium. For example, in
>	digital electronics, a 0 could be defined as anything below .2 volts
>	and a 1 as anything above 4 volts. This is a simple distinction.
>	An analog representation of a signal (e.g., in an audio amplifier)
>	requires a much finer grain of distinctions--it exploits the
>	continuity of voltage to represent, for example, the loudness
>	of a sound.

So far so good. Analog representations "exploit" more of the properties 
(e.g., continuity) of the "representational" (physical?) medium to carry
information. But then is the difference between an A and a D representation
just that one is more (exploitative) and the other less? Is it not rather that
they carry information and/or represent in a DIFFERENT WAY? In what
does that difference consist? (And what does "exploit" mean? Exploit
for whom?)

>	A related notion of digital and analog can be obtained by considering
>	what kinds of transformations can be applied without losing
>	information. Digital signals can generally be transformed in more
>	ways--precisely because they do not exploit as many properties of the
>	representational medium. Hence, if we add .1 volts to a digital 0 as
>	defined above, the result will either still be 0 or else be undefined
>	(and hence [un]detectable). A digital 1 remains unchanged under
>	addition of .1 volts. However, the analog signal would be
>	changed under ANY addition of voltage.

"Preserving information under transformations" also sounds like a good
candidate. But it seems to me that preservation-under-transformation
is (or ought to be) a two-way street. Digital representations may be
robust within their respective discrete boundaries, but it hardly
sounds information-preserving to lose all the information between .2
volts and 4 volts. I would think that the invertibility of analog
transformations might be a better instance of information preservation than
the irretrievable losses of A/D. And this still seems to side-step the
question of WHAT information is preserved, and in what way, by analog
and digital representations, respectively. And should we be focusing on
representations in this discussion, or on transformations (A/A, A/D,
D/D, D/A)? Finally, what is the relation between a digital
representation and a symbolic representation?

Please keep those definitions coming.

Stevan Harnad
{allegra, bellcore, seismo, packard}  !princeton!mind!harnad
harnad%mind@princeton.csnet
(609)-921-7771