[comp.ai] D/A Distinction and Symbols

marken@aero.ARPA (Richard Marken) (11/12/86)

In article <3490001@hpfcph.HP.COM> Bob Myers makes an eloquent debut to the
D/A distinction debate with the following remarks:

>The difference between "analog" and "digital" is nothing more than the
>difference between a table of numbers and the corresponding graph; in a
>digital representation, we assign a finite-precision number to indicate the
>value of something (usually a signal) at various points in time (or frequency,
>or space, or whatever).  An "analog" representation is just that - we choose
>to view some value (voltage, current, water pressure, anything) as hopefully
>being a faithful copy of something else.  An excellent example is a
>microphone, which converts a varying pressure into an "analogous" signal -
>a varying voltage.  This distinction has nothing to do with the accuracy of
>the representation obtained, the technology used to obtain, or any of a host
>of other items that come to mind when we think of the terms "analog" and
>"digital".

We haven't heard for some time from the usually prolific Dr. Har-
nad, who started the debate with a request for definitions of the
A/D distinction. It seems to me that the topic  was  broached  in
the  first  place because Harnad had some notion that "analog" or
"non-symbolic" robots are, in some way, a better subject for a test
of  machine  intelligence (a la Turing) than the"symbol manipula-
tor" envisioned by Turing himself. 

Whether this was where Harnad was going or not, I would  like  to
make  one point. It seems to me, based on the cogent A/D distinc-
tion made by Myers, that both analog and digital  representations
are "symbolic". In both cases, some variable (number, signal lev-
el) is used to represent another. The relationship between  the
variables  is  _arbitrary_   in,  potentially, two ways: 1) the
nature of the analog signal or number  used   to   represent  the
other  variable is arbitrary- other  types of signals 
or other number values could have also been used. Using  electri-
city   to   represent   sound   pressure   level   is   arbitrary
(though, possibly, a good enginnering decision)-- sound  pressure
level   could   have been represented by height of a needle (hey,
it is) or by water pressure or whatever.

2) the values of  the  analog  (or  digital)  variable  used   to
represent  the  values of another variabl are, in principle, also  arbi-
trary.  Randomly different voltages could be used  to   represent
different   sound   pressure levels. This would be difficult (and
possibly ridiculous) to try to implement but it could be done
(like where changes over time in the variable  being
 represented are very slow).

 Maybe the best way to put this is as follows:
 in digital or analog representation we have some variable, y,that 
 represents some other, x, so that y= f(x). Regardless of the analog
 or digital characteristics of x and y, y "symbolizes" x because
 1) another variable, y', could be used to represent x (so y is arbitrary)
 and 2) y could be defined by a different function, f',so f is arbitrary.

I think 1) and 2) capture what is meant when  it  is  said   that
symbols  are arbitrary representations of events. Symbols are not
completely arbitrary.  Once y and f are selected  you've  got  to
stick  with  them (in the context of  your  application) or the



symbol system is useless.  Thus,  the  sounds  that  we  use   to
represent  events  (f)  and  the fact that we use sounds (y) is an
arbitrary  propery of our language symbol system.  But  now  that
we've  settled  on   it   we've got to stick with it for it to be
useful (for communication). We  could (like  humpty-dumpty)  keep
changing the relationship between words  and events but this kind
of arbitrariness would make communication impossible.

Conclusion: I don't believe that the A/D distinction is a distinction
between non-symbol vs symbol systems. If there is a difference between
robots (that deal with "real world" variables) and turing machines
(that deal with artificial symbol systems) I don't believe it can turn
on the fact that one deals with symbols and the other doesn't. They
both deal with symbols. So what is the difference? I think there
is a difference between robots (of certain types) and turing machines--
and a profound one at that. But that's another posting.

--------------------------------------------------------------------
Disclaimer-- The opinions expressed are my own. My employer, mother
wife and teachers should not be held responsible -- though some tried
valiantly to help.

Richard Marken                      Aerospace Corp.
(213) 336-6214                      Systems Simulation and Analysis  
				    P.O. Box 92957
				    M1/076
				    Los Angeles, CA 90009-2957

marken@aero.ARPA    
kk