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