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The distinction between digital and analog is in our minds.

"digital" and "analog" are just names of design methodologies that
engineers use to build large systems.  "digital" is not a property of
a signal, or a machine, but rather a property of the design of the
machine.  The design of the machine may not be a part of the machine.
(For example, in many computers, the design of the computer is never
given to the customer.)

If I gave you a music box (which played music naturally), and
you might not be able to tell whether it was digital or analog (even
if you could open it up and look at it and probe various things with
oscilliscopes or other tools).

  Suppose I gave you a set of schematics for the box in which
everything was described in terms of voltages and currents, and which
included an explanation of how the box worked using continuous
mathematical functions.  The schematics might explain how various
subcomponents interpreted their inputs as real numbers (even though
the inputs might be a far cry from real numbers e.g. due to the
quantization of everything by physicists).  You would probably
conclude that the music box was an analog device.

  Suppose, on the other hand, that I gave you a set of schematics for
the same box in which all the subcomponents were described in terms of
discrete formulas (e.g. truth tables), and included an explanation of
how the inputs from reality are interpreted by the hardware as
discrete values (even though the inputs might be a far cry from
discrete values e.g. due to ``noise'' from the uncertainty of
everything).  You would probably conclude that the music box was a
digital device.

  The idea is that a "digital" designer and "analog" designer might
very well come up with the same hardware to solve some problem, but
they would just understand the behaviour differently.

  If designers could handle the complexity of thinking about
everything, they would not use any of these abstractions, but would
just build hardware that works.  Real designers, on the other hand,
must control the complexity of the systems they design, and the
"digital" and "analog" design methodologies control the complexity of
the design while preserving enough of reality to allow the engineer to
make progress.

  If you buy my idea that digital and analog litterally are in our
minds, rather than in the hardware, then the problem is not one of
deciding whether some particular system is digital (such questions
would be considered ill-posed).  The real problem, as I view it, is to
distinguish between the digital and analog design methodologies.

  We can try to understand the difference by looking at the cases
where we would use one versus the other.

   We often use digital systems when the answer we want is a number.
    (such as the decimal expansion of PI to 1000 digits)
   We often use analog systems when the answer we want is something
    physical (I don't really have good examples.  Many of the things
    which were traditionally analog are going digital for some of the
    reasons described below.  e.g. music, pictures (still and moving),
    the control of an automobile engine or the laundry machine)
   We often use digital systems when there are lots of cheap
    digital components available.  (This is not really a circular
    argument.  The reason I personally might build a digital control system for
    something rather than an analog control system is that digital
    components are cheap for me to buy.)
   Digital components are nice because they have specifications which
    are relatively straightforward to test.  To test an analog
    component seems harder.  Because they are easier to test,
    they can be considered more "uniform" than analog components (a
    TTL "OR" gate from one mfr is about the same as a TTL "OR" gate
    from another).  (The same argument goes the other way too...)
   Analog components are nice because sometimes they do just what you
    wanted.  For example, the connection from the gas peddle to the
    throttle on the carburator of a car can be made by a mechanical
    linkage which gives output which is a (approximately) continuous
    function of the input position.  To "fly by wire" (i.e. to use a
    digital linkage) requires a lot more technology.


 (When I say "we use a digital system", I really mean that "we design
such a system using a digital methodology", and correspondingly for
the analog case)

 There are of course all sorts of places between "digital" and
"analog".  A system may have digital subsystems and analog subsystems
and there may be analog subsystems inside the digital subsystems and
it goes on and on.  This sort of thing makes the decision about
whether some particular design methodology is digital or analog hard.

 -Bradley
   bradley@think.com (arpa)
   think!bradley (uucp)