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Date: Tue, 9 Mar 93 09:20:31 -0500
From: Victor "A." Carreno <vac@gov.nasa.larc.air16>
To: corella@com.ibm.watson
Subject: Re: Analysis and hardware verification
In-Reply-To: Mail from 'corella@watson.ibm.com' dated: Sun, 7 Mar 93 16:38:26 EST
Cc: info-hol@edu.uidaho.cs.ted, vac@gov.nasa.larc.air16


Francisco Corella says:

> "Analysis" does come up in hardware verification.  The ordering on
> Time (the set of time instants) is isomorphic to the ordering of the
> real numbers, and thus time is a continuum.

Remember that continuum is a mathematical model. If you *measure* time, you
attempt to map the physical reality to the mathematical model. There is a
theoretical limit on measurements and the way we perceive physical events.
This is more than a philosophical argument. For example Rayleigh's criteria
says that two objects are indistinguishable of each other unless they have
an angular separation of more than 
                                      -1   1.22 Lambda
                                   sin     -----
                                             d

where d is the diameter of the light source and Lambda the wave length [1].

If two events occur and we can not determine which one occurs first; of
what value is a model that says that one *must* have occurred first since we
can divide time indefinitely?

At the Bureau of standards, if you ask what time it is, they will tell you:

  10:15 plus or minus .0000002 seconds   :-)

> So if you want to verify asynchronous circuits and "do things right", [...]

Which model you use to do things right is the model that works for the
given application.

Victor. (A very opinionated guy)

[1] Halliday, Resnick; Physics, part 2 p. 1114