FOM: Alice, Carol and Leibniz

Insall montez at
Tue Apr 16 18:56:31 EDT 2002

     First, let me comment that Wiman Lucas Raymond, in an off-list email,
correctly pointed out that his original posting had dealt somewhat with the
issue I raised in my posting.

     As for the comment below, this is really the basis for the use of two
different approaches in physics, chemistry, engineering, etc., to the
concept of a ``control volume''.  One may draw a stationary spatial boundary
as a control volume, and accept the fact that flow across the boundary
occurs, and make use of that fact to study (or design) a process, for
various purposes, all of which accept that in the final analysis, there is
(guaranteed to be) some error.  On the other hand, one may consider the
spatial boundary to be flexible (i.e. membraneous), so that there is no flow
across the boundary, and the ``identities'' of the original two bodies of
fluid, which are located on opposite sides of the boundary from one another,
are ``maintained'', in the sense that throughout the time period over which
one studies the process in question, the molecules of the fluid on the one
side of the boundary are at all times the same molecules.  Again, in these
studies, one does not claim that some metaphysical consequence leading to a
``loss of identity'' occurs.  One merely studies or designs a process, and
accepts the fact that the approach allows some error in the outcome.  When
one considers this latter approach on all levels of scale, one must accept
the fact that the boundary geometry is time-dependent and becomes
(microscopically) complicated, in order that one may account for the
assumption that no molecules cross the boundary, but that motions like
brownian motion occur.  This is one way that so-called ``fractal analysis''
can be of use to these scientists.

Matt Insall

-----Original Message-----
From: Ross A. Finlayson [mailto:apex at APEXINTERNETSOFTWARE.COM]
Sent: Tuesday, April 16, 2002 2:40 PM
To: Insall
Subject: Re: FOM: Alice, Carol and Leibniz

If the analogy carries, then draw an invisible line across the bucket.
Sure, the two gallons are miscible, but only one gallon is on each side
of the line at a time.


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