John,
I like your writing. Following your thoughts is one way to get a foot into
"systems thinking". Your example is one of the most basic systems and is
taught already at school (linar second order differential-equation with
restistance, spring and external force), yet it is a fact that only few
people really understand the implications and applications of this model.
It is worth the time to understand this example as a basic exercise in
systems thinking.
This said, there are at least two extensions far beyond this simple model:
1. Non linear equations: The field of "deterministic chaos", including
dynamics "far from equilibrium". One can say, that linear equations are
approximations close to equilibrium.
2. Introduction of many variables: leading to regions like "stochastic
system dynamics", (statistical) thermodynamics (linear),
non-equilibrium-thermodynamics (non-linear) discribing state transitions
(water -> ice).
The analogy of the latest models with life has always be drawn, but life
proofed also always to be far beyond. So the further development of
systems science may be motivated by the idea of a "science of life", I do
not believe they will reach this goal, for the simple reason, that the
language of empirical science is not adequate to life. The next higher
step of language is hermeneutical and I think that "systems thinking"
comes close to hermeneutical mutual understanding. But there are forms of
communication far beyond hermeneutics.
Finally I have just one little correction to your description. You said:
> However, if you put the two resistances in parallel -- the flow can divide
> and go through both simultaneously -- then the total resistance is reduced
> to half the original value.
> In the latter case, introducing resistance actually increases the flow.
In fact, you don't introduce resistance but a second path. Admittedly this
path may not be superconducting, but yet it is mainly a second path and
not another resistance that has been introduced and therefore the total
resistance is reduced.
Best regards, Winfried
--Winfried.Dressler winfried.dressler@voith.de
Learning-org -- An Internet Dialog on Learning Organizations For info: <rkarash@karash.com> -or- <http://world.std.com/~lo/>