Re: "boundary condition" definition

Neil W Rickert <rickert+nn@xxxxxxxxxx> writes:

Haines Brown <brownh@xxxxxxxxxxxxxxxxxxxxxxx> writes:

Herbert Simon, when discussing post-WWII cybernetics, says that "info
theory explains organized complexity in terms of the reduction of
entropy (disorder) that is achieved when systems absorb energy from
external sources and convert it into pattern or structure."

Interesting. That gives me a better perspective on what you have been
trying to get at in this thread.

Really? I was being critical of his statement ;-(

I tend to be a bit skeptical of Simon.

Some people say that "entropy" as used in information theory is the
same thing as "entropy" as used in thermodynamics. Others say that
the two are quite unrelated, except that the mathematics happens to be
similar. I am of the second school. I don't believe that information
theory explains "organized complexity."

I am inclined to agree with both your points.

At one time, people used the slogan "nature abhors a vacuum".
However, we recognize that as a pseudo-explanation. Likewise, what
you describe as Simon's view strikes me as a pseudo-explanation,
though perhaps a useful one.

It's not even an explanation, but an incomplete description. To
"absorb" energy and "convert" it into structure doesn't explain
anything, although it is true, I suppose, that the creation of structure
is driven by a dissipation of energy. But energy dissipation, ceteris
paribus, does the opposite: it moves a system toward a more probable
state.

My own view is that this is, in some sense, Darwinian. As we now
now, the solid rigid static world of physical objects is not static
at all. There is a lot of activity (molecular motion, particle
exchange, etc). With all of this activity, the more stable
configurations are more likely to persist than the less stable
configurations. And often, what makes a configuration more stable,
is that it requires energy to go to a different configuration.

Let me provide a little context.

I had indeed assumed that all things are processes (a safe assumption
these days). By "process" I mean the existence of empirical constraints
on causal potency (an unconventional definition, but there a no other
non-empiricist definitions that I am aware of). Process theory is
committed to scientific realism. So this causal potency is real,
although not actual until it results in some empirical effect.

It seems to me that if systems are open (a safe assumption given that a
truly isolated system is merely a hypothetical), the causal potency will
exist as a range of real possibilities for effects (depending also on
the disposition of the affected system). That is, I am inclined to
extend the concept of a probabilistic phase space (in real physical
rather than merely mathematical terms) to macro systems (see for a
thermodynamic example, Peter Martin, "Probability as a Physical Motive",
Entropy, 9 (2007), 42-57).

By boundary condition, I mean an empirical constraint on that
probabilistic phase space other than the empirical constraints operative
in the process's hypothetical initial state. Such a constraint
necessarily alters the probability distribution. Because this
proposition is intuitive, that is why I raised my initial question. If
one constrains a probabilistic phase space, are you necessarily altering
the probability distribution? Further, I assume the constraint (boundary
condition, mediation, wall, interface, membrane, etc.) has no free
energy to do work itself, but puts heat into the environment so that the
outcome or subsystem state will become improbable in relation to the
initial state or base system.

Notice that I avoid the word entropy, for you may well be right that
information theory and thermodynamics are merely analogous and not
aspects of one thing. For my own purposes, I need only speak of relative
probabilities, and I would actually like to avoid speaking in terms
specific to thermodynamics or information theory.

Your questioning any of these propositions or pointing out those that
are unclear would be much appreciated.

As for your further comments, I have no problems with them. You refer to
large scale statistical trends, but in my field of interest, the concern
is not to describe them, but to explain them. Besides, the measurement
needed for mathematization is generally impossible. You explain (in
Boltzmannian terms) why things on the whole tend to dissipate, but my
concern is instead with emergence of novel structures. This is why I
brought up boundary conditions (constraints on probabilistic phase
space) as the explanation.
--

Haines Brown, KB1GRM



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