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John M,
I think your confusion is understandable, especially when M,R and
M-R and MR etc are thrown around in discussions about Rosennean Complexity
Theory, relying on the context of the sentence to clarify meaning... except that
in my father's work the context could seem to point either way. But I think I
can clear up the confusion here. Let me know if this helps:
The model my father created to illustrate the bare
minimum necessary behaviors of a system in order to be a living
organism is his (M,R)-System diagram. In this diagram, M stands for Metabolism
and R stands for Repair. The diagram (and name) itself is an example of a
modeling relation: formalism (diagram) to natural system
(organism).
There is another diagram my father created, of the modeling
relation itself. In it, the natural system has "causal loops" of entailment and
the model has "impredicative loops" of entailment. There's an arrow going from
the natural system to the model that is labeled "encoding" and another arrow
going from the model back to the natural system, labeled "decoding". Those
arrows embody the relation between a model and its corresponding natural system:
a modeling relation. (Perhaps it's worth pointing out that any model is
only as good as the encoding/decoding that relates it to the natural system it
models. It obviously behooves us to get it as right as possible.)
You can also have a modeling relation between two models (for
example; between a formalism on paper and a laboratory rat-- which is standing
in as a model of a human being-- in medical research). This is where it gets
very dangerous: The more times removed from the original natural system being
modeled, the more inaccuracies will become part of the results predicted by the
models.
The reason there is so much written in all my father's books about
the subject of the modeling relation (metaphor, similarity, optimality,
computability, etc) is because modeling is one of the main tools of
science; BUT if it is done poorly then what we learn from it is of
questionable value. Worse, if the model becomes the focus and the original
system is forgotten.... then we learn about the model, not the natural
system it models. But the decisions we make based on the model are going to be
applied to the natural system. Doing this generates "side effects". The
disconnect between the model, then, and the natural system is a disconnect in
the "modeling relation".
Judith
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