It seems like you've become confused about the nature of the modeling relation.
The encoding and decoding Rosen, Casti, others and I refer to are MAPPINGS.
How can complexity reside in mappings?
There are at least two pretty well defined usages of complexity in these
discussions. I'll risk stating a sketchy version of Bruce's and simply
remind you to reread Rosen's last artical in Louis Rocha's journal to
see that he writes it as:
--------->
A <--------- B
He then says "...in which the arrows represent what we called ENCODINGS and
DECODINGS of propositions about A into those of B, and which satisfy a
property of commutivity"
He then goes on to explain that it represents (in the context of that
discussion) an impredicativity which implies that A and B themselves
possess other models which are non formalizable or non computable. He then
says that the above diagram has a multitude of inherently semantic
INTERPRETATIONS............and proceeds to conclude that the diagram
itself is a complex object! He then applies these ideas to the measurement prob
lem in quantum physics and other things.
May I suggest that your attempt to "localize" the complexity in
a part of the diagram, rather than in the whole, is a throwback to our common
reductionist training? If we wish to take that tack, then I think Bruce has
provided us a better tack ....namely to recognize a commonly accepted
categorization of complexities (computational, structural, Chaitin, casti, etc.)
to apply to the formal systems we place in position "B" in the above diagram.
I hark back to the Benard cell. Newtonian physics is perfectly adequate
in position B for the periods BEFORE and AFTER the transition. However,
the transition itself has no way of being captured by THOSE manifestations
of the modeling relation. We have no formal system for B. The encoding and
decoding mappings are trivial. Hence, most would seem to see the Benard cell
as complex. I hope this clears it up, because I suspect the waters got very
muddy after that one!
Best regards,
Don Mikulecky