I wanted to comment on a few terms/ideas.
First, Don refers to the number of distinct ways we interact
with the natural system. I'd like to see if you (all) agree with the
following idea: that a distinct way in which we interact with a
natural system is precisely the same as the encoding and decoding
arms. Therefor, if it is possible to interact with the same natural
system in two different ways, then we would have the following
situation:
(Bruce, entertain for the moment the possibility of having the
natural system in the modeling relationship)
In one distinct way (#1) of interacting with the natural system:
decoding arm (#1)
Natural system A formal system a
encoding arm (#1)
In another distinct way (#2) of interacting with the natural system
decoding arm (#2)
Natural system A formal system b
encoding arm (#2)
Would it be that any notion of complexity should be among
(or between) the distinct modeling relationships, not within
any one of them?
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Where is the complexity? If it is not in the Natural system,
then I think the following would necessarily be true.
Lets concentrate, for a moment, on forming a modeling relationship
between a formal system on the left and the necessary corresponding
system on the right. Consider that it is possible to look (or interact)
with the formal system on the left in a self-referential or
complex way. One example would be with putting the number
theory formalism on the left and looking at it (as Godel did) in the
self-referential way. Then, to complete the modeling relationship,
one would have to put something that wasn't the formalism to
number theory on the right.
For me, this is the big take-home question. Is biology actually
a mechanism...just plain effective computational processes
(nothing more)...and that is what goes on the left of the modeling
relationship...and then as clever individuals (a little too clever),
we are able to look at it (biology) in a complex (self-referential
way) and then conclude that something other than effective
processes must go on the right-hand-side of the modeling
relationship. But all in all, there is nothing complex about
biology...just in the way we CAN look at things. Any talk about
complexity is divorced from the natural world and doesn't belong
to science of the natural world. (just the science of our imaginations).
Of course one could ask if a science of the natural world is even
possible at all...
The other option (to me) is that (in addition to complexity being
related to the way we interact with the world), complexity can
exist in the Natural world (independently of us and how we interact
with the natural world). This would be for systems that have
internal predictive models. For such systems, it wouldn't be US
that provides the encoding and decoding arms, but the system
itself. Thus, if the providing of the encoding and decoding arms
entails the complexity, then systems that did that themselves would
also have to be considered complex.
The question is Do WE have to be in the loop for the system (or
complexity) to exist?.
Of course there is also the question of whether we can know of
any such complexity in the natural world...because anything we
know is entailed in part by our own encoding and decoding
arms.
Pondering...
Jeff Prideaux