|
Just for clarity's sake...
Tim Gwinn wrote: ... "Non-equivalence" refers to whether or not two models can be transformed or reduced to one another. As Judith has mentioned many times before, something like a car engine (for example) can be a simple system OR it can be a complex system. It depends entirely on how one defines the system called "car engine". Any system, regardless of its
organization type, can be included or subsumed into a larger
system, even one with different organization; either "more" or "less"
complex than the system we started with. Similarly, any system can be
fractionated into components, which are likely to be all over the map in terms
of their individual organization, if we analyzed each one as a separate system.
Some components may be more complex than the original system, some may be
less complex... This is why I keep stressing the fact that complexity of any
given system, according to Rosennean definitions of complexity, is an
organizational property of that particular system, intact. I
think it is significant that an ecosystem, indeed the entire biosphere, is
not as complex in this sense as a single-celled algae. It is also how a
car or a car engine could be a simple system, and be made up of atoms, which are
complex systems. It's critical to understand how Robert Rosen could say this is
so, if you want to really understand all that he was saying about entailment,
about causality in the universe, about the power inherent in the concept of a
relation, about science and where it misses a ton of information due to various
factors...
TG: That definition will insinuate the way(s) in which we
can interact with that system as defined, and therefore the ways in which the
system is modeled, and therefore the set of models for that system, and finally,
if that set of models can be transformed or reduced into a largest model,
then the system is complex; if not (i.e., there are non-equivalent models in the
set of models), then it is a simple system.
This gets a little tricky: It's easy
to misunderstand the phrase "ways in which we can interact with the system..." I
don't think Tim is doing this here, but the whole notion of "counting the ways
we can interact with the system" such that the number of ways we can come up
with is somehow a gauge of the system's complexity.... is a red herring. That
was Don's misrepresentation of what my father actually wrote (and which I quoted
in the post Tim refers to and is included, below). Such a "test" would be more a
reflection of the complexity of the human mind coming up with "different ways to
interact with the system" than having anything to do with the system's
organization whatsoever. My father didn't mean "interact" as in Can we
dance with it... he didn't mean Can we wear it as a hat... He
said earlier in that discussion that any observation we make of a
system is a form of interacting with that system, as is
"perturbing" the system in some way to observe its behavior in relation to that
perturbation... and from that kind of interaction we can
create models. But the "interaction" itself isn't the most important aspect of
this process... It's the number of independent encodings, though, that matters
here. "Independent encodings" are models which are
non-equivalent.
Another aspect of this quote, below,
is that he (RR) is deliberately cagey about the number of independent encodings
having a relation to the "level" of complexity of the system.... He said
"Intuitively speaking, if the system is such
that we can interact with it in only a few
ways, there will be correspondingly few distinct encodings we can make of the qualities which we
perceive thereby, and the system will appear to
us as a simple system." But we
have already discussed the fact that one of the "tests" of complexity is that if
a system has at least one non-equivalent model, then it's complex. So what he's
doing in his quote here is leaving room for the stipulation that complexity
isn't a quality of accretion, whereby adding more of "it" to a system
makes the system "more complex". It doesn't work that way. Complexity
is not an ingredient, in that sense, although complex organization does make a
system behave as if it has far more components (ingredients) than it
actually has when we try analyzing it via
fractionation.
As Judith quoted Robert Rosen in a 3/25/04
post:
|