[Date Prev][Date Next][Thread Prev][Thread Next]   [Date Index] [Thread Index] [Author Index

Re: Inequivalence of models



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:
"We are going to relate our capacity to produce independent
encodings[non-equivalent models] of a given natural system with the
complexity of it. Roughly speaking, the more such encodings we can produce,
the more complex we will regard the system. Thus, contrary to traditional
views regarding system complexity, we do not treat complexity as a property
of some particular encoding. Nor is complexity entirely an objective
property of the system, in the sense of being itself a directly perceptible
quality which can be measured by a meter. Rather, complexity pertains at
least as much to us as observers as it does to the system; it reflects our
ability to interact with the system in such a way as to make its qualities
visible to us. 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. If the system is such
that we can interact with it in many ways, we will be able to produce
correspondingly many distinct encodings, and we will correspondingly regard
the system as complex."  [AS p. 83, ital. orig.] 
 
Clearly, in this example, there is a weak link in this "test" which is that an incompetent observer/modeler could mislabel a system's complexity (or lack of it) based on his/her incompetence and not because of anything pertaining to the system's organization.
 
Judith