Complexity is that property of real systems that makes it necessary to
intereact with them in more than one distinct way. Therefore there are not
degrees of complexity in this sense.......only degrees of complication in the
formal system used to moodel some aspect of the complex system.
John J. Kineman wrote:
> I have two points of interest regarding my question: "What is the best
> definition of 'ecological complexity?'
>
> 1. If complexity is defined in terms of non-linear interactions (most
> common approach?) and measured in terms of computational complexity (e.g.,
> Algorighmic Information Content), then ecosystems are clearly complex but
> we don't have adequate models to base the measure of complexity on, and
> arguably never can have.
Here again I would say that all ecosystems are complex. What you are looking
for is a degree of complication in the formal systems used to maodel them. I
got Chaitin to see why I adopted this from Rosen, but he also swims with the
tide and is willing to speak of the formal system as complex rather than
complicated.
> 2. If complexity is synonymous with life (Rosen cites Rutherford that
> "every material system is a simple system"),
as a NEGATIVE example contrary to his own notion of complexity!
> then it may not apply to
> ecosystems, which, while composed of living organisms, may themselves not
> qualify as a living organism and may be describable as material systems
> with non-material (living) components. "The system" is something we define,
> so "the ecosystem" can be (and is often) defined as the material
> relationships and patterns.
I think Rosen's point is that the reductionist/mechanists want even ecosystems
to reduce to simple physical laws!
>
>
> Rosen is indirect regrading this question in "Life Itself" (he refers to
> his definition of complexity in a 1977 paper, which I havn't yet seen) --
> but indicates that it is related to the degree of "entailment," either
> causal (material) or inferential (theoretical). His first examples of
> complexity are with regard to mathematics and number theory, which are not
> containable within a formal syntactical model and are thus "open" with
> regard to entailment (the ability to alter itself) and hence complex. All
> this makes sense but does not directly address the comlexity of nature
> (unless we consider mathematics to be a part of nature - which is OK with
> me and yields the same conclusion I reach in the next paragraph).
It is because the essence of Rosen's complexity comes from the failure of the
Newtonian paradigm, not the complicatedness of any given formal system. His
point about the complexity of number theory was simply that........no amount of
formalization could capture all of number theory. There would always be stuff
left unentailed in any formalism. Hence even an infinite number of formalisms
can not capture number theory...it is therefore complex!
>
>
> It seems to me that these various definitions of complexity (let alone
> measures) are really "inferential" (in Rosen's terms), not material.
Rosen's is unique in its separation of the qualities of the natural system from
the formalisms used to try to describe it.
> Given
> that we can only model nature incompletely, complexity seems to refer more
> to the model than to something natural.
In Rosen's language just the opposite...all natural systems are complex.....we
use complexity in another way when we address the formalism in the model...this
SHOULD be termed complicatedness...not complexity.
> Relative (measures of) complexity
> applies, then, only to limited views of nature, which necessarily are
> theories and models.
Only to the formalisms...then it is really complicatedness
> Complexity of a theory is not the same thing as a
> theory about the complexity of nature. Complexity then becomes entirely
> subject to how we define a system, at what scale, etc. Furthermore, the
> necessary incompleteness of our descriptions of nature would seem to imply
> that all of nature is actually complex (i.e., it can't be completely
> described or contained in any formalism).
> that's it!
> -----------------------------------------------
> John J. Kineman, Physical Scientist/Ecologist
> National Geophysical Data Center
> 325 Broadway E/GC1 (3100 Marine St. Rm: A-152)
> Boulder, Colorado 80303 USA
> (303) 497-6900 (phone)
> (303) 497-6513 (fax)
> jjk@ngdc.noaa.gov (email)
respectfully,
Don Mikulecky