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.
2. If complexity is synonymous with life (Rosen cites Rutherford that
"every material system is a simple system"), 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.
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 seems to me that these various definitions of complexity (let alone
measures) are really "inferential" (in Rosen's terms), not material. Given
that we can only model nature incompletely, complexity seems to refer more
to the model than to something natural. Relative (measures of) complexity
applies, then, only to limited views of nature, which necessarily are
theories and models. 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).
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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)