Honored Forum:
It would seem that something as endlessly, infinitely, necessarily dynamic
as life can never be understood by "conventional" mathematics, and if
metamathematics is but an impossible dream, perhaps the most we can hope for
is to observe, test, and adjust. That means, I suspect, that ecology is, in
the view of literal believers, "doomed" to be "applied." A more cheerful
view might be that one could rejoice about that instead. Perhaps being at
ease with the provisional nature of conclusions is "close enough" for
"practical purposes?" Not good enough for a Nobel Prize, certainly, but if
what I am provisionally calling "trend theory," "relevance testing," and
"resolution of forces" can be worked out to some broad level of
understanding and communication from which principles can be derived, a way
of "adjusting ahead" if not predicting might provide the missing element,
"proof." But that, ipso facto, will be provisional, since it has to be
sphereless. But most likely modelers will produce a Holy Grail, rendering
all that left-field stuff moot, eh?
WT
----- Original Message -----
From: "Wirt Atmar" <[email protected]>
To: <[email protected]>
Sent: Wednesday, January 21, 2009 10:35 AM
Subject: Re: [ECOLOG-L] Ecological Modelling
Bill Silvert writes:
As for the statement that "the state of practice of eco-modeling beyond
simplistic (and wrong) Lotka-Volterra-like things is somewhat of a nasty
business" is partly true - the field is a mess. But the LV equations are
greatly underrated. Although they are a poor representation of most
systems
from a purely quantitative point of view, most continuous models are
generalisations of LV systems and they are great for developing a
qualitative understanding of ecosystem dynamics.
Exactly so.
The goal of mathematical modelling is not prediction but understanding.
Complexly coupled systems that are critically dependent on initial
conditions
are inherently unpredictable, but that doesn't mean that the time spent in
exploring the governing equations is a waste of time. In fact, there is no
other
way to gain an understanding of a complex system's behavior.
As Robert H. MacArthur said, "Every mathematical model is a lie -- but one
that
hopefully allows us to glimpse a bit of the truth."
Wirt Atmar
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