Degrees of Freedom Fw: Re: Eco-Math

[Eubulides <paraconsistent@xxxxxxxxxxx>]

[A lesson worthwhile for those engaged in political economy-ecology. From
the Ecological Society of America...]


----- Original Message -----
From: "Patrick Foley" <patfoley@xxxxxxxx>
To: <ECOLOG-L@xxxxxxxxxxxxxxxx>
Sent: Friday, July 18, 2003 5:48 PM
Subject: Re: Eco-Math


> Warren,
>
> Mathematics is very powerful in physics because the laws of physics are
> simple. Ecology, while ultimately dependent on physics, is far too messy
> to follow simple axioms and provide exact results.
>
> As Burnham and Anderson point out in their 2002 book, Model Selection
> and Multimodel Inference, the actual number of degrees of freedom in
> ecological models is so large that it might as well be infinite. Our
> attempts to use parsimony as a guide are often just dumb (that's me
> speaking not B and A, I think). Often the most elegant and beautiful
> theory is the correct one in physics. Not so, in ecology.
>
> Patrick Foley (ecologist and recovering mathematician)
> patfoley@xxxxxxxx
>
> Warren W. Aney wrote:
>
> >How useful and basic is mathematics in the field of ecology?  I'm not
> >talking about just using mathematics (and statistics) to describe,
model,
> >and test.  I'm talking about the basic idea posed by Edward O. Wilson
that
> >there is a natural body of mathematics that will serve as a natural
language
> >for biology and hints that mathematics may even provide a bridge that
> >unifies all sciences (Consilience, pp. 103-104, 212-214).
> >
> >An article by Max Tegmark in the May issue of Scientific American
discusses
> >the correspondence between mathematics and physics (and, presumably,
natural
> >sciences in general) and how it goes back to Greek philosophy:
> >
> >"According to the Aristotelian paradigm physical reality is fundamental
and
> >mathematical language is merely a useful approximation.  According to
the
> >Platonic paradigm, the mathematical structure is the true reality and
> >observers percieve it imperfectly." (page 49)
> >
> >Elsewhere in the article Tegmark says that scientists discover
mathematical
> >structures rather than create them and quotes physicist Eugene P.
Wigner:
> >"the enormous usefulness of mathematics in the natural sciences is
something
> >bordering on the mysterious."
> >
> >I guess I tend to have an Aristotelian view of mathematics, but E. O.
Wilson
> >probably has advanced to the Platonic view.  I could expand on this,
but I'd
> >like to hear other viewpoints instead.
> >
> >Warren W. Aney
> >Senior Wildlife Ecologist
> >
> >
> >