[A lesson worthwhile for those engaged in political economy-ecology. From the Ecological Society of America...]
----- Original Message ----- From: "Patrick Foley" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> 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) > [EMAIL PROTECTED] > > 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 > > > > > >
