Subject: Re: CCL:orbitals

From: Richard Walsh <rbw=at=ahpcrc.org>
Date: Mon, 2 Jun 2003 09:17:16 -0500

On Sun, 01 Jun 2003 16:09:02 EDT, Dr. N. Sukumar:

>There seems to be an inconsistency here: that of extrapolating beyond the
>known range of validity of the model. I would modify this to say that all
>scientific theories should be, in principle, falsifiable or refutable. A
>theory that isn't so is not science, but religion. The only exceptions are
>axioms and they are to be regarded as merely working hypotheses. Axioms are
>not falsifiable, but they can cease to be useful. In science there are no
>self-evident truths. Problems arise when axioms are confused for facts.
>Replacement of one set of fundamental axioms (as for example, the
>centrality of the earth) for another often leads to a major paradigm shift
>in science.

"Problems arise when axioms (models) are confused for facts (realities)" ... 
and axioms/models that have long dominated the contemporary culture of the mind are 
likely to be confused in just this way ... and in forgetting what they are, we 
can over extend ... "the known validity of the model."  This would seem to be 
at the heart of the matter and the issue arises at a deeper level than orbitals.

Perhaps the most primitive axiom is the principle of identity upon which 
the concept of counting is based.  Who would argue against its usefulness? 
As Poncaire said, "If everyting springs from the principle of identity, then 
everything must be reducible to it."  Yet, how can truly identical things 
be distinguished?  What risks do we run when we assume the reality/usefulness 
of "two-ness" ... ;-) ... forgetting mere orbitals for the moment ...

Who is ready to discard counting and all that flows from it (it seems to 
continue to be useful and is the most interesting game in town), but are we 
all aware of the risks we are taking in over extending this axiom and in 
relying on the countableness of the Universe ... ;-) ... as scientists, we 
must find it "in principle" discardable or falsifiable, oui? ... are we
left with anything that is irrefutable? ... for any given scientist, the first 
reality and only irrefutable model or non-discardable axiom would seem to 
have to be "I am" which I think precedes "I think" regardless of what Descartes 
thought.

Given existence, identity, counting, and ... their less palpable consequences 
... orbitals (while they are useful) ... computational chemistry remains an
interesting game of both discovery and creation.

;-) ... 

rbw

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