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From: turpin@ut-sally.UUCP (Russell Turpin)
Newsgroups: sci.philosophy.tech
Subject: Re: Science and Aesthetics
Message-ID: <8707@ut-sally.UUCP>
Date: Mon, 10-Aug-87 12:35:16 EDT
Article-I.D.: ut-sally.8707
Posted: Mon Aug 10 12:35:16 1987
Date-Received: Tue, 11-Aug-87 04:07:59 EDT
References: <120@snark.UUCP> <86@thirdi.UUCP>
Organization: U. Texas CS Dept., Austin, Texas
Lines: 66
Keywords: beauty truth
Summary: Perhaps epistemology has shaped our idea of "beauty".

In article <86@thirdi.UUCP>, sarge@thirdi.UUCP (Sarge Gerbode) writes:
> In article <120@snark.UUCP> eric@snark.UUCP (Eric S. Raymond) writes:
> 
> >Beauty tends to be a good heuristic for what's *interesting* in
> >pure mathematics, but it doesn't tell you what's true. In other fields the
> >connection is even more tenuous.
> 
> I think what you say in your submission is correct, so far as it goes -- that
> we tend to see things as beautiful when we understand them (like F = ma).
> 
> However, I think beauty *is*, in fact, used as a criterion of truth.  Given two
> theories that equally well explain the facts, I think anyone would pick the one
> that was the most "elegant", i.e. that had the most aesthetic appeal.  I
> wouldn't go so far as to *define* beauty as truth, as Keats did.  But I think
> it *is* an important criterion for choosing between rival theories.
> 
> I think part of the reason for this is that, as Aristotle says, "pleasure is a
> sign of the good".  Likewise, aesthetics might be regarded as a "sign of the
> true".  We tend to feel good when we discover truth.  From past experience, we
> have learned that discovery of truth (as in your dx/dt example) is accompanied
> by an aesthetic sensation.  So now, when we have an aesthetic sensation, we
> tend to regard that as a sign of being on the right track.
> 
> So I don't think it's a "typical-for-philosophically-naive=westerners
> misprojection.  It could be regarded as "true by induction".
> 
> At least I get a good aesthetic feeling about it.
> 
> But then, there's no accounting for tastes.  Or is there?  :-)
> -- 
> "Absolute knowledge means never having to change your mind."
> 
> Sarge Gerbode

Given two physical theories with the same explanatory power, when
do scientists claim one is more elegant or beautiful than the
other? Frequently, the criterion for "elegance" is that one
theory makes fewer unexplained assumptions about the world. Thus,
the more elegant theory is the one that explains as much with
less. 

Certain kinds of assumptions also seem to be preferred over other
kinds of assumption. Suppose that two theories were (a) identical
in their explanatory power, and (b) identical in their
assumptions except for one. For this one assumption, one theory
assumes space is homogenous (physical laws are the same
everywhere), and the other theory, while not requiring
homogeneity, introduces a new force law. Most scientists would
find the latter theory less elegant.

Both of these criteria for elegance, namely parsimony of
assumptions and preference for general principles of symmetry or
invariance over the introduction of new forces, can strongly be
argued for on philosophical grounds. In short, scientists call
theories beautiful because they are more true, or at least, less
wrong. 

What about two theories that have both identical explanatory
power and identical assumptions? I think most physicists would
view these theories as identical physical theories, but with
different mathematical exposition. While one mathematical
exposition might be preferred to the other, on whatever grounds
some mathematics can be judged more elegant than other, the
"physics" is the same.

Russell