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From: gwyn@brl-vgr.UUCP
Newsgroups: net.physics,net.astro.expert
Subject: Re: simplicity and symmetry in cosmology
Message-ID: <2142@brl-vgr.ARPA>
Date: Thu, 17-May-84 15:21:10 EDT
Article-I.D.: brl-vgr.2142
Posted: Thu May 17 15:21:10 1984
Date-Received: Fri, 18-May-84 07:10:41 EDT
References: <294@utastro.UUCP>
Organization: Ballistics Research Lab
Lines: 49

There is no way I am going to convey the meaning of simplicity etc. in
a reasonable number of words, but let me at least give a practical guide
to comparing two competing theories of the fundamental laws of physics,
in order to convey something of what I have in mind.

Theory A consists of:
	(1) acceptance of several common mathematical ideas;
	(2) postulation of seven fundamental properties (charm, etc.?);
	(3) adoption of four principles of quantization, renormalization,
	    and so forth;
	(4) acceptance of a Lagrangian with three independent coupling
	    constants, of fourth order in the fundamental entities;
	(5) a 20-dimensional space;
	(6) a preferred frame of reference;
	(7) one principle of variation.

Theory B consists of:
	(1) acceptance of several common mathematical ideas;
	(2) postulation of one fundamental property;
	(3) adoption of two operational principles;
	(4) acceptance of a second-order Largrangian with no added constants;
	(5) a 4-dimensional space;
	(6) no preferred reference frame;
	(7) one principle of variation.

Then I would certainly claim that Theory B is the "simpler" theory,
since it has considerably fewer things put into it a priori.  This
of course does not mean that Theory B is guaranteed to describe
reality better than Theory A, although if it is comparable in
accuracy one should be strongly inclined to prefer it over Theory B.

(Note:  Theories A & B are meant to remind one of certain real
candidates, but the detailed counts of the basic enities, assumptions,
etc. do not necessarily correctly reflect those of any actual theories.)

There is even a quantitative method of assigning a measure to the
degree to which a field theory constrains its basic entities (the
basic idea is the asymptotic degrees of freedom of the higher-
order Taylor coefficients of the fields).  It is amusing that the
measure number for the Einstein-Straus-Kaufman unified field theory
(which I do NOT support) is precisely "42".  Now we know what the
ultimate question was (Life, the Universe, and Everything).

Einstein preferred a "stronger" theory to a "weaker" (i.e. less
asymptotic freedom) in the absence of any other criterion for
choosing between competing theories.  I prefer the "weaker" on
the intuitive grounds that it is less of a special-case theory...
Of course we assume that the theories in question agree with
reality sufficiently well; otherwise the choice is trivial.