🚀 go-pugleaf

In article <717712154.5@mailbox.bison.mb> Jim.Giles@mailbox.bison.mb.ca (Jim Giles) writes:
>Organization: Los Alamos National Laboratory
>
>In article <1992Sep24.190216.13493@riacs.edu>, danforth@riacs.edu (Douglas G. Danforth) writes:
>|> [...]
>|> If by hypothesizing a new structure that subsumes two other descriptive
>|> models then the new structure gains significance via its generality
>|> and reduction in parts.  The possibility of a unified field that
>|> corresponds with QM and GR leads one to look for such an explanation. 
>
>Only if that new hypothesis has *testable* consequences.  If not, it's
>an exercise in mysticism.  Now, don't get me wrong - have nothing against
>mysticism.  Imagination and wishful thinking may *lead* to testable
>ideas.  I just oppose mysticism being promoted as known fact.

Of course, mathematics has been a branch of mysticism ever since the
Pythagoreans (if not earlier).  As a mathematician, if one could
find a mathematical model from which quantum mechanics and general
relativity both "fell out" in some natural manner, it would count
as an outstanding achievement even if it had no testable consequences.
Elegance, generality and "reduction in parts" are very important in
mathematics and also physics to the extent that it is mathematical!
This is indeed the mystical side of physics, relying as it does on
the faith that "mathematics is the language of nature" (to paraphrase
Galileo) which yields the "unreasonable effectiveness of mathematics"
(to quote Wigner).  However, this mystical faith is time-tested and
proven; one need only study how Kepler arrived at his 3 laws, or how
Einstein arrived at general relativity, to see that the pursuit of
mathematical beauty, in conjunction with painstaking attention to the
empirical clues provided by nature, can lead to theories that *later*
turn out to have empirical consequences.  One should not be in too much
of a rush to demand testable consequences; mathematics that is both
rigorous and elegant has a strong tendenccy to come in handy eventually.