Deryk Barker responding to Jon Gallant wrote:

>Moreover, where in music, are the equivalents of theorems and proofs?

Key to understanding the relationship(s) between music and mathematics
is to see them as symbolic systems, languages basically, which could
possibly be reduced further to "code."  If we don't fall into the trap
of trying to establish priority (which I have just fallen into), and
avoid determining which is a branch of which, if we leave them in their
respective spheres, we might come closer to comprehending their
complementarity and higher unity.  The age-old distinction between the
sciences and the arts can be seen through.  In science theorems and
proofs serve to analyse and simplify; the arts conversely synthesize,
idealize, and serve heuristically to expand formulas or equations.
Music's demonstrations are performances.

Look to the language being used: "find ourselves on firmer ground," "deep
roots in the real world," "founded in the real world."  There is a lot
of nostalgia here for stability but I find greater firmness not so much
in "the real world" as I do in the sense and coherence of a mathematical
formula or the resolution of a chord.  The invisible logical realms of
number and quanta, of fields and spectra, of emotion and aspiration are
as real, perhaps more real (that trap again), than field mice and enigma
machines.  So take your pick: proof or performance.  I enjoy both.

Leslie Bruder