Christopher Webber completely misreads the intent of my remarks.

>The beauty of the best pure mathematics is often intensely personal -
>I've often heard fine examples described as "elegant", very much in
>the way we might describe a Mozart concerto movement.

Certainly, but the meaning is objective.  I use mathematics a great
deal, and I have a genuine appreciation for its beauty, but the meaning
is very clear.  That's the whole point of mathematics.

>It's not so much the thought as the expression which counts.

Not to engineers or others who model the "real world" with mathematics.

>The theoretical basis of pure mathematics is of course no more (or
>less) amenable to proof than that of a musical scale.

I just can't make any sense out of this assertion.  Pure mathematics may
be synthetic, but its foundations remain grounded in objective reality
(counting). And again, its meaning is not subject to individual
interpretation, or influence by the interpretor's moods.

>How does Len know that music was "subjective in origin"?

I don't know if you're trying to be whimsical or snide, but I said "is"
not "was", and I meant that the creation of and subsequent interpretation
of a piece of music is a subjective process.

>Is he keeping something from us? Maybe he there in that old ossitorium
>with Ludwig Van Caveman? I'd have imagined that music was at least as
>likely to be representational ("factual?") in its origins as mathematics
>- birdsong, timbre and pitch of wood and bone, the rhythms of wind and
>rain ...

This is your hypothesis.  And even if the origin of the first music was
indeed fostered by imitation of natural sounds, it is still, compared to
counting, a subjective experience.

len.