Jon Gallant ([log in to unmask]) wrote:
>I think we will find ourselves on firmer ground if we take music as A
>BRANCH of mathematics: abstracted from the symbolic system of quantity
>relationships which, we find, has deep roots in the real world.
I've always heard that there is a strong relationship between mathematics
and music and since I was a math major and am a composer, I will tell
you what it is for me (your mileage may vary). For me both are forms of
architecture. In music small musical ideas are used as building blocks
- combined, structured, transformed, etc. into large architectural works
that exist as a cohesive whole that is greater than the sum of its parts.
In math, small ideas, say the axioms of a field, are combined, structured,
and transformed into a whole (the field) that is greater than the sum
of its parts. Both math and music proceed through time in that you have
to carefully use what you have established as true (in math) or significant
(in music) as progenitors to the next level. "Elegance" is achieved in
both when nothing is included "unless" its required and nothing is stated
"until" it is required. "Genius" is demonstrated by the cleverness in
approach to the tectonicity of the architecture. There's more but its
too deep to go into after working all day:-). I think that math and music
are both a subset of a third "thing" but I'm not sure what to call it -
"meta-zen-philosophy" perhaps. This is why some think that we will never
understand how the mind works - because its more complicated than we
"can" understand. (I don't share that view being an AI guy)
Deryk Barker opined ...
>Well, I think many pure mathematicians would disagree with your descripton
>of mathematics as being founded in the real world.
As for the real world, I will fall back on a quote from Robin Williams
"Reality, what a concept"
The more I learn, the fuzzier (more vague) the real world becomes. The
real world might be a figment of a poor imagination.
IMHO, IMHO, IMHO, IMHO, ad infinidum
Bill Pirkle
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