[Aiwendil]

I had not meant to imply that the purpose changes; merely the laws derived from said rigorous observations. Of course, now, experimental methods do change!

Ah. Yes, our knowledge concerning the true laws changes as we discover more things.

I am not prepared to equate the two; however, I would say that there is an aesthetic character to mathematics. That does not make it necessary for the two to be equal, but merely that the exercise of mathematics seems to satisfy an aspect of the human psyche that longs for order in a quantifiable and observable way. In that way, mathematics satisfies an aesthetic requirement.

I agree with this as well.

I suppose I just decided to shift to the variable idea of possibilities and analogies for the Music that do not specifically address the physical concepts, but the concept that physics could be another way to explain the Music (not necessarily that the Ainur would have considered such a thing but that we, as having access to physics as it is currently, would think of such a thing). I couldn't begin to explain it, though!

If what you're saying is that the music of the Ainur plays a role in Arda similar to the role played by the equations of physics in our world, then I agree. That role is, specifically, to describe the world. Note that there is a slight difference with regard to the metaphysics of free will and of Iluvatar's intervention in Arda.

But I still think that if one is interested in the fundamental nature of the creation of Arda, it is artistic in a way in which our universe is not.

I can't argue with that! I don't seek to destroy or bring the myth down to material level, but to rhapsodize upon it, rather to speculate that those who wrote the histories might compare the Music to such things, because those are the things they know and can understand. Certainly the aforesaid instruments would have to be extraordinary to produce the Music as it would filter into Arda as the sound of water and wind on the mountains, etc. I wonder at the cosmic nature of these 'instruments,' and wonder if the songs played upon them could have a mathematical aesthetic such as you have said, permeates the entire world, for everything can be reduced to mathematics.

Yes, I certainly think there's an interesting argument to be had concerning whether the music of the Ainur was literally music or not. As I said, I come down on the literal side. But I can certainly see the points in favor of the other and the appeal of that side.

I hope that was clearer; not sure though!

Yes, I think I understand you now. I feared that you might be a constructivist! But I think that we are largely in agreement.