[Aiwendil]

Kalessin:

but the attempt to reduce (or reappraise) music as a mathematical form is one I would take issue with

First of all, as I said before, I diasagree that treating music mathematically is a reduction. Second: at some basic level, music must be mathematical. The universe is mathematical; at some very fundamental level, music can be described through wave mechanics.

For example - two scientists can formulate a logical theory, and might each begin with a series of the same simple equations (rather like a chess game, perhaps). But the equations will always look, and mean, the same thing. On the other hand, two singers may sing the same piece, but the difference is obvious. Music is personal, physical AND cerebral - it is communal and individual.

But the differences between two performances of the same piece are surely quantifiable. One performer crescendos more quickly than the other; one tongues the triplets and the other slurs them; etc. These are mathematical, measurable qualities.

However, a performance of a piece of music certainly exemplifies certain emergent properties - properties of a complex system that are inherent in the fundamental mathematics, but not of the same kind as the fundamental mathematics. For example, the rules of chess form a complex mathematical system. Chess strategy is an emergent property of that system; it is derived from the mathematical fundamentals, but it more than the mathematical fundamentals. I would say that emotion, personality, and so forth are emergent properties of music - contained in the quantities but greater than mere quantities.

Basically, I don't think this is the primary case - in effect the element of measurement or 'neutral' observation is not necessarily as important or meaningful as all the aspects of experiencing a work of art.

I did not say that the observation must be neutral. Even if the observation is tinged with subjectivity, it is still at some phase a measurement. The act of experiencing a painting necessarily involves measuring the wavelengths of the various colors and the sizes of the various shapes. But, taking what you said more broadly, I think you do have a point. I still insist that all experience of art involves measurement, but I concede that one's experience cannot be treated simply as the measurement of a single quantity.

Since we both unquestionably have staying power in these kind of debates, let's temporarily get back to Tolkien and the origin of our particular debate

Agreed. By the way, I have also thoroughly enjoyed this and other debates we have had, however unwilling we each seem to be won over by the other's arguments.

the question is how a writer can succeed in his footsteps without either being derivative or imitating, or on the other hand self-consciously avoiding anything that could be seen as Tolkeinesque influence or resonance.

I don't think that it is impossible for a writer to achieve a great work by imitating Tolkien; but it is very unlikely. I believe the main problem is this: Tolkien's work was great because he to some extent believed what he wrote. He did not, of course, believe that the events in his works literally took place; but he believed that his mythology was consistent (physically, psychologically, and theologically), and that it in some way reflected truths about our world. The problem, then, is that the imitators attempt to write the same sort of stuff, but without that belief. I do not say this to disparage the imitators. The fact is that the fantasy genre is defined by Tolkien's beliefs - beliefs with which not a great many people are in complete agreement. Also, most writers today are not inclined to invest this kind of belief in their works, even if it were possible. Tolkien was one of few authors who felt that the story he was telling was important in itself. He wrote neither to convey some message beyond his story (as "literary" writers do) nor to appeal to lots of people and sell millions of books (as mass-market authors do). Yet he was successful in creating a work with both literary significance and mass appeal.

I'm rambling, and without any clear purpose. I suppose my main point an author is more likely to create a great work if he or she is interested in the story as a story (rather than as an allegory or as a step toward profit), and if he or she believes that the story is on some level "true" (or at least consistent with the author's beliefs and way of thinking).

Cudae:

But the imbalance is not exactly an imbalance if it was intentional.

This entails a very broad definition of "balance" - but I understand your point.

but if my theory of math being the basis for everything works then that means that the deepest emotional feeling has some mathematical root.

With this statement I am in perfect agreement.