[Aiwendil]

When I read the method, what I got out of it was, "the students run the class and the teacher watches and makes a few comments." Sounded like chaos, really. But, back to the real purpose!

Yes, constructivism is I suppose a rather broad trend that has affected quite a few disciplines. In philosophy of science, constructivism (which was championed by Thomas Kuhn) is (broadly speaking) the view that science is just a social construct and is not in any way more priveliged, more objective, or more 'true' than other social constructs. This is in opposition to the more traditional view that science is the business of discovering true things about the world, and that it is based in objectivity.

I think the idea that made this particular concept resonate (so to speak) was the constant striving of certain mathematicians and astronomers (Ptolemy, Pythagoreas, Kepler, etc.) to find a harmony in the mathematical descriptions of the motions of the planets, thus my comment earlier on the "Music of the Spheres."

Yes, I can see how this is a very appealing notion. And indeed the Ainulindale fits rather well with it. But I think that in Tolkien's creation legend there is altogether a greater emphasis on art, on 'sub-creation', on the will of the artist, than on balance, mathematics, and perfection - not that I think that these two things are in opposition but rather that they differ subtly.

The concept of the Music of the Spheres seems to draw science, philosophy and religion together somehow in that all seek this harmony.

I'm not sure I see how this is true. Certainly there is something philosophical about the idea, but not any more so (I think) than in any sort of science, if one looks at it hard enough. And religion? Certainly one could invent religion to 'explain' the Music of the Spheres, but so could one invent religion in any case, to 'explain' whatever aspect of science one would like.

The sacred songs of medieval times were constrained to the 'perfect' harmonic ratios (1, 5, and 6, I think, but I'm working from a 25 year old memory here!).

Hmm. The 'perfect' intervals are the octave, the fourth, and the fifth. And indeed these were the intervals that were at first deemed 'consonant', when harmony was young. I can't recall at the moment when the third and the sixth were admitted as consonances, but I think it must have been during the middle ages (possibly the late middle ages).

But perhaps it would do us well to recall that in the end, Kepler's theory about planetary orbits being based on the perfect polyhedra turned out not to work. As a matter of fact, this story has become something of an morality legend among scientists. For despite spending most of his life working on the theory and staking so much of himself on it, when it became clear that the theory could not work, he accepted this and admitted the objective inadequacies of his cherished view. And thanks to his willingness to admit this, out of his failed attempt came several important laws concerning planetary motion.

I'm not sure that that story has all that much bearing on the discussion at hand, but I find it quite inspirational - and also a good warning against assuming an underlying connection between the basic physics of the universe and personal aesthetics.

[ November 23, 2003: Message edited by: Aiwendil ]