I think that as a lay-person there is serious room for doubt regarding whether what modern academic composers are doing is as competent, judged as an attempt to create the most interesting/advanced/sophisiticated music possible, as what the Beatles were doing. It would be nice to know what Beethoven would have thought.
I agree. Of course interesting/advanced/sophisticated is ill-defined and perhaps irreducibly subjective.
At least in math we can see that Wiles was doing roughly the same thing Fermat was doing
For a sufficiently broad notion of “roughly” :-).
I think that it’s fair to say that Fermat’s work represents more originality (picking up on a thousand year old theme and pushing it considerably further than it previously had been in contrast with Wiles who was in some sense working within a well-defined context) whereas Wiles’ work represents a higher standard of technical virtuosity (Fermat never wrote hundred-page-long dense technical manuscripts relying on thousands of pages of background material). To what extent they would be able to interchange roles had they lived in different time periods is difficult to judge.
I guess that one indicative question regarding math would be “How well recognized was Wiles by his professional peers before his famous proof?”.
Wiles was very highly regarded before his proof of Fermat’s Last Theorem. His earlier papers were few but of very high quality. He was best known for his proof of the first infinite family of cases of the Birch and Swinnerton-Dyer conjecture (with his advisor John Coates) and his proof of the main conjecture of Iwasawa theory with Barry Mazur.
It’s possible to easily indicate how the former achievement ties in with classical mathematics (c.f. the first chapter and page 92 of Neal Koblitz’s Introduction to Elliptic Curves and Modular Forms.
The latter achievement is less immediately intelligible but the methods are supposed to be close to those that Ribet used to prove his portion of the Herbrand-Ribet theorem which is a natural sharpening of the criterion which Kummer used in the mid-1800′s to prove many cases of Fermat’s Last Theorem.
(Note: Wiles’ eventual proof of Fermat’s Last Theorem was along completely different conceptual lines from Kummer’s work although some of the machinery that Kummer developed is relevant.)
Of course interesting/advanced/sophisticated is ill-defined and perhaps irreducibly subjective.
It’s so convenient to be able to say that, isn’t it? A great way to save oneself the trouble of having to enter a detailed technical discussion. I think it’s a good idea to beware of such get-out-of-jail-free cards.
Yes, given anything you choose, there exists a possible mind in mind-design space that regards that thing as “interesting”. However, unless you think it’s a genuinely open question whether “Mary Had A Little Lamb” is as interesting as the Eroica, I feel that such assertions are ultimately disingenuous.
It’s so convenient to be able to say that, isn’t it? A great way to save oneself the trouble of having to enter a detailed technical discussion.
I’d like to have a more detailed discussion; my disinclination to do so up until now is a matter of short-term time constraints more than anything else.
However, unless you think it’s a genuinely open question whether “Mary Had A Little Lamb” is as interesting as the Eroica, I feel that such assertions are ultimately disingenuous.
I’m not a total aesthetic subjectivist when it comes to human music appreciation.
I do think that there are some genuinely differing aesthetic preferences between humans on account of differing genetic and environmental factors. For a simple example; I’m highly noise sensitive and this bars me from appreciating very loud music independently of how aesthetically valuable somebody who is not noise-sensitive might find it.
The question in my mind is not so much whether “Mary Had A Little Lamb” is as interesting as the Eroica as much as whether (for example) Philip Glass is as interesting as a famous academic contemporary composer. I find it quite possible that different people might have different views on this last point on account of having differing neurotypes.
I’d like to have a more detailed discussion; my disinclination to do so up until now is a matter of short-term time constraints more than anything else.
Right, but that’s the kind of thing that would enable one to evade a technical discussion (i.e. a semantic stopsign), and hence is an intellectual warning sign. (I don’t necessarily think evasion is your actual intent, of course).
I’m highly noise sensitive and this bars me from appreciating very loud music independently of how aesthetically valuable somebody who is not noise-sensitive might find it.
For the most part, at least in my opinion, the relevant musical variable is not absolute loudness measured in decibels, but relative loudness in the context of a piece. (Of course, the more degrees of loudness are used, the wider the range has to be in absolute terms.)
I agree. Of course interesting/advanced/sophisticated is ill-defined and perhaps irreducibly subjective.
For a sufficiently broad notion of “roughly” :-).
I think that it’s fair to say that Fermat’s work represents more originality (picking up on a thousand year old theme and pushing it considerably further than it previously had been in contrast with Wiles who was in some sense working within a well-defined context) whereas Wiles’ work represents a higher standard of technical virtuosity (Fermat never wrote hundred-page-long dense technical manuscripts relying on thousands of pages of background material). To what extent they would be able to interchange roles had they lived in different time periods is difficult to judge.
Wiles was very highly regarded before his proof of Fermat’s Last Theorem. His earlier papers were few but of very high quality. He was best known for his proof of the first infinite family of cases of the Birch and Swinnerton-Dyer conjecture (with his advisor John Coates) and his proof of the main conjecture of Iwasawa theory with Barry Mazur.
It’s possible to easily indicate how the former achievement ties in with classical mathematics (c.f. the first chapter and page 92 of Neal Koblitz’s Introduction to Elliptic Curves and Modular Forms.
The latter achievement is less immediately intelligible but the methods are supposed to be close to those that Ribet used to prove his portion of the Herbrand-Ribet theorem which is a natural sharpening of the criterion which Kummer used in the mid-1800′s to prove many cases of Fermat’s Last Theorem.
(Note: Wiles’ eventual proof of Fermat’s Last Theorem was along completely different conceptual lines from Kummer’s work although some of the machinery that Kummer developed is relevant.)
It’s so convenient to be able to say that, isn’t it? A great way to save oneself the trouble of having to enter a detailed technical discussion. I think it’s a good idea to beware of such get-out-of-jail-free cards.
Yes, given anything you choose, there exists a possible mind in mind-design space that regards that thing as “interesting”. However, unless you think it’s a genuinely open question whether “Mary Had A Little Lamb” is as interesting as the Eroica, I feel that such assertions are ultimately disingenuous.
I’d like to have a more detailed discussion; my disinclination to do so up until now is a matter of short-term time constraints more than anything else.
I’m not a total aesthetic subjectivist when it comes to human music appreciation.
I do think that there are some genuinely differing aesthetic preferences between humans on account of differing genetic and environmental factors. For a simple example; I’m highly noise sensitive and this bars me from appreciating very loud music independently of how aesthetically valuable somebody who is not noise-sensitive might find it.
The question in my mind is not so much whether “Mary Had A Little Lamb” is as interesting as the Eroica as much as whether (for example) Philip Glass is as interesting as a famous academic contemporary composer. I find it quite possible that different people might have different views on this last point on account of having differing neurotypes.
Right, but that’s the kind of thing that would enable one to evade a technical discussion (i.e. a semantic stopsign), and hence is an intellectual warning sign. (I don’t necessarily think evasion is your actual intent, of course).
For the most part, at least in my opinion, the relevant musical variable is not absolute loudness measured in decibels, but relative loudness in the context of a piece. (Of course, the more degrees of loudness are used, the wider the range has to be in absolute terms.)
I’ll reply futher later.