Is it your contention that modern musicians write Clasical minuets and Baroque fugues which are in some cases better than the best of the older works that are still listened to, but that no-one cares because much of the value of those works is in their role in a canon?
I could easily believe that in those cases, but I simply don’t believe it in the case of Opera. The Opera cannon is just not very large. Some people have heard the whole thing and only like a few dozen operas. It doesn’t seem likely that there isn’t demand among such people for higher quality new material in old styles, so if no new material is becoming popular then the un-met demand makes me think that contemporary music students are failing to produce work that this audience actually values due to now knowing how to replicate the merits of older compositions.
It should really be pretty easy to do a controlled experiment with a naive population to see how common it is for modern artists to be able to impress an audience as much as their 18th and 19th century precursors did.
I’m seriously interested in someone performing some experiments on this subject. It seems to me that it would provide an extremely practically important measurement of the quality of university education in fields inaccessible to outsiders, but I don’t expect to be able to attract funding for such research because it sounds impractical at the face of it.
I guess that my major reason for holding the contrary position was largely because modern musicians and composers, more than painters and authors, are the results of university education and I fairly strongly suspect university education of destorying artistic ability and distracting artists with intellectual games that simply lack the merits of the fields that the academic subjects are derived from. I suspect this in math as much as in music, and I think Von Neumann agreed with me, as this quote suggests.
“As a mathematical discipline travels far from its empirical source, or still more, if it is a second or third generation only indirectly inspired by ideas coming from ‘reality’, it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely l’art pour l’art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much ‘abstract’ inbreeding, a mathematical subject is in danger of degeneration.”
Is it your contention that modern musicians write Clasical minuets and Baroque fugues which are in some cases better than the best of the older works that are still listened to, but that no-one cares because much of the value of those works is in their role in a canon?
I myself would guess that none of the works produced over the past hundred years would be judged by the majority of an impartial audience to be significantly more compelling than (for example) Bach’s Chaconne.
It should really be pretty easy to do a controlled experiment with a naive population to see how common it is for modern artists to be able to impress an audience as much as their 18th and 19th century precursors did.
I’m seriously interested in someone performing some experiments on this subject.
Same here.
I guess that my major reason for holding the contrary position was largely because modern musicians and composers, more than painters and authors, are the results of university education and I fairly strongly suspect university education of destorying artistic ability and distracting artists with intellectual games that simply lack the merits of the fields that the academic subjects are derived from. I suspect this in math as much as in music, and I think Von Neumann agreed with me, as this quote suggests.
I’m impressed that you’re familiar with the Von Neumann quote (which is sadly little known in the mathematical community but which my friend Laurens is fond of); but on the face of things it doesn’t seem to directly support your paragraph above. Explain further if you’d like?
Several points here:
My impression is that there are issues of bad social/cultural institutions destroying artistic ability outside of academia. I have some friends artistically genuine who have spent some time as painters and become disillusioned with the signaling games and hypocrisy present within the communities of painters that they’ve come across. Note that fledging painters and authors face greater financial pressures than academics and that this can lead to perverse incentives (to appeal to the lowest common denominator or to current fashions for greater marketability). See Minhyong Kim’s comment here.
The absence of new empirical sources for mathematics seems to me more a consequence of the stagnation of theoretical physics than the social structure of the mathematical community.
In my own view insufficient emphasis on exposition has played a significant role in whatever stagnation has occurred within the mathematical community since, e.g. the 1800′s. The barrier to entry has gotten progressively higher as mathematics has developed and in such a setting, in absence of strong efforts to to cast background material in an accessible and readily digestible form, the pressures toward specialization and fragmentation get progressively stronger. There aren’t career-based incentives for expository work so mathematicians who are interested in exposition either conform to the research-based publish or perish norms or leave.
I’d be happy to compile an annotated list of relatively accessible survey papers if you’d be interested and find it useful for getting a sense for the state of some of contemporary mathematical research.
The absence of new empirical sources for mathematics seems to me more a consequence of the stagnation of theoretical physics than the social structure of the mathematical community.
From my perspective in applied math things are exactly opposite. We’re practically drowning in empirical sources begging for better numerics. There is hardly a scientific or engineering field today that couldn’t be revolutionized by a breakthrough in a relevant area currently under study in the applied math community. The problem isn’t lack of necessity, inspiration, or motivation, the problem is the problems are damn hard, and I’m far from convinced that we attract the best minds.
Even with very clear, objective goals, progress can still be painfully slow!
In my own view insufficient emphasis on exposition has played a significant role in whatever stagnation has occurred within the mathematical community since, e.g. the 1800′s.
I very much agree. Incentives are out of line for most areas of science, but I think the fallout from this is especially poignant for math. I view part of our discipline’s responsibility as curating the common mathematical knowledge used by all other disciplines.
Like mathematicians, musicians who only write for experts are unmoored from empirical feedback and are thus dependent on unusually good taste if they are to do something valuable. It’s not fair to expect people who can’t evaluate their work to conclude that they have such good taste even if they are acknowledge to be very smart.
Fledging painters can paint for both the lowest common denominator AND for themselves if they want to. Academics can’t do popular work without that counting against them with other academics.
There’s lots of need for math in complexity theory and other domains. Quantum computing for instance. Really all over the place. Crypto is very popular. Probably lots of engineering examples.
I’d be happy if someone else we both know who shares this concern would review that list.
Like mathematicians, musicians who only write for experts are unmoored from empirical feedback and are thus dependent on unusually good taste if they are to do something valuable. It’s not fair to expect people who can’t evaluate their work to conclude that they have such good taste even if they are acknowledge to be very smart.
I agree. I guess the reason why I took pause is because Von Neumann’s quote does not immediately suggest that he concurs with
I fairly strongly suspect university education of destorying artistic ability and distracting artists with intellectual games that simply lack the merits of the fields that the academic subjects are derived from.
his quotation more just obliquely raises the possibility that you suggest.
Fledging painters can paint for both the lowest common denominator AND for themselves if they want to.
It’s not clear to me that this is true. Doesn’t it depend on what the lowest common denominator is? Van Gogh painted for himself and is reported to have been unable to support himself by selling his paintings. Are you suggesting that things have changed since his time? If so, how and under what evidence?
Academics can’t do popular work without that counting against them with other academics.
My observation has been that this is mostly true.
There’s lots of need for math in complexity theory and other domains. Quantum computing for instance. Really all over the place. Crypto is very popular. Probably lots of engineering examples.
(1) It should be noted that Von Neumann was in large measure an applied mathematician and so it’s natural to expect him of being biased in favor of applied topics.
(2) There is widespread agreement among most sophisticated contemporary mathematicians as to the high aesthetic value of some of the pure mathematical achievements over the past few decades. I agree that it’s difficult for an outsider to quickly ascertain that there’s something substantive going on here but I give you my word for whatever it’s worth :-).
(3) I’ve had a less pronounced positive aesthetic response to most applied math topics than to some of my favorite pure mathematical topics. I’ve found that applied topics are more ad hoc and lacking in internal coherence and a large part of what I find compelling about pure math is the high degree of internal coherence.
As I’ve said elsewhere in this thread, the danger of generalizing from one example here is very serious and I do not question to sincerity of those who are passionate about applied topics (or pure topics like graph theory and elementary analytic number theory which I personally find disappointingly ad hoc and lacking in internal coherence but which some people eagerly devote their lives to).
(4) My own interest in applied math topics comes more from the applications than from the math involved.
(5) I would differentiate between “early” applied math (e.g. of the type that Newton and Maxwell did) which was closer to pure math (on account of the fact that so little of either was developed and the fact that it was necessary to develop pure math further in order to get to the point of being able to do something useful) and modern applied math; the former is not necessarily representative of the latter.
(6) Some theoretical and mathematical physicists draw a sharp distinction between physics and applied math. I don’t have subject matter knowledge here; but have the rough impression that theoretical physics has more internal coherence than most applied mathematical topics. This is why I referenced theoretical physics in particular as a source of inspiration that seems to have dried up on account of lack of empirical feedback.
(7) The utilitarian value of the pure mathematical achievements alluded to above is questionable in light of the fact that (a) very few people are able to appreciate them and (b) they don’t have foreseeable technological applications in the near future. The second point has heightened significance in light of the fact that it seems very possible that an intelligence explosion is not far off.
I’m interested in popularizing some of the pure mathematical achievements that are regarded among elite pure mathematicians as being of great aesthetic value. Aside from the immediate enjoyment attached to enriching people’s lives; my interest in doing this is with a view toward giving people opportunities to develop heightened aesthetic sense and spreading humanistic values, in particular making a case that there are things in the world beautiful enough so that it’s worth working toward the long-term survival of the human race. I feel like I’ve seen a “promised land” of the sorts of intellectual experiences that lie beyond the boundaries of current human mind space.
I’d be happy if someone else we both know who shares this concern would review that list.
Sure, I would too. I’ll probably get around to it sometime over the next few weeks.
My one caveat with your claims here is that Van Gogh was severely insane, which probably impaired his ability to support himself quite a bit.
Also, how likely does it seem to you that applied math lacks pure math’s aesthetic value because its done by less aesthetically sensitive people (positive feedback loop) rather than because it couldn’t be like classical applied/pure math?
My one caveat with your claims here is that Van Gogh was severely insane, which probably impaired his ability to support himself quite a bit.
This is a fair point. I would guess / vaguely remember that there are plenty of examples of psychologically sound great painters who had trouble making a living but don’t have a list off hand. Laurens suggested Cezanne as an example but I have not independently verified that he qualifies. I don’t know very much about visual arts.
Note that in general there’s a selection effect where artists/scientists who have dim prospects for making a living doing what they do are disproportionately likely to leave relative to other artists/scientists of their quality. It’s hard to know how significant this selection effect is in a given domain.
Also, how likely does it seem to you that applied math lacks pure math’s aesthetic value because its done by less aesthetically sensitive people (positive feedback loop) rather than because it couldn’t be like classical applied/pure math?
There’s almost certainly some effect of this type; I’m uncertain as to how large the effect. Two relevant points:
To the extent that applied math involves features specific to how humans interact with the world (i.e. taking into account contingent constraints specific to human needs) arbitrariness creeps in on account of the fact that humans were generated by a random process.
There seem to be arbitrage opportunities for mathematical expertise to bring clarity to areas that were previously somewhat obscure. For example, SarahC has suggested that principle component analysis might be utilized to better understand what’s referred to as autism (a fact that I haven’t previously seen discussed explicitly). The existence of such apparent arbitrage opportunities suggests that there may be quite fertile unexplored ground within applied math.
I’m interested in popularizing some of the pure mathematical achievements that are regarded among elite pure mathematicians as being of great aesthetic value.
Sweet! Do you know of any existing works that attempt this (perhaps at a higher level of sophistication)? Also, what are the mathematical achievements you would focus on?
One good compilation of “pure mathematical achievements that are regarded among elite pure mathematicians as being of great aesthetic value” is Proofs from THE BOOK.
Is the Joshua Bell experiment the kind of thing you had in mind? If so, it pretty conclusively confirms your suspicions.
Not really, because Joshua Bell was playing mostly (maybe even exclusively) old music in that experiment, if I recall correctly.
Vassar’s suspicion was that people nowadays don’t know how to write in old styles well enough to be indistinguishable from old composers.
Edit: but just to go along with it for a minute, do you really think Bell’s status is the result of a random process? Maybe with respect to other “great” violinists, yes, but certainly not with respect to the average person, or even the average professional violinist.
Not really, because Joshua Bell was playing mostly (maybe even exclusively) old music in that experiment, if I recall correctly.
Right, it proves the (arguably) stronger result that even the old music, with its canon status, can’t appeal to the uninitiated. Impressing the indoctrinated is not impressive. The hard part is to impress the unindoctrinated.
But just to go along with it for a minute, do you really think Bell’s status is the result of a random process?
Of course not, just as I can’t make my friends laugh by generating random utterances. But that doesn’t mean that the average person is somehow deficient for not laughing at our inside jokes—or that I can go on denying that it’s an inside joke.
But that doesn’t mean that the average person is somehow deficient for not laughing at our inside jokes—or that I can go on denying that it’s an inside joke.
Here, the analogous situation would be an “average person” denying the joke was funny because they weren’t in on it, despite the fact that they saw a bunch of people laughing hysterically at it.
(...a bunch of people who were willing to welcome them into their group if they caught up on the group’s history, so they would be able to get the jokes!)
But people don’t claim that their inside jokes are the highest form of culture and that others are somehow deficient for not wanting to join in on it.
I understand that if you invest some effort E into appreciating something, you’ll appreciate it. The fact that I appreciate it for some (potentially huge) E does not somehow justify the effort—you can say that about anything.
The appropriate comparison would be “what ways of amusing myself for that level of personal investment are the best”? And given these opportunity cost considerations, it’s quite understandable why the utter indifference of the public is a strike against the field.
Is the Joshua Bell experiment the kind of thing you had in mind? If so, it pretty conclusively confirms your suspicions.
No, not really. In the concert hall, you would have no problems distinguishing Bell from a random violinist: he’s actually much better. The Joshua Bell experiment was an experiment in seeing how someone who was unambiguously a top-class artist held up with inferential distance deliberately hugely increased—not a test of “is status in music a lie?” but “how arrogant is a top-class artist taken out of their depth?” And, y’know, Bell did pretty well and came across as a perfectly reasonable fellow.
In the concert hall, you would have no problems distinguishing Bell from a random violinist: he’s actually much better.
That doesn’t matter if there are so many more appealing cultural venues than concert hall.
And, y’know, Bell did pretty well
No, he made less than the typical busker and really only attracted those who were trained to identify the signals.
I don’t dispute that the music is good, for some people. I just think it’s ridiculous how much more money it commands for the wrong reasons. His skill isn’t so much better than the mere 95% percentile to justify that—that’s why they have to rely on so much more than musical skill to market him to royalty.
and came across as a perfectly reasonable fellow.
I don’t see what difference that makes. But yes, he surprisingly did recognize how much his self-worth collapses when he’s not pre-validated (i.e. performing for people who haven’t paid lots of money for it).
I meant “did pretty well” in terms of not reacting with arrogance, that being what was actually being tested. The trope in play (what made it a story that you remember) was Fish Out Of Water.
(The way to make money as a busker is to, whatever your instrument, play the Beatles. Over and over. And over and over. And over and over. And over and over.)
The trope in play (what made it a story that you remember) was Fish Out Of Water.
I’m actually quite willing to believe that Silas remembered it because (he thought) it proved his theory.
For my part, I viewed it as a test of how well the average person can detect subtly presented costly signals when under distraction. (Answer: not very well.)
The detail I remembered most was how children would stop with interest, only to be dragged away by their hurried parents.
I’m actually quite willing to believe that Silas remembered it because (he thought) it proved his theory.
Not really. I remember it because it’s fun watching people try to explain it away—I get a new answer every time for why the highest cultural achievements get utterly ignored, at that must be a problem on the beholder’s side.
The detail I remembered most was how children would stop with interest, only to be dragged away by their hurried parents.
Is that the standard you really want to go by? What children like?
Er, I’m not. The water is the world where people know the sort of music he plays and can form communicable opinions on how well he does it.
Okay, and the water for theologians is the community of theologians. Does that mean they’re accomplishing something truly great, or that they’re a clique?
Though to be fair, arguing over aesthetics on this level is like arguing over which variety of heroin is best to be addicted to. Battles to the death for insanely low stakes. Having us all taken out and shot is not an unreasonable passing fancy.
Your analogy would only be valid if theology was the study of an aesthetic matter. (I might think it was better approached as one, but I doubt we’ll find many theologians to agree.)
Well, not really. You’re asserting music that you have a greater than negligible inferential distance to is a fraudulent field, and you’re comparing it to a field you already consider fraudulent.
As such: the difference is that music is about aesthetics, not about the qualities of claimed supernatural beings. And in art, there is such a thing as inferential distance. Long post on the subject here. A given piece of art is created in a time, place and culture, to press the buttons in people’s heads, preferably starting with those of the artist. You will appreciate it more if you learn more about the time, place and culture, right down to the inside of the artist’s head as far as that can be ascertained, thus getting closer to the place in inference space of its birth.
Theology doesn’t, as far as I know, make the existence of God more believable if you know more of it; however, it is possible to learn about the cultural reference point for a piece of art and appreciate more what the artist was doing.
Is it your contention that modern musicians write Clasical minuets and Baroque fugues which are in some cases better than the best of the older works that are still listened to, but that no-one cares because much of the value of those works is in their role in a canon?
Depending on who you’re considering to be doing the caring and not-caring, this may very well be an apt description of the situation. But the main point I would make is that these are student exercises. Writing works in older styles is a skill that one learns in school; it’s very much like how math students are asked to re-prove theorems of Euler or Cauchy. You may be seen as a genius if you rediscover the proof of the fundamental theorem of algebra, but nobody’s going to give you the same kind of credit they give Gauss. Likewise writing a really great fugue in your counterpoint class isn’t going to make you Bach. Part of the reason is that Bach already did this stuff (so you’re not in the “canon”), but also when Bach was doing it it was at the frontier of musical thought, which it isn’t today, as evidenced by the fact that it is taught to undergraduates. Whereas Bach’s challenge was to be as inventive as possible, today’s students have to be as inventive as possible while still sounding like eighteenth-century music, which is a challenge of a different kind, and will tend to produce different musical results.
I could easily believe that in those cases, but I simply don’t believe it in the case of Opera. The Opera cannon is just not very large. Some people have heard the whole thing and only like a few dozen operas.
First of all, the total number of operas written since the form was invented (something like 40,000, if I recall correctly) is much larger than any single human could plausibly have heard. You must be talking about the active repertory of famous opera houses, which is indeed probably something like a few dozen. However, there are good reasons apart from artistic merit to expect that the number of operas in regular production would be small: namely, staging an opera is typically a very costly and laborious undertaking. (So is composing one, by the way, which is why doing so is not a typical student exercise the same way writing a fugue is.) This will push toward conservatism in repertory selection, with companies sticking to the pieces they already know “work”. There are all kinds of obscure operas by great composers (such as Handel) that have only recently begun to see the light of day for this reason, and being by such composers, their artistic quality is quite high. If folks want more old operas, there’s plenty of digging to be done (and it’s being done).
It should really be pretty easy to do a controlled experiment with a naive population to see how common it is for modern artists to be able to impress an audience as much as their 18th and 19th century precursors did.
It would be very hard to find a truly naive audience with enough musical ability to make the results of interest. Best you could do would probably be musically gifted children who had been deliberately kept uneducated in music history. (Then you’d have to ask what the appropriate age is, etc.)
That said, if it could be done, I’d be all in favor of doing it. My prediction would be that there wouldn’t be much of a difference between the perceived “impressiveness” of actual Baroque fugues and the best imitations of Baroque fugues from today.
I guess that my major reason for holding the contrary position was largely because modern musicians and composers, more than painters and authors, are the results of university education and I fairly strongly suspect university education of destorying artistic ability and distracting artists with intellectual games that simply lack the merits of the fields that the academic subjects are derived from
Let me be clear: this absolutely does go on, no question. But it probably goes on in all fields that have university departments—including (as you note), math, and yes, the empirical sciences. And my suspicion is that while it may give mediocre practitioners of a field the illusion that they’re doing better and more important work than they are, it doesn’t actually stop the best folks from doing genuinely high quality work. (At least not all of them.)
However, if that’s your theory, what then do you think of European “modernist” composers, who are similarly “inaccessible” but have less association with universities?
But what the Beatles were doing was more like being as inventive as possible while still being fun to listen to for untrained people, a constraint that Bach shared.
I just don’t know enough about modernist composers to say, but I would give them more benefit of the doubt. It’s also noteworthy though that I know non-professionals who claim to enjoy them, which seems like very good Bayesian evidence that they are doing something significant.
I don’t think that your response on the opera question is really a satisfying rebuttal to my point.
But what the Beatles were doing was more like being as inventive as possible while still being fun to listen to for untrained people, a constraint that Bach shared.
Only as a result of the historically contingent fact that Bach’s wildest musical ideas happened to still be comprehensible to untrained people, because the inferential gulf wasn’t yet very large.
(Seriously, it’s not as if Bach secretly invented and wished he could write Schoenberg-style music, but reluctantly restrained himself because of his social obligations. What Bach produced—at least some of his output—was literally the most inventive music he could think of; and sometimes he was indeed criticized for going beyond the “norms” of the day.)
It’s also noteworthy though that I know non-professionals who claim to enjoy them, which seems like very good Bayesian evidence that they are doing something significant.
Yes. Though this is a point which unfortunately tends to get lost, there are indeed non-professionals who enjoy contemporary art music, and there are in fact “ways into” the music for them; things they can learn to enhance their enjoyment, even if they don’t quite reach the full level of appreciation that a professional might. And there are actually some folks who are musically gifted enough that they just “get it” right away, even though they don’t happen to be musicians.
I don’t think that your response on the opera question is really a satisfying rebuttal to my point.
I don’t know whether this will help either, but I did want to make the point that the most gifted composers tend not to want to spend their time writing in old styles, for the same reason that the most gifted mathematicians tend not to want to spend their time rediscovering old theorems. This is a better explanation for why we don’t see large quantities of Bach-quality Baroque-style music being churned out today than “lost knowledge” or historical genetic anomaly. (And why didn’t we see more of composers literally imitating Baroque music during the Classical and Romantic eras?)
A slightly different point, but when I brought up the possibility of current composers writing in the old styles and thus creating attractive music, several people told me that it’s simply too hard to write music in an old style.
There seemed to be a strong consensus there, but perhaps the problem is that they were applying too high a standard of authenticity. I’d be content with music which supplied many of the pleasures of baroque or classical—it doesn’t have to pass for period music to a well-informed listener.
I have a notion that you can tell which sf artists have been to art school. The composition, anatomy, and perspective are all excellent, but there’s no sense of motion.
When I say it’s a notion, I mean that I haven’t checked it in any way, it just seems like a plausible way of explaining paintings with those characteristics.
So far as mathematics is concerned, aren’t there two streams—empirical and for the pleasure of the mathematicians? Neither of these are the same as working on whatever math is publishable, though.
Is it your contention that modern musicians write Clasical minuets and Baroque fugues which are in some cases better than the best of the older works that are still listened to, but that no-one cares because much of the value of those works is in their role in a canon?
I could easily believe that in those cases, but I simply don’t believe it in the case of Opera. The Opera cannon is just not very large. Some people have heard the whole thing and only like a few dozen operas. It doesn’t seem likely that there isn’t demand among such people for higher quality new material in old styles, so if no new material is becoming popular then the un-met demand makes me think that contemporary music students are failing to produce work that this audience actually values due to now knowing how to replicate the merits of older compositions.
It should really be pretty easy to do a controlled experiment with a naive population to see how common it is for modern artists to be able to impress an audience as much as their 18th and 19th century precursors did.
I’m seriously interested in someone performing some experiments on this subject. It seems to me that it would provide an extremely practically important measurement of the quality of university education in fields inaccessible to outsiders, but I don’t expect to be able to attract funding for such research because it sounds impractical at the face of it.
I guess that my major reason for holding the contrary position was largely because modern musicians and composers, more than painters and authors, are the results of university education and I fairly strongly suspect university education of destorying artistic ability and distracting artists with intellectual games that simply lack the merits of the fields that the academic subjects are derived from. I suspect this in math as much as in music, and I think Von Neumann agreed with me, as this quote suggests.
“As a mathematical discipline travels far from its empirical source, or still more, if it is a second or third generation only indirectly inspired by ideas coming from ‘reality’, it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely l’art pour l’art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. In other words, at a great distance from its empirical source, or after much ‘abstract’ inbreeding, a mathematical subject is in danger of degeneration.”
I myself would guess that none of the works produced over the past hundred years would be judged by the majority of an impartial audience to be significantly more compelling than (for example) Bach’s Chaconne.
Same here.
I’m impressed that you’re familiar with the Von Neumann quote (which is sadly little known in the mathematical community but which my friend Laurens is fond of); but on the face of things it doesn’t seem to directly support your paragraph above. Explain further if you’d like?
Several points here:
My impression is that there are issues of bad social/cultural institutions destroying artistic ability outside of academia. I have some friends artistically genuine who have spent some time as painters and become disillusioned with the signaling games and hypocrisy present within the communities of painters that they’ve come across. Note that fledging painters and authors face greater financial pressures than academics and that this can lead to perverse incentives (to appeal to the lowest common denominator or to current fashions for greater marketability). See Minhyong Kim’s comment here.
The absence of new empirical sources for mathematics seems to me more a consequence of the stagnation of theoretical physics than the social structure of the mathematical community.
In my own view insufficient emphasis on exposition has played a significant role in whatever stagnation has occurred within the mathematical community since, e.g. the 1800′s. The barrier to entry has gotten progressively higher as mathematics has developed and in such a setting, in absence of strong efforts to to cast background material in an accessible and readily digestible form, the pressures toward specialization and fragmentation get progressively stronger. There aren’t career-based incentives for expository work so mathematicians who are interested in exposition either conform to the research-based publish or perish norms or leave.
I’d be happy to compile an annotated list of relatively accessible survey papers if you’d be interested and find it useful for getting a sense for the state of some of contemporary mathematical research.
From my perspective in applied math things are exactly opposite. We’re practically drowning in empirical sources begging for better numerics. There is hardly a scientific or engineering field today that couldn’t be revolutionized by a breakthrough in a relevant area currently under study in the applied math community. The problem isn’t lack of necessity, inspiration, or motivation, the problem is the problems are damn hard, and I’m far from convinced that we attract the best minds.
Even with very clear, objective goals, progress can still be painfully slow!
I very much agree. Incentives are out of line for most areas of science, but I think the fallout from this is especially poignant for math. I view part of our discipline’s responsibility as curating the common mathematical knowledge used by all other disciplines.
Like mathematicians, musicians who only write for experts are unmoored from empirical feedback and are thus dependent on unusually good taste if they are to do something valuable. It’s not fair to expect people who can’t evaluate their work to conclude that they have such good taste even if they are acknowledge to be very smart.
Fledging painters can paint for both the lowest common denominator AND for themselves if they want to. Academics can’t do popular work without that counting against them with other academics.
There’s lots of need for math in complexity theory and other domains. Quantum computing for instance. Really all over the place. Crypto is very popular. Probably lots of engineering examples.
I’d be happy if someone else we both know who shares this concern would review that list.
I agree. I guess the reason why I took pause is because Von Neumann’s quote does not immediately suggest that he concurs with
his quotation more just obliquely raises the possibility that you suggest.
It’s not clear to me that this is true. Doesn’t it depend on what the lowest common denominator is? Van Gogh painted for himself and is reported to have been unable to support himself by selling his paintings. Are you suggesting that things have changed since his time? If so, how and under what evidence?
My observation has been that this is mostly true.
(1) It should be noted that Von Neumann was in large measure an applied mathematician and so it’s natural to expect him of being biased in favor of applied topics.
(2) There is widespread agreement among most sophisticated contemporary mathematicians as to the high aesthetic value of some of the pure mathematical achievements over the past few decades. I agree that it’s difficult for an outsider to quickly ascertain that there’s something substantive going on here but I give you my word for whatever it’s worth :-).
(3) I’ve had a less pronounced positive aesthetic response to most applied math topics than to some of my favorite pure mathematical topics. I’ve found that applied topics are more ad hoc and lacking in internal coherence and a large part of what I find compelling about pure math is the high degree of internal coherence.
As I’ve said elsewhere in this thread, the danger of generalizing from one example here is very serious and I do not question to sincerity of those who are passionate about applied topics (or pure topics like graph theory and elementary analytic number theory which I personally find disappointingly ad hoc and lacking in internal coherence but which some people eagerly devote their lives to).
(4) My own interest in applied math topics comes more from the applications than from the math involved.
(5) I would differentiate between “early” applied math (e.g. of the type that Newton and Maxwell did) which was closer to pure math (on account of the fact that so little of either was developed and the fact that it was necessary to develop pure math further in order to get to the point of being able to do something useful) and modern applied math; the former is not necessarily representative of the latter.
(6) Some theoretical and mathematical physicists draw a sharp distinction between physics and applied math. I don’t have subject matter knowledge here; but have the rough impression that theoretical physics has more internal coherence than most applied mathematical topics. This is why I referenced theoretical physics in particular as a source of inspiration that seems to have dried up on account of lack of empirical feedback.
(7) The utilitarian value of the pure mathematical achievements alluded to above is questionable in light of the fact that (a) very few people are able to appreciate them and (b) they don’t have foreseeable technological applications in the near future. The second point has heightened significance in light of the fact that it seems very possible that an intelligence explosion is not far off.
I’m interested in popularizing some of the pure mathematical achievements that are regarded among elite pure mathematicians as being of great aesthetic value. Aside from the immediate enjoyment attached to enriching people’s lives; my interest in doing this is with a view toward giving people opportunities to develop heightened aesthetic sense and spreading humanistic values, in particular making a case that there are things in the world beautiful enough so that it’s worth working toward the long-term survival of the human race. I feel like I’ve seen a “promised land” of the sorts of intellectual experiences that lie beyond the boundaries of current human mind space.
Sure, I would too. I’ll probably get around to it sometime over the next few weeks.
Thanks for the very thoughtful and clear post.
My one caveat with your claims here is that Van Gogh was severely insane, which probably impaired his ability to support himself quite a bit.
Also, how likely does it seem to you that applied math lacks pure math’s aesthetic value because its done by less aesthetically sensitive people (positive feedback loop) rather than because it couldn’t be like classical applied/pure math?
This is a fair point. I would guess / vaguely remember that there are plenty of examples of psychologically sound great painters who had trouble making a living but don’t have a list off hand. Laurens suggested Cezanne as an example but I have not independently verified that he qualifies. I don’t know very much about visual arts.
Note that in general there’s a selection effect where artists/scientists who have dim prospects for making a living doing what they do are disproportionately likely to leave relative to other artists/scientists of their quality. It’s hard to know how significant this selection effect is in a given domain.
There’s almost certainly some effect of this type; I’m uncertain as to how large the effect. Two relevant points:
To the extent that applied math involves features specific to how humans interact with the world (i.e. taking into account contingent constraints specific to human needs) arbitrariness creeps in on account of the fact that humans were generated by a random process.
There seem to be arbitrage opportunities for mathematical expertise to bring clarity to areas that were previously somewhat obscure. For example, SarahC has suggested that principle component analysis might be utilized to better understand what’s referred to as autism (a fact that I haven’t previously seen discussed explicitly). The existence of such apparent arbitrage opportunities suggests that there may be quite fertile unexplored ground within applied math.
I have always been intrigued by Kenneth Rexroth’s take.
Thanks for the link. That was a delightful essay.
Sweet! Do you know of any existing works that attempt this (perhaps at a higher level of sophistication)? Also, what are the mathematical achievements you would focus on?
One good compilation of “pure mathematical achievements that are regarded among elite pure mathematicians as being of great aesthetic value” is Proofs from THE BOOK.
Is the Joshua Bell experiment the kind of thing you had in mind? If so, it pretty conclusively confirms your suspicions.
Fame feeds on fame, status on status. Which is why it’s all the more important to constantly check that a field hasn’t lost its moorings.
Not really, because Joshua Bell was playing mostly (maybe even exclusively) old music in that experiment, if I recall correctly.
Vassar’s suspicion was that people nowadays don’t know how to write in old styles well enough to be indistinguishable from old composers.
Edit: but just to go along with it for a minute, do you really think Bell’s status is the result of a random process? Maybe with respect to other “great” violinists, yes, but certainly not with respect to the average person, or even the average professional violinist.
Right, it proves the (arguably) stronger result that even the old music, with its canon status, can’t appeal to the uninitiated. Impressing the indoctrinated is not impressive. The hard part is to impress the unindoctrinated.
Of course not, just as I can’t make my friends laugh by generating random utterances. But that doesn’t mean that the average person is somehow deficient for not laughing at our inside jokes—or that I can go on denying that it’s an inside joke.
Here, the analogous situation would be an “average person” denying the joke was funny because they weren’t in on it, despite the fact that they saw a bunch of people laughing hysterically at it.
(...a bunch of people who were willing to welcome them into their group if they caught up on the group’s history, so they would be able to get the jokes!)
But people don’t claim that their inside jokes are the highest form of culture and that others are somehow deficient for not wanting to join in on it.
I understand that if you invest some effort E into appreciating something, you’ll appreciate it. The fact that I appreciate it for some (potentially huge) E does not somehow justify the effort—you can say that about anything.
The appropriate comparison would be “what ways of amusing myself for that level of personal investment are the best”? And given these opportunity cost considerations, it’s quite understandable why the utter indifference of the public is a strike against the field.
No, not really. In the concert hall, you would have no problems distinguishing Bell from a random violinist: he’s actually much better. The Joshua Bell experiment was an experiment in seeing how someone who was unambiguously a top-class artist held up with inferential distance deliberately hugely increased—not a test of “is status in music a lie?” but “how arrogant is a top-class artist taken out of their depth?” And, y’know, Bell did pretty well and came across as a perfectly reasonable fellow.
That doesn’t matter if there are so many more appealing cultural venues than concert hall.
No, he made less than the typical busker and really only attracted those who were trained to identify the signals.
I don’t dispute that the music is good, for some people. I just think it’s ridiculous how much more money it commands for the wrong reasons. His skill isn’t so much better than the mere 95% percentile to justify that—that’s why they have to rely on so much more than musical skill to market him to royalty.
I don’t see what difference that makes. But yes, he surprisingly did recognize how much his self-worth collapses when he’s not pre-validated (i.e. performing for people who haven’t paid lots of money for it).
I meant “did pretty well” in terms of not reacting with arrogance, that being what was actually being tested. The trope in play (what made it a story that you remember) was Fish Out Of Water.
(The way to make money as a busker is to, whatever your instrument, play the Beatles. Over and over. And over and over. And over and over. And over and over.)
I’m actually quite willing to believe that Silas remembered it because (he thought) it proved his theory.
For my part, I viewed it as a test of how well the average person can detect subtly presented costly signals when under distraction. (Answer: not very well.)
The detail I remembered most was how children would stop with interest, only to be dragged away by their hurried parents.
Point. I suppose I mean “why they bothered to run the story.” They weren’t running it to expose Bell as a charlatan, they ran it as Fish Out Of Water.
Yeah :-D
Unfortunately, the distractibility of the people with the money is why busking for money involves Beatles. Lots of Beatles. More Beatles.
Not really. I remember it because it’s fun watching people try to explain it away—I get a new answer every time for why the highest cultural achievements get utterly ignored, at that must be a problem on the beholder’s side.
Is that the standard you really want to go by? What children like?
But what’s the water then? And why is the fish’s greatness so brittle that you have to define the water so narrowly?
Er, I’m not. The water is the world where people know the sort of music he plays and can form communicable opinions on how well he does it.
Are you really claiming they wrote that story to demonstrate Bell was a fraud, rather than as a fish out of water story?
Okay, and the water for theologians is the community of theologians. Does that mean they’re accomplishing something truly great, or that they’re a clique?
I have just corrected the systematic downvoting of Silas. His general point seems important.
As it happens, I was also the victim of systematic drive-by downvoting in the last few minutes.
I don’t know what the relationship between these two facts is.
(Edit: I didn’t participate in the downvoting of Silas, I don’t think.)
I have a long-standing policy of not voting in discussions in which I am strongly opinionated and participating in, which applies here.
As was I. Go rationality!
Though to be fair, arguing over aesthetics on this level is like arguing over which variety of heroin is best to be addicted to. Battles to the death for insanely low stakes. Having us all taken out and shot is not an unreasonable passing fancy.
That’s an impressively sane analogy to keep in mind. Thanks.
Your analogy would only be valid if theology was the study of an aesthetic matter. (I might think it was better approached as one, but I doubt we’ll find many theologians to agree.)
*redefines theology as the study of aesthetic matter*
You don’t get away that easily. If your entire argument rests on, “I’ve chosen to apply this symbol, this way” then I think we’re done here.
Well, not really. You’re asserting music that you have a greater than negligible inferential distance to is a fraudulent field, and you’re comparing it to a field you already consider fraudulent.
As such: the difference is that music is about aesthetics, not about the qualities of claimed supernatural beings. And in art, there is such a thing as inferential distance. Long post on the subject here. A given piece of art is created in a time, place and culture, to press the buttons in people’s heads, preferably starting with those of the artist. You will appreciate it more if you learn more about the time, place and culture, right down to the inside of the artist’s head as far as that can be ascertained, thus getting closer to the place in inference space of its birth.
Theology doesn’t, as far as I know, make the existence of God more believable if you know more of it; however, it is possible to learn about the cultural reference point for a piece of art and appreciate more what the artist was doing.
Depending on who you’re considering to be doing the caring and not-caring, this may very well be an apt description of the situation. But the main point I would make is that these are student exercises. Writing works in older styles is a skill that one learns in school; it’s very much like how math students are asked to re-prove theorems of Euler or Cauchy. You may be seen as a genius if you rediscover the proof of the fundamental theorem of algebra, but nobody’s going to give you the same kind of credit they give Gauss. Likewise writing a really great fugue in your counterpoint class isn’t going to make you Bach. Part of the reason is that Bach already did this stuff (so you’re not in the “canon”), but also when Bach was doing it it was at the frontier of musical thought, which it isn’t today, as evidenced by the fact that it is taught to undergraduates. Whereas Bach’s challenge was to be as inventive as possible, today’s students have to be as inventive as possible while still sounding like eighteenth-century music, which is a challenge of a different kind, and will tend to produce different musical results.
First of all, the total number of operas written since the form was invented (something like 40,000, if I recall correctly) is much larger than any single human could plausibly have heard. You must be talking about the active repertory of famous opera houses, which is indeed probably something like a few dozen. However, there are good reasons apart from artistic merit to expect that the number of operas in regular production would be small: namely, staging an opera is typically a very costly and laborious undertaking. (So is composing one, by the way, which is why doing so is not a typical student exercise the same way writing a fugue is.) This will push toward conservatism in repertory selection, with companies sticking to the pieces they already know “work”. There are all kinds of obscure operas by great composers (such as Handel) that have only recently begun to see the light of day for this reason, and being by such composers, their artistic quality is quite high. If folks want more old operas, there’s plenty of digging to be done (and it’s being done).
It would be very hard to find a truly naive audience with enough musical ability to make the results of interest. Best you could do would probably be musically gifted children who had been deliberately kept uneducated in music history. (Then you’d have to ask what the appropriate age is, etc.)
That said, if it could be done, I’d be all in favor of doing it. My prediction would be that there wouldn’t be much of a difference between the perceived “impressiveness” of actual Baroque fugues and the best imitations of Baroque fugues from today.
Let me be clear: this absolutely does go on, no question. But it probably goes on in all fields that have university departments—including (as you note), math, and yes, the empirical sciences. And my suspicion is that while it may give mediocre practitioners of a field the illusion that they’re doing better and more important work than they are, it doesn’t actually stop the best folks from doing genuinely high quality work. (At least not all of them.)
However, if that’s your theory, what then do you think of European “modernist” composers, who are similarly “inaccessible” but have less association with universities?
But what the Beatles were doing was more like being as inventive as possible while still being fun to listen to for untrained people, a constraint that Bach shared.
I just don’t know enough about modernist composers to say, but I would give them more benefit of the doubt. It’s also noteworthy though that I know non-professionals who claim to enjoy them, which seems like very good Bayesian evidence that they are doing something significant.
I don’t think that your response on the opera question is really a satisfying rebuttal to my point.
Only as a result of the historically contingent fact that Bach’s wildest musical ideas happened to still be comprehensible to untrained people, because the inferential gulf wasn’t yet very large.
(Seriously, it’s not as if Bach secretly invented and wished he could write Schoenberg-style music, but reluctantly restrained himself because of his social obligations. What Bach produced—at least some of his output—was literally the most inventive music he could think of; and sometimes he was indeed criticized for going beyond the “norms” of the day.)
Yes. Though this is a point which unfortunately tends to get lost, there are indeed non-professionals who enjoy contemporary art music, and there are in fact “ways into” the music for them; things they can learn to enhance their enjoyment, even if they don’t quite reach the full level of appreciation that a professional might. And there are actually some folks who are musically gifted enough that they just “get it” right away, even though they don’t happen to be musicians.
I don’t know whether this will help either, but I did want to make the point that the most gifted composers tend not to want to spend their time writing in old styles, for the same reason that the most gifted mathematicians tend not to want to spend their time rediscovering old theorems. This is a better explanation for why we don’t see large quantities of Bach-quality Baroque-style music being churned out today than “lost knowledge” or historical genetic anomaly. (And why didn’t we see more of composers literally imitating Baroque music during the Classical and Romantic eras?)
A slightly different point, but when I brought up the possibility of current composers writing in the old styles and thus creating attractive music, several people told me that it’s simply too hard to write music in an old style.
There seemed to be a strong consensus there, but perhaps the problem is that they were applying too high a standard of authenticity. I’d be content with music which supplied many of the pleasures of baroque or classical—it doesn’t have to pass for period music to a well-informed listener.
I have a notion that you can tell which sf artists have been to art school. The composition, anatomy, and perspective are all excellent, but there’s no sense of motion.
When I say it’s a notion, I mean that I haven’t checked it in any way, it just seems like a plausible way of explaining paintings with those characteristics.
So far as mathematics is concerned, aren’t there two streams—empirical and for the pleasure of the mathematicians? Neither of these are the same as working on whatever math is publishable, though.