Article Discussion: Re: "Can One Hear the Sound of a Theorem"

Can One Hear the Sound of a Theorem?  Rob Schneiderman
Notices of the American Mathematical Society August 2011
http://www.ams.org/notices/201107/rtx110700929p.pdf

--------------------------------------------------------------------------------------------------
In this blog, I believe I find myself generally having a positive tone. Normally I am writing about musicians and concerts, and have been having a great time, and, as I understand it, the general practice of critiquing music, perhaps more so in North America than in Europe, but nonetheless, is to acknowledge what has been given and achieved, and only then perhaps state which elements one might take exception to.

However, from my philosophical studies, I've learned also that the world of Acadamia is happy to enter battles of opinions rather more overtly, without mincing words.

Rob Schneiderman's article is of this nature, and my response to it is equally so.

I originally sent my response to the editor of the AMS, who wrote back to say I would have been invited to submit it for publication, but that I'd written too late. I blame summer/fall musician travels - the mind is elsewhere.

In any case, here goes. I will dig in. Oh, and yes, I include my credentials at the end.

Dear AMS Editor,

I am mystified as to what the point of Schneidermann's rather contrarian article "Can One Hear the Sounds of a Theorem" in the August issue might be, other than that it is very difficult to prove a rigorous correlation between mathematics and music. Certainly, his own examples don't hold up to his kind of scrutiny, any more than the examples of others he takes such pains to shoot down. The article reads more like a rant than a discussion or constructive criticism, and lacks a basic knowledge in the philosophy of aesthetic theory.
Take for example his attempt to distinguish between music/mathematics from other arts and sciences, via assigning "intrinsic meaning". Schneiderman realizes that this is a problematic concept (without a meaning-giver, ie. a person, is there actually meaning?) - and tries to get out of it by whittling down "intrinsic meaning" to "degrees of intrinsic meaning" ... but if a thing doesn't exist, how can you have degrees of it? As anyone who has studied the problems surrounding both formalism and hermeneutics knows, the concept of meaning is very difficult if not impossible to extract from human qualities and experiences. Equally problematic is his assertion regarding reference, that "both mathematics and music frequently do refer to the natural world". Reference, as philosophy of language tells us, is as troublesome a concept as meaning, and in taking the viewpoint that music and mathematics can refer, Schneiderman suddenly adopts a hermeneutic viewpoint that is completely unsupported by anything else in his article, and actually contradicted by his formalist stance elsewhere. Just as unsupported is his opinion that music is somehow more abstract than other art forms, which he defends solely on the basis of his own intuition, "I stand by the claim," and an attempt to describe his definition as "what is special to mathematics and music is that their content is capable of being expressed entirely in terms of their own raw material, namely, logical thought and audible sound". However, this latter sentence is merely a definition of abstraction, which exists in all the other art forms - painting as expressed in terms of interplays of light, dance as expressed in terms of motion, poetry as expressed in uniqueness of form, which may contain jibberish - the Jabberwocky poem of that great mathematician/writer Lewis Carroll comes to mind. Schneidermann tries to get out his dilemma by stating that abstracted poetry is music - but this is just an easy way out: "abstracted anything is mathematics or music", and takes us to a circular definition.
In the end, it appears that he is making the claim that "patterns that do not rely on sensory perception" are the core of his special categorization of mathematics and music. But again, this definition contradicts what he wrote earlier, having included "audible sound" as a "raw material" of music. Setting aside that discrepancy (and the floodgate of the artforms that the "raw materials" admission allows, as discussed above), it is unclear how he is establishing that there is anything that is especially non-sensory about music, other than his claim that it is somehow mathematical.

Another distinction he is missing is that between analysis and creativity, two opposites in terms of attitude. One similiarity between creating/discovering a musical piece and developing a theory along a branch of mathematics is that one sees how far an idea can go. The difference is that mathematical rules are less subjective, most will agree with what is proper or improper procedure, whereas in music one can decide at any moment to do anything - to create - and the result will be either more or less pleasing to various audiences, or up for argument. He dimisses all music that is inspired by mathematics - but where is the mention of some of the greatest "mathematical" composers, for example, Milton Babbitt, Iannis Xenakis, or even Pierre Boulez? There is a distinction between being inspired by and using mathematical constructs in musical composition, and creating new forms utilizing them (as so many 20th-and 21st-century composers do and with great success), and adhering to a rigorous one-to-one mapping between a mathematical concept and some (arbitrarily) chosen correspondence in the sound world, as appears to be the thing Schneiderman is railing against. The beauty and elegance of a composer's meaningful and convincing message using complicated mathematical constructs, is precisely that, on the basis of what appears to touch people, it need not be via one-to-one correspondence, and that we can feel a strong message even if the mathematical idea utilized is hidden. His example of Bach's crab canon is apt here - where the correspondence is too strong, the message we feel is that it is a little too perfect: it works, it tells us something, but there is something not entirely natural-feeling about it. And that is a difference between mathematics and music - we are supposed to be able to work out and understand mathematics to the last degree, and perfection of symmetry can be an end, but music is meant to leave something inexplicable, and also tell us something about ourselves - why do we find ourselves attracted to one form or another?

Perhaps his thesis is actually, that correlation between mathematics and music is merely metaphorical - for precisely the reason that mathematics does not take "raw material" to fill its place-holders, and music does. But if he wishes to claim that music is as pattern-oriented as mathematics, in order to support his claim that music is of an abstract nature, then he has again taken the leap of faith he criticizes in the other authors. Yet perhaps it is precisely this leap of faith that we must take in order to get the "what, if anything, do-music-and-math-have-in-common" project off the ground at all. That would be an interesting idea to develop further - and amazingly, would lead us not to need to reform the school curriculum anywhere as violently as he suggests, for his currently narrow view of what he considers "correct" in this regard would, I posit for the reasons I've mentioned above, open up to many more possibilities.

Sincerely,

Claudia Schaer

Faculty, Bloomingdale School of Music, New York City

D.M.A. Stony Brook University, Violin Performance
Graduate Certificate Equivalent - Philosophy and Music

Aesthetics and Logic studies at Columbia University
MM, BM, The Juilliard School, Violin Performance

PAUL TAYLOR @ LINCOLN CENTER - Performance Review 2012.03.20

PAUL TAYLOR @ LINCOLN CENTER

Tues. Mar. 20, 2012

There are days when all that should be, converges.

After a long bout of busy-ness, I finally found myself with a fortuitous evening free, to see Paul Taylor Dance Company perform in their debut at Lincoln Center's David H. Koch Theater, formerly known as the New York State Theater and home to the New York City Ballet, and until this past season, the New York City Opera (whose departure has led to an ongoing bitter dispute between that company's musicians and their management). It has been a very long 15 years since I was first thrilled by the Paul Taylor Company, at City Center, as a wide-eyed freshman violinist-with-dancer-roommate at Juilliard, and I was utterly excited to revisit those vivid memories tonight.

On a budget, as always, I had been alerted to the possibility of affordably attending, courtesy of the Lincoln Center box office "Atrium Discountix" email efforts, at home in the new David Rubinstein Atrium on Broadway and 63rd Street. The Atrium is a beautiful public space, converted from a climbing wall to a classy destination with tables and chairs and wifi-zone and regular concerts and lush vegetation purifying the air and gloriously creeping up the walls. I always enjoy visiting it - but in the end only the expensive tickets were on sale, which still left them somewhat expensive for me, and so I bought my ticket directly from the Koch Box Office, where a $12 student rush ticket transported me to one of the best seats in the house: F4, - sixth row from the front, in the center left of the orchestra section. With even more joy in this serendipity, I began to chat with my very sweet seat neighbour, an about Paul-Taylor-aged gentleman who, as I would learn, had been the company's first manager.

As a musician, one of the things that had drawn me to this performance was the music: a suite of tin-pan-alley ragtime, Poulenc's Gloria, and Bach's Brandenburg Concertos #6 and #3. In particular, I was curious what Taylor would do with the Bach, so familiar to us all.

The dancing and the choreography were, to my appreciator's eye, superb. Though my only claim to any dancing knowledge is watching some ballet growing up, and attending my beloved Juilliard roommate's many performances during her studies and later with Martha Graham company, I can discern just as every audience member call feel when a piece and its dancers can hold thousands of people spell-bound, rapt, entranced and enthralled by the thread of what is unfolding onstage. There is a hush in the theater as thousands of breaths are held, and it is sublime; we are all in the moment. It is what we all strive for as artists, and it was exquisite tonight, particularly in the third piece, the Bach, titled "Brandenburgs", in which the dancers have beautiful solos, and extend themselves, twirling to the fullest, in their forest green. The choreography wove a stunning counterpoint through the concertos, enhancing Bach's lines, and also his capacity to go on and on and on, in some moments bordering on humourous caricature with signature Paul Taylor gestures of fun, but catching itself while still joyous and rejoining the celebration. It was so wonderful, I hope I can return tomorrow, though I fear life may get in the way.

The second piece, Poulenc, titled "Beloved Renegade", takes the titles of its movements from writings of Walt Whitman, and deals with death among us. The choreography as well as the costumes played with the idea of statues, and the motifs of fate, and inevitability wove their way through it, yet alongside the with the happy obliviousness of youth. The piece and performance were again breathtakingly beautiful, and as my seat-neighbour said to me, "Death is portrayed so much more beautifully than it really is". Is that so? But if in death we find the memory of life, perhaps our hearts carry on as art can. The music is gorgeous also, and it was beautifully sung and played. But by whom I do not know, as the programme does not list which recording was used.

Unless you are a member of local 802, perhaps you will think, "Recording?? But isn't the music live?"

Alas, no.

My neighbour and I conversed about this, as a result of my saying to him I had last been to see the company perform 15 years ago, and when he looked a little shocked, then told me he and the company go way back, I thought I'd better explain that my long hiatus is solely that I attend more concerts than dance performances, since I am a musician (and I'll admit to being flattered that he'd thought I was a dancer; which musician wouldn't be!) As the lights were dimming before the 1st piece, he said that he could understand my hiatus if I were a musician, and he'd tell me later why.

All through the first piece, the ragtime "Oh, you kid!", though I enjoyed its boisterous energy, and heard many understanding chuckles in response to its humour, I was bothered by the recorded music. It was out of tune, it seemed to come from just one side of the stage, the sound quality was decidedly tinned, and, by virtue of being a recording, it was thoroughly inflexible. There would be no responding to a dancer's mood tonight, no allowing the audience to clap a little more for an especially well-communicated solo. I felt as though I'd visited a gourmet restaurant, but was eating my fine entrée accompanied by shredded inorganic ice-berg-lettuce and plastic-bottle fat-free ranch dressing. A large part of this event was far removed from being "in the moment". 

The disparity between the two also led me to meditate on the one-way-street of non-communication between the dancers and the "musicians", and how we respond to electronic media in a world filled with technology today - accepting the old recording, a snapshot of the musicians-of-then, as something to communicate with, as we accept the written medium, the electronic translators of the telephone, then VOIP, email, chat - as stand-ins for meeting in person. Which can be very useful, and all, but will never be quite the same thing. I found this atmosphere rather high-school-musical-on-a-budget-esque, though the dancers were doing a wonderful job of pretending the music was alive. (With lesser-quality performers, I'd wonder, can't they tell the difference?)

My neighbour informed me that of course, the dance company would love to have live musicians, of course it's better, the quality can't compare. But, it would increase the budget by nearly a third.

As I am a card-carrying member of local 802, and heard about the protests not to use live musicians, I can sympathize the counter-attitude that, well, funds to hire musicians should be raised. At the same time, I am aware of the strength of the musician's union, and that union wages would result in the musicians being paid more than the dancers, and of the high expense a union orchestra would create. Furthermore, as much as I appreciate the union's quest to achieve fair pay for musicians, there are surely situations in which the pre-decided "fair pay" would genuinely kill the job - as perhaps in this case - and I don't see the sense in killing jobs, particularly during a recession. It would be more helpful to focus on creating jobs. At the risk of jeopardizing the image of my pro-union stance, I would consider it fair pay for musicians to be paid about the same as dancers in dance performances (the dancers work harder for the job, but musicians are responsible for acquiring instruments in addition to education and technique). Furthermore, I for one would find it thrilling to play the repertoire in a chamber-ensemble version, which certainly would be possible with at least the Bach and the ragtime from tonight. (The Poulenc is more expansive and the use of choir in addition to orchestra would make it more difficult, though not impossible, to replicate in a chamber version.) Small ensembles would work well artistically with the small size of Paul Taylor's company, and certainly would sound better than the canned version. As grateful as I am for union-scale orchestral work when it comes, I also much prefer the artistic freedom and excitement of one-on-a-part playing, in which what I do matters as much as what the dancers do. (I am aware of being far from alone in this sentiment.) I'd be willing to shorten my coffee break for the increased artistic freedom and the sense that my work really matters. (Not to mention how thrilling this kind of collaboration can be between musicians and dancers, as many other Juilliard alumni recall from their days there, and now from collaborations with other dance companies, such as Mark Morris, that explore the chamber music genre).
Am I making a sales-pitch here? - Sure, why not?

A flip side to the question of what-kind-of-music to play with dance, which I discussed with my neighbour, is whether music should ever be played without dance ... what should one look at, in a concert? Since music is not really about the musician - how does one let one's imagination wander? I confided that I can sympathize with this question; I have had the associative imagery at, particularly orchestral concerts, of looking into a see-through glass dishwasher, seeing how the gears turn and all. It happens to be a life-long dream, since I saw my first see-through glass dishwasher at the age of six, to own one someday, but that is another story.

In the end, as much as the quality of tonight's music bothered me at the beginning, the superb dancing and the choreography pulled me into its world, enhanced by well-placed lighting design and striking costumes, so I too could stop paying attention to the music's shortcomings, and thoroughly enjoy my evening. As I sensed from the rest of the audience - our standing ovation was sincere.

Now that I'm done writing my review, can I make it there again tonight??