La Donna del Lago, Santa Fe Opera 2013

This year's Santa Fe Opera's production of Rossini's La Donna del Lago (based on Sir Walter Scott's 1810 novel The Lady of the Lake) was a treat.  Musically, quite a nice piece.  I don't feel like giving a very definite appraisal of the opera itself without hearing it more, but it has plenty of excellent arias along with some that were less striking, some really nice orchestral parts (the opening scene, for instance), and good choral sections, along with what feels, at times, like more pedestrian sections (hardly unheard-of in Rossini).  Unquestionably worth seeing in a good production like this one.

Joyce DiDonato is a fascinating singer and convincingly characterized the main female role of Elena.  She has a very flexible mezzo with an extended high end, perhaps somewhere between a soprano and mezzo in tone, and great agility in coloratura.  Ornamentation and fancy passagework is all there, not approximated, although very occasionally I felt like this was getting in the way of natural phrasing.  Moreover she can usually do this while remaining relaxed, which probably contributes to her effectiveness as a vocal actress.  There was a lot for her to do in this opera, besides the last-act showstopper Tanti affetti, and she did it all (including Tanti affetti) masterfully.

Tenor Lawrence Brownlee, as King James of Scotland (disguised as one "Uberto" during the first act), gave a solid performance but his voice, while clear and reliable, seemed a bit overmatched, in volume and projection, by Ms. DiDonato's at times; indeed, I occasionally  wondered if she was holding back a bit so as not to overpower him.  (On the other hand, she had a lot of singing to do over the course of the evening, so could have been pacing herself.)  His singing came across as slightly reserved, perhaps a little stiff, although this was perhaps not completely out of character for a king.  His voice seemed smooth, refined, his tone a bit burnished.  I will definitely be interested in checking out his work in other settings.  I thought he came into his own a bit more in the final scene, where he is king in his court, rather than disguised to investigate the situation in his realm (and court Elena).

Tenor René Barbera was superb as Rodrigo di Dhu, the leader of another clan, whom Elena's father Duglas (Douglas) intends for Elena to marry.  His voice had a lot of color and texture to it, and projected well into the house.  And he sang with plenty of power and passion.  His voice showed no stress in climactic moments, and he did a good job of musically shaping phrases and whole arias, and of portraying Rodrigo as a vigorous, passionate young leader, not used to being thwarted.  I'd keep on the lookout for opera's he's in---his participation is a reason to go.

Bass-baritone Wayne Tigges was also superb as Elena's father Duglas.  He managed to convey real fatherly affection along with dictatorial control over his daughter's life, including the attempt to impose a marriage on her for reasons in part political and military.  Both his appearance (tall, with tousled dirty-blond hair) and his singing, in a clear, flexible but not soft, somewhat commanding but not bellowing voice, contributed to the picture of a fairly rough-hewn Scottish clan-leader, whose character mixes some nobility with some crudeness and violence.

As Malcolm Groeme, Elena's own choice for a main squeeze, mezzo Marianna Pizzolato sang beautifully, and her somewhat darker mezzo worked well with DiDonato.  She too was very solid in complex passagework.  Their duet cavatina Vivere io non potro was a highlight of the evening, and one of the high points of Rossini's opera.  She perhaps did not match DiDonato in acting skill; her long Act 2, scene 2 aria came off as a bit static.  But she is an excellent singer.

After seeing Maometto II last year, I wonder if Rossini had a particular interest in the theme of romantic love reaching across the divide of military conflict.  In this opera, it ultimately succeeds in bringing peace.  The quick peacemaking in the court scene at the end is perhaps a little bit unconvincing, but maybe further experience with the opera will clarify that aspect of the plot.

Last season, I began to wonder if Santa Fe plans a season have a theme running through several operas.  Last season, it would have been the damage caused to people seeking to live lives of love, art, peaceful spirituality, by the alliance of religion with state power.  This year, I'd say it was romantic love and powerful women against patriarchy.  This was the obvious theme of Rossini's opera, and I think the director underlined it by having some of the men behave extra-badly: some pretty aggressive come-ons by King James to Elena in the first act, violent treatment of women by clansmen in some of the choral scenes.

Some of the staging was perhaps a bit static, but the production did well to keep the original setting, and the sets were excellent, emphasizing rusticity and desolation over romantic lochs.  (In fact, the lake seemed to have gone missing.)  The chorus and orchestra were both very strong.

Overall, a good opera with moments of magic, extremely well produced and cast, and with a thought-provoking theme.  Lots of excellent music, though sometimes padded out with lesser music, and with a story providing food for thought, and mostly effective drama, though probably not up with the best operas in the dramatic department.  An opera I'd definitely see again, and hope to see done this well.

A thought on resistance to Bayesian statistics

I'm not a statistician, and as a quantum theorist of a relatively abstract sort, I've done little actual data analysis.  But because of my abstract interests, the nature of probability and its use in making inferences from data are of great interest.  I have some relatively ill-informed thoughts on why the "classical statistics" community seems to have been quite resistant to "Bayesian statistics", at least for a while, that may be of interest, or at least worth logging for my own reference. Take this post in the original (?) spirit of the term "web log", rather than as a polished piece of the sort many blogs, functioning more in the spirit of online magazines, seem to aim at nowadays.

The main idea is this.  Suppose doing Bayesian statistics is thought of as actually adopting a prior which specifies, say, one's initial estimate of the probabilities of several hypotheses, and then, on the basis of the data, computing the posterior probability of the hypotheses.  In other words, what is usually called "Bayesian inference". That may be a poor way of presenting the results of an experiment, although it is a good way for individuals to reason about how the results of the experiment should affect their beliefs and decisions.  The problem is that different users of the experimental results, e.g. different readers of a published study, may have different priors.  What one would like is rather to present these users with a statistic, that is, some function of the data, much more succinct than simply publishing the data themselves, but just as useful, or almost as useful, in making the transition from prior probabilities to posterior probabilities, that is, of updating one's beliefs about the hypotheses of interest, to take into account the new data. Of course, for a compressed version of the data (a statistic) to be useful, it is probably necessary that the users share certain basic assumptions about the nature of the experiment.  These assumptions might involve the probabilities of various experimental outcomes, or sets of data, if various hypotheses are true (or if a parameter takes various values), i.e., the likelihood function;  they might also involve a restriction on the class of priors for which the statistic is likely to be useful.  These should be spelled out, and, if it is not obvious, how the statistic can be used in computing posterior probabilities should be spelled out as well.

It seems to me likely that many classical or "frequentist" statistics may be used in such a way; but, quite possibly, classical language, like saying that statistical inference leads to "acceptance" or "rejection" of hypotheses, tends to obscure this more desirable use of the statistic as a potential input to the computation of posterior probabilities.  In fact, I think people tend to have a natural tendency to want some notion of what the posterior probability of a hypothesis is; this is one source of the erroneous tendency, still sometimes found among the public, to confuse confidence levels with probabilities.  Sometimes an advocacy of classical statistical tests may go with an ideological resistance to the computation of posterior probabilities, but I suppose not always.  It also seems likely that in many cases, publishing actual Bayesian computations may be a good alternative to classical procedures, particularly if one is able to summarize in a formula what the data imply about posterior probabilities, for a broad enough range of priors that many or most users would find their prior beliefs adequately approximated by them.  But in any case, I think it is essential, in order to properly understand the meaning of reports of classical statistical tests, to understand how they can be used as inputs to Bayesian inference.  There may be other issues as well, e.g. that in some cases classical tests may make suboptimal use of the information available in the data.  In other words, they may not provide a sufficient statistic: a function of the data that contains all the information available in the data, about some random variable of interest (say, whether a particular hypothesis is true or not). Of course whether or not a statistic is sufficient will depend on how one models the situation.

Most of this is old hat, but it is worth keeping in mind, especially as a Bayesian trying to understand what is going on when "frequentist" statisticians get defensive about general Bayesian critiques of their methods.

Poulenc --- Complete Works (EMI)

Over the last few weeks I've been listening to "Francis Poulenc:  Oeuvres Complètes"  on EMI Classics (972165 2).  The short take: if you like classical music, buy it.  Amazing value at $44 for 20CDs (prices vary but$50ish for the new set seems about par).  These are mostly, perhaps entirely, French performances, in many cases by artists (like pianists Gabriel Tacchino and Jacques Février) long associated with Poulenc.  There's a lot of superb music here and it's fascinating to have all of Poulenc's music in one place, sorted by genre (piano music first, then chamber music, then orchestral works, then sacred music, then dramatic vocal and other choral works, then songs).

Some highlights:  lots of superb piano music.  The "15 Improvisations", on disc 1, is a good place to start.  All of the chamber music is interesting; highlights include the wonderful 1926 Trio for piano, oboe, and bassoon. I was familiar with this from an excellent Deutsche Grammophon recording ("Francis Poulenc: Chamber Music") with the Ensemble Wien-Berlin on winds and James Levine on piano. The French EMI recording, with Robert Casier on oboe, Gérard Faisandier on bassoon, and Jacques Février on piano seems --- I could be influenced by the fact that the performers are French, but I think this is a real musical difference --- to have an earthier, perhaps Gallic, flair to it, with the winds sounding reedier, the phrasing more influenced by popular music.  The piece seems to blend influences from Classical and perhaps also rococo periods in music, with ones from the music-hall and popular traditions, and the more Germanic ensemble on DG seems to give a smoother, more ornamental sound emphasizing the classical connections more; the French one certainly doesn't overemphasize the popular elements (which are subtly infused into the music in any case), but does bring them out more.  Both performances bring out the humorous element that is usually essential to Poulenc, alongside expressiveness and singing beauty, but the French performers seem to fuse these two elements more closely and the result somehow seems a bit more sincerely felt, whereas the humorous aspects of the DG version have a bit more of the feel of parody.  Levine's piano playing is of course excellent, but seems a bit "blocky" at times compared to Février's.  I'm glad that I have both versions.  If I had to have only one, it would be the EMI one.

The Sonata for cello and piano is a masterpiece, that for violin and piano probably is also.  Poulenc worked on both over a good portion of the 1940s.   The latter is a bit more agitated in feeling (perhaps relatively chromatic for Poulenc?), the cello sonata more majestic, mellow, and songful.  The 1918 sonata for two clarinets and 1922 sonata for clarinet and bassoon are wonderful; they and the 1922 sonata for horn, trumpet, and trombone handle the unusual instrumentation masterfully.  The 1957 Elegy for horn and piano, dedicated to the memory of English French horn player Dennis Brain, is another masterpiece, with Février on piano and Alain Civil getting wonderful timbres from his horn.

I was less familiar with Poulenc's orchestral music before getting this box set, and it has been fascinating to get to know.  The ballet Les Biches, written for Diaghilev's Ballets Russes and premiered in Monte Carlo in 1924, is probably the place to start.  Another wonderful piece, with lighthearted eighteenth-century-influenced pieces alternating with more avant-garde sounds and some very effective, more somber-sounding movements with chorus.  The choral movements are omitted in a later orchestral suite, which I have not heard; to me they are essential to the impact of the work heard here.

The piano-and-orchestra works have so far been a bit harder for me to wholeheartedly commit to... the Aubade starts very interestingly, but becomes rather bombastic-sounding, which even if intended humorously, doesn't quite draw me in.  I liked the earlier Concerto for piano and orchestra better, but will have to do some more listening to develop a real opinion.  Some of the pieces have a lot of music that sounds closely related to lush 1930s movie music, interesting but perhaps a bit too much.  The organ concerto has some really effective parts but I'll have to listen more carefully.  (Listening while cooking or doing dishes, which has been the situation for some of this orchestral music so far, doesn't really count as a fair hearing...).  Much of the orchestral music is conducted by the superb and very idiomatically French Georges Prêtre, and it is hard to imagine it better played.

Of the vocal works with orchestra on these discs, I have so far listened only to the first act of the opera Dialogues des Carmélites, which seems superb as a work of music, and probably of drama, and superbly sung and played; the choir and orchestra are those of the Paris Opera, under the excellent Pierre Dervaux.  (Dervaux' recording of Bizet's Pearl Fishers  with Nicolai Gedda as Nadir is one of the reference recordings of that piece, discussed elsewhere on this blog; it evidences the clarity of texture and line, and the restrained but expressive approach to tempo variation and phrasing, that one might think of as characteristically French, and which are shared by Prêtre's conducting here and elsewhere.)  The musical language seems quite influenced, at times, by the more modal side of Debussy and Ravel (and probably also by centuries of church music), and this language provides a superb vehicle for maintaining musical interest during the kind of dialogue that has often been scored, over the course of operatic history, as stereotyped recitative.  I am moved to go back to Débussy's Pélleas et Mélisande to see if it is a source for this style in opera (I have to admit that I never quite got into Pélleas, as conducted by Boulez, but probably didn't give it enough of a chance.)  Parts of the first act already have a stunning musical and dramatic impact, so I'm looking forward to finishing listening to this work.  I have listened, in other versions, to other vocal works by Poulenc, but it's been a long time, so I'm looking forward to getting familiar with them again.

I haven't yet delved into the five discs of songs, mostly for solo voice and piano but sometimes for vocal ensembles, that cap off the set.  Many involve one of my favorite singers, baritone Gérard Souzay accompanied by Dalton Baldwin (their Débussy songs on DG are sublime), and I suspect the less familiar singers will be wonderful discoveries.

The booklet contains discographic information in French and a valuable essay, discussing Poulenc and general and covering each piece briefly.   It's unfortunate that it doesn't include librettos for the dramatic pieces and lyrics for the songs, although that probably would have made the booklet unmanageably large.  I would guess that for most pieces you can find lyrics on the web, but that is not nearly as nice as having them all in one place stored with the relevant CDs.  The central section of the booklet features wonderful historic photos of Poulenc with friends and colleagues.

This set is an amazing value, of a sort that seems to be increasingly available from major record companies.  It contains many, many works that seem to me essential to any lover of classical music, in performances that it's hard to imagine improving upon.

2010 Chateau Mayne-Guyon, Blaye Côtes de Bordeaux

I liked the 2009 Chateau Mayne-Guyon Blaye Côtes de Bordeaux a lot, in fact thought it one of the best values around in red wine.  A quick note to let you know I liked the 2010 Chateau Mayne-Guyon, also available at Trader Joe's, even better.  I drank it a few months ago, so you can take details with a grain of salt, but I'd say it's more elegant, less chunky and tarry, than the 2009, but still fairly full-bodied and quite flavorful.  More emphasis on delicious berry fruit, a bit less on dark/minerally tastes, but still enough of the latter for complexity, enough tannin to avoid flabbiness and suggest ageability, and perhaps a bit better balanced than the 2009 as well.  I'd guess this would be serious competition for much more expensive (and properly aged) Bordeaux---perhaps not 2nd classed growths but probably some of the better Crus Bourgeois---in a blind tasting.  Another no-brainer for multiple bottle purchases at \$8.  If one has to rate, I guess I'd say 8/10 on a 10-point scale that goes to 11, corresponding to around 87-89 Parker points, and I'm probably being conservative here.  On my last visit to TJ's there was a big empty spot with one or two bottles of this on the shelf, so perhaps the secret is out... I already got my stash of four or five bottles.

I had a look at Jacob Bekenstein's 1973 Physical Review D paper "Black holes and entropy" for the answer to my question about Susskind's presentation of the Bekenstein derivation of the formula stating that black hole entropy is proportional to horizon area.  An argument similar to the one in Susskind's talk appears in Section IV, except that massive particles are considered, rather than photons, and they can be assumed to be scalar so that the issue I raised, of entropy associated with polarization, is moot.  Bekenstein says:

we can be sure that the absolute minimum of information lost [as a particle falls into a black hole] is that contained in the answer to the question "does the particle exist or not?"  To start with, the answer [to this question] is known to be yes.  But after the particle falls in, one has no information whatever about the answer.  This is because from the point of view of this paper, one knows nothing about the physical conditions inside the black hole, and thus one cannot assess the likelihood of the particle continuing to exist or being destroyed.  One must, therefore, admit to the loss of one bit of information [...] at the very least."

Presumably for the particle to be destroyed, at least in a field-theoretic description, it must annihilate with some stuff that is already inside the black hole (or from the outside point of view, plastered against the horizon). This annihilation could, I guess, create some other particle. In fact it probably must, in order to conserve mass-energy.  My worry in the previous post about the entropy being due to the presence/absence of the particle inside the hole was that this would seem to need to be due to uncertainty about whether the particle fell into the hole in the first place, which did not seem to be part of the story Susskind was telling, and the associated worry that this would make the black hole mass uncertain, which also didn't seem to be a feature of the intended story although I wasn't sure. But the correct story seems to be that the particle definitely goes into the hole, and the uncertainty is about whether it subsequently annihilates with something else inside, in a process obeying all relevant conservation laws, rendering both of my worries inapplicable. I'd still like to see if Bekenstein wrote a version using photons, as Susskind's presentation does. And when I feel quite comfortable, I'll probably post a fairly full description of one (or more) versions of the argument. Prior to the Phys Rev D paper there was a 1972 Letter to Nuovo Cimento, which I plan to have a look at; perhaps it deals with photons. If you want to read Bekenstein's papers too, I suggest you have a look at his webpage.

Question about Susskind's presentation of Bekenstein's black hole entropy derivation

I'm partway through viewing Leonard Susskind's excellent not-too-technical talk "Inside Black Holes" given at the Kavli Institute for Theoretical Physics at UC Santa Barbara on August 25.  Thanks to John Preskill,  @preskill, for recommending it.

I've decided to try using my blog as a discussion space about this talk, and ultimately perhaps about the "Harlow-Hayden conjecture" about how to avoid accepting the recent claim that black holes must have an information-destroying "firewall" near the horizon.  (I hope I've got that right.)  I'm using  Susskind's paper "Black hole complementarity and the Harlow-Hayden conjecture"  as my first source on the latter question.  It also seems to be a relatively nontechnical presentation (though much more technical than the talk so far)... that should be particularly accessible to quantum information theorists, although it seems to me he also does a good job of explaining the quantum information-theoretic concepts he uses to those not familiar with them.

But first things first.  I'm going to unembarassedly ask elementary questions about the talk and the paper until I understand.  First off, I've got a question about Susskind's "high-school level" presentation, in minutes 18-28 of the video, of Jacob Bekenstein's 1973 argument that in our quantum-mechanical world the entropy of a black hole is proportional to its area (i.e. the area of the horizon, the closed surface inside which nothing, not even light, can escape).   The formula, as given by Susskind, is

$S = (\frac{c^3}{4 \hbar G}) A$,

where $S$ is the entropy (in bits) of the black hole, and $A$ the area of its horizon.  (The constant here may have been tweaked by a small amounts, like $4 \pi$ or its inverse, to reflect considerations that Susskind alluded to but didn't describe, more subtle than those involved in Bekenstein's argument.)

The argument, as presented by Susskind, involves creating the black hole out of photons whose wavelength is roughly the Schwarzschild radius of the black hole.  More precisely, it is built up in steps; each step in creating a black hole of a given mass and radius involves sending in another photon of wavelength roughly the current Schwarzschild radius.  The wavelength needs to be that big so that there is no information going into the hole (equivalently, from the point of view outside the hole, getting "plastered" (Susskind's nice choice of word) against the horizon) about where the photon went in.  Presumably there is some argument about why the wavelength shouldn't be much bigger, either...perhaps so that it is sure to go into the hole, rather than missing.  That raises the question of just what state of the photon field should be impinging on the hole...presumably we want some wavepacket whose spatial width is about the size of the hole, so we'll have a spread of wavelengths centered around some multiple (roughly unity) of the Schwarzschild radius.  Before there is any hole, I guess I also have some issues about momentum conservation... maybe one starts by sending in a spherical shell of radiation impinging on where we want the hole to be, so as to have zero net momentum.  But these aren't my main questions, though of course it could turn out to be necessary to answer them in order to answer my main question.  My main question is:  Susskind says that each such photon carries one bit of information: the information is "whether it's there or not".  This doesn't make sense to me, as if one is uncertain about how many photons went into creating the hole, it seems to me one should have a corresponding uncertainty about its mass, radius, etc...  Moreover, the photons that go in still seem to have a degree of freedom capable of storing a bit of information:  their polarization.  So maybe this is the source of the one bit per photon?  Of course, this would carry angular momentum into the hole/onto the horizon, so I guess uncertainty about this could generate uncertainty about whether or not we have a Schwarzschild or a Kerr (rotating) black hole, i.e. just what the angular momentum of the hole is.

Now, maybe the solution is just that given their wavelength of the same order of the hole, there is uncertainty about whether or not the photons actually get into the hole, and so the entropy of the black hole really is due to uncertainty about its total mass, and the mass M in the Bekenstein formula is just the expected value of mass?

I realize I could probably figure all this out by grabbing some papers, e.g. Bekenstein's original, or perhaps even by checking wikipedia, but I think there's some value in thinking out loud, and in having an actual interchange with people to clear up my confusion... one ends up understanding the concepts better, and remembering the solution.  So, if any physicists knowledgeable about black holes (or able and willing to intelligently speculate about them...) are reading this, straighten me out if you can, or at least let's discuss it and figure it out...

The Marriage of Figaro, Santa Fe 2013

The 2013 opera season at Santa Fe ended last night (well, two nights ago as this is posted) with a performance of Offenbach's comic operetta The Grand Duchess of Gerolstein.  I went to all five operas, and thought this one of the strongest seasons I've been to at Santa Fe.  As the first installment of a report on the season, I'll cover the August 20th performance of Mozart's The Marriage of Figaro.

This was the first time I've seen this opera, though I have a video of it I used to enjoy.  Figaro is well known to be one of the greatest and most enjoyable operas so I won't cover the basics; if you think you might be interested in opera, it is one of the first ones you should get to know, particularly if you are looking for something combining melodic beauty, at times soaring, at times restrained, with elegance and lightness of spirit. (If you're looking for more consistently over-the-top emotion and big tunes, like perhaps if you're into metal or arena rock and looking to explore opera, the "big three" operas of Verdi's middle period (La Traviata, Rigoletto, Il Trovatore), or even more over-the-top, the big Puccinis (especially Tosca or Madama Butterfly, also Turandot) are probably the ticket for an introduction to opera.)   All elements of this production were top-notch.  In Phillips, Fons, Oropesa, and Nelson, and probably several others, it featured some of the best singers I've heard at Santa Fe.  Susanna Phillips as the Countess and Emily Fons as Susanna were in beautiful form, both with strong, sweet voices, Phillips a soprano, Fons a very lyric mezzo.  The opera moves from the first act's exposition, silly business and plotting into more serious emotional territory with the Countess' first appearance, in the opening scene of Act II, in the beautiful lament Porgi, amor, qualche ristoro (Give me, love, some solace). Phillips portrayed the Countess' emotion superbly, with great dynamic control and plenty of power and projection when necessary without forcing the voice or losing sweetness of tone. Another in our party disliked the somewhat broad vibrato she unleashed at times, but I thought it was just right, part of a classic powerful operatic soprano presentation that still remained controlled and appropriate for Mozart. She was also superb in ensembles, and in her other major aria, the third act's Dove sono i bei momenti (Where are those beautiful moments?), especially the allegro section (Ah! se almen la mia costanza... (Oh! If only my constancy...)) that ends it. (I'm not sure if the notion of a fast cabaletta to cap off a broad aria had developed by this time, or if Mozart was helping to invent it here.) If I have any minor complaint about Phillips' singing, it might be that although her pianissimo singing can be incredibly sweet, it occasionally was so soft, the dynamic contrast so great, that it seemed a bit mannered, especially when used to end a phrase on a high note (more difficult, to be sure, than a loud high note, and achieved here with perfect control). But this is a very minor cavil and could be completely baseless, not even apparent from a different seat with different acoustics. (The member of our party who objected to Phillips' vibrato singled out her piano singing for special praise.) Overall, I thought this was opera singing of the highest caliber, in which the musicality of Phillips' phrasing and the beauty of her voice were inseparable from the communication of emotion and through it, her part in the the development of the drama.

The Santa Fe New Mexican, in a glowing review of the June 29th performance, wrote that

Phillips took a while to settle in, as Countesses often do, but she arrived at a firm, full-throated performance. Her voice has been evolving impressively in recent years, and one senses that she may be on the verge of the vocal luxuriance that has marked the most memorable Countesses over the years.

Her relationship with the role must have continued evolving in the month and a half since that early performance, because vocal luxuriance was abundantly, though not overbearingly, present, she needed no time to settle in, but had me by the heartstrings from the first notes of "Porgi, amor", and her performance will certainly live in my memory.

In the "trouser role" of Cherubino, soprano Emily Fons was equally superb. She did a good job with the comic elements of the character (a young boy discovering the delights of love with various local girls, and infatuated with the Countess as well---"Narciseto, Adoncino de amor", as Figaro characterizes him in the famous aria "Non piu andrai, farfallone amoroso, notte e giorno d'intorno girando, delle belle turbando il riposo" (No longer will you go, amorous butterfly, running around night and day disturbing the peace of pretty girls" ) with which he bids him goodbye as the Count attempts (unsuccessfully, it turns out) to send him away to join the army). The comedy was perhaps a bit muggy and telegraphed, the makeup a bit heavy viewed with binoculars, but that's probably part of such a role, and Fons kept it light and flitty, like an amorous butterfly indeed. Her voice is as good as Phillips', just slightly smoother and lighter in tone, and with a bit less prominent vibrato, but still quite full and sweet, definitely a sweetly lyric rather than a throaty mezzo, hence perfect, in my judgement, for this role. Her Voi che sapete, che cosa e l'amore ("You who know what love is"), yet another of the many classic arias you probably know even if you've never attended the opera or listened to it on your stereo (or phone, pad, pod, or computer), was as good as I can imagine. I will count either of these artists, Fons or Phillips, as among the best women singing today and reason enough to attend any opera they're in; keep a lookout for them if you follow opera. As Susanna, Lisette Oropesa's performance was of similar caliber; I don't remember specific moments as moving as the abovementioned arias of the Contessa and of Cherubino, but find myself wishing I could attend another performance to focus more on Susanna; her acting and singing were, as far as I can recall, flawless and her voice, like the other women's, clear, unstrained and musical, and carried well in what may be a slightly difficult (because open at the sides) theater.

Zachary Nelson did a superb job as Figaro. He is clearly---and with reason---rising very fast in the world of opera, as he was in the apprentice singer program last summer (2012) at Santa Fe. His performance was completely assured, his acting and musicality top-notch, with nothing to indicate anything but a seasoned and confident singer. Strangely, before looking in the program and finding out how recently he'd been an apprentice, I got the impression, just from his very pleasing tone, of a relatively young voice, perhaps in transition to a fuller, darker voice. That's arguably quite appropriate for Figaro, who is already quite competent and arguably making a similar transition from youthful adulthood to maturity, with marriage in view. He had plenty of power, never oversung or forced and achieved good projection, with perhaps occasional slight loss of power on the very lowest notes, or just slightly falling in the shadow of one of the sopranos (always a bit difficult for a baritone to balance with a powerful soprano, I suspect). But again, I could be off-base with such minor cavils, and overall this was a consistently excellent performance, probably the best by a baritone that I heard this season at Santa Fe, with excellent musicality and control in both solo and ensemble situations, a very interesting voice with some color and texture to it (making me think of walnut with a natural oil finish, maybe very fine tweed) but also a kind of clarion, though not cutting or harsh, quality that helps it stand out and project.  Wonderful, balanced characterization of Figaro, carried through ensemble, recitative and conversational duets and also solo arias,  lighthearted and witty, yet competent and with seriousness of purpose.  Se vuol ballare, signor contino ("If you want to dance, little Mr. Count") was a perfect example, with an overall affect of restrained glee at the prospect of teaching the Count a lesson, but not completely without menace and genuine outrage, either.  Non piu andrai was similarly deftly done.  Nelson is definitely another singer to go out of your way to hear.

Daniel Okulitch's Count was also extremely well sung and acted.  Though it still has some depth, his voice is perhaps is a little harder-edged and more brilliant than Nelson's, which seemed to suit his more authoritarian and rigid character.  The part doesn't offer as many star turns as does Figaro, but Okulitch played it perfectly.

I would have had to attend multiple times (I know a guy who goes to multiple performances of each opera, getting standing room to make it affordable) in order to evaluate the supporting singers with any accuracy; such evaluation is not really what I want to focus when I'm going once to enjoy an opera. What I can say is that overall the supporting singers were very solid, with no weaknesses that I noticed.  Keith Jameson, as the music master Basilio, stood out not only because he was a tenor (the heroic or lead-lover tenor was perhaps less established in Mozart's day, especially, I guess, in comic opera), but for the excellence and clarity of his voice and pacing, and Rachel Hall as Barbarina had a noticeably pleasing voice and sang well also.  A really excellent ensemble cast and chorus.

The production was excellent too, true to the original setting of the play and beautifully detailed, doing a wonderful job of creating a believable setting in an eighteenth-century aristocratic estate without needing to go over the top, fitting seamlessly with the particular requirements of Santa Fe's stage. The (presumably artificial) bunches of flowers planted all over the stage, and removed by topcoated and bewigged aristocrats from the front portion of the stage during the latter part of the overture, leaving the ones in back to serve as the garden exterior to the house when appropriate, were a spectacular and creative touch. Costumes were period-appropriate, with luxurious detail where appropriate but still lively and fresh rather than stodgy.

I didn't focus too hard on the orchestra's performance, conducted by John Nelson, but can say that it was light, lively, elegant, and integrated well with the vocal work. Obviously, no flaws drew unwanted attention to it. An instance of particularly memorable and perfectly-executed orchestral playing was the eighteen bars before the Count's famous plea for forgiveness "Contessa, perdono" , accompanying the Count's realization of the last of many deceptions that have been played on him ("O cielo, che veggio...", Oh heavens, what do I see...", sung by the Count, Dr. Bartolo the music teacher, Basilio, and Antonio the gardener.  (This passage begins with the second system on page 343 in the BMG/Ricordi piano/vocal score, or on page 48 of the pdf (390 of the original) of the full score from Peters, other sections downloadable here.)  The orchestra takes off in with running eight notes, scalar passages with frequent direction changes and turn-like flourishes, rapidly modulating through major and minor keys, including some fairly remote ones like Eb major (the ambient key signature is G major although the section starts in G minor), with a cascade down the cycle of fifths from G to Bb in the middle of the section, for a somewhat unearthly, magical, flying feeling creating an atmosphere like that in parts of the Magic Flute.  There is some baroque influence evident especially when the line does something ornamental, but it is not pastiche, definitely something new and probably uniquely Mozartean.  The passage is also reminiscent of a recurrent motif in Mozart's next opera on a Da Ponte libretto, Don Giovanni, which however features somewhat more regular ascending and then descending scales in minor, the whole ascending descending figure repeating in higher and higher keys, for a similar effect of suddenly becoming unmoored from ordinary reality and gliding through an eerily magical realm, but in a more tension-building, and definitely ominous, way. These eighteen bars are one of the many pinnacles of Mozartean magic reached in this opera. I recently read (it would have been in a collection "Other Entertainment" of Ned Rorem's essays, or in Dietrich Fischer-Dieskau's memoirs or Gerald Moore's book The Schubert Song Cycles) an approvingly quoted aphorism along the lines of "The only thing that matters in music is that which cannot be explained", and it is tempting to think of this passage as an example of such inexplicable magic, except that I think that while it's absolutely magical, it's mostly quite explicable---some of the discussion above is a start, and the passage would clearly repay more careful analysis, which I may do and post separately. Such analysis is probably more important to one who wants to understand how to achieve similar effects, rather than one who just wants to enjoy the magic... Mozart and a good opera orchestra like Santa Fe's are enough to ensure the latter. With a superb vocal cast and excellence in all aspects of production, this added up to a production that --- although I've not seen another live Figaro --- would be hard to top, an evening filled with all manner of Mozartean magic.

Bohm on measurement in Bohmian quantum theory

Prompted, as described in the previous post, by Craig Callender's post on the uncertainty principle, I've gone back to David Bohm's original series of two papers "A suggested interpretation of the quantum theory in terms of "hidden" variables I" and "...II", published in Physical Review in 1952 (and reprinted in Wheeler and Zurek's classic collection "Quantum Theory and Measurement", Princeton University Press, 1983).  The Bohm papers and others appear to be downloadable here.

Question 1 of my previous post asked whether it is true that

"a "measurement of position" does not measure the pre-existing value of the variable called, in the theory, "position".  That is, if one considers a single trajectory in phase space (position and momentum, over time), entering an apparatus described as a "position measurement apparatus", that apparatus does not necessarily end up pointing to, approximately, the position of the particle when it entered the apparatus."

It is fairly clear from Bohm's papers that the answer is "Yes". In section 5 of the second paper, he writes

"in the measurement of an "observable," Q, we cannot obtain enough information to provide a complete specification of the state of an electron, because we cannot infer the precisely defined values of the particle momentum and position, which are, for example, needed if we wish to make precise predictions about the future behavior of the electron. [...] the measurement of an "observable" is not really a measurement of any physical property belonging to the observed system alone. Instead, the value of an "observable" measures only an incompletely predictable and controllable potentiality belonging just as much to the measuring apparatus as to the observed system itself."

Since the first sentence quoted says we cannot infer precise values of "momentum and position", it is possible to interpret it as referring to an uncertainty-principle-like tradeoff of precision in measurement of one versus the other, rather than a statement that it is not possible to measure either precisely, but I think that would be a misreading, as the rest of the quote, which clearly concerns any single observable, indicates. Later in the section, he unambiguously gives the answer "Yes" to a mutation of my Question 1 which substitutes momentum for position. Indeed, most of the section is concerned with using momentum measurement as an example of the general principle that the measurements described by standard quantum theory, when interpreted in his formalism, do not measure pre-existing properties of the measured system.

Here's a bit of one of two explicit examples he gives of momentum measurement:

"...consider a stationary state of an atom, of zero angular momentum. [...] the $\psi$-field for such a state is real, so that we obtain

$\mathbf{p} = \nabla S = 0.$

Thus, the particle is at rest. Nevertheless, we see from (14) and (15) that if the momentum "observable" is measured, a large value of this "observable" may be obtained if the $\psi$-field happens to have a large fourier coefficient, $a_\mathbf{p}$, for a high value of $\mathbf{p}$. The reason is that in the process of interaction with the measuring apparatus, the $\psi$-field is altered in such a way that it can give the electron particle a correspondingly large momentum, thus transferring some of the potential energy of interaction of the particle with its $\psi$-field into kinetic energy."

Note that the Bohmian theory involves writing the complex-valued wavefunction $\psi(\mathbf{x})$ as $R(\mathbf{x})e^{i S(\mathbf{x})}$, i.e. in terms of its (real) modulus $R$ and (real) phase $S$. Expressing the Schrödinger equation in terms of these variables is in fact probably what suggested the interpretation, since one gets something resembling classical equations of motion, but with a term that looks like a potential, but depends on $\psi$. Then one takes these classical-like equations of motion seriously, as governing the motions of actual particles that have definite positions and momenta. In order to stay in agreement with quantum theory concerning observed events such as the outcomes of measurements, m theory, one in addition keeps, from quantum theory, the assumption that the wavefunction $\psi$ evolves according to the Schrödinger equation. And one assumes that we don't know the particles' exact position but only that this is distributed with probability measure given (as quantum theory would predict for the outcome of a position measurement) by $R^2(\mathbf{x})$, and that the momentum is $\mathbf{p} = \nabla S$. That's why the real-valuedness of the wavefunction implies that momentum is zero: because the momentum, in Bohmian theory, is the gradient of the phase of the wavefunction.

For completeness we should reproduce Bohm's (15).

(15) $\psi = \sum_\mathbf{p} a_{\mathbf{p}} exp(i \mathbf{p}\cdot \mathbf{x} / \hbar).$

At least in the Wheeler and Zurek book, the equation has $p$ instead of $\mathbf{p}$ as the subscript on $\Sigma$, and $a_1$ instead of $a_\mathbf{p}$; I consider these typos, and have corrected them. (Bohm's reference to (14), which is essentially the same as (15) seems to me to be redundant.)

The upshot is that

"the actual particle momentum existing before the measurement took place is quite different from the numerical value obtained for the momentum "observable,"which, in the usual interpretation, is called the "momentum." "

It would be nice to have this worked out for a position measurement example, as well. The nicest thing, from my point of view, would be an example trajectory, for a definite initial position, under a position-measurement interaction, leading to a final position different from the initial one. I doubt this would be too hard, although it is generally considered to be the case that solving the Bohmian equations of motion is difficult in the technical sense of complexity theory. I don't recall just how difficult, but more difficult than solving the Schrödinger equation, which is sometimes taken as an argument against the Bohmian interpretation: why should nature do all that work, only to reproduce, because of the constraints mentioned above---distribution of $\mathbf{x}$ according to $R^2$, $\mathbf{p} = \nabla S$---observable consequences that can be more easily calculated using the Schrödinger equation?
I think I first heard of this complexity objection (which is of course something of a matter of taste in scientific theories, rather than a knockdown argument) from Daniel Gottesman, in a conversation at one of the Feynman Fests at the University of Maryland, although Antony Valentini (himself a Bohmian) has definitely stressed the ability of Bohmian mechanics to solve problems of high complexity, if one is allowed to violate the constraints that make it observationally indistinguishable from quantum theory. It is clear from rereading Bohm's 1952 papers that Bohm was excited about the physical possibility of going beyond these constraints, and thus beyond the limitations of standard quantum theory, if his theory was correct.

In fairness to Bohmianism, I should mention that in these papers Bohm suggests that the constraints that give standard quantum behavior may be an equilibrium, and in another paper he gives arguments in favor of this claim. Others have since taken up this line of argument and done more with it. I'm not familiar with the details. But the analogy with thermodynamics and statistical mechanics breaks down in at least one respect, that one can observe nonequilibrium phenomena, and processes of equilibration, with respect to standard thermodynamics, but nothing like this has so far been observed with respect to Bohmian quantum theory. (Of course that does not mean we shouldn't think harder, guided by Bohmian theory, about where such violations might be observed... I believe Valentini has suggested some possibilities in early-universe physics.)

A question about measurement in Bohmian quantum mechanics

I was disturbed by aspects of Craig Callender's post "Nothing to see here," on the uncertainty principle, in the New York Times' online philosophy blog "The Stone," and I'm pondering a response, which I hope to post here soon.  But in the process of pondering, some questions have arisen which I'd like to know the answers to.  Here are a couple:

Callender thinks it is important that quantum theory be formulated in a way that does not posit measurement as fundamental.  In particular he discusses the Bohmian variant of quantum theory (which I might prefer to describe as an alternative theory) as one of several possibilities for doing so.  In this theory, he claims,

Uncertainty still exists. The laws of motion of this theory imply that one can’t know everything, for example, that no perfectly accurate measurement of the particle’s velocity exists. This is still surprising and nonclassical, yes, but the limitation to our knowledge is only temporary. It’s perfectly compatible with the uncertainty principle as it functions in this theory that I measure position exactly and then later calculate the system’s velocity exactly.

While I've read Bohm's and Bell's papers on the subject, and some others, it's been a long time in most cases, and this theory is not something I consider very promising as physics even though it is important as an illustration of what can be done to recover quantum phenomena in a somewhat classical theory (and of the weird properties one can end up with when one tries to do so).  So I don't work with it routinely.  And so I'd like to ask anyone, preferably more expert than I am in technical aspects of the theory, though not necessarily a de Broglie-Bohm adherent, who can help me understand the above claims, in technical or non-technical terms, to chime in in the comments section.

I have a few specific questions.  It's my impression that in this theory, a "measurement of position" does not measure the pre-existing value of the variable called, in the theory, "position".  That is, if one considers a single trajectory in phase space (position and momentum, over time), entering an apparatus described as a "position measurement apparatus", that apparatus does not necessarily end up pointing to, approximately, the position of the particle when it entered the apparatus.

Question 1:  Is that correct?

A little more discussion of Question 1.  On my understanding, what is claimed is, rather, something like: that if one has a probability distribution over particle positions and momenta and a "pilot wave" (quantum wave function) whose squared amplitude agrees with these distributions (is this required in both position and momentum space? I'm guessing so), then the probability (calculated using the distribution over initial positions and momenta, and the deterministic "laws of motion" by which these interact with the "pilot wave" and the apparatus) for the apparatus to end up showing position in a given range, is the same as the integral of the squared modulus of the wavefunction, in the position representation, over that range.  Prima facie, this could be achieved in ways other than having the measurement reading being perfectly correlated with the initial position on a given trajectory, and my guess is that in fact it is not achieved in that way in the theory.    If that were so it seems like the correlation should hold whatever the pilot wave is.  Now, perhaps that's not a problem, but it makes the pilot wave feel a bit superfluous to me, and I know that it's not, in this theory.  My sense is that what happens is more like:  whatever the initial position is, the pilot wave guides it to some---definite, of course---different final position, but when the initial distribution is given by the squared modulus of the pilot wave itself, then the distribution of final positions is given by the squared modulus of the (initial, I guess) pilot wave.

But if the answer to question 1 is "Yes", I have trouble understanding what Callender means by "I measure position exactly".  Also, regardless of the answer to Question 1, either there is a subtle distinction being made between measuring "perfectly accurately" and measuring "exactly" (in which case I'd like to know what the distinction is), or these sentences need to be reformulated more carefully.  Not trying to do a gotcha on Callender here, just trying to understand the claim, and de Broglie Bohm.

My second question relates to Callender's statement that:

It’s perfectly compatible with the uncertainty principle as it functions in this theory that I measure position exactly and then later calculate the system’s velocity exactly

Question 2: How does this way of ascertaining the system's velocity differ from the sort of "direct measurement" that is, presumably, subject to the uncertainty principle? I'm guessing that by the time one has enough information (possibly about further positions?) to calculate what the velocity was, one can't do with it the sorts of things that one could have done if one had known the position and velocity simultaneously.  But this depends greatly on what it would mean to "have known" the position and/or velocity, which --- especially if the answer to Question 1 was "Yes"--- seems a rather subtle matter.

So, physicists and other readers knowledgeable on these matters (if any such exist), your replies with explanations, or links to explanations, of these points would be greatly appreciated.  And even if you don't know the answers, but know de Broglie-Bohm well on a technical level... let's figure this out!  (My guess is that it's well known, and indeed that the answer to Question 1 in particular is among the most basic things one learns about this interpretation...)

Rorem on Bizet... and Gedda and Vanzo in "Je crois entendre encore"

Reading Ned Rorem's essay on Bizet's Carmen, I can understand how he can say, even while admitting that Carmen is a "chef d'oeuvre", that it "does not make my mouth water. (No offense, neither does Schubert.) I like everything about it but it. .... One can admit to the fact of, and even cheer, certain universal marvels without needing them, while in the private heart one elevates to Parnassus lesser works which merely (merely?) satisfy."  I'm not sure I'd join him in this, although it's true I haven't sought out the opera very actively, except for a recent listen to the unusual recording (Prêtre conducting) with Callas late in her career.   The movie with Plácido Domingo as José, though, is memorable even though I haven't seen it since its first release, several decades ago now.  But I definitely can't join Rorem in his opinion that "There are no flukes in art.  Yet Carmen is a fluke.  Its high quality, if not its style, is incongruous in Bizet's catalogue."  Bizet was in his 37th year when he died of a heart attack (three months after the premiere of Carmen).  It's just as likely that Carmen was Bizet breaking through, not all that late, to his full power as composer, a power amply presaged by the best moments in his early work.  Rorem says that "Even his best works---the young Symphony, Jeux d'Enfants, parts of The Pearl Fishers---are in the salonistic genre of his period."  Well, I'm motivated to get to know the Symphony and Jeux by this.  And I suppose there is something salonistic, perhaps occasionally slightly cheesy, in parts of the Pearl Fishers.  More seriously, not all of Pearl Fishers is inspired...although good, transparent conducting, well recorded like Dervaux' in the 1960 Paris studio version with Nicolai Gedda as Nadir, Charles Blanc as Zurga, and Janine Micheau as Leila reveals plenty of beauty throughout.  And I guess my taste is somewhat more tolerant than Rorem's for the "salonistic" in music, and especially French music where Rorem admits "my taste buds crave a Frenchness that did not yet exist, a longing for the almost edible sadness that resides in the sharp seventh recipes of Debussy and Ravel."  Well, I find these delectable too (as I do the recipes with ninths thrown in, or a dash of pentatonicism), although not only when sadness is at issue.  But I sense that the modal moods of Debussy and Ravel show light, but important, traces of nineteenth-century "salonistic" influences, even, I think, of the Bizet of Carmen and the Pearl Fishers. I'll admit that the prismatic aperçus and pellucid vistas of Debussy and Ravel usually surpass the slightly overripe, though oh-so-tasty, sensuality of a Reynaldo Hahn, or even of Fauré in his early songs---Aprés un Rêve, which I do love, being just the most obvious example.  The great thing, of course, is that we don't need to choose between the two, except as a matter of allocating limited listening time---we can have both.

With the best of Pearl Fishers, though, Bizet makes it clear that Carmen was no fluke, but just the first mature fruit of a genius that was already perfectly evident, indeed in places perfectly realized, in the earlier work.  The tenor-baritone duet Au fond du temple saint, and the tenor romance Je crois entendre encore, both from Act I, are generally considered the greatest moments of Pearl Fishers.  Au fond is indeed wonderful, but after repeated listening to many versions of both (as they both do make my mouth water), I think Je crois is the greater of the two.   Salonistic, sentimental, whatever, it is the kind of aria that most composers can only dream of writing, nearly divine in its perfection and beauty.

The two singers I like best in this are Alain Vanzo and Nicolai Gedda.  I've linked some Youtubes of Vanzo singing this earlier, but I'll link another below.  Vanzo, in the second video below, uses the voix mixte to great effect, with a certain airiness in his timbre where Gedda's, in the first video, is smoother, probably a bit louder and more standardly operatic, with great clarity and perhaps slightly more control (they both have good control, though, and shape the line beautifully).  The last video, however, is of a 1953 recital performance by Gedda, whose timbre here is much closer to Vanzo's, and perhaps a bit more expressive too.  As is common in recital (for those uncommon singers who can do it), Gedda takes the final line that in the operatic arrangement is allotted to the English horn (over the singer's held note), going up to a piano high C.  (Vanzo can do this beautifully too, as he does in the video linked in an earlier post.)

Gedda, 1960:

Vanzo:

Gedda, 1953 recital: