Archive for the ‘Music’ Category

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The pure mathematical universe

Published by peter on 2012-11-08 in Mathematics, Matherati and Music. 0 Comments

Somewhere on his blog, the indefatigable Cosma Shalizi has written about the disciplinary universe of mathematics – that in addition to pure mathematics itself, pure mathematics is used in (and is essential to) the disciplines of Statistics and Computer Science.  This idea struck a chord, and I began to wonder exactly what particular aspect of pure mathematics was being used in each of these other disciplines and where else such methods or approaches were being used.  Of course, having trained as a pure mathematician who turned to mathematical statistics and then eventually to computer science, I know precisely what parts or theories of  pure math were being used in these two disciplines, so this is not my question.    For example, the theory and practice of mathematical statistics draw on probability theory (which itself draws on measure theory and the theory of integration, which in turn require Cantor’s theory of infinite collections), and, in statistical decision theory,  on the differential geometry of information.    (Indeed, I recall being strongly annoyed in my introductory statistics courses that so often proofs of theorems were postponed until “after you know measure theory.”)  Rather, what interests me is what abstract processes – what we might call, mathematical styles of thinking (mathmind, as distinct from, say, the styles of thinking of anthropology or history or chemistry)  – were being used, and where.
Not for the first time, I considered an input-process-output model.  From this viewpoint, we can view pure mathematics itself as a process of (mostly) deductive reasoning that transforms facts about abstract formal objects into other facts about abstract formal objects.   The abstract formal objects may have a basis in some (apprehension of some manifestation of) some real domain or objects, but such a basis is neither necessary nor important to the mathematics.   Until the mid 20th century, people used to say that mathematics was the theory of number, although why they thought this when the key examplar of this theory was Euclidean geometry, a theory which is mostly number-free and scale-invariant, I don’t know.    Since the mid-20th century, people have tended to say that mathematics is the theory of structure and relationship, which better describes most parts of pure mathematics, including Euclidean geometry, and better describes the potential applications and utility of the subject.
Many of the disciplines in the mathematical universe use the same processes – essentially deductive reasoning and, sometimes, calculation – to transform different inputs to certain outputs.   Here is my list (to be added to, when I think of others).
Pure Mathematics

  • Input = Abstract formal structures and objects
  • Process = Manipulation based on deductive reasoning (and, occasionally, calculation)
  • Output = Knowledge about abstract formal structures and objects

Theoretical Physics

  • Input = Mathematical models of physical reality
  • Process = Manipulation based on deductive reasoning and calculation
  • Output = Knowledge about (mathematical models of) physical reality

Mainstream Economics

  • Input = Mathematical models of economic reality
  • Process = Manipulation based on deductive reasoning and calculation
  • Output = Knowledge about (mathematical models of) economic reality

Computational Economics

  • Input = Computational models of economic reality
  • Process = Manipulation based on deductive and inductive reasoning, calculation and simulation
  • Output = Knowledge about (computational models of) economic reality

Exploratory Statistics:

  • Input = Raw data
  • Process = Processing and manipulation
  • Output = Information

Computer Processing:

  • Input = Information
  • Process = Processing and manipulation, including operations derived from both deductive and inductive reasoning, and simulation
  • Output = Information

Statistical Decision Theory (quantitative decision theory)

  • Input = Information
  • Process = Processing and manipulation, both inductive and deductive reasoning
  • Output = Knowledge, Actions

Computer Science:

  • Input = Abstract formal structures and objects, intended as models of computational processes
  • Process = Manipulation based on both deductive and inductive reasoning, and simulation
  • Output = Knowledge about (abstract formal structures and objects, as models of) computational processes

Engineering:

  • Input = Physical objects and materials
  • Process = Manipulation based on deductive reasoning and calculation
  • Output = Physical objects and materials

(Formal) Logic

  • Input = Formal representations of statements and arguments
  • Process = Manipulation based on deductive reasoning
  • Output = Formal representations of statements and arguments

AI Planning

  • Input = Information, actions
  • Process = Manipulation based on deductive reasoning and simulation
  • Output = Knowledge, actions, plans

Qualitative Decision Theory

  • Input = Information, actions
  • Process = Processing and manipulation, both inductive and deductive reasoning
  • Output = Knowledge, actions, plans.

Musical composition

  • Input = Abstract formal structures and objects with a sonic semantics
  • Process = Manipulation, based on deductive-like reasoning or simulation-like generation
  • Output = (Plans for the production of) sounds

Some of the statements implied by these input-process-output schemas are contested.  I would argue that, for instance, any knowledge gained by mathematical economics is only ever knowledge about the mathematical model being studied, and not about the real world which the model is intended to represent.   But this is not the view of most economists, who seem to think they are talking about reality rather than their model of it.  Perhaps this view explains why economics seems peculiarly immune to the major revision or rejection of models on the basis of their failure to predict or describe actual empirical data.
A word on the last schema above:   The composition, performance and even the auditing of music may involve thinking, as I argue here.  Some of the specific modes of musical thinking involved have much in common with deductive mathematical reasoning, in the sense that they can involve the working out of the logical consequences of musical ideas, where the logic being used is not Modus Ponens or Reductio ad Absurdum (as in pure mathematics), but a logic of sounds, pitches, rhythms, timbre and parts.

Music and Physics on the Strand

Published by peter on 2012-10-19 in History, Music and Science. 0 Comments

The Music Shop at no. 436 Strand

Monday 22 October 2012, 6.00pm-7.30pm
Venue: King’s College London
Strand Building 2:39 (English Seminar Room)
Introduced by Clare Pettitt
“From the age of fourteen until his late teens, Charles Wheatstone worked in his uncle’s musical instrument shop on the Strand, modifying instruments and conducting experiments in acoustics at the back of the shop until he left to take up a scientific career, later moving down the road to become Professor of Experimental Philosophy at King’s College London and inventing the stereoscope, improving the concertina (Wheatstone’s musical instrument makers is still a going concern and makes concertinas) and inventing, with Cooke, the telegraph. When he was only 19 years old in September 1821, Wheatstone caused quite a sensation by inventing and exhibiting the ‘Enchanted Lyre or Aconcryptophone’ at his father’s music school/shop on Pall Mall and subsequently at the Adelaide Gallery of Practical Science on the Strand.
This session will concentrate on the crossover between musical, commercial and scientific culture and will ask whether it is possible to map the multiple utility of spaces on the Strand (shops which are schools which are galleries which are scientific workshops etc.) onto the radical rearrangement of the senses in this period which made new technologies of seeing, hearing and communication possible.”
[Text from here, where references and suggestions for further reading may also be found.]

The fungus of Wagner

Published by peter on 2012-09-29 in History and Music. 0 Comments

Composer Thomas Ades in an interview with Tom Service:

Ades:  It’s too psychological.  I’m thinking of The Ring more than Tristan, there’s an awful lot of psychology in it which I find tedious. And naive, in a sort of superficial way. I mean, so much of Parsifal is dramatically absurd, which would be fine if the music was aware of the absurdity, but it is as if the whole piece is drugged and we all have to pretend that it’s not entirely ridiculous. And it seems to me that a country that can take a character as funny as Kundry seriously, this woman who sleeps for aeons and is only woken up by this horrible chord, a country that can seriously believe in anything like Parsifal without laughing, was bound to get into serious trouble.
Service:  You’re obviously not convinced by the music?
Ades: I don’t find Wagner’s an organic, necessary art. Wagner’s music is fungal. I think Wagner is a fungus. It’s a sort of unnatural growth. It’s parasitic in a sense – on its models, on its material. His material doesn’t grow symphonically – it doesn’t grow through a musical logic – it grows parasitically. It has a laboratory atmosphere.
 

Brass in Tyalgum

Published by peter on 2012-09-13 in Concerts, Music and Reviews. 0 Comments

The Brass Band of the Queensland Conservatorium of Music is the only English-style brass band in an Australian tertiary music college, which says something about the impoverished musical taste of those who run Australian music education institutions. Because the brass are mostly little-used in orchestral music (relative to, say, the strings, who play all the time), orchestral brass players usually also play in other wind ensembles and bands, both for the practice and to build their stamina. So a distaste for brass band music is usually not something shared by orchestral brass players.  And a good thing too, given the high calibre of the best brass bands.
With about 100 other people, I caught the QCM Brass Band last weekend, performing as part of the 21st Tyalgum Festival of Classical Music.    The band was led by Peter Luff and Greg Aitken, both of the QCM.  The festival began in this small and isolated mountain village after some performers had experienced the very good acoustics of the Tyalgum Literary Institute Hall, the main public hall in the town.   The acoustics of the Hall are indeed excellent, although surely not of a design praised in modern architecture schools.   The Hall, built in 1908, is a single rectangle, with side walls made of wooden planks, having many windows and doors.  On one side is an enclosed verandah, open to the main room.  The roof has a single pitch and is made of corrugated iron, and there is no ceiling – the iron reflects sound well, and the undulations would send it in all directions.  Mostly, the band sat on the floor at the front beneath the stage, with only the percussion on the small stage, yet the sound in the middle of the room was clear, very full and very loud.  The reverberation was noticeable but not overly long.    Apart from rust (and thus the need for regular replacement), the only downside of corrugated iron roofs is that nothing else can be heard when it is raining.
Tyalgum lies under the calming shadow of Mount Warning, a mountain named by James Cook in 1770, and which is the first place on the Australian land-mass to see the sun each morning.   We could see the close-by mountain from inside the hall.  So it was fitting, then, that the walls were decorated with several paintings of the mountain.  Oddly, though, all these images showed the mountain from the usual eastern vantage point, yet the village itself is on the western side.   So what you saw on the walls did not match what you saw through the windows.  (For that matter, the same wrong view of the mountain is on the Festival poster and web-page.)
The Band made very good use of the space.  A fanfare by Ann Carr-Boyd was played before the concert from the upstairs front windows to people in the street.  This fanfare was repeated inside at the start of the concert, with the composer present in the audience.   Later, a piece by Gabrieli for three brass choirs was played with the choirs arranged around the hall:  At the front, 5 players in SAT (Soprano, Alto, Tenor) instrumental combination, at the side under the enclosed verandah (ATB) and in the first-floor balcony at the back (SAT).  This was superb use of space for surround sound, and stunning playing.
There were some moments to treasure.   The open side doors allowed a sudden breeze to blow away the music of the tenor trombone during the Vivaldi.    As with any music from this period, intonation was difficult, particularly for the horn player, and at times for the two solo piccolo trumpets.   With lots of fast-moving duo passages (the horn with one or other trombone) – very typical of Vivaldi – creating havoc for the three performers accompanying the soloists, it is perhaps not surprising that one trumpet soloist had a look of absolute astonishment on his face when the players ended the third movement together.
The pieces for the full ensemble were all well played, although perhaps more attention was needed to choreography of the percussionists.   Some of the 5 people who were at one time or another on stage in the percussion section appeared unfamiliar with that part of the band.
The complete program was:

  • Ann Carr-Boyd:  Britannia Fanfare
  • Aaron Copland:  Fanfare for the Common Man
  • Antonio Vivaldi:  Double Trumpet Concerto (arranged for 2 piccolo trumpets, french horn, tenor and bass trombone)
  • Leonard Bernstein:  Excerpts from West Side Story
  • Giovanni Gabrieli:  Canzon Septimi Octavi Toni for 3 brass choirs
  • Henry Purcell:  The Fairy Queen
  • Philip Sparke:  Music of the Spheres.

Some of the same players were seen here.

Bird cries from the mountaintop

Published by peter on 2012-09-10 in Art, Music, Religion and Uncertainty. 0 Comments

When the wild bird cries its melodies from the treetops,
Its voice carries the message of the patriarch.
When the mountain flowers are in bloom,
Their full meaning comes along with their scent.

I have remarked twice before that modern westerners, even very clever ones, fail to understand the nature of synchronicity in Taoist and Zen philosophy when discussing the art of John Cage.  If you believe the universe is subject to invisible underlying forces, as Taoist and Zen adherents may do (and as Cage did), then there is no chance, no randomness, no lack of relationships between events, only a personal inability to perceive such relationships.  The I Ching is intended as a means to reveal some of these hidden connections.
In a recent essay on Silence in the TLS, Paul Griffiths ends with:

Another of Cage’s favourite maxims, this one taken from Ananda Coomaraswamy and delivered five times in Silence, was that the purpose of art is to “imitate nature in her manner of operation”, which is almost another way of stating his first catchphrase, since natural objects and phenomena have nothing to say. They are not, of course, saying it. We say it for them. And in our doing so, experiencing their voicelessness and taking it into ourselves, a great deal comes to be said. There is no message in the changing pattern of cloud shadow and reflected sunlight on the sea. It may, nevertheless, thrill us, calm us, and fix our sustained attention.”

But, of course, for a Zen adherent there are indeed messages in the changing patterns of clouds and in sunlight reflected on the sea.   Even more so are there messages in human artefacts such as musical compositions, even those (perhaps especially those!) using so-called random methods for creation.    For Cage, the particular gamuts (clusters of sounds) that he selected for any particular one of his random compositions were selected as the direct result of the spiritual forces acting on him at that particular moment of selection, through his use of the I Ching, for instance.   Similarly, under this world-view, the same forces are active in those compositions allowing apparently-random leeway to the performers or listeners.
One can criticize or reject this spiritual world-view, but first one has to understand it. Griffiths, like so many others, has failed to understand it.
 

Recent reading 5

Published by peter on 2012-08-01 in Books, Computer Science, Concats, History, Intelligence and Espionage, Music, Politics and Recent Reading. 0 Comments

A list, sometimes annotated, of books recently read:

  • Richard Bassett [2012]: Hitler’s Spy Chief. New York: Pegasus. A biography of Admiral Wilhelm Canaris, head of the Abwehr. This book appears to be a reissue (also revised?) of a book first published in 2005. The subject and argument of the book are fascinating, but sadly this is not matched by the writing, which is just appalling.

    The first problem is with the status of the book. The inside cover pages say “copyright 2011”, and “First Pegasus Books hardcover edition 2012”, yet the Acknowledgements section is dated 2004. Various references to contemporary events throughout the book also indicate a date of writing of around 2003 or so. The front section contains a “Preface to the American Edition” which is undated, but cites letters written in 2008 and 2009. The author’s sloppiness with dates is manifest throughout the book, and it is often very hard for a reader to determine exactly which year events being described actually happened.

    A further great sloppiness concerns the use of names – many people, like citizens of Indonesia, appear only to have surnames. Later references will often find a first name attached to the surname – is this the same person, one wonders? It is as if the author assumes we know as much as he seems to know about minor Nazi officials, and temporary clerks in MI6.

    The book actually reads like the author’s narrative notes for a book rather than the book itself, with much background information missing or assumed to be known by the reader. Is this his first draft perhaps, ready for editing? How could one write on the topic of German foreign intelligence in WW II without discussion of the XX Committee, for example? Admittedly, the author does make one single reference to this operation (on page 280, out of 296 pages of text), but with no explanation of what the committee was doing or an evaluation of its work, and not even a listing in the index. And given the author’s argument that Canaris was an internal opponent of Hitler from before the start of WW II, then an analysis of the alleged success of the XX operations in outwitting Nazi intelligence is surely needed here. Was Canaris complicit in these operations, for example? Especially if, as the author believes, Canaris met with his British opposite number, Sir Stewart Menzies, during WW II.

    And like a person too eager to please, the author’s sentences run on and on and on, with clause after subordinate clause, each introducing a new topic or change or direction, or dropping yet another name, in some drunken word association game. Where were the editors when this book was submitted? On vacation? On strike? Reading the book requires a reader to fight past the author’s appalling prose style to reach the interesting content. Sadly, Admiral Canaris still awaits a good English-language biography.

    The book makes a very strong claim, which is not supported by the citation given by Bassett. On page 167, we read:

    “in Finland where the British forces sent to help the Finns against the Soviets in 1940 were actually assisted in their passage by the Germans. German air and land forces were instructed not to interfere with the progress of these British forces.”

    For this very bold claim, Bassett cites Frederick Winterbotham, The Nazi Connection, p. 164 (London 1978). But Winterbotham’s book seems to have nothing about the Winter War. Finland is not even in the index.

    Basset also cites Winterbotham for a claim that Luftwaffe General Milch visited the Royal Air Force in Britain before the war. However, none of the pages of Winterbotham’s book which mention Milch say this.

  • Dan Raviv and Yossi Melman [2012]:  Spies Against Armageddon:  Inside Israel’s Secret Wars. Levant Books.
  • Milton Bearden and James Risen [2004]: The Main Enemy:  The Insider Story of the CIA’s Final Showdown with the KGB.  Presidio Press.
  • Natalie Dykstra [2012]:  Clover Adams:  A Gilded and Heartbreaking Life.  Houghton Mifflin Harcourt.   An intelligent and sympathetic life of Marian (“Clover”) Hooper Adams (1843-1885), pioneer of art photography, wife of Henry Adams, and a daughter of transcendentalist poet, Ellen Sturgis Hooper.   She was a friend and muse to Henry James, and a distant relative of the step-family of George Santayana.
  • Archie Brown [2010]:  The Rise and Fall of Communism.  Vintage.
  • James Douglass [2008]:   JFK and the Unspeakable:  Why he Died and Why it Matters. Maryknoll, New York: Orbis Books.
  • Sidney Ploss [2009]:  The Roots of Perestroika:  The Soviet Breakdown in Historical Context. McFarland and Company.
  • David Maraniss [2012]:  Barack Obama:  The Story.  Simon and Schuster.
  • Ben MacIntyre [2012]: Double Cross:  The True Story of the D-Day Spies.  London: Bloomsbury. Reviewed here.
  • Colin Eatock [2009]: Mendelssohn and Victorian England.  London: Ashgate.  A detailed and comprehensive account of Mendelssohn’s visits to England (and his one visit to Scotland), and his activities, musical and other, while there.
  • George Dyson [2012]:  Turing’s Cathedral:  The Origins of the Digital Universe.  Allen Lane.   A fascinating account of the involvement of the Institute of Advanced Studies (IAS) in Princeton, NJ, in the early development of scientific computing, led by that larger-than-life character, Johnnie von Neumann.
  • Gordon Brook-Shepherd [1988]: The Storm Birds:  Soviet Post-War Defectors.  Weidenfeld & Nicolson.
  • Neil Sheehan [2010]:  A Fiery Peace in a Cold War:  Bernard Schriever and the Ultimate Weapon. Vintage Books.  A fascinating history of the US inter-continental ballistic missile program in the 1950s, told through a biography of one of its parents, USAF General Bennie Schriever.    It is easy to forget how much practical expertise was needed for successful missile and satellite launches, as with any new and complex technology.   As a consequence, we forget how few of the early test launch attempts were successful.  The Vanguard 3 rocket, for example, launched just 3 satellites out of 11 attempts between December 1957 and September 1959. (Vanguard was a USN project.)

Canopis in Egypt

Published by peter on 2012-06-29 in Concerts and Music. Closed

The Great Egyptian Hall of Mansion House in the City of London was the venue last night for a concert by the Orchestra of the Age of Enlightenment, under Edward Gardner.  The first half saw a performance of Mendelssohn’s E minor violin Concerto by Alina Ibragimova, as well as a Rossini overture.
I discerned nothing Egyptian about the Great Hall.   The decorations include various Greek statues, some in states of undress, large stained glass windows at each end of the room, and miscellaneous pottery. The hall is long and rectangular, two very tall stories high (with a gallery running around the upper story), with nine tall stone columns down each side, and all topped with cylindrical roof.   Apparently, the building is 250 years old this year.
The performers were raised only slightly above the level of the audience, and sitting at one end of the rectangle. There were about 20 rows of seats of 20 seats each, all full, so the room had about 400 people present. The placement of the seats could have been much better than it was: staggering consecutive rows may not look as nice to eyes seeking symmetry, but it allows people not to be sitting directly behind one another, and thus gives the audience a better chance of seeing the performers.  Likewise, allowing room between seats, rather than forcing all seats to touch their neighbours, allows for those of us with normal size bodies to sit beside each other.   Only a small percentage of people – those who were at least 6’6″ and very thin – would have been comfortable with this placement of seats.
Its shape and dimensions mean the Hall probably has very good acoustics for opera, or oratorio, or trumpet concertos, where performers stand facing the audience, projecting sound outwards horizontally.   Similarly, for piano concertos, at least when played on a grand piano with an open lid.  When the orchestra played alone, the sound was loud, full and direct, and was quite clear even at the back.   When the solo violinist began, however, her sound went up, not out, and disappeared into the ceiling, 60-odd-feet above us.   Sadly, the result was perhaps the least satisfying performance of Mendelssohn’s concerto I have ever experienced.   One could tell Ms Ibragimova was very good just by looking at her playing; one could not unfortunately confirm this by listening, as the sound of her instrument was so weak, overwhelmed in those passages where the orchestra played, and only ever a plaintive whisper when playing alone, like a small child trying to speak when surrounded by a party of loud-talking adults.
The third movement struck me as taken a tad too fast, with the orchestra panting to keep up with the violin.  And playing original instruments always means risks, especially for those instruments which have experienced significant technological change these last two centuries.  Thus, we should not be surprised that the horns entered this movement slightly sharp, since intonation was always (and always is) a problem for original horns.   The technological changes of modern instruments were not introduced for no reason, a view lost on those riding the original instruments landau.
In conclusion, a very fine and confident performance of the Mendelssohn concerto for everyone sitting in the first few rows.   For the rest of us, a great performance of the orchestral part, since that is what we could mostly hear.   The careers of artists are not enhanced by performances in halls with poor acoustics.   The acoustics could be improved greatly with the installation of a suitable canopy over the orchestra – a curved ceiling to catch the violinist’s sound and bounce it back out and down toward the audience.     In the meantime, memo to self:  avoid performances of violin concertos in The Great Egyptian Hall of Mansion House.
I notice that Mendelssohn himself, despite his 95 public performances in Britain, does not seem to have ever played in this room (according to the list of his UK performances in Appendix B of Eatock 2009).
UPDATE (2012-08-20):  Apparently the violin sound was fine from the double bass stand.   And presumably the FT’s reviewer was seated near the front, given his praise for the room’s acoustics.  The reviewer for The Arts Desk, in contrast, also had problems with the acoustics of the Hall and too thought the third movement of the concerto was taken too fast for the orchestra: 

The Mansion House acoustic may be fine for annual speeches from the Chancellor of the Exchequer, but it is not a solo violin’s friend.  .  .   .  .  .
We also suffered in the concerto’s finale from a mismatch between orchestra and soloist, which Gardner, for all his alert gestures, seemed powerless to prevent. Mercurial arabesques flew from Ibragimova’s fingers, with the orchestra always a fraction behind, panting to keep up like PC Plod.  Maybe Ibragimova just wanted to get the concerto finished, for there were certainly signs here and there of a lack of interest in what Mendelssohn had to offer.  Most violinists pounce on the finale’s playful opening arpeggios as a chance to wink and scintillate.  Ibragimova left them uninflected.  “Boring, boring,” she seemed to be saying; “Now, where’s my Roslavetz?” “

 
Reference:
Colin T. Eatock [2009]:  Mendelssohn and Victorian England. Farnham, Surrey: Ashgate.

Vale: Graeme Bell

Published by peter on 2012-06-18 in Jazz, Music and Obituaries. 0 Comments

Farewell, Graeme Bell (1914-2012), legendary Australian trad jazz man. His band’s tour of Czechoslovakia in 1947 was still fondly remembered almost four decades later by patrons of JazzKlub Parnas when I first visited Prague in 1984.