Archive for the 'Matherati' Category Page 2 of 6



The pure mathematical universe

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.




RIP: Ernest Kaye

While on the subject of Britain’s early lead in computing, I should mention the recent death of Ernest Kaye (1922-2012).  Kaye was the last surviving member of the design team of the LEO computer, the pioneering business and accounting machine developed by the Lyons Tea Shop chain in the early 1950s.  As with jet aircraft, computers were another technological lead gained and squandered by British companies.

Kaye’s Guardian obituary is here.   A post on his LEO colleague John Aris is here.  An index to Vukutu posts on the Matherati is here.




Michael Dummett RIP

The death has just occurred of the philosopher Michael Dummett (1925-2011), formerly Wykeham Professor of Logic at Oxford.    His writings on the philosophy of language and the philosophy of mathematics have influenced me, particularly his thorough book on intuitionism.   Having been educated by pure mathematicians who actively disparaged intuitionist and constructivist ideas, I found it liberating to see these ideas taken seriously and considered carefully.  The precision of Dummett’s writing and thought clearly marked him out as a member of the Matherati, as also his other formal work, such as that on voting procedures.

POSTSCRIPT (2012-01-21):  The logician Graham Priest remembers Dummett as follows:

It is clear that Dummett was one of the most important — perhaps the most important — British philosopher of the last half century. His work on the philosophy of language and metaphysics, inspired by themes in intuitionist logic, was truly groundbreaking. He took intuitionism from a somewhat esoteric doctrine in the philosophy of mathematics to a mainstream philosophical position.

Perhaps his greatest achievement, as far as I am concerned, was to demonstrate beyond doubt the intellectual respectability of a fully-fledged philosophical position based on a contemporary heterodox logic. Philosophers in the United Kingdom, even if they do not subscribe to Dummett’s views, no longer doubt the possibility of this. Dummett had an influence in Australia, too. It was quieter there than in the U.K., but the relevant philosophical lesson was amplified by logicians who endorsed heterodox logics of a different stripe (for which, I think, Dummett had little sympathy). The result has been much the same.

In the United States, though, Dummett had virtually no significant impact. Indeed, I am continually surprised how conservative philosophy in the United States is with regard to heterodox logics. It is still awaiting a Dummett to awaken it from its dogmatic logical slumbers.

Graham Priest, City University of New York Graduate Center, and the University of Melbourne (Australia)

References:

His Guardian obituary is here.  An index to posts about members of the Matherati can be found here.

M. Dummett [1977/2000]: Elements of Intuitionism. (Oxford: Clarendon Press, 1st edition 1977; 2nd edition 2000).




The Matherati: Matthew Piers Watt Boulton

Portrait_Of_Matthew_Piers_Watt_Boulton_by_Sir_Francis_Grant

Matthew Piers Watt Boulton (1820-1894, pictured in portrait by Sir Francis Grant, ca. 1840) was the eldest grandson of the great engineer Matthew Boulton, and was named for James Watt, his grandfather’s partner-in-steam.   He inherited significant wealth and attended Eton and Trinity College, Cambridge, where his first tutor was the mathematician George Peacock (1791-1858), undergraduate friend of Charles Babbage and Alexander d’Arblay.    At Cambridge, Boulton studied mathematics, logic, and classics. He declined to apply for scholarships, despite his evident ability and in the face of entreaties from his tutor and his father, on the grounds that they bred unpleasant competitiveness – perhaps he was someone after my own heart.  It is likely that, for the same reason, he did not sit the Tripos examinations.

 

He was however of strong mathematical bent.  In 1868, he patented a method for lateral control of aircraft in flight, inventing what are now called ailerons.  Being a gentleman of wealth and leisure, he was able to read and write at will, and published translations of classic literature, some poetry, and pamphlets on solar energy, in addition to a work on aircraft stability.   Kinzer (2009) makes a compelling case for him also being the author of several works of philosophy published by someone calling himself “M. P. W. Bolton,” mostly in the 1860s.

Kinzer quotes the following words from Boulton’s paper,  “Has a Metaphysical Society any raison d’etre?”, read to a meeting of the Metaphysical Society, held at the Grosvenor Hotel on 9 April 1874 and chaired by William Gladstone:

There is no question, however apparently non-metaphysical, which may not be pursued till we come to the Metaphysical.  The question of whether Tarquin lived, and whether Lucretia committed suicide, is about as non-metaphysical as any question can be: yet disputants engaged in its discussion may persist till they open up the general question of the credibility of testimony; and this may open that of the credibility of memory, the nature of belief, what grounds we have for believing the existence of other persons, and an external world . . .  Whenever we try to bottom a question or subject, to use Locke’s word (the French word would be “approfondir”) then Metaphysics come in sight  . . . Every sentence involves, in some shape or other, the verb “to be”, and this, if pursued long enough, leads to the heart of Metaphysics  . . . Scientific persons often speak of Metaphysics  with scorn, calling them an Asylum Ignorantiae, useful enough to the vulgar, but in no way needed by themselves.  They imagine their science to be perfectly luminous, far above the lower regions where Metaphysical mists prevail.  But in reality they share the common lot:  the ideas of Force, Law, Cause, Substance, Causal or Active Matter, all dwell in the region of metaphysical twilight, not in the luminous ether. “

 

References:

For some reason, reading the quoted passage brought to mind Richard Dawkins and memes.

I am grateful to Bruce Kinzer for some information here.

There is an index here to posts about members of the Matherati.

Billie Andrew Inman [1991]:  Pater’s Letters at the Pierpont Morgan Library.  English Literature in Transition, 1880-1920, 34 (4):401-417.

Bruce Kinzer [1979]: In search of M.P.W. Bolton. Notes and Queries, n.s., 26 (August 1979): 310-313.

Bruce Kinzer [2009]:  Flying under the radar:  The strange case of Matthew Piers Watt Boulton. Times Literary Supplement, 1 May 2009, pp. 14-15.




Vale Dennis Ritchie (1941-2011)

A post to note the passing on of Dennis Ritchie (1941-2011), co-developer of C programming language and of the Unix operating system.  The Guardian’s obituary is here, a brief note from Wired Magazine here, and John Naughton’s tribute in the Observer here.    So much of modern technology we owe to just a few people, and Ritchie was one of them.

An index to posts about the Matherati is here.




In memoriam: Christophe Bertrand

This post is a memorial to my friend Christophe Bertrand (1981.04.24 – 2010.09.17), a young French composer and pianist who died a year ago this month.   I first heard his chamber work, Treis, at a concert by Manchester-based new music group Ensemble 11 ten years ago.   Impressed by this music, I contacted him and we began a long and deep friendship, discussing his music, along with music and life more generally. 

I had the honour and good fortune to be able to commission some music from him (Quartet #1 and Arashi).   Christophe’s compositions were marked by the use of Fibonacci sequences and other mathematical patterns and constructs, and so I recognized a fellow member of the matherati.  An early death is always sad, especially of someone whose life had had such achievement and even more promise.

Christophe co-founded a contemporary chamber ensemble, Ensemble in Extremis, and there are details of his works and prizes here.  Also, this site seems to have updated information about performances of his music, although without  mentioning his passing on.   The composer Pascal Dusapin has dedicated his work, Microgrammes (2011), 7 pieces for string trio, to Christophe.

I think of all the conversations and interactions we had, and feel the pain of losing future conversations which can now not occur.  And I recall George Santayana’s poem on the death of a close friend, here

Below I list Christophe’s complete works and works in preparation (derived from his former website,  here).   One work listed there, Dall’inferno, Christophe told me he intended to retract from his catalog, after some of the performers found the score too difficult to play.

POSTSCRIPT (2013-05-27):   Someone has uploaded to Youtube a recording of a performance by the Mangalam Trio of Virya along with co-ordinated images of the score.  That is a nice tribute.

POSTSCRIPT 2 (2013-10-31):  The Music of Today series at London’s Royal Festival Hall, curated by Unsuk Chin, held a free concert by players from the Philharmonia Orchestra led by Alejo Perez of Christophe’s works on 31 October 2013.  Works performed were:  Virya, Madrigal, and Yet.   About 100 people were present.  I wondered if anyone else in the audience knew him, and felt his loss.  Here is a review by Sofia Gkiousou, who had not heard Christophe’s music before this concert, and to whom the music spoke.

POSTSCRIPT 3 (2014-01-21):  A concert to remember Christophe was held in Paris last night, with his music performed by his group, Ensemble in Extremis, and Ensemble Court-circuit.   How difficult it must have been for his former colleagues to play his music last night?  But what an honour to do so.  Details here.

 

CHRISTOPHE BERTRAND LIST OF WORKS:

Works in Preparation:

O K H T O R  pour orchestre (15′)
Commande du Mécénat musical Société Générale
Création 11 février 2011
Orchestre Philharmonique de Strasbourg ; dir. Marc ALBRECHT

Q U A T U O R  I I   pour  quatuor à cordes (15′)
Commande du Festival Musica pour le Quatuor ARDITTI
Création au Festival Musica 2011

A R K A  pour soprano, cor, violon et piano (12′)
Texte original de Yannick Haenel
Commande de l’Orchestre National d’Ile-de-France avec le soutien de la SACEM
Ensemble des Musiciens de l’Orchestre National d’Ile-de France ; Françoise KUBLER, soprano
Création mai 2012 – Festival Iles de découvertes

Nouvelle Œuvre pour clarinette, violon et piano (12′)
Commande de l’Ensemble Accorche-Note
Création à définir

 

Completed and acknowledged works:

A y a s (2010) Fanfare pour onze cuivres et percussions (2′)
Commande de l’Orchestre Philharmonique de Strasbourg
A Cristina Rocca
Création mondiale : novembre 2010, Palais de la Musique et des Congrès de Strasbourg – Orchestre Philharmonique de Strasbourg

S c a l e s (2008-2009) pour grand ensemble (20′)
Co-commande de l’Ensemble Intercontemporain et du Concertgebouw d’Amsterdam
A Susanna Mällki et les musiciens de l’Ensemble Intercontemporain
Création mondiale : 24 avril 2010, Concertgebouw d’Amsterdam – Ensemble Intercontemporain, dir. Susanna Mälkki
Première allemande : 9 mai 2010, Philharmonie de Cologne – Ensemble Intercontemporain, dir. Susanna Mälkki

D i a d è m e (2008), pour soprano, clarinette et piano (9′)
Commande de l’Ensemble Accroche-Note
A Frédéric Durieux
Création mondiale : 5 ocotbre 2010, Festival Musica – Françoise Kubler, soprano; Ensemble Accroche-Note

S a t k a (2008), pour flûte, clarinette, violon, violoncelle, percussions et piano (13′)
Commande du Festival d’Aix-en-Provence
A Jean-Dominique Marco
Création mondiale : 11 juillet 2008, Festival d’Aix-en-Provence – Jérémie Siot (vn), Florian Lauridon (vc), Cédric Jullion (fl), Jérôme Comte (cl), Jean-Marie Cottet (pno), François Garnier (pc), Guillaume Bourgogne, direction.
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

H a ï k u (2008) pour piano (6′)
Commande d’Ars Mobilis, pour le festival “Les Solistes aux Serres d’Auteuil”
Création mondiale : 31 août 2008 – Festival des Serres d’Auteuil – Ferenc Vizi (piano)
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

D a l l ‘ i n f e r n o (2008), pour flûte, alto et harpe (9′) (Retracted:  see note above)
Commande du Musée du Louvre
non encore créé
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

A r a s h i (2008), pour alto seul (5′)
Commande de P. Mc Burney
A Peter Mc Burney et Vincent Royer
non encore créé
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

K a m e n a i a (2008), pour douze voix solistes (6′)
Commande de l’Ensemble Musicatreize
A Roland Hayrabedian et l’Ensemble Musicatreize
Création mondiale : 15 mai 2008 – Marseille, Eglise Saint-Charles – Ensemble Musicatreize, dir. Roland HAYRABEDIAN
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

H e n d e k a (2007), pour violon, alto, violoncelle et piano (11′)
Commande du Festival “Les Musicales”
A Bruno Mantovani
Création mondiale : 10 mai 2008 – Colmar, Les Musicales – Ilya Gringolts (vn), Silvia Simionescu (al), Marc Coppey (vc), Claire-Marie Le Guay (pno)
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

V e r t i g o (2006-2007), pour 2 pianos et orchestre (20′)
Commande de l’Etat Français et du Festival Musica
Création mondiale : 20 septembre 2008 – Strasbourg, Festival Musica – Hideki Nagano, Sébastien Vichard (pnos) – Orchestre Philharmonique de Liège, dir. Pascal ROPHÉ
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

S a n h (2006), pour clarinette basse, violoncelle et piano (11′)
Commande de l’Etat Français
A Armand Angster
Création mondiale : 11 octobre 2007 – Strasbourg, Festival Musica / Ensemble Accroche-Note
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

Q u a t u o r (n°1) (2005-2006), pour quatuor à cordes (20′)
Commande du Beethovenfest de Bonn et de M. P. McBurney
Dédié au Quatuor Arditti
Création mondiale : 19 mars 2006 – Bruxelles, Festival Ars Musica – Quatuor Arditti
Création française : 20 juillet 2006 – Festival d’Aix-en-Provence – Quatuor Arditti
Création mondiale de la première version : 24 septembre 2005 – Kunstmuseum Bonn – Mandelring Quartett
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

M a n a (2004-2005), pour grand orchestre (10′)
Commande du Festival de Lucerne
A Pierre Boulez
Création mondiale : 9 septembre 2005 – Lucerne KKL – Lucerne Festival Academy Orchestra, dir. Pierre BOULEZ
Création française : 2 juin 2006 – Orchestre Philharmonique de Radio-France, dir. Hannu LINTU
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

M a d r i g a l (2004-2005), pour soprano et ensemble (11′)
Commande de la Fondation André Boucourechliev
A Françoise Kubler et Armand Angster
Création mondiale : 30 septembre 2005 – Strasbourg, Festival Musica – Ensemble Accroche-Note
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

V i r y a (2004), pour flûte, clarinette en sib (+ clarinette basse), percussions et piano (7′)
Commande de M. Francis Rueff
A Frédéric Kahn
Création mondiale : 19 mars 2004 – Espace 110 Illzach – Ensemble In Extremis
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

A u s (2004), pour alto, saxophone soprano, clarinette en sib (+ clarinette basse) et piano (8′)  
Commande de la Radio de Berlin-Brandeburg
A Philippe Hurel
Création mondiale : 24 janvier 2004 – Berlin, Ultraschall-Festival – Ensemble Intégrales
Enregistrement : CD “European Young generation” par l’Ensemble Intégrales aux éditions Zeitklang (ez-21019)
Pour l’acheter : www.amazon.fr
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

H a o s (2003), pour piano seul (10′)
Commande du Festival Rendez-vous Musique Nouvelle de Forbach
A Laurent Cabasso
Création mondiale : 9 novembre 2003 – Forbach, Festival RVMN – Raoul Jehl, piano
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

I ô a (2003) pour choeur de femmes à huit voix (3′)
A Catherine Bolzinger
Création mondiale : 23 mai 2003 – Strasbourg, Palais du Rhin – Ensemble Vocal Féminin du Conservatoire de Strasbourg, dir. Catherine BOLZINGER
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

Y e t (2002), pour vingt musiciens (10′)  
Commande de l’Ensemble Intercontemporain
A Pascal Dusapin
Création mondiale : 29 septembre 2002 – Strasbourg, Festival Musica – Ensemble Intercontemporain ; dir. Jonathan NOTT
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

E k t r a (2001), pour flûte seule (5′)
A Olivier Class
Création mondiale : 16 juin 2001 – Strasbourg, Cercle européen, Académie des Marches de l’Est – Olivier Class, flûte
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

D i k h a (2000-2001), pour clarinette/clarinette basse et dispositif électronique (9’30)  
Réalisée dans le cadre du cursus de composition et d’informatique musicale de l’IRCAM
A Pierre Dutrieu
Création mondiale : 15 juin 2002 – Paris, Festival Agora, Espace de Projection de l’IRCAM – Pierre Dutrieu, clarinette
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

T r e i s (2000), pour violon, violoncelle et piano (10′)
Mention d’honneur au Festival Gaudeamus 2001/1er Prix Earplay 2002 Donald Aird Memorial Composers Competition
A Rosalie Adolf, Anne-Cécile Litolf et Godefroy Vujicic
Création mondiale : 7 octobre 2000 – Strasbourg, Festival Musica – Rosalie Adolf (vn), Godefroy Vujicic (vc), Anne-Cécile Litolf (pno)
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

L a  C h u t e  D u  R o u g e (2000), pour clarinette, violoncelle, vibraphone et piano (11′)  
A Ivan Fedele
Création mondiale : 11 mai 2000 – Strasbourg, Oratoire du Temple-Neuf – Ensemble du Conservatoire de Strasbourg
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

S k i a ï (1998-1999), pour cinq instruments (8′)
A Pierre-Yves Meugé
Création mondiale : 11 mai 1999 – Strasbourg, Musée de l’Œuvre Notre-Dame – Ensemble du Conservatoire de Strasbourg
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

S t r o f a II (1998), voix de femme, violon et piano (5’30) (Retiré du catalogue)
Création mondiale : 11 mai 2000 – Strasbourg, Oratoire du Temple-Neuf – Ensemble du Conservatoire de Strasbourg
inédit © Christophe BERTRAND

S t r o f a IIb (1998-2000), pour voix de femme, flûte alto (également flûte en ut), et piano (5’30)
Création mondiale : 2 juillet 2000 – Wangen (67), Vieux Freihof – Aline Metzinger (voix), Olivier Class (fl), Christophe Bertrand (pno)
© Edizioni Suvini Zerboni/SugarMusic S.p.A, Milano

Photo credit:  Pascale Srebnicki (2008).




Think again, Helen Vendler, think differently!

Helen Vendler wrote a superb and indispensible commentary on Shakespeare’s Sonnets, deconstructing the poems’ complex and subtle verbal gymnastics and providing a guide to the unmatched mental ingenuity Shakespeare manifests.   As her exegesis clearly shows, Vendler, as well as Shakespeare, is a master of verbal intelligence.   However, she seems to believe that the only intelligence that is, is linguistic.  

In a recent article in Harvard Magazine, Vendler presents a case for primary school education to centre around reading and words, with just a nod to mathematics.    It is good that she included mathematics there somewhere, since I presume she would like her electricity network to keep humming with power, her sewers flushed, her phones connected, her air-travel crash-free, her food and drink and flowers freshly delivered, her weather forecasted, her borders defended, and her online transactions safely encrypted.    None of these, in our modern, technologically-centred world, would be sure to happen if our schools produced only literati.  

But 15 periods per day – 1 of mathematics and 14 for reading – and yet no time for children to draw or paint?  They can look at art and discuss it (periods #7 and #10) but not do it!  How revealing is THAT about Ms Vendler’s opinions of the relative importance of words and images!    And no time in those 15 periods for learning or playing music, apart from group singing?  The only singing allowed in her day is the “choral singing of traditional melodic song (folk songs, country songs, rounds)” ?  Why should traditional melodies be so privileged?   That is like saying that children should only read books written before 1900.   Surely, a person so concerned with words and reading would be delighted if children engaged in rap, that most verbal and linguistically-intellectually-challenging of musics?    This list of activities begins to look merely like an anti-contemporary-world tirade of the sort we have seen before.

Not only does her syllabus have an anti-modern bias, but there is also a bias against other forms of human thinking, such as drawing-as-thought, and music-as-thought.   The philosopher Stephen Toulmin noted the pro-text tendency our culture has evidenced these last four centuries.  While this tendency still dominates us all, we are at last seeing the rise of minority tendencies:  an increasing role for film and video and image in our culture generally; the use of GUIs in devices which interact with humans; the use of graphically-oriented software development tools (so that no longer do all programmers have to be left-brained text manipulators); an attention to design in product development;  and the rise – for the first time since Euclid’s geometry – of a western mathematical discipline where reasoning occurs over diagrams.  

We are just at the beginning at understanding, modeling, systematizing, and using visual thinking and reasoning over diagrams, or musical and sonic reasoning.  We’ve hardly started this effort for the other types of human intelligence we know about:  spatial, kinesthetic, interpersonal, intrapersonal, naturalistic, and existential.   And all the non-human forms of intelligence await even recognition and discovery.   What a great shame if all this rich diversity of intelligent modes of thought were to be squeezed out by a narrow school syllabus favouring just one-and-a-bit types of thinking.  

References:

Helen Vendler [1999]:  The Art of Shakespeare’s Sonnets.  Cambridge, MA: Belknap Press.

Helen Vendler [2011]:  Reading is elemental.  Harvard Magazine, September-October 2011.




The Matherati: Index

The psychologist Howard Gardner identified nine distinct types of human intelligence. It is perhaps not surprising that people with great verbal and linguistic dexterity have long had a word to describe themselves, the Literati. Those of us with mathematical and logical reasoning capabilities I have therefore been calling the Matherati, defined here. I have tried to salute members of this group as I recall or encounter them.

This page lists the people I have currently written about or mentioned, in alpha order:

Alexander d’Arblay, John Aris, John Atkinson, John Bennett, Christophe Bertrand, Matthew Piers Watt Boulton, Joan Burchardt, David Caminer, Boris N. Delone, the Delone family, Nicolas Fatio de Duillier, Michael Dummett, Sean Eberhard, Edward FrenkelMartin Gardner, Kurt Godel, Charles Hamblin, Thomas Harriott, Martin Harvey, Fritz JohnErnest Kaye, Robert May, Robin Milner, Isaac NewtonHenri PoincareMervyn Pragnell, Malcolm Rennie, Dennis Ritchie, Ibn Sina, Adam Spencer, Bella Subbotovskaya, Bill Thurston, Alan Turing, Alexander Yessenin-Volpin.

And lists:

20th-Century Mathematicians.




Connections, south of my days

I have previously posted Judith Wright’s famous poem South of My Days, here.  For anyone growing up in rural eastern Australia, this poem with its stories of the great cattle droves of the late 19th and early 20th century resonates.

The SMH recently carried an obituary for John Atkinson (1940-2011), a mechanical engineering lecturer at Sydney University and member of the Matherati.  Atkinson’s mother, Gwen Wilkins, had been a university friend of Judith Wright (1915-2000) at Sydney University in the 1930s.  Atkinson’s father Tom managed a cattle station in Southern Queensland for Wright’s father, Phillip, and Judith apparently introduced Atkinson’s parents to each other.

This long-ago connection of farming families reminded me of the 50th anniversary commemoration of the Stinson aircrash in the remote and treacherous sub-tropical jungles of the Lamington Ranges National Park in Southern Queensland in February 1937, a commemoration I attended.  The crash was the occasion of a famous rescue by bushman, Bernard O’Reilly, trekking alone on a hunch, recounted on the O’Reilly Guest House site here.  My father, with me that day in 1987, was surprised to encounter a work colleague also present.  It turned out that the O’Reilly family had farmed in the Kanimbla Valley in the Blue Mountains in central NSW, on a property adjoining my father’s colleague’s family property, before moving up to the McPherson Ranges in 1911.  Despite the distance (about 600 miles) and the remoteness of both locations, the two families had kept in touch through the intervening 76 years, with each new generation becoming friends.

O’Reilly wrote a famous book about his pioneering bush experiences and the Stinson rescue.  Among those I met that day were members of the rescue party that O’Reilly gathered together in 1937.

POSTSCRIPT (2011-12-23):  I remembered that Judith Wright wrote a poem about James Westray, who initially survived the Stinson crash, a poem I have posted here.

 

References:

Bernard O’Reilly [1940]:  Green Mountains.  Brisbane, Australia.

The report and documents of the official Queensland Government Inquest into the Stinson crash are here.

A remembrance of John Atkinson by a bush-walking friend is here.  Apparently, Dr Atkinson drowned in the surf.




Australian improv comedy pre-history

My father saw a young Melbourne comedian named Barry Humphries try out an act as an ordinary Moonee Ponds housewife in a Review at the Phillip Street Theatre in Sydney in about 1955.   He and I saw undergraduate mathematician Adam Spencer winning theatre sports improv contests at The Harold Park Hotel in about 1988.   As well as being so witty that I would remember his name all this time, he also still had a full head of blonde hair.