The Matherati: Matthew Piers Watt Boulton

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.

Christopher Hitchens RIP

I have long been annoyed by the abuse of power that media organizations – even noble and high-minded ones – are prone to engage in.  Newspapers, for example, often run obituaries of people who work for them in support roles, such as their administrative and printing staff.  However virtuous or locally-influential such lives may have been, these people were not public figures, and it strikes me as a mis-use of media power for them to be given prominent public obituaries merely because they happened to have worked for an organization that prints such obituaries.  Until it introduced a section of its obits page for readers’ own accounts of the lives of recently-departed ordinary people, The Guardian, for example, was a key offender in this, with all manner of obscure back-office staff being given national obituaries.   Is this newspaper just an in-house magazine for its employees?
The death of Christopher Hitchens has allowed The Grauniad to fall back on its old ways, with pages and pages devoted to Hitchens and all his works – a seeming HitchFest – as if his death were a major world event.  Vaclav Havel,  who died shortly afterwards, received fewer column inches, yet demonstrably had a greater impact on the world.    I expect that The Guardian has given so many pages to Hitch because he seems to have been known to and had great influence on other journalists, and because it can.  That latter reason, it seems to me, is a mis-use of their power;  it is also something Hitchens himself would have objected to.
Bloggers have also devoted much attention to his passing on.   I have no problem with this, as blogging does not pretend to be a public service activity.   Although I have tried over the years to read most everything Hitchens ever published, usually with great enjoyment, I have hesitated at his passing on to write about my reactions to his work and life.     I never knew him (although I know people who did) so I will not comment on his personality or his personal life.    As a writer, he was an extremely elegant and well-turned stylist, and always provocative to thinking.   His invective, even when I disagreed with it or its targets, was always finely-honed and often very amusing.  I will miss reading him immensely.
I had several major disagreements with his views (at least as far I knew them from his writings).  Firstly,  someone who could join a Trotskyist political groupoid had to have very poor political judgement. (The same could be said for that other early-Trotskyist, late-onset neocon, Norman Geras.). The people in these groups in the 1960s and 1970s were in general in my experience not pleasant, not rational, not open to reason, and not realistic about what works in the world.  And  each group was not unlike a cult.   They were often very elitist, believing they could see the future which the rest of us dummies could not;  and few of the Trotskyists I have encountered in my life had any empathy for working people.   I can only see membership of such a groupoid as evidence of gross mis-understanding about the world, of how it is, and of what it may become.  Of course, we all lack understanding of the world when we are young, and some of us gain our wisdom faster than others.
Secondly, for all his internationalism, Hitch never “got” Barack Obama.  I read his writings in the US Presidential campaign of 2007-2008, and subsequently, and mis-understanding and mis-construals were evident throughout.  Sometimes I thought his mis-readings were deliberate and wilful (as in his accusation that Obama was  not a sincere religious believer), while at other times he was simply mistaken.   From the very first time I heard Obama speak (in 2004), I knew him immediately.  He reminded me of scores of dedicated foreign aid workers I know from Africa and Asia:  “We are the ones we have been waiting for“, “Yes, we can“, etc.  This is the language of community empowerment, of working-with not working-through people, of helping the poor and downtrodden through empathy from a position at their level, not condescending to them from a position at some level above or outside them.    Tim Geithner, with his superb social-parsing skills,  is, it seems, another  person in the same mould.
Hitchens apparently thought such statements by Obama vacuous.  Why would Hitchens – an internationalist – not also understand this about Obama, I wondered?  Hitchens had traveled a great deal, and often to nasty places, but as far as I know he never lived in any such place for any time.   He had not ever had to negotiate a foreign culture over the long term, except that of the USA, which is certainly different to Britain, but not so different as Indonesia, say, or Kenya.   And perhaps Marxism, with its impersonal theory of history across all time, and Trotskyism, with its belief in global revolution across all space, together make it hard to see the impacts of specific cultures, histories and societies – in the here and in the now – on the lives of people, and on their political possibilities, and on what actions are needed to change these lives and possibilities.  And, for the same reason, perhaps a person focused on dialectical analysis of grand theories of global history simply cannot easily understand someone seeking to improve the lot of a single group of people in one housing estate in Chicago, a community organizer say.  This far from the Bolshevik Revolution, it is easy to forget that many on the left (and particularly Trotskyists) disparaged acting locally, to the point where small-scale actions even received their own term of socialist invective: ameliorism.
And, finally, Hitchens seemed to not fully understand religion.  I was with him all the way in his criticism of the evils and sins committed by organized religion, and  in its name.   I was also with him in his refusal to bow down:  Any God that required our worship is not worthy of it.  Certainly no believer in the universal rights of man would countenance such feudal fealty.   Too, I was with him in his courageous refusal to run scared, to adopt religion as a crutch or consolation, as a candle for the dark nights of life.   But, even after all these aspects are considered, there remain other reasons for human religious or spiritual impulses, reasons which are good and valid and true.   Despite what Norm thinks, one may be drawn to sights unseen without any prior beliefs and without any desire to worship deities, but merely with a desire – often unexpressed or even unexpressable – to experience contact with elements of the non-material.   Such a desire motivates many mathematicians and musicians and artists, in addition to explaining the mystic strain evident in most religions.    Is there a non-material realm, outside the world of our five senses?  An entire branch of contemporary physics – String theory and M-theory – is posited on there being such a realm, comprising further dimensions of space-time inaccessible to us, despite the absence yet of any inter-subjective and replicable scientific evidence for it.    Do non-material or spiritual entities exist?   To me, that question is the same as:  Do mathematical objects exist?   On this aspect of religion, Hitchens (from his writings) seemed completely tone-deaf, just as if he lacked  the sense of hearing, or sight.
But, as I said, I will miss reading him immensely.
 
POSTSCRIPT (2012-01-14):  The Times Literary Supplement of 6 January 2012 publishes a letter by Mary Kenny which criticizes Hitchen’s simple-minded, black-and-white approach to religion, in regard in particular to his reporting on the Irish divorce referendum of 1995.    As she says,   “Yet a good journalist, let alone a great journalist –  as Michael Dirda (also December 23 & 30, 2011) claims Hitchens to have been  – would not  have scribbled off such a slapdash and superficial polemic:  a journalist in the tradition of Geroge Orwell would have examined such a social juncture in all its many nuances.”  The polemic by Hitchens that Kenny refers to is in his book, God is Not Great.
 
Footnote:
Andrew Sullivan’s tributes here, and links to Normblog’s and other tributes here.

Poem: The Lost Man

Judith Wright’s poem, The Lost Man, was written about James Guthrie Westray, a survivor of the crash of the Stinson in the McPherson ranges of SE Queensland in 1937, who died after falling over a waterfall when hacking through the jungle to seek help.   The “gold bird dancing” refers to the aircraft, although the poem may also be read as a description of our journey through life.  The religious allusions, including the pun in the last line, are immensely powerful. This poem has been set to music by Ross Edwards.

The Lost Man
To reach the pool you must go through the rain-forest –
through the bewildering midsummer of darkness
lit with ancient fern,
laced with poison and thorn.
You must go by the way he went – the way of the bleeding
hands and feet, the blood on the stones like flowers,
under the hooded flowers
that fall on the stones like blood.
To reach the pool you must go by the black valley
among the crowded columns made of silence,
under the hanging clouds
of leaves and voiceless birds.
To go by the way he went to the voice of the water,
where the priest stinging-tree waits with his whips and fevers
under the hooded flowers
that fall from the trees like blood,
you must forget the song of the gold bird dancing
over tossed light; you must remember nothing
except the drag of darkness
that draws your weakness under.
To go by the way he went, you must find beneath you
that last and faceless pool, and fall.  And falling
find between breath and death
the sun by which you live.

 
Photo:   A pool on the Stinson Walk, Lamington Ranges National Park, Queensland.  Credit:  Life Cycle.

Havel na Hrad!

A memorial salute to Vaclav Havel (1936-2011), who died yesterday.  I first read his Letters to Olga in the 1980s, and have found this and his other writings inspiring.  Havel’s life, too, reads like one of his own plays, and I long admired his courage, his profound self-awareness, and his integrity-of-purpose.

In one of his memoirs, Havel mentions the trepidation which Mikhail Gorbachev apparently felt prior to their first meeting, a meeting that took place in Moscow in 1990 shortly after Havel’s assumption of the Presidency of Czechoslovakia in December 1989, and immediately following Havel’s first official trip to the USA.  Gorbachev, a victim like any other citizen of Soviet misinformation and propaganda, it seems had never met a genuine dissident before and feared what Havel would say or do in the meeting, perhaps even fearing that Havel would attack him physically.
This anecdote came to mind today while reading a surreal account (Chodakiewicz 2011) of the fall of communism in Eastern Europe and the USSR, which claims the entire process of political transformation 20 years ago there was engineered by the Russian Communist nomenklatura as a grand, multi-national, multi-party, multi-year, multi-political-party conspiracy to remain in power.   Among Chodakiewicz’s offensive absurdities is to claim that the leadership of the Polish United Workers Party (the Polish communist party) was second only to that of Bulgaria in its servility to Moscow in the post-war period.   One wonders just why, then, did Poland experience no Stalinist show-trials in the early 1950s?  Why then was Wladyslaw Gomulka arrested, stripped of his posts and detained for several years in the same period, without being interrogated or tried or punished or executed (as were, say, his equivalent colleagues in Hungary and Czechoslovakia) and then later restored to a leadership position?  Was this, too, a charade that was part of the grand conspiracy?    How could such evident nonsense be published in a reputable refereed journal?
Footnote (2011-12-26):
In an interview with David Remnick of The New Yorker (2003), Havel says regarding his first meeting with Gorbachev (in which the two negotiated the withdrawal of Soviet armed forces from Czechoslovakia):

I met Gorbachev about two months after I was elected President.  We went to Moscow, for my first visit to the Kremlin, and we met for eight or nine hours.  At first, Gorbachev looked at me as if I was some kind of exotic creature – the first living dissident he ever saw, who was coming to him as the head of a state that had been part of his realm.  But, gradually, we developed a kind of friendship, which had even begun to develop at the end of that first long visit to the Kremlin.”   

References:
Guardian obituary here, and Economist tribute here.  The Economist claims that Charter 77 was the “first open manifestation of dissent inside the Soviet empire”.  That claim rather ignores the various uprisings going back at least to 1953 (in the DDR), in Hungary in 1956, in Poland on numerous occasions, and even in Moscow – the public protest by the Moscow Seven in August 1968 against the Warsaw Pact invasion of Czechoslovakia, which was indeed, one of several protests in the USSR and elsewhere in the Eastern Bloc.
A salute to another Czech hero here, along with a note on the leninist nature of Gorbachev’s reforms.   And here a tribute to the Moscow Seven.
Marek Jan Chodakiewicz [2011]: Active measures gone awry:  Transformation in Central and Eastern Europe, 1989-1992.  International Journal of Intelligence and Counter-Intelligence, 24 (3): 467-493.
David Remnick [2003]:  Exit Havel.  The New Yorker, 17 February 2003.

Moscow Soloists in London

This past week I attended a concert in the Cadogan Hall by the Moscow Soloists String Chamber Ensemble, led by violist Yuri Bashmet.  The concert seems to have attracted many in London’s large Russian-speaking community, and there were idling limousines outside the Hall.

Although technically the playing was very proficient, the concert and the performance left me disappointed.  First, everyone on stage was dressed entirely in black, even the soloists.   Was this a convention of undertakers, I wondered? Second, almost nobody smiled, again not even many of the soloists. Why so glum? Third, a grand Steinway was used for the first concerto, and then remained stuck there on stage, like some silent, brooding animal.   All the movements of furniture between pieces was done by several of the ensemble members, rather than by the Hall staff, and it is true that the piano was moved a few inches.  But not out of the way, nor offstage.   It therefore blocked the sound (and the view) of the ensemble, and meant that the sound we in the audience heard was not projected uniformly to us.   Where I was sitting on the right-hand side of the hall I heard the two cellos and the lone double bass well, but not the violins, who were hidden by the piano.    I regard this failure to move the piano out of the way as unprofessional, although who was to blame for it is not clear.  Surely, the Hall staff should have moved it aside.

And the glumness!  The first item played was Bach’s Keyboard Concerto in D minor (BWV 1052) with soloist Ksenia Bashmet.  Her playing was technically excellent, although not from memory.   But the music was played with such po-faced seriousness, and without any apparent emotion.   This concerto is one of the great humorous compositions of all time, perhaps the greatest before Shostakovich’s Piano and Trumpet Concerto.  A few minutes with the score would tell you the composer was having fun as he wrote it, since it is filled with adornments and flourishes, completely unnecessary and joyful in the extreme, which feel exactly right under the fingers.   This is music written by someone who really liked playing a keyboard.   Moreover, the first movement has a rondo form, with the first theme returning and returning and returning, as if without end.   There is even a solo cadenza, which would traditionally be placed near the end of the movement, which here comes in the middle;  so even after we hear the cadenza, the movement still does not end.   This is Bach having fun.   But where was the fun or the joy from these performers?   Perhaps the fact that Ms Bashmet was not playing the music from memory meant she had had not yet internalized the score sufficiently to allow herself to have free reign with its interpretation.  This performance was not a patch on the last time I heard this concerto played – by Joanna MacGregor in Cottonopolis, a few years ago, whose physical joy at the music was evident from from the get-go.

Similarly, for Mendelssohn’s D Minor Violin Concerto, played by Alena Baeva.   Again the playing here was technically excellent, although also not from memory.   However, only in the third movement did we hear some emotion – at last, some passion and joy from the soloist in what is a very joyful movement.   The earlier movements were played, in contrast, without great passion, although very well.

The two middle soloists in the first half, Dinara Alieva (soprano) and Alexander Buzlov (cello), did smile at us after their performances, but their chosen music was less intellectually enriching.  Buzlov played a theme and variations by Rossini, something the audience seemed to like more than anything else they heard, but which I found superficial in comparison with the Bach or Mendelssohn.  I did  not stay for the second half, the concert already running too long.

Overall, I believe these performers were technically very proficient as musical performers, but not superb as communicators of musical ideas;  sadly, they did not achieve their potential on this occasion, and seemed to lack any group spark or chemistry.  Perhaps this was due to the presence of the brooding piano, obstructing complete interaction with the audience, or perhaps there were other reasons.  Oddly, the ensemble did not tune up on stage at the start of the concert:  I wonder if this explained the lack of social chemistry evident.

References:
Here is a review of the concert by Hugo Shirley of The Telegraph, who likewise noticed an absence of passion.

Ein Deutsche Hamlet

Earlier this month, I caught Schaubuhne Berlin’s Hamlet at the Barbican London.  What an amazing ride!  This was Hamlet as a comedy – contemporary, knowing, witty, and alive.   I imagine the experience is the closest we could come to a modern version of the experience that Shakespeare’s own audience would have had.  The play was presented in German (mostly), with English surtitles.

The performance began with the words from Hamlet’s most famous soliloquy, ending with “and perchance to dream”.  Was all that followed, then, a dream?   We were confronted with grainy, silent black and white images of people in dark formal dress, like newsreels of pre-war Eastern Europeans.  Again, was this a deliberate allusion, perhaps a reminder of the last time we all were happy innocents prior to a great crime.   Only after some time did we realize that the film we were seeing was not some collection of past newsreels, but live shots of the actors at the back of the stage, taken by young Hamlet wielding a hand-held video camera.

The first scene of the play then was the burial of old Hamlet, with lots of theatrical dirt and hose-pipe rain.    The dirt and often the rain were present throughout the performance, like some muck that stuck to everyone regardless of how often they cleaned it off.  The funeral degenerated into farce, and then the real fun began: the wedding of Claudius and Gertrude was presented as a typical Balkan wedding, with kitschy music, belly dancing, drunken announcers, and even  –  a very funny touch of realism here – someone firing off a machine gun. We learn this was Laertes!

Much of the humour, in the German theatrical tradition perhaps, was slapstick and not to my taste.  Why did Hamlet have to wear a fatsuit, for example?   Some of the humour, however, was witty and clever.  Three times the actors turned to the audience, the house lights going up, and we then became part of the action.  The best of these times was during the late soliloquy of Claudius (Act 3, scene 3) – when he seems to confess:  “O my offence is rank, it smells to Heaven.”  Claudius played this scene as an episode of a Jerry Springer show, coming down as the compere into the audience to ask our opinions of the offence.

Several times, too, the actors pretended to lose their place or forget their words (in German), so looked up to the English surtitles to see what they should be saying next.  Similarly, great fun was had when the court was informed that Hamlet intended to stage a play.  Well, Claudius was informed, not so much a play as a theatre-piece (“theaterstuck”); Claudius repeated this word with all the disdain one can imagine a man of his age and class having for avant-garde theatre.  This was very funny.   Even the final death scene, although mostly serious, was played for laughs, with all us knowing that it was an act and not for real.

Because the cast was small (six actors), there was much doubling.   A different coloured wig transformed Gertrude to Ophelia, and the transformation of the actress, Judith Rosmair, from a middle-aged, Jacqueline Kennedy-lookalike  to teenage girl was immensely convincing.  Her voice, her words, her stance, her mannerisms, her movements – all changed, and instantly.  And how clever to allude to Mrs Kennedy-Onassis when portraying Gertrude!  Hamlet was played by Lars Eidinger.

This was “Hamlet” done brilliantly, original and thought-provoking.   And immensely funny.   Superb!
Any earlier review of the Berlin production is here.  And a Liverpudlian blog devoted to Hamlet is here.

(HT: Benjamin Leitch.)

Balmain boys don't cry

One of my great-great-great-grandfathers, William Graham Peverley (1811 – 1893), established a ship-building business in East Balmain, Sydney, in 1853 or 1854.    The location was east of St Mary’s Street and south of Pearsons Wharf,  an area which is nowadays a harbourside park, Illoura Reserve.  The suburb of Balmain had been named for Dr William Balmain (1762-1803), a surgeon with the First Fleet, and later Principal Surgeon in the colony of New South Wales, who was first to be granted land on the peninsula.   They have always bred them tough there – the saying is: Balmain boys don’t cry.  Among the residents have been two Premiers of NSW, Sir Henry Parkes and Neville Wran, neither someone to mess with.  And the State MLA for Balmain in recent times was the very tough Dawn Fraser, Olympic swimmer and publican, elected as an Independent.

It therefore felt like a chance meeting of a long-disappeared friend to enter the Church of St Giles-in-the-Fields in London’s West End this week, and discover it had been Dr Balmain’s home church upon his return to Britain in 1802.   At the back of the church is a plaque erected by The Balmain Association.   The church was the venue for a performance of Handel’s Messiah, by Solistes de Musique Ancienne and Siglo de Oro, under the direction of  the latter’s founder, Patrick Allies.   This was the second time I have  seen SMA perform, having heard their superb Sloane Square concert earlier in the year.   This time they had an audience of about 50 people, perhaps one quarter of the church’s capacity.

Despite the empty seats, the acoustics of this church were much better than that of Holy Trinity Sloane Square, and the performance was just superb.    St. Giles has two long parallel first-floor balconies, each about 1/4 of the width of the building, running the length of the church, and these two overhangs, together with their supporting columns and multiply-surfaced stone decorations, created strong reverberation, with a medium-duration delay.  The result was to make the choir and orchestra sound at least 5 times their size, filling the space with sound.   Even sitting at the back of the church, the sound was both warm and clear, something rare in churches, whose acoustics usually make concert performances sound either fuzzy or cold.   As with their previous concert, SMA made use of the space, having two of the trumpeters in Part I play from the left balcony.

This was one of the greatest Messiahs I have ever heard.  All the vocal soloists were excellent, and projected well.  Similarly, we could hear well the instrumental soloists (which was not the case in the earlier SMA concert).   Unfortunately, the program notes did not list the names of the soloists specifically; I was only able to infer the name of one vocal soloist, William Morrison, who’s aria in Part I was extremely clear and very moving.  Joel Newsome’s trumpet solo, on an instrument with cylindrical valves, on “The trumpet shall sound” in Part III, was also very powerful.    I left the church uplifted and inspired.

I had not known before reading the program notes that Handel’s librettist for The Messiah, Charles Jennens (1700-1773), was a supporter of the Stuarts, and that his words for the oratorio – people in darkness awaiting a redeemer who returns in triumph and glory, etc – could be taken as political commentary on the Hanoverians, even as late as this (1741).

A very different experience last night, in another London church, St. Sepulchre-without-Newgate.  This was a performance of (excerpts from) Bach’s Christmas Oratorio and his Mass in B Minor, by the Medici Choir and the Brandenburg Baroque Soloists.  The church this time was overflowing, with perhaps 250 people seated and more standing at the back.    The acoustics of this church with its much higher ceiling and absence of balconies was very different to that of St. Giles.  The performers were not raised above the audience, and their sound disappeared upwards; it seemed not to come back to us.

Sitting behind a column meant I head some sounds with clarity — those of the choristers I could see — while  other singers and the orchestra were fuzzy.   For the most part, the soloists sang without projecting their voices.  At first, I thought this was due to the acoustics, but on occasion the soloists did project, and the difference was noticeable.   Why would a professional opera singer, as these soloists were, not project, I wonder?  Why not seek to fill the space one is performing in?  The lady who sang “Schlafe, mein Liebster” in the Oratorio, was particularly disappointing, filling powerfully the ears of the lucky people in the first row, it seemed, and no one else.   Those of us at the back of the church could barely hear her.   Was this due to some silly authentic-performance notion or a Lutheran disdain for aural spectacle, perhaps?

I suspect some silly notion at play.   Bach’s music in the Mass was “improved” by the addition of a new section composed by director John Baird for this concert.  One has to admire the self-confidence of someone willing to try to complete what Bach did not himself finish.  However, the real absurdity for me, and evidence of a lack of musical seriousness, was to end the concert with the congregational singing of Christmas carols:  rather than leaving with the sound of Bach in one’s ears, instead it would be, “We wish you a merry Christmas”.  It was important for me that my ears and mind be not so corrupted, so I left before the end.   What a contrast in integrity of musical purpose between these two concerts!  And how great again were the Solistes de Musique Ancienne and Siglo de Oro.

Digital dumbing down

Despite being all the rage, touchscreens have never impressed me.   I did not put my finger (metaphor chosen deliberately) on the reasons why until reading Edward Tufte’s criticism:  they have no hand!  They lack tactility, and of all the many possible diverse, sophisticated, subtle, and complex motions that our hands and fingers are capable of, touchscreens seem designed to accommodate just two very simple motions:  tapping and sliding.   Not something to write home about when you wake up each morning eager to digitally percuss, or have hands able  to think.    Bret Victor has a nice graphically-supported argument about the lack of embodiment of touchscreens in the world of those of us with opposable thumbs, here.  As Victor says:

Are we really going to accept an Interface Of The Future that is less expressive than a sandwich?

A brief history of mathematics

Australian category-theorist Ross Street has an elegant, one-page summary of the first 2,500 years of western mathematics, here.  This was apparently a handout given in a talk to the Macquarie University Philosophy Students Society in 1984.  I found Street’s high-level view of what (some important) mathematicians have (mostly) been doing illuminating and thought-provoking, and so I reproduce it here.
A nice way to think about topoi, of course, is that due to Rob Goldblatt:  a topos is the most general object that has all the properties of the category of sets.
 

Space, Sets and Beyond
First Cycle:  General spaces advance the study of naive geometry
1. Naive geometry:  Zeno, Eudoxus.
2. Axiomatic geometry (unique model intended): Euclid, Apollonius (c. 300-200 BC).
3. Algebraic techniques (coordinate geometry): Descartes 1596-1650.
4. Non-Euclidean geometry (independence of the “parallels axiom”:  models without parallels axiom constructed from a model with it):  Gauss, Bolyai, Lobatchewski (early 19C).
5. Locally Euclidean spaces:  Riemann 1826-1866, Lie.
6. Relationships between spaces (continuity, linearity): Cauchy, Cayley, Weierstrass, Dedekind (1880-present).
 
Second Cycle:  Toposes can be viewed as even more general spaces
1. Naive set theory: Peano, Cantor (c. 1900).
2. Axiomatic set theory (unique model intended): Hilbert, Godel, Bernays, Zermelo, Zorn, Fraenkel.
3. Abstract algebra (mathematical logic): Boole, Poincare, Hilbert, Heyting, Brouwer, Noether, Church, Turing.
4. Non-standard set theories (independence of the “axiom of choice” and “continuum hypothesis”; Boolean-valued models; non-standard analysis): Godel, Cohen, Robinson (1920-1950).
5. Local set theory (sheaves): Leray, Serre, Grothendieck, Lawvere, Tierney (1945-1970).
6. Relationships between toposes (a “topos” is a generalized set theory): 1970-present.