The death has just occurred of Martin Gardner (1914-2010), for 25 years (1956-1981) the writer of the superb Mathematical Games column of Scientific American. I remember eagerly seeking each new copy of SciAm in my local public library to read Gardner’s column each month, and devouring all of his books that I could find. His articles interested me despite my general contempt for games and competitions, and for ad hoc approaches to mathematical reasoning.
Scientific American’s tribute page is here, and here is a just-posted transcript of a February 1979 conversation between Gardner and other mathematicians. This transcript contains a wonderful statement by mathematician Stan Ulam:
In fact, you know, yesterday Ron Graham gave a marvelous, really interesting lecture about some esoteric question; and I was wondering during it, Well, the question sounds very complicated, why devote so much ingenuity? Then I remember what, I think, Fourier or Laplace wrote: That mathematics—one reason for its being—is to defend the honor of the human mind.”
It has been some time since we had any Horace, so here is Ode X from Book II (translated by David West):
You will take a better course, Licinius
if you do not always thrust over the deep sea,
or hug the dangerous coast too close,
shivering at the prospect of squalls.
Whoever loves the Golden Mean
is safe (no squalor for him in a filthy garret),
and temperate (for him no mansion
that men will envy).
The huge pine is more cruelly tossed
by the winds, the loftiest towers
have the heaviest fall and lightning strikes
the tops of mountains.
The heart well prepared hopes in adversity
for a change in fortune, and fears it in prosperity.
Jupiter brings back ugly winters
removes them. If all goes badly now, some day
it will not be so. Sometimes Apollo rouses
the silent Muse with his lyre. He does not always
stretch his bow.
In a difficult strait show spirit
and courage, and when the wind
is too strong at your back, be wise
and shorten the bulging sail.
Horace [1997 AD/23 BCE]: The Complete Odes and Epodes. Translation by David West. Oxford, UK: Oxford University Press.
Previous poems by Horace: Tu ne quaesieris (Ode I: XI) and Vides ut alta (Ode I: IX).
Rory Stewart, new British MP for Penrith and the Border, is not the only accomplished writer to enter the House of Commons in the May 2010 elections. Joining him is fellow Conservative, Zac Goldsmith, an environmentalist journalist and now MP for Richmond Park and North Kingston, and, for Labour, historian Tristam Hunt, now MP for Stoke-on-Trent Central. As surely befits an MP representing The Potteries, Hunt is an historian of Britain’s great industrialisation of the nineteenth century and wrote a superb life of Friedrich Engels.
Given their diverse backgrounds, it would be fascinating to hear Stewart and Hunt debate the legacies of empire on modern Britain, and how their respective constituencies – at opposite extremes of the rural-city divide – can both prosper. Personally, I believe that commercial development of the environmental and energy sector is the only way that manufacturing in the old-world will survive this century, and this is also a sector with the potential to better connect city and country (eg, through the deployment of small-scale power-generating plants). A web-dialog or a joint TV series, anyone?
Tristam Hunt: The Frock-Coated Communist: The Revolutionary Life of Friedrich Engels. (London, UK; Allen Lane). I reviewed this book briefly here.
Previous posts on books and articles by Rory Stewart here, here and here.
This is a belated farewell to Mike Zwerin (1930-2010), jazz trombonist and jazz correspondent for the International Herald Tribune. An American in Paris, he was open in his musical tastes and usually generous in his criticisms; his IHT writings personally sustained many a long journey across far meridians, and helped reinforce the urbane, cosmopolitan, expatriate feel that the IHT had last century (now sadly lost, since the NYT bought out the Washington Post and brought it home to Manhattan). Obits: London Times and The Guardian.
Being a traveling organ recitalist has its own challenges. All pipe and most electric organs are unique. A recitalist needs to practice beforehand on the organ he or she will perform on, to get a feel for the instrument’s capabilities, to know its sounds and colours, and to become familiar with its physical layout. Thus, deciding what music best fits a particular organ and how best to voice that music on that organ requires the organist to spend some time alone with the organ. Organs are one of the last remaining examples in modern Western life of the primacy of the local, the particular, the here-and-now, over the universal and general and eternal (in the analysis of Stephen Toulmin). It is not surprising that the art of improvisation remains alive in organ recitals, alone among current classical music performance practices.
For this reason, American organist Cameron Carpenter tries his best not to decide recital programs in advance of seeing the organ. Last night in Manchester, playing on a large cinema-style organ in the Bridgewater Hall (not the Hall Organ), he gave an outstanding performance of the following works (as best I can recall):
- Bach’s Toccata in F minor (though played in F#)
- One of his own Three Intermezzi for Cinema Organ
- Bach’s Preludes and Fugues from the Well-Tempered Clavier, Book I, in C minor, C# minor and D major
- Schubert’s Erl-King, in Carpenter’s transcription for organ
- Two Chopin Etudes for piano, in Carpenter’s transcription for organ.
- Bach’s Prelude and Fugue for Organ in G major (with an inserted cadenza improvisation, cinema-organ style)
- He ended the concert with two improvisations.
- The audience then recalled him three times for encores, which including a cinema-organ version of Mozart’s Rondo Alla Turk (famous as the usual music for the chase scenes in silent films) and (I think) a Prelude and Fugue by Mendelssohn.
What a wonderful, thought-provoking performance this was! Before the concert even began, Carpenter spent 20 minutes in the lobby, greeting members of the audience as they arrived, something unknown in classical music (at least since Franz Liszt, who, in addition, chatted to the audience between pieces and even while playing). Carpenter’s performances then likewise played masterful havoc with the fusty organ recital tradition! But not arbitrarily – the guy had thought intelligently about the music and knew what he was doing. For instance, in Bach’s proto-minimalist Prelude in C minor (WTC, Book I), the left-hand part was taken by the feet, and the subtle melody which emerges from the leading notes of the right-hand part was played on a different keyboard (and thus with different tone colours) to the notes from which it emerges. Pianists often foreground the leading melody notes while pushing the other right-hand notes into the background; Carpenter did not do this, which I think better matches the minimalist tenor of the music – ie, it is the background here that is really the foreground. His was an intelligent and reflective treatment, and showed an understanding of the ideas in this music. (In case the mention of Bach and minimalism in the same breath surprises you, I think there is a close connection between Minimalism and Pietism, a relationship which deserves its own post.)
Would old JS have liked this treatment of his music? Of course, he would have! The man who imported colorful Italian and French musical styles into the moribund North German church music tradition and wrote a cantata in praise of coffee would surely have loved it. And one only has to listen to Bach’s Piano Concerto in D minor (BWV 1052), with its humorous flourishes and its repeated notes (more minimalism!), to know that this was a man who liked to play the keyboard.
And Carpenter’s delight and enthusiasm at playing the organ was evident throughout. Hands stretched across two, three and even four keyboards, or jumping back and forth between them, along with feet playing 4-note chords or impossible contrapuntal parts (such as the opening voice of the D Major Fugue) or imitating the wild horses in the Erl-King, all showed a man enjoying himself immensely. Even when a technical problem caused one keyboard not to sound, he remained enthusiastic. The hall was only about half full, and all of us who heard him were lucky to have experienced this superb combination of enthusiasm, black-belt technical mastery, and intelligent musicianship. Life has been better ever since!
POSTSCRIPT (2010-08-10): Not everyone shares my enthusiasm for Carpenter’s organ-playing. I note that the writer and reviewers quoted in that review are themselves organists (or the children of), and wonder if Carpenter’s messing with tradition is what really upsets these folk. For some reason I think of Karl Marx’s dictum that tradition comprises the collected errors of past generations.
Cameron Carpenter web-site. Edition Peters page.
Guardian preview here. Pre-concert interview with BBC In Tune here (limited time only).
This post is to mark the passing on of Don Day (1924-2010), former member of the New South Wales Legislative Assembly (the so-called “Bearpit”, roughest of Australia’s 15 parliamentary assemblies) and former NSW Labor Minister. I knew Don when he was my local MLA in the 1970s and 1980s, when he won a seat in what was normally ultra-safe Country Party (now National Party) country – first, the electorate of Casino, and then, Clarence. Indeed, he was for a time the only Labor MLA in the 450 miles of the state north of Newcastle. His win was repeated several times, and his seat was crucial to Neville Wran’s surprise 1-seat majority in May 1976, returning Labor to power in NSW after 11 years in opposition, and after a searing loss in the Federal elections of December 1975.
In his role as Minister for Primary Industries and Decentralisation, Don was instrumental in saving rural industries throughout NSW. Far North Coast dairy farmers were finally allowed to sell milk to Sydney households, for example, breaking the quota system, a protectionist economic racket which favoured only a minority of dairy farmers and which was typical of the crony-capitalist policies of the Country Party. Similarly, his actions saved the NSW sugar industry from closure. NSW Labor’s rural policies were (and still are) better for the majority of people in the bush than those of the bush’s self-proclaimed champions.
Like many Labor representatives of his generation, Don Day had fought during WW II, serving in the RAAF. After the war, he established a small business in Maclean. He was one of the most effective meeting chairmen I have encountered: He would listen carefully and politely to what people were saying, summarize their concerns fairly and dispassionately (even when he was passionate himself on the issues being discussed), and was able to identify quickly the nub of an issue or a way forward in a complex situation. He could usually separate his assessment of an argument from his assessment of the person making it, which helped him be dispassionate. Although The Grafton Daily Examiner has an obit here, I doubt he will be remembered much elsewhere on the web, hence this post.
Update (2010-06-12): SMH obit is here.
Over at Normblog, Norm begins a post with the words:
“Here’s another in that series: religious beliefs vindicated by being redefined to mean something different from what people used to think they meant. We’ve had religion not being about beliefs so much as about practices; . . .”
Well, actually, not quite. Nothing has been redefined, and most people did not previously think the way asserted here. Unless, of course, by “people” Norm means merely, “educated Westerners since the Enlightenment”. But that group constitutes a small (and often blinkered) minority of the world’s human population. For most of the world’s people, for most of human history, religion has indeed been mostly about practices and not about beliefs. I am thinking of Taoism, Buddhism (particularly Zen), large parts of Hinduism, and the mystical strands of Judaism (eg, the Kabbala), of Christianity (eg, the Name-Worshipping of Russian Orthodox believers), and of Islam (eg, Sufism). In the tradition of The People of The Book (Judaism, Christianity and Islam), one hears and accepts The Good News and then engages in religious actions such as worship, prayer, and meditation. In the Eastern tradition, by contrast, it is the repeated doing of certain religious actions (Yoga, Zen sesshin) which may lead the practitioner to Enlightenment, not the other way around. I have argued this before, for example here and here.
That beliefs should or do always precede actions is a peculiarly western and peculiarly modern notion, part of the prevailing paradigm of post-Reformation Western thought. That this fact is hard for many modern westerners to grasp is evidence of the strength of the prevailing paradigm on our thought. However, the strength of a paradigm on the minds of our best and brightest is not itself evidence of the paradigm’s necessity, nor its uniqueness, nor its truth, nor even its comparative usefulness.
Congratulations to Rory Stewart, newly-elected Conservative MP for England’s largest electorate, Penrith and the Border.
I heard Stewart speak in December 2009, shortly after his pre-selection, at a bookshop in Penrith. At the time, he was walking across his prospective constituency as a way to learn about it and to meet people. He was most impressive – intelligent, urbane, witty, sincere, respectful, and also very laid-back. He read from his book on Iraq, and talked about Afghanistan and Iraq, even quoting the poetry of TS Eliot. The audience then had a good debate with him and with each other about do-gooding foreign wars and about the UK-USA relationship. From their comments, I would say about half the audience were probably Labour voters.
Stewart, as good a facilitator as Bill Clinton or Barack Obama, got us all to say who we were and what were our concerns. He did not interrupt anyone, listened attentively and respectfully (even when he disagreed), and remembered everyone’s name and profession; I’m sure he charmed some of the audience there and then into voting for him. When someone said they’d like to vote for him personally, but could not face voting Conservative (calling it “the Work-House Party”), he laughed at the description and said this was a decision they’d have to make for themself. He didn’t even present a case for voting for him personally while ignoring the party label, as most politicians I have known would have done at that point. In fact, he proceeded to give an honest assessment of his own strengths and weaknesses as a candidate – if he was selling himself, this was an extremely soft-sell.
The whole event struck me as remarkable: Here was a modern-day soldier, colonial administrator, and educator of America’s nomenklatura campaigning in rural Cumbria and doing so very explicitly on his Iraq and Afghan experience. And, more surprisingly, people seemed to respond with great passion to his message, with its key theme being that the West needs to understand and accept the limits to its own power to change other societies. It says something about the effect these two wars have had on people in Britain that such a message would have even been listened to seriously in a local campaign, let alone that it would resonate with people.
Some British commentators have compared Stewart to Winston Churchill, who also had had colonial military adventures and had written some damn fine and exciting prose before entering Parliament. I think that other writer and warrior Teddy Roosevelt is a better comparison, as TR appears (from this distance) to have been more respectful of human diversity and difference than was young Winnie. One does not have to be a Conservative to be pleased that a person of Rory Stewart’s intelligence, sophistication, integrity, courage and wisdom should now be in the Mother of Parliaments.
Another account of the same meeting here. My memory is that the dog was not small, as the photographs confirm.
Here is a profile from National Geographic (undated, but before Stewart’s appointment as a Harvard professor).
And here is Ian Parker’s profile in The New Yorker (2010-11-15).
Through his American mother, Winston Churchill knew TR, and once stayed with the Roosevelts in Albany when TR was Governor of New York.
Excerpts from Appendix C (page 164) from Keith . All results assume a 12-tone equal-tempered scale.
Number of diatonic scale classes: 3
Number of note names (A-G); number of notes in a common scale; number of white keys per octave on a piano: 7
Number of scales one note different from the Major scale: 9
Number of notes in the most common equal-tempered scale: 12
Number of common musical keys (C + 1-6 flats/sharps): 13
Number of 7-note diatonic scales (=7 * 3): 21
Number of elementary 2-fold polychords: 23
A k-fold polychord is an n-note chord sub-divided into k non-empty subchords, for k=1, . . ., n. For example, the 6-note chord <C, D, E, F#, G, A> can be subdivided into the 3-note 2-fold polychords, <C, E, G> and <D, F#, A>.
Number of 7-note chords: 66
Number of distinct interval sets (partitions of 12): 77
Number of 7-note triatonic scales (=7*35): 245
Number of notationally-distinct diatonic scales (=13 *21): 273
Number of distinct chord-types (= N(12) – 1): 351
Number of 7-note musical scales (=7*66): 462
Number of scales (=Number of n-note scales, summed over all n) (=2^(12-1) = 2^11): 2048
Number of chords without rotational isomorphism (= 2^12 – 1): 4095
Number of notationally-distinct scales (=13 * 462): 6006
Number of non-syncopated 8-bar 1/4-note rhythmic patterns: 458,330
Number of non-syncopated 8-bar 1/8-note rhythmic patterns: 210,066,388,901
Michael Keith : From Polychords to Polya: Adventures in Musical Combinatorics. (Princeton, NJ: Vinculum Press.)
Inspired by The Guardian column of the same name, I decided to list here my key learnings of the last several years regarding Computer Science and Artificial Intelligence (AI). Few of these are my own insights, and I welcome comments and responses. From arguments I have had, I know that some of these statements are controversial; this fact surprises me, since most of them seem obvious to me. Statements are listed, approximately, from the more general to the more specific.