A dialog from Nadine Gordimer’s novel, A Guest of Honour (page 222):
‘Why does playing safe always seem to turn out to be so dangerous?’
‘It’s unlucky . . .
. . . because you’re too scared to take a chance.’
‘It’s unlucky to lack courage?’
‘That’s it. You have to go ahead into what’s coming, trust to luck. Because if you play safe you don’t have any, anyway.’
‘It’s forfeited?’
‘Yes.’
Following my recent post on the meaning of life, I recalled Georges Perec’s great novel, Life: A User’s Manual, which I first encountered in a 1987 book review by Paul Auster in the New York Times, here.
If anyone can be called the central character in this shifting, kaleidoscopic work, it would have to be Percival Bartlebooth, an eccentric English millionaire whose insane and useless 50-year project serves as an emblem for the book as a whole. Realizing as a young man that his wealth has doomed him to a life of boredom, Bartlebooth undertakes to study the art of watercolor with Serge Valene for a period of 10 years. Although he has no aptitude whatsoever for painting, he eventually reaches a satisfactory level of competence. Then, in the company of a servant, he sets out on a 20-year voyage around the world with the sole intention of painting watercolors of 500 different harbors and seaports.
As soon as one of these pictures is finished, he sends it to a man in Paris by the name of Gaspard Winckler, who also lives in the building. Winckler is an expert puzzle-maker whom Bartlebooth has hired to turn the watercolors into 750-piece jigsaw puzzles. One by one, the puzzles are made and stored in wooden boxes. When Bartlebooth returns from his travels and settles back into his apartment, he will methodically go about putting the puzzles together in chronological order. By means of an elaborate chemical process, the borders of the puzzle pieces have been glued together in such a way that the seams are no longer visible, thus restoring the watercolor to its original integrity. The painting, good as new, can then be removed from its wooden backing and sent to the place where it was originally executed. There it will be dipped into a detergent solution that eliminates all traces of the painting, yielding a clean and unmarked sheet of paper.
In other words, Bartlebooth will be left with nothing, the same thing he started with.
The idea of wasting the second half of your life trying to make sense of all you did in the first half I have found to be increasingly insightful as I age.
FWIW, Auster’s 1987 review appears to have been plagiarized, without any acknowledgement, in this 1999 post.
Talking of his grandfather who had overcome poverty and blindness to become a US Senator, Gore Vidal once wrote that no challenge is finally insurmountable if you mean to prevail. I was reminded of this in reading Edward Frenkel’s superb memoir, Love and Math. Frenkel overcame the widespread and systemic anti-semitism in Soviet Mathematics to establish himself as a world-leading mathematician at a very young age.
Denied entry in 1984 because of his ethnicity to Moscow State University’s (MGU’s) Department of Mechanics and Mathematics (Mekh-Mat), the leading undergraduate mathematics programme in the USSR, he entered instead the mathematics program at Kerosinka, the Moscow Institute of Oil and Gas. Anti-semitism (and anti-Armenianism, anti-Chinese racism, etc) in the admissions process at Mekh-Mat was so widespread, that other Moscow institutions, such as Kerosinka, were able to recruit very good Jewish and minority students. One theory is that this policy was deliberate, since having all the Jewish mathematicians studying in one or two institutions made their monitoring easier for the KGB.
Frenkel had grown up in Kolomna – only 70 miles from Moscow, but well into the provinces – and had not attended a special mathematics school (as did, for example, Vadim Delone at FizMat #2), nor had an opportunity to participate in the mathematical study circles that were widespread in the larger soviet cities. He did have the help of a local mathematician, Evgeny Petrov, a professor at a teacher training college in Kolomna. Frenkel was very fortunate to have such help. I recall my envy on learning on the first day of lectures in my first year at university that some of my fellow students, who had grown up near to the university, had been meeting our professors for years previously for after-school mentoring and coaching. (On the other hand, even the brightest of my fellow students so mentored ended up winning no Fields Medal, nor even becoming a mathematician.)
Good mathematical undergraduates from Kerosinka and other specialized institutes in Moscow literally scaled the fences at MGU to attend, illegally but often with the encouragement of the teachers, lectures at Mekh-Mat. Frenkel did this and was again fortunate in being befriended by some very great mentors: Dmitry Fuchs (now at UC Davis), his student Boris Feigin, and Yakov Khurgin. Their generous mentoring was unpaid, time-intensive, and often brave, given the society they lived in. As a result, Frenkel wrote his first research paper in only his second year as an undegraduate, a paper subsequently published in Israel Gelfand’s famous journal, Functional Analysis and Applications. Gelfand was someone that even my professors, in the 1970s and in faraway Australia, spoke of with awe.
With the opening of perestroika, the Mathematics Department at Harvard University decided to invite some young Soviet mathematicians for research visits, and Frenkel was one of these: He received his invitation in March 1989, before he had even completed his first degree. While at Harvard, he had another Russian mentor, Vladimir Drinfeld (now at University of Chicago), and Frenkel completed his PhD there, in 1 year, under the supervision of another Russian, Joseph Bernstein (now at Tel-Aviv). Frenkel is very generous in his acknowledgement of the support he received from his mentors and from others, and his story warms the heart. Despite the anti-semitism he experienced, he has prevailed in the end, being now a professor at U-Cal Berkeley (and a film-maker). Reading his account, I was reminded repeatedly of the ancient spiritual wisdom: When the disciple is ready, the guru will appear.
Frenkel interleaves his personal story with an account of his changing research focus along the way, a focus which has mostly followed the powerful thread of the Geometric Langlands Programme. His writing is fluent, wise and witty, and he manages to convey well the excitement and pure, joyous exhilaration that mathematical thinking can provide. His writing makes most of the underlying mathematical ideas clear to non-experts. That said, however, the text has a couple of weaknesses, both minor, although both I found irritating. No one who does not already know something of category theory would understand it, even at a high level, from the single paragraph devoted to it on page 156. Another minor criticism is that the text does not always adequately explain the diagrams, or what is being done with them. But then I have particular views about reasoning over diagrams.
In summary, this is a superb book – wise, generous, witty, and heart-warming – and reading it will enlarge your knowledge of mathematics, of the Langlands Program, and of the power of the human spirit. Everyone in the pure mathematical universe should read it.
An index to posts on the Matherati is here.
Reference:
Edward Frenkel [2013]: Love and Math: The Heart of Hidden Reality. New York, NY: Basic Books.
Gertrude Stein:
One plunges here and there with energy and misdirection during the storm and stress of the making of a personality until at last we reach the twenty-ninth year the straight and narrow gateway of maturity and life which was all uproar and confusion narrows down to form and purpose and we exchange a great dim possibility for a small hard reality.”
Keeping open a great dim possibility, and thus avoiding a narrowing to a small hard reality, is the main purpose of life.
The death has occured of British philosopher and logician Peter Geach (1916-2013).
There is a famous story, perhaps apocryphal, of the logician Alfred Tarski, Polish-born but in American exile from WW II, asking his American City College of New York colleague Emil Post why he, Post, was the only prominent propositional logician who was not Polish. Post replied that he was not born American, but had come to the USA as a child, and had in fact been born in Poland (although at the time part of the Russian empire). It has seemed at times that Poland cornered the market in logicians and we find yet another example in Peter Geach. According to his Guardian obituary, his maternal grandparents were Polish.
Long ago, I wrote an essay, in a logic course taught by Paul Thom and Malcolm Rennie, exploring a system of entailment due to Geach. Then, as now, pure mathematicians mostly disparaged logic, and my university offered no further courses in the discipline that has since become the single most important to artificial intelligence and automated reasoning. Universities are very good at preparing their graduates for the past; for the future, not so much.
The death occurred last month of Natalia Gorbanevskaya (1936-2013, pictured in 1967), Russian poet and Soviet dissident, and one of the Moscow Seven, brave opponents of the occupation by forces of the Warsaw Pact of Czechoslovakia in August 1968. From 1975 she lived in exile, initially in Israel and then in France. For most of this time she was stateless, and did not have a passport until 2006, when granted Polish citizenship. As in the 19th century, Russia disowns its best and brightest children. The Economist has an obituary here.
There was more than this one protest against the invasion, with over 200 people involved in protests elsewhere in the USSR and across the Eastern Bloc. A list of 160 Soviet protesters against the invasion, prepared by Memorial, is here. The courage of the Moscow Seven and these others has been recognized by the Czech Republic, but not yet by the Russian Federation. Indeed, Russia has still to apologize to Czechslovakia for the invasion.
From Gorbanevskaya’s poetry (translation by Daniel Weissbort):
The crime has not yet been expunged,
the hour of truth has not yet struck.
logs in the stove still ticking over,
although the fire’s already out.
The latest in a sequence of lists of recently-read books.
David Eagleman [2010]: Sum: Tales from the Afterlives. (London, UK: Canongate). A superb collection of very short stories, each premised on the assumption that something (our bodies, our souls, our names, our molecules, etc) lives beyond death. Superbly fascinating. One will blow your mind! (HT: WPN).
A. C. Grayling [2013]: Friendship. (New Haven, CT and London, UK: Yale University Press).
Andrew Sullivan [1998]: Love Undetectable: Reflections on Friendship, Sex and Survival. (London, UK: Vintage, 1999).
Michael Blakemore [2013]: Stage Blood. (London, UK: Faber & Faber). A riveting account of Blakemore’s time at the National Theatre in London.
Continue reading ‘Recent Reading 10’
Having created lists of concerts I have attended, bands I have heard, galleries I have visited, etc, I overlooked theatre and dance productions I have seen. Herewith a list, sometimes annotated, to be updated as and when I remember additional events.
Last night, I caught the BBC Symphony Orchestra, under Sakari Oramo, with Olli Mustonen (piano) and Sergei Nakariakov (trumpet), at the Barbican, playing Tristan Murail’s Reflections/Reflets and Shostakovich’s Piano Concerto #1. The Murail work was in two parts, the first (Spleen) a response to Baudelaire’s Les fleurs du mal, oozed sound colours slowly and langorously across the horizon, while the second (High Voltage) involved rapid-fire scales and runs. I liked the first part more than the second. The composer was in the audience.
In the Shostakovich, Nakariakov’s trumpet was superb. I have never heard the sad, muted solo of the second movement played so hauntingly: His tone there was breathtaking, and it was as if the sound was coming from another room, perhaps by some form of ventriloquism (a trumpet ventriloquy?). What came immediately to mind was the similarly sublime green-tinged, luminous moon of Arkhip Kuindzhi’s famous 1881 painting Moonlit Night on the Dniepr (pictured). In contrast, Mustonen’s piano playing was disappointing. His left hand was decidedly softer than the right for most of the piece. At first, I thought this may be an acoustic artefact of where I was sitting (at the front left, almost directly facing the pianist’s back), but when he deployed his left hand loudly I did hear it loudly. The issue is that for much of the work, Shostakovich was writing – as he does so often – in the style of a two-part invention, not a music-hall song with a cantabile solo with uninteresting accompaniment, so the two hands need to play equally loudly so that we hear the parts clearly.
The performance had another, more existential, problem: This concerto is one of the funniest works in the entire orchestral repertoire, and yet last night’s interpretation was intensely serious. Perhaps having in charge two Finns – a nation notoriously dour – overwhelmed the fun in the music. And, I think it would have been better had the pianist not had his back to the trumpeter. The entire work is a sharp-tongued dialogue between the two, particularly the duel at the end, and to hear what is meant to be fast-witted banter played so seriously was disappointing.
I have argued before that I believe few organizations did as much to prevent the Cold War turning into a hot one than the various intelligence agencies, CIA and KGB among them. The reason for this is that each side lacked accurate knowledge of the true beliefs and intentions of the other side, and the intelligence agencies were at the forefront of identifying, calibrating and verifying those beliefs and intentions.
A good example was the series of NATO military exercises in 1983 which the USSR erroneously feared would be a cover for a pre-emptive nuclear strike against them. To preclude that possibility, the Soviet leadership came very close to launching their own pre-emptive nuclear strike. New evidence has come to light about the mis-understandings that each side had about the other, as reported here:
A classified British Joint Intelligence Committee (JIC) report written shortly afterwards recorded the observation from one official that “we cannot discount the possibility that at least some Soviet officials/officers may have misinterpreted Able Archer 83 and possibly other nuclear CPXs [command post exercises] as posing a real threat.” The cabinet secretary at the time, Sir Robert Armstrong, briefed Thatcher that the Soviets’ response did not appear to be an exercise because it “took place over a major Soviet holiday, it had the form of actual military activity and alerts, not just war-gaming, and it was limited geographically to the area, central Europe, covered by the Nato exercise which the Soviet Union was monitoring”.
Armstrong told Thatcher that Moscow’s response “shows the concern of the Soviet Union over a possible Nato surprise attack mounted under cover of exercises”. Much of the intelligence for the briefings to Thatcher, suggesting some in the Kremlin believed that the Able Archer exercise posed a “real threat”, came from the Soviet defector Oleg Gordievsky.
Formerly classified files reveal Thatcher was so alarmed by the briefings that she ordered her officials to “consider what could be done to remove the danger that, by miscalculating western intentions, the Soviet Union would over-react”. She ordered her officials to “urgently consider how to approach the Americans on the question of possible Soviet misapprehensions about a surprise Nato attack”.
Formerly secret documents reveal that, in response, the Foreign Office and Ministry of Defence drafted a joint paper for discussion with the US that proposed “Nato should inform the Soviet Union on a routine basis of proposed Nato exercise activity involving nuclear play”.
I wonder if the UK Government communicated anything to the Soviets about the exercises not being a cover for a surprise attack. And, if so, was their message believed? Of course, as I’ve discussed before, merely telling your enemy something does not mean that they will believe that something, and nor should it. And this is why Governments need subtle, strategic analysis of intelligence, not merely the raw data. The case of Yuri Nosenko is a good example where what the other side believes you believe has consequences, and these consequences need to be considered when deciding what to believe. And for this reason, clever espionage agencies try to ensure the existence of channels of communication to the enemy which the enemy trusts, so that messages sent through the channel are likely to be believed. Perhaps, for example, British intelligence knew that Kim Philby and his Cambridge colleagues were Soviet agents many years before they fled to the USSR.