Speakers’ Corner, Hyde Park, London.
Author Archive for peter
On Friday, I was privileged to see a final dress rehearsal of King’s Shakespeare Company’s production of Measure for Measure. Performed as a cabaret, the production is set in Weimar Germany, and the songs make this a production to remember. They are fast, witty, tuneful and memorable expressions of the interior lives of the main characters, and they add a depth of meaning to a play which is otherwise confusing. It is impressive how much intellectual heft the cabaret setting gives to the play.
The production is directed by Lauren O’Hara, with music by Henry Keynes Carpenter, and the cast includes: Rhia Abbott, Henry Keynes Carpenter, Hannah Elsy, Freddie Fullerton, Serena Grasso, William Holyhead, and Rupert Sadler. The production is only on for five nights, tomorrow Monday 21 July to Friday 25 July 2014, at the Bierkeller in Bristol. Go see it if you are anywhere nearby.
On the categories email list on 5 March 2006, Ronald Brown quoted the following paragraph on mathematical speculation from a 14 June 1983 letter he had received from Alexander Grothendieck:
Your idea of writing a “frantically speculative” article on groupoids seems to me a very good one. It is the kind of thing which has traditionally been lacking in mathematics since the very beginnings, I feel, which is one big drawback in comparison to all other sciences, as far as I know. Of course, no creative mathematician can afford not to ‘speculate’, namely to do more or less daring guesswork as an indispensable source of inspiration. The trouble is that, in obedience to a stern tradition, almost nothing of this appears in writing, and preciously little even in oral communication. The point is that the disrepute of ‘speculation’ or ‘dream’ is such, that even as a strictly private (not to say secret!) activity, it has a tendency to vegetate – much like the desire and drive of love and sex, in too repressive an environment. Despite the ‘repression’, in the one or two years before I unexpectedly was led to withdraw from the mathematical milieu and to stop publishing, it was more or less clear to me that, besides going on pushing ahead with foundational work in SGA and EGA, I was going to write a wholly science-fiction kind [of] book on ‘motives’, which was then the most fascinating and mysterious mathematical being I had come to meet so far. As my interests and my emphasis have somewhat shifted since, I doubt I am ever going to write this book – still less anyone else is going to, presumably. But whatever I am going to write in mathematics, I believe a major part of it will be ‘speculation’ or ‘fiction’, going hand in hand with painstaking, down-to-earth work to get hold of the right kind of notions and structures, to work out comprehensive pictures of still misty landscapes. The notes I am writing up lately are in this spirit, but in this case the landscape isn’t so remote really, and the feeling is rather that, as for the specific program I have been out for is concerned, getting everything straight and clear shouldn’t mean more than a few years work at most for someone who really feels like doing it, maybe less. But of course surprises are bound to turn up on one’s way, and while starting with a few threads in hand, after a while they may have multiplied and become such a bunch that you cannot possibly grasp them all, let alone follow.”
In a subsequent posting (2006-03-14), Brown wrote this about rigour in category theory:
The situation is more complicated in that what could be classed as speculation may get published as theorem and proof. For example, in algebraic topology, sometimes proofs of continuity are omitted as if this was an exercise for the reader, yet the formulation of why the maps are continuous (if they are necessarily so) may contain a key aspect of what should be a complete proof. This difficulty was pointed out to me years ago by Eldon Dyer in relation to results on local fibration implies global fibration (for paracompact spaces) where he and Eilenberg felt Dold’s paper on this contained the first complete proof. I have been unable to complete the proof in Spanier’s book, even the second edition. (I sent a correction to Spanier as the key function in the first edition was not well defined, after Spanier had replied `Isn’t it continuous?’) Eldon speculated (!) that perhaps 50% of published algebraic topology was seriously wrong!
van Kampen’s original 1935 ‘proof’ of what is called his theorem is incomprehensible today, and maybe was then also.
Efforts to give full details of a major result, i.e. to give a proof, are sometimes derided. Of course credit should be given to the originator of the major steps towards a proof.
Grothendieck’s efforts to develop structures and language which would reduce proofs to a sequence of tautologies are notable here. Colin McLarty’s excellent article on “The rising sea: Grothendieck on simplicity and generality” is relevant.
Some scientists snear at the mathematical notion of rigour and of proof. On the other hand many are attracted to math because it can give explanations of why something is true. But ‘explanations’ need a higher level of structural language than for what might be called proofs.
I can’t resist mentioning that one student questionaire on my first year analysis wrote “Professor Brown puts in too many proofs.” So I determined to rectify the situation, and next year there were no theorems, and no proofs. However there were lots of statements labelled ‘FACT” followed by several paragraphs labelled ‘EXPLANATION’. This did modify the course because something labelled ‘explanation’ ought really to explain something! I leave you all to puzzle this out!
In homotopy theory, many matters, such as the homotopy addition lemma, had clear proofs only years after they were well used.
Surely much early algebraic topology is speculative, in that the language has not yet been developed to express concepts with rigour so that a clear proof can be written down. It would be a curious ahistorical assumption that there is not at this date another future level of concepts which require a similar speculative approach to reach towards them.”
Is it because I trained as a pure mathematician that I find this lack of rigor and completeness in what should be caregorial fundamentals immensely disturbing?
From sometime before 1933 right down to the present day, members of my family have had on their walls reproductions of George Lambert’s 1899 Wynne-Prize-winning painting Across the Black Soil Plains, and so this image is part of my cultural heritage. (Image due to AGNSW.)
George Washington Thomas Lambert (1873-1930) was an Australian artist born, after his father had died, in St Petersburg of an American father and English mother. The family emigrated to New South Wales in 1887. In Australia, he is most famous for his painting, Across the Black Soil Plains, now in the Art Gallery of New South Wales, which was based on his time living at Warren, NSW. During WWI, he was an official Australian war artist.
George’s son, Leonard Constant Lambert (1905-1951) was a jazz-age British composer and conductor, and co-founder of Sadler’s Wells dance company.
Constant’s son, Christopher (“Kit”) Sebastian Lambert (1935-1981) was a record producer and manager, and part-creator of rock band, The Who.
The latest in a sequence of lists of recently-read books.
Francis King : A Domestic Animal. Faber Finds, 2014. A well-written account of unrequited love that becomes an obsession. Both the plot and the dialogue are, at times, unbelievable, although the obsession and the emotions it provokes in holder and object are very credible.
Sheila Fitzpatrick : A Spy in the Archives: A Memoir of Cold War Russia. London, UK: I. B. Taurus. This is a very readable account of the author’s travels to the USSR in the 1960s as an historian of the first decade of Soviet power. She seems to have met everyone and known many of them. With such an intriguing story, and such an interesting person recounting it, the major disappointment of this book is that Fitzpatrick tells us so little about herself. We learn the names of some of her partners, but only hapharzardly, and usually with only little context. She seems such a fascinating person, we hunger for more about her life and relationships, to know the whole story. And how could an academic historian publish a memoir with no index? What – or who – is she trying to hide?
Ben Macintyre : A Spy Among Friends: Kim Philby and the Great Betrayal. London, UK: Bloomsbury. This is a well-written and interesting account of spy Kim Philby and his apparent treachery. The only flaw in the book is the author’s omission of the most plausible theory as to why Philby was not unmasked by the British as a Soviet agent for so long: Because he was so unmasked, long before his flight to Moscow, and then used by MI6 (and perhaps also by CIA and its predecessors) as a conduit for passing messages to the KGB that were intended to be believed.
Merely for MI6 to tell the KGB something would almost certainly guarantee that it would not be believed, as is discussed here. So how can MI6 pass messages to their enemy which MI6 want to be believed, for example, messages about western intentions in the face of a nuclear war? The most effective way is for intelligence agents of the KGB, implanted in western agencies, to pass these messages on. The irony in Philby’s case is that the Soviets were never sure about his true loyalties - for how could a double agent so senior remain undetected by the British or Americans for so long? Because of this suspicion, perhaps the messages he delivered were not always readily believed by the Soviets.
Lisa C. Paul : Swimming in the Daylight: An American Student, a Soviet-Jewish Dissident, and the Gift of Hope. New York City: Skyhorse Publishing. This is an account of the friendship between Paul and Inna Meiman, a dissident and refusenik, that began in the 1980s when Paul was an exchange student in Moscow. The story is not without interest, and the depth of their friendship is clearly portrayed. But the book has far too much detail, far too many letters printed in full, far too much of interest only to the two protagonists. The book lacks an index, which means one would have to read it to find the single mention of Vadim Delone (in a footnote on page 88). Throughout, one has the feeling that this is a very personal story, albeit one played against major historical events. But the events, like the footnote on the 1968 Red Square protest against the Warsaw Pact invasion of the CSSR, are mentioned only in passing if at all, as if they were of no interest to the author.
Kai Bird : The Good Spy: The Life and Death of Robert Ames. New York: Crown Publishers. A riveting biography of Ames, who was CIA’s initiator and main contact to radical Arab groups, particularly the PLO. One doesn’t make peace with one’s friends, as the saying goes, so such contacts were vital. They still are. As I have argued before, we cannot accurately predict the actions of our enemies without knowing their beliefs, mindset and worldview, and intentions, and knowing these requires at least sympathy and perhaps great empathy. Demonising people or groups gets in the way of understanding, so CIA is to be admired for having and nurturing people such as Robert Ames.
An excerpt from a 1959 Australian Broadcasting Commission TV programme on the Beats, featuring interviews with Sydney University students, Clive James and Robert Hughes (pictured, image from ABC).
Last week was the 25th anniversary of the violent suppression by the Chinese People’s Liberation Army of the non-violent protest in Tiananmen Square, Beijing, on 4 June 1989. How distant now is that spirit of hope and confidence that existed in the Spring of that year, a spirit slaughtered on the Square?
In the years since, we have learnt that not all the senior leadership of the Chinese Communist Party were among the butchers of Tiananmen. In particular, the brave Zhao Zhiyang (1919-2005), at the time the General-Secretary of the Central Committee of the CCP, opposed the action and suffered politically and personally for his views. It seems that Zhao was not alone. A New York Times investigation reports that Major-General Xu Qinxian, leader of the 38th Group Army, refused to execute an order to participate in the action, a refusal for which he was court-martialed, imprisoned, and expelled from the CCP. Other military officers, possibly including the Defence Minister himself, Qin Jiwei (1914-1997), also opposed the action and/or refused to shoot civilians.
By this post, I wish to remember all those who struggled for freedom and democracy across China that spring, and especially all those who died in that struggle. Those, like Zhao and Xu, who bravely refused to join the action are also remembered.
A Luta Continua!
It is hard to see how Catholicism can survive in Ireland, given that the Church seems to have been involved in maltreatment, starvation, and mass burial of innocent children in septic tanks, and within living memory. Who could belong to such an organization? The church apologists have already started arguing that we should not judge the past with the criteria of the present, but when was it ever morally acceptable to murder children? Like the Communist Party of the USSR, the Roman Catholic church in Ireland was a criminal conspiracy that captured the State, and as with the CPSU, it needs to be outlawed. Only by closing down the whole shebang and starting afresh can any moral worth be retrieved from this evil, shameful, despicable organization.
Kriegsspiel 1914: A war game re-enactment of the battles between German and Allied (French, Belgian, BEF) forces on the Western Front between late August and late September 1914, organized by Philip Sabin of the War Studies Department at King’s College London. Our team comprised Evan Sterling, Nicholas Reynolds and myself, and played as Germany. We beat the Allies, capturing more territory than Germany had captured in actuality in 1914. In other words, we not only beat the Allies, we beat History.
The photo shows the final placement of German forces (black boxes) after 6 rounds of fighting, with the yellow boxes showing territory held by Germany. Cells without yellow boxes are held by the Allies. This was immense fun. (Photo credit: Nicholas Reynolds.)