Interesting books

In an effort to understand a bit about India I have been reading some books (somewhat like imagining that one is travelling by reading travel books). Here ia a partial list of books which I found interesting that I have read or have been browsing through recently. Just finished reading Bernard Cohn's "India: The Social Anthropology of a Civilization", "Colonialism and its Forms of Knowledge", Partha Chatterjee's "The Politics of the Governed", Gurajada Apparao's "Kanyasulkam" and its translation "Girls for Sale" by Velcheru Narayana Rao. Browsing through Sanjay Subrahmanyam's "Penumbral Visions", Brian Larkin's "Signal and Noise' and K.V. Ramanaraddi's "Mahodayam". From the last, I learnt that the family name Gurajada was originally Gurujada.

Links September14, 2008

Is export-led growth passe? from Dani Rodrik's blog
Why invest in America? from Trade Diversion
My five minutes of fame from Brad Setser
Going on an Imperial Bender by Tom Engelhardt
Mission-Creep Map from Mother Jones
Enquiry based science education? from SciDev.net
Climate change hot spots from SciDev.net
India Hopes New Fellowships Will Attract Expat Scientists from Sciencemagazine

An organizer in the Bradman class

There is some interest in Telugu sites and Telugu blogs about scientists of Telugu origin. My remembrance is that many were multiligual and multicultural but remembering the origins may help others with their aspirations. In 2004, I wrote a somewhat personal account about Komaravolu Chandrasekharan from Bapatla, a town about 7 miles from Chintayapalem where I finished school. At that time I did not see my friend Raghunathan's excellent article "Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene" in this issue of Current Science. It is rather long and if there are any copy right problems, I will remove it. I think that it gives a more objective assessment by one of our best mathematicians. It is difficult to share thoughts or enthusiasm about excellence in specialized fields with others but Raghunathan does it well. Here it is in his own words:
"the people I have spoken about so far are no more. The next person I am going to talk about, K. Chandrasekharan, is living – in retirement in Zurich, Switzerland. He was born in 1920 and was initiated into mathematics by – who else – Ananda Rau in Madras. He went to the Institute for Advanced Study in Princeton to do postdoctoral work. Chandrasekharan worked in number theory and summability – like many others of his generation. His mathematical achievements are of the first rank, but his even greater contribution to Indian mathematics, I think, lies elsewhere. He was an extraordinarily gifted organizer and administrator of science – in the Bradman class, if we use Hardy’s terminology. Homi Bhabha visited Princeton in 1949 when Chandrasekharan was there and offered him a position at the Tata Institute of Fundamental Research. There is a story about this which I have not attempted to authenticate, but it rings true.

Chandrasekharan was taking a walk with the great von Neumann when they saw
Bhabha walking with Einstein at a distance. von Neumann asked Chandrasekharan if it was true that he was planning to move to Bombay to work at Bhabha’s institute. When Chandrasekharan responded in the affirmative, von Neumann said, ‘That man is as good a physicist as any, but do not let him intimidate you – stand up to him’, or words to that effect. It would appear that KC as Chandrasekharan was known, followed that advice – differences of opinion with Bhabha seem to have been among the causes that led to his leaving TIFR in 1965 and move to Zurich.

I should like to tell you another anecdote relating to KC, of which I have first-hand knowledge. This again goes back to my Princeton visit in 1966–67. I once accompanied a friend with expensive tastes to a clothing shop in Princeton. My friend ordered a suit for himself, while I acquired a scarf (which cost me 16 dollars – in 1966, mind you!). The shopkeeper who kept up a conversation
right through asked us if we knew, von Neumann and we said that we knew of him. Then he asked us if we knew Chandrasekaran and we told him that we did indeed know him; at which point he said, ‘They are the only two gentlemen from that Institute who knew how to dress!’

In the decade and a half that he spent at TIFR, Chandrasekharan transformed the fledgling School of Mathematics there into a centre of excellence, respected
the world over. Chandrasekharan initiated a very successful programme of recruitment and training of Research Scholars at TIFR; the programme continues to this day, along the same lines that he set down. He was uncompromising in insisting on high standards. In his Princeton days, he became acquainted with many of the leading mathematicians of the world and put these contacts to excellent use. Herman Weyl gifted his collection of Mathematische Annalen volumes to the TIFR, thanks to Chandrasekharan. With his unusual abilities, he was able to persuade many leading
mathematical figures to visit the Tata Institute and deliver courses of lectures
over a period of two months and more, to his carefully selected Research Scholars.
Among the many distinguished men who visited the Tata Institute in the fifties,
two names stand out: L. Schwartz (a Fields medallist) and C. L. Siegel. They both had tremendous influence on the way mathematics evolved at TIFR. Schwartz persuaded many of his colleagues and students to visit the Tata Institute. Research Scholars were asked to write notes for the lectures given and these lecture notes enjoy a great reputation in the mathematical community to this day.

Chandrasekharan was an excellent judge of mathematics even in areas outside his own specialization, and responded quickly to the achievements of his wards. Equally, non-performance at the high level he had set had no place at TIFR. Chandrasekharan managed to instill in the students at TIFR, strong commitment to hard work without their losing their romantic attachment to mathematics. One important reason for
his success was the freedom he gave the students to work on what they pleased. The visitors gave them exposure to different mathematical areas, many of them far removed from KC’s own interests, and students were encouraged to pursue whatever caught their fancy. Rev Father Racine from Madras whom Chandrasekharan knew from his Madras days and whom he held in great respect, provided him with a steady stream of talent......

Chandrasekharan’s influence went well beyond Indian mathematics. For some 24 years from the mid-fifties, he was a member of the Executive Committee of the International Mathematical Union (IMU). He also served as the Secretary for two terms and as President for one term. His initiatives on this committee were numerous and valued greatly. He was responsible for the IMU sponsoring the International Mathematical Colloquium held once every four years at the Tata Institute starting 1956. These meetings have been on diverse topics in mathematics; topics that are of current interest internationally and to which Indian mathematicians have contributed
substantially. They have been a great success over the years and an invitation to the meeting is considered prestigious.

I should like to mention a personal experience in this connection. In 1964, Tata Institute held a Colloquium on ‘Differential Analysis’ and the organizing committee headed by Chandrasekharan extended an invitation to me to give atalk. A few weeks before the colloquium, I was told that I should rehearse my lecture before KC in his office. My teacher Narasimhan was also present at the rehearsal. Chandrasekharan’s own mathematical interests had little to do with the subject of mytalk; nevertheless, he listened to me patiently for more than an hour, interjecting now and then to tell me how I should present something and generally giving me tips on lecturing. I had in those days, a reputation as a poor speaker (which I hope does not hold now) but as it turned out, thanks to Chandrasekharan, I gave a lecture that
was received very well indeed.

In the fifties, Chandrasekharan held the editorship of the Journal of the Indian Mathematical Society. During this period, several great papers appeared in the journal thanks to Chandrasekharan’s abilities at persuading some of the great
names in the field to publish there.

We at the Tata Institute certainly owe a great deal to Chandrasekharan and are
grateful for the great start he gave us."

Interesting article by Jonathan Haidt

on WHAT MAKES PEOPLE VOTE REPUBLICAN? leads to very interesting commentaries on truth, science, religion, morals etc by Daniel Everett, Howard Gardner, Michael Shermer, Scott Atran, James Fowler, Alison Gopnik, Sam Harris, James O'Donnell, Roger Schank (via 3quraksdaily). It is the kind of discourse that I have been waiting for. Unfortunately, the punchline may be Roger Schank's:
"Republicans do not try to change voter's beliefs. They go with them. Democrats appeal to reason. Big mistake."

A momentary aberration

From a poetry discussion by space_bar, a quote of Revathy Gopal:

I could match her now, word for word.
I could meet her now, on equal terms. I think
I could draw blood.

('Lines on Meeting a Cousin, Long-Lost'. Revathy Gopal)

Even out of context, as space_bar says, it stands by itself. I think that I have seen this sort of emotion among cousins and sisters (men actually draw blood, I think). I tried to see how to say it in Telugu. Since I do not know any thing about metre, I freely translated thus:

ఇప్పుడు మా అక్కంటె నాకు అంత లెక్క లేదు
దానితో సమానంగా వాదించగలను
దాని వంక చురచురా చూడగలను
కావాలంటే ఒక వాత కూడా పెడతా
Any other versions are welcome.

Martin Wolf on the coming US presidential election

Martin Wolf says in What the presidential choice could mean:
"This presidential election might well determine the character of the next, possibly final, epoch of Anglo-American global hegemony. The question is whether the American people will choose the instinct for conflict or that for co-operation."

Luxury cars and farmers

From Luxury car tax defeated in the Senate; Rudd angry:
"PRIME Minister Kevin Rudd accused the Coalition of pandering to Porsche and Ferrari drivers by blocking a luxury car tax hike......
Senator Fielding said the Government's tax hike would hurt farmers and tourist operators.
"How can you slug them when they are doing it tough," he said."

Browsing through Telugu blogs

I have been trying to find Telugu blogs with discussions about contemporary social and political issues. Many seem to have come up in the last few years.
The two aggregates kindly supplied by Maganti Vamsi and Sirish koodali and jalleda, have led to posts like this, this,this and this. Any links to specific blogs of this type are welcome.

Remembering Fr. Racine

Seeing the obituaries of Henri Cartan I am reminded of Fr. Charles Racine, one of the big influences in the development of modern mathematics in India and started wondering whether his name will be recalled much after some more years and whether I would have done mathematics without him.
I do not remember being interested in mathematics or any thing in school days. I was an average student though I seem to have done well once in mathematics in the ninth grade ( I came to know about it since Umamaheswararao sitting next to me who was usually first in the class tore off his answer sheets). My doing well might have some thing to do with the teacher Paruchuri Sambasivarao and his reputation as a good teacher as well as a womanizer. At one stage, I was too young to get admission in an Engineering college and my father decided that I should do Mathematics Honours since it might help in getting better scores for I.A.S. exams. My date of birth was also adjusted so that I would get four chances rather than the usual three. It was then in 1956 that I joined Loyola College, Madras where Fr. Racine was the Head of the Math. Dept. People loke Ramamathan Krishnan and Akbar Khaleeli were still in the college and we were more fascinated by them than discrepit teachers. Later I learnt that two of the students who were wearing dhotis the Tamil way were Raghavan Narasimhan and C.P. Ramanujam. For some reason, we had once a week a discussion type class by one Krishnamutrthy. I forget his first name but he is the only good teacher I remember from college days and was wonderful teacher. Up to that time mathematics was just manipulations and calculations which I could do some extent but did not find particularly fascinating. Krishnamurthi wore dhoti the Telugu way, wore a cotton jacket and traditional headwear. He was serene, had beatiful handwriting, rarely backtracked his steps on the board and his pace was just right for me. He explained to us about natural numbers, rational numbers, real numbers and why there were more real numbers than rational numbers. For the first time, mathematics seemed to be about things one could understand and not just manipulations. And there were beautiful concepts and arguments like Cantor's diagonal argument and I was converted. I started borrowing books from the library read with partial understanding many books and parts of books outside the syallabus. Some like "Men of Mathematics" indicated that a life of mathematics could be exciting. Two books from those days which I still cherish are Artin's "Galois Theory" and Hausdorff's "Set Theory", the second determined the research direction that I was to take later. I slowly found much of the class material outdated and boring and by next year started cutting classes.

I still did not meet Fr. Racine. Around this time I started growing (nearly ten inches in one year) and found it more and more difficult to attend classes and was thrown out of college. I might have met Fr. Racine around this time but I am not sure. What I remember is that Fr. Racine wrote to my father that I had potential and that I should come back to college, The next year I went to college again but the story repeated ieslf. It was during this time that I used to go to his room in the fathers' quarters, chat about mathematics, borrow books from him. But I had to leave again, I heard that he was unhappy but could not dissuade the authorities.

After a few months at home, I found that the only one I could discuss mathematics was my mother and went to another college where attendance was not strict and after my bachelor's degree, Fr. Racine asked to come again to Madras. This time, the college did not insist on attendance or other protocols. I survived two boring years and joined TIFR, Bombay in 1964 full ten years after finishing school. At last, I could study and work on whatever I liked. Senior colleagues would sometimes go out of their way to study and lecture on topics that I was interested in even when they did not specialize in those areas. I pursued Topology of which I had some glimpses in Hausdorff's "Set Theory". It was only later I found that I was given a wide bearth because many seniors were Fr. Racine's students and there were some requests from him about dealing with me. Since then until recently when social problems started bothering me, it has been a life of mathematics. I do not know how well I did or whether I fulfilled Fr. Racine's expectations but most of the time I did not feel that I was working since I was 'working' on things that interested me. It was also during this period in Bombay I found out about his influence on Indian mathematics. He was in touch with some of the top French mathematicians and some of their latest work was available to him . Through seminars in Madras, he seemed to have influenced many mathematicians like K. Chandrasekharan, Meenakshisundaram others. More of this later. I was probably a difficult case but he did modernize courses as much as possible under the university restrictions. N.U.Prabhu in Probabilty modelling across continents talks of the influence of the mathematics courses on Analysis from the books of De La Valle Poussin and Goursat by Fr.Racine. I found that the mechanics courses taught from the books in early 1900's for British polytechics particularly horrible. When I got to know him, I complained and he immediately gave some notes that he prepared himself which were more in the spirit of Banach's "Mechanics".
His interest in his students continued even after we left Loyola College. Around the end of 1974, I visited France for a few months and before my visit, Fr. Racine wrote to me asking me to say 'hello' to Henri Cartan. Henri Cartan was an institution in France and I duly ignored the advice. One day, I saw an old gentleman near one of the steps outside IHES in Bures sur Yvette, and the gentleman said "You must be Swarup, Racine wrote to me about you". It turned out to be H. Cartan and soon after he translated a paper of mine (which, unfortunately was not a good paper) and published it in Comptes rendus. Here is Ragunathan's description of some of Fr. Racine's contributions:
"Father Racine was born at Tomay-Charente in France in 1897. He enlisted for active service in the First World War in 1916 and was demobilized three years later after an ankle injury that left a limp for the rest of his life. He then entered the Jesuit order and was ordained a priest in 1929. He spent four years studying
mathematics in Paris and obtained a doctorate in 1934. He was sent to India to
work at St. Joseph’s College, Tiruchirappalli. He moved to Loyola College, Madras in 1939 and stayed there till his death in 1976, nine years after his retirement in 1967.
Father Racine had worked with Élie Cartan and Hadamard, both legendary figures in mathematics. He counted André Weil and Henri Cartan (another famous mathematician and Élie Cartan’s son) among his friends. With this background, Racine naturally had an excellent perspective on mathematics, which he brought to India with him. He began weaning some Indian mathematicians away from traditional Cambridge-inspired
areas and Minakshi was his first big success; and there was a galaxy of brilliant
students to follow; the list would occupy substantial space in any ‘who’s who’ of Indian mathematics. To mention a few names: K. G. Ramanathan, C. S. Seshadri, M. S. Narasimhan, Raghavan Narasimhan, C. P. Ramanujam.

Father Racine was apparently not an exciting speaker. Students found his classroom lectures difficult to follow. His French accent combined with what amounted to mumbling to the blackboard, made things worse. It was, however, outside the classroom that his influence was decisive. He was remarkably good at spotting talent and then encouraging it. He liked talking informally to his students, especially the talented ones and gave them invaluable advice in their career decisions. Mathematical activity was by no means Father Racine’s sole preoccupation. Apparently, he was a spiritual adviser to the Jesuit community of the college and was engaged in resolving personal problems for the Catholic laity around him. The French government conferred on him the coveted ‘Legion d’honeur’ in 1962. In all the 42 years he spent in India, he made only two trips to France; yet he remained very much a Frenchman. But there can be little doubt that he loved India more than France. I was not privileged to be his student, but remember with pleasure the one long and informal meeting I had with him in the company of my teacher M. S.
Narasimhan. He was an excellent example – by no means unique – of the coexistence of the cassock with a lively disposition."
Ragunathan's article Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene appeared in Current Science, 2003 and has a photograph of Fr. Racine. Raghunathan's photo appears in the photo section of this blog.

This made my day

Today is our day to babysit. Soon after Leila came, I went out to smoke (I know, I should give up)and Jhansi said "bad thatha". Leila responded "No, good thatha".

I have been trying nursery rhymes, wiggles etc to put her to sleep but a Telugu song, not exactly a lullaby seems to work best. After a few of other stuff, I try Yedu Kondala Vada. She listens to it once, says 'again' and falls asleep.

Poetry according to Nannechoda

From The Arrow and the Poem by David Shulman:
"An arrow shot by an archer
or a poem made by a poet
should cut through your heart,
jolting the head.
If it doesn't, it's no arrow,
it's no poem."
P.S. A new book by David Shulman Spring, Heat, Rains: A South Indian Diary

"Bridging the divide between science and politics'

Sci.Dev editorial here. Excerpt:
"When SciDev.Net was established seven years ago, it was an article of faith among its founders that developing countries needed better ways to incorporate scientific information into their decision-making machinery. Our network and website were seen as ways of making this happen.

This need has been confirmed by one of the largest international studies to examine the interface between science and development policy. The study was commissioned last summer from researchers at the London-based Overseas Development Institute (ODI). The full results have just been published, and are based on responses to an electronic survey of more than 600 scientists, intermediaries and policymakers (see Survey backs intermediaries in science communication)."
The link to ODI report does not seem to work but one can go directly to ODI Working Papers and it is Working Paper no.294: 'Political Science? Strengthening science�policy dialogue in developing countries' by Nicola Jones, Harry Jones and Cora Walsh.

Egalitarianism starts early

Editor's summary in Nature of a recent paper by Fehr and colloborators Cooperation is child's play:
"The way that children interact in specially designed tests (well, games) can illuminate the mechanisms behind human altruism and cooperation. Fehr et al. present evidence that young children's other-regarding preferences (where 'Smarties, jellybabies and fizzers' are the rewards in a sharing game and an envy game) take a particular form — inequality aversion. This behaviour pattern develops between the ages of 3 and 8 years. Aged 3 or 4, most children behave selfishly, while by the age of 7 or 8 the vast majority prefer resource allocations that remove inequality. But if the removal of advantageous inequality involves costly sharing, the egalitarian allocation is chosen less often and children tend to favour members of their own social group. These findings suggest that egalitarianism and parochialism have deep developmental roots."
The summary has links to related papers which need subscription. Nature News also has a summary which does not need subscription Children learn rules of equality by age eight. Excerpts:
"Although this might seem an obvious finding, it's important to confirm anecdotal evidence with experiments, says Matthias Sutter of the University of Innsbruck in Austria, who studies fairness and trust behaviour in children. "Having children myself, I can confirm [that 3-year-olds are selfish]," he says. "But we don't know when the change happens, or the magnitude of the change."

Several other factors influenced how egalitarian the children were. The team found that children without siblings were 28% more likely to share than children with siblings. On the other hand, the youngest children in a family were 17% less willing to share than children who had only younger siblings. Sutter, who is one of five children, thinks these results make sense: "You have to take care that you get some of the pie," he says. "If you're an only child, there's no need for that."

In addition, if children knew that their partner was from the same playgroup or school (an 'ingroup' member), they were more concerned about being fair, and with age this bias increased. This suggests that being nice to people you know – parochialism – is something that develops alongside a sense of equality, says Fehr.

Chimps versus children
The findings are also interesting from an evolutionary perspective, the team suggests. Similar experiments performed on chimpanzees show that the animals aren't willing to provide food for a partner even if it doesn't affect the food they receive2. "Chimps seem not to care about the other's welfare in this game, whereas children at age eight already care a lot, but children at age three care only a little," Fehr says.

Further work along these lines could reveal more about why humans are so bothered about fairness, and the part this has played in building human societies. Without it, says Sutter, "there would be no education, no socialization, no social norms"".

A TedTalk by Sugata Mitra

Can kids teach themselves? (via Bayesianheresy)

Several old Telugu film songs

have been recently uploaded on YouTube. Search under VSVutukuri, Mukkamala2020,
MadhuraGeetalu, TeluguBoss, vjdnld etc. My favourite site for old telugu songs is old Telugu songs. The companion discussion site
has useful comments, particularly by Paruchuri Sreenivas. Some other sites for old (and some new) Telugu songs are:
surasa.net
pathabangaram
chimatamusic
and many more. Videos at saradaga, discussion, songs and videos at జానుతెనుగు సొగసులు . A blog onAnnamacharya Samkirtanalu and one on Natakam. There are many more but these will keep me going for a while.

Sublimal advertising

by Derren Brown from a comment in Found: A Solution to Our Problems!! . More discussion in
Naked Capitalism.

Lalita Mukherjea

passed away a few days ago. Here are a couple of posts randomly selected from her blog:
A caller tune and a story
Sex between sects

Gidugu's birthday

Medepalli seshu from New Delhi just reminded me that today is the birthday of Gidugu Venkata Ramamoorty:
"Sri Gidugu Ramamoorty is the grandfather of “colloquial telugu language movement a.k.a vyavaharika telugu bhasha”. He has brought literary prose to the colloquial language. He explained the beauty and ease in the colloquial telugu."
P.S. From The Hindu report:
"The Andhra Pradesh Official Language Commission has asked the district Collectorates and educational institutions to celebrate Telugu Language Day on August 29, coinciding with the birth anniversary of renowned Telugu language scientist Gidugu Ramamurthy."

A mathematical digression

and possibly a platitude. Recently, I discovered Bernard Cohn when I found a relatively cheap copy of his book "Colonialism and its forms of knowledge" in a book shop and found it very interesting. I then borrowed his "An anthrpologist among the historians" from the library and found it even more interesting. Some of the essays there seem to have become bases for later books by people like Nicholas Dirks and in one of the articles he suggests the choice of topics and methodolgy for research which seems cocrete and useful. But there is demand for all three copies of the book in the library and I was asked to return it before reading it completely. While travelling on the train to return it, I tried to see whether I could still think some mathematics which I have not been doing for a while. Surprisingly I could and it was about a couple of problems that I struggled with in the seventies and both solved now. The solutions suggest a conclusion which ia a platitude but it did not come to me naturally.
Both the problems are related to low dimensional topology and group theory. Before the days of Thurston and Perelman that was what most of us were doing. One of the questions is now a famous theorem "finitely generated three manifold groups are finitely presented" proved by Peter Scott in 1972 (independently by Peter Shalen but unpublished) and second is a theorem of Klaus Johannson that certain three manifolds are completely determined by their fundamental groups.
A group is like integers, both positive, negative and zero. Every element has an inverse (negative of it) so that if you add them, you get the identity element zero. Zero is called the identity since if you add it to any element, it does not change it. Any two elements can be added and addition is associative. Gadgets with these properties are called groups. But integers are a bit special in that the addition is commutative; whether you add a to b or b to a, you get the same result. This is because integers are just generated by one element 1, by adding it to itself repeatedly and taking negatives, one gets all the integers. If one takes gadgets like above with some addition operation which is associative, has identity and negatives, it is called a group. In general they are not commutative and if we start with some objects say a,b,c etc and form words freely and their negatives (usually called inverses when multiplicative notation is used) we get what is called a free group on the objects a,b,c etc. If there are n such, it is called free group on n generators and any group on n generators can be got from it by adding some relations. If the number of relations needed is finite (which we may not know before hand) the group is called finitely presented. Finitely presented groups can be represented by finite spaces and are usually more desirable than the complentary ones.
To show that finitely generated implies finitely presented for 3-manifold groups what one expects is a proposition of this type:
Prposition P: If G is finitely generated and indecomposable (as explained below), then the group obtained by adding sufficiently many finite number of relations is already indecomposable.
That finitely generated three manifold groups are finitely presented was proved in 1972 by Peter Scott (and independently by Peter Shalen, but unpublished). A key technical prposition involves decompositions of groups. The operation forming free groups from infinite cyclic groups generated by a,b,c etc above is called free product formation and the inverse operation 'a free product decomposition'. A group which cannot be decomposed into a free product is called 'indecomposable'. Any finitely generated group G can be written G=G1*G2*...*Gm*G(m+1)*...*G{m+n)where the last n factors are infinite cyclic and the first m factors are indecomposable but not infinite cyclic. The numbers m,n depend only on the group and the ordered pair (m+n,n) is called the complexity c(G) of the group G. A crucial technical proposition that Scott proves is:
Prposition Q: If there is a onto homomorphism from G to H which is one-to-one on the indecomposable factors of G other than the infinite cyclic ones, then c(G) is bigger than or equal to c(H) and equality holds if and only if the map is an isomorphiam (which means G,H are indistinguishable and are the same except in name. A homomorphism is a map which preserves the operations).
Somehow, this was not enough to prove Proposition P which is the natural approach to the original 3-manifold question and some more hard work and trickery was needed. Then after nearly 30 years, I met Thomas Delzant in a conference, and he told me during a lecture I could not follow that Proposition P was true. What all one had to do was to extend the notion of complexity to an onto homomorphism between groups, rather than just for a group.
A similar thing with respect to Johannson's theorem. In 1972, I found a simple proof by reducing it a group problem and showing that a certain group was trivial. There was an obvious relative version which was also useful but I could not prove. Again after 30 years, a colloborator (by some coincidence Peter Scott) insisted that I prove it and it turned out to be equivalent to saying that a cetain homomrphism of groups was trivial (every thing maps to zero).
Looking at both the problems, the crucial change seems to be that instead of looking at an object by itself, one had to look at a relation ( in these cases natural maps which are special cases of relations) between objects. Put this way, it seems to be a platitude but it did not occur to me for nearly 30 years.
It seems that I may have to keep doing mathematics until a copy of Bernard Cohn is available.

Coment

by somebody about somebody whose posts and articles were puzzling to me:
"C is a master of the vague platitude"