Category: tBC

Seriously now, where was the Bourbaki wedding?

Published November 25, 2009 by lievenlb

A few days before Halloween, Norbert Dufourcq (who died december 17th 1990…), sent me a comment, containing lots of useful information, hinting I did get it wrong about the church of the Bourbali wedding in the previous post.

Norbert Dufourcq, an organist and student of Andre Machall, the organist-in-charge at the Saint-Germain-des-Prés church in 1939, the place where I speculated the Bourbaki wedding took place, concluded his comment with :

“P.S. Lieven, you _do_ know about the Schola Cantorum, now, don’t you?!?”.

Euh… actually … no, I did not …

La Schola Cantorum is a private music school in Paris. It was founded in 1894 by Charles Bordes, Alexandre Guilmant and Vincent d’Indy as a counterbalance to the Paris Conservatoire’s emphasis on opera. Its alumni include many significant figures in 20th century music, such as Erik Satie and Cole Porter.

Schola Cantorum is situated 69, rue Saint Jacques, Paris, just around the corner of the Ecole Normal Superieure, home base to the Bourbakis. In fact, closer investigation reveals striking similarities and very close connections between the circle of artists at la Schola and the Bourbaki group.

In december 1934, the exact month the Bourbaki group was formed, a radical reorganisation took place at the Schola, when Nestor Lejeune became the new director. He invited several young musicians, many from the famous Dukas-class, to take up teaching positions at the Schola.

Here’s a picture of part of the Dukas class of 1929, several of its members will play a role in the upcoming events :
from left to right next to the piano : Pierre Maillard-Verger, Elsa Barraine, Yvonne Desportes, Tony Aubin, Pierre Revel, Georges Favre, Paul Dukas, René Duclos, Georges Hugon, Maurice Duruflé. Seated on the right : Claude Arrieu, Olivier Messiaen.

The mid-1930s in Paris saw the emergence of two closely-related groups with a membership which overlapped : La Spirale and La Jeune France. La Spirale was founded in 1935 under the leadership of Georges Migot; its other committee members were Paul Le Flem, his pupil André Jolivet, Edouard Sciortino, Claire Delbos, her husband Olivier Messiaen, Daniel-Lesur and Jules Le Febvre. The common link between almost all of these musicians was their connection with the Schola Cantorum.

On the left : Les Jeunes Musiciens Français : André Jolivet on the Piano. Standing from left to right :
Olivier Messiaen, Yves Baudrier, Daniel-Lesur.

Nigel Simeone wrote this about Messiaen and La Jeune France :
“The extremely original and independent-minded Messiaen had already shown himself to be a rather unexpected enthusiast for joining groups: in December 1932 he wrote to his friend Claude Arrieu about a letter from another musician, Jacques Porte, outlining plans for a new society to be called Les Jeunes Musiciens Français.
Messiaen agreed to become its vice-president, but nothing seems to have come of the project. Six months later, in June 1933, he had a frustrating meeting with Roger Désormière on behalf of the composers he described to Arrieu as ‘les quatre’, all of them Dukas pupils: Elsa Barraine, the recently-deceased Jean Cartan, Arrieu and Messiaen himself; during the early 1930s Messiaen and Arrieu organised concerts featuring all four composers.”

Finally, we’re getting a connection with the Bourbaki group! Norbert Dufourcq mentioned it already in his comment “Messiaen was also a good friend of Jean Cartan (himself a composer, and Henri’s brother)”. Henri Cartan was one of the first Bourbakis and an excellent piano player himself.

The Cartan family picture on the right : standing from left to right, father Elie Cartan (one of the few older French mathematicians respected by the Bourbakis), Henri and his mother Marie-Louise. Seated, the younger children, from left to right : Louis, Helene (who later became a mathematician, herself) and the composer Jean Cartan, who sadly died very young from tuberculoses in 1932…

The december 1934 revolution in French music at the Schola Cantorum, instigated by Messiaen and followers, was the culmination of a process that started a few years before when Jean Cartan was among the circle of revolutionados. Because Messiaen was a fiend of the Cartan family, they surely must have been aware of the events at the Schola (or because it was merely a block away from the ENS), and, the musicians’ revolt may very well have been an example to follow for the first Bourbakis…(?!)

Anyway, we now know the intended meaning of the line “with lemmas sung by the Scholia Cartanorum” on the wedding-invitation. Cartanorum is NOT (as I claimed last time) bad Latin for ‘Cartesiorum’, leading to Descartes and the Saint-Germain-des-Pres church, but is in fact passable Latin (plur. gen.) of CARTAN(us), whence the translation “with lemmas sung by the school of the Cartans”. There’s possibly a double pun intended here : first, a reference to (father) Cartan’s lemma and, of course, to La Schola where the musical Cartan-family felt at home.

Fine, but does this brings us any closer to the intended place of the Bourbaki-Petard wedding? Well, let’s reconsider the hidden ‘clues’ we discovered last time : the phrase “They will receive the trivial isomorphism from P. Adic, of the Order of the Diophantines” might suggest that the church belongs to a a religious order and is perhaps an abbey- or convent-church and the phrase “the organ will be played by Monsieur Modulo” requires us to identify this mysterious Mister Modulo, because Norbert Dufourcq rightfully observed :

“note however that in 1939, it wasn’t as common to have a friend-organist perform at a wedding as it is today: the appointed organists, especially at prestigious Paris positions, were much less likely to accept someone play in their stead.”

The history of La Schola Cantorum reveals something that might have amused Frank Smithies (remember he was one of the wedding-invitation-composers) : the Schola is located in the Convent(!) of the Brittish Benedictines…

In 1640 some Benedictine monks, on the run after the religious schism in Britain, found safety in Paris under the protection of Cardinal Richelieu and Anne of Austria at Val-de-Grace, where the Schola is now housed.

As is the case with most convents, the convent of the Brittish Benedictines did have its own convent church, now called l’église royale Notre-Dame du Val-de-Grâce (remember that one of the possible interpretations for “of the universal variety” was that the name of the church would be “Notre-Dame”…).

This church is presently used as the concert hall of La Schola and is famous for its … musical organ : “In 1853, Aristide Cavaillé-Coll installed a new organ in the Church of Sainte-geneviève which had been restored in its rôle as a place of worship by Prince President Louis-Napoléon. In 1885, upon the decision of President Jules Grévy, this church once again became the Pantheon and, six years later, according to an understanding between the War and Public Works Departments, the organ was transferred to the Val-de-Grâce, under the supervision of the organ builder Merklin. Beforehand, the last time it was heard in the Pantheon must have been for the funeral service of Victor Hugo.
In 1927, a raising was carried out by the builder Paul-Marie Koenig, and the inaugural concert was given by André Marchal and Achille Philippe, the church’s organist. Added to the register of historic monument in 1979, Val-de-Grâce’s “ little great organ ”, as Cavaillé-Coll called it, was restored in 1993 by the organ builders François Delangue and Bernard Hurvy.
The organ of Val-de-Grâce is one the rare parisian surviving witnesses of the art of Aristide Cavaillé-Coll, an instrument that escaped abusive and definitive transformations or modernizations. This explain why, in spite of its relatively modest scale, this organ enjoys quite a reputation, and this, as far as the United States.”

By why would the Val-de-Grace organiste at the time Achille Philip, “organiste titulaire du Val-de-Grâce de 1903 à 1950 et professeur d’orgue et d’harmonie à la Schola Cantorum de 1904 à 1950”, be called ‘Mister Modulo’ in the wedding-invitations line “L’orgue sera tenu par Monsieur Modulo”???

Again, the late Norbert Dufourcq comes to our rescue, proposing a good candidate for ‘Monsieur Modulo’ : “As for “modulo”, note that the organist at Notre-Dame at that time, Léonce de Saint-Martin, was also the composer of a “Suite Cyclique”, though I admit that this is just wordplay: there is nothing “modular” about this work. Maybe a more serious candidate would be Olivier Messiaen (who was organist at the Église de la Trinité): his “modes à transposition limitée” are really about Z/12Z→Z/3Z and Z/12Z→Z/4Z. “

Messiaen’s ‘Modes of limited transposition’ were compiled in his book ‘Technique de mon langage musical’. This book was published in Paris by Leduc, as late as 1944, 5 years after the wedding-invitation.

Still, several earlier works of Messiaen used these schemes, most notably La Nativité du Seigneur, composed in 1935 : “The work is one of the earliest to feature elements that were to become key to Messiaen’s later compositions, such as the extensive use of the composer’s own modes of limited transposition, as well as influence from birdsong, and the meters and rhythms of Ancient Greek and traditional Indian music.”

More details on Messiaen’s modes and their connection to modular arithmetic can be found in the study Implementing Modality in Algorithmic Composition by Vincent Joseph Manzo.

Hence, Messiaen is a suitable candidate for the title ‘Monsieur Modulo’, but would he be able to play the Val-de-Grace organ while not being the resident organist?

Remember, the Val-de-Grace church was the concert hall of La Schola, and its musical organ the instrument of choice for the relevant courses. Now … Olivier Messiaen taught at the Schola Cantorum and the École Normale de Musique from 1936 till 1939. So, at the time of the Bourbaki-Petard wedding he would certainly be allowed to play the Cavaillé-Coll organ.

Perhaps we got it right, the second time around : the Bourbaki-Pétard wedding was held on June 3rd 1939 in the church ‘l’église royale Notre-Dame du Val-de-Grâce’ at 12h?

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Where was the Bourbaki wedding?

Published October 26, 2009 by lievenlb

I’m pretty certain I got the intended date & time of the Bourbaki-Pétard wedding right : June 3rd 1939 at 12h.
Finding the exact location of the wedding-ceremony is an entirely different matter. And, quite probably, we are reading way too much in these pranks of the Weil-clan.

Still, it’s fun trying to find an elegant answer, based on the (intended or imagined) clues in the text and the little we know about the early Bourbaki-days. Here, the translation of the relevant part of the wedding announcement :

“They will receive the trivial isomorphism from P. Adic, of the Order of the Diophantines, in the Principal Cohomology of the Universal Variety, on the third of Cartember, year VI, at the usual hour.
The organ will be played by Monsieur Modulo, Assintant Simplex of the Grassmannian (with lemmas sung by the Scholia Cartanorum). The collection will be donated in full to the retirement home for Poor Abstracts. Convergence will be guaranteed.”

First solution : Perhaps one might read “in the Principal Cohomology of the Universal Variety” as : “in the Principal Church of the generic type/name”. In many French cities the main church is the Cathedral and an awful lot of them are called Notre Dame, so it might mean : in the Notre Dame Cathedral. But even then, we have to choose between these two

On the left, the Notre Dame Cathedral in Paris. On the right the Cathédrale Notre-Dame-de-l’Annonciation in Nancy. As the invitation promises guests to be entertained after the ceremony by Monsieur et Madame Bourbaki at their ‘Fundamental Domains’, the choice depends on the location of the Bourbaki-household in June 1939.

‘Bourbaki’ made two applications to become an AMS-member. The first, in 1948, tells us that Bourbaki is a scientific advisor to the Hermann Publishing Co. in Paris since 1934, and, the second in 1950, that he is ‘Directeur Libre de Recherches a l’Université de Nancy’.
I couldn’t find out when exactly Nicolas did change cities, and even Liliane Beaulieu’s talk Bourbaki a Nancy does not provide an answer.

Second solution : Or, one can read that sentence as a mathematical, perhaps proto-motivic, statement, and, hunt for clues elsewhere in the text. But then, what are these clues?

Mass is celebrated by “P. Adic, of the Order of the Diophantines”. This suggests that the church itself belongs to a monastic order, and is perhaps a convent-church.
Hymns are “sung by the Scholia Cartanorum”. Scholia Cartanorum is Latin of sorts and refers perhaps to the Paris’ Latin Quarter, le Quartier Latin.
The collection is donated to the “retirement home for Poor Abstracts”. Perhaps the church is connected to a saint for the poor.

Let’s consider “Scholia Cartanorum” more closely. It may be Latin, admittedly very bad Latin, for ‘the Scholiums of Cartesius’, that is, ‘of Descartes‘.

One of the more famous ‘Scholia’ in scientific history is Newton’s general scholium to the Principia, which is a prime example of Descartes-bashing. Newton attacks Descartes on his vortical theory of planetary motion, his aeter to explain gravity, his God-axiom (unlike Descartes, Newton induced God from nature, rather than starting with God as an axiom) and his hypothetico-deductive method. So, there is a link between Descartes and ‘Scholium’, although the genitive form ‘Cartesiorum’ might be fairly inappropriate…

But then, Descartes died on 11 February 1650 in Stockholm (Sweden) where he was buried, so there won’t be a connection to a French or Parisian church, right? Well, not quite. The fate of Descartes’ remains is a rather strange story : “In 1666, sixteen years after his death, the bones of René Descartes
were dug up in the middle of the night and transported from Sweden to
France under the watchful eye of the French Ambassador. This was only
the beginning of the journey for Descartes’ bones, which, over the
next 350 years, were fought over, stolen, sold, revered as relics,
studied by scientists, used in séances, and passed surreptitiously
from hand to hand. ” For example, during the French Revolution, his remains were disinterred for burial
in the Pantheon in Paris among the great French thinkers. But today, his ashes are burried in…

the abbay church of Saint-Germain-des-Prés, located in the Quartier Latin, within walking distance of the Bourbaki-café Capoulade and the Ecole Normal Superieure.

Now all the hints fall handsomely in place. St-Germain-des-Prés is the oldest church in Paris. Parts of it date to the 6th century, when a Benedictine abbey was founded on the site by Childebert, son of Clovis. Hence the sentence ‘in the Principal Cohomology of the Universal Variety’ might simply mean ‘in the first church, ever’. In medieval times, the Left Bank of Paris was prone to flooding from the Seine, so much of the land could not be built upon and the Abbey stood in the middle of fields, or prés in French, thereby explaining its appellation.

The other part of its name, Saint Germain, comes from Saint Germanus of Paris, also known as the ‘father of the poor’ (!). His remains were interred in St. Symphorien’s chapel in the vestibule of St. Vincent’s church, but in 754, when he was canonized, his relics were solemnly removed into the body of the church, in the presence of Pepin and his son, Charlemagne, then a child of seven, and the church was reconsecrated as Saint-Germain-des-Prés. That is, also the remains of the ‘father of the poor’ are buried in this church.

Here’s my best guess : the Bourbaki-Pétard wedding was held on June 3rd 1939 in the church Saint-Germain-des-Prés at 12h. Genuine aficionados of the Da Vinci code may regret it wasn’t held in the neighboring Saint-Sulpice church, but then, perhaps someone can bend the clues accordingly…

Remains this problem : who was the organist, Monsieur Modulo? Suggestions anyone?

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the bumpy road to the first Bourbaki congress

Published October 22, 2009 by lievenlb

The first Bourbaki congress took eventually place in Besse-en-Chandesse. But, its organization suffered from the ‘usual’ inter-departemental fighting, and also from a power-struggle within the group itself. On many issues de Possel and André Weil were on opposite sides, and it didn’t really help that there was a woman involved…

Because Mandelbrojt, de Possel and Coulomb all held a position at the University Blaise Pascal of Clermont-Ferrand I assumed that the Bourbaki-group had no problem procuring the universities’ biology-outpost in Besse-en-Chandesse for their first congress in 1935. However, the relevant Bourbaki files tell a different story. As might have been expected, the project suffered from the ‘usual’ inter-departemental fighting, but also from a power-struggle within the group itself.

An excellent account of the first 10 ‘proto-Bourbaki’ meetings in the Capoulade-Café, 63 boulevard Saint- Michel, is told magnificently by Liliane Beaulieu in her 1993 paper A Parisian Café and Ten Proto-Bourbaki Meetings(1934-1935). Here we will concentrate on the preparations of the Besse congress.

At their very first meeting on december 10th 1934, they already state the importance of the upcoming summer-congress where a precise plan and a distribution of the writing-load for the first volumes will be discussed : “Aux prochaines grandes vacances aura lieu une réunion pléniere d’ou sortira un plan définitif tres précis et une répartition du travail de rédaction des différents fascicules”. The second meeting, on january 14th 1935, decides that the definite list of Bourbaki-members will consist of those (among the nine ‘possibles’ Weil, Delsarte, Mandelbrojt, Cartan, Dubreil, Dieudonné, de Possel, Chevalley and Leroy) present at the congress : “Il est entendu que la liste définitive, extraite de la précédente, sera composée des noms des membres présents a la réunion pléniere d’Aout ou Septembre prochain, réunion dans laquelle sera dressé le plan définitif et précis du traité”.

On march 25th 1935, the first precise plans are made about the location, the lodgings and the extremely important issue of the meals which will be taken in a nearby Hotel of which “la cuisine est, parait-il, fort bonne”.

René de Possel obtained a mandate to do whatever it took for the group to have their congress in Besse between 12 and 25 July, and, to enquire until what date they could still change their mind.
His biography contains the following lines :
“On many issues de Possel and André Weil were on opposite sides in the arguments. At the first Bourbaki congress in July 1935 de Possel was still an active member of the group and much involved with contributing but, largely due to differences with Weil, he dropped out of the project. De Possel married Yvonne Liberati on 12 August 1935; they had three children, Yann, Maya, and Daphné.”

By and large, the Bourbaki-differences between de Possel and Weil were of a professional nature. They had different mathematical interests, different mathematical talents, different ambitions, and, a different level of commitment wrt. the work ahead (Weil being the lazier one of the two). Still, it is difficult to understand the group-dynamics of the first generation Bourbakis without mentioning a personal tragedy, often ‘forgotten’ (as in the above biography) or given no more than half a sentence, in passing…

Aged 24, René de Possel marries Evelyne Gillet in 1929 and their son, Alain, is born on august 16th 1931. However, the marriage breaks up, one account dates the separation in 1933, another around the time of the Besse conference in 1935.

What is certain is that Evelyne Gillet and André Weil start a relationship no later than the autumn of 1935. At that time, Weil is concocting the Bourbaki Comptes-Rendus note and as the Academy demands a short biography of the author, he has to come up with a first name (at the Besse conference, they only decided on the name ‘N. Bourbaki’). Evelyne chooses Nicolas and is referred to ever after as ‘Bourbaki’s godmother’. Early 1936, the couple spends a vacation together in Spain.

Early 1937, the official divorce papers come through, allowing Weil and Evelyne to marry on october 30th 1937. The very same year, René de Possel remarries with Yvonne Liberati. For more information, you can traverse Evelyne’s genealogy-tree here, but bear in mind that not all information is included (for example, Evelyne died on may 24th, 1986).

Contrary to the suggestion made in the biography, there is no evidence that de Possel left the Bourbaki-group as a result of this affaire or because of his arguments with Weil. In fact, at least until the second Chançay-congress in 1937, de Possel was one of the hardest workers in the group, present at all meetings, doing his share of the write-up and even chastising his fellow-Bourbakis for not being as committed to the project as they ought to be, see for example the 7 theses of Chançay document. It was only in the fall of 1941 that de Possel asked to be transferred to the university of Algiers and left the Bourbaki-group.

At the meeting of march 25th 1935, de Possel attempts a coup d’état. He comes up with an entirely new plan for the summer-congress. Paul Valéry, the French poet, essayist, and philosopher (in the notules he is described as ‘le célebre fantaisiste’) proposed the Bourbaki-group to use his ‘centre universitaire mediterranéen’ (the proto-University of Nice) as their place of venue. They could choose any period between july and october and they wouldn’t have to pay a thing! de Possel was in contact with Valéry at that time, he was writing a 44 page booklet on game theory Sur la théorie mathématique des jeux de hasard et de réflexion, with a preface by Paul Valéry, which appeared later in 1937 via Valéry’s center for mediterranean studies.

There is one small catch though … Valéry insists that de Possel should be president of the Bourbaki-group during the meeting! Naturally, this wasn’t received enthusiastically by the others, but they didn’t rule the plan out, requesting additional information and observing that july and august may be way too hot in Nice.

The next meeting (May 6th 1935), de Possel tries to increase the pressure by asserting that the original Besse-plan is in danger because “Les naturalistes de Clermond-Ferrand semblent vouloir se servir de ce qui leur appartient” (the biologists of Clermond-Ferrand want to use their facilities themselves). But the others are not impressed and they give de Possel “pleins pouvoirs pour réagir avec violence.”

A fortnight later, Weil demands to know the latest on the Besse-negotiations and de Possel replies “en principe les biologistes de Clermond-Ferrand pourront y séjourner des le 15 juin, il y a tout lieu de présumer que ces derniers ne seront que trois ou quatre; ils seront donc fort peu génante étant donné le nombre des locaux dont nous pourrons disposer”, that is, there won’t be more than 3 or 4 biologists around, and, there’s plenty of room for everyone!

Putsch averted, the Bourbakis can start packing their suitcases, hire a secretary for the meeting, and split the costs among all committee-members. Because even this circulaire is preserved, we now know such trivia as the cost of full-pension in the Besse-Hotel with the excellent kitchen : 25 Ffr/day…

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